The steps below show the work of a student used to calculate the number of yards in 804.5 meters.

(1 mile = 1,609 meters)
(1 mile = 1,760 yards)

Step 1: 1,609 meters is being multiplied by conversion factor 1 mile over 804.5 meters equals 2 miles

Step 2: 2 miles is being multiplied by conversion factor 1760 yards over 1 mile equals 3,520 yards

Step 3: 3,520 yards
(1 mile = 1,609 meters)
(1 mile = 1,760 yards)

How can the error in the student's work be corrected? NEEDS SUBMITTING TODAY PLZ HELP ASAP

Answer:

9/25

Step-by-step explanation:

Answer:

f(g(x)) = x² + 4x + 3

Step-by-step explanation:

f(x) = x² − 1

g(x) = x + 2

To find the composite f(g(x)), replace x in f(x) with g(x).

f(g(x)) = (g(x))² − 1

Now substitute the expression for g(x).

f(g(x)) = (x + 2)² − 1

Simplify by distributing.

f(g(x)) = x² + 4x + 4 − 1

f(g(x)) = x² + 4x + 3

Answer:

this triangle is a acute angel so it 3

ANSWER:

324 square feet

STEP-BY-STEP EXPLANATION:

We have that the area of a square can be calculated with the following formula:

Replacing:

The area is 324 square feet

Answer:

=10x−5

Step-by-step explanation:

=8x+−5+2x

Combine Like Terms:

=8x+−5+2x

=(8x+2x)+(−5)

=10x+−5

Answer:

10x-5

Step-by-step explanation:

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

The mean absolute deviation of the data is equal to 4.75.

In Mathematics and Geometry, the mean for a data set can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

F(x) = 5 + 8 +8+10+13+14+16+22

F(x) = 96.

Next, we would determine the mean as follows;

Mean = [F(x)]/n

Mean = 96/8

Mean = 12.

Generally speaking, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;

MAD = 1/n ∑|x - μ|

Where:

By substituting the given parameters into the MAD formula, we have the following;

MAD = 1/8 [(5 - 8) +  (8 -8) +(8-8)+(10-8)+(13-8)+(14-8)+(16-8) + (22-8)]

MAD = 1/8(3 + 0+0+2+5+6+8+14).

MAD = 1/8(38)

MAD = 4.75

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Answer:

a)  0.0721

Step-by-step explanation:

Let the random variable X be the score on the ACT exam.

Given:

Therefore, the random variable X is normally distributed:

\(X \sim\textsf{N}(21,5^2)\)

Z-score for a sample mean

\(\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)\)

\(\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}\)

Given:

Therefore, the test statistic is:

\(\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)\)

Using the Z-tables to find the probability:

\(\implies \text{P}(Z \leq -1.46)=0.0721\)

Answer:

92%

Step-by-step explanation:

138 is 92% of 150

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

Check the picture below.

We know that two vertical angles are equal.

\(108° \: = \: (12x \: + \: 24)°\)

\( - 12x \: = \: 24 \: - \: 108\)

\( - 12x \: = \: -84\)

\( \boxed{ \bold{x \: = \: 7°}}\)

We know that a complete angle measures 360°.

\(108° \: + \: 108° \: + \: z \: + \: z \: = \: 360°\)

\(216 \: + \: 2z \: = \: 360\)

\(2z \: = \: 360 \: - \: 216\)

\(2z \: = \: 144\)

\( \boxed{ \bold{z \: = \: 72°}}\)

From the table , the insurance cost for the second year based on the prescription given is : $1329

Using the prescription table, the six cylinder compact , second year car with a mileage of 14000 falls in the mid table category with the 13000 mileage label .

The operating cost in insurance for the second year is therefore $1329.

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Answer:

2. 40

3. 10,500

4. 240

Step-by-step explanation:

The formula for volume is Length * Width * Height.

2. 5*2*4 = 40

3. 35*15*20= 10,500

4. 6*4*10=240

The value of constant in the equation is, 1.5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The points on the graph is,

⇒ (1, 1.5) , (2, 3) , (4, 6) (4, 9)

Now, We know that;

The constant in the graph is find as;

⇒ y / x

⇒ 1.5 / 1

⇒ 1.5

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By answering the above question, we may state that Romania $766.51 $646.96.80 leu 0.940 and by equation United States $4,141.00 $1,242.20 dollars 0.000 $4,141

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematics statement that proves the equality of two formalisms is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two statements that are inscribed on opposite sides of a letter. Frequently, the trademark and the particular software are identical. like in 2x - 4 = 2, for example.

z = (x - μ) / σ

where x is the $1,500 wage, is the average income across all countries, and is the standard deviation across all countries.

