Answers
The expression in ascending order is [tex]e^{log4} < log_326 < log_233 < log_22^6[/tex].
We have,
Using a log and exponent calculator we get,
log 4 = 0.60
So,
[tex]e^{log 4}[/tex] = [tex]e^{0.60}[/tex] = 1.82
[tex]log_233[/tex] = 5.044
[tex]log_22^6[/tex] = 6
[tex]log_326[/tex] = 2.97
Now,
Arranging from least to greatest:
[tex]e^{log4} < log_326 < log_233 < log_22^6[/tex]
Thus,
The expression in ascending order is [tex]e^{log4} < log_326 < log_233 < log_22^6[/tex].
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Related Questions
Find the area of a triangle if the base (b) is 12 inches and the height (h) is 18 in.
(a) 216 in. ²
(b) 12 in.²
(c) 43 in.²
(d) 108 in ²
Answers
The area of the triangle will be 108 square inches. Thus, the correct option is D.
Given that:
Height, h = 18 inches
Base, b = 12 inches
Area refers to the measurement of the extent or size of a two-dimensional surface, expressed in square units.
Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
The area of the triangle is given as,
A = 1/2 x 12 x 18
A = 12 x 9
A = 108 square inches
Thus, the correct option is D.
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The square represents a scale model that was created by using a factor of 4.
8 ft
8 ft
[Not drawn to scale]
Which is true of the measures of the sides of the original square?
O Each side of the original square is the length of each side of the scale model.
O Each side of the original square is 4 times the length of each side of the scale model.
Each side of the original square is the same length as each side of the scale model.
OEach side of the original square is 4 feet less than the scale model.
Answers
A statement which is true of the measures of the sides of the original square include the following: D. Each side of the original square is 4 feet less than the scale model.
What is a scale factor?In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).
In Mathematics and Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
(Scale factor of dimensions)² = Scale factor of area
Therefore, the surface area of pentagonal prism B, the image can be calculated as follows;
Side length of of image = 4 × side length of original square
Side length of original square = 1/4 × side length of of image
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
2.4 Show with steps which one is larger: 2.4.1 3
[tex] {3}^{2} [/tex]
or 4³
Answers
To compare the values [tex] {3}^{2} [/tex] and 4³, we need to calculate each expression separately.
First, let's calculate [tex] {3}^{2} [/tex]:
[tex] {3}^{2} = 3 \times 3 = 9 [/tex]
Now, let's calculate 4³:
4³ = 4 × 4 × 4 = 64
Therefore, [tex] {3}^{2} [/tex] is smaller than 4³.
To summarize:
[tex] {3}^{2} [/tex] = 9
4³ = 64
Hence, 4³ is larger than [tex] {3}^{2} [/tex].
(2.4)^3
= 2.4 x 2.4 x 2.4
= 13.824
Now, we can compare 13.824 and 64:
13.824 < 64
Therefore, we can conclude that 4^3 or 64 is larger than (2.4)^3 or 13.824. Hence:
4^3 > (2.4)^3 or 64 > 13.824
Note: I used the value of (2.4)^3 in the comparison, because it was given with the option of 3².
a large rectangle is made by joining 3 identical small rectangles
the perimeter of 1 small rectangle is 21cm
the width of 1 small rectangle is xcm
work out the perimeter of the larger rectangle
Answers
Since three identical small rectangles are joined to form a large rectangle, the large rectangle will have three times the length and the width of a small rectangle.
Let's assume the width of one small rectangle is x cm. Therefore, the length of one small rectangle will be 21 cm - 2x cm (since two widths are subtracted from the total perimeter).
The perimeter of one small rectangle is given by:
Perimeter = 2 * (length + width)
Perimeter = 2 * ((21 - 2x) + x)
Perimeter = 2 * (21 - x)
Perimeter = 42 - 2x
Since the large rectangle is formed by joining three identical small rectangles, the perimeter of the large rectangle will be three times the perimeter of one small rectangle.
Perimeter of the larger rectangle = 3 * (42 - 2x)
Perimeter of the larger rectangle = 126 - 6x
Therefore, the perimeter of the larger rectangle is 126 - 6x cm.
One side of a rectangular piece of metal becomes double the other side, when the longer side is increase by 3x and the shorter side is increased by 2m. The area is also doubled. Find the dimensions of the given piece of metal
Answers
Answer:
Length (L) = 3x
Step-by-step explanation:
Let's break down the problem step by step.
