1. A basketball player made 8 out of 50 free throws she attempted which is 16%. She wants to know how many consecutive free throws more in a row she would have to make to raise her overall successful baskets divided by attempts or percent of successful free throws to 60%.



(a) Write an equation to represent this situation.



(b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 60%?





1 pt for correct answer to part (b), 4 pts for showing steps you took to get the correct answer and showing the formula with variable x that you used in part (a).



Note: correct answer to part (a) has only one variable, the variable x. Need to set up a ratio and cross multiply to solve for x.



X represents how many more consecutive tries she needs to make in a row



to raise her overall average up to 60%





2.



Simplify the expression 3x-12/x^2-15x+44. Show your work.



(NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors. )





3.



1. Write the expression as a simplified rational expression. Show your work.



14x+4



-----------



2 1



----- + -----



3x 2x+1





Thank you for any help

Answer:

density = 22.35 g/30 cm^3 = .745 g/cm^3

A is the correct answer.

Answer:

0.75

Step-by-step explanation:

The density of a material is defined as its mass per unit volume. In this case, we are given the mass of the wooden prism and its dimensions, so we can calculate its volume and then use the formula for density.

The volume of the rectangular prism is:

V = l x w x h = 3 cm x 2 cm x 5 cm = 30 cm³

where l, w, and h are the length, width, and height of the prism, respectively.

The density of the wooden prism is then:

density = mass / volume

density = 22.35 g / 30 cm³

density = 0.745 g/cm³

Therefore, the density of the wood that the rectangular prism is made of is 0.745 g/cm³.

Answer:

Yes, they are totally correct, I've checked with a calculator

The surface area and volume of the triangular prism are:

S = [tex]204 in^2[/tex]

V = [tex]144 in^3[/tex]

The area= 12 inches

The volume = 144 cubic inches

The area of each triangular face is already calculated (A = 12 square inches). The three rectangular faces have dimensions 5 x 12, 6 x 12, and 4 x 12.

Calculate the area of each rectangular face:

5 * 12 = 60 square inches

6 * 12 = 72 square inches

4 * 12 = 48 square inches

Now, sum the areas of all faces to get the surface area (S):

S = (2 * 12) + 60 + 72 + 48 = 204 square inches.

So, the surface area and volume of the triangular prism are:

S = [tex]204 in^2[/tex]

V = [tex]144 in^3[/tex]

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As per the given geometric sequence, the sum of the greater and lesser consequents is 51.

We are given that the antecedents (which are just the first three terms) of a geometric sequence are 2, 3, and 5. Let's call the common ratio of this sequence r. Using the definition of a geometric sequence, we can write the terms of this sequence as 2, 2r, 2r² (since the first term is 2 and the common ratio is r), 3, 3r, 3r², 5, 5r, 5r².

Next, we are told that the product of the consequents (which are just the terms after the first three) is 810. To find the product of the consequents, we just multiply all the terms after the first three together. So we have:

(2r³) * (3r²) * (5r) = 30r⁶

We know that this product is equal to 810, so we can set up the equation:

30*r⁶ = 810

Solving for r, we get:

r⁶ = 27

r = 3 (since 3⁶ = 729)

Now that we know the common ratio is 3, we can find the terms of the sequence by multiplying each antecedent by 3. So the terms of the sequence are:

2, 6, 18, 3, 9, 27, 5, 15, 45

The greater and lesser consequents are 45 and 6, respectively. So the sum of the greater and lesser consequents is:

45 + 6 = 51

Therefore, the answer to the problem is 51.

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Complete Question:

In a series of equal geometric ratios, the antecedents are 2, 3, and 5. If the product of the consequents is 810, find the sum of the greater and lesser consequents.

To find the median of the data, we first need to arrange the numbers in order from smallest to largest:

3, 14, 624

Since we have an odd number of data points, the median is the middle number. In this case, the median is 14.

Therefore, the median of the data collected is 14 meters.

The height of the cone is approximately 3.4 cm.