Country typical monthly income (U.S. dollars) Normative deviation (U.S. dollars) original money Z score for a mean income of $1,500 in dollars

Republic of the Czech 1,059 korunas, or $158.80, $1,096.89 -0.913

Latvia $790 Lats $118.60 $1,515.77 -0.877

$2,245 $673.60 in Korean Won $1,956.24 -0.498

Romania $766.51 $646.96.80 leu 0.940

United States $4,141.00 $1,242.20 dollars 0.000 $4,141

As $1,500 per month for Romania corresponds to the highest z score of 0.94, suggesting that the income is rather high compared to Romania's mean wage, the computer programmer from Romania will probably be the most happy with the offer.

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In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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Answer:

x=5

Step-by-step explanation:

Answer: Choice D.  15 - (-18)

This results in 15 - (-18) = 15 + 18 = 33.

So from -18 to 15 on a number line is 33 spaces.

We can also say

|-18 - 15| = |-33| = 33

The use of absolute value is to ensure the distance is never negative.

Answer:

-10/3, -2, 2/7

Step-by-step explanation:

An expression for given sequence of operations is: j + 3^9

In this question, we need to write an expression for the sequence of operations described below.

raise 3 to the 9th power, then add the result to j

Consider the part of given statement,

raise 3 to the 9th power

We write this as: 3^9

then we add this result to j.

So, we get an expression: 3^9 + j

Therefore, an expression for given sequence of operations is: j + 3^9

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Answer:

1: 50

2: 2.5

3: 5

1: multiply 10 by 100 and then divide the total by 5

as follows:

(10 x 100) / 5multiply 10 by 100 and then divide the total by 5 as follows:

(10 x 100) ÷5

equals 200

2: 90 is 250% of 36

3: 4: 20*100 =

(4*100): 20 =

400: 20 = 20

The formula for a two-sample z-interval for a population proportion is used to calculate the endpoints of the confidence interval, which can vary with each new sample and the probability that p is in the interval is equal to the level of confidence for the interval.

A  confidence interval is a range of values used to estimate an unknown population proportion, p. It is calculated using the sample proportion, P, and the sample size, n. The formula for a two-sample z-interval for a population proportion is P ± zα/2*√(P*(1-P)/n). Where zα/2 is the critical value of the standard normal distribution for the desired level of confidence, usually 95%. This formula is used to calculate the endpoints of the confidence interval. It is important to note that the endpoints of the interval can vary with each sample and that the population proportion p is fixed, but the sample proportion p can vary from sample to sample. The probability that p is in the interval is equal to the level of confidence for the interval, but whether the interval captures p is not known with certainty.

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2x - 37 = 85

Number of crayons that Rachel has = 85

Let the number of crayons that Joshua has be represented by x

The number of crayons that Rachel has is 37 less than twice what Joshua has

Number of Rachel's crayons = 2(Number of Joshua's crayons) - 37

85 = 2x - 37

2x - 37 = 85

Therefore, the equation representing the given situation is:

2x - 37 = 85

Answer:

10,502

Step-by-step explanation:

The formula seems to have three sections added together

f(x) = [x] + [(x+1)^2] + [1 + 2x]

f(100) = 10,502

Answer: 375

Step-by-step explanation:

Ruling out each number:

6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.

3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.

2 & 4 & 8: Is proven wrong in the 4th clue.

7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.

1: Is proven wrong after 7 is proven true.

Figuring out placement:

5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.

3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.

7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.

Answer:

A

Step-by-step explanation:

A

Answer:

Q9 -  Option 1---- A -  15.6 Square Units

Q10 --Option --- (B) RECTANGLE

Step-by-step explanation:

Q9 --

we know area of triangle  = 1/2 ab sin theta

Where theta is the angle included between sides A and side B

A  = 5.2

B = 7

theta  = 121 degrees

1/2 * 5.2 * 7 * sin 121 degrees = 15.6 Square Units

Conclusion

The area of the triangle is 15.6 Square Units

Option --- (B) RECTANGLE

Hope this helps!

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)