From home, Mary’s work is two thirds along the way to training. Training is 2.5km from work. Mary normally goes to work, then training and then home again. However, today she forgot her shoes. How far will Mary travel in total today if she has to go home before training to get her shoes?

Answer:

  (x +5)

Step-by-step explanation:

The problem statement is telling you that one factor of (x⁴ +5x³ -3x -15) is (x³ -3). It is asking for the other factor. Clearly, you can find the other factor by dividing the polynomial by the given factor.

That is ...

  (x⁴ +5x³ -3x -15) / (x³ -3) = (x +5)

so ...

  (x⁴ +5x³ -3x -15) / (x +5) = (x³ -3)

The divisor of interest is (x +5).

Answer:

(x+5)

The answer is c.

To construct a 95% confidence interval for the population proportion, calculate the sample proportion p' and its complement q', determine the Z-score for 95% confidence, calculate the margin of error using the formula E = Z*sqrt((p'q')/n), and add/subtract E from p' to get the lower and upper bounds.

To construct a 95 percent confidence interval for the population proportion p using the given sample data, we must first calculate the sample proportion (p') and its complement, the estimated proportion of failures (q'). Using the formula p' = x/n, we find that p' = 162/195. Next, we determine q' by calculating q' = 1 - p'.

With the sample proportion and its complement, we can use the standard formula for a confidence interval for a population proportion: p' ± Z*sqrt((p'q')/n), where Z* is the Z-score corresponding to the given degree of confidence. For a 95% confidence level, the Z-score is approximately 1.96.

By substituting the values of p', q', n, and the Z-score into the formula, we calculate the margin of error (E) and then the lower and upper bounds of the 95 percent confidence interval.

Suppose p' is 0.83 and q' is 0.17 for n = 195 and the Z-score for a 95% confidence interval is 1.96. The margin of error (E) would then be 1.96 * sqrt((0.83*0.17)/195), and the confidence interval would be p' ± E, resulting in a specific numerical range which would constitute our 95% confidence interval for the true population proportion.

The 95% confidence interval for the population proportion [tex]\( p \)[/tex] is [tex]\( (0.7783, 0.8833) \)[/tex].

To construct a confidence interval for the population proportion [tex]\( p \),[/tex] we will use the given information: sample size [tex]\( n = 195 \)[/tex], number of successes [tex]\( x = 162 \),[/tex] and a confidence level of 95%.

The formula for the confidence interval for a population proportion [tex]\( p \)[/tex] is:

[tex]\[ \hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]

where:

- [tex]\( \hat{p} \)[/tex] is the sample proportion [tex](\( \frac{x}{n} \)),[/tex]

- [tex]\( z^* \)[/tex] is the critical value from the standard normal distribution corresponding to the desired confidence level.

Calculate the sample proportion [tex]\( \hat{p} \):[/tex]

[tex]\[ \hat{p} = \frac{x}{n} = \frac{162}{195} \][/tex]

[tex]\[ \hat{p} \approx 0.8308 \][/tex]

For a 95% confidence level, the critical value [tex]\( z^* \)[/tex] can be found using the standard normal distribution table or a calculator. It corresponds to the middle 95% of the distribution, which leaves 2.5% in each tail.

The critical value [tex]\( z^* \)[/tex] for a 95% confidence level is approximately 1.96.

Calculate the standard error [tex]\( SE \):[/tex]

[tex]\[ SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ SE = \sqrt{\frac{0.8308 \cdot (1-0.8308)}{195}} \\ SE \approx \sqrt{\frac{0.8308 \cdot 0.1692}{195}} \\ SE \approx \sqrt{\frac{0.1405}{195}} \\ SE \approx \sqrt{0.0007205} \\ SE \approx 0.0268 \][/tex]

Now, we can construct the 95% confidence interval for [tex]\( p \):[/tex]

[tex]\[ \hat{p} \pm z^* \cdot SE \][/tex]

[tex]\[ 0.8308 \pm 1.96 \cdot 0.0268 \][/tex]

Calculate the margin of error:

[tex]\[ 1.96 \cdot 0.0268 \approx 0.0525 \][/tex]

So, the confidence interval is:

[tex]\[ 0.8308 \pm 0.0525 \][/tex]

Finalize the interval: [tex]\[ (0.7783, 0.8833) \][/tex]

The 95% confidence interval for the population proportion [tex]\( p \)[/tex] is approximately [tex]\( (0.7783, 0.8833) \)[/tex]. This means we are 95% confident that the true population proportion [tex]\( p \)[/tex] lies between 0.7783 and 0.8833.

Answer:

x = 16.

Step-by-step explanation:

Given : Transverse line b and parallel line e and f.

To find : What is the value of x.

Solution : We have given Transverse line b and parallel line e and f.

Corresponding angles : When two lines are crossed by another line the angles in matching corners are called corresponding angles.

corresponding angles are always equal.

2x + 18 = 4x - 14.

On subtracting both sides by 4x

2x -4x + 18 = -14.

- 2x + 18 = - 14 .

On subtracting both sides by 18

- 2x = - 14 -18 .

- 2x = - 32 .

On dividing both sides by -2 .

x = 16.

Therefore, x = 16.

Answer:

the value of 2xy if x =3 and y= 2 is 12

Step-by-step explanation:

The speed of 70 miles per hour is approximately equivalent to 1.17 miles per minute. This conversion is done by dividing the speed in miles per hour by 60, the number of minutes in an hour.

