The total area of your neighbor's backyard is 900 ft2. she wants to use 240 ft2 more area for landscaping than for a pool. how much area will she use for the pool? the landscaping?

Answer:

y=-4x

Step-by-step explanation:

WE need to write the equation for the given graph

In the graph y intercept is (0,0)

The equation of linear graph is y=mx+b

where m is the slope and b is the y intercept

From the given graph y intercept is 0 so b=0

to find slope pick two points from the graph

(0,0) and (1, -4)

slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-4-0}{1-0} = -4[/tex]

m=-4  and b=0

So the equation becomes

y= -4x+0

y= -4x

rope = 36 feet

first piece = x

2nd piece = 2x ( twice as long as the first piece)

3x=36

x=12

first piece = 12 feet

 2nd piece = 2 x 12 = 24 feet

Final answer:

The third quartile (Q3) of IQ scores, which separates the top 25% of scores, is approximately 110.125 for a normal distribution with a mean of 100 and a standard deviation of 15.

Explanation:

To find the third quartile (Q3) of IQ scores, which is the value that separates the top 25% from the others in a normally distributed data set, we use the properties of the normal distribution. The mean IQ score is 100 and the standard deviation is 15. Q3 corresponds to the 75th percentile in a normal distribution.

To find the third quartile (Q3), we often refer to the z-score table or use a statistical software or calculator that can handle normal distribution calculations. The z-score corresponding to the 75th percentile is approximately 0.675. We can then use the formula for z-scores:

Q3 = mean + z*(standard deviation)

Q3 = 100 + 0.675*15

Q3 = 100 + 10.125

Q3 = 110.125

Thus, the third quartile IQ score, separating the top 25% of scores from the rest, is approximately 110.125.

To find Q3 for IQ scores (mean 100, SD 15), calculate 75th percentile: [tex]\( Q3 = 100 + 0.674 \times 15 = 110.11 \).[/tex]

To find the third quartile (upper Q3) of IQ scores, we need to determine the IQ score that separates the top 25% from the rest. Given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to find this value.

1. Identify the z-score corresponding to the third quartile (Q3):

  - The third quartile (Q3) corresponds to the 75th percentile of the normal distribution.

  - Using the standard normal distribution table or a calculator, the z-score for the 75th percentile is approximately 0.674.

2. Convert the z-score to an IQ score:

  - Use the formula for converting a z-score to a value in a normal distribution:

    [tex]\[ X = \mu + z \sigma \][/tex]

    where:

    - [tex]\( \mu \)[/tex] is the mean (100)

    - [tex]\( \sigma \)[/tex] is the standard deviation (15)

    - [tex]\( z \)[/tex] is the z-score (0.674)

3. Calculate the IQ score:

  [tex]\[ Q3 = 100 + (0.674 \times 15) = 100 + 10.11 = 110.11 \][/tex]

Therefore, the third quartile (Q3) IQ score, which separates the top 25% from the others, is approximately 110.

The area of a rectangle can be directly calculated using the formula:

A = l * w

Where l is the length or the depth while w is the width

Therefore,

A = 50 feet * 100 feet

A = 5000 square feet

Answer:

Option D. is the correct answer.

Step-by-step explanation:

In this graph, polygon PQRST has been dilated by a scale factor of 3 keeping origin as the center of dilation to form P'Q'R'S'T'.

We know when two polygons are similar, their angles will be same and their corresponding sides will be in the same ratio.

Therefore, option D.which clearly says that the ratio of side SR and S'R' is 1 : 3, will be the answer.

This is an example of a sine wave function. A given sine wave function has a standard form of:

y = A sin [B (x + C)] + D 

Where,

A = absolute value of amplitude

2 π / B = the period of the sine wave

D = is the midline of y

C = phase of the sine wave

Rewriting the given equation into this form will yield:

f (x) = -7 sin[4 (x – π / 4)] + 2

Therefore from this form, we can get the answers:

Amplitude = 7

Period = 2π / 4 = π / 2

Midline = 2

The equation to model the suspension cables of a bridge, where the lowest point of the cable is 40 feet above the bridge, and the towers are 100 feet tall and 200 feet from the center, is y = -0.0015x^2 + 60.

