Given the following question:
[tex]\begin{gathered} -2x+7=4+4x \\ 7-7=0 \\ 4-7=-3 \\ -2x=4x-3 \\ 4x-4x=0 \\ -2x-4x=-6x \\ -6x=-3 \\ -6x\div-6=x \\ -3\div-6=0.5 \\ x=0.5 \end{gathered}[/tex]What is the amount of error in Lamont's estimate is
The percentage of error is given by:
[tex]Error=\frac{|Measured-Real|}{Real}\times100[/tex]Where:
Measured = 160
Real = 159
so:
[tex]Error=\frac{|160-159|}{159}\times100=\frac{1}{159}\times100\approx0.6[/tex]Answer:
0.6%
8a.
Amount of error = Measured - real = 160 - 159 = 1
Write the equations for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).
From the graph, let's write the equations for f(x) and g(x).
Apply the slope-intercept form of linear equations:
y = mx + b
Where m is the slope and b is the y-intercept.
• For f(x):
To find the slope apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Take two points on the line of f(x):
(x1, y1) ==> (0, -1)
(x2, y2) ==> (-2, 0)
Thus, we have:
[tex]\begin{gathered} m=\frac{0-(-1)}{-2-0} \\ \\ m=\frac{0+1}{-2} \\ \\ m=-\frac{1}{2} \end{gathered}[/tex]The y-intercept (b), is the point the line crosses the y-axis.
Therefore, the y-intercept for f(x) is at b = -1
Therefore, the equation for f(x) is:
[tex]f(x)=-\frac{1}{2}x-1[/tex]• For g(x):
Take two points on the line of g(x).
(x1, y1) ==> (-2, 0)
(x2, y2) ==> (2, 2)
Apply the slope formula to find the slope:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{2-0}{2-(-2)} \\ \\ m=\frac{2}{2+2} \\ \\ m=\frac{2}{4} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]The y-intercept of g(x) is: b = 1
Therefore, the equation for g(x) is:
[tex]g(x)=\frac{1}{2}x+1[/tex]To determine the reflection that transforms f(x) to g(x):
From the graph, we can see the red line represents f(x) while the blue line is that of g(x).
Apply the transformation rules for functions.
When f(x) becomes -f(x), there is a reflection over the x-axis.
Here, the parent function f(x) becomes -f(x) = g(x)
[tex]-\frac{1}{2}x-1=-(-\frac{1}{2}x-1)=\frac{1}{2}x+1[/tex]Therefore, there was a reflection over the x-axis that transforms the grah f(x) to g(x).
ANSWER:
• f(x) = -½x - 1
,• g(x) = ½x + 1
• Reflection over the x-axis.
Descriptive statistics consist of the collection, organization, summarization, and presentation of data and allows the problem solver to form a new understanding about a population. Which type of statistics allows us to make predictions about a population?.
Inferential statistics allows us to make predictions about a population .
Inferential statistics is a branch of statistics that uses a range of analytical approaches to get population estimates from sample data. Inferential analytics, like inferential statistics, is a subset of statistics. Inferential statistics help to form inferences about the population, whereas descriptive statistics summaries the characteristics of the data collection.
There are two types of inferential statistics: t - tests and regression analysis. The sampling for inferential statistics must be representative of the entire population. We can learn more about statistical approaches in this essay, including their classifications, examples, and key formulas.
By studying the samples acquired from the population data, inferential statistics helps to gain a good knowledge of it. It aids in making demographic generalizations through the use of various analytical tests and instruments.
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A standard deck of playing cards is shuffled and three people each choose a card. Find the probability that the first two cards chosen are clubs and the third card is black if the cards are chosen with replacement, and if the cards are chosen without replacement.A) The cards are chosen with replacement. ______B) The cards are chosen without replacement. ______
We will have the following:
First, we have that an standard deck of cards has 52 cards in total, and 13 cards of each description (hearts, clubs, spades and diamonds) and 26 are red and 26 are black.
Now, with this information we will calulate the probabilities:
A)
*Without replacement:
[tex]p=\frac{13}{52}\cdot\frac{12}{51}\cdot\frac{26}{50}\Rightarrow p=\frac{13}{425}\Rightarrow p=0.03058823529\ldots[/tex]*With replacement:
[tex]p=\frac{13}{52}\cdot\frac{13}{52}\cdot\frac{26}{52}\Rightarrow p=\frac{1}{32}\Rightarrow p=0.03125[/tex]Consider the following linear equation.y=6Identify if the given line is horizontal or vertical and give its slope.AnswerKeyboard ShortcutsSelecting the alternative option for a text box will replace the entered value. If the option is not selected, the entered answer is used.Type of line: Slope:
Given the linear equation:
y = 6
Let's identify if the line is horizontal or vertical.
