5. The following table shows the number of students in a given class according to their age and sex. Age Sex Male Female 18 What percent of class are 13 years old? 13 15 Total 21 27​

Answer:

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

$76.00 × .68 = $51.68

5^2 is equal to 25.
lol its kinda easy

Answer:

25.

Step-by-step explanation:

The symbol "^" representa exponents.

The exponet (second number) means how many times you mutiply 5 by itself. In this case, it's 2.

2. 5 x 5 = 25

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 number which we increase by 15 percent gives 356.5 is the number

Given that,

if we increase a number by 15 percent, we get 356.5

Let x be the unknown number.

Then the given statement can be numerically written as,

x + (15% of x) = 356.5

x + (15/100) of x = 356.5

x + 0.15x = 356.5

1.15x = 356.5

Dividing both sides by 1.15, we get,

x = 356.5 / 1.15 = 310

Hence the unknown number is 310.

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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 first derivative of the function h is given by [tex]h'(x)= x^4 - x^3 + x[/tex]. The graph of h is concave down at (−∞,−0.455). Therefore the correct answer is option D.

Given, the first derivative of the function,

[tex]h'(x)=x^{4} -x^{3} +x[/tex]

The second derivative of the function,

[tex]h''(x)=4x^{3} -3x^{2} +1[/tex]

When h''(x)<0, then the function is said to be concave down.

h′′(x)<0

=> [tex]4x^{3} -3x^{2} +1 < 0[/tex]

Finding the root of the equation,

[tex]f(x)=4x^{3} -3x^{2} +1=0[/tex]

This equation has only one real solution,

At x = -0.5, f(−0.5)<0

f(-0.5)<0

At x = -0.4, f(−0.4)>0

f(-0.4)>0

So according to the intermediate value theorem, there is a root in (-0.5, -0.4)

From the option, that root can be x = -0.455

So if the function concave down h''(x) < 0

Interval : (−∞,−0.455)

Therefore, the graph of h is concave down at (−∞,−0.455).

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Answer:

4[tex]a^{9}[/tex][tex]b^{8}[/tex]

Step-by-step explanation:

[tex]\frac{8a^{6}b^{12} x 4a b^{3} }{8x^{-2}b^{7} }[/tex]

[tex]\frac{32a^{7} b^{15} }{8a^{-2} b^{7} }[/tex]

4[tex]a^{9}[/tex][tex]b^{8}[/tex]

Helping in the name of Jesus.

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.

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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The value of the test statistic is -8.2542.

We have,

p'= 0.87, p= 0.93 and n= 1232

We know, the equation for the Test statistic for a population proportion  is mathematically given as

z = (p' - p)/ √p(1-p)/ n

So, z= (0.87 - 0.93)/ √0.93(1-0.93)/ 1232

z = (-0.06) / 0.007269

z = -8.2542

So, the value of the test statistic is -8.2542.

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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

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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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

If there is enough evidence to reject the null hypothesis and conclude that the new process produces less than 90% good product.

The appropriate hypotheses for this scenario would be:

Null hypothesis (H0): The true proportion of good product produced by the new process is equal to or less than 0.9.
Alternative hypothesis (Ha): The true proportion of good product produced by the new process is greater than 0.9.

To test these hypotheses, we can use a one-sample proportion test. The test statistic for this test is calculated using the formula:

z = (p - P0) / sqrt(P0 * (1 - P0) / n)

where:
- p is the proportion of good product in the sample (0.87 in this case)
- P0 is the hypothesized proportion of good product (0.9)
- n is the sample size (49)

Using an alpha level of 0.05, we can find the critical z-value from a standard normal distribution table. For a one-tailed test (since our alternative hypothesis is one-sided), the critical z-value is 1.645.

Calculating the test statistic using the formula above, we get:

z = (0.87 - 0.9) / sqrt(0.9 * 0.1 / 49) = -1.17

Since the calculated z-value (-1.17) is less than the critical z-value (1.645), we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true proportion of good product produced by the new process is greater than 0.9. The quality manager should investigate the process further to improve the proportion of good product before certifying it.

