What is the rule for the pattern below?
47, 54, 61, 68, 75

Answer:

61.3°

Step-by-step explanation:

For angle x, 12 is the adjacent leg. 25 is the hypotenuse.

The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.

cos A = adj/hyp

cos x = 12/25

x = cos^-1 12/25

x = 61.3°

Answer:

112 cm

Step-by-step explanation:

14 x 8 = 112

The equation of the circle is (x-3)^2 + (y-4)^2 = 85.the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are     y = (-4/3)x + 11 and y = (-4/3)x + 9.

First, we find the center of the circle. Since the circle touches the line 3y-4x-24=0 at the point (0,8), the center must lie on the line perpendicular to this line and passing through (0,8), which has the equation 4y + 3x - 32 = 0. The intersection of this line with the line passing through (7,9) and perpendicular to the line 3y-4x-24=0 gives us the center of the circle:

Solving the equations 3y - 4x - 24 = 0 and 4y + 3x - 32 = 0 gives us the point (3,4), which is the center of the circle.

Now, we can find the radius of the circle by using the distance formula between the center (3,4) and the point (7,9):

r = √((7-3)^2 + (9-4)^2) = √(85)

So the equation of the circle is (x-3)^2 + (y-4)^2 = 85.

To prove that the circle also touches the x-axis, we need to show that the distance from the center (3,4) to the x-axis is equal to the radius. The equation of the x-axis is y=0, so the distance from (3,4) to the x-axis is simply 4. Since the radius is sqrt(85), which is also approximately equal to 9.22, we can see that 4 is indeed equal to the radius, so the circle touches the x-axis.

To find the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0, we first find the slope of this line, which is 3/4. The slope of a line perpendicular to this line is the negative reciprocal, which is -4/3.

To find the points of tangency, we need to find the intersection points of the line passing through (3,4) with slope -4/3 and the circle (x-3)^2 + (y-4)^2 = 85. This gives us two points of tangency: (0,7) and (6,1).

The tangent lines at these two points can be found using the point-slope form of the equation of a line, with the slope equal to the negative reciprocal of the slope of the line 3y-4x-24=0:

At (0,7), the tangent line has the equation y - 7 = (-4/3)(x-0), which simplifies to y = (-4/3)x + 7 + 4 = (-4/3)x + 11.

At (6,1), the tangent line has the equation y - 1 = (-4/3)(x-6), which simplifies to y = (-4/3)x + 9.

Therefore, the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.

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Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

Answer:

$40.80

Step-by-step explanation:

$24 for 10

Therefore, divide by 10 to get amount per wing:

$2.40 for 1

Now multiply by 17 to get amount for 17:

$40.80 for 17

Answer:

40.80

Step-by-step explanation:

Answer:

Question 1: (5,0) Question 2: (1,1) Question 3: (-1, -7) Question 4: (0, 5) Question 5: (8, -3)

Step-by-step explanation:

Drop a comment if you have any questions about my working.

Step-by-step explanation:

\( \frac{30}{wz} = \frac{40}{32 + 40 } \\ wz = 54\)

\( \frac{40}{40 + 32} = \frac{28}{xz} \\ xz = 50.4\)

So the Perimeter is

\(54 + 50.4 + (40 + 32) = 176.4\)

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

15.625 m³

Step-by-step explanation:

The volume of a cube has a formula: V = a³

V = volume

a = side length

The side length is given 2.5 meters.

V = 2.5³

Solve for V.

V = 15.625

The volume is 15.625 cubic meters.

Answer:

15.625cm^3

Step-by-step explanation:

Formula:

V=lxwxh

Given:

l=2.5m

w=2.5m

h=2.5m

Answer:

V=lxwxh

V=2.5m*2.5m*2.5m

V=6.25m^2*2.5m

V=15.625m^3

Hope this helps :)

Answer:

True we put them in a box and take them out and substitute them for wrap paper

into the equation. The findings for x are the new wrapping paper of y that was cancelled and the answer for the each is x to be substituted for y as that is first cancelled.

The answer is substituted for y when x is cancelled at start line of each set.

Could represent how the wrapping paper is opposite variable to what was taken away at point of cancelation. This is before subtraction of the remainder to the total for each so the last two steps are finding a gift wrap for the first cancelation so y cancelled = x substitution.

a. The probability that X is less than 95 is approximately 0.0668

b. The probability that X is between 95 and 97.5 is approximately 0.1359

c. The probability that X is above 102.2 is approximately 0.0228

d. The value of X for 65% chance is 99.23

We know, z=(X-mean)/ (S.D./sqrt N)

Thus, putting in the values for the respective cases, we get

(a) z value corresponding to X=95 is,

z=(95-100)/(10/sqrt 25)= -2.5

Therefore, required probability= area under the standard normal curve left to

z= -2.5 = 0.5000- 0.4938= 0.0062

(b) z value corresponding to X=95 is -2.5 and X=97.5 is,

z=(97.5-100)/(10/sqrt 25)= -1.25

Therefore, required probability= area under the standard normal between

z= -2.5 and z= -1.25= 0.4938- 0.3944= 0.0994

(c) z=(102.2-100)/(10/sqrt 25)= 1.1

Therefore, required probability= area under the standard normal curve right to

z= -2.5 = 0.5000- 0.3643= 0.1357

(d) 65%= 0.6500 is an area on the left side of the z value.

