Which function is represented by the graph?
A f(x) = -12x + 6f(x) = - 1 2 x + 6
B f(x) = 12x + 6f(x) = 1 2 x + 6
C f(x) = -2x + 6f(x) = -2x + 6
D f(x) = 2x + 6

The values of the composite functions are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126

Given that we have the function definitions

The composite functions are calculated below

(g o f)(x) = g(f(x))

(g o f)(x) = (f(x))² - 5f(x)

So, we have

(g o f)(x) = (3/2x + 1)² - 5(3/2x + 1)

Evaluate

(g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex]

Next, we have

(j o g)(x) = j(g(x))

(j o g)(x) = 3g(x) + 1

So, we have

(j o g)(x) = 3(x² - 5x) + 1

(j o g)(x) = 3x² - 15x + 1

Next, we have

(g o h)(x) = g(h(x))

(g o h)(x) = (h(x))² - 5h(x)

So, we have

(g o h)(x) = ((2x - 1)/33)² - 5((2x - 1)/33)

Evaluate

(g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex]

Lastly, we have

(g o g)(-2) = g(g(-2))

(g o g)(-2) = (g(-2))² - 5g(-2)

So, we have

(g o g)(-2) = ((-2)² - 5(-2))² - 5((-2)² - 5(-2))

(g o g)(-2) = 126

Hence, the values are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126

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Answer:

Option C

Step-by-step explanation:

To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:

2x = 6

Simplifying, we get:

x = 3

Substituting x = 3 into either of the original equations, we get:

3 + y = -4

Solving for y, we get:

y = -7

Therefore, the solution to the system of equations is (3, -7), which is option C.

Answer:

The answer is -5

Step-by-step explanation:

Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.

Answer:

1/6

Step-by-step explanation:

Chances of getting 2 = 1/6

scientific notation to express the number of bacteria that would be in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex].

With scientific notation, one can express extremely big or extremely small values.

When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.

The given number of bacteria in the dirt sample is 8.6 × [tex]10^7[/tex], and the weight of the sample is 1 gram. To find the number of bacteria in a sample weighing 19 grams, we can use the following proportion:

number of bacteria / weight of sample = constant

We can solve for the constant by using the given information:

8.6 ×[tex]10^7[/tex] / 1 gram = constant

constant = 8.6 × [tex]10^7[/tex]

Now we can use this constant to find the number of bacteria in a 19-gram sample:

number of bacteria / 19 grams = 8.6 × [tex]10^7[/tex]

number of bacteria = 8.6 ×[tex]10^7[/tex] × 19 grams

To express the answer in scientific notation, we can multiply the two numbers and adjust the exponent accordingly:

number of bacteria = 1.634 × [tex]10^9[/tex]

Therefore, the number of bacteria in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex]

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Answer:

Simple interest= PRT/100

parameters

price =300

Rate=6%

Time=4years

300*6*4/100

7200/100

=72

Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.

Here,

Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).

The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.

To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:

P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)

= (1/2) x (1/3)

= 1/6

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If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.

The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.

In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:

So, scale factor = A'B'/AB,

Substituting the values,

We get,

Scale factor = 9/12,

Scale Factor = 3/4,

Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.

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The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

|(x + 3) | if x > 5

This can be written as,

= |x + 3|

Now,

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Thus,

The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

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The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.

To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.

Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.

15 m = 1500 cm

Next, we can set up a proportion:

0.5 cm / x = 1500 cm / (3x)

where x is the scale of the zoomed-in map.

Simplifying the proportion, we get:

0.5(3x) = 1500

1.5x = 1500

x = 1000

Therefore, the answer is (B) 1cm = 10 m.

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An equation that models the position of the object at time t is:

s(t) = -2cos(2πt/5).

The general form for the equation that will model a wave is:

±a (sin/cos) (2π(x - p)/T)

where:

a is the amplitude

p is the phase shift

T is the period.

The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.

The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.

In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.

Thus, this equation is: s(t) = -2cos(2πt/5).

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The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

---------------------

Given triangle MNO with vertices:

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

So the coordinates of the image are:

This is matching the option D.

See attached for visual representation of the problem.

Answer:

Step-by-step explanation:

8,800x0.09=792. The salesperson earns $792 in commission.

Answer:

$792

Step-by-step explanation:

8800×0.09= 792

9÷100=0.09

commission =$792

(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) 2x/3 + 4 = 10 equation does x = 9.

Hence the correct option is (b).

(11) The given expression is,

3/y + 2y/4 = 3/y + y/2

Substituting the value of y = 4 we get,

3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The given expression is,

12/y + 3y/4

Substituting y = 8 in the given equation we get,

12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) Given the solution is x =9.

For first option: (2/3)*9 - 6 = 6 - 6 = 0

2x/3 - 6 = 12 does not satisfied by x = 9.

For second option: (2/3)*9 + 4 = 6 + 4 = 10

So, x = 9 satisfies 2x/3 + 4 = 10.

For third option: 3*9 - 12 = 27 - 12 = 15

So x = 9 does not satisfy 3x - 12 = 21.

For fourth option: 3*9 + 12 = 27 + 12 = 39

So x = 9 does not satisfy 3x + 12 = 19.

Hence the correct option is (b).

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The correct options are rectangular prism, square pyramid.

When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.

The shapes that have rectangular cross sections when they are cut perpendicular to the base are:

Rectangular prism

Square pyramid

Therefore, the correct options are rectangular prism, square pyramid.

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Complete question:

By using the corresponding angles, vertically opposite angles, alternate interior angles, and linear pair theorems, the measure of the angles are:

m ∠1 = 39°

m ∠2 = 141°

m ∠3 = 141°

m ∠4 = 39°

m ∠5 = 39°

m ∠6 = 141°

m ∠7 = 39°

From the question, we are to calculate the measure of the unknown angles in the given diagram

By the Linear pair theorem,

We can write that

m ∠5 + 141° = 180°

Thus,

m ∠5 = 180° - 141°

m ∠5 = 39°

Likewise

m ∠7 + 141° = 180°

m ∠7 = 180° - 141°

m ∠7 = 39°

By the vertical angles theorem,

We can write that

m ∠6 = 141° (Vertically opposite angles)

By the corresponding angles theorem,

We can write that

m ∠2 = 141° (Corresponding angles)

m ∠2 = m ∠3 (Vertically opposite angles)

Therefore,

m ∠3 = 141°

m ∠4 = m ∠5 (Alternate interior angles)

m ∠4 = 39°

m ∠1 = m ∠4 (Vertically opposite angles)

Therefore,

m ∠1 = 39°

Hence,

The measure of angle 1 is 39°

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As A is the only option that is three units distant from (5, 3), the response is: A) (1, 3) (1, 3) .

The placement of a point in a particular space or on a certain graph is represented by coordinates, which are numbers. Coordinates are normally two figures written in parenthesis and separated by a comma in two-dimensional space, where x denotes the point's horizontal position and y denotes its vertical position. Three integers enclosed in parentheses and separated by commas are used to indicate coordinates in three-dimensional space. The three numbers are generally represented as (x, y, z), where x, y, and z stand for the positions all along x-, y-, and z-axes, respectively. The location of objects, points, and other entities in space is described using coordinates frequently in the domains of mathematics, physics, engineering, and many others.

given

Any other vertex must be three units away from the specified vertex because the square has three units on each side.

The distance between the supplied vertex (5, 3) and each of the possible answers can be calculated using the distance formula:

Option A: Distance between (1 and 3) = sqrt((1 - 5)2 + (3 - 3)2) = sqrt(16) = 4 (not three units away)

Option B: Distance between (8 and 6) = sqrt((8 - 5)2 + (6 - 3)2) = sqrt(27) (not three units away)

Option C: (4, 0)

Distance is equal to sqrt((4 - 5)2 + (0 - 3)2 = sqrt(10) (not three units away)

Option D: Distance = sqrt((2 - 5)2 + (1 - 3)2) = sqrt(10) for the pair (2, 1). (not three units away)

As A is the only option that is three units distant from (5, 3), the response is: A) (1, 3) (1, 3) .

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Among the given options, V [tex]57^\circ[/tex]   is the closest estimate for the measure of the other acute angle.

To find the measure of the other acute angle, we can use the fact that the sum of the angles of a triangle is 180°. Let x be the measure of the other acute angle. Then we have:

[tex]x + 32.9^\circ + 90^\circ = 180^\circ[/tex]

Simplifying the equation, we get:

[tex]x = 180^\circ - 32.9^\circ - 90^\circ[/tex]

[tex]x = 57.1^\circ[/tex]

So the exact measure of the other acute angle is [tex]57.1^\circ.[/tex]

Therefore, Among the given options, V [tex]57.1^\circ.[/tex] is the closest estimate for the measure of the other acute angle.

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From the discrete distribution given, the standard deviation is of 0.83 children.

The distribution is:

P(X=1) =0.5

P(X=2) =0.25

P(X=3) =0.25

The mean is 1.75.

The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.

Hence:

The standard deviation is 0.83 children.

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Answer:

3 yards

Step-by-step explanation:

The surface area of the prism is 360in²

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

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism and B is the base area , p is the perimeter of the base.

Base area = 1/2 × 5 × 12

= 5 × 6 = 30 in²

Perimeter of the base = 5+12+13

= 30 in²

height = 10 in

SA = 2 × 30+30× 10

= 60 + 300

= 360 in²

therefore the surface area of the prism is 360 in²

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Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses.

The parameter of interest is the difference in population proportions of females and males who took advanced math courses. We can denote this parameter by p₁ - p₂, where p₁ is the population proportion of females who took advanced math courses, and p₂ is the population proportion of males who took advanced math courses.

