Make a conjecture about the value or geometric relationship.

the relationship between the volume of a prism and a pyramid with the same base

The missing side has a length of 15 in the given triangle.

The given triangle is a right angle triangle.

The hypotenuse is 19.

The angle between the hypotenuse and adjacent side is 36 degrees.

We have to find the length of adjacent side.

As we know the cosine function is a ratio of adjacent side and hypotenuse.

Cos36=y/19

0.809=y/19

y=19×0.809

y=15

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cos(36) = y/19

y = 19 * 0.809

y = 15.4 (Rounded)

The variable y represents the cost of the gym for x months and the varible x represents the number of months of membership for the gym.

So the meaning of the y-value for x = 1 is the cost a person will need to pay in order to use the gym for 1 month.

Answer:

The volume of the cone is;

Explanation:

Given the cone with diameter 8 feet and height 5 feet;

The volume of cone can be calculated using the formula;

Substituting the given values;

Therefore, the volume of the cone is;

Answer:

y=6x+9

Step-by-step explanation:

y=mx+b

add 6x on both sides

The answer is that the mathematician solved 2k problems on the day he drank coffee.

Let's assume that the mathematician works for x hours a day and can solve y problems per hour. Also, the mathematician drinks some coffee and discovers that he can now solve z problems per hour. So, the mathematician works for n hours that day. We are given that:x*y = number of problems solved in a dayz * n = number of problems solved on the day he drank coffee

Then, we can write the equations:x*y = n * 2*z (he still solves twice as many problems as he would in a normal day)andx = n (he only works for n hours that day)Now, we need to simplify these equations to solve for the number of problems solved on the day he drank coffee. Here is how to do it:$$x*y = n * 2*z$$$$\frac{x*y}{x} = \frac{2*n*z}{x}$$$$y = 2 * \frac{n*z}{x}$$Since x, y, n, and z are all positive integers, we can say that the expression 2*n*z/x is also a positive integer. Therefore, we can write:$$\frac{2*n*z}{x} = k$$$$y = 2k$$where k is a positive integer.

Finally, the number of problems solved on the day he drank coffee is:y = 2k Therefore, the answer is that the mathematician solved 2k problems on the day he drank coffee.

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Answer:

54,710

Step-by-step explanation:

multiply the average by 5 to get the amout that they should all have togetehr (271,000) and the add the 4 people's money together (216,290) and then subtract them

The annual income of the fifth salesperson is $54710 if the average annual income for five salespeople last year was $54,200.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

It is given that:

The average annual income for five salespeople last year was $54,200. Four of the salespeople earned these annual amounts: $58,125; $53,190; $48,975 and $56,000.

Let x be the annual income of the fifth salesperson:

$54,200 = ($58,125+$53,190+$48,975+$56,000+x)/5

271000 = 216 290 + x

x = $54710

Thus, the annual income of the fifth salesperson is $54710 if the average annual income for five salespeople last year was $54,200.

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The equation that models the height of the baseball is determined as H(t) = 5 + 49.64t -16(t)².

The maximum height reached by the baseball is calculated as follows;

H = y₀ + v₀yt + ¹/₂gt²

Assuming negative direction for upward motion

H = y₀ + v₀yt - ¹/₂gt²

0 = y₀ + vt -16(t)²

0 = 5 + 3.2v - 16(3.2)²

0 = 5 + 3.2v - 163.84

3.2v = 158.84

v = 158.84/3.2

v = 49.64

H(t) = 5 + 49.64t -16(t)²

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Answer:C?

Step-by-step explanation:

edge

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

D. y+1=4(x-1)

Step-by-step explanation:

look up point slope form equation

Answer:

Step-by-step explanation:

need points

Answer:

20,640

Step-by-step explanation:

32 lots of 645

so 32×645=20,640

The value of the variable, S when  C = 6, n = 8, T = 1 and k = 18 is 1. 036

To make a variable the subject of formula, we have to make it stand alone on one end of the equality sign.

