Consider a random sample of size 32 from a distribution with mean 40 and variance 8. find the (approximate) probability that the sample mean is between 39.75 and 41.25.

The speed of Joshua's skating rate is given by the equation A = 7 m/s

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The rate of Joshua's skating is given by S = 35 meters / 5 seconds

So , the rate S = 35/5

And , the unit rate of Joshua's skating rate is given by A = 35/5

On simplifying the equation , we get

The unit rate of Joshua's skating rate is given by A = 7 meters per second

The unit rate of Joshua's skating rate is given by A = 7 m/s

Hence , the skating rate of Joshua's skating is 7m/s

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Answer:

she should charge $10 for interest or even more is she wants to make $1005 per year from investing

In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.

What are the perimeter and area?

The area is the region covered by shape or figure whereas the perimeter is the distance covered by the outer boundary of the shape. The unit of area is given by a square unit or unit2 and the unit of the perimeter is the same as the unit.

(a)

Area of a rectangle = length ×  breadth

              =(8×6)

              =48 feet²

Perimeter of the rectangle = 2(length + breadth)

                           =2(6+8)

                           =28 feet

(b)

Area of a rectangle = length ×  breadth

              = (4×4) yards²

              = 16 yards²

Perimeter of the rectangle = 2(length + breadth)

                           =2(4+4)

                           =16 inches

(c)

Area of a rectangle = length ×  breadth

              =(9×4) inches²

              = 36 inches²

Perimeter of the rectangle = 2(length + breadth)

                           =2(9+4)

                           =26 inches

(d)

Area of a rectangle = length ×  breadth

              =(7×4) meters²

              =28 meters²

Perimeter of the rectangle = 2(length + breadth)

                           =2(7+4)

                           =22 meters

Hence, In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.

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The cost of transporting 17 tons of sugar is $8750.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

here, we have,

It will cost $4500 to rent trucks,

and it will cost an additional $250 for each ton of sugar transported.

we know,

Multiplication and division do not separate the terms of an equation.

now,

The given information can be related as,

C = 250S + 4500.

Now, when tons of sugar is 17 we'll simply replace S with 17.

∴ C = 250(17) + 4500.

C = 4250 + 4500.

C = 8750.

Hence, The cost of transporting 17 tons of sugar is $8750.

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The annual property tax for the Joseph family is $8749.8.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

The Joseph family took out a $175,000,

25-year mortgage at an APR of 4%.

The assessed value of their house is $9,000.

The annual property tax rate is 97.22% of assessed value.

The annual property tax = 9000 x 97.22/100

The annual property tax = $8749.8

Therefore, the annual property tax = $8749.8

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Alisha needs to use a fraction of 3/8 of each of the ingredients on the recipe.

We know that a pancake recipe calls for 8 eggs and some other ingredients.

But Alisha only has 3 eggs, so she needs to adjust the recipe.

The fraction of each one of the other ingredients that she needs to use is equal to the fraction between the number of eggs that she has and the number of eggs that the recipe calls, it is:

N = 3/8

So she needs to use 3/8 of each of the ingredients that the recipe calls.

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Answer:

The answer is B. 5 1/4 twisties

Jay is given 65% discount

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred

Percentage discount can be gotten with the formula below:

Discount % = (Discount/Original Price) × 100.

From the question,

Jay pays 27300, instead of 42000

Using the percentage discount above

Percentage Discount = 27300/42000 x 100

Percentage Discount = 65%

Hence, jay got 65% discount from the school

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Answer:

f= 68

g= 88

h= 100

i= 114

Step-by-step explanation:

The correct way to report the length of the rectangle in centimeters would be (b)"15.6 cm".

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°).

The general practice is to report measurements to the appropriate number of significant digits. In this case, "15.6 cm" accurately reflects the measurement to the nearest tenth of a centimeter and uses the proper unit symbol (cm). "15.600 cm" and "15.60 cm" include more significant digits than are necessary and "16 cM" uses an incorrect unit symbol.

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Triangle ABC is similar to triangle ADE by AA test of similarity

Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.

here, we have,

There are different types of similarity test by which we can prove the similarity of triangles.

We are given that BC is parallel to Line DE

As the lines are parallel the respective angle are corresponding angles

hence Angle D = Angle B

And Angle E = Angle C

And both triangle have angle A as common angle

By AA test of similarity we can say that the two triangles are similar

Hence by AA test similarity the two triangles are similar

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Answer:

8x + 8 * 2 = 200

Step-by-step explanation:

Let's assume that each friend received x flyers to pass out.

The equation would be:

8x + 8 * 2 = 200

8x = 184

x = 23

So each friend received 23 flyers and 2 bags, and in total, they received 23 * 8 + 8 * 2 = 200 items.

So, if they plan to practice a total of 45 minutes and have only completed 18.5 minutes that means they have 26.5 minutes of practice remaining (45-18.5).

Answer:

Step-by-step explanation:

The area of the base of this prism is 2. 5 square inches

It Is important to note the properties of a triangular prism, they include;

From the information given, we have that;

Base area = 1/2 base × height

Substitute the values, we get

Base area = 1/2 × 5 × 1

Multiply the values

Base area = 2. 5 square inches

Hence, the value is 2. 5 square inches

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Normally distributed residuals is not an assumption of the general linear model and hence option b is correct

Linear regression models relate to some assumptions about the distribution of error terms. If they are violated violently, the model is not suitable for drawing conclusions. Therefore, it is important to consider the suitability of the model for information before further analysis can be performed based on this model.