The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

We are given that the radius of the cone is 3 cm and the volume is 94.2 cm^3. Substituting these values into the formula, we get:

94.2 = (1/3)π(3^2)h

Simplifying:

94.2 = 9πh

h = 94.2 / (9π)

h ≈ 3.4

Therefore, the height of the cone is approximately 3.4 cm.

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Stem plots (also known as stem-and-leaf plots) have several advantages over frequency distributions, including:

1. Stem plots show individual data points: Unlike frequency distributions, which group data into intervals, stem plots show each individual data point. This makes it easier to see the distribution of the data, including the shape, the range, and any outliers or gaps. Stem plots can also reveal patterns and trends in the data that may not be apparent from a frequency distribution.

2. Stem plots are easy to construct: Constructing a stem plot requires minimal computation and is relatively simple to create by hand. It involves only sorting the data and then splitting each data point into a stem (the leading digits) and a leaf (the trailing digit). This makes stem plots a convenient tool for quick exploratory data analysis, especially when dealing with small to moderate-sized datasets. In contrast, constructing a frequency distribution can be more time-consuming, as it requires choosing appropriate intervals and counting the number of data points in each interval.

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For given equation x = (-b ± √(b²-4ac))/2a the equation in the form c= is: c = -x²(a/b) - x.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.

What is goal of equation?

The goal of solving an equation is to determine the value or values of the variable that make the equation true. Equations are used extensively in mathematics and science to describe relationships between quantities and to solve problems.

Starting with the equation:

x = (-b ± √(b²-4ac))/2a

We can simplify and rearrange it to the form c= as follows:

Multiply both sides by 2a to get rid of the denominator:

2a x = -b ± √(b²-4ac)

Add b to both sides:

2a x + b = ± √(b²-4ac)

Square both sides:

(2a x + b)² = b² - 4ac

Expand the left side:

4a² x² + 4abx + b² = b² - 4ac

Simplify:

4a² x² + 4abx = -4ac

Divide both sides by 4a:

x² + bx/a = -c/a

Rearrange to the form c=:

c = -x²(a/b) - x

Therefore, the equation in the form c= is:

c = -x²(a/b) - x

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Using the combine clues method:

[tex]R_1=7\\\\R_2=9\\\\R_3=8\\\\S_1=2\\\\S_2=4\\\\S_3=5\\\\T_1=10\\\\T_2=14[/tex]

Certain items that must be worn, used, or accessed in order to access particular clues. The maximum skill level needed to solve each master clue is shown.

Clue 1: [tex]R_1 + R_2 + R_3 = 24[/tex]

Clue 2: [tex]R_1 + R_2 =16[/tex]

Since, [tex]R_1 + R_2 + R_3 = 24[/tex] (from clue 1)

[tex]R_1 + R_2 + R_3 = 24\\\\16 + R_3 = 24[/tex]

Subtract both the sides by 16,

[tex]R_3=8[/tex]

Clue 3:

We need to find the blank [tex]R_1 +[/tex] __ [tex]+S_2=20[/tex] and [tex]S_2=4[/tex]

Since, [tex]R_1 + R_2 = 16[/tex] (from clue 2)

So,

[tex]R_1 + R_2 + S_2 = 20\\\\16 + S_2 = 20[/tex]

Subtract 16 from both sides.

[tex]16 + S_2 - 16 = 20 -16\\\\S_2 = 4[/tex]

So,

[tex]R_1 + R_2 + S_2 = 20[/tex]

Clue 4:

We need to find the blank [tex]R_2[/tex] = __

[tex]S_2 + R_2 = 13[/tex]

Since, [tex]S_2 = 4[/tex]

[tex]S_2 + R_2 = 13\\\\4 + R_2 = 13[/tex]

Subtract 4 from both sides.