Or, we can say 35%= 0.3500 is on the right side of the z value.

therefore, the corresponding z value is -0.385 approximately.

Thus, for X value,

-0.385= (X-100)/(10/sqrt 25)

-0.385= (X-100)/2

-0.77= X-100

X= 99.23

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The calculated value of the rate of the graph is 0.8

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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The t-test value for the given collected data of hours of studying and exam grade is equal to 10.45.

As given in the question,

n = 5

Mean of the data ( time ) μ₁ = ( 1+ 3 + 4 + 3+ 6)/ 5

                                           = 3.4

Mean of the exam grade μ₂  = ( 55 + 75 + 80 + 85 + 99) / 5

                                           = 78.8

Standard deviation of time σ₁ = 1.82

Standard deviation of exam grade σ₂ = 16.04

Standard error of time = σ₁/√n

                                   = 1.82 / √5

                                   =0.81

Standard error of time =σ₂/√n

                                   = 16.04/ √5

                                   =7.17

Difference in mean of time and exam grade  = 78.8 - 3.4

                                                                      = 75.4

Standard error of difference 'S.E'= √ (0.81)² + (7.17)²

                                            = 7.215

t - test for the given data

= | μ₁ -  μ₂| / S.E.

= | 3.4 - 78.8| / 7.215

= 75.4 / 7.215

= 10.45

P value and statistical significance:

Two-tailed P value is smaller than 0.0001

Therefore, the t-test value for the given collected data is equal to 10.45.

The above question is incomplete , the complete question is:

Researchers have collected data on the hours of studying in a week and the exam grade of a student. you are given the data below (10 points). hint: this questions is similar to q1 in hw7.

hours of studying                            exam grade

1                                                       55

3                                                      75

4                                                      80

3                                                      85

6                                                      99

Calculate the t -test and interpret the data?

Answer:

Step-by-step explanation:

50x < 330 + 30x

Answer:

small dogs= 5

large dogs= 3

Step-by-step explanation:

Step one:

given data

let the  number of small dogs be x

and the number of large dogs be y

Ryan earns $5 for each small dog he walks and $8 for each large dog he walks.

He walked 8 dogs and made a total of $49

so

5x+8y=49----------1

x+y=8---------------2

x=8-y

5(8-y)+8y=49

40-5y+8y=49

collect like terms

3y= 49-40

3y=9

divide both sides by 3

y=9/3

y=3

put y= 3 in eqn 2

x+3=8

x=8-3

x=5

Answer:

I think B

Cuz : he said that the medicine is equal to two-thirds the weight of the child's in pound which means 2/3 multiple 45 is 30

Isn't it?

Answer:

248 teachers

Step-by-step explanation:

Answer:

\(f(-3)=3\)

Step-by-step explanation:

\(f(x)=x^2+2x\\\\f(-3)=(-3)^2+2(-3)\\\\f(-3)=9-6\\\\f(-3)=3\)

Answer:

f(-3) = 3

Step-by-step explanation:

plug in -3 for x in the equation.

(-3)^2 + 2(-3)

9 + (-6)

9 - 6

3

Answer:

dude I ain't no albert einstein but I think it's 61

Step-by-step explanation:

stay groovy man

Answer:

Thx for free points lol

Step-by-step explanation:

Answer:

walk by again

Step-by-step explanation:

defwb8fvhyvybbeegttbggtbu

Answer:

The equation is = y2-y1/x2-x1

Step-by-step explanation:

we have

Multiply in cross

square root both sides

see the attached figure to better understand the problem

the solution is the interval {-6,6}

the solution in the number line is the shaded area at right of x=-6 (close circle) and the shaded area at left of x=6 (close circle)

The set {A, B, C} is a subset of the set of letters of the alphabet.

A subset is a set that contains only elements that are also in another set, called the superset. In other words, all of the elements in the subset are also contained in the superset.

For example, suppose we have a superset S = {1, 2, 3, 4, 5}. Then, the following sets are subsets of S:

{1, 2, 3}, {2, 4, 5}, {1}, and {} etc.

Here we have

{A, B, C} a subset  

As we know, the set of the alphabet = { A, B, C, D,...  Z }  

which also includes the elements A, B, and C

Hence,

The set {A, B, C} is a subset of the set of letters of the alphabet.

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Answer:

Before a variable there is no coefficient.

There is an invisible 1 infront bc there is no real number. so the 1 appears.

The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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The rule that relates the total distance is d =20g

From the question, we have the following parameters that can be used in our computation:

Most cars can travel around 20 miles per gallon of gas that is in their tank

This means that

Rate = 20 miles per gallon

Given that

Distance = d

Gas = g

We have

d = 20 * g

Evaluate

d =20g

Hence, the rule is d =20g

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Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation: