HELP! During the period 1998–2002, the number y (in millions) of juvenile books shipped to bookstores can be modeled by the equation y = -15x^2 + 64x + 360 where x is the number of years since 1998. During what year were there 400 million juvenile books shipped to bookstores?

Answer: option c.

Step-by-step explanation:

 To solve the given exercise and write the expression as a single logarithm, you must keep on mind the following properties:

[tex]m*log(a)=log(a)^m[/tex]

[tex]log(a)-log(b)=log(\frac{a}{b})[/tex]

Therefore, by applying the properties shown above, you can rewrite the expression given, as following:

[tex]2logx-6log(x-9)=logx^2-log(x-9)^6=log(\frac{x^2}{(x-9)^6})[/tex]

Then as you can see, the answer is the option c.

Answer:

Probability of drawing a black card =  [tex]\frac{3}{10}[/tex] or 0.3 .

Step-by-step explanation:

Given : You draw a card at random from a deck that contains 3 black cards and 7 red cards.

To find : What is the probability of drawing a black card.

Solution : We have given that

Deck that contains  black cards  = 3.

Red cards = 7.

Total card = 10.

Probability of drawing a black card = [tex]\frac{3}{10}[/tex].

Probability of drawing a black card = 0.3.

Therefore,  Probability of drawing a black card =  [tex]\frac{3}{10}[/tex] or 0.3 .

Answer:

Probability of drawing a black card =   or 0.3 .

Step-by-step explanation:

Given: You draw a card at random from a deck that contains 3 black cards and 7 red cards.

To find: What is the probability of drawing a black card.

Solution: We have given that

A deck that contains  black cards  = 3.

Red cards = 7.

Total card = 10.

Probability of drawing a black card = .

Probability of drawing a black card = 0.3.

Therefore,  Probability of drawing a black card =   or 0.3 .

The system has two solutions: [tex]\( (2, -2) \) and \( (-1, 4) \),[/tex] found by solving their simultaneous equations.

let's solve the system step by step:

Given the system of equations:

[tex]1. \( y = -2x + 2 \)\\2. \( y = x^2 - 3x \)[/tex]

We want to find the values of [tex]\( x \) and \( y \)[/tex] that satisfy both equations simultaneously.

First, we set the equations equal to each other since they both equal [tex]\( y \):[/tex]

[tex]\[ -2x + 2 = x^2 - 3x \][/tex]

Now, let's rearrange this equation to get a quadratic equation:

[tex]\[ x^2 - 3x + 2x - 2 = 0 \]\[ x^2 - x - 2 = 0 \][/tex]

Now, we can use the quadratic formula to solve for [tex]\( x \):[/tex]

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

where [tex]\( a = 1 \), \( b = -1 \), and \( c = -2 \).[/tex]

[tex]\[ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}} \]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \]\[ x = \frac{{1 \pm 3}}{2} \][/tex]

So, we have two potential values for [tex]\( x \): \( x = 2 \) and \( x = -1 \).[/tex]

Now, let's find the corresponding [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex] value using either of the original equations:

For [tex]\( x = 2 \):[/tex]

[tex]\[ y = -2(2) + 2 = -4 + 2 = -2 \][/tex]

For [tex]\( x = -1 \):[/tex]

[tex]\[ y = -2(-1) + 2 = 2 + 2 = 4 \][/tex]

So, we have two solutions for the system:[tex]\( (2, -2) \) and \( (-1, 4) \).[/tex] Therefore, the system has 2 solutions.

731934030

7.31934039*10^8

Answer:

731,934,030

Step-by-step explanation:

Answer: x=12

Explanation:

In a parallelogram, adjacent angles equals 180 (consecutive angles). Therefore, (132-x)+(6x-12)=180

Simplify:

-x+6x+132-12=180

5x+120=180

5x=60

x=12

Answer:

(2,0) is not a solution of the system. The point does not belong to any of the graphs.

Step-by-step explanation:

To easily solve this question, we can graph both equations in a graphing calculator, and verify the intersection point, which is equal to the solution of the system of equations.

Plotting the graphs

y = 3x + 2

g = |x-1| +1

We obtain the intersection point

(0,2)

Solution of the system of equations

The transformed parallelogram P'Q'R'S' is smaller than the original parallelogram PQRS, due to a scale factor of less than 1 (0.75) being applied in this dilation.

The given transformation (x, y) → (0.75x, 0.75y), the scale factor is 0.75, indicating a reduction in size. This means that the transformed parallelogram P'Q'R'S' is smaller than the original PQRS. The scale factor of 0.75 signifies that both the x and y coordinates of every point in the original parallelogram are multiplied by 0.75, leading to a proportional reduction in dimensions. Therefore, option B) stating that Parallelogram P'Q'R'S' is smaller than parallelogram PQRS due to the scale factor being less than 1, accurately describes the transformation, illustrating the diminished size of the transformed figure in comparison to the original one.

