Complete the pyramid and write each expression in its simplist form

Answer:

If the original price of the car was $32600 and the dealership increased the price by 13%, we can start by calculating the amount of the increase:

Increase = 13% of 32600

Increase = 0.13 x 32600

Increase = 4238

So the increase in price is $4238. To find the new price of the car, we need to add this increase to the original price:

New price = Original price + Increase

New price = 32600 + 4238

New price = 36838

Therefore, the new price of the car is $36,838.

Answer: x=5.9

Step-by-step explanation:

Use SOH CAH TOA to find full length then subtract to find x

full angle is 27+8=35

they gave adjacent and opposite to the angle so use TOA

tan 35 =[tex]\frac{y}{31}[/tex]

y=31 tan 35

y=21.71  this is the full length

now we do same for the shorter part lets call z

tan 27 = [tex]\frac{z}{31}[/tex]

z= 31 tan 27

z= 15.80 this is th bottom part of line

subtract to find x

x = y - z

x = 21.71 - 15.80

x=5.9

Answer:

  see attached

Step-by-step explanation:

You want a line plot of the given data.

A line plot of the data can be formed by making a mark above the number line for each point that has that value. For example, there are two instances of the value 1.50, so the plot will have two marks above 1.50 on the number line.

The line plot is shown in the attachment.

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Answer:

(3[tex]x^{2}[/tex]+4)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

Answer:

The table displays a higher rate because the slope in the table is bigger than the slope in the graph.

What does a graph's slope mean?

The graph's slope serves as a gauge for a line's steepness. It is the ratio of any two places on the line's vertical change (rise) to horizontal change (run). Slope is defined mathematically as: Slope (m) = (change in y)/(change in x).

The slope from the table is:

y2 - y1/x2 - x1

m = 42 - 30/7 - 5

= 6

The slope from the graph is:

8 - 0/1.5 - 0

m = 5.33

From hypothesis testing, the p-value is greater than the level of significance ( 0.01), so there's no sufficient evidence to reject the null hypothesis or support the owner's claim that 75% of all the items in the store are less than $5.

Hypothesis Testing for a Proportion : Hypothesis testing is a statistical way carried out to determine whether the null hypothesis should be rejected or whether it is not to be rejected. We have to owner'claim regarding the limited of prices all the items in the store. For this Set null and alternative hypotheses: [tex]H_o : P = 0.75 [/tex]

[tex]H_a : P ≠ 0.75 [/tex]

Calculate the test statistic value by z test,

[tex]z = \frac{ \hat p - p)}{\sqrt{ \frac{ p( 1 -p)}{n}}}[/tex]

Calculate the sample proportion, [tex]\hat p = \frac{105}{146}[/tex] = 0.72

then, [tex]z = \frac{ 0.72 - 0.75)}{\sqrt{ \frac{ 0.75( 1 -0.75)}{146}}}[/tex]

= - 0.84

Now, using the distribution table, the p-value for z = -0.84 is equals to the 0.401. As we see the p-value is greater than the level of significance, there's no sufficient evidence to reject the null hypothesis. aSo, the 75% of all the items in the store are less than $5.

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The due date of the loan in the amount of $14,800, opened on January 22, at an interest rate of 9% and with the maturity value of the loan as $15,799, is a. October 22nd.

The due date can be determined using an online finance calculator, which shows that it will take almost 9 months for the loan's due date.

I/Y (Interest per year) = 9%

PV (Present Value) = $14,800

PMT (Periodic Payment) = $0

FV (Future Value) = $15,799

Results:

Loan Period (N) = 8.742 months

≈ 9 months

Total Interest = $999.00

Thus, 9 months to January 22 falls on October 22nd.

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The minimum sample size required to construct a 90% confidence interval with an error of no more than 0.06, given a population mean of 3 fast food meals per week and a population variance of 1.69, is 166.

To find the minimum sample size required to construct the specified confidence interval, we need to use the following formula

n = [Z² × σ²] / E²

where n is the sample size, Z is the Z-score for the desired level of confidence (90% in this case), σ² is the population variance, and E is the maximum error or margin of error.

First, we need to find the Z-score for the 90% confidence level using a standard normal distribution table or calculator. For a two-tailed test, the Z-score is 1.645.

Next, we plug in the given values

n = [1.645² × 1.69] / 0.06²

n = 165.82

We round up to the nearest whole number since we cannot have a fraction of a person in our sample

n = 166

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The measure of the angle m∠T for triangle formed by the tangent line ST is equal to 66°

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

The triangle SQU is an isosceles triangle which implies that;

m∠SQU + 2(78°) = 180° {sum of interior angles of an isosceles triangle}

m∠SQU + 156° = 180°

m∠Q = 180° - 156° {collect like terms}

m∠Q = 24°

m∠T + m∠Q + m∠S = 180°

m∠T + 24° + 90° = 180°

m∠T + 114° = 180°

m∠T = 180° - 114°

m∠T = 66°.

Therefore, the measure of the angle m∠T for triangle formed by the tangent line ST is equal to 66°

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The Surface Area of the cube that has a side length of 4 yards is calculated as: 96 square yards.

