The n-th term of a number pattern is as follows:

Tn = 7n + 6 if n is a prime number and Tn = n²-8 if n is not a prime number
Determine the value of T9 - T7​

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

B. 1 foot per hour

Step-by-step explanation:

It takes the snail 30 minutes or half an hour to move 6 inches. After another 30 minutes the snail will have moved 12 inches. 12 inches is also equal to 1 foot.

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer: 16 ft

Step-by-step explanation: The ratio given is 2ft=1in, therefore 2ft/1in=1. Multiplying anything by 1 equals itself, so multiplying 8in*(2ft/1in)=16ft where the number of inches cancel out.

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\( \cos( \alpha ) = \frac{3}{5} \\ \)

\( {sin}^{2}( \alpha ) = 1 - {cos}^{2} ( \alpha )\)

\( {sin}^{2}( \alpha ) = 1 - ({ \frac{3}{5} })^{2} \\ \)

\( {sin}^{2}( \alpha ) = 1 - \frac{9}{25} \\ \)

\( {sin}^{2}( \alpha ) = \frac{25}{25} - \frac{9}{25} \\ \)

\( {sin}^{2}( \alpha ) = \frac{16}{25} \\ \)

\( sin( \alpha )= ± \sqrt{ \frac{16}{25} } \\ \)

In Quadrant IV , sin is negative .

Thus ;

\(sin( \alpha ) = - \sqrt{ \frac{16}{25} } \\ \)

\( \sin( \alpha ) = - \frac{4}{5} \\ \)

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\( \tan(2 \alpha ) = \frac{ \sin(2 \alpha ) }{ \cos(2 \alpha ) } \\ \)

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\( \sin(2 \alpha ) = 2. \sin( \alpha ). \cos( \alpha ) \)

\( \sin(2 \alpha ) = 2 \times ( - \frac{4}{5} ) \times ( \frac{3}{5} ) \\ \)

\( \sin(2 \alpha ) = - \frac{24}{25} \\ \)

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\( \cos(2 \alpha ) = {cos}^{2}( \alpha ) - {sin}^{2}( \alpha ) \)

\( \cos(2 \alpha ) = ({ \frac{3}{5} })^{2} - ({ - \frac{4}{5} })^{2} \\ \)

\( \cos(2 \alpha ) = \frac{9}{25} - \frac{16}{25} \\ \)

\( \cos(2 \alpha ) = - \frac{7}{25} \\ \)

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\( \tan(2 \alpha ) = \frac{ \sin(2 \alpha ) }{ \cos(2 \alpha ) } \\ \)

\( \tan(2 \alpha ) = \frac{ - \frac{24}{25} }{ - \frac{7}{25} } \\ \)

\( \tan(2 \alpha ) = - \frac{24}{25} \div - \frac{7}{25} \\ \)

\( \tan(2 \alpha ) = - \frac{24}{25} \times - \frac{25}{7} \\ \)

\( \tan(2 \alpha ) = \frac{24}{7} \\ \)

Thus the correct answer is (( C )) .

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Answer:

we have

cos θ = 3/5.

sin²θ=1-cos²θ

sin²θ=1-9/25

sin²θ=16/25

sinθ=±4/5

since it lies in IV qyadrant so

sinθ=-4/5

we have

tan2θ=sin2θ/cos2θ=2sinθcosθ/[cos²θ-sin²θ)

=(2×-4/5×3/5)/(9/25-16/25)=24/7

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Answer:

Rene made = 90 on her math test

If she answer =20problems correctly

we know,

how many problem were there = ?

there where = 90-20

= 70

There where 70 problems

(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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The probability of both people being right-handed is approximately 0.8836, the probability of both people being left-handed is approximately 0.0036, the probability of one person being right-handed and the other being left-handed is approximately 0.1128, and the probability of at least one person being right-handed is approximately 0.9964.

Using basic probability rules, we can solve this problem. Let R denote right-handedness and L denote left-handedness.

A. P(RR) = P(R) * P(R) = 0.94 * 0.94 = 0.8836 A. P(Both are right-handed) = P(RR) = P(R) * P(R) = 0.94 * 0.94 = 0.8836 (rounded to four decimal places)

B. P(LL) = P(L) * P(L) = 0.06 * 0.06 = 0.0036 B. P(Both are left-handed) = P(LL) = P(L) * P(L) = 0.06 * 0.06 = 0.0036

C. P(one right-handed, one left-handed) = P(RL) + P(LR) = 2 * P(R) * P(L) = 2 * 0.94 * 0.06 = 0.1128 (rounded to four decimal places)

D. P(At least one right-handed person) = 1 - P(LL) = 1 - 0.0036 = 0.9964 (rounded to four decimal places)

As a result, the odds of both people being right-handed are approximately 0.8836, the odds of both people being left-handed are approximately 0.0036, the odds of one person being right-handed and the other being left-handed are approximately 0.1128, and the odds of at least one person being right-handed are approximately 0.9964.

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Nancy's weekly net pay is $442.84.

Two or more expressions with an Equal sign is called as Equation.

Given that Nancy earns a gross weekly salary of $564.20

We need to find the net pay if she pays $69.73 in federal income tax, $34.98 in Social Security tax, $8.18 in Medicare tax, and $8.47 in state tax

Net pay = Gross salary - (Federal tax + Social Security tax + Medicare tax + State tax)

Net pay = $564.20 - ($69.73 + $34.98 + $8.18 + $8.47)

= $564.20 - $121.36

= $442.84

Hence, Nancy's weekly net pay is $442.84.