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The correct answer is B: Parallelogram P'Q'R'S' is smaller than parallelogram PQRS because the dilation scale factor is 0.75, which is less than 1.

The question asks about the effect of a given dilation on a geometric figure, specifically a parallelogram named PQRS, which is transformed into parallelogram P'Q'R'S'.

This transformation is performed using the dilation rule (x, y) → (0.75x, 0.75y), which indicates that every point on the original parallelogram is multiplied by the scale factor of 0.75 when creating the new parallelogram.

Since the scale factor is less than 1, each coordinate is reduced to 75% of its original value, resulting in a figure that is proportionally smaller than the original.

Therefore, the correct statement about the relationship between the original parallelogram PQRS and the dilated parallelogram P'Q'R'S' is Option B: Parallelogram P'Q'R'S' is smaller than parallelogram PQRS, because the scale factor is less than 1.

After calculating the perimeters, both the square and the rectangle have the same perimeter of 32 inches when the square has each side measuring 8 inches and the rectangle has dimensions of 6 inches by 10 inches.

To determine which shape has the greater perimeter, calculate the perimeter of both the square and the rectangle. The formula for the perimeter of a square is 4 × side length, and the formula for the perimeter of a rectangle is 2 × (length + width).

For the square with each side measuring 8 inches, its perimeter is 4 × 8 = 32 inches.

For the rectangle with a width of 6 inches and a length of 10 inches, its perimeter is 2 × (10 + 6) = 2 × 16 = 32 inches.

Therefore, both the square and the rectangle have the same perimeter of 32 inches.

Answer:

5.92

Step-by-step explanation:

-71/-12=5.92

Answer:

[tex]\frac{71}{12}[/tex]

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact Form :

[tex]\frac{71}{12}[/tex]

Decimal Form :

  5.916

Mixed Number Form :

5[tex]\frac{11}{12}[/tex]

Hope this helps,

Davinia.

First we need to find the length. So we do 126/3 to get 42. The length is 42. Now to find perimeter we do 2(42)+2(3) or 42+42+3+3.

Both ways are right ways. The perimeter is 90 meters.

Hope that helps!!

To find the perimeter of a rectangular flowerbed, divide the area by the width to find the length. Then, use the formula Perimeter = 2(length + width) to calculate the perimeter.

To find the perimeter of a rectangular flowerbed, we need to add up the lengths of all its sides. In this case, we're given that the width of the flowerbed is 3 meters, but we need to find the length. We can find the length by dividing the area of the flowerbed by its width.

Area = length × width

126 = length × 3

length = 126/3

length = 42 meters

Now that we know the length and the width, we can calculate the perimeter.

Perimeter = 2(length + width)

Perimeter = 2(42 + 3)

Perimeter = 2(45)

Perimeter = 90 meters

Answer:

Area_lawn = 393.75 π ft^2

Step-by-step explanation:

Maximum radius : 30 feet

Minimum radius:  30 feet - 0.25*(30feet)  =  22.5 feet

(25 percent reduction)

To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.

Since the sprinklers have a circular area:

Area = π*radius^2

Max area  = π*(30 ft)^2 = 900π ft^2

Min area  = π*(22.5 ft)^2 = 506.25π ft^2

Maximum area of lawn that can be watered by the sprinkler:

Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2

Area_lawn = 393.75 π ft^2

Answer:

1,590.4 sq ft

Step-by-step explanation:

Answer:

The surface area is [tex]2,440\ m^{2}[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The surface area of a triangular prism is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular face

H is the height of the prism

Find the area of the base B

[tex]B=\frac{1}{2}(42)(20)=420\ m^{2}[/tex]

Find the perimeter of the base P

[tex]P=(42+29+29)=100\ m[/tex]

we have

[tex]H=16\ m[/tex]

substitute the values

The surface area is

[tex]SA=2(420)+100(16)=2,440\ m^{2}[/tex]

Dividing 4x by 4 isolates x on one side of the equation

I think it's B, because the grah becomes greater and greater by every point. It starts from - infinite and it keeps going up to + infinite.

The graph tells us the following about the value of c in this function: D. c is less than zero.

In Mathematics and Euclidean Geometry, a radical function or nth root function can be represented by using the following mathematical equation:

[tex]f(x)=a(x+k)^{\frac{1}{n} }+c[/tex]

where:

By critically observing the graph shown above, we can logically deduce that the graph represents a nth root function and the value of c does not equal zero because it isn't symmetrical about the x-axis.

Since the parent nth root function was vertically shifted down and horizontally to the left, it implies that the value of c must be negative and less than zero.