Let's assume the original dimensions of the rectangular piece of metal are:
Length = L
Width = W
According to the problem, when the longer side (length) is increased by 3 times (3x) and the shorter side (width) is increased by 2 meters (2m), the new dimensions become:
New length = L + 3x
New width = W + 2
We are also told that the new dimensions result in an area that is double the original area.
Step 1: Calculate the original area
Original area = Length × Width = L × W
Step 2: Calculate the new area
New area = New length × New width = (L + 3x) × (W + 2)
According to the problem, the new area is double the original area, so we can set up the equation:
2 × Original area = New area
Substituting the values, we have:
2 × (L × W) = (L + 3x) × (W + 2)
Step 3: Simplify the equation
Expand the equation:
2LW = LW + 2L + 3xW + 6x
Combine like terms:
LW - 2L - 3xW - 6x = 0
Now, let's rearrange the equation to group the variables together:
LW - 3xW - 2L - 6x = 0
Factoring out common terms:
W(L - 3x) - 2(L + 3x) = 0
At this point, we can see two terms multiplied by (L - 3x) and (L + 3x). We set each of these factors to zero:
L - 3x = 0
L + 3x = 0
Solving these equations individually, we get:
L = 3x
L = -3x
Since we are dealing with the dimensions of a physical object, negative values don't make sense in this context. Therefore, we can ignore the solution L = -3x.
Hence, the dimensions of the given piece of metal are:
Length (L) = 3x
Width (W) = Any value
Please note that the width can have any value as long as the length is three times the value of x.
Solve the system of equations below:
2x + y = 10
y= - 4x + 16
Answers
Answer: x = 3, y = 4; (3, 4)
Step-by-step explanation:
To solve, we will substitute one equation into the other and solve.
Given:
2x + y = 10
Substiute:
2x + (- 4x + 16) = 10
2x - 4x + 16 = 10
Combine like terms:
-2x + 16 = 10
Subtract 16 from both sides of the equation:
-2x = -6
Divide both sides of the equation by 3:
x = 3
Given:
y= - 4x + 16
Substuite:
y= - 4(3) + 16
Compute:
y = 4
We can also solve by graphing both of the equations. The point of intersection is the solution. See attached.
So I have some confusion and I'm having a hard time following the logic of how you convert a linear equation from slope intercept form to standard form.
Here is an example
How is it when you are converting from slope intercept form to standard form:
1.) When you are subtracting 3x from both sides in this example, I could see that both 3xs cancel out but I'm confused about how you can subtract it from y ( a different variable) and also end up with 3x on the side underneath y (How do they switch places)
2.) Also how does the variable y end up right next to -3x? Also, how is 3x negative? is it just dragged down or something?
Answers
Answer:
-3x and y are terms that cannot be combined, so their sum is -3x+y.
Step-by-step explanation:
You want an explanation of how y = 3x +4 becomes -3x +y = 4.
BalanceA balance is a mechanical contraption with two pans joined by a "beam" that rests on a pivot point between them. When the weights in the two pans are the same, the contraption is "balanced" and the pans sit level.
When the contraption is unbalanced, the heavier pan sits lower than the lighter one and the beam is not level.
The feature of the balance that is of interest here is that we can add or subtract weight from either pan. As long as we do the same thing to the other pan, it will remain balanced (the beam will be level).
ExampleConsider a balance with yellow marbles and green marbles on both sides. Let the number of green marbles be 4, and the number of yellow marbles be 3.
If I remove 3 yellow marbles from the right side of the balance, so only the 4 green ones remain, I must also remove 3 yellow marbles from the left side to maintain the balance.
EquationAn equation is similar to a balance in that the parts on the left side and the parts on the right side of the equal sign have the same value when it is "true" or "balanced".
We can keep the statement of equality true as long as we perform the same operation on both sides of the equal sign.
The equation ...
y = 3x +4
says the value of y is the same as the value of the sum of 3x and 4. When I subtract (remove) 3x from the right side of this equation, it will only remain true (balanced) if I also remove 3x from the left side. Written on one line, this operation looks like ...
(-3x) +y = (-3x) +3x +4 . . . . . . -3x added to both sides
On the left side, the terms -3x and y have different variables. They are "unlike" terms, so cannot be combined. Their sum is "indicated" as ...
-3x +y
On the right side of the equal sign, the terms -3x and 3x have the same variable. They are "like" terms, so can be combined. The total number of instances of x in this sum is 0:
-3x + 3x = (-3 +3)x = 0x = 0
After the addition of -3x to both sides of the equation, the resulting equation is ...
-3x +y = 0 +4
We know that 0 is the additive identity element, so this can be further simplified to ...
