p = $110
r = 6% = 6/100
t = 2 years
[tex]SI=\frac{prt}{100}=\frac{110\times6\times2}{100}=\frac{1320}{100}=\text{ \$}13.2[/tex]simple interest = $13.2
The future value will be
[tex]\begin{gathered} FV=110(1+0.06)^2 \\ FV=110(1.06)^2 \\ FV=110\times1.1236 \\ FV=123.596=\text{ \$123.596} \end{gathered}[/tex]Help needed! please help math
PLEASEEE!!! Math 8th grade
Total gallons of water used in the park after the ride is installed
= 9.51 * 10^5 GALLONS.
What is exponent addition?Exponent addition is the process of multiplying a number by its exponents or powers, whether or not the base is the same. Exponents, which show how many times a number can be multiplied by itself, are also known as the power of numbers. As an illustration, 3^2 = 3*3, where 3 is the base and 2 the exponent.
How to add exponents?When the base and exponents are the same, exponents can be added. Sometimes the base and exponent will differ, but adding can still be done for certain formulas. Let's examine the procedures for adding exponents.
Step 1: Verify that the expression's terms all have the same base and exponents. 22 + 22, as an illustration. As can be seen, the exponent and base are both 2.
Step 2: Calculate the expression using individual terms if the base and exponent are different. for instance, 53 plus 42. Exponents and bases are different.
Step 3: Add the results together.
As per the question:water used in the park initially = 8.6*10^5 gallons
water used by the additional ride added = 9.1 *10^4 gallons
=0.91*10^5 gallons
Total gallons of water used in the park after the new ride is installed
= (8.6*10^5 + 0.91*10^5) gallons
= (8.6+0.91) *10^5 gallons
= 9.51* 10^5 gallons
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find the image Matrix that represents the rotation of the polygon then graph the polygon and its image
SOLUTION
[tex]\text{The image matrix at 90}^o\text{ rotation is derived using the formula }[/tex][tex]\begin{gathered} \begin{bmatrix}{\cos \theta} & -\sin \theta & {} \\ \sin \theta & {\cos \theta} & {} \\ {} & {} & {}\end{bmatrix}\text{ where }\theta\text{ is 90}^{} \\ \text{This becomes the matrix of } \\ \begin{bmatrix}{0} & {-1} & {} \\ {} & {} & {} \\ {1} & {0} & {}\end{bmatrix}\text{ }\times\text{ }\begin{bmatrix}{2} & {4} & {6}{}{} \\ {2} & {5} & {1}\end{bmatrix}\text{ = }\begin{bmatrix}{0-2} & {0-5} & {0-1}{}{} \\ {2+0} & {4+0} & {6+0}\end{bmatrix}\text{ = } \\ \\ \begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \\ \\ \text{Therefore, the image matrix is }\begin{bmatrix}{-2} & {-5} & {-1}{}{} \\ {2} & {4} & {6}\end{bmatrix} \end{gathered}[/tex]The graph is shown below
A man has 32 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 545 cents, how many dimes does he have?
A dime is worth 10 cents and a quarter is worth 25 cents.
Let D be the number of dimes and Q be the number of quarters.
Since the total amount of coins in the pocket is 32, then:
[tex]D+Q=32[/tex]On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:
[tex]10D+25Q=545[/tex]Notice that we have found a 2x2 system of equations:
[tex]\begin{gathered} D+Q=32 \\ 10D+25Q=545 \end{gathered}[/tex]Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:
[tex]\begin{gathered} D+Q=32 \\ \Rightarrow D=32-Q \\ \\ 10D+25Q=545 \\ \Rightarrow10(32-Q)+25Q=545 \\ \Rightarrow320-10Q+25Q=545 \\ \Rightarrow25Q-10Q=545-320 \\ \Rightarrow15Q=225 \\ \Rightarrow Q=\frac{225}{15} \\ \\ \therefore Q=15 \end{gathered}[/tex]Replace back Q=15 into the expression for D to find the amount of dimes:
[tex]\begin{gathered} D=32-Q \\ =32-15 \\ =17 \end{gathered}[/tex]Therefore, the amount of dimes that the man has is 17.