[tex]R_2 = 9[/tex]

So, [tex]R_2 = 9[/tex]

Clue 5:

We need to find the blank ___ [tex]+ T_2 = 22[/tex] and [tex]T_2=[/tex] ___

[tex]R_3 + T_2 = 22[/tex]

Since, [tex]R_3 =8[/tex] (from the Clue 2)

[tex]R_3 + T_2 = 22[/tex]

[tex]8 + T_2 = 22[/tex]

Subtract both the sides by 8,

[tex]T_2 = 14[/tex]

So, [tex]R_3 + T_2 = 22[/tex]

Clue 6:

We need to find the blank [tex]T_1 +[/tex] ___ = 24 and ___ = 10

Since, [tex]T_1 + T_2 = 24[/tex] (from the Clue 5)

[tex]T_1 + 14 = 24[/tex]

Subtract both the sides by 14,

[tex]T_1 = 10[/tex]

Clue 7:

We need to find the value of [tex]S_1[/tex],

Given [tex]T_1 + R_3 + S_1 =20[/tex]

Since, [tex]T_1=10[/tex] and [tex]R_3=8[/tex]

[tex]10+ 8 + S_1 = 20\\\\18 + S_1 = 20[/tex]

Subtract both the sides by 18,

so, [tex]S_1=2[/tex]

Combining this with what we learned from Clue 2 and Clue 6, we know

[tex]S_1=2[/tex]

Now, we need to find the blank, [tex]S_1 + S_2 +[/tex] ___ = 11

Combining this with what we learned from Clue 3 and Clue 7, we know:

___ = 5

[tex]S_1 + S_2 + S_3 = 11\\\\2 + 4 + S_3 = 11\\\\6 + S_3 = 11[/tex]

Subtract both the sides by 6,

[tex]S_3 = 5[/tex]

For [tex]R_1[/tex]

Since,

[tex]R_1 + R_2 + R_3 = 24\\\\R_1 + 9 + 8 = 24\\\\R_1 + 17 = 24[/tex]

Subtract both the sides by 17,

[tex]R_1 = 17[/tex]

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Answer: 5 1/4

Step-by-step explanation: 3/4 times 7/1 equals 5.25

Turn the decimal to a fraction and get 5 1/4

Using boosting with 1,000 trees on the Hitters data set, after removing observations with unknown salary information and log-transforming salaries, results in a test set MSE (Mean Squared Error) value.


1. Remove observations with unknown salary information from the Hitters data set.
2. Log-transform the remaining salaries.
3. Create a training set with the first 200 observations and a test set with the remaining observations.
4. Apply the boosting algorithm on the training set, using 1,000 trees as the parameter.
5. Evaluate the performance of the boosting model on the test set by calculating the Mean Squared Error (MSE). The test set MSE will give you an indication of the model's accuracy in predicting salary based on the provided data.

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answer:

Step-by-step explanation:

first you want to multiply them together then divide it by 2 it's bh/2

Answer: Therefore, the team was producing 10 parts per hour prior to switching to the new technology.

Step-by-step explanation:Let's denote the number of parts produced per hour before the technology upgrade by x.

After the upgrade, the team produces 6 more parts per hour than before, so their new production rate is x + 6 parts per hour.

In 8 hours, the team produces 8x parts in total.

In 6 hours with the new technology, the team produces 120% of what they previously produced in 8 hours, or 1.2(8x) = 9.6x parts in total.

We can set up an equation based on the information above:

6(x + 6) = 9.6x

Simplifying the equation:

6x + 36 = 9.6x

Subtracting 6x from both sides:

36 = 3.6x

Dividing both sides by 3.6:

x = 10

Answer:

Step-by-step explanation:

To understand the relationship between -41/2 and its opposite position in relation to zero on a number line, let's first plot them on the number line.

We start by marking the position of zero at the center of the number line, and then we can represent -41/2 and its opposite position by moving to the left and right of zero respectively.

When we move 41/2 units to the left of zero on the number line, we reach the point -41/2. This means that -41/2 is located to the left of zero on the number line.

On the other hand, the opposite position of -41/2 is obtained by moving the same distance (41/2 units) to the right of zero. This position is represented by the point 41/2 on the number line.

Therefore, we can see that -41/2 and its opposite position (41/2) are equidistant from zero on the number line, with zero located exactly halfway between them. In other words, -41/2 and 41/2 are located at equal distances from zero but in opposite directions. This relationship is often referred to as the symmetry property of the number line.

If left to leak at this rate indefinitely, the tank will not empty all of its contents as a result of this crack, as it would take approximately 853.33 days for the tank to reach zero capacity

To determine whether the tank will empty all of its contents as a result of the crack,

we need to find out how long it will take for the tank to reach zero capacity.

Using the given model, the rate at which the contents spill out over time is 200 - 0.075t,

where t is the number of days since the leak began on October 10th, 2021.

We can set up an equation to find out when the tank will reach zero capacity:

5000 - (200 - 0.075t) = 0

Simplifying this equation, we get:

0.075t = 4800

t = 64000/75

t = 853.33

Therefore, if left to leak at this rate indefinitely, the tank will not empty all of its contents as a result of this crack, as it would take approximately 853.33 days for the tank to reach zero capacity.

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question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.

Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.

Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!

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Answer:

w

Step-by-step explanation:

w

The average x-coordinate of the points in the prism is 3.

A prism is a polyhedron that has two parallel and congruent polygonal bases that are linked by parallelogram faces that are lateral. The height of the prism is the perpendicular distance between the bases.

The formula for calculating the average x-coordinate of the points in the prism D = {(x,y,z):0 ≤ x ≤ 6,0 ≤ y ≤ 18-3x, 0 ≤ z ≤ 4} is$$\frac{\text{sum of all x-coordinates}}{\text{number of vertices}}$$

The vertices of a prism are the points where two adjacent edges meet. There are eight vertices in a rectangular prism, and the x-coordinate of each vertex is either 0 or 6. The x-coordinates of the vertices are $$0,0,0,0,6,6,6,6.

$$The sum of all the x-coordinates is 24. Thus, the average x-coordinate of the points in the prism is$$\frac{24}{8}=\boxed{3}.

$$Hence, the average x-coordinate of the points in the prism is 3.

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The translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B.   shift of 2 units left and then shift of 1 unit up.

In geometry, a translation is a transfer that occurs either horizontally to a left or right as well as vertically up or down. It may also consist of a mix of the two.

Given data:

Parent function- y = x²

New function -  y = (x - 2)² +1

Thus, the translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B.   shift of 2 units left and then shift of 1 unit up.

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Complete question:

1. Which of the following most accurately describes the translation of the graph from y = x² to y = (x - 2)² +1?

A.  shift of 2 units right and then shift of 1 unit up.

B.   shift of 2 units left and then shift of 1 unit up.

The most reasonable estimate for the number of Auto Wheel Magazine subscribers who own fewer than 2 vehicles is 102.

To estimate the number of Auto Wheel Magazine subscribers who own fewer than 2 vehicles, we can use the proportion of subscribers in the sample who reported owning fewer than 2 vehicles. We can assume that this proportion is representative of the proportion of all subscribers who own fewer than 2 vehicles.

The proportion of subscribers in the sample who own fewer than 2 vehicles is:

15/50 = 0.3

This means that 30% of the sample subscribers own fewer than 2 vehicles. To estimate the number of all subscribers who own fewer than 2 vehicles, we can multiply this proportion by the total number of subscribers:

0.3 x 340 = 102

Hence, the most reasonable estimate = 102.

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If Tamekia and Marsha work for 22 hours, Marsha will earn $27.50 more than Tamekia.

To determine the amount of money each person can earn, we need to know the hourly rate and the number of hours worked. Tamekia estimates that she can earn between $6.00 and $6.25 per hour. Let's assume that she can earn $6.25 per hour. If Tamekia works for 22 hours, her total earnings will be:

Total earnings for Tamekia = Hourly rate x Number of hours worked = $6.25 x 22 = $137.50

Now let's look at Marsha's earnings. Marsha estimates that she can earn between $7.50 and $8.00 per hour. Let's assume that she can earn $7.50 per hour. If Marsha works for 22 hours, her total earnings will be:

Total earnings for Marsha = Hourly rate x Number of hours worked = $7.50 x 22 = $165.00

To determine how much more money Marsha will earn than Tamekia, we need to subtract Tamekia's total earnings from Marsha's total earnings:

Difference in earnings = Total earnings for Marsha - Total earnings for Tamekia = $165.00 - $137.50 = $27.50

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The ages of the​ teacher's three children whose product is 72 will be 3,3,8.

