Robbie grew 6 inches in eight months. What is his average growth rate per month?

To create a cubic model, we need to find a cubic equation in the form of [tex]y = ax^3 + bx^2 + cx + d[/tex] that fits the given data. Let's use the data provided in the table and the equation [tex]y = 0x^3 + x^2 + x + 0[/tex].

Since the coefficient of [tex]x^3[/tex] is 0, the cubic term does not contribute to the equation. Therefore, the cubic model simplifies to [tex]y = x^2 + x[/tex].

The equation [tex]y = x^2 + x[/tex]represents a quadratic function rather than a cubic function.

Thus, if we assume that the cubic term is indeed meant to be 0, we can use the simplified equation [tex]y = x^2 + x[/tex] as the cubic model based on the given data.

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hi

what's the title of the question?

The correct statement regarding the exponential functions in this problem is given as follows:

D. The functions both have the same y-intercept.

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The functions in this problem are given as follows:

Hence the y-intercept for each function is given as follows:

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hello

the answer to the question is:

Tan (x) = 6.7/4.9 = 1.3673 ----> x = 53.81° or 54°

Answer:

s(x) = 0.23x + 400

Step-by-step explanation:

Let x = cost of merchandise sold

We start by finding the slope which is the percent of commission Alysse receives.

Let's start with doing 607 - 515. This is because we are subtracting the commissions, which also can be y2 - y1. Then, we do 900-500=400 (x2-x1). This is how to find the slope of the function. [tex]\frac{y2-y1}{x2-x1}=\frac{92}{400} =0.23[/tex], 0.23 being the slope.

s(x) = b+0.23x, now substitute values making the money received as s(x).

515 = b+0.23(500)

515=b+115

-115   -115

400 = b

607 = 400+0.23(900)

607 = 400 + 207

607 = 607

So, s(x) = 0.23x + 400

The Probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.

The probability that the average weight of our sample is greater than 15.8 oz, we need to use the concept of the sampling distribution of the sample mean and the Central Limit Theorem.

Given:

Population mean (μ) = 16 oz.

Population standard deviation (σ) = 1.25 oz.

Sample size (n) = 40 bags of candy.

The Central Limit Theorem states that for a large enough sample size (typically considered n > 30), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

In this case, we can assume that the sampling distribution of the sample mean is approximately normally distributed.

To calculate the probability, we need to standardize the sample mean using the z-score formula:

z = (x - μ) / (σ / sqrt(n))

where x is the given value (15.8 oz), μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values:

z = (15.8 - 16) / (1.25 / sqrt(40))

z = -0.2 / (1.25 / 6.3246)

z = -0.2 / 0.1988

z ≈ -1.006

Now, we need to find the probability that the standardized sample mean is greater than -1.006. Since we want the probability of the sample mean being greater than 15.8 oz, we need to find the area under the normal curve to the right of z = -1.006.

Using a standard normal distribution table or a calculator, we can find that the corresponding probability is approximately 0.8438.

Therefore, the probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.

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Answer:

tan pi/6 is tan 30

Step-by-step explanation:

tan 30 is a special degree in trigonometric ratios which makes it easy to solve

tan 30=1√3 .this is the same as √3/3(B)

They are similar because AB is four more than ED, AC is three more than DF, and BC is three more than EF.

To determine if two triangles are similar, we need to compare the ratios of the corresponding sides.

In this case, the given information allows us to compare the lengths of the corresponding sides of triangle ABC and triangle DEF.

We have:

AB = 16 and ED = 12 (AB is four more than ED)

AC = 12 and DF = 9 (AC is three more than DF)

BC = 1 and EF = 9 (BC is three more than EF)

The corresponding sides are proportional because the ratios of the lengths are consistent:

AB/ED = 16/12 = 4/3

AC/DF = 12/9 = 4/3

BC/EF = 1/9

Since the ratios of the corresponding sides are the same, we can conclude that triangle ABC and triangle DEF are similar

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Answer:B,C

hope it helps

Answer:  d. Y=2

Step-by-step explanation:

1 2/3 yards is equal to 5 1/3 feet.

To convert from yards to feet, we know that 1 yard is equal to 3 feet. Therefore, we can calculate:

1 2/3 yards = (1 + 2/3) yards = (3/3 + 2/3) yards = 5/3 yards

Now, to convert yards to feet, we multiply by 3:

5/3 yards * 3 feet/1 yard = 15/3 feet = 5 feet

Therefore, 1 2/3 yards is equal to 5 1/3 feet.

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Yes, the mass of the Earth is much larger than the mass of an atom of hydrogen.

A hydrogen atom weighs around 1.67 x 10⁻²⁷ kilograms (kg) in mass. The mass of a hydrogen atom is approximately 1051 times smaller than that of the Earth, which has a mass of about 5.97 x 10²⁴ kg.

The majority of the mass of the Earth is made up of the following elements: iron, oxygen, silicon, magnesium, Sulphur, nickel, calcium, and aluminium. Despite its minor presence, hydrogen does not significantly contribute to the mass of the Earth.

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Hello !

   D

   I\
   I  \  
   I    \
   I      \    7cm
   I        \
   I          \
   I            \

 E    4cm     F  

The ratio = hypotenuse ; opposite

⇒ calculate sin(D)

sin(D) = opposite/hypotenuse = 4/7

arcsin(4/7) ≈ 34,84.. ≈ 35°

The angle D measures 35°.

The area of the square A is 19.98 square feet

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

Two squares constructed on the sides of a rectangle.

Let the side lengths of square C be x

Let the side lengths of rectangle B be x and y

So, we have

x² = 5

xy = 10

Solving for x and y, we have

x = 2.24 and y = 4.47

The area of square A is

Area = y²

So, we have

Area = 4.47²

Evaluate

Area = 19.98

Hence, the area of the square A is 19.98 square feet

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Answer:

[tex]\sf m = -2\\\\y-intercept =\dfrac{-5}{4}[/tex]

Step-by-step explanation:

Slope and y-intercept of the line:

     Write the equation in slope y-intercept form: y =mx +c

Here, m is the slope and c is the y-intercpet.

To isolate y, add 8x to both side,

            -8x - 4y = 5

                   -4y  = 8x + 5

Now, divide the entire equation by (-4),

                        [tex]\sf \dfrac{-4y}{-4}=\dfrac{8x}{-4} + \dfrac{5}{-4}\\\\\\y = -2x -\dfrac{5}{4}[/tex]

Now, compare with y = mx +c

          [tex]\boxed{\sf m= -2}\\\\\\\boxed{\sf y-intercept=\dfrac{-5}{4}}[/tex]

Answer:

y-intercept = -5/4

slope = -2

Step-by-step explanation:

To quickly find the slope and y-intercept of a given linear equation, we can express it in the following form, called the slope-intercept form:

[tex]\boxed{y = mx + c}[/tex],

where:

m ⇒ slope

c ⇒ y-intercept

In order to take the given equation into the slope-intercept form, we have to  make y the subject of the equation:

[tex]-8x - 4y = 5[/tex]

⇒ [tex]-4y = 8x + 5[/tex]                 [Adding 8x to both sides of the equation]

⇒ [tex]y = -\frac{1}{4}(8x + 5)[/tex]              [Dividing both sides of the equation by -4]

⇒ [tex]y = -2 x - \frac{5}{4}[/tex]

Comparing the above equation with the slope-intercept form, we can see that m = -2 and c = -5/4.

Therefore, y-intercept = -5/4, and slope = -2.

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The value of the missing probability for the given probabilities and condition of independent events is equal to 0.45.

Here,

Probability of the events A and B are,

P(A) = 7/10

P(A or B) = 167/200

Apply the formula for the probability of the union of two events,

P(A or B) = P(A) + P(B) - P(A and B)

Since events A and B are independent, we know that,

P(A and B) = P(A) x P(B)

This implies,

P(A or B) = P(A) + P(B) - P(A) x P(B)

Substitute the values we have,

⇒ 167/200 = 7/10 + P(B) - (7/10) x P(B)

⇒ 167/200 = [ 7 + 10P(B) - 7P(B) ] /10

⇒167/20 = 7 + 3P(B)

⇒3P(B) = 167/20 - 7

⇒ 3P(B) = (167 - 140)/20

⇒3P(B) = 27 /20

⇒P(B) = 9/20

⇒P(B) = 0.45

Therefore, the value of the probability P(B) is equal to 0.45.

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complete question:

Events [A] and [B] are independent. Find the missing probability.

P(B) = ?

P(A) =

7/10

P(A or B)

167/200

The result of adding these numbers is 14.

To add the vectors 10, -3, and 7, we simply sum their corresponding components.

In mathematics, vectors typically represent quantities that have both magnitude and direction. They are usually denoted by an arrow or boldface letters. However, in your question, the numbers provided (10, -3, and 7) are not explicitly described as vectors. They are just numerical values.

To add these numbers together, you can simply perform the arithmetic operation of addition:

10 - 3 + 7 = 14

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Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of shapes, this shape can be separated into 2 basic shapes, triangle and rectangle.

The calculated value of x in the circle is 7

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

The circle

From the circle, we have

Center = H

Also, we have

LIne GH bisects the chord FD

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

DG = FG

So, we have

5x + 2 = 7x - 12

This gives

2x = 14

So, we have

x = 7

Hence, the value of x is 7

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Sure. Here are the steps on how to solve the equation 3|x + 1| ≥-6:

Divide both sides of the equation by 3.

Simplify both sides of the equation.

Isolate x on the left-hand side of the equation.

Test each solution in the original equation to make sure it makes the equation true.

Write the solution in interval notation.

Here are the detailed steps:

Divide both sides of the equation by 3:

3|x + 1| ≥-6

|x + 1| ≥ -2

Simplify both sides of the equation:

|x + 1| ≥ -2

x + 1 ≥ -2 or x + 1 ≤ -2

Isolate x on the left-hand side of the equation:

x + 1 ≥ -2

x ≥ -2 - 1

x ≥ -3

x + 1 ≤ -2

x ≤ -2 - 1

x ≤ -3

Test each solution in the original equation to make sure it makes the equation true.

Test x = -3 in the original equation:

3|-3 + 1| ≥-6

3|-2| ≥-6

3(2) ≥-6

6 ≥-6

True

Test x = -4 in the original equation:

Answer:

Unknown but formula (Check step by step solution)

Step-by-step explanation:

Without the image of the base of the crayon, I cannot determine the exact dimensions of the triangular prism or calculate the volume of a single crayon. However, I can give you a general formula for calculating the volume of a triangular prism and use it to find the total volume of wax needed to make a box of 8 crayons.

The formula for the volume of a triangular prism is:

Volume = (1/2) x base x height x length

where base is the area of the base of the triangular prism, height is the height of the triangular prism, and length is the length of the triangular prism.

Assuming all the crayons in the box have the same dimensions, let's say the base of the triangular prism has a length of L and a width of W. We can calculate the area of the base of one crayon as:

Base area = (1/2) x L x W

Since the crayon is 90 millimeters long, its height is 90 millimeters. Therefore, the volume of one crayon is:

Volume of one crayon = (1/2) x L x W x 90

To find the total volume of wax used to make a box of 8 crayons, we can multiply the volume of one crayon by the number of crayons:

Total volume of wax = Volume of one crayon x 8

Total volume of wax = (1/2) x L x W x 90 x 8

Total volume of wax = 360 x L x W

Again, without knowing the exact dimensions of the triangular prism, I cannot calculate the total volume of wax used to make a box of 8 crayons. But you can use the formula above and substitute the values of L and W based on the dimensions of the base of the crayon to find the answer.

The horizontally compressed function is [tex]\(\text{g(x)} = x^2 + 6\)[/tex]. The correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].

To horizontally compress the function [tex]f(x) = x^2[/tex], we can modify the equation by introducing a horizontal compression factor. Let's call the compressed function [tex]g(x)[/tex].

The general equation for a horizontally compressed function can be expressed as [tex]g(x) = f(ax)[/tex], where a is the compression factor.

In this case, we want to compress [tex]f(x) = x^2[/tex]. Let's choose a compression factor of [tex]\frac{1}{2}[/tex].

Therefore, the equation for [tex]g(x)[/tex] would be:

[tex]\[ g(x) = f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 \][/tex]

Simplifying this equation, we have:

[tex]\[ g(x) = \frac{x^2}{4} \][/tex]

Hence, the equation of [tex]g(x)[/tex] is:

[tex]\[ \text{g(x)} = \frac{x^2}{4} \][/tex]

So, the correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].

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Hello !

100% - 60% = 40%

=> 40% of police officers have ride-alongs

                                                                      total

number of policier            258          ?           ??

frequency in %                  60%        40%      100%

3.1 Calculate the number of of the police officers have ride-alongs with teenagers who want to join the police force

? = 258 x 40 ÷ 60 = 172

3.2 Calculate the total

?? = 258 + 172 = 430

In total there are 430 police officers.

Have a good day !

The volume of the given hexagonal prism is 212.4 cubic units.

Given that, the hexagonal prism below has a base area of 36 square units and a height of 5.9 units.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, volume = 36×5.9

= 212.4 cubic units

Therefore, the volume of the given hexagonal prism is 212.4 cubic units.

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The length of side j, considering the trigonometric ratios, is given as follows:

j = 7.88.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 21º, we have that:

Hence the length j is obtained as follows:

sin(21º) = j/22

j = 22 x sine of 21 degrees

j = 7.88.

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We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:

Step 1 - Picture a

Step 2 - Picture b

Step 3 - Picture c

Step 4 - Picture c.

Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.

The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.

A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.

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Answer:

Step-by-step explanation:

The family traveled from Camp Carol to Phoenix at an average speed of approximately 84.44 kilometers per hour.

Speed is simply referred to as distance traveled per unit time.

It is expressed mathematically as:

Speed = Distance / time

Given that the family traveled 38 km from Camp Carol to Phoenix in 27 minutes:

Distance traveled = 38 kilometers

Time taken = 27 minutes

First, convert the time from minutes to hours:

Time taken = ( 27 / 60 ) hours

Time taken = 0.45 hour

We can now calculate the average speed using the above formula as follows:

Average speed = Distance / time

Average speed = 38 km / 0.45 h

Average speed = 84.44 km/h

Therefore, the average speed is approximately 84.44 km/h.

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The revenue function for the cakes can be shown as: R(x1, x2, x3, x4, x5) = $9x1 + $12x2 + $4x3 + $5x4 + $8x5

The revenue function is described as  the total amount of money earned from selling a certain quantity of cakes.

We make the following  

Cake 1 sold =  x1

Cake 2 =  x2

Cake 3 = x3,

Cake 4 =  x4,

Cake 5=  x5.

The revenue generated from selling each cake is:

Revenue1 = $9 * x1

Revenue2 = $12 * x2

Revenue3 = $4 * x3

Revenue4 = $5 * x4

Revenue5 = $8 * x5

Total revenue = Revenue1 + Revenue2 + Revenue3 + Revenue4 + Revenue5

Total revenue = $9 * x1 + $12 * x2 + $4 * x3 + $5 * x4 + $8 * x5

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The function that gives the amount of Iodine-131, A, in grams, t days later is A(t) = 5(1/2)^(t/10), and the amount after 20 days is 5/4 grams.

To find the function that gives the amount of Iodine-131, A, in grams, t days later, we can use the given formula A(t) = A0e^(kt).

Given that the half-life of Iodine-131 is approximately 10 days, we know that after each 10-day period, the amount of Iodine-131 will be reduced by half. This information allows us to determine the value of k.

Let's substitute the initial values into the equation:

A(0) = A0 = 5 grams.

We know that after 10 days, the amount is reduced by half. Therefore:

A(10) = 5/2 grams.

Using these two points, we can solve for k:

5/2 = 5e^(10k).

Dividing both sides by 5, we get:

1/2 = e^(10k).

Take the natural logarithm (ln) of both sides:

ln(1/2) = 10k.

Now, solve for k:

k = ln(1/2) / 10.

Now that we have the value of k, we can use it to find the function for the amount of Iodine-131, A, in grams, t days later.

The function is:

A(t) = A0e^(kt).

Substituting the known values:

A(t) = 5e^((ln(1/2)/10)t).

Simplifying:

A(t) = 5(1/2)^(t/10).

To find the amount of Iodine-131 after 20 days, we substitute t = 20 into the equation:

A(20) = 5(1/2)^(20/10).

A(20) = 5(1/2)^2.

A(20) = 5(1/4).

A(20) = 5/4 grams.

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By the complex conjugate root theorem, there must also be another zero -  [tex]5-i[/tex].

Therefore

[tex]f(x)=(x-2)(x-(5+i))(x-(5-i))\\f(x)=(x-2)(x-5-i)(x-5+i)\\f(x)=(x-2)((x-5)^2+1)\\f(x)=(x-2)(x^2-10x+25+1)\\f(x)=(x-2)(x^2-10x+26)\\f(x)=x^3-10x^2+26x-2x^2+20x-52\\f(x)=x^3-12x^2+46x-52[/tex]