Are girls better at spelling than boys? An SRS of 200 boys and an SRS of 150 girls was administered a
spelling test. The average score for boys was 48.4 with standard deviation 12.96. The girls had an average score
of 48.9 with standard deviation 11.85. Construct and interpret a 95% confidence interval to estimate the true
mean difference in the scores of the spelling test between boys and girls. Does this interval suggest a
difference? Explain.

The solution for x in the trapezoid is x = 12

The midsegment of a trapezoid is a line segment that connects the midpoints of the parallel sides of the trapezoid.

The midsegment of a trapezoid is parallel to the bases of the trapezoid and is equal in length to half the sum of the lengths of the two bases. That is:

DE = 1/2 * (KL + JM)

14 = 1/2 * (11 + 3x - 19)

14 = 1/2 * (3x - 8)

14 * 2 = 3x - 8

28 = 3x - 8

3x = 28 + 8

3x = 36

x = 36/3

x = 12

Learn more about trapezoid on:

https://brainly.com/question/29122051

#SPJ1

Answer:

Step-by-step explanation:

If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a normal distribution.

If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a normal distribution. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that, as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution. This means that even if the original population distribution is skewed, bimodal, or any other shape, the distribution of the sample means will tend towards a normal distribution as the sample size increases.

The reason for this is that the sample means are essentially an average of a number of independent random variables, and the normal distribution is the result of the combination of many independent random variables. When the sample size is large, the distribution of the sample means becomes very close to a normal distribution, even if the underlying population is far from normal.

In the case of a bimodal distribution, the sample means will still approach a normal distribution as the sample size increases, but the distribution may have a different mean and standard deviation than the original population.

In the case of a very skewed distribution, the sample means will also approach a normal distribution as the sample size increases, but the distribution may still be skewed, just less so than the original population.

In conclusion, the Central Limit Theorem states that the distribution of the sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.

If my answer has satisfied your requirements, I would appreciate it if you would give me a rating : Brainliest Answer!

Answer:

Width: [tex]9[/tex] Length: [tex]21.[/tex]

Step-by-step explanation:

Let's say [tex]l[/tex] is the length, and [tex]w[/tex] is the width. We can rewrite [tex]l[/tex] as [tex]2w + 3.[/tex] So  [tex]2(2w + 3) + 2w = 60,\\4w + 6 + 2w = 60,\\6w + 6 = 60,\\6w = 54,\\w = 9.\\[/tex]So the length of the rectangle is [tex]2 \cdot 9 + 3 = 21[/tex] and the width is [tex]9.[/tex]

Hope that helps!

You made a profit of $382.50 from selling the 45 shares of the telecommunications company.

First we need to determine the total cost of purchasing those shares, and then subtract that from the total revenue from selling them.

The total cost of purchasing the 45 shares at a price of $63.00 per share is:

45 shares x $63.00 per share = $2,835.00

The total revenue from selling the 45 shares at a price of $71.50 per share is:

45 shares x $71.50 per share = $3,217.50

To calculate the profit, we subtract the cost from the revenue:

Profit = Revenue - Cost

Profit = $3,217.50 - $2,835.00

Profit = $382.50

Therefore, you made a profit of $382.50 from selling the 45 shares of the telecommunications company.

Learn more about profit here : brainly.com/question/1078746

#SPJ1

Answer:

661,068.8j

Step-by-step explanation:

The car has 661068.8 J of potential energy at a height of 62 m having a mass of 1088 grams.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.

We know, The gravitational constant is 9.8 m/s².

From the given information, m = 1088 grams, h = 62 meters.

Therefore, The amount of potential energy the car has is,

PE = mgh.

PE = 1088×9.8×62 J.

PE = 661068.8 J.

learn more about potential energy here :

https://brainly.com/question/12807194

#SPJ5

Answer: $9080.13

Step-by-step explanation:

use the equation y=b(x)^t, where b is the original profit, x is the percent remaining after one year, and t is the amount of years.

SUBSTITUTE:

y=9500(0.991)^5

Use calculator, and y=9080.126 in 2019. Round off to $9080.13

hope this helps!

MM

Answer:

A. 513 cubic units

Step-by-step explanation:

trust me bro.

[tex]a*b[/tex] must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

Let n be an integer and a, b be relatively prime integers, each of which divides n. This means that a and b have no common factors other than 1. According to the Fundamental Theorem of Arithmetic, the prime factorization of n can be written as n = p1^k1 * p2^k2 * ... * pn^kn. Since a and b divide n, each of their prime factorizations must contain all of the prime factors of n, and the exponents must be less than or equal to the exponents of n. Therefore, a*b must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ4

For every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.

What is Inequalities?

Inequalities are mathematical statements used to express the comparison between two values. Unlike equalities (e.g., 3 + 4 = 7), which use the "equals" sign (=), inequalities use symbols such as "greater than" (>), "less than" (<), "greater than or equal to" (>=), and "less than or equal to" (<=) to express a relationship between the values.

Let's call the number of $10 notes Mrs. Chong used as "x".

We know the total amount she paid was $64, and the number of notes used was 15, so we can set up an equation:

10x + 5y + 2z = 64

Where "y" is the number of $5 notes used and "z" is the number of $2 notes used. We know that x + y + z = 15 (because this is the total number of notes used).

We can substitute x = 15 - y - z into the first equation:

10(15 - y - z) + 5y + 2z = 64

Expanding the equation:

150 - 10y - 10z + 5y + 2z = 64

Combining like terms:

150 - 5y + 3z = 64

Subtracting 150 from both sides:

-5y + 3z = -86

Dividing both sides by -5:

y - (3/5)z = 17.2

So, for every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.

Learn more about Inequalities click here:

https://brainly.com/question/28755685

#SPJ1

Answer:

5

Step-by-step explanation:

The expression 5^2.5^0 is equal to 5^(2.5^0), which can be simplified as follows:

2.5^0 = 1 (because any number raised to the power of 0 is equal to 1)

So, 5^2.5^0 = 5^1 = 5

Therefore, the answer is 5.

Answer:

choice C.  y = -4/3x + 2

Step-by-step explanation:

slope of a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the first line.

m = -4/3  (negative reciprocal of 3/4)

Now use point-slope form to find the y-intercept (b):

y-2 = -4/3(x-0)

y = -4/3x + 2

Answer:

The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:

(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i

= 20 - 8i + 15i - 6i^2

= 20 + 7i - 6(-1)

= 26 + 7i

So the answer is (4) 26 + 7i.

I believe the answer is (d) 26 + 7i.

Answer:  Weight of water in 1 cubic foot water (in pounds)

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Given: One cubic foot holds 7.48 gallons of water.

One gallon of water weighs 8.33 pounds.

To find the weight of water in 1 cubic foot water in pounds we apply Unitary method.

Weight of water in 1 cubic foot water (in pounds)

⇒Weight of water in 1 cubic foot water (in pounds)

Since , 1 pound = 16 ounces .

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

======================================================

Explanation:

If we plugged x = 4 into the expression, then we'll have 0 in the denominator. This causes a division by zero error.

Luckily the numerator factors to (x-4)(x-2)^2. This is found by using the Rational Root Theorem, along with either synthetic division or polynomial long division. I'll skip these steps unless you need me to write them out.

Once we know the numerator factors this way, we can then write the following steps:

[tex]L = \displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}\frac{(\text{x}-4)(\text{x}-2)^2}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}(\text{x}-2)^2\\\\\\L = (4-2)^2\\\\\\L = 4\\\\\\[/tex]

Therefore,

[tex]\displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}=4\\\\\\[/tex]

You can use graphing software like Desmos or GeoGebra to confirm the answer is correct. WolframAlpha is another good choice.

Percentage of change in the stock's price since the beginning of the year is: 12.32%

The price at which a stock's share is currently trading on the market is referred to as the stock price. Every publicly listed company issues its shares at a price, which is an estimation of their value that, ideally, corresponds to the worth of the firm itself.

The market forces of supply and demand govern a company's share price once it becomes public and its shares begin trading on a stock exchange. Price increases will occur if there is a large demand for its shares. A stock's price might be reduced by sellers if the company's prospects for future growth appear uncertain.

Given that,

Closing price today = $21.20

Closing price on the previous trading day= $28.83

Difference between closing price today and closing price on the previous trading day= $21.20 - $28.83

= $7.63

Percentage of change in the stock price since the beginning of the year

= Year-to-date % change

= 12.32%

To know more about stock's price refer to:

https://brainly.com/question/29362234

#SPJ1

The number of bees that will equal the mass of a single moose is 5 × 10⁶.

Given the data in the question;

To determine the number of bees that will equal the mass of a single moose.

Let the number be represented by x.

Hence;

Number of bees × mass of bee = mass of moose

n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³

Divide both sides by ( 2.5 × 10⁻⁴ ).

n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )

n = 1250 / 0.00025

n = 5,000,000

Therefore, the number of bees is 5,000,000.

Learn more about scientific notation here: https://brainly.com/question/16936662

#SPJ1

The rate of change of the function on the interval specified as in the task content is; 7.

It follows from the task content that the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h] is to be determined.

Since the function is a linear function, it follows that the rate of change is a constant and hence is given by;

f'(x) = 7.

Ultimately, the rate of change of the function on the given interval is; 7.

Read more on rate of change of linear functions;

https://brainly.com/question/24655859

#SPJ1

Inverse function for the function f(x)= |x+5|, x>-5 is f⁻¹(x) = -5 ± x

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

Given function,

f(x) = |x + 5| , x>-5

It can be written as

y = |x + 5|

Replacing x with y

x = |y + 5|

Solving for y

y + 5 = ± x

y = -5 ± x

Replacing y with f⁻¹(x)

f⁻¹(x) = -5 ± x

Hence, f⁻¹(x) = -5 ± x is the inverse function for function f(x)= |x+5|, x>-5

Learn more about inverse function here:

https://brainly.com/question/2541698

#SPJ9

If a bundle of strip flooring has 25 sq ft and 30% extra is provided for side and end matching, 12.2 bundles of strip flooring are required to cover a rectangle floor space 16 ft by 14 ft 6 in size.