Find the slope through ( 0, 0) and ( -2, 4) by computing
ANSWER:
The slope is - 2
STEP-BY-STEP EXPLANATION:
We have the slope, we calculate it by means of the following formula
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The points are (0,0) and (-2, 4), replacing:
[tex]m=\frac{4-0}{-2-0}=\frac{4}{-2}=-2[/tex]Look at the following problem, find the mistake.Solve for x. 6x − 3x + 14 = 176x − 3x + 14 = 17 9x + 14 = 17 - 14 -14 9x = 3 /9 /9 x = 1/3Solve for x. 6x − 3x + 14 = 17
If P = (-1, 0, 1, 2, 4} and Q = (4, 5, 6}, find Pu Q.O (-1, 0, 1, 2, 4, 5, 6}Of0 (4)O (-1, 0,1, 2, 4}
Statement Problem: If;
[tex]P=\mleft\lbrace-1,0,1,2,4\mright\rbrace,Q=\mleft\lbrace4,5,6\mright\rbrace[/tex]Find;
[tex]P\cup Q[/tex]Solution:
The union of two sets is a set containing all elements that are in the two sets.
The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Thus, the union of set P and set Q is;
[tex]P\cup Q=\mleft\lbrace-1,0,1,2,4,5,6\mright\rbrace[/tex]
Given a line with slope = 5 and passing through ( 5 , 9 ) , which of the following is the correct point-slope equation of the line?
The point - slope equation of the line passing through the point (5,9) and having a slope of 5 is 5x - y = 16.
As per the question statement, we are supposed to find the point - slope equation of the line passing through the point (5,9) and having a slope equal to 5.
Before solving this, we need to know that point slope form of the equation is given as y - y1 = m (x - x1)
Where (x1, y1) are the points through which line is passing and "m" is the slope of the line.
Here x1 = 5 and y1 = 9 and m = 5
Substituting the values in the formula written above, we get
y- 9 = 5(x - 5)
y - 9 = 5x - 25
5x - y = 25 - 9
5x - y = 16
Hence the point - slope equation of the line passing through the point (5,9) and having a slope of 5 is 5x - y = 16.
Point slope form: The equation of a line in which we utilize any point which lies on the line and its slope to find the line's equation.Slope: This value indicates about the steepness of the line.To learn more about line and its characteristics, click on the link given below:
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Find the Slope and the Y-Intercept of the line with the given equation
Answer: Slope is -4/5 and Y-int is 6
Step-by-step explanation: From the y=mx+b you can see the m is -4/5 and the b is 6. So in this case the slope would be -4/5 and y int would be 6
Can you help me with number 13? Thank you I am having trouble with it.
In triangle ABC, a is the length of the side opposite to angle A (side BC), b is the length of the side opposite to angle B (side AC), and c is the length of the side opposite to angle C (side AB)
We can use the cosine rule to find the length of each side
[tex]\begin{gathered} a=\sqrt[]{b^2+c^2-2bc\cos A} \\ b=\sqrt[]{a^2+c^2-2ac\cos B} \\ c=\sqrt[]{a^2+b^2-2ab\cos C} \end{gathered}[/tex]From the given figure we can see triangle ABC, where We will use the cosine rule to find c
[tex]c=\sqrt[]{a^2+b^2-2ab\cos 90^{\circ}}[/tex]Since cos(90) = 0, then
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2-2ab(0)} \\ c=\sqrt[]{a^2+b^2-0} \\ c=\sqrt[]{a^2+b^2} \end{gathered}[/tex]The expression equivalent to c is
[tex]\sqrt[]{a^2+b^2}[/tex](C) 0.845 ÷ 5 I need help explaining the answer
The given expression is
[tex]\frac{0.845}{5}[/tex]As long division, we solve it as follows
So, the answer is 0.169.Observe that we have to add a zero first in the quotient in order to transform 0.845 into 845, then we divide it by 5 as a normal long division.
The product of -1/a≠ 0, and it's reciprocal is?
A. a/2
B. 2/a
C. -2/a
D. None are correct
The product of -1/a and its reciprocal will be equal to unity or 1.
What is the meaning of reciprocal of a number?For any number [a], the reciprocal will be given by [1/a] such that -
a x 1/a = 1
Given is the following expression -
A = -1 / a
From the definition of the reciprocal of a number, the reciprocal of the number -
A = -1 / a
will be
1/A = 1/(-1/a) = -a
Now, the product of the number and its reciprocal will be -
A x 1/A = -1/a x -a = 1
A x 1/A = 1
Therefore, the product of -1/a and its reciprocal will be equal to unity or 1.
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The line y − 14 = 6(x − 2.5) represents Barry’s profit, y, from selling x painting, aftser buying some canvas. What was the cost of the canvas?
The cost of the canvas will be 6x.
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line is,
⇒ y - 14 = 6 (x - 2.5)
Now,
The line represents Barry’s profit, y, from selling x painting, after buying some canvas.
Here, The equation of line is,
⇒ y - 14 = 6 (x - 2.5)
Simplify the equation as;
⇒ y - 14 = 6 (x - 2.5)
⇒ y - 14 = 6x - 15
⇒ y = 6x - 15 + 14
⇒ y = 6x - 1
Since, Barry’s profit, y, from selling x painting, after buying some canvas.