To find the equation that models the suspension cable of a bridge, we use the properties of a parabolic shape. Since the cable is attached to towers that are 100 feet tall and the lowest point of the cable is 40 feet above the bridge, we know the vertex of the parabola is 60 feet (100 - 40) below the top of the towers.

Let's define the coordinate system with the origin at the lowest point of the cable. Then the towers are at (-200, 60) and (200, 60) because the bridge is 400 feet long, so each tower is 200 feet horizontally from the center. The parabolic equation takes the general form y = ax^2 + bx + c. Because the vertex is at (0, 60), c = 60.

Using the points (-200, 60), we can substitute into the parabolic equation and write a system to solve for a and b. Since the parabola is symmetric, b = 0. The system becomes 60 = a(-200)^2 + 60, which simplifies to a = -60/40000.

Thus, the equation to model the cables is y = -60/40000x^2 + 60, or simplified, y = -0.0015x^2 + 60.

A) 2/5 = 0.4

B) 4% = 0.04

C) 0.29

D) 27/100 = 0.27

 least = 0.04, then 0.27, then 0.29, then 0.4

 so B, D, C A is the order

The mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .

To find the mean, variance, and standard deviation of a binomial distribution with given values of [tex]\( n \)[/tex] and [tex]\( p \)[/tex], we use the following formulas:

Mean [tex](\( \mu \)) = \( n \times p \)[/tex]

Variance [tex](\( \sigma^2 \)) = \( n \times p \times (1 - p) \)[/tex]

Standard Deviation [tex](\( \sigma \)) = \( \sqrt{\text{Variance}} \)[/tex]

Given:

[tex]\( n = 123 \)[/tex]

[tex]\( p = 0.85 \)[/tex]

Let's calculate each of these:

Mean [tex](\( \mu \))[/tex]:

[tex]\( \mu = n \times p \)[/tex]

[tex]\( \mu = 123 \times 0.85 \)[/tex]

[tex]\( \mu = 104.55 \)[/tex]

Variance [tex](\( \sigma^2 \))[/tex]:

[tex]\( \sigma^2 = n \times p \times (1 - p) \)[/tex]

[tex]\( \sigma^2 = 123 \times 0.85 \times (1 - 0.85) \)[/tex]

[tex]\( \sigma^2 = 123 \times 0.85 \times 0.15 \)[/tex]

[tex]\( \sigma^2 = 104.55 \times 0.15 \)[/tex]

[tex]\( \sigma^2 = 15.6825 \)[/tex]

Standard Deviation [tex](\( \sigma \))[/tex]:

[tex]\( \sigma = \sqrt{\sigma^2} \)[/tex]

[tex]\( \sigma = \sqrt{15.6825} \)[/tex]

[tex]\( \sigma \approx 3.9599 \)[/tex]

Therefore, the mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .

The graph of the cosine function, f(theta) = cos(theta), has properties such as amplitude, period, domain, range, and x-intercepts, and these properties can be related to the unit circle definition of cosine.

The graph of the cosine function, f(theta) = cos(theta), has several properties:

These properties can be related to the unit circle definition of cosine. The amplitude corresponds to the distance from the origin to the maximum or minimum value of cosine on the unit circle. The period corresponds to the distance traveled along the unit circle to complete one cycle of the cosine function. The x-intercepts of the cosine function correspond to the angles at which the terminal side of theta intersects the x-axis on the unit circle.

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1550*0.8=1240

1240/120 = approximately 11 months to pay off

1240/180=approximately 7 months to pay off

11-7 =4

 so it would be paid off 4 months sooner, so C is the answer

Option: C is the correct answer.

                   C. 4 months sooner.

Total amount of the item is: $ 1550

Also, Tiffany paid 20% of the amount by down payment.

Hence, the amount left to pay after the down payment is:80% of total amount.

i.e. 0.80 of total amount.

