Find all primes p, q such that p^2-p=37q^2-q

The 90 percent confidence interval for the data is given as  396.02, 727.98

The formula is fx/n

= Mean, μ = 562.2

sum up the data and divide by 5

sd =  

Σ(xi - μ)2/N

= (361 - 562.2)² + ... + (631 - 562.2)²/5

= 151806.8/5

= 30361.36

sd = √30361.36

= 174.24511470914

1 - confidence level

= 1 - 0.90

= 0.1

df = 4

Using excel

T.INV.2T(0.1, 4) = ±2.13

562 +- 2.13 x  174.245/√5

562- 165.98, 562+ 165.98

= 396.02, 727.98

Hence the confidence interval can be calculated to be 396.02, 727.98

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Answer:

mother age 37

sons age 12

Answer:

x = 5

Step-by-step explanation:

Since the line is vertical,

the equation of the line then is x = (some value).

Since this particular line passes throught (5,-4), where the x coordinate is 5, we can deduce the equation of this line to be x = 5.

Using trigonometric identities, the simplified expression, without quotients, is given as follows:

A. [tex]\cos{\beta}\cot{\beta}[/tex]

The cosecant of an angle is given by one divided by the sine of the angle, hence:

[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]

The sine and the cosine of an angle are related as follows:

[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]

[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]

The cotangent of an angle is:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

The expression given is:

[tex]\csc{\beta} - \sin{\beta}[/tex]

Simplifying the cosecant:

[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]

Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:

[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]

Hence option A is correct.

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The brief report about what the attached data in the box plot shows that: "Women appear to marry around three years younger than males, although the shape and dispersion of the two distributions are extremely comparable."

A boxplot is a type of graph that shows how the values in the data are distributed.

A boxplot is a standardized technique of representing data distribution based on a five-number summary ("minimum", first quartile (Q1), median, third quartile (Q3), and "maximum").

It can provide information about your outliers and their values.

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Full Question:

In​ 1975, did men and women marry at the same​ age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.

Answer:

Step-by-step explanation:

Comment

Let the number of pages = x

Play =    1/3x

Actors = 1/4(x - 1/3 x)

Actors = 1/4(2/3x)

Actors = 2/12 x

Producer Director etc = 2 pages

Equation

Actors = 2 pages

2/12 x = 2

Solution

2x/12 = 2               Multiply both sides by 12

12*2x/12 = 2*12     Combine

2x = 24                  Divide by 2

2x/2 = 24/2           Combine

x = 12

Answer

The program had 12 pages.

The best sampling method that Is most appropriate for the town planner is called Stratified Sampling.

The best sampling method that I would recommend for the town planner is called Stratified Sampling.

The reason for using stratified sampling is because it is a method of sampling that involves dividing a population into smaller groups–called strata and in this case, the rows of houses can be used as a strata.

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The sum of the exponential expression is e^8x + e^2x

Exponential functions are inverse of logarithmic function

Given the exponential function below;

(e^4x)² + e^2x

Expand

e^8x + e^2x

Hence the sum of the exponential expression is e^8x + e^2x

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The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

According to the question

Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:

Row one, 1| 5 6 6 7 9 :

This means there are 5 data set for the first row which are:

15, 16, 16, 17, 19

Row two, 2|0 1 3 :

There are 3 data here, which are:

20, 21, 23

Row 3, 3|2: = 32

Row 4, 4|2: = 42

So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Correct option is C.

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the area of the rectangle is 80. 1  cm²

From the given information, let's say one side of rectangle = a

The other side  =  (36 - 2a)/2  

=  18 - a   cm

The angles between the diagonals of the rectangle is 78°

Then, the angle diagonal has with base will give

=  (180° - 78°)/2

= 102/2

= 51°

We have the angle to be 51 degrees, using the tan ratio

Tan θ = opposite/ adjacent

Opposite of angle 51 degrees = a

Adjacent = 18 - a

Thus,

[tex]tan 51 = \frac{a}{18 - a}[/tex]

[tex]1. 2349 = \frac{a}{18-a }[/tex]

cross multiply

[tex]18 -a ( 1. 2349) = a[/tex]

[tex]22. 23 - 1. 2349a = a[/tex]

collect like terms

[tex]a + 1. 2349a = 22. 23[/tex]

[tex]2. 2349 a = 22. 23[/tex]

[tex]a = \frac{22. 23}{2. 2349}[/tex]

a = 9. 95

If a = 9. 95cm

Then, 18 - a = 18 - 9. 95 = 8. 05cm

The formula of area of a rectangle is given as;

Area = width × length

Area = 9.95 x 8.05

Area = 80. 1  cm²

Thus, the area of the rectangle is 80. 1  cm²

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Answer:

D = 50t

Step-by-step explanation:

we see, with every additional hour the distance increases by 50.

that means in general that the number of hours are multiplied by 50 to get the distance.

in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.

A geometric shapes that can be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

It should be noted that geometric shapes are the figure of area that is closed by a boundary.

In this case, a geometric shapes that. an be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

This is because all the sides in a square are equal.

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Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Step-by-step explanation:

Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
[tex]20x=1450[/tex]
[tex]x= 72.5[/tex]
If we just used the Alexanders it would of took 72 hours and 30 minutes.

Now lets look at the Jenkins family sprinkler, lets define it as Y.
[tex]25y=1450[/tex]
[tex]y = 58[/tex]
With only the Jenkins it would of took 58 hours.

Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
[tex]20x= 725[/tex]
[tex]x=36.25[/tex]

Jenkins
[tex]25y=725[/tex]
[tex]y=29[/tex]

Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.

Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take [tex]\frac{5}{4}[/tex] hours. We know that 1 hour contains 60 minutes, which means [tex]\frac{1}{4}[/tex] of a hour contains 15 minutes.

So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.

So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the

Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.

Answer:

[tex]0.75[/tex]

Step-by-step explanation:

750metres÷1000

Answer:

Step-by-step explanation:

that is a regular rhombus, by definition it has perpendicular diagonals, so in the center there are 4 90 ° angles, so your answer is x = 90 °

The value of x is 22

Based on the description in the question,

The angles 5x -40 and 5x are angles on a straight line

So, we have:

5x - 40 + 5x = 180

Evaluate the like terms

10x = 220

Divide by 10

x = 22

Hence, the value of x is 22

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By evaluating the quadratic function, we will see that the differential quotient is:

[tex]\frac{f(2 + h) - f(2)}{h} = 8 + h[/tex]

Here we have the quadratic function:

[tex]f(x) = x^2 + 4x + 5[/tex]

Evaluating the quadratic equation we get:

[tex]\frac{f(2 + h) - f(2)}{h}[/tex]

So we need to replace the x-variable by "2 + h" and "2" respectively.

Replacing the function in the differential quotient:

[tex]\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}[/tex]

If we simplify that last fraction, we get:

[tex]\frac{8h + h^2}{h} = 8 + h[/tex]

The third option is the correct one, the differential quotient is equal to 8 + 4.

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The parametrization for the tangent line at time [tex]t_{0}[/tex] is (41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)

The point of intersection is (40, -4, 0)

The given curve is defined parametrically by the equations

x = 3t + 2

y = 4 cos t

z = 4 sin t

To find the parametrization for the tangent line at time t0 = 13, we need to find the point of tangency and the direction vector of the tangent line.

The point of tangency is the position of the curve at time t0, which is

(3 * 13 + 2, 4 cos 13, 4 sin 13) = (41, -4/3, 4/3)

The direction vector of the tangent line is the derivative of the curve at time t0, which is

(3, -4 sin 13, 4 cos 13) = (3, -4/3, 4/3)

Therefore, the parametrization for the tangent line is

(41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)

b. To find the point where this line intersects the -plane, we set z = 0 and solve for t. This gives us

4/3 + 4t/3 = 0

t = -1/2

Therefore, the point of intersection is

(41 - 3/2, -2, 0) = (40, -4, 0).

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Answer:

X=-14

Step-by-step explanation:

16+22+x=24

38+x=24

x=24-38

x=-14

Answer:

10

Step-by-step explanation:

[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]

Given equation:

[tex]2y=x^3+2x^2[/tex]

Isolate y by dividing both sides by 2:

[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]

Differentiate with respect to x:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]

Finally, substitute x = 2 into the differentiated equation:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]

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Answer:

t= d/r t=5

Step-by-step explanation:

divide each side by d to isolate t

The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)

The equation is given as:

y = 3^x

Let x = 0, 1 and 2

y = 3^0 = 1

y = 3^1 = 3

y = 3^2 = 9

So, we have the following ordered pairs (0,1), (1,3) and (2,9)

Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)

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The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰

The given degree is:

45⁰ 32' 55''

This can be converted to decimal as shown below

[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]

This can be simplified further as:

[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]

Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰

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Answer:

Step-by-step explanation:

Q3 asks for reasons of statements in a theorem proof.

1 Given is correct

2 Definition of right angle is correct

3 should be sum of interior angles in a triangle

4 is substitution

5 subtracting 90degree from left and right hand side

6 is definition of complementary

The area of QOR from the given diagram is 2π square centimeters

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Given the following parameters

<QOR = 180 - <POQ

<QOR = 180 - 135

<QOR = 45 degrees

Determine the radius

L = rβ

π = r(π/4)

1 = r/4

r =  4

Determine the area of QOR

Area = 4²(π)/8

Area = 2π

Hence the area of QOR from the given diagram is 2π square centimeters

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Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.

The payment options contemplated by the employer are distributed as follows:

Option A

Option B

Note: This question is incomplete because there is some information missing. Here is the missing information:

Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.

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I don’t have an answer but by any chance did you complete the assignment?

Answer:

C

Step-by-step explanation:

For lines AC and EF, line FC is a transversal.

Angles ACF and EFC are same side interior angles.

Since their measures add to 180°, then the lines are parallel.

Answer: Choice C

The average price paid by him for the shares after 3 months is ksh. 163.33

Average price paid for the shares after 3 months

= (120 + 160 + 210) / 3

= 490 / 3

= 163.333333333333

Approximately,

ksh. 163.33

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Hi

the trick is to define price by referring only to one item.  

Here the bootle of water is you reference.  

there is 3 gallons  of milk

             6 bottles of water

              6 bags of chips

let's call bottle of water  " X"  

water cost  = X

milk = X+1.7

chips =  X/2

So we have  :  

3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1

3X+ 5.1 + 6X + 6X/2 = 29.1

3X +6X + 3X + 5.1 = 29.1

 12X +5.1 = 29.1

  12X = 29.1 - 5.1

   12 X =  24

        X = 24/12

        X = 2

price of bottle is  2 dollars  

then milk is  2 + 1.7 = 3.7

        chips =  2/2 = 1

let's check =  3*3.7 + 6*2 + 6*1 =   11.1+12+ 6 = 29.1