To construct a confidence interval for the difference in population proportions, we need to check the following conditions,

The sample of high school students should be a simple random sample.

The sample of high school students should be independent of each other.

Both groups of females and males who took advanced math courses should have at least 10 successes and 10 failures.

The sample proportions of females and males who took advanced math courses can be calculated as follows,

p₁ = 53/150 = 0.353

p₂ = 89/275 = 0.324

The sample size of females and males can also be calculated as follows,

n₁ = 150

n₂ = 275

The standard error of the difference in sample proportions can be calculated as follows,

SE = √[(p₁(1 - p₁))/n₁ + (p₂(1 - p₂))/n₂]

= √[(0.353(1 - 0.353))/150 + (0.324(1 - 0.324))/275] ≈ 0.048

Using a t-distribution with (n₁ + n₂ - 2) degrees of freedom and a 98% confidence level, we can construct a confidence interval for the difference in population proportions as follows:

(p₁ - p₂) ± t*SE

where t is the t-score corresponding to a 98% confidence level and (n₁ + n₂ - 2) degrees of freedom. Using a t-table, we can find that t ≈ 2.33.

Substituting the values into the formula, we get,

(0.353 - 0.324) ± 2.33*0.048

0.029 ± 0.112

True difference in population proportions of females and males who took advanced math courses lies between 0.029 and 0.147.

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.

Yes, our interval from part A gives convincing evidence of a difference between the population proportions because it does not contain zero. The interval (0.029, 0.147) is entirely positive, which means that the proportion of females who took advanced math courses is higher than the proportion of males who took advanced math courses. Additionally, the interval does not contain the value of one, which means that the difference in population proportions is not due to chance. Therefore, we can conclude that there is a significant difference in the population proportions of females and males who took advanced math courses.

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To find the expected number of dog owners who brush their dog's teeth, we can multiply the total number of dog owners (639) by the percentage that brush their dog's teeth (18% or 0.18).

Expected number of dog owners who brush their dog's teeth = 639 x 0.18

= 115.02 (rounded to the nearest whole number)

So, we can expect about 115 dog owners out of 639 to brush their dog's teeth.

The area of each circle would be given below:

Circle A= 153.86 in²

Circle B = 314in²

Circle C = 615.44in²

Circle D = 452.16 in²

To calculate the area of a circle, the formula that should be used is given below such as follows:

Area of circle = πr²

For circle A;

radius = 7 in

area = 3.14×7×7 = 153.86 in²

For circle B;

radius = 3+7 = 10in

area = 3.14×10×10 = 314in²

For circle C;

radius = 10+4 = 14 in

area = 3.14×14×14

= 615.44in²

For circle D;

radius = 14-2 = 12in

radius = 3.14×12×12

= 452.16 in²

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well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

Answer:

The IQR (interquartile range) of 13 is the most accurate measure of variability to use in this case, since the data is skewed and contains some outliers.

The IQR is a measure of variability that is less sensitive to extreme values than the range, and is calculated as the difference between the upper and lower quartiles (the 75th and 25th percentiles). It provides a measure of the spread of the middle 50% of the data, which is useful for understanding the typical range of donations received.

In this case, the IQR is calculated as follows:

- The median of the data is 51 (the value in the middle).

- The lower quartile (Q1) is the median of the lower half of the data, which is 42.

- The upper quartile (Q3) is the median of the upper half of the data, which is 54.

- The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 54 - 42 = 12.

So the IQR of 13 is a useful measure of variability to use for this data set, since it captures the spread of the middle 50% of the data while being less sensitive to the outliers at the higher end of the distribution.

a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.

b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.

Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.

Probability is represented as a fractional value using decimals, fractions, or percentages.

The percentage of students taking a math class =79%

The percentage of students taking an English class = 70%

The percentage of students taking both classes = 67%

Let the event that a student is taking a math class = m

Let the event that a student is taking an English class = e

The probability of m is p(m) = 0.79

The probability of e is p(e) = 0.70

The probability of m and e is p(m and e) = 0.67

The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)

The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)

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The value of sin(A-B) is 2334/6625

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Example of trigonometric identity include;

cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.

1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ

1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ

Sin(A-B) = = sin A cos B- cos Asin B

if tan A = 4/3, then 4 is the opp and 3 is the adj,

hyp² = 4²+3²

= 16+9

hyp² = 25

hyp = √25

= 5

cos A = 3/5 and sinA = 4/5

if sinB = 28/53, then opp is 28 is the opp and 53 is the hyp

adj = √ 53²-28²

adj = √ 2809 - 784

adj = √2025

adj = 45

cos B = 45/58

sin(A-B) = 4/5 × 45/58 - 3/5× 28/53

= 18/29 - 84/265

= (4770-2436)/6625

= 2334/6625

therefore the value of sin(A-B) = 2334/6625

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