The whole page Tysm plsssssss step by step btw

The trigonometric ratio cosA = [tex]\frac{3}{5}[/tex] which is in the lowest form.

Trigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, and tangent are three popular trigonometric ratios. (tan).

The given triangle is a right angle,

To find the cos angle we need to take the ratio of the length of the side which is next to the angle, it is also called an adjacent side to the length of the longest side of the triangle called the hypotenuse.

[tex]cosA = \frac{Length of the side next to the angle}{length of the longest side of the triangle} \\cosA = \frac{Adjacent side}{Hypotenuse} \\cosA = \frac{6}{10}\\ cosA = \frac{3}{5}[/tex]

Therefore [tex]cosA= \frac{3}{5}[/tex]

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The composite functions are:

a) f ∘ g = 3x² + 4, with domain of all real numbers.

b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.

c) f ∘ f = 9x + 16, with domain of all real numbers.

d) g ∘ g = x⁴, with domain of all real numbers.

To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.

a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:

f(g(x)) = 3g(x) + 4 = 3x² + 4

The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:

g(f(x)) = (3x + 4)² = 9x² + 24x + 16

The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:

f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16

The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:

g(g(x)) = (x²)² = x⁴

The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

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Answer:

C

Step-by-step explanation:

If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C

Let's replace now.

For C,

Let's take y=-4/3x-10 into consideration at the point (-12,6)

Y should be equal to 6 when we replace x by -12

Let's try

Y = -4/3(-12) - 10 = 16 - 10 = 6

Yup. C is your answer.

1. The coordinates of the vertices of the preimage in the first column of the table are; (2, 2), (-1, 2) (-1, 1) (-2, 1) (-2, -2) (1, -2) (1, -1) (2, -1).

2. The scale factor for the dilation is 3

3. The coordinates for the image are,  (6,6) (-3, 6) (-3, 3) (-6, 3)(-6, -6) (3, -6) (3, -3)(6, -3)

4. The sketch has been attached below;

5. The dilation multiplies the length of line segments by the scale factor.

6. The dilation did not affect the angle measures. The angles in the image are the same as the angles in the preimage.

To calculate the scale factor for the dilation, we look at what has been provided (x, y) → (3x, 3y)

x =1 x2 = 3

1 multiplied by what will give us 3

1×? = 3

1/1 = 3/1 = 3

If we multiply 3 to every vertices of the preimage, we will find the coordinated of the image.

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The solutions of the inequalities are shown below

x [tex]\geq[/tex] 5

x< 13

x[tex]\geq[/tex]1

x> 1

Solving inequalities involves finding all possible values of a variable that make the inequality true. The process for solving an inequality depends on the type of inequality and the operations involved.

[tex]6^x + 4 \leq 6^{2x - 1} \\x + 4 \leq 2x - 1\\x - 2x\leq -1 - 4\\-x \leq -5\\x \geq 5[/tex]

[tex]2^{x + 3} > 4x^{x - 5} \\2^{x + 3} > 2^{2x - 10}\\x + 3 > 2x - 10\\x - 2x > - 10 - 3\\-x > - 13\\x < 13[/tex]

[tex]9^x \leq 9^{2x - 1}\\ x \leq 2x - 1\\x - 2x \leq -1\\-x \leq -1\\x \geq 1[/tex]

[tex]5^4 > 25^{2x} \\5^4 > 5^{4x} \\4 > 4x\\x > 1[/tex]

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The solution to the exponential equation is given as follows:

x = 0.8.

The exponential equation in the context of this problem is defined as follows:

[tex]\left(\frac{1}{64}\right)^{0.5x - 3} = 8^{9x - 2}[/tex]

64 is the sixth power of two, while 8 is the third power of two, hence:

Applying the power of power rule, the equation can be given as follows:

[tex]2^{-6(0.5x - 3)} = 2^{3(9x - 2)}[/tex]

[tex]2^{-3x + 18} = 2^{27x - 6}[/tex]

Exponential functions are one-to-one, meaning that the solution is obtained as follows:

-3x + 18 = 27x - 6

30x = 24

x = 0.8.

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Out of 60 bikes in the repair department, 25 need two repairs and the range of bikes that need both tire and handlebar repairs without needing to fix the seat is 25 out of 60 bikes.

Let's use F, H, and S to represent the events that a bike has a flat tire, bent handlebars, and ripped seat, respectively. Then, we are given:

P(F) = 0.25

P(H) = 0.05

P(S) = 0.10

P(F ∩ H ∩ S) = 1/12

We want to find the number of bikes in the repair department and the number of bikes that need two repairs.

Let N be the total number of bikes in the repair department. Then, the number of repairs needed for each category is:

Flat tires: 0.25N

Bent handlebars: 0.05N

Ripped seats: 0.10N

The number of bikes that need all three repairs is:

P(F ∩ H ∩ S)N = (1/12)N

The number of repairs needed for these bikes is:

3P(F ∩ H ∩ S)N = (1/4)N

The number of repairs needed for bikes that need only two repairs is:

2[P(F ∩ H) + P(F ∩ S) + P(H ∩ S)]N = (5/12)N

The number of repairs needed for bikes that need only one repair is:

[P(F) + P(H) + P(S)]N = 0.4N

The total number of repairs needed is given as 101, so we have:

(1/4)N + (5/12)N + 0.4N = 101

Simplifying this equation gives:

N = 60

Therefore, there are 60 bikes in the repair department.

The number of bikes that need two repairs is:

(5/12)N = 25

Next, we need to find the range of bikes that need both the tires and handlebars repaired without needing to fix the seat. Let's use T and H to represent the events that a bike needs tire and handlebar repairs, respectively. We want to find P(T ∩ H ∩ not S).

We know that P(T ∩ H ∩ S) = P(F ∩ H ∩ S) = 1/12. Also, P(S) = 0.10, so P(not S) = 0.90. Therefore:

P(T ∩ H ∩ not S) = P(T ∩ H) - P(T ∩ H ∩ S)

= 2[P(F ∩ H) + P(F ∩ H ∩ S) + P(H ∩ S)] - P(F ∩ H ∩ S)

= 2(5/12) - 1/12

= 5/12

So, less than half of all the bikes have a ripped seat, and the range of bikes that need both the tires and handlebars repaired without needing to fix the seat is 5/12 of all the bikes, or 25 out of 60 bikes.

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Step-by-step explanation:

This is a right triangle , so the Pythagorean theorem applies

c^2 = a ^2 + b^2        c  is the hypotenuse   a and b are the legs

15^2 = 9^2 + x^2

15^2 - 9^2 = X^2

x  = 12 ft

The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.

What is a sphere?

The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.

We are given diameter as 20 inches.

So, the radius is half of the diameter which comes out to be 10 inches.

From this, we get the volume as

⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]

⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]

⇒ Volume = [tex]\frac{4000}{3}[/tex] π

⇒ Volume = 4186.67 cubic inches

Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.

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If "function-g" defined for all real numbers as g(x) = x² + 6, then the value of g(-5) = 31, g(-2) = 10 and g(-1) = 7.

In mathematics, a function is generally denoted by a symbol such as "f" or "g", and its definition is given by an equation or formula that specifies the relationship between the input and output values.

The function "g" is given as : g(x) = x² + 6;, which is defined for all "real-numbers",

So, to find g(-5), g(-2), and g(-1), we simply substitute these values of x into the function "g" and simplify the resulting expressions:

⇒ g(-5) = (-5)² + 6 = 25 + 6 = 31,

⇒ g(-2) = (-2)² + 6 = 4 + 6 = 10,

⇒ g(-1) = (-1)² + 6 = 1 + 6 = 7.

Therefore, g(-5) = 31, g(-2) = 10, and g(-1) = 7.

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The given question is incomplete, the complete question is

Suppose that the function G is defined for all real numbers as g(x) = x² + 6. Find g(-5), g(-2) and g(-1).

The constant of proportionality of the line is slope m = 2/3

Given data ,

Let the line be represented as A

Now , the value of A is

Let the point on the straight line be P ( 2 , 3 )

Now , from the proportionality , we get

y = kx

Divide by x on both sides , we get

k = y/x

So , the slope of the line is k

k = 2/3

Hence , the proportion is y = ( 2/3 )x

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The variables that Natalie used in the data collected was C. Number of flowers in each bouquet.

The bar graph that Natalie crafted utilized the variable "number of flowers in each bouquet." This particular type of graph reveals the frequency or count associated with every number of flowers contained within a single bouquet.