-3x +y = 4
Bringing downIf we had the addition equation ...
70 + y = 30 +4
and we wanted to add -30 (same as subtract 30) to both sides, we could write this sum in a vertical format as ...
[tex]\begin{array}{rrcrr}70&+y&=&30&+4\\-30&&=&-30&\\\cline{1-5}40&+y&=&&+4\end{array}[/tex]
The sum in the left column is the sum of the like terms there. Since we started with something we could subtract 30 from, the resulting sum is a numerical value (40).
Your example seeks to show the same sort of operation, except that there are no like terms to add -3x to. The resulting sum of nothing (0) and -3x is -3x.
In the above example, if 70 were 0, the value on the bottom line in the first column would be -30. That is, the -30 would be "brought down", since it remains unchanged by addition to 0.
[tex]\begin{array}{rrcrr}0&+y&=&30&+4\\-30&&=&-30&\\\cline{1-5}-30&+y&=&&+4\end{array}[/tex]
Your example has -3x instead of -30. The ideas remain the same. Yes, the "-30" or "-3x" is "brought down", because there is nothing to add it to.
This vertical format for adding equations is often seen in a teaching setting. It is intended to show the equality of the stuff being added, and how it lines up with terms already there. When the vertical alignment is not preserved (as in your example), the comparison to the vertical alignment of columns in addition of multidigit numbers is lost. This tends to obscure the conceptual similarity.
Some may prefer the horizontal expression:
(-3x) +y = (-3x) +3x +4 . . . -3x added to both sides
-3x +y = 4 . . . . . . . . . . . . simplified
Standard formAs your example attempts to show, the standard form of the equation for a line is ...
Ax +By = C
The conditions on this form are generally ...
the leading coefficient is positivethe coefficients are mutually prime integersPlease note that the example you are presented shows addition of -3x to both sides of the equation. The property of equality also applies to multiplication: equality is preserved if both sides of the equation are multiplied by the same number.
In order to make the leading coefficient (the coefficient of x) be positive, we can multiply both sides of the equation by -1:
-1·(-3x +y) = -1·(4)
Parentheses are eliminated using the distributive property.
3x -y = -4 . . . . . . . . . the standard form of the equation for your line
__
Additional comment
The standard form can be used for horizontal and vertical lines. In these cases, one of the coefficients is zero:
Ax = C . . . . . a vertical line at x = C/A
By = C . . . . . a horizontal line at y = C/B
The equation of a vertical line in slope-intercept form is impossible, because its slope is "undefined."
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Express seven ninths pi in degrees.
Answers
Answer: 140 degrees
Step-by-step explanation:
To convert radians to degrees, you multiply by 180/π. Therefore, to convert seven-ninths pi (7/9 π) radians to degrees, you would do the following calculation:
(7/9 π) * (180/π) = (7/9) * 180
This simplifies to 140 degrees.
Which of the following equations is not a linear equation?
A. y = -4
B. x 3=1
C. 2x – 4y = 1
D. y = x – 2
Answers
x³ = 1 is not a linear equation because the variable x is raised to the power of 3, which makes it a cubic equation.
Linear equations are equations in which the highest power of the variable(s) is 1.
They can be expressed in the form "y = mx + b," where m is the slope and b is the y-intercept.
Linear equations represent straight lines on a graph.
y = -4 is a linear equation with a slope of 0 and a y-intercept of -4.
x³ = 1 is not a linear equation because the variable x is raised to the power of 3, which makes it a cubic equation.
2x - 4y = 1 is a linear equation in standard form.
It can be rewritten as -4y = -2x + 1 or y = (1/2)x - 1/4. It represents a straight line.
y = x - 2 is a linear equation with a slope of 1 and a y-intercept of -2.
It represents a straight line.
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To translate the graph of the equation y = 5 two units left,
the equation is altered. What is the new equation?
0₁ y=5²-2
Oy=5²+2
Ocy=5²-2
OD y = 5²+2
Answers
The equation of the new function is y = 5ˣ ⁺ ²
Describing the transformation of f(x) to g(x).From the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = 5ˣ
Also, we have
The graph of f(x) translated two units left to get g(x)
This means that
g(x) = f(x + 2)
So, we have
g(x) = 5ˣ ⁺ ²
Hence, the equation of the new function is y = 5ˣ ⁺ ²
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Payments of $3,150 due 18 months ago and $3,950 due in three years are to be replaced by an equivalent stream of payments consisting of $2,850 today and two equal payments due two and four years from now. If money can earn 9.75% compounded semiannually, what should be the amount of each of these two payments?