Then give the slope.
Since the line is the y-coordinate of a point: y = 4, we can say the line passes the graph at all y = 4.
Therefore, the line is a horizontal line.
Horizontal line have zero slope because it is flat and has no steepness.
Since the line is a horizontal line, the slope of the line is zero.
ANSWER:
• Horizontal line
,• Slope = 0
Read and analyze the given problems. Show your complete solutions:A wave with a frequency of 900 Hz is traveling at a speed of 200 m/s. What is the wavelength?
We know λ = v / f where
λ=wavelength
v=velocity
f=frequency
λ = 200 / 900
λ = 2/9 meters
2The fire department in California decided to take a poll to see if residents would pay a monthly fee for their services. They polled 22 people in the stateand concluded that residents were not willing to pay a monthly fee. What is wrong with this poll?
Since they polled 22 people and this is a very small sample size to represent the entire population,
So it would have large chances to get inaccurate results.
Then, the wrong with this poll is
"The conclusion is based on a small sample."
60° 600 16 inches An equilateral triangle is folded in half. What is x, the height of the equilateral triangle? 8V3 in 16 in 16V3 in 8 in
Given the right angles triangle derived from dividing a trainmgle into half, the base value will be;
b = 16/2 = 8 inches
Height = x
the right base an =
P = $3300, r = 5.3%, t = 8 monthsCalculate the simple interest earned. Round to the nearest cent.
The formula for finding simple interest is as given below
[tex]I=\frac{\text{PRT}}{100}[/tex][tex]\begin{gathered} I=\text{Interest} \\ P=P\text{rincipal} \\ r=\text{Rate} \\ t=\text{time in years} \end{gathered}[/tex]The following were given in the question
[tex]\begin{gathered} P=\text{ \$3300} \\ r=5.3\text{ \%} \\ t=8\text{months}=\frac{8}{12}\text{years}=\frac{3}{4}=0.75\text{years} \end{gathered}[/tex]Substitute the given into the formula to get the value of the interest as shown below
[tex]I=\frac{\text{Prt}}{100}=\frac{3300\times5.3\times0.75}{100}[/tex][tex]\begin{gathered} I=\frac{13117.5}{100} \\ I=131.175 \end{gathered}[/tex]Hence, the simple interest earn is $131. 175
Having. Problems understanding this question. I know it has something to do with the rectangle box with the line above the number line but I don't know how to start to get the answer.Xx
Solution:
Given the data below:
when arranged in ascending order, we have
[tex]60,63,63,65,65,66,66,66,66,68,68,70[/tex]For the first six data:
[tex]Q_1=median=64[/tex]For the second six data:
[tex]Q_3=median=67[/tex]For the entire data,
[tex]Q_2=median=66[/tex]Since the smallest and largest data value are 60 and 70 respectively, we can conclude that the box plot that correctly represents the data is
The correct option is
The perimeter of a rectangle is 38 yards. The difference of the length and width of the rectangle is 7 yards. Find the length and width
The perimeter of a rectangle is computed as follows
perimeter = 2l + 2w
where l is the length and w the width.
The difference between the length and width of the rectangle is 7 yards means:
l - w = 7
or
l = 7 + w
Replacing this equation into perimeter's equation, we get:
perimeter = 2(7 + w) + 2w
perimeter = 2(7) + 2(w) + 2w distributing
perimeter = 14 + 4w combining similar terms
The perimeter is 38 yards, then
38 = 14 + 4w
38 - 14 = 14 + 4w - 14 subtracting 14 at both sides
24 = 4w
24/4 = 4w/4 dividing by 4 at both sides
6 = w
l = 7 + w
l = 7 + 6
l = 13
The length is 13 yards and the width is 6 yards
A study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household.The equation of the line of best fit for this data is : y = 1.218x -0.09What does it mean to have a slope of 1.218 in this situation? Is this realistic?
The relationship between the amount of daily food waste measured in pounds and the number of people in a household.
Equation of the line : y = 1.218x -0.09
Slope is 1.218
Slope meaning the rate of change of y coordinates with respect to the x coordinatei.e steepness of the line
In the given situation the : The quantify food that is wasted by person in the house is more than 1.218 times
helpppppppppppp meeeeeeeeeeee pleaseee!!!
The y-intercept of the given graph is at (0, 1), hence g(0) = 1.
Solution to a graphThe given graph is a graph of a modulus expression. The parent form of a modulus function is given as g(x) = |x|.