Thus, The cost of the canvas 6x.
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Consider the function f(x)=(x+4)(x+2). Dilate f(x) by x to create a new function of a higher degree.
f(x) = (x+4)(x+2).
f(x) = x² + 2x + 4x + 8
f(x) = x² + 6x + 8
Dilate by x:
x³ + 6x² + 8x
Describe how the given equation represent a transformation of the function f(x)
A function that transforms one function or graph into another, typically related function or graph is referred to as a function in mathematics.
For instance, when a quadratic graph is translated, the vertex and axis of symmetry are moved, but the parabola's general form remains the same.
What is the translational equation?
The translation equation or formula is written as g(x) = f(x+k) + C.
Replace "x" in a function with "x-h" to translate it horizontally.
The graph's left or right shift is determined by the value of the variable "h."
Since h = -4 in our example, the graph moves 4 units to the left.
Add 'k' to the end of a function to translate it vertically.
f(x+k) + C.
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Find the real solutions, if any, of the following equation. Use the quadratic formula.
EXPLANATION
Given the equation 6x^2 = 5x
We can apply the following procedure :
Subtracting -5x to both sides:
[tex]6x^2-5x=0[/tex]Apply exponent rule:
[tex]a^{(b+c)}=a^ba^c[/tex][tex]x^2=\times[/tex][tex]=6\times-5x[/tex]Factor out common term x:
[tex]x\mleft(6x-5\mright)=0[/tex][tex]\mathrm{Using\: the\: Zero\: Factor\: Principle\colon\quad \: If}\: ab=0\: \mathrm{then}\: a=0\: \mathrm{or}\: b=0[/tex][tex]x=0\quad \mathrm{or}\quad \: 6x-5=0[/tex][tex]\mathrm{Add\: }5\mathrm{\: to\: both\: sides}\text{ from 6x -5=0}[/tex][tex]6x-5+5=0+5[/tex][tex]Simplify\colon[/tex][tex]6x=5[/tex][tex]\mathrm{Divide\: both\: sides\: by\: }6[/tex][tex]\frac{6x}{6}=\frac{5}{6}[/tex][tex]Simplify\colon[/tex][tex]x=\frac{5}{6}[/tex][tex]\mathrm{The\: solutions\: to\: the\: quadratic\: equation\: are\colon}[/tex][tex]x=0,\: x=\frac{5}{6}[/tex]Hence, the solution set is as follows:
{0 , 5/6}
For the diagram below, angles 4 and 6 would be referred to as _______ angles.Select one:a.supplementaryb.verticalc.alternate interiord.alternate exterior
Answer:
c. alternate interior
Explanation:
If a transversal line intersects two parallel lines, the angles formed on the interior are called the interior angles. For example, in the given diagram, angles 3, 4, 6, and 5 are interior angles.
Now the pair of angles that formed in the interior but on the opposite side of the transversal line are called alternate interior angles. For example, angels 4 and 6 are alternate interiors. angles 3 and 5 also alternate interior.
Therefore, choice C is the correct answer choice that describes angles 4 and 6.
Can you please help me out with a question
There are 360 degrees in a circle.
We can write:
[tex]Arc\text{LAM}+Arc\text{MBL}=360\degree[/tex]Given, Arc LAM = 256°, we can find Arc MBL:
[tex]\begin{gathered} Arc\text{LAM}+Arc\text{MBL}=360\degree \\ 256+\text{ArcMBL}=360 \\ \text{ArcMBL}=360-256 \\ \text{ArcMBL}=104 \end{gathered}[/tex]The central angle that subtends Arc MBL also measures 104 degrees.
[tex]\angle\text{MPL}=104\degree[/tex]We also know,
[tex]\angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL}[/tex]Angle MPB and Angle BPL are equal, so we have:
[tex]\begin{gathered} \angle\text{MPL}=\angle\text{MPB}+\angle\text{BPL} \\ 104=2\angle\text{BPL} \\ \angle\text{BPL}=\frac{104}{2} \\ \therefore\angle\text{BPL}=52\degree \end{gathered}[/tex]Now,
Arc LB subtends the central angle BPL, so they are same in measure.
Thus,
[tex]\text{ArcLB}=52\degree[/tex]What principal would you need to invest at a rate of 4% to earn $500 in 6 months? Round your answer to the nearest cent.
From the information available, we have the following;
Rate = 4% (0.04)
Time = 0.5 (half a year/6 months)
Interest = 500
Principal = ???