Answers
Answer:
the answer for this question is $4,769.97
Step-by-step explanation:
Note that each of the two equal payments due two and four years from now should be approximately $1,446.48
How to compute the above?To find the amount of each of the two equal payments, we can use the concept of present value and set up an equation based on the given information.
The present value (PV) of a future payment can be calculated using the formula -
PV = Payment / (1 + (r/n))[tex]^{nt}[/tex])
Where -
- PV is the present value
- Payment is the future payment
- r is the interest rate per compounding period
- n is the number of compounding periods per year
- t is the number of years
Given -
- Payment 1 - $3,150 due 18 months ago (1.5 years)
- Payment 2 - $3,950 due in three years
- Interest rate - 9.75% compounded semiannually
- Current payment - $2,850 today
- Two equal payments due two and four years from now
Let's solve for the amount of each payment -
First, let's calculate the present value of Payment 1 -
PV1 = $3,150 / (1 + (0.0975/2))³
= $3,150 / (1 + 0.04875)³
= $3,150 / (1.04875)³
≈ $2,875.49
Next, let's calculate the present value of Payment 2 -
PV2 = $3,950 / (1 + (0.0975/2))⁽³ˣ²⁾
= $3,950 / (1 + 0.04875)⁶
= $3,950 / (1.04875)⁶
PV2 ≈ $2,717.47
Now, let's set up the equation using the present values -
$2,850 + Payment 1 + Payment 2 = PV1 + PV2
$2,850 + Payment 1 + Payment 2 ≈ $2,875.49 + $2,717.47
Payment 1 + Payment 2 ≈ $2,875.49 + $2,717.47 - $2,850
Payment 1 + Payment 2 ≈ $5,742.96 - $2,850
Payment 1 + Payment 2 ≈ $2,892.96
Since the two equal payments are the same, let's denote each payment as P.
2P ≈ $2,892.96
Dividing both sides by 2 -
P ≈ $1,446.48
So , each of the two equal payments due two and four years from now should be approximately $1,446.48.
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Determine which integer in the solution set will make the equation true.
6x − 6 = 2(2x + 5)
Answers
The integer in the solution set that will make the equation true is determined as x = 8.
What is the integer solution of the equation?The integer in the solution set that will make the equation true is calculated as follows;
The given equation;
6x - 6 = 2 (2x + 5)
Simplify the equation as follows;
6x - 6 = 4x + 10
Collect similar terms as follows;
6x - 4x = 10 + 6
2x = 16
Divide both sides of the equation by 2;
2x/2 = 16/2
x = 8
Thus, the integer solution of the equation is determined as x = 8.
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Answer the question below. Type your response in the space provided. What is the value of arctan (-√3/3) in degrees? (Omit the degree sign from your response.)
Answers
The value of arctan (-√3/3) in degrees is 150
How to determine the value of arctan (-√3/3) in degrees?From the question, we have the following parameters that can be used in our computation:
the value of arctan (-√3/3) in degrees
This means that
x = arctan (-√3/3)
When evaluated, we have
x = -30
So, the angle is
Angle = 180 - 30
Evaluate
Angle = 150
Hence, the measure of the angle is 150 degrees
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4 012 5 097 umhuly 092 ACTIVITY 1 INTRODUCTION, DEFINITION AND EXPLANATION 1.1 Define the concept Impact Study and give TWO examples of impact studies that can be conducted in our country. (2+2)= [4] 1.2 Briefly explain FOUR contributing factors that need to be considered when conducting impact studies. (4x2)= [8] ACTIVITY 2 RESEARCH, EXPLANATION, DISCUSSION AND APPLICATION Conduct an impact study on how the South African higher education institutions are addressing the student challenges in the following FOUR areas: M W M M Central Applications Office (CAO) Online Registrations Postal Registrations Late Registrations 2.1 Provide a brief explanation on how the South African higher education institutions provide support to prospective students in each of the FOUR areas listed above. (4x2)= [8] 2.2 Critically discuss each of the FOUR areas you have explained above. In your answer do the following: Ad & olis M Provide the pros and cons for each area. Also provide your own conclusion for each area. M [12] (4x4)=[16] (4x2)=[8] 2.3 Recommend FOUR ways on how the South African higher education institutions can improve each area listed above. (4x4)= [16]
Answers
An impact study is a systematic examination of the effects, consequences, or outcomes resulting from a particular intervention, policy, program, or event.