As an illustration, let us suppose there were 20 bouquets holding 5 flowers, 30 bouquets possessing 10 flowers, and 15 bouquets that had 15 flowers each; consequently, the bar chart would exhibit exactly three bars symbolizing the count for all three categories as outlined above.

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Answer:

(A)

[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]

[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]

[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]

The rocket splashes down after 13.79 seconds.

(B) h'(t) = -9.8t + 43 = 0

t = 43/9.8 = 215/49 = 4.39 seconds

h(4.39) = 433.34 meters

At t = 4.39 seconds, the rocket peaks at

433.34 meters above sea level.

We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

Here, we have,

H0 : μ ≥ 6

H1 : μ < 6

Test statistic :

n = 20

Sample Mean, x = 3

σ = 1.5

Test statistic = (x - μ) ÷ σ/sqrt(n)

Test statistic = (3 - 6) ÷ 1.5/sqrt(20)

Test statistic = - 3 / 0.3354101

Test statistic = −8.944271

Since, sample size is < 30 ;

Obtaining the Critical value using the from T;

Tcritical at 0.05, df = 19 = - 1.729

Tstatistic < Tcritical

−8.944271 < - 1.729

Hence, we reject the Null:

We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

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Therefore , the solution of the given problem of unitary method  comes out to be  a 95% degree of certainty that the genuine average commute time falls within this range.

To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.

Here,

We may use the following calculation to determine the 95% confidence interval for the actual average commute time:

=> CI = x' ± t*(s/√n)

Finding the essential t-value is the first step. We can apply a two-tailed t-test with a significance level of = 0.05/2 = 0.025 because we have 16 useable findings (sample size: n = 16) and

we require a 95% confidence interval. The crucial t-value, which we determine using a t-distribution table or calculator, is roughly 2.131.

=> CI = 21.4 ± 2.131*(1.8/√16)

=>  21.4 ± 0.95

The genuine average commute time has a 95% confidence interval of 20.45 to 22.35 minutes.

Based on our sample of 16 travel times, we can thus say with a 95% degree of certainty that the genuine average commute time falls within this range.

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An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.

An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.

Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.

However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.

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A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.

Answer:

[tex]m = \frac{10 - 7}{7 - 3} = \frac{3}{4} [/tex]

The surd forms are simplified to give;

21. 10√6 - 12√10

23. -56a  - 5√2a - 25

25. -4√15x - 25x + 3

Surds are described as values in square root that can no longer be simplified into whole numbers or integers

They are also seen as irrational numbers.

From the information given, we have that;

√15(2√10 - 4√6)

Expand the bracket and multiply the surd forms

2√150 - 4√90

Factorize the forms

2√25 ×√6 - 4√9 × √10

find the square root

10√6 - 12√10

23. (√2a - 5)(7√2a - 5)

expand the bracket

7√4a² - 5√2a - 35√4a² + 25

find the square root, we have;

7×2a - 5√2a - 35×2a + 25

collect the like terms

14a - 70a - 5√2a - 25

-56a  - 5√2a - 25

25. (√3 + √5x)(√3 - 5√5x)

expand the bracket

3 - 5√15x + √15x - 5√25x²

find the square root

3 - 5√15x + √15x - 25x

collect the like terms

-4√15x - 25x + 3

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These are absolute value expressions evaluated under different conditions:

|x + 3| if x > 5:

Here x is greater than 5, so x + 3 will also be positive. In this case, |x + 3| = x + 3.

|x + 3| if x > 2:

Similar to the above, x is greater than 2, so x + 3 will be positive. Thus, |x + 3| = x + 3.

|x + 3| if x = 2:

In this case, x + 3 = 2 + 3 = 5, and the absolute value of 5 is just 5. Thus, |x + 3| = 5.

|x - 3| if x > 5:

If x is greater than 5, then x - 3 will be positive. Hence, |x - 3| = x - 3.

|120 + x| if x < -120:

Since x is less than -120, 120 + x will be negative. But the absolute value of a negative number is its positive counterpart, so |120 + x| = -(120 + x).

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Answer:x=-8

Step-by-step explanation:

3.2+(−1/2)x−2=4.8x+2−5.2x

−0.1x=0.8

x=-8

Answer:

x=-8

Step-by-step explanation:

x=-8

Area of sector XYZ is 81.45 feet².

