multiply (x – 4)(x + 3)

The value of 'd' such that the specifications cover 95% of the measurements can be determined using the z-score corresponding to a 95% confidence interval, and is found to be 0.392 by multiplying with the known standard deviation.

In this case, you're looking to find the value for d such that specifications cover 95% of the measurements. We know that the measurements follow a normal distribution, with a mean of 1.5 and a standard deviation of 0.2.

According to the Empirical Rule (for a bell-shaped, symmetric distribution), approximately 95 percent of the data is within two standard deviations of the mean. Here, however, we want to find the distance d from the mean that encapsulates 95% of the data. We already know that d falls within a 95% confidence interval, which splits the excluded 5% evenly between the upper and lower tails of the distribution.

So, we will use a z-score corresponding to 95% of the measurements. The z-score corresponding to 95% is approximately 1.96 (covering 2.5% in each tail). Multiply this z-score by the standard deviation to get the value of d (1.96 * 0.2 = 0.392). Thus, d = 0.392 should be the value that ensures the specifications cover 95% of the measurements.

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Answer:

  15,700 cubic feet

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

where r is the radius (half the diameter), and h is the height.

Put the given numbers into the formula and do the arithmetic.

  V = (3.14)(10 ft)²(50 ft) = 15,700 ft³

__

An estimate of the arithmetic will get you to the right answer choice:

  πr²h = π(100)(50) = 5000π ≈ 3×5000 = 15,000 . . . . close to 15,700

Answer:

 15,700 cubic feet

Step-by-step explanation:

Answer:

2/ 21

Step-by-step explanation:

2/3 ÷ 7

Copy dot flip

2/3 * 1/7

2/ 21

Answer:

The Exact answer is 287740837743404332336.

The Decimal Answer is 2.87740837  ⋅  10 ^20.

Answer:

(a) The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of both plots is also same that is 75 pounds.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively

(b) Any data point which is greater than 155 or smaller than 80 will be considered an outlier.

Step-by-step explanation:

A box plot is a graph which shows five statistical characteristics of a data set.

1. Maximum value

2. Minimum value

3. Median

4. Upper Interquartile

5. Lower interquartile

(a) Compare the distributions of weights for the two dog breeds

Please refer to the attached diagram of the question.

The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of Anatolian Shepherd is,

Range = Maximum value - Minimum value

Range = 175 - 100 = 75 pounds

The range of Black Russian Terrier is,

Range = Maximum value - Minimum value

Range = 155 - 80 = 75 pounds

Therefore, the range of both plots is also same that is 75 pounds.

A box-plot is considered to be normally distributed when the median is at the center of upper quartile and lower quartile.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively distributed.

(b) What weights would a Black Russian Terrier have to be to be considered an outlier?

An outlier is a data point in the data set that is very different from the other data points.

In this case, the maximum and minimum values in the Black Russian Terrier box-plot are

Maximum = 155

Minimum = 80

Therefore, any data point which is greater than 155 or smaller than 80 will be considered an outlier.

To compare the distributions of weights for the Anatolian Shepherd and Black Russian Terrier, we can look at the boxplots provided. If a Black Russian Terrier were to be considered an outlier, its weight would be significantly different from the other weights in the sample.

To compare the distributions of weights for the Anatolian Shepherd and Black Russian Terrier, we can look at the boxplots provided. The boxplot for each breed shows the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value. We can compare the positions of these measures to determine the differences between the two breeds.

If a Black Russian Terrier were to be considered an outlier, its weight would be significantly different from the other weights in the sample. An outlier is typically defined as a value that is more than 1.5 times the interquartile range (IQR) above the upper quartile (Q3) or below the lower quartile (Q1). To find the weight that would be considered an outlier for Black Russian Terriers, we need to calculate the IQR and use it to determine the threshold for outliers.

Answer:

48- Teddy will need 48 gallons of ice.

Step-by-step explanation:

2.5 ÷ 4 = 1.6

1.6 x 30 = 48!

Teddy will need 48 gallons of ice.

Hope i helped ^^

Using the formula

[tex]a^2-b^2=(a+b)(a-b)[/tex]

We can write

[tex](4^2)^2-1 = 16^2-1 = (16+1)(16-1)=17\cdot 15[/tex]

Since 17 is prime and the factors of 15 are 3 and 5, the three prime factors of this number are 3, 5 and 17.

The required prime factors of the given expressions are given as 3, 5, and 17.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,
Given expression,
=[4²]² -1
= 16² - 1

Since (a² - b²) = (a + b)(a - b)
= (16 + 1)(16 - 1)
= 17 × 15

= 17 × 3 × 5

Thus, the required prime factors of the given expressions are given as 3, 5, and 17.