From the information given, we have the equation as;

C = n/Tk(1 + S²)

Now, let's cross multiply to make 'S' the subject of formula, we get;

C× Tk(1 + S²) = n

Divide both sides by the coefficient of S

1 + S² = n/CTk

collect '1' to the other side;

S² = n/CTk + 1

Take the square root of both sides

S = \(\sqrt{\frac{n}{CTk} + 1 }\)

Now, substitute the values

S = \(\sqrt{\frac{8}{6* 1 * 18} + 1 }\)

Multiply the values

S = \(\sqrt{1. 074}\)

S = 1. 036

Thus, the value is 1. 036

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Answer:

It should be -24

Step-by-step explanation:

I found it online, since I wasn't entirely sure, but remember that studying can be fun, and everyone have an amazing day :)

let the pounds be 12

the cost = 12× 6

= 72 dollars

Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Answer:

The expression indicates that when polynomial P(x) is divided by divisor x - a, the remainder of the division is 0

Step-by-step explanation:

The question would be better answered if you gave option. Since there is no option, I'll answer the question generally.

Given

\(P(a) = 0\)

The above expression indicates that when polynomial P(x) is divided by divisor x - a, the remainder of the division is 0

Take for instance, the polynomial is:

\(P(x) = x^2 - x - 2\)

And the divisor is x - 2, then P(2) = 0 because (x - 2) is a divisor of the equation.

\(\frac{P(x)}{x} =\frac{x^2 - x - 2}{x - 2}\)

Factorize the numerator

\(\frac{P(x)}{x} =\frac{(x- 2)(x + 1)}{x - 2}\)

\(\frac{P(x)}{x} =x + 1}\)

See that x - 2 is a divisor

To check

Set x - 2 to 0

\(x -2 = 0\)

\(x = 2\)

So, we have:

\(P(x) = x^2 - x - 2\)

\(P(2) = 2^2 - 2 - 2\)

\(P(2) = 4 - 2 - 2\)

\(P(2) = 0\)

Answer:

10080

Step-by-step explanation:

Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

Let's calculate the z-score:

Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.

Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).

Therefore, approximately 87.1% of people have an IQ score less than 117.

Answer:angle nkl is congruent to angle zwx

Step-by-step explanation: it is equal so it matches

Answer:

angle nkl is congruent to angle zwx

Step-by-step explanation:

The value of phi-coefficient is -0.2 negative association correlation.

Given that the researcher's data that is shown in attached images.

The completed table is shown below:

Gender          Likes the taste of vegemite

0=male                        0=no

1=female                      1=yes

0                                      0

0                                      0

0                                      1

0                                      1

0                                      1

1                                       0

1                                       0

1                                       0

1                                       1

1                                       1

Here, the code '0' means 'male' and '1' means 'female'. Also, code '0' means 'Does not like the taste of vegemite' and code '1' means 'likes the taste of vegemite'.

Phi-correlation is the most appropriate correlation here because we are dealing with binary variables in this study.

Phi-correlation coefficient is given by

Ф=(AD-BC)/√((A+B)(C+D)(A+C)(B+D))

Here, by the given informtion A=2, B=3, C=3, D=2

Ф=(2(2)-3(3))/√((2+3)(3+2)(2+3)(3+2))

Ф=(4-9)/√(5×5×5×5)

Ф=-5/√625

Ф=-5/25

Ф=-1/5

Ф=-0.2

Hence, the value of phi-coefficient for the researcher's data that is shown in attached images is -0.2.

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The radius of the third circle is found out to be as , 1cm.

The radius of 1st circle = 1

radius of second circle = 4

Let XYR be external tangent of the circle which is centered at C,.

Then if we will extend the line PQ to R ,

the result will be , XPR being similar to triangle YQR ,

Therefore,

RQ = x

and length of RP = x   + 5

Therefore, x / x+ 5 = 1/4

=> 4x = x + 5

=> x = 1

So , the length of QR is found out to be as 1cm.

A tangent to a circle is known as a straight line which touches the circle exactly at one point . A circle can have infinite number of tangents.

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Answer:

whatever 31-18 is i think

Step-by-step explanation:

Answer:

Here is the answer.

Step-by-step explanation:

Hope this helps!!

The clearance required from the edge of the roadway to comply with the Super elevation and Side Friction Factor Design (SSD) criteria is 1.68 inches.

To determine the clearance required from the edge of the roadway to comply with the Super elevation and Side Friction Factor Design (SSD) criteria, we need to calculate the maximum lateral displacement of the vehicle as it travels through the curve.

The lateral displacement is given by the following formula

d = V^2 / (g * R)

where:

V = design speed = 50 mph

g = gravitational constant = 32.2 ft/s^2

R = radius of curvature = 1400 ft

Substituting the values, we get

d = (50 mph)^2 / (32.2 ft/s^2 * 1400 ft)

= 0.056 ft = 0.67 inches

Therefore, the maximum lateral displacement is 0.67 inches.