Let's formulate the appropriate hypotheses and test them using an alpha:

The quality manager at Newvis Pharmaceutical Company wants to ensure that the new process produces at least 90% good product. We can define the null hypothesis (H0) and the alternative hypothesis (H1) as follows:

H0: p ≥ 0.90 (The process produces 90% or more good product)
H1: p < 0.90 (The process produces less than 90% good product)

Now, let's test these hypotheses using an alpha (significance level), which is typically set at 0.05.

1. Calculate the test statistic using the sample proportion (p-hat) and sample size (n):
p-hat = 0.87 (87% of the 49 containers were good)
n = 49

2. Find the standard error of the sample proportion:
SE = √(p * (1-p) / n)

3. Calculate the z-score:
z = (p-hat - p) / SE

4. Compare the z-score to the critical value from the z-table corresponding to the chosen alpha level. If the z-score is less than the critical value, reject the null hypothesis in favor of the alternative hypothesis.

If you complete these steps, you can determine if there is enough evidence to reject the null hypothesis and conclude that the new process produces less than 90% good product.

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to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{-4}{2 +2} \implies \cfrac{ -4 }{ 4 } \implies - 1[/tex]

Answer: 5400

Step-by-step explanation:

For a cube V=lwh

Volume for the larger box = 4.5 x 5 x 3.75 =84.375 or 675/8

Volume for smaller box =.25 x .25 x .25 = .015625 or 1/64

divide the larger by smaller.

84.375/.015625=5400

or

[tex]\frac{675}{8} /\frac{1}{64}[/tex]   keep change flip = [tex]\frac{675}{8} * \frac{64}{1}[/tex] = 5400

Answer:you need to multiply and ur answer u would get is 64

Step-by-step explanation: multiply 4x16 and you get ur answer.

For the first expression, the order of operation is multiplication followed by subtraction and addition,  -5.56.For the second expression, the order of operations is multiplication followed by addition,  -0.9.

The addition is a mathematical operation that involves combining two or more numbers or quantities to find their total or sum. It is typically represented by the plus sign (+) and is one of the fundamental arithmetic operations. Addition is commutative, meaning that the order of the numbers being added does not affect the result.

For the first expression:

Operations:

Multiplication: 1.2 x (-1.3)

Subtraction: 1.2 x (-1.3)

Addition: 1.2 x (-1.3) + 4

Order of operations:

Multiplication: 1.2 x (-1.3) = -1.56

Subtraction: -1.56 - 4 = -5.56

For the second expression:

Operations:

Multiplication: 2 x 2.5

Addition: -3.5 - 1.4 + (2 x 2.5)

Order of operations:

Multiplication: 2 x 2.5 = 5

Addition: -3.5 - 1.4 + 5 = -0.9

Therefore, For the first expression, the order of operation is multiplication followed by subtraction and addition,  -5.56.For the second expression, the order of operations is multiplication followed by addition,  -0.9.

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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 statement "the confidence interval formula for a sample size is the same as the sample size formula for a mean" is false because they serve different purposes and cannot be used interchangeably.

The formula for a confidence interval depends on several factors, including the sample size, the level of confidence, and the standard deviation of the sample. The formula for a confidence interval for a mean is:

Confidence interval = sample mean ± (t-value) x (standard error)

where the t-value is based on the level of confidence and the degrees of freedom, and the standard error is the standard deviation of the sample divided by the square root of the sample size.

In summary, while both formulas involve the sample size and are used in statistical analysis, the confidence interval formula and the sample size formula for a mean are distinct and cannot be used interchangeably.

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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:

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

The table should be completed by writing each part of the exponential function as follows;

Geometric sequence        Exponential function      Mathematical meaning

gₙ                                             f(x)                                  dependent variable

g₁/r                                            a                                    coefficient of power

r                                                b                                    base of power

n                                               x                 independent variable (exponent)

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

By comparison, we have:

gₙ  = f(x) (dependent variable)

g₁/r = a (coefficient of power)

r = b (base of power).

n = x (independent variable or exponent).

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Answer: c

Step-by-step explanation: I'm pretty sure this is right

Could you possibly repost your question with a clear image?

The details on this image are unreadable and, therefore, make it difficult to help.

Will bookmark this question so I can find your new post if posted again.

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:

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 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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