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9514 1404 393

Answer:

  9 days

Step-by-step explanation:

Divide quantity by rate to find time.

  (3 cups)(1/3 cup/day) = 3/(1/3) days = 3(3/1) days = 9 days

Answer:

look below im smart and im just a seventh grader O w O

Step-by-step explanation:

2f(1.6m)

X=24

X=2*24/1.6

X=2*15

X= 30 m

Answer:

[tex] \frac{61}{3} = 20 \frac{1}{3} [/tex]

Step-by-step explanation:

[tex]20 + \frac{2}{6} [/tex]

[tex] \frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3} [/tex]

[tex]20 + \frac{1}{3} = \frac{20}{1} + \frac{1}{3} = \frac{20 \times 3}{1 \times 3} + \frac{1}{3} [/tex]

[tex] \frac{60}{3} + \frac{1}{3} = \frac{60 + 1}{3} = \frac{61}{3} [/tex]

[tex] \boxed{\green{= \frac{61}{3} = 20 \frac{1}{3}}} [/tex]

Answer:

proportional

Step-by-step explanation:

Answer:

c is correct

Step-by-step explanation:

edge

the arc length of the following segment of a circle is c. 18.6.

Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.

here, we have,

given that,

the following segment of a circle.

angle=97°

radius=11

so, the arc length= 18.6

hence, the arc length of the following segment of a circle is c. 18.6.

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Answer:

A) 9.49 ft

Step-by-step explanation:

The area of the rectangle is:

[tex]A = (18\,ft)\cdot (5\,ft)[/tex]

[tex]A = 90\,ft^{2}[/tex]

The length of the square is:

[tex]l = \sqrt{90\,ft^{2}}[/tex]

[tex]l \approx 9.487\,ft[/tex]

Answer: 9pi

Step-by-step explanation:

Answer:

  $27,318.18

Step-by-step explanation:

The build cost is multiplied by 1.03 each year. After 3 years, it will be multiplied by 1.03^3, so will be ...

  $25,000×1.03^3 ≈ $27,318.18

Answer:

D. (3, -4)

Step-by-step explanation:

Imagine you are going 4 right and 3 up.

Now if you turn this 90o clockwise, you are going 4 down and 3 right.

that is (3, -4)

Final answer:

Rotating the point (4, 3) 90 degrees clockwise about the origin results in the point (3, -4), making option D the correct answer.

Explanation:

The question asks about rotating the point (4, 3) 90 degrees clockwise about the origin and determining the coordinates of the resulting point. To rotate a point 90 degrees clockwise around the origin, you can switch the x and y coordinates and then change the sign of the new y-coordinate. Thus, the original point (4, 3) becomes (3, -4) after the rotation.

This process can be visualized as a transformation where the point's x-coordinate effectively becomes the y-coordinate but negative, and the y-coordinate becomes the new x-coordinate. This transformation corresponds to choice D. (3, -4) as the correct answer. This method is a straightforward application of rotation in the coordinate system, relying on the rules of rotating points in two-dimensional space.

Answer:

B

Step-by-step explanation:

Because since they are increasing $8.50 by 10% you got to divide by 10 to get the answer. Because 10% is equal as multiplying .10 or dividing by 10. So when you divide by 10 you get 0.85. So B is the answer to the question.

Answer:

35

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

Answer: They can buy 140 ​vans, 70​ small trucks, and 70 large trucks.

Step-by-step explanation:

Let x represent the cost of each commercial van.

Let y represent the cost of each small truck.

Let z represent the cost of each large truck.

The total number if vehicles that they want to purchase is 280. It means that

x + y + z = 280- - - - - - - - - - - 1

Each commercial van will cost ​$55 000​, each small truck ​$20000​, and each large truck ​$70000. The total amount to be spent is $14000000. It means that

55000x + 20000y + 70000z = 14000000- - - - - - -2

Past experience shows that they need twice as many vans as small trucks. It means that

x = 2y

Substituting x = 2y into equation 1 and equation 2, it becomes

2y + y + z = 280

3y + z = 280

z = 280 - 3y - - - - - - - - -3

55000(2y) + 20000y + 70000z = 14000000

110000y + 20000y + 70000z = 14000000

130000y + 70000z = 14000000- - - - - - - 4

Substituting equation 3 into equation 4, it becomes

130000y + 70000(280 - 3y) = 14000000

130000y + 19600000 - 210000y = 14000000

130000y - 210000y = 14000000 - 19600000

- 80000y = -5600000

y = -5600000/- 80000

y = 70

x = 2y = 2 × 70

x = 140

z = 280 - 3y = 280 - 3(70)

z = 280 - 210

z = 70

Answer:

[tex]\chi^2 =\frac{50-1}{0.2025} 0.3844 =93.015[/tex]

The degrees of freedom are given by:

[tex] df = n-1= 50-1=49[/tex]

And the p value is given by:

[tex]p_v =P(\chi^2 >93.015)=0.00015[/tex]

Since the p value is very low compared to the significance level provided we have enough evidence to conclude that the true deviation is higher than 0.45

Step-by-step explanation:

Information given

[tex]\alpha=0.05[/tex] represent the confidence level  

[tex]s^2 =0.62^2 =0.3844 [/tex] represent the sample variance obtained

[tex]\sigma^2_0 =0.45^2 =0.2025[/tex] represent the value that we want to test

System of hypothesis

On this case we want to check if the true deviation is higher than 0.45, so then we can create the following system of hypothesis:

Null Hypothesis: [tex]\sigma^2 \leq 0.2025[/tex]

Alternative hypothesis: [tex]\sigma^2 >0.2025[/tex]

The statistic for this case is given by:

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

Replacing we got

[tex]\chi^2 =\frac{50-1}{0.2025} 0.3844 =93.015[/tex]

The degrees of freedom are given by:

[tex] df = n-1= 50-1=49[/tex]

And the p value is given by:

[tex]p_v =P(\chi^2 >93.015)=0.00015[/tex]

Since the p value is very low compared to the significance level provided we have enough evidence to conclude that the true deviation is higher than 0.45

Answer:

on the no. line the negative no.s are to the left of zero. -5 is less than 4 because -5 lies to the left of 4 on the no. line -1 is greater than -3 because -1 lies to the right of -3 on the no. line . for less than you can use the sign <- sign

Step-by-step explanation:

-2>-9

7x^2 > -2x^2

6 > -8

pls mark me brainliest if you feel this answer helps you.

if you have any question pls feel to ask in the comment section.

thanks.

Answer:

Cost to buy and run the first car for 5 years=$24000

Cost to buy and run the second car for 5 years=$26000

I think we should buy the first car, because It is cheaper to buy and maintain

Step-by-step explanation:

first car:

Cost $18000 to buy

Cost $100 to maintain each month

5years =5 x 12=60months

Cost to maintain for 60months=100x60=$6000

First car cost to buy and run over the 5 year period=18000+6000=$24000

Second car:

It cost $22400 to buy

Cost $60 to maintain each month

5years=60months

Cost to maintain for 60months is 60 x 60=$3600

Cost to buy and run over the second car for 5years is 22400+3600=$26000

Answer:

y = -3x + 5

Step-by-step explanation:

Usually by drawing a simple graph, you can tell what the equation is, even if the graph isn't 100% accurate. From the points alone, you can tell that the slope is negative, since as you increase in x you decrease in y (which is a negative relationship). You can tell that it's +5 rather than -5 because the graph sketched shows that the line goes above 0 (indicating a positive number), rather than below (a negative number).

The slope of the line through points (2, -1) and (5,-10) is -3. With y-intercept +5, the line's equation in slope-intercept form is y = -3x + 5.

The subject of your question is in the field of Mathematics, specifically algebra.

You are looking for the equation of the line in slope-intercept form, which is y = mx + b where m is the slope and b is the y -intercept. We first calculate the slope using the formula (y2 - y1) / (x2 - x1). Plugging in the values we get, m = (-10 - (-1)) / (5 - 2) = -9 / 3 = -3. Thus, m = -3. Then, to find the y-intercept, we use the point-slope form of a line equation y - y1 = m(x - x1), and plug in one of the points (2, -1) and the slope value, and then solve for b. The equation in slope-intercept form will be y = -3x + 5.

So the answer to your question is y = -3x + 5.

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The photosphere is approximately 5.62 times brighter per unit area than the sunspot.

Stefan-Boltzmann Law: We'll use the Stefan-Boltzmann Law, which states that the radiant emittance (power emitted per unit area) of a black body is proportional to the fourth power of its absolute temperature (T). Mathematically, this can be expressed as:

M = σ * T^4

Where:

M is the radiant emittance (W/m²)

σ is the Stefan-Boltzmann constant (5.670374 x 10^-8 W m^-2 K^-4)

T is the absolute temperature (Kelvin)

Radiant Emittance: Calculate the radiant emittance of the sunspot and the photosphere using their respective temperatures:

Sunspot: M_sunspot = σ * T_sunspot^4 = 5.670374e-8 * 3900^4 ≈ 83.32 x 10^12 W/m²

Photosphere: M_photosphere = σ * T_photosphere^4 = 5.670374e-8 * 5760^4 ≈ 468.37 x 10^12 W/m²

Brightness Ratio: Calculate the ratio of the photosphere's radiant emittance to the sunspot's radiant emittance to determine how much brighter the photosphere is per unit area:

Brightness Ratio = M_photosphere / M_sunspot ≈ 468.37 x 10^12 W/m² / 83.32 x 10^12 W/m² ≈ 5.62

Therefore, the photosphere is approximately 5.62 times brighter per unit area than the sunspot.