According to the American Association of State Highway and Transportation Officials (AASHTO) Green Book, the minimum desirable clearance from the edge of the roadway to an obstruction is 2.5 times the maximum lateral displacement.

So, the clearance required from the edge of the roadway to comply with the SSD criteria is

Clearance = 2.5 × 0.67 inches = 1.68 inches

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a).  2^38 bytes of memory

b). 12 bits

c). The maximum number of entries in the single-level page table would be 2^38.

d). The size would be 2^38 * 4KB, which equals 2^20 pages.

e). The maximum number of entries it can have depends on the remaining bits of the logical address.

f). The amount of bits required to denote an index into the inner page table is obtained by subtracting the offset and outer page index bits from the logical address.

a. To address a physical memory size of 128GB (2^37 bytes), a 64-bit architecture would require 38 bits for the logical address, allowing access to a maximum of 2^38 bytes of memory.

b. Given that the page size is 4KB (2^12 bytes), 12 bits would be needed to specify the displacement into a page. This means that the lower 12 bits of the logical address would be used for page offset or displacement.

c. With a single-level page table, the maximum number of entries would be equal to the number of possible logical addresses. In this case, since the logical address requires 38 bits, the maximum number of entries in the single-level page table would be 2^38.

d. The size of the single-level page table is determined by the number of entries it contains. Since each entry maps to a page of size 4KB, the size of the single-level page table can be calculated by multiplying the number of entries by the size of each entry. In this case, the size would be 2^38 * 4KB, which equals 2^20 pages.

e. For a two-level page table, the size of the outer page table is determined by the number of entries it can contain. Since the outer page table uses 4KB pages, the maximum number of entries it can have depends on the remaining bits of the logical address. The number of bits used for the index into the outer page table is determined by subtracting the bits used for the inner page index and the offset from the total number of bits in the logical address.

f. The number of bits used to specify an index into the inner page table can be determined by subtracting the bits used for the offset and the bits used for the outer page index from the total number of bits in the logical address. The remaining bits are then used to specify the index into the inner page table.

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Answer:

The slope is 3, the function in the table has a slope of 3.5

Step-by-step explanation:

For the equation, you can just look at the number before x for the slope. For the table, you need to form an equation. (1,5.5) (2,9) are the points that I would use. The equation is y=3.5x-2, the slope is 3.5.

The function in the table has greater rate  of change .

Given,

Line equation : y = 3x - 6

Tabular data .

Now,

In line,

y = 3x - 6

Compare it with the standard form of line

y = mx + c

Hence the slope of line is 3 .

Now the slope of table,

m = y2 - y1 /x2 - x1

m = 9 - 5.5 / 2 - 1

m = 3.5

Slope of table is 3.5 .

Thus the table data has greater slope and thus have a greater rate of change than the line .

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$k = 3\sqrt{2}$.

We have:

\begin{align*}

\int^k_0 (2x^3 -kx^2 +2k)dx &= \left[\frac{1}{2}x^4 - \frac{k}{3}x^3 + 2kx \right]^k_0 \

&= \frac{1}{2}k^4 - \frac{k^4}{3} + 2k^2 \

&= \frac{3}{6}k^4 - \frac{2}{6}k^4 + \frac{12}{6}k^2 \

&= \frac{1}{6}k^4 + 2k^2

\end{align*}

Since we are given that this equals 12, we have:

\begin{align*}

\frac{1}{6}k^4 + 2k^2 &= 12 \

\frac{1}{6}k^4 &= 12 - 2k^2 \

k^4 &= 72 - 12k^2 \

k^4 + 12k^2 - 72 &= 0

\end{align*}

This is a quadratic in $k^2$, so we can solve for $k^2$ using the quadratic formula:

\begin{align*}

k^2 &= \frac{-12 \pm \sqrt{12^2 - 4(1)(-72)}}{2(1)} \

&= \frac{-12 \pm \sqrt{576}}{2} \

&= -6 \pm 12

\end{align*}

Since $k^2$ cannot be negative, we take the positive value:

�

2

=

6

+

12

=

18

k

2

=6+12=18

Thus, $k = \pm\sqrt{18}$. However, since $k$ represents the length of a side of the square, we must take the positive value:

�

=

18

=

3

2

k=

18

​

=3

2

​

Therefore, $k = 3\sqrt{2}$.

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