The point where x = 0 is the point where the line intersect the y-axis of the graph. From the graph shown, you can see that the line intersects at only one point.
Since the y-intercept of the line is at (0, 1), hence the value of the function g(0) is equivalent to 1.
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Laura has p times as many photographs as Darnel. Darnel has 16 photographs. Write an expression that shows how many photographs Laura has.
This is pretty simple once you get the hang of it, all you need to do is see when a question says times then you know it is multiplying, that would be 16p. Hope this helps.
16p is the required expression that shows the number of photographs that Laura has.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
Given that,
Number of photographs that Darnel has = 16.
Also, Laura has p times photographs of Darnel.
To find the expression that shows photographs, Laura has.
Let Laura has x number of photographs.
Since, Laura has p times photographs of Darnel's
Implies that,
Number of photograph that Laura has = 16p
The required expression,
x = 16p.
The expression for photograph that Laura has can be given as 16p.
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Identify the graph of the linear equation 2x + 2y - z=-4 in three dimensional space.
The answer is option C
The points graph must be a solution to the equation. Then, in graph C, we have three points:
(0 , -2, 0)
(-2, 0, 0)
(0, 0, 4)
Now let's try each in the equation:
[tex]\begin{gathered} \mleft(0,2,0\mright)\Rightarrow2\cdot0+2(-2)-0=-4 \\ -4=-4 \end{gathered}[/tex][tex]\begin{gathered} \mleft(-2,0,0\mright)\Rightarrow2\cdot(-2)+2\cdot0-0=-4 \\ -4=-4 \end{gathered}[/tex][tex]\begin{gathered} (0,0,4)\Rightarrow2\cdot0+2\cdot0-4=-4 \\ -4=-4 \end{gathered}[/tex]
A side of the triangle below has been extended to form an exterior angle of 117 deg Find the value of x.
Answer:
x=149
Step-by-step explanation:
our survey found that 56% of college students live on campus, 62% have a campus meal program, and 42% do both. while dining in a campus facility open only to students with meal plans, you meet someone interesting. what is the probability that your new acquaintance lives on campus?
our survey found that 56% of college students live on campus, 62% have a campus meal program, and 42% do both. while dining in a campus facility open only to students with meal plans, you meet someone interesting. The percent of people, who either lives or eats on campus is 34 %
In mathematics, sets are collections of discrete things that can be grouped together. A collection of items in a set includes a collection of numbers, days of the week, different kinds of cars, etc.
Let the total number of people be 100.
Let set A be people who live in campus = 56
Let set B be people who participate in meal = 62
Let set be people who do both = 42
According to set theory,
(A∪B) = A+ B - (A∩B)
= 56 + 62 - 42
= 76
Then either lives or eats is given by,
= (A∪B) - (A∩B)
= 76 - 42
= 34
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The sequence below shows the amount of bacteria that occurs after each hour:4, 12, 36, 108,Which formula can be used to determine the amount of bacteria in the next hour, NEXT, if the number of NOW bacteria is known?
The first term is, 4.
The second term is, 12.
That is,
[tex]12=4\times3[/tex]The third term is 36. That is,
[tex]36=12\times3[/tex]Similarly forth term 108 can be written as,
[tex]108=36\times3[/tex]Therefore, the sequence is,
[tex]4,\text{ 3}\times4=12,3\times12=36,3\times36=108,\ldots[/tex]Therefore, the next term will be, 108 x 3. That is,
[tex]\text{NEXT}=3\times NOW[/tex]OPtion a is correct.
evaluate the function of (). () = + put only the value
Ok, evaluate the function of f(5) is just to replace x=5 in the function, so let's do it:
[tex]f(5)=2(5)+9=10+9=19[/tex]This mean that f(5)=19.
Find the missing angle B if side c=43 and side b=5Round your answer to the nearest hundredth if necessary.
In order to find the missing angle B, we can use its sine relation.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (B)=\frac{b}{c} \\ \sin (B)=\frac{5}{43} \\ B=\arcsin (\frac{5}{43}) \\ B=6.68\degree \end{gathered}[/tex]So the angle B is 6.68°.
tensile testing is not appropriate for hard brittle materials such as ceramics. what is the test commonly used to determine the strength properties of such materials? why there is scatter in the measured strength data for ceramics?
The tests commonly used to determine the strength properties of such materials are 3-point load test, direct tension test, cylinder split test.
What is Cylinder split test?In this method, a lone loading along length is applied at diametrically end points. Due to this loading cylinder splits into two parts.