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Answer:

=55m

Ahh. Correct me if I'm wrong.

Answer:

The state with the second lowest population has the lowest population density.

Step-by-step explanation:

The state with the second lowest population has the lowest population density.

State B has the second lowest population, and it has the lowest population distance considering it has a substantial amount of area compared to other states, yet 1, 333, 089 people, in comparison it therefore as the lowest population density.

The statement "The state with the second-lowest population has the lowest population density." is true.

The population density can be found by dividing the total population of an area by the area.

We must calculate the population densities of all the states to determine which state has the highest density.

This can be done as shown below:

State A:

Population density = Population/Area

= 1,055,173/2,677

= 394.162

State B:

Population density = Population/Area

= 1,333,089/36,418

= 36.605

State C:

Population density = Population/Area

= 3,596,677/5,543

= 648.87

State D:

Population density = Population/Area

= 6,745,408/10,555

= 639.072

We can see that the state with the second-lowest population has the lowest population density.

Therefore, we have found that the statement "The state with the second-lowest population has the lowest population density." is true. The correct answer is option B.

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Solving systems of equations by elimination involves creating a new equation where one variable cancels out when the equations are added or subtracted. This often means multiplying one or both of the original equations by a certain number. Once one variable is found, it can be substituted back into an original equation to solve for the remaining variable.

To solve the system of equations by the elimination method, you need to create an equation where one of the variables cancels out when you add or subtract the two equations. This is often done by multiplying one or both of the equations by a number.

For example, for the system of equations given by Equation A: 3x + 4y = 52 and Equation B: 5x + y = 30, you would multiply Equation B by 4 to get 20x + 4y = 120. If you subtract Equation A from this new equation, you eliminate y, with the result being 17x = 68, or x = 4. You can then substitute x = 4 into either original equation to solve for y.

The other options in the question follow the same basic procedure, with the aim being to cancel out one variable in order to solve for the other, and then substituting back in to find the value of the remaining variable.

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The correct first steps for applying the elimination method involve multiplying the equations to facilitate the elimination of one variable. Specific correct steps include multiplying Equation B by -4, Equation B by 2, and Equation A by -3 in their respective systems.

To solve the system of equations using the elimination method, we need to manipulate the equations so that adding or subtracting them eliminates one of the variables. Let's examine the potential steps for different systems provided:

For equations A (3x + 4y = 52) and B (5x + y = 30), multiplying Equation B by -4 provides: -4(5x + y) = -4(30) => -20x - 4y = -120.

For equations A (-2x + 3y = -1) and B (x + 5y = 25), multiplying Equation B by 2 gives: 2(x + 5y) = 2(25) => 2x + 10y = 50.

For equations A (2x + y = 2) and B (-3x + 3y = 10), there is no need to multiply, as elimination isn't straightforward here.

For equations A (4x + y = 3) and B (6x + 3y = 9), multiplying Equation A by -3 yields: -3(4x + y) = -3(3) => -12x - 3y = -9.

Therefore, the correct first steps for applying the elimination method are:

Multiply Equation B by -4 for the first system.

Multiply Equation B by 2 for the second system.

Multiply Equation A by -3 for the fourth system.

Answer:

a) 68%; b) 99.5%

Step-by-step explanation:

The empirical rule states that 68% of data falls within 1 standard deviation of the mean; 95% of data falls within 2 standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.

For part a,

We are asked the approximate percentage of women whose platelet counts are within 1 standard deviation of the mean.  According to the empirical rule, this is 68%.

For part b,

We are given the endpoints of the interval.  The lower endpoint is 181.5; this is 250.8-181.5 = 138.6 away from the mean.  Dividing by the standard deviation, 69.3, we have

138.6/69.3 = 2

This is 2 standard deviations away from the mean.

The higher endpoint is 320.1; this is 320.1-181.5 = 138.6 away from the mean.  Dividing by the standard deviation, 69.3, we have

138.6/69.3 = 2

This is standard deviations away from the mean.

This means this interval includes about 95% of women.

Final answer:

Using the empirical rule, approximately 68% of women have platelet counts within 1 standard deviation of the mean (181.5 to 320.1), and approximately 95% have counts within 2 standard deviations of the mean (112.2 to 389.4).

Explanation:

The question asks to apply the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:

Approximately 68% of the data falls within 1 standard deviation of the mean.

Approximately 95% of the data falls within 2 standard deviations of the mean.

Approximately 99.7% of the data falls within 3 standard deviations of the mean.

We have a mean (μ) of 250.8 and a standard deviation (σ) of 69.3 for the blood platelet counts.

Part (a)

Within 1 standard deviation of the mean (181.5 to 320.1):

Approximately 68% of the women fall in this range.