To calculate the conversion from miles per hour to miles per minute, you divide the speed in mph by 60, as there are 60 minutes in an hour. So if we are given a speed limit of 70 miles per hour, that would convert to approximately 1.17 miles per minute.

This is calculated as 70 miles per hour ÷ 60 minutes per hour = 1.17 miles per minute

It's important to remember to use the correct conversion factor related to time, in this case that there are 60 minutes in an hour, to ensure the accuracy of the conversion.

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16/7 = 12/y

84/16

84/16 = 5.25

5.25+7 = 12.25

 x = 12.25

The equation that would be used to determine the value of w is expressed as: C. w² + 5w - 300

Area of a rectangle = (length)(width).

Given the following:

Therefore, equation that would be used to find the value of w is:

(w + 5)(w) = 300

w² + 5w = 300

w² + 5w - 300

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Answer:

Given the statement:

Lines a and b are parallel and lines e and f are parallel.

if [tex]m \angle 1 = 89^{\circ}[/tex]

By supplementary angles:

[tex]m\angle 1+ m\angle 2 = 180^{\circ}[/tex]

⇒[tex]89^{\circ}+ m\angle 2 = 180^{\circ}[/tex]

Subtract 89 degree from both sides we have;

[tex]m \angle 2 = 91^{\circ}[/tex]

Since,

m∠4 = m∠5        [Vertically Opposite angles]           .....[1]

m∠4 = m∠3          [Alternate Interior angle]              .....[2]

By [1] and [2] we have;

m∠5  =m∠3                                   ....[3]

Also;

m∠2 = m∠3       [Alternate interior angle]                 ....[4]

by [3] and [4] we have;

m∠5  = m∠2

Substitute the given values we have;

[tex]m \angle 5 = 91^{\circ}[/tex]

Therefore, the measure of [tex]m \angle 5[/tex] is, [tex]91^{\circ}[/tex]

7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.

To determine the amount of chemical to mix with 4 1/5 gallons of water, you need to use the given ratio of 1 3/4 ounces of chemical per gallon of water.

1.)  Convert 4 1/5 gallons to a mixed number:

4 1/5 = 21/5 gallons.

2.)  Multiply the amount of water by the chemical-to-water ratio:

(21/5) gallons * (7/4) ounces = 147/20 ounces.

3.)  Convert 147/20 ounces to a mixed number:

147/20 = 7 7/20 ounces.

Therefore, 7 7/20 ounces of chemical should be mixed with 4 1/5 gallons of water.

Answer: 1800°

Step-by-step explanation: In this problem, we're given that a polygon has 12 sides and we're asked find the sum of the measures of its interior angles.

The formula for finding the sum of the measures of the interior angles of a polygon is 180 (n - 2) where n represents the number of sides.

So here, since our polygon has 12 sides, we can plug a 12 in for the n in our formula and we have 180 (12 - 2) which is our equation.

Simplifying inside the parentheses first, 12 - 2 is 10 so we have 180 (10) which is 1800.

So if a polygon has 12 sides, then the sum of the measures of its interior angles is 1800°.

The correct answer to this is that:

Any irrational number when added to 2 / 5 still produces an irrational number.

For example, if we use π to add to 2/5 or 0.4. As far as we know the decimal digits for π just go on forever and do not have a repeating cycle hence making it an irrational number. Adding a rational number such as 0.4 to the value of π does not really greatly change the value of π. The decimal digits (hundredths place and so on) of the resulting number will still go on forever without a continual repeat.

So 0.4 + π is still irrational.

Answer:

5

Step-by-step explanation:

According the diagram given the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.

Given :

Triangle LNM.

Acccording to the given triangle (attached below):

Therefore, the correct statements are: The hypotenuse is LN; The side opposite [tex]\rm \angle L[/tex] is NM and The side opposite to [tex]\rm \angle N[/tex] is ML.

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In triangle LNM, the side opposite angle L is NM, and the side opposite angle N is ML. The side adjacent to angle L is NM, and the side adjacent to angle N is ML. The hypotenuse of triangle LNM is LN, not NM.

In triangle LNM, the side opposite angle L is NM, so the statement "The side opposite ∠L is NM" is true.

In triangle LNM, the side opposite angle N is ML, so the statement "The side opposite ∠N is ML" is true.

The hypotenuse of triangle LNM is LN, not NM, so the statement "The hypotenuse is NM" is false.

The side adjacent to angle L is NM, so the statement "The side adjacent ∠L is NM" is true.

The side adjacent to angle N is ML, so the statement "The side adjacent ∠N is ML" is true.

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To prove that there are no integers m and n that satisfy 2m + 4n = 7, we can assume the opposite and show that it leads to a contradiction. We can rearrange the equation and analyze the parity of the terms to prove there are no integer solutions.

To prove that there does not exist integers m and n such that 2m + 4n = 7, we can start by assuming that such integers do exist. Let's suppose m and n are integers that satisfy the equation.

Rearranging the equation, we have 2m = 7 - 4n. This means that 2m is an even number and 7 - 4n is an odd number. However, there is no way for an even number and an odd number to be equal. Therefore, our assumption was incorrect, and there are no integers m and n that satisfy the equation 2m + 4n = 7.

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