Brittle ceramics are typically not subjected to tensile tests. These materials are challenging to mold into the right test structure, they are challenging to handle without breaking, and it is challenging to align the test samples to prevent bending stresses that could damage the samples.
A three-point bending apparatus is used to measure the stress-strain behavior of brittle ceramics, and from the results, an equivalent modulus of elasticity is calculated.
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Which of the following is the approximate measure of one of the sides of the Pentagon?
5) The circumcircle is the circle we can draw around the pentagon, where the pentagon is inside the circle.
The diameter of that circumcircle is 483.28 meters.
We have to find the length of one of the sides.
The diameter can be converted to a radius dividing it by 2:
[tex]r=\frac{D}{2}=\frac{483.28}{2}=241.64[/tex]We will need to also know the measure of the interior angle of the pentagon.
For regular polygons we can calculate it as:
[tex]\begin{gathered} \alpha=\frac{(n-2)}{n}\cdot180\degree \\ \alpha=\frac{(5-2)}{5}\cdot180\degree \\ \alpha=\frac{3}{5}\cdot180\degree \\ \alpha=108\degree \end{gathered}[/tex]We can then draw a right triangle that will let us calculate the side length (a):
As the radius R bisects the interior angle, we have an angle in the triangle that is half the interior angle: 108/2 = 54°.
Then, we can use trigonometric ratios to find a:
[tex]\begin{gathered} \cos(54\degree)=\frac{Adjacent}{Hypotenuse}=\frac{a\/2}{R} \\ R\cdot\cos(54\degree)=a\/2 \\ a=2R\cdot\cos(54\degree) \\ a\approx2\cdot241.64\cdot0.5877 \\ a\approx284.06 \end{gathered}[/tex]Answer: 284.06 meters.
Mr.brown asked his students to create a representation with a rate of change of 2.5. Circle the students who correctly completed the task. Options: Elijah- y=2.5+x Zane- Four boxes of tissue cost $10. Marco- y=2.5x
The student that correctly completed the task of Mr Brown is the student that gave the option as follows : Four boxes of tissue cost $10
What is rate of change?Rate of change refers to the ratio which shows how a certain item changes over the another item.
In the question, Mr brown requested for a rate of change that is equal to 2.5. Zane gave an option that suits this by showing the example as explained mathematically
If Four boxes of tissue cost $10 then 1 will cost
4 boxes = $10
1 box = ?
cross multiply gives
? * 4 = 10 * 1
dividing through by 4 gives
? = 10 / 4
? = 2.5
Hence the rate at which the price of the boxes change is 2.5
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The rate representation when Mr.brown asked his students to create a representation is Marco - y = 2.5x.
Which of the students correctly completed the task?
Given that: Four boxes of tissue cost $10. The rate is the price of one tissue. To get the rate, we need to divide the cost by the number of tissue:
rate = 10 / 4 = 2.5
Let y and x represent the cost and number of tissue respectively. Since the rate is 2.5, that means x number of tissue will cost 2.5x.
Therefore, we can represent the cost as y = 2.5x. So the student Marco- y = 2.5x completed the task correctly.
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Determine the magnitude of the sum of vectors. please help i’m not sure what to do once i have the components.
Answer:
110.24
Explanation:
First, let us decompose the vectors into their components.
For the vector on the right, decomposing into components gives:
x - component: 80 cos (30°)
y - component: 80 sin (30°)
Therefore.
[tex]v_{right}=[80\cos(30^o),80\sin(30^o)][/tex]Now for the vector on the left, we have
x - component: 91 cos (130°)
y - componentL 91 sin (130°)
Therefore,
[tex]v_{left}=[91\cos(130^o),91\sin(130^o)][/tex]Now adding these two vectors gives
[tex]v_{r\imaginaryI ght}+v_{left}=[80\cos(30^o),80\sin(30^o)]+[91\cos(130^o),91\sin(130^o)][/tex]Adding the components gives
[tex]v_{r\imaginaryI ght}+v_{left}=[80\cos(30^o)+91\cos(130^o),80\sin(30^o)+91\sin(130^o)][/tex]Now since cos (30) = √3/ 2, sin 30 = 1/2, cos (130) = -.0643, and sin (130) = 0.766; the above becomes
[tex]v_{r\mathrm{i}ght}+v_{left}=[\frac{80\sqrt{3}}{2}+91(-0.643),80*(1/2)+91*(0.766)][/tex]the above simplifies to give ( using a calculator)
[tex]v_{r\mathrm{i}ght}+v_{left}=[10.79,109.71][/tex]Now the final step is to find the magnitude of the above vector.