A cube has equal side length, and all its faces have the same area. Therefore, we have:

Surface Area of a cube = 6a² [note that a is the length of the side or edge of the cube].

Given the following:

Side length (a) = 4 yards

Plug in the value of a into the formula:

Surface Area of the cube = 6(4²)

Surface Area of the cube = 6(16)

Surface Area of the cube = 96 square yards.

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Answer:

your writing to read difficult

Answer: .1 or 12.2%

Step-by-step explanation:

probability is the part out of the whole

the part = those taken high school only and over 40  =388+1448=1836

the whole are all the people which is 15048

1836/15048=.1  or 12.2%

The total amount spent by Vishaka on the concert was ₹16,71,614.

To find the total amount spent by Vishaka, we need to add up all of the expenses she incurred. This is known as the "total" of the expenses. We can do this using addition, which is a fundamental mathematical operation.

In this scenario, we have four expenses: ₹4,74,560 for musical instruments, ₹8,12,320 for food, ₹3,28,254 for decoration, and ₹56,480 for advertisement. To find the total amount spent by Vishaka, we can add these expenses together as follows:

Total amount spent = ₹4,74,560 + ₹8,12,320 + ₹3,28,254 + ₹56,480

To make the addition easier, we can align the numbers according to their place values, as follows:

   4,74,560

 + 8,12,320

 + 3,28,254

   56,480

_____________

16,71,614

-------------------------

By adding these expenses together, we get the total amount spent of ₹16,71,614.

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Answer:

Step-by-step explanation:

It's a negative slope so A and B are out

-.89 slope is a little flatter than -1   I think the correlation is a little flatter so I'd go with C.   Could be D, since the slopes are so similar and you are just estimating.  But I think C looks better.

Step-by-step explanation:

9/81  =   3^2 / 3^4   =  3^ (2-4) =  3 ^-2

- 9/81 =  - (3^-2 )

Answer:

32% off the original price = 68% of the original price. So the sale price is:

$76.00 × .68 = $51.68

To get the limit of the function (lim(√(1 + 7x) - √(1 - 4x))/x as x → 0), let's first try an elementary method. However, in this case, the elementary method does not seem to lead to a simple solution. Therefore, we will use l'Hospital's Rule, which can be applied when the limit is in the form of 0/0 or ∞/∞.

Step:1. First, differentiate the numerator and denominator with respect to x:
Numerator derivative: d(√(1 + 7x))/dx - d(√(1 - 4x))/dx = (7/2)(1 + 7x)^(-1/2) - (-4/2)(1 - 4x)^(-1/2)
Denominator derivative: dx/dx = 1
Step:2. Now, apply l'Hospital's Rule by taking the limit of the derivatives:
lim((7/2)(1 + 7x)^(-1/2) - (-4/2)(1 - 4x)^(-1/2))/1 as x → 0
Step:3. Plug in x = 0:
(7/2)(1)^(-1/2) - (-4/2)(1)^(-1/2) = (7/2) - (-4/2) = 11/2
Therefore, the limit of the function as x → 0 is 11/2.

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Answer:

28 quart jars

Step-by-step explanation:

We know that there are 4 quarts in a gallon.

7 gallons * 4 quarts/gallon = 28 quarts

She needs 28 quart jars

Answer:

11.5

Step-by-step explanation:

96 divided by 8 is 11.5

Answer:

12in

Step-by-step explanation:

If a rectangle has an area of 96 in²

and 1 side is 8in, then this means we have to find the other side length.

The formula for a rectangle area is:

[tex]A=lw[/tex]

We know the area and length so let's substitute:

96=8w

divide both sides by 8

12=w

The other side is 12in, hope this helps!

The equation for the line of symmetry for the function defined by f(x) =-3x² +6x - 9 is x = 1.

Given the function in the question;

f(x) = -3x² + 6x - 9

To find the equation for the line of symmetry, we need to use the formula:

x = -b/2a,

Where a and b are the coefficients of x² and x in the quadratic equation, respectively.

Given the function:

f(x)= -3x² +6x - 9

We have:

a = -3 and b = 6.

Hence, the equation for the line of symmetry is:

x = -b/2a

x = -6 / ( 2(-3))

x = -6/(-6)

x = 1

The equation for the line of symmetry is x = 1.

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Thus, we get a total of 210 + 90 + 6 + 60 = 366 number of ways to distribute the 7 apples among the 4 lecturers.

To solve this problem, we can use a combination of techniques from combinatorics and basic arithmetic. Since each lecturer can receive at most two apples, we can break down the problem into several cases:

1. Each lecturer receives 2 apples: In this case, we simply need to distribute the 7 apples among the 4 lecturers in a way that each receives 2. This can be done in (7 choose 2) * (5 choose 2) * (3 choose 2) * (1 choose 2) = 210 ways.

2. Three lecturers receive 2 apples and one receives 1 apple: In this case, we need to choose one of the lecturers to receive 1 apple, and then distribute the remaining 6 apples among the other three in pairs. There are 4 ways to choose the lecturer who receives 1 apple, and then (6 choose 2) * (4 choose 2) * (2 choose 2) = 90 ways to distribute the remaining apples.