Therefore, we would substitute these into the simple interest formula as shown below;
[tex]\begin{gathered} I=P\times R\times T \\ \text{Make P the ubject of the equation;} \\ \text{Divide both sides by R x T and you'll have;} \\ \frac{I}{R\times T}=\frac{P\times R\times T}{R\times T} \\ \frac{I}{R\times T}=P \\ \frac{500}{0.04\times0.5}=P \\ \frac{500}{0.02}=P \\ P=25000 \end{gathered}[/tex]ANSWER:
The principal to be invested therefore is $25,000
Giving a test to a group of students, the grades and gender are summarized belowIf one student is chosen at random,Find the probability that the student was male OR got an "B".
ANSWER:
0.6875
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the probability that the gender is male and also the probability that the grade is B, separately, like this:
[tex]\begin{gathered} P(\text{male})=\frac{42}{80} \\ P(B)=\frac{19}{80} \end{gathered}[/tex]Therefore, since it is the probability that it is male OR got and "B", it is the union of both events, and it would look like this:
[tex]P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B)[/tex]Now, the intersection of both events would be the probability that he is a man and gets a B, it would look like this:
[tex]P(male\cap B)=\frac{6}{80}[/tex]We replace to be able to calculate the union, like this:
[tex]\begin{gathered} P(\text{male}\cup B)=P(male)+P(B)-P(male\cap B) \\ P(\text{male}\cup B)=\frac{42}{80}+\frac{19}{80}-\frac{6}{80} \\ P(\text{male}\cup B)=\frac{55}{80}=\frac{11}{16}=0.6875 \end{gathered}[/tex]The probability that the student was male OR got an "B" is 0.6875
Find the 20% trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
Lengths of Longest 3-Point Kick for NCAA Division 1-A Football
29 30 35 37 38 40 40 43 44 45
47 48 49 49 50 53 55 55 58 59
Using the methodology of Trimmed Mean to the tune of 20%, the result derived is given as 45.5. See further explantion below.
What is Trimmed Mean?A truncated mean (another name for Trimmed Mean), like the mean and median, is a statistical measure of central tendency.
It entails calculating the mean after deleting specified sections of a probability distribution or sample at the high and low ends, often an equal proportion of both.
In the above instance, since the instruction is to trim 20% of 20 observations is 4.
Hence, 2 observations from the start and 2 from the rear will be removed. This leaves us with:
35 37 38 40 40 43 44 45 47 48 49 49 50 53 55 55. (Note that the observations must be arranged from low to high)
Hence the Trimmed Mean = (35 + 37 + 38 + 40 + 40 + 43 + 44 + 45 + 47 48 + 49 + 49 + 50 + 53 + 55 + 55)/ 16
= 728/16
=45.5
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solve for x: In(x+2)= -5
The given equation is:
ln (x + 2) = -5
Take the exponent of both sides
[tex]e^{\ln (x+2)\text{ }}=e^{-5}[/tex]The exponential cancels the ln on the Left Hand Side:
[tex]\text{x + 2 = e}^{-5}[/tex]Subtract 2 from both sides:
[tex]\begin{gathered} \text{x + 2 - 2 = e}^{-5}-2 \\ x=e^{-5}-2 \end{gathered}[/tex]A scale drawing for a restaurant is shown below. In the drawing, 2 I'm represents 3 m. Assuming the dinning hall is rectangular, find the area of the real dining hall
To solve this question, follow the steps below.
Step 01: Find the real measures of the dining hall.
The measure of the drawing is 2cm x 6cm.
Given: 2cm = 3m.
Then, 6cm = 2cm + 2cm + 2cm = 3m + 3m + 3m = 9m
The real measure of the dining hall is 3m x 9m.
Step 02: Find the area of the dining hall.
The dining hall is a rectangle and the area (A) of a rectangle is:
[tex]A=l*h[/tex]Where l and h are the sides of the rectangle.
Then, the area of the dining hall is:
[tex]\begin{gathered} A=3*9 \\ A=27m^2 \end{gathered}[/tex]Answer: The area of the dining hall is 27 m².
Which equation or inequality represents the following description? & Multiply the quantity 2 more than a number by 8. The result is at least 12 times the number subtracted from 76.A. 8(2n) < 76 - 12B. 8n + 2 = 12n - 76C. 8(n + 2) > 76 - 12nD. 8(2n) = 76 – 12n
We can translate the wording part as follows:
1. Multiply the quantity 2 more than a number by 8:
8 * (2 + n)
2. The result is at least: it means that the value is the value in question or values greater than this number, therefore, we have an inequality here ( >=).