Examples of Impact Studies in South AfricaImpact study on renewable energy projects: This study would assess the impact of renewable energy initiatives, such as solar or wind farms, on the local economy, job creation, energy security, carbon emissions, and social development. It would analyze the benefits and challenges associated with the adoption of renewable energy sources in the country.
Impact study on land reform policies: This study would examine the consequences of land reform policies on agricultural productivity, rural livelihoods, social cohesion, economic growth, and political stability. It would assess the effectiveness and equity of land redistribution programs and their impact on landowners, farmers, and local communities.
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Create an activity where procedural and conceptual understanding co-exist. Revisit your content area and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning processes
Answers
Sure, I can try to help you with that. Procedural and conceptual understanding are two types of knowledge that are important for learning mathematics and science. Procedural understanding is the ability to perform facts and algorithms, such as adding fractions or balancing chemical equations. Conceptual understanding is the ability to reason and comprehend mathematical concepts, operations and relations, such as why fractions can be added by finding a common denominator or why chemical equations need to be balanced to conserve mass.
An activity where procedural and conceptual understanding co-exist is one that requires students to apply both types of knowledge to solve a problem and explain their reasoning. For example, in geometry, an activity could be to find the area and perimeter of a rectangle with given dimensions, and then explain how the area and perimeter formulas work and why they are useful for real world situations. This activity would involve procedural understanding to select and use the correct formulas, and conceptual understanding to understand what area and perimeter mean and how they relate to the properties of rectangles.
Another example, in chemistry, an activity could be to design an experiment to test how different factors affect the rate of a chemical reaction, such as temperature, concentration, or catalysts. This activity would involve procedural understanding to follow the steps of scientific inquiry, such as formulating hypotheses, measuring variables, controlling confounding factors, and repeating measurements. It would also involve conceptual understanding to understand why these steps are essential for ensuring objectivity, reliability, and validity of the experiment.
To link procedural and conceptual knowledge to the teaching and learning processes, it is important to provide students with opportunities to practice both types of knowledge and receive feedback on their performance and understanding. It is also important to encourage students to make connections between different skills and concepts, and to explain their thinking using appropriate terminology and representations. Some strategies that can help with this are:
- Using multiple representations, such as words, symbols, diagrams, graphs, tables, etc., to illustrate concepts and procedures.
- Asking students to compare and contrast different methods or solutions for solving a problem.
- Providing students with open-ended or non-routine problems that require them to apply their knowledge in new or unfamiliar contexts.
- Asking students to justify their answers or critique the reasoning of others using evidence and logic.
- Providing students with feedback that focuses on both their accuracy and their understanding of the underlying concepts and principles.
Activity: Exploring Quadratic Equations
Content Area: Mathematics
Objective:
To demonstrate how procedural and conceptual understanding can co-exist in solving quadratic equations.
Materials Needed:
Whiteboard or blackboardMarkers or chalkHandouts with quadratic equations (for individual or group work)Instructions:
Begin the activity by introducing the concept of quadratic equations to the students. Explain that quadratic equations are second-degree polynomial equations in a single variable (x) and are commonly written in the form ax^2 + bx + c = 0.Discuss the standard form of a quadratic equation and its components (coefficients a, b, and c).Present a step-by-step procedural approach to solving quadratic equations using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Go through each step and highlight the importance of understanding the purpose of each operation.Divide the students into small groups or pairs and distribute handouts with various quadratic equations.Instruct the students to work collaboratively to solve the quadratic equations using the procedural approach discussed earlier. Encourage them to show all the steps involved, including the substitution of values into the quadratic formula and simplifying the equation.As the students work on the problems, circulate the classroom to provide guidance and support. Observe their problem-solving strategies and address any misconceptions that arise.After the groups have completed their solutions, reconvene as a whole class. Ask each group to share their approach and solutions on the board. Encourage them to explain their reasoning and highlight the conceptual understanding behind each step.Facilitate a class discussion by focusing on the link between procedural and conceptual understanding. Emphasize that procedural knowledge alone may lead to successful computation, but without conceptual understanding, students may struggle to interpret the meaning of the solutions or apply their knowledge to real-world problems.Provide additional examples or real-life scenarios that require solving quadratic equations and discuss how conceptual understanding helps in interpreting the results.Conclude the activity by summarizing the importance of developing both procedural and conceptual understanding in mathematics. Encourage students to continue practicing problem-solving techniques while deepening their conceptual understanding of quadratic equations.By combining procedural steps with conceptual understanding, students develop a solid foundation for solving quadratic equations. This approach helps them not only perform the necessary calculations but also comprehend the underlying concepts and their applications in various contexts.