Once the length and breadth of a rectangle are determined, the area is computed. The area of a rectangle may be calculated by multiplying its length and width.

In this question, because the rectangular floor has an area of 16 ft by 14 ft 6 in, we can compute the total area of the floor by multiplying 16 ft by 14 ft 6 in, which is 234 [tex]ft^{2}[/tex]. We also know that a strip flooring bundle comprises 25 square feet. As a result, we must determine how many bundles of strip flooring are required to cover the floor.

We must account for side and end matching, which is computed by increasing the total floor area by 30%. To determine the extra space required for side and end matching, multiply 234 ft2 by 0.3. This equates to 70.2 [tex]ft^{2}[/tex].

We can now compute the total area required to cover the floor. This is 234 [tex]ft^{2}[/tex] + 70.2 [tex]ft^{2}[/tex] = 304.2 [tex]ft^{2}[/tex].

Because each strip flooring bundle includes 25 square feet, we can divide 304.2 [tex]ft^{2}[/tex] by 25 to determine the total number of bundles required to cover the floor.

This corresponds to 12.2 bundles.

Therefore, 12.2 bundles of strip flooring are needed to cover a rectangular floor area 16 ft by 14 ft 6 in size, with 30% extra for side and end​ matching.

To know more about the area of rectangle, visit

brainly.com/question/20693059

#SPJ1

Answer:

r = 4 cos(2θ)

See the attached image for a graph.

Step-by-step explanation:

The points given by the table are in the graph of a cosine rose with 4 petals whose amplitudes are 4.

For the equation r = a cos(nθ), a is the amplitude of the petals (4), and n is half the number of petals, as there are an even number of petals (4/2 = 2).

Hence,

r = 4 cos(2θ)

Answer:384 children and 123 adults swam at the public school.

Step-by-step explanation:

There are a total of 13 different ornaments to choose from, with 3 types of ornaments.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

When Cherry chooses at least 1 of each type, she will have to select a total of 5 ornaments. This means that Cherry can make a total of 13C5 (13 choose 5) different selections. This is equal to 715 different selections.

This can also be calculated by first selecting 1 ornament from each of the 3 types, which gives 3 different selections. Then, for the 2 remaining ornaments, Cherry can select any of the 13 ornaments, giving a total of 3 x 13 = 39 different selections. In total, this gives 3 + 39 = 42 different selections.

To conclude, Cherry can make a total of 715 different selections when she chooses at least 1 of each type of ornament.

To know more about total number click-
https://brainly.com/question/23286885
#SPJ1

The second telephone pole is 72 feet tall. Since the ratio of the height of the first telephone pole to the length of its shadow is 24/6 = 4.

We can use this ratio to find the height of the second telephone pole.

If the second telephone pole casts a shadow of 18 feet at the same time of day, we can set up the following proportion:

height of second pole / length of shadow of second pole = height of first pole / length of shadow of first pole

Letting x be the height of the second pole, we can plug in the values we know and solve for x:

x / 18 = 24 / 6

Multiplying both sides by 18, we get:

x = 72

Therefore, the second telephone pole is 72 feet tall.

The answer is (e) 72.

Learn more about mathematics here: brainly.com/question/24600056
#SPJ4

Complete question:

On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.

a. 6

b. 12

c. 24

d. 36

e. 72

Answer:

The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.

Step-by-step explanation:

The value in 6 years is $3050.43

The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life.

Using the formula:

Value = P(1-r)^n

From the question, the original value is $9,000, the depreciation rate is 16.5% or 0.165, and the time is 6 years. Plugging in the values:

Putting the values into the formula

Value = 9000(1-0.165)^6

Value = 3050.43

Hence, the value of the car after 6 years will be $3050.43

Learn more about depreciation at:https://brainly.com/question/1203926

#SPJ1

Answer: 4745

Step-by-step explanation:

3250 = 100%

Percent Increase = +46%

46% of 3250 = 1495

3250 (100%) + 1495 (46%) = 4745

The distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.

Complex numbers can be geometrically interpreted using the complex plane. They add like vectors when addition is applied. Polar coordinates make it simpler to represent the product of two complex numbers, whose magnitude or modulus is the sum of their absolute values.

The coordinates of the point A are (-3, -2).

If we extend the line from the origin to the point A it forms a right angled triangle with base = 3 and height = 2.

Using the Pythagoras theorem:

c² = a² + b²

Substituting the values:

c² = (2)² + (3)²

c = √13

Hence, the distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

Learn more about graph here:

https://brainly.com/question/10712002

#SPJ1