[tex]|v_{r\mathrm{i}ght}+v_{left}|=\sqrt{(10.79)^2+(109.71)^2}[/tex][tex]\boxed{|v_{r\mathrm{i}ght}+v_{left}|=110.24.}[/tex]which is our answer!
Find side length X.* AABC-AXYZ A 20 N 50 X X B 40 O 30 O 15 O 25 40
20 / 40 = x / 50
cross-multiply
40x = 20(50)
40x = 1000
Divide both-side of the equation by 40
x= 25
an airplane is flying at a constant altitude of 5km and speed of 300km per hour towards a radar station on the ground ahead. the distance along the ground from the point directly below the plane to the radar station is 12km. at what rate is the distance along a straight line from the radar to the plane decreasing?
The rate at which the distance along a straight line from the radar to the plane decreasing is 330.0 km/hr.
What is defined as the rate of decreasing?The rate of decrease expresses a decrease as a percentage of the original amount. To determine the rate of decrease, you must first know the original and final amounts.For the given question;
To begin, assume that the radar system is already at ground level. Then there's a right triangle:
s² = x² + y² by the Pythagorean theorem.
Consider the time derivative of a Pythagorean relationship now.
Using chain rule, we get:
2s ds/dt = 2x dx/dt.
Notice that there is no 2y dy/dt term because y is always constant.
Remove the 2s from this final equation, and we get:
s ds/dt = x dx/dt
When s = 12 km, we are told that s decreases at such a rate of 300 km/hr. What is the current horizontal speed dx/dt?
The last derivative equation for dx/dt is as follows:
dx/dt = (s/x) ds/dt
But, x = (s2 - y2)1/2
So, we can write
dx/dt = [s/(s² - y² )¹/₂ ]ds/dt
s = 12 km, y = 5 km, ds/dt = -300 km/hr, in which the negative sign indicates that the hypotenuse of the right triangle drawn above is shrinking.
dx/dt = {(12 km) /[(12 km)² - (5 km)²]¹/₂ }(-300 km/hr)
dx/dt = {(12 km) / [144 km² - 25 km²]¹/₂} (-300 km/hr)
dx/dt = -330.0 km/hr
Thus, the rate at which the distance along a straight line from the radar to the plane decreasing is 330.0 km/hr.
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Find the real numbers that satisfy the equation below. Express your answer in set-builder notation. |x| = x
Answer:
Explanation:
We were given that:
[tex]|x|=x[/tex][tex]undefined[/tex]all the numbers 2, 3, 4, 5, 6, 72,3,4,5,6,7 are assigned to the six faces of a cube, one number to each face. for each of the eight vertices of the cube, a product of three numbers is computed, where the three numbers are the numbers assigned to the three faces that include that vertex. what is the greatest possible value of the sum of these eight products?
These eight products, abc, abe, bcd, bde, acf, cdf, aef, and def, can add up to the greatest possible value of 729.
Let's give our cube's six sides the letters a, b, c, d, e, and f, with a being opposite d, a being opposite e, and b being opposite f.
As a result, we have the following products for the eight vertices:
abc, abe, bcd, bde, acf, cdf, aef, and def.
Let's calculate the total of these products:
= abc + abe + bcd + bde + acf + cdf + aef + def
We see that the first four terms are factors of b, while the last four terms are factors of f.
= b(ac + ae + cd + de) + f(ac + ae + cd + de)
Now we can factor it again:
= (b + f) (ac + ae + cd + de)
= (b + f) (a (c + e) + d (c + e))
= (b + f) (a + d) (c + e)
The given numbers for a cube's six faces are 2, 3, 4, 5, 6, and 7.
We possess the product. The factors are sums of opposite faces, as you can see. The biggest sum that may be reached by adding all three factors (7 + 2), (6 + 3), and (5 + 4) is:
= (7 + 2)(6 + 3)(5 + 4)
= 9 x 9 x 9
= 729
Thus, The greatest possible value of the eight products is 729.
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find the value of Y
With the concepts of alternative angles and straight lines, y measures 15°
What is the relation between alternative angles?Alternative angles in the case of the transversal are equal.
What is the relationship between angles lying next to each other?Angles lying next to each other in the case of transversal sums to 180°.
Since (8x-10)° and (7x)° are alternative angles hence,
8x-10=7x
x=10°
Now, (6y+20)° and (7x)° angles lying next to each other.
Hence, 6y+20+7x= 180°
Substituting the value of x,
6y+20+70=180°
6y=90°
y=15°
Hence angle y measures 15°.
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4 water bottles cost 10$ how many would 3 bottles cost
10/4=2.5
2.5 times 3=
7.5
3 water bottles would cost 7dollars and 50 cents