3. Two lecturers receive 2 apples each, and two receive 1 apple each: In this case, we need to choose two of the lecturers to receive 2 apples each, and then distribute the remaining 3 apples among the other two in a way that each receives 1. There are (4 choose 2) = 6 ways to choose the two lecturers who receive 2 apples, and then (3 choose 1) * (2 choose 1) = 6 ways to distribute the remaining apples.

4. One lecturer receives 2 apples, and three receive 1 apple each: In this case, we need to choose one of the lecturers to receive 2 apples, and then distribute the remaining 5 apples among the other three in a way that each receives 1. There are 4 ways to choose the lecturer who receives 2 apples, and then (5 choose 1) * (4 choose 1) * (3 choose 1) = 60 ways to distribute the remaining apples.

Adding up the results from each case, we get a total of 210 + 90 + 6 + 60 = 366 ways to distribute the 7 apples among the 4 lecturers.

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Answer:

The area of the tile can be found by dividing it into two triangles and one trapezoid. The area of the trapezoid is (5+3)/2 x 6 = 24 cm^2. The area of the two triangles can be found using the height of 5 cm and the base of 6 cm and 2 cm, respectively. The total area is then 24 + (5 x 6)/2 + (5 x 2)/2 = 24 + 15 + 5 = 44 cm^2. Therefore, the closest answer choice is 42.5 cm^2. The answer is (C) 42.5 cm^2.

Step-by-step explanation:

gg

The product of 2*(-4) by using a pattern is determined as - 8.

The product of 2*(-4) is calculated by using  a pattern where we multiply the initial value by the desired factor and then divide by the original factor.

Starting from (-2)(-4), we can find 2(-4) as follows:

(-2)*(-4) = 8

To get to 2*(-4), we multiply the initial value (8) by 2 and then divide by the original factor (-2);

(8 x 2) / (-2) = -8

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$15000\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years \end{cases}[/tex]

[tex]30000 = 15000e^{0.0475\cdot t} \implies \cfrac{30000}{15000}=e^{0.0475t}\implies 2=e^{0.0475t} \\\\\\ \log_e(2)=\log_e(e^{0.0475t})\implies \log_e(2)=0.0475t \\\\\\ \ln(2)=0.0475t\implies \cfrac{\ln(2)}{0.0475}=t\implies 14.6\approx t[/tex]

Step-by-step explanation:

15.

the area of the whole region is the sum of the area of the rectangle BCDE and the triangle ABE.

the area of a rectangle is

length × width

the area of a triangle is

baseline × height / 2

as a nice coincidence (that reduced the amount of work we have to do) the points of the rectangle are on the same x and y lines parallel to the x-axis and y-axis.

so, we can directly see, the distance BC = 5 (only the x- difference matters, as both have the same y- coordinate).

the distance CD = 4 (only the y- difference matters, as they have the same x-coordinate).

DE = 5, EB = 4. so, a true rectangle.

for the triangle we need the length of the baseline (EB = 4) and the length of the height to that baseline (FA = 2 from -2 to 0 of the x-values, and again they have the same y- coordinate).

so, the area of the rectangle is

5×4 = 20 units²

the area of the triangle is

4×2/2 = 4 units²

therefore, together, the shaded area is 20+4 = 24 units².

24.

there is no shaded region (all is white), but I assume we are taking about the inner regions with all sides being continuous lines.

that area is the area of the total rectangle AGDH minus the 2 right-angled triangles BGC and EFH.

the same formulas for the area of rectangle and a triangle apply as before.

right-angled triangle have a big advantage, as their legs can be used as baseline and corresponding height.

again, the points are sharing x- and y- coordinates, so that we only need to calculate the difference of either the x- or the y coordinates.

AG = 5

BG = 2

GC = 5

GD = 14 (6+8)

EH = 2

FH = 11 (6+5)

so, the area of the large rectangle is

14×5 = 70 units²

the area of BGC is

5×2/2 = 5 units²

the area of EFH is

11×2/2 = 11 units²

the total inner area is then

70 - 5 - 11 = 54 units²

The distance between given point A and point B on the graph is 3√2 units.

Hence the correct option is (A).

We know that the distance between two points having coordinates (a, b) and (c, d) is = √((c - a)² + (d - b)²).

From the given graph we can see that,

the coordinates of the point A = (-2, -1)

the coordinates of the point B = (1, 2)

So the distance between the point A and point B is given by,

= √((1 - (-2))² + (2 - (-1))²)

= √((1 + 2)² + (2 + 1)²)

= √(3² + 3²)

= √(9 + 9)

= √18

= 3√2 units

Hence the correct option will be (A).

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The response variable in this study is the exam performance of the students.

The response variable is the main outcome measure of interest in a study. In this case, the researcher is interested in testing the effect of light level on the exam performance of students, which is the response variable. The researcher is also concerned about the potential differences in the effect of light levels between men and women, so wants to ensure that both groups are equally represented in each treatment.

By measuring the exam performance of the students under different lighting conditions, the researcher can determine whether light levels have a significant impact on exam performance and whether this effect differs between men and women.

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