The fit of the model is related to the remaining behavior complying with the basic assumptions for error values in the model. When a regression model is constructed from a series of data, it should be shown that the model responds to the standard statistical assumptions of the linear model because of conducting inference. Residual analysis is an effective tool to investigate hypotheses. This method is used to test the following statistical assumptions for a simple linear regression model:

-Regression function is linear in parameters,

-Error conditions have constant variance,

-Error conditions are normally distributed,

-Error conditions are independent.

Normally distributed residuals is not an assumption of the general linear model and hence option b is correct

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The ratio of the given expression is equal to 1:16.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Sometimes, pupils struggle to understand the relationship between ratio and proportion.

We have x=1 and y=2, and we have to find the ratio of x4:y4,

x=1 and y=2 (given)

[tex]x^4:y^4=(1)^4:(2)^4\\\\x^4:y^4=1:16=1/16[/tex]

the ratio of the given expression is equal to 1:16.

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$0.80 required for a 200g packet cost and $0.01 required for a 100g packet cost

To find the cost of a 200g packet,

you can use the unit price,

which is the cost per gram of the biscuits.

To get the unit price, divide the cost of the 600g packet by its weight: $2.40 / 600g = $0.004/g.

Then multiply the unit price by the weight of the 200g packet to get its cost:

$0.004/g * 200g = $0.80.

To find the cost of a 100g packet of Orea's,

Use the same process as above:

$2 / 200g = $0.01/g.

Then multiply the unit price by the weight of the 100g packet to get its cost:

$0.01/g * 100g = $0.01.

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The height of the corresponding to the longest side is 25.03 cm

Given data :

Let the sides of triangles are 3x,5x and 7x.

And perimeter of the triangle is 120cm.

So , 3x + 5x +7x =120

       15x = 120

         x = 8

so, the sides are triangle are 3(8) = 24cm, 5(8) = 40cm , 7(8) = 56cm

so , the longest side is 56 cm.

Area of triangle =   [tex]\sqrt{s(s - a)(s -b)(s-c)}[/tex]

here , s = 64  and a = 24, b = 40c = 56

= [tex]\sqrt{64*(64-24)(64-40)(64-56)}[/tex]

= [tex]\sqrt{64*(40)(24)(8)}[/tex]

=[tex]\sqrt{491520}[/tex]

= 701.08

So, the area of triangle is 701.08 cm 2 and the height corresponding to longest side

h = 2 x 701.08 / 56 = 25.03 cm

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Answer:=1±√5

Step-by-step explanation:

aight so bassically i looked this shi up and yeah thats what what i got bro

The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."

The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.

The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.

Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.

In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.

Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

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The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."

The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.

The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.

Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.

In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.

Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

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Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.

The QR factorization is the factorization of a matrix A into an orthogonal matrix Q and an upper triangular matrix R. Given matrices A and Q, the matrix R can be calculated as:

R = Q^T * A

Where Q^T is the transpose of Q.

Note that this calculation assumes that Q is an orthogonal matrix, meaning that its transpose is equal to its inverse. If Q is not orthogonal, it will not have an inverse and the QR factorization cannot be calculated in this manner.

Therefore, Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.

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If the equation be 2x² + 7x – 30 then the solution to this equation be 2.5.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Let the given equation be 2x² + 7x – 30 = 0

Factorizing it as

(2x – 5) (x + 6) = 0

then we get

2x – 5 = 0 or x + 6 = 0

simplifying the equation we get

2x = 5 or x = –6

x = 5/2 or x = –6

x = 2.5 or x = –6

Therefore, the correct answer is option a) 2.5.

The complete question is:

Which value of x is a solution to this equation?

2x² + 7x – 30

a) 2. 5

b) 5

c) -2. 5

d) -3

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Answer:

5a + 45

Step-by-step explanation:

5(a+9)

5a + 45

Answer:

well if 4 is x and y is -6 but =2 then it's 8

Step-by-step explanation:

hope u have a good day

The slope-intercept equation of the line that includes the points (1, 1) and (2, 8) is y = 7x - 6.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (1, 1) and (2, 8) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 1 = (8 - 1)/(2 - 1)(x - 1)

y - 1 = 7(x - 1)

y = 7x - 7 + 1

y = 7x - 6

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Answer:

7.77

Step-by-step explanation:

49.77 - 42 = 7.77

The price a customer pays for a printer which the company bought for $1700 is $2125 and the price the company paid for a printer which was sold to a customer for $2500 is $2000.

percentage, a relative value indicating hundredth parts of any quantity.

Given that a company sells its printers to customers in order to make a profit of 25%.

We have to find the price a customer pays for a printer which the company bought for $1700.

x-1700/1700=25%

x-1700=425

Add 1700 on both sides

x=$2125.

We need to find the price the company paid for a printer which was sold to a customer for $2500

2500-x/2500=25%

x=2000

Hence, the price a customer pays for a printer which the company bought for $1700 is $2125 and the price the company paid for a printer which was sold to a customer for $2500 is $2000.

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The amount of raw materials in Entry (5), which would raise the raw materials balance from $15,000 to $25,000, might cost $85,000.

Entry (5) can refer to a $85,000 purchase of raw materials. The raw materials balance would rise from $15,000 to $25,000 as a result. The raw materials account's balance is shown in the t-account above both before and after the entry. The raw materials balance was $15,000 prior to this entry. The raw materials balance is now $25,000, an increase of $10,000 after this input. This increase is attributable to the $85,000 purchase of raw materials. This transaction is documented in entry (5), which represents a $85,000 debit to the account for raw materials. The raw materials account now has a balance of $25,000 instead of just $15,000. This is how entry (5) may describe a $85,000 purchase of raw materials.

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