Answer:

  448.69 in^3

Step-by-step explanation:

The volume of a sphere is given by the formula ...

  V = (4/3)πr^3

We want to use diameter, so we can substitute r = d/2 into the formula:

  V = (4/3)π(d/2)^3 = (4/(3·8))πd^3

  V = (π/6)d^3

For the given numbers, ...

  V = (3.14/6)(9.5^3) ≈ 448.69 in^3 . . . . volume of a basketball

Answer:

so first you cross multiply the first fractions' numerator by the other fractions denominator.

and then you do the same for the other one

then you multiply both denominators

the answer u got from cross multiplying, you get those numbers and subtract

them. the denominator doesn't need anything done to it.

Step-by-step explanation:

hope it helps (pls brainliest if u can)

Answer:

a) [tex]36401.1-2.262\frac{18230.58}{\sqrt{10}}=23360.63 \approx 23361[/tex]    

[tex]36401.1+2.262\frac{18230.58}{\sqrt{10}}=49441.56 \approx 49442[/tex]  

b) increasing the sample size or decreasing the confidence level

Since if we increase the sample size the margin of error would be lower and if we decrease the confidence level the margin of error would be reduced since the critical value t would be lower

Step-by-step explanation:

We have the following data given

22,485 56,758 59,762 17,671 16,301 12,262 48,307 51,196 47,326 31,943

We can calculate the sample mean and deviation with this formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\bar X=36401.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean

s= 18230.58 represent the sample standard deviation

n=10 represent the sample size  

Part a

The confidence interval for the mean is given by:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]

The  Confidence level is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]t_{\alpha/2}=2.262[/tex]

Replacing the info given we got:

[tex]36401.1-2.262\frac{18230.58}{\sqrt{10}}=23360.63 \approx 23361[/tex]    

[tex]36401.1+2.262\frac{18230.58}{\sqrt{10}}=49441.56 \approx 49442[/tex]    

Part b

The confidence interval can be made narrower:

increasing the sample size or decreasing the confidence level

Since if we increase the sample size the margin of error would be lower and if we decrease the confidence level the margin of error would be reduced since the critical value t would be lower

Answer:

The 95​% confidence interval for p₁-p₂

( -0.01564 ,0.04044 )

Step-by-step explanation:

Explanation:-

Given data Of the 1230 males​ surveyed, 176 responded that they had at least one tattoo

Given the first sample size 'n₁' = 1230

Given x = 176

The first sample proportion

[tex]p_{1} = \frac{x}{n_{1} } = \frac{176}{1230} =0.1430[/tex]

q₁ = 1-p₁ =1-0.1430 = 0.857

Given data Of the 1079 females​ surveyed, 141 responded that they had at least one tattoo

Given the second sample size n₂ = 1079

and x = 141

The second sample proportion

[tex]p_{2} = \frac{x}{n_{2} } = \frac{141}{1079} = 0.1306[/tex]

q₂ = 1-p₂ = 1-0.1306 =0.8694

The 95​% confidence interval for p₁-p₂

[tex](p_{1} - p_{2} - Z_{\frac{\alpha }{2} } se(p_{1} - p_{2}) ,p_{1} - p_{2} + Z_{\frac{\alpha }{2} } se(p_{1} - p_{2})[/tex]

where

        [tex]se(p_{1}-p_{2}) = \sqrt{\frac{p_{1}q_{1} }{n_{1} }+\frac{p_{2} q_{2} }{n_{2} } }[/tex]

[tex]se(p_{1}-p_{2}) = \sqrt{\frac{0.143(0.857) }{1230}+\frac{ 0.1306(0.8694) }{1079 }[/tex]

 se(p₁-p₂) = 0.01431

[tex](p_{1} - p_{2} - Z_{\frac{\alpha }{2} } se(p_{1} - p_{2}) ,p_{1} - p_{2} + Z_{\frac{\alpha }{2} } se(p_{1} - p_{2})[/tex]

[tex][(0.1430-0.1306) - 1.96(0.01431) , 0.1430-0.1306) + 1.96(0.01431)[/tex]

On calculation , we get

( 0.0124- 0.0280476 ,0.0124+ 0.0280476)

(   -0.01564 ,0.04044 )

Conclusion:-

The 95​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

(   -0.01564 ,0.04044 )