A={yy is an integer and -5 ≤y<-3}
A=
Answers
The inequality is solved and the solution is y = { -5 , -4 }
Given data ,
The set A can be defined as A = {y | y is an integer and -5 ≤ y < -3}.
Now , an integer is a whole number that can be positive, negative, or zero.
-5 ≤ y < -3: This is the condition or constraint placed on the values of y in set A. The inequality states that y must be greater than or equal to -5 but less than -3. In other words, y can take any integer value between -5 and -3, but it cannot include -3 itself.
Putting these two conditions together, the set A consists of all integers within the specified range, excluding -3. So, A = {-4, -5}.
Hence , the set A can be written as A = {-4, -5}, where y represents the elements in the set A that satisfy the given inequality conditions.
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A theater can hold 160 giants or 240 elves. If there is 100 giants inside, how many elves can also be admitted so that the theater is full?
Answers
Answer:We can use the concept of ratios to solve this problem. The ratio of giants to elves in terms of capacity is 160:240, which simplifies to 2:3. This means that for every 2 giants, there are 3 elves in terms of capacity.
If there are already 100 giants inside, we can determine the corresponding number of elves by setting up a proportion:
2 giants / 3 elves = 100 giants / x elves
Cross-multiplying, we get:
2x = 3 * 100
2x = 300
Dividing both sides by 2:
x = 150
Therefore, if there are already 100 giants inside the theater, there can be an additional 150 elves admitted so that the theater is full.
Step-by-step explanation:
Answer:
The answer is 150 elves
Step-by-step explanation:
160giants=240elvea
100giants=x
x=240×100/160
x=150elves
Pleasee help me 30 points
Answers
Answer:
7.5
Step-by-step explanation:
Wendell wants to make a wooden lid for a decorative box.
The lid needs to be 6 1/2
inches wide and 8 1/2
inches long with sides 2 inches deep.
Part A
Find the area of wood that Wendell will need to make the lid.
Drag numbers to complete the measurements.
Each tile may be used once or not at all.
The numbers are the options for the blanks. Please help my math test is tomorrow and I really need to get a good grade.
Answers
The total area of wood that Wendell will need to make the lid is 350.5 square inches.
What is Area of Rectangle?The area of rectangle is length times of width.
Surface area of the lid = area of top + area of bottom + area of four sides
The area of the top is equal to the product of the length and width of the lid:
Area of top = 6 1/2 inches × 81/2 inches
convert the fractions
Area = 13/2 ×17/2
= 221/4 square inches
The area of each side can be found by multiplying the height (2 inches) by the perimeter of the lid (which is the sum of the length and width of the lid):
Perimeter of lid = 2 ( 6 1/2 + 8 1/2)
= 2 × (13/2 inches + 17/2 inches)
= 60/2 inches = 30 inches
Area of one side = 2 inches × 30 inches = 60 square inches
Since there are four sides, the total area of the sides is:
Area of four sides = 4 × 60 square inches = 240 square inches
Therefore, the total area of wood that Wendell will need to make the lid is Area of top + area of bottom + area of four sides = 221/4 + 221/4 + 240 = 221/2 + 240 = 110.5 + 240 = 350.5 square inches.
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How much would $14,250 be worth in a savings account after 12 years if the account has a 5.25% APY and the interest is compounded weekly?
Answers
After 12 years of weekly compounding at a 5.25% APY, $14,250 would be worth approximately $19,536.18 in the savings account.
To calculate the future value of $14,250 in a savings account after 12 years with a 5.25% annual percentage yield (APY) and weekly compounding, we can use the formula for compound interest:
Future Value = Principal × (1 + (Rate / Compounding Frequency))^(Compounding Frequency × Time)
Given:
Principal (P) = $14,250
Rate (R) = 5.25% = 0.0525 (converted to decimal)
Compounding Frequency = Weekly (52 weeks in a year)
Time (T) = 12 years
Substituting the values into the formula:
Future Value = $14,250 × (1 + (0.0525 / 52))^(52 × 12)
Future Value = $14,250 × (1.001009615)^624
Using a calculator or spreadsheet, we can evaluate the expression inside the parentheses and calculate the future value.
Future Value ≈ $14,250 × 1.373731797
Future Value ≈ $19,536.18
Therefore, after 12 years of weekly compounding at a 5.25% APY, $14,250 would be worth approximately $19,536.18 in the savings account.
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Ruby is 6, Edward is 8, Claire is 9, David is 14 and Emma is 15. They are given birthday money in the ratio of their ages. In total they receive £156. How much do they each receive?