3. The result is at least 12 times the number subtracted from 76:
76 - 12n
Therefore, the inequality that represents the description is:
[tex]8\cdot(2+n)\ge76-12n[/tex]Then, the correct option is C.
The width of a rectangle is 2 its length. The perimeter of the rectangle is 540 ft. What is the length, in feet, of the rectangle?
To solve this problem we can write one equation for each condition so:
the width of a rectangle is 2 its length so:
[tex]W=2L[/tex]and one for the perimeter so:
[tex]2W+2L=540[/tex]Now we replace the first equation into the second one so:
[tex]\begin{gathered} 2(2L)+2L=540 \\ 4L+2L=540 \\ 6L=540 \\ L=\frac{540}{6} \\ L=90 \end{gathered}[/tex]So the length of the rectangle is 90 ft
What is the sum of the two odd numerals following 26 in the following sequence?
2,3,5,6,7,9,10,11,13…
The two odd numbers are 11 and 15. The sum of the odd numbers in the sequence will be 26.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that,
The sequence is,
2,3,5,6,7,9,10,11,13…
As we know the given series is an arithmetic progression with a common difference is 2.
The sequence is further obtained as,
2,3,5,6,7,9,10,11,13, 15
From the given condition the sum of the numerals has to be 26.After applying a lot of addition to the sequence we get only two odd numbers 11 and 15 which will give the sum of 26 as,
= 11 + 15
=26
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How do you write – 7.83 as a fraction into simples form?
7.83 can be written as a fraction in simplified form as [tex]7 \frac{80}{100}[/tex].
A fraction, which is expressed in the form p/q, where p and q are both integers, denotes a portion of a whole. Here, we'll explain the steps involved in converting 7.83 decimal numbers to fraction form and mixed numbers. In order to convert 7.83 to a fraction, do the following:
Write the decimal number split by one first as follows:
7.83/1
Since the numerator has two digits after the decimal point, we must multiply the numerator and denominator by 102 = 100, removing the decimal point.
7.83 × 100/1 × 100 = 783/100
We can also express 7.83 as a mixed number because the improper fraction is caused by the numerator being bigger than the denominator; as a result, 783/100 is equal to:
[tex]7 \frac{80}{100}[/tex]
Therefore, 7.83 is 783/100 as a fraction, and its mixed number form is [tex]7 \frac{80}{100}[/tex].
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DG and EG are tangent to circle C and circle F. The points of tangency are A, B, D, and E. if M
From the question and the given diagram, we were told that:
DG and EG are tangent to circle C and circle F.
The point of tangency are A, B, D, and E.
If M
We are to find m
In solving this, we will have to need or consider the similarity theorem.
Its says that if corresponding angles are congruent, then their angles are similar.
It in essence states that, C
Andy Lee is the punter for the San Francisco 49ers. He had a stellar 2011 season with an average punt length of 50.9 yards with a standard deviation of 3.5. His punt distance follows a normal distribution. Andy Lee's first punt of the season was 66 yards. what is the z-score for this punt?A. -2.4B. 2.4C. 4.3D.5.5
The z-score of a normal distribution is defined by
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x\text{ is the score we want to find } \\ \mu\text{ is the mean value of the distribution} \\ \sigma\text{ is the standard deviation of the distribution} \end{gathered}[/tex]Then, using the formula for the z-score in our problem we have
[tex]Z=\frac{66-50.9}{3.5}=\frac{15.1}{3.5}=4.3[/tex]Then the z score for that punt is 4.3.
The graph below shows the relationship between the number of hours and thenumber of miles jogged.Y161514131211109Miles8322356HoursBased on the information in the graph, what is the unit rate in miles per hour?How did u get the unit rate
Since the graph shows a proportional relationship, in order to find the unit rate in miles per hour, we just need to choose a point in the graph and divide the number of miles by the number of hours.
Looking at the graph, we can choose the point (2.5, 8), so we have:
[tex]\text{unit rate}=\frac{8\text{ miles}}{2.5\text{ hours}}=3.2\text{ miles/hour}[/tex]So the unit rate is 3.2 miles per hour.
Please help! Functions and Relations. The function h(x) is a transformation of the square root function, f(x)= square root of x. What function is h(x)? Thanks!
In general, given a function g(x), a horizontal shift is given by the transformation below
[tex]\begin{gathered} g(x)\rightarrow g(x-a) \\ a>0\rightarrow\text{ a units to the right} \\ a<0\rightarrow\text{ a units to the left} \end{gathered}[/tex]Thus, in our case, notice that the graph of h(x) is that of f(x) shifted 1 unit to the left; then,
[tex]h(x)=\sqrt{x+1}[/tex]The answer is option C.