Part (b)

Within 2 standard deviations of the mean (112.2 to 389.4):

Approximately 95% of the women fall in this range.

Answer:

[tex]a_n=-12-4(n-1)[/tex]

Step-by-step explanation:

The given sequence is

-12,-16,-20...

The first term of this sequence is [tex]a_1=-12[/tex].

The common difference is

[tex]d=-16--12[/tex]

[tex]d=-16+12=-4[/tex]

The nth term of this arithmetic sequence is;

[tex]a_n=a_1+d(n-1)[/tex]

We substitute the values for the first term and the common difference to obtain;

[tex]a_n=-12-4(n-1)[/tex]

Answer:

[tex]a_{n} = -12-4(n-1)[/tex]

Step-by-step explanation:

We have given a arithmetic sequence.

-12,-16,-20,...

We have to find formula for a given sequence.

The general formula for nth term of sequence is :

[tex]a_{n} = a_{1}+d(n-1)[/tex]

In given sequence,

[tex]a_{1} = -12[/tex]

d is the common difference between consecutive terms.

d = -16-(-12)  = -16+12

d = -4

Putting given values in formula, we have

[tex]a_{n} = -12-4(n-1)[/tex] which is the answer.

Answer:

  b.  6 cm

Step-by-step explanation:

Q is the midpoint of PR, so QR = PR/2 = (12 cm)/2 = 6 cm

Answer:

Picture 1 is the answer.

Step-by-step explanation:

The expression states that the absolute value of a number x , is equal to the number 7. Absolute Values have an 2 inputs for every output (except for 0), the negative and positive inputs both output the same positive number.

Example: abs(-5) = abs(5) = 5

The Absolute value of -5 and 5 both output 5. Therefore, there are two possible x values for the answer to be 7 and those values are -7 and 7. Since these are the only possible values they would be represented on a number line as closed dots.

The only picture with closed dots on both -7 and 7 is picture 1. So that is the answer.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: graph one

Step-by-step explanation:

Answer:

The formula to calculate standard deviation from probability is \sqrt(n*p*(1-p)). n is the sample size, and 200 in this case (number of putts for practice). p is 80% or 0.8, the probability that he can make it. So the standard deviation is \sqrt(200*0.8*(1-0.8)=\sqrt(200*0.8*0.2)=\sqrt(16)=4.

Answer:

16 feet

Step-by-step explanation:

Since the scale is 3 in : 4 ft, the model car is 16 ft.

To find the actual length of a model car given a scale of 3 inches : 4 feet with the model car being 12 inches long, set up a proportion to calculate the actual car length, which is 16 feet.

A scale of 3 inches : 4 feet means that for every 3 inches on the model car, the actual car is 4 feet long. Given that the model car is 12 inches long, you can set up a proportion:

Solving for x, you get the actual length of the car to be 16 feet.

Answer:

So first lets figure out how many pints it is in a year which is 366. Then find out how many pints are in a gallon which is 8 then divide 366 by 8 which is 45.75

im pretty sure it’s D

The k value in the equation y = f(x) + k causes a vertical shift of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down. Thus, the correct answer is B.

In the function transformation y = f(x) + k, the term k represents a vertical shift of the graph. Specifically:

Thus, the correct answer to the question is:

B. Shifts the graph up k units.

To summarize, the value k in the equation y = f(x) + k causes a vertical shift upwards if it's positive and downwards if it's negative.

The height of a triangle with an area of 3.6 cm² and a base of 6 cm is calculated using the area formula, resulting in a height of 1.2 cm.

To find the height of a triangle when the area and base are known, we use the formula for the area of a triangle, which is area = 1/2 × base × height. The given area is 3.6 cm2, and the base is 6 cm. Rearranging the formula to solve for the height, we get height = (2 × area) / base.

Plugging the values in, we get height = (2 × 3.6 cm2) / 6 cm = 7.2 cm2 / 6 cm = 1.2 cm.

Thus, the height of the triangle is 1.2 cm, which corresponds to option B.

The height of a triangle with an area of 3.6 cm² and a base of 6 cm is found by rearranging the formula for the area of a triangle. The calculated height comes out to be 1.2 cm.

To find the height of a triangle given the area and base, we can use the formula for the area of a triangle which is Area = (1/2) × base × height. In this case, the area is 3.6 cm² and the base is 6 cm.

Rearranging the area formula to find the height, we get height = (2 × Area) / base. Plugging in the values, we have:

height = (2 × 3.6 cm²) / 6 cm = 7.2 cm² / 6 cm = 1.2 cm.

Therefore, the correct answer to the question is B. 1.2 cm.

Answer:

42 correct; if all were answered, that means 7 were wrong. 7/49 reduces to 1/7; one seventh were wrong.