Let the age of three children be x, y, z

x × y × z = 72

x + y + z = No. of rooms

Now possible answers can be three numbers whose product is 72

There are two possible answers in which the product of the number is 72 and the sum of the number is also same

1) 2 × 6 × 6 = 72  and 2 + 6 + 6 = 14

2) 3 × 3 × 8 = 72  and 3 + 3 + 8 = 14

Now teacher gave a hint that his oldest child is good at math

Oldest means one of the three child is oldest so the only possible answer could be 3,3,8

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1. The growth factor for the number of customers over a year is approximately 1.4266.

2. the growth factor in customers over a decade period is approximately 5.927.

Factors that affect how many consumers there are in a year are

c(12)/c(0) = (400 x (1.03)¹²) / (400 x (1.03)⁰)

= (1.03)¹²

= 1.4266....

Therefore, the growth factor for the number of customers over a year is approximately 1.4266.

2. To write an equation for the number of customers c as a function of the number of years y, we can substitute m = 12y into the original equation

[tex]c(y) = 400 x (1.03)^{12y}[/tex]

one decade = 10 years

= 120 months

We must calculate the value of the equation at m=120 and divide it by the equation's value at m=0.

c(120) / c(0) = [400 x (1.03)¹²⁰] / [400 x (1.03)⁰]

= (1.03)¹²⁰

= 5.927...

Therefore, the growth factor in customers over a ten-year period is approximately 5.927.

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Given Question is incomplete, complete question is given below:

A small printing company launched an online ordering system to expand its business. The equation [tex]c=400(1. 03)^m[/tex] represents the number of customers c it has in terms of the number of months m since it launched the ordering system.

1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value

2. If y is time in years, write an equation for the number of customers c as a function of the number of years y after the introduction of the ordering system. If this model continues to apply for a decade, by what factor will the number of customers grow in one decade?

The radius of the circle is 2mm

It is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.

The equation is written as;

C = 2πr

Such that the parameters are;

From the information given, we have thatt;

The radius of the circle = r

The circumference = 12.56mm

Substitute the values, we have;

12. 56 = 2×3.14r

Multiply the values

r = 12. 56/6. 28

divide the values

r = 2mm

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Answer:well i don't know what you're asking for but i got this

Blouses, she earned $26

Skirts, she earned $33

Pants, she earned $175

So basically she s c a m m i n g but she still got that bank she made though

Step-by-step explanation:

25x2=50; 38x2=76; 76-50=26

15x3=45; 26x3=78; 78-45=33

30x5=150; 65x5=325; 325-150=175

A restaurant meal cost $90 and there was a 6% meals tax on the price of the meal. The meal tax was $5.40 and the total price of the meal with the meal tax was $95.40.

Find the meal tax, you need to calculate 6% of the $90 meal cost.
Convert the percentage to a decimal by dividing by 100, so 6% = 0.06.
Multiply the meal cost by the decimal. In this case, $90 × 0.06 = $5.40.
So, the meal tax was $5.40.
Find the total price of the meal with the meal tax, you need to add the meal tax to the original cost of the meal.
Add the meal tax to the original cost, so $90 + $5.40 = $95.40.
The total price of the meal with the meal tax was $95.40.

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Answer:

Angle 1 is 77

Angle 2 is 103

Angle 4 is 103

Step-by-step explanation:

Angles that are vertical to each other like 2 and 4, 1 and 3

will always equal each other

since 3 is = to 77, 1 is also = to 77

You can also find the angles by thinking of supplementary angles (180 degrees) Straight angle basically

You see that 3 is 77 and 4 is part of the straight line so it needs to equal 180

so 180-77 it will equal 103.

Hope this helps