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The standard form of the equation of this hyperbola with vertices at (12, 0) and (–12, 0) is: y squared over 144 minus x squared over 25 equals 1.

Mathematically, the standard form of the equation of a hyperbola is represented by this mathematical expression:

(y - k)²/a² - (x - h)²/b² = 1          .......equation 1.

Where:

From the information provided above, we have the following parameters:

Vertices = (12, 0) and (–12, 0)

h = 0

k = 0

Asymptote = ±5/12(x) = bx/a      ......equation 2.

Comparing equation 1 and equation 2, we have:

b = 5

a = 12

Substituting the given parameters into the the standard form, we have;

(y - k)²/a² - (x - h)²/b² = 1

(y - 0)²/12² - (x - 0)²/5² = 1

(y - 0)²/144 - (x - 0)²/25 = 1

y²/144 - x²/25 = 1

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The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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The graph of the equation 3x + 4y = 0 is a straight line with a negative slope passing through the origin.

The given equation, 3x + 4y = 0, represents a linear graph in the Cartesian coordinate system. Let's analyze its characteristics.

First, note that the equation is in the standard form for a linear equation, which is Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 4, and C = 0.

To graph this equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating y, we have y = (-3/4)x + 0. Since the y-intercept (b) is 0, the line intersects the y-axis at the origin (0,0).

Next, we can examine the slope. The coefficient of x, -3/4, represents the ratio of the change in y (vertical) to the change in x (horizontal) as we move along the line. In this case, the slope is negative, indicating that the line descends from left to right. The magnitude of the slope, 3/4, implies that for every 4 units moved horizontally to the right, the line goes 3 units down vertically.

Therefore, we can conclude that the graph of the equation 3x + 4y = 0 is a straight line passing through the origin (0,0) with a negative slope. It extends indefinitely in both directions, with the line getting steeper as we move to the right.

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Answer:

<A = 60°

Step-by-step explanation:

The triangle is 180° Angle A and B add up to 118°

4y° + (3y + 13)° = 118°

7y + 13 = 118°

7y = 105

y = 15

Since you solve for y, plug your y into the angles to solve.

<A = 4y

<A = 4 * 15

<A = 60°

Answer:10−45

Step-by-step explanation: if you actually saw it then you will get that answer

a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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Here you will find the answer.

Link:https://www.symbolab.com/solver/step-by-step/-x-8y%3D2%20and%20x-5y%3D-15

Answer:

x= -10, y= 1

Step-by-step explanation:

-x -8y= 2 -----(1)

x -5y= -15 -----(2)

From (2):

x= 5y -15 -----(3)

Substitute (3) into (1):

-(5y -15) -8y= 2

Expand:

-5y +15 -8y= 2

-13y +15= 2

13y= 15 -2

13y= 13

Divide both sides by 13:

y= 13 ÷13

y= 1

Substitute y= 1 into (3):

x= 5(1) -15

x= 5 -15

x= -10

There are 6 skates in store with 5 wheels.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, Let the number of 4 wheel skates in display be x

         and the number of 5 wheel skates in display be y

       Total number of skates = 17

       Total number of wheel = 74

Now, according to question

        x + y = 17     ................(i)

        4x + 5y = 74 ..................(ii)

From equation (i), we get

          x = 17 - y   ................(iii)

put the value of y in equation (ii), we get

      4(17 - y) + 5y = 74

       68 - 4y + 5y = 74

          y + 68 = 74

          y = 6

Put the value of y in equation (iii), we get

          x = 17 - 6

          x = 11

Thus, there are 6 skates in store with 5 wheels.

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maybe 61km from northeast

Answer:

x>0

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

On each linear pair, there is one of the Vertical angles and an angle shared between the two angles. This means we can use the fact that supplements of the same angle are congruent.

The basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

In the provided figure.

∠1 + ∠2 = 180 degrees ( linear pair of angles)...(i)

∠ 1 + ∠4 = 180 degrees ( linear pair of angles)...(ii)

According to transitive property, if a = b and b = c then a = c

Therefore,

∠1 + ∠2 = ∠1 + ∠4...(iii)

⇒∠2 = ∠4

Similarly, we can prove that

∠1 = ∠3

Therefore, we conclude that vertically opposite angles are always equal.

Hence, the basis for the proof vertical angles are congruent is " two angles that are each supplementary to a third angle are congruent".

Thus, statement c is correct.

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Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

Let A and B be the number of advance and same-day tickets sold. From the question we can write the following relations:

From this, we can isolate A in the first relation and substitute it in the second. This way we can find the value of B, as follows:

From this, we can substitute the value of B in the first relation to find A.

From this, we conclude that:

The number of advance tickets sold is 40

The number of same-day tickets sold is 30

Answer:

Gina would need to take 10 classes.

Step-by-step explanation:

Cost of x classes at dance studio:

\(y_d(x) = 15x\)

Cost of x classes at toe tappers:

\(y_t(x) = 25 + 12.5x\)

How many classes would Gina need to take for the total cost to be the same at both dance studios?

This is x for which:

\(y_d(x) = y_t(x)\)

So

\(15x = 25 + 12.5x\)

\(2.5x = 25\)

\(x = \frac{25}{2.5}\)

\(x = 10\)

Gina would need to take 10 classes.

Answer:

10 just took it on edge

Answer:  A) 3 x 4

Step-by-step explanation:

The dimensions of a matrix are ROWS x COLUMNS.

The given matrix has 3 rows and 4 columns,

therefore the dimensions are: 3 x 4

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.