= 0.80×1550

= $ 1240

Now the number of month it will take if she pay $ 120 a month is:

[tex]=\dfrac{1240}{120}=10.3333[/tex]

which is approximately equal to 11 months.

Similarly, the number of month it will take if she pay $ 180 a month is:

[tex]=\dfrac{1240}{180}=6.8889[/tex]

which is approximately equal to 7 months.

Hence, the number of months sooner she will pay off is:

                                11-7=4 months.

Answer:

2143.6 in

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

i got u homies

The length of the rectangular parking lot is  130 meters.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, The length of a rectangular parking lot is 10 meters less than twice it's width.

Assuming the width of the rectangle is x meters, therefore length would be

(2x - 10) meters and the perimeter is 400 meters.

We know the perimeter of a rectangle is 2(length + width).

∴ 2( x + 2x - 10) = 400.

2(3x - 10) = 400.

6x - 20 = 400.

6x = 420.

x = 70 meters and length is (2.70 - 10) = 130 meters.

learn more about rectangles here :

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Answer:  First Option is correct.

Step-by-step explanation:

Since we have given that

[tex](4x^3+2x^2-18x+38)\div(x+3)[/tex]

We will apply the "Remainder Theorem ":

So, first we take

[tex]g(x)=x+3=0\\\\g(x)=x=-3\\\\and\\\\f(x)=4x^3+2x^2-18x+38[/tex]

So, we will put x=-3 in f(x).

[tex]f(-3)=4\times (-3)^3+2\times (-3)^2-18\times (-3)+38\\\\f(-3)=-108+18+54+38\\\\f(-3)=2[/tex]

So, Remainder of this division is 2.

Hence, First Option is correct.

The remainder of the given expression is 2 and this can be determined by using the factorization method.

Given :

Expression  --  [tex]\rm \dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]

The factorization method can be used in order to determine the remainder of the given expression.

The expression given is:

[tex]\rm =\dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]

Try to factorize the numerator in the above expression.

[tex]\rm =\dfrac{4x^3+12x^2-10x^2-30x+12x+36+2}{x+3}[/tex]

[tex]\rm = \dfrac{4x^2(x+3)-10x(x+3)+12(x+3)+2}{(x+3)}[/tex]

Simplify the above expression.

[tex]\rm = (4x^2-10x+12) + \dfrac{2}{(x+3)}[/tex]

So, the remainder of the given expression is 2. Therefore, the correct option is A).

For more information, refer to the link given below:

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To estimate the average SAT score of first-year students at a college with a 95% confidence interval and a margin of error of 25 points, you would need to sample approximately 554 students.

This question involves using the concepts of mean, standard deviation, margin of error, and confidence intervals from probability and statistics. To determine the sample size needed to estimate the average SAT score with a certain margin of error, we'll use the formula for the sample size required for estimating a population mean in statistics:

n = (Z*σ/E)^2

Where:

Plugging the values into the formula, we get:

n = (1.96*300/25)^2 ≈ 553.47

As we cannot have a fraction of a student, we always round up to ensure our margin of error requirement is met. Therefore, you would need to sample approximately 554 students.

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To limit the margin of error of your 95% confidence interval to 25 points, given the standard deviation is 300, use the formula for the margin of error for a confidence interval and solve for the sample size 'n'. Approximately 553 students should be sampled.

For this question, we can use the formula for the margin of error for a confidence interval which is calculated as: Margin of Error = z * (σ/√n). Here, 'z' represents the z-score, 'σ' is the standard deviation, and 'n' is the sample size.

In this case, we wish to have a 95% confidence level. From z-tables, we know that the z-value for a 95% confidence level is approximately 1.96. We want a margin of error of 25 points. The standard deviation (σ) for the dataset is said to be 300.

So, we can rearrange our formula to solve for 'n', giving us: n = (z * σ / Margin of Error)². Substituting in our numbers, we get n = (1.96 * 300 / 25)². So, to limit the margin of error on your 95% confidence interval to 25 points, you will need to sample approximately 553 students.

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