Answers
Answer:
Ruby: £18
Edward: £24
Claire: £27
David: £42
Emma: £45
Step-by-step explanation:
6 + 8 + 9 + 14 + 15 = 52
Each one receives the following fraction of the total:
Ruby: 6/52
Edward: 8/52
Claire: 9/52
David: 14/52
Emma: 15/52
Ruby: 6/52 × £156 = £18
Edward: 8/52 × £156 = £24
Claire: 9/52 × £156 = £27
David: 14/52 × £156 = £42
Emma: 15/52 × £156 = £45
Answer:
Ruby: £18
Edward: £24
Claire: £27
David: £42
Emma: £45
Answer:
Ruby=18, Edward=24, Charlie=27, David=42, Emma=45
Step-by-step explanation:
sum of ratios is 52
for each one write the ratio over the sum of ratio multiplied by total amount
[tex]\frac{6}{52} *156[/tex]=18
[tex]\frac{8}{52} *156[/tex]=24
[tex]\frac{9}{52} * 156[/tex]=27
[tex]\frac{14}{52} * 156[/tex]=42
[tex]\frac{15}{52} * 156[/tex]=45
and to check add all of them and they give 156 pounds
Suppose there is a gene which, if someone has it, causes them to turn into a werewolf if they are exposed to a full moon. Let W be someone having the werewolf gene. You know that P(W) = 0.3. One can test for the gene by taking someone's blood and dropping it on a sheet of silver and seeing if it reacts. Let S be this `silver test', and suppose that you are told that P(S) = 0.65. Suppose, finally, that you know that the `silver test' has a type-2 error rate of 0.05.
What is the type-1 error rate of the `silver test'?
Answers
Let's use Bayes' rule to find the type-1 error rate of the `silver test'. We want to find P(S|~W), the probability that the silver test is positive given that the person does not have the werewolf gene.
P(S|~W) is the probability of a false positive, which is the type-1 error rate.
We know that P(W) = 0.3, which means that P(~W) = 0.7.
Let's assume that the `silver test' is independent of whether or not someone has the werewolf gene.
Using Bayes' rule, we have:
P(S|~W) = P(~W|S) * P(S) / P(~W)
We can find P(~W|S) using Bayes' rule:
P(~W|S) = P(S|~W) * P(~W) / P(S)
We know that P(S) = 0.65, P(W) = 0.3, and P(~W) = 0.7.
We can find P(S|W) using the type-2 error rate:
P(S|W) = 1 - type-2 error rate = 1 - 0.05 = 0.95
Using Bayes' rule, we have:
P(W|S) = P(S|W) * P(W) / P(S)
We can find P(S|~W) and P(~W|S) using the above equations:
P(S|~W) = P(~W|S) * P(S) / P(~W)
P(~W|S) = P(S|~W) * P(~W) / P(S)
Plugging in the values, we get:
P(S|~W) = P(~W|S) * P(S) / P(~W) = (1 - P(W|S)) * 0.65 / 0.7 = 0.54
P(~W|S) = P(S|~W) * P(~W) / P(S) = 0.54 * 0.7 / 0.65 = 0.58
Consider a glass block that is 0.6 mm thick and has a refractive index of 1.55. How long will it take for a pulse of light to pass through the block?
Answers
Answer:
[tex]3.10\times 10^{-12}[/tex] seconds
Step-by-step explanation:
The explanation is attached below.
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f(t)= -16t^2+64 gives the height of an egg t seconds after being dropped
a. make a table using the domain 0_
b. describe where the function is increasing and decreasing in interval notation
Answers
Answer:
the function f(t) = -16t^2 + 64 is increasing for the interval (0, ∞) and decreasing for the interval (-∞, 0).
Step-by-step explanation:
To create a table using the given function f(t) = -16t^2 + 64 for the domain 0 ≤ t, we can substitute different values of t into the equation and calculate the corresponding heights.
Let's create a table with values of t and f(t):
t f(t)
0 64
0.5 48
1 48
1.5 48
2 32
2.5 0
3 -40
3.5 -88
4 -144
4.5 -208
5 -280
Now, let's describe where the function is increasing and decreasing in interval notation.
The given function f(t) = -16t^2 + 64 is a quadratic function with a coefficient of -16 for the t^2 term. Since the coefficient is negative, the parabola opens downwards.
The function will be increasing when the derivative is positive, and decreasing when the derivative is negative.
To find the derivative, we differentiate f(t) with respect to t:
f'(t) = -32t
The derivative f'(t) is a linear function with a coefficient of -32. Since the coefficient is negative, the function f(t) is decreasing.