The area of a sector is a measure of the size of a portion of a circle enclosed by two radii and an arc between them. It is expressed in square units, such as square centimeters, square meters, or square inches.

To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.

The formula for the area of a sector is:

Area of sector = (central angle / 360°) x π x r²

where r is the radius of the circle, π is the mathematical constant pi (approximately 3.14), and the central angle is measured in degrees.

n is the area of sector XYZ

n/360=115/255(X)

n/255=115/360(V)

(The same elements are proportional)

n=115/360×255

n=81.4583≈81.45 feet²

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The balance after 10 years is equal to: A. $1491.82.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]A(t) = P_{0}e^{rt}[/tex]

Where:

When time, t = 10 years, the future value can be calculated as follows:

[tex]A(t) = 1000e^{0.04 \times 10}\\\\A(t) = 1000e^{0.4}[/tex]

A(t) = 1000(1.49182469764)

A(t) = 1491.82469764 ≈ $1491.82.

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The value of x and y will be

a) x= 48  y= 72

b) x= 10   y= 3

c) x= 18  y= 3

What is triangle proportionality theorem ?

Triangle Proportionality Theorem Statement

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

DA/BD = EC/BE

How we can calculate the value of x and y from the figure ?

The value of x and y can be calculated as

a ) x/4 + 5 =x/2-7                  y/3-6=66-2/3y

   x/4- x/2 = -7-5                   y/3+ 2y/3= 66 + 6  

   x-2x/4=-12                          3y/3= 72

    x= 48                                   y=72

b) x/5 +3 = 4x-35                   2y + 1 = 5y-8

  x/5 - 4x = -35-3                    2y-5y= -8-1

 x-20x/5 = -38                        -3y=-9

 -1 9x/5 = -38                            y=3

    x= 10

c) x/3 + 2= 2x/3-4                    5y=7y/3+8

   x/3-2x/3= -4-2                      5y-7y/3=8

  -x/3 = -6                                  15y-7y=8x3

   x= 18                                           y=3

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Answer:

distance = rate x time

where distance is 300 kilometers and time is t hours. Rearranging this formula to solve for rate, we get:

rate = distance / time

Substituting the given values, we get:

r = 300 / t

Therefore, the equation that represents the train's rate in kilometers per hour based on how many hours the trip takes is r = 300/t.

Step-by-step explanation:

The volume of the prism is 143.44 in³

A prism is a solid shape that is bound on all its sides by plane faces.

The general formula for the volume of a prism is expressed as;

V = base area × height

The prism is a rectangular prism, therefore the volume will be calculated as

V = l× w × h

where l is the length of the base and w is the width of the base

V = 8.5× 4.5 × 3.75

V = 143.44 in³

therefore the volume of the rectangular prism is 143.44 in³

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Answer:

what arecrosses on line 2

Answer:

75%

Step-by-step explanation:

To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.

According to the information provided:

55% of the team does not like to run.

Of those who do not like to run, 70% enjoy cycling.

Of those who enjoy running, 80% also enjoy cycling.

To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.

Percentage of athletes who do not like to run and enjoy cycling:

= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)

= 55% * 70% = 38.5%

Percentage of athletes who enjoy running and enjoy cycling:

= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)

= (100% - 55%) * 80% = 45% * 80% = 36%

Total percentage of athletes who enjoy cycling:

= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling

= 38.5% + 36% = 74.5%

Therefore, the correct answer is:

74.5%

After the first quarter, the interest earned would be:

$1,000.00 * 0.02 = $20.00

So the new balance would be:

$1,000.00 + $20.00 = $1,020.00

After the second quarter, the interest earned would be:

$1,020.00 * 0.02 = $20.40

So the new balance would be:

$1,020.00 + $20.40 = $1,040.40

After the third quarter, the interest earned would be:

$1,040.40 * 0.02 = $20.81

So the new balance would be:

$1,040.40 + $20.81 = $1,061.21

After the fourth quarter, the interest earned would be:

$1,061.21 * 0.02 = $21.22

So the final balance after 4 years would be:

$1,061.21 + $21.22 = $1,082.43

Therefore, the balance after 4 years would be $1,082.43.