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The function f(t) = -16t^2 + 64 describes the height of an egg t seconds after being dropped.
a. To make a table using the domain 0 ≤ t ≤ 2, we can plug in values for t and calculate the corresponding values for f(t) as shown in the image I provided.
b. The function is decreasing on the interval [0, ∞) because the leading coefficient of the quadratic term is negative. This means that as t increases, the value of f(t) decreases.
Area = 108 in²
base =20 in
what is the volume of the prism?
Answers
Answer:
Answer: the volume of the prism is 2160
Step-by-step explanation:
multiple the base and the area to get the volume
3. A colony of bacteria triples in population every year. If there were 25 bacteria to
start. How many total bacteria, y, will there be after x years? Write an equation
to model the situation y = bx
a.) y = 3*25*
b.) y = 25 + 3x
c.) y = 3 + 25*
d.) y = 25 * 3*
Answers
What is the product?
StartFraction 2 a minus 7 Over a EndFraction times StartFraction 3 a squared Over 2 a squared minus 11 a + 14 EndFraction
StartFraction 3 Over a minus 2 EndFraction
StartFraction 3 a Over a minus 2 EndFraction
StartFraction 3 a Over a + 2 EndFraction
StartFraction 3 Over a + 2 EndFraction
Answers
The simplified form of the given fraction is 3a/(2a-2).
Given that, (2a-7)/a × 3a²/(2a²-11a+14).
Here, (2a-7)/a × 3a²/(2a²-7a-4a+14)
= (2a-7)/a × 3a²/2a(2a-7)-2(2a-7)
= (2a-7)/a × 3a²/(2a-7)(2a-2)
= 3a/(2a-2)
Therefore, the simplified form of the given fraction is 3a/(2a-2).
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Answer:
Its B on edge 23
Step-by-step explanation:
ignore what the guy above says
Ethan puts $700.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 9 years?
Round your answer to the nearest cent.
Answers
Answer:
$2462.51
Step-by-step explanation:
You want to know the value of an investment of $700 earning 15% compounded annually for 9 years.
Compound interestThe compound interest formula tells you the amount is ...
A = P(1 +r)^t
A = $700(1 +0.15)^9 ≈ $2462.51
There will be $2462.51 in the account after 9 years.
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Determine the angle measure between vectors u and v: u = 5i – 4j and v = 7i + 2j .
Answers
Answer:
Step-by-step explanation:
The angle measure between vectors u and v is approximately 19.18 degrees.
The angle measure between vectors u and v, we can use the dot product formula:
u · v = |u| |v| cos θ
where u · v is the dot product of vectors u and v, |u| and |v| are the magnitudes of u and v respectively, and θ is the angle between the two vectors.
First, let's find the magnitudes of vectors u and v:
|u| = √(5^2 + (-4)^2) = √(25 + 16) = √41
= √(7^2 + 2^2) = √(49 + 4) = √53
Next, let's find the dot product of vectors u and v:
u · v = (5)(7) + (-4)(2) = 35 - 8 = 27
Now we can substitute these values into the formula:
27 = √41 √53 cos θ
To isolate cos θ, we divide both sides by √41 √53:
cos θ = 27 / (√41 √53)
Using a calculator, we can evaluate this expression to find:
cos θ ≈ 0.942
Finally, we can find the angle θ by taking the inverse cosine (cos^-1) of 0.942:
θ ≈ cos^-1(0.942)
Using a calculator, we find:
θ ≈ 19.18 degrees
Therefore, the angle measure between vectors u and v is approximately 19.18 degrees.
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The probability that an international flight leaving the United States is delayed in departing (event D) is .31. The probability that an international flight leaving the United States is a transpacific flight (event P) is .62. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .15. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.)
Answers
The probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight is 0.2419 (approx).
Given that the probability that an international flight leaving the United States is delayed in departing (event D) is .31. The probability that an international flight leaving the United States is a transpacific flight (event P) is .62.
The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .15.
(a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight?
Solution:Given, P(D) = .31, P(P) = .62 and P(D ∩ P) = .15P(D | P) = Probability that the flight is delayed in departing given that it is a transpacific flight.By using Bayes' theorem,P(D | P) = P(D ∩ P) / P(P)
We have, P(D ∩ P) = .15 and P(P) = .62 Substitute these values in the above equation,P(D | P) = .15 / .62 = 0.2419 (approx)Note:Bayes’ Theorem is named after Reverend Thomas Bayes, who first proposed the approach in the 18th century. It is a mathematical formula that helps to calculate conditional probabilities.
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