Your school is 5 miles west and 2 miles south of your apartment. You bicycle 3 miles east and then 5 miles south from your apartment to a friend's house. Find the distance between your friend's house and your school.

The margin of error for the 90% confidence interval is 3.

To find the margin of error for a 90% confidence interval, we can use the formula:

Margin of Error = (Upper Limit - Lower Limit) / 2

Given the confidence interval (72, 78), where 72 is the lower limit and 78 is the upper limit, we can substitute these values into the formula to calculate the margin of error.

Margin of Error = (78 - 72) / 2

Margin of Error = 6 / 2

Margin of Error = 3

Consequently, the 90% confidence interval's margin of error is 3.

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Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be congruent if all the three angles and three sides of one triangle is equal to the three sides and three angles of the other triangle.

Statement                             Reason

RS ⊥ TS and RV ⊥ TV           Given

∠S = ∠V are right angles      Definition of perpendicular. Since RS ⊥ TS,

                                               hence ∠S = 90° and RV ⊥ TV hence ∠V = 90°

ST ≅ VT                                  Given

RT ≅ RT                                  Reflexive property of congruence

ΔTSR  ≅ ΔTVR                      Hypotenuse leg congruence theorem. For

                                              two right triangles, if the hypotenuse and leg

                                              of one triangle is the same as the hypotenuse

                                              and leg of the second triangle, then the two

                                               triangles are congruent.

RS ≅ RV                                  Definition of congruency.

Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

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Answer:

Below

Step-by-step explanation:

For compounding annually , the formula would be

4x  =  x  ( 1+ .1)^n      x = deposit amount    4x = quadrupled

                    i = decimal interest (.10)      and n = years

  you can divide 'x' out of the equation to get :

4 = (1.1)^n     solve for 'n'  by taking LOG of both sides

log 4 = n log 1.1

log 4/log 1.1 = n = 14.54 years  - ~~ 15 years

Answer: -3

Step-by-step explanation:

-8x - 5y = -1

-8(2) -5y = -1

-16 -5y = -1

-5y = 15

y = -3

Answer:

B or D

Step-by-step explanation:

I would go with D

Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

It is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}\)

\(P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}\)

P = $26,731.23.

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Answer:

(D)

Step-by-step explanation:

Given that Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at least $8.

x represent the number of pounds of lettuce that Kendra buys and y represent the number of pounds of tomatoes that Kendra buys.

We are to select the inequality that represents the situation.

We have

total amount of money that Kendra spends on lettuce is given by

and the total amount of money that she spends on tomatoes is

Therefore, the inequality can be written as

Thus, option (D) is CORRECT.

Answer:

256

Step-by-step explanation:

we have the following:

therefore, the answer is:

Answer:

100

Step-by-step explanation:

You're correct :) good job

Answer:

2:21 pm

Step-by-step explanation:

Finished 4:12

He spent 1 hour and 33

4:12 - 1 hour 33

minus the hour

3:12

minus 33

12-33

2:21pm

Answer:

He would have 48

Step-by-step explanation:

1 set: 8

2 sets: 16

3 sets: 24

4 sets: 32

5 sets: 40

5 sets: 48

OR

{4(8)} + 2(8)

32 + 2(8)

32 + 16

48

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Answers

48

Steps

4+2=6

8 times 6= 48

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer: x = 17

Step-by-step explanation:

The value of h is equals to 2m/3 .

What is cone ?

A cone is a three-dimensional geometric shape that tapers smoothly from a circular base to a pointed apex or vertex.

V = (1/3)πR2H = 2m3 (everything's capital to represent that of the larger cone)

(1/3)πR2(2m) = 2m3

(π/3)R2 = m2

R2 = (3/π)m2

R = m√(3/π)

⇒ D = 2m√(3/π) is the diameter of the base of the larger cone

Now when looking at v = (1/3)πr2h for the smaller cone, we will derive the volume with respect to the height to find the height that yields the optimal volume. Before we can do that, we need to replace r with something in terms of h. You can tell that they have a linear relationship, but it let's first lay down the (height, diameter) coordinate pairs.

We have (h = 0, d = 2m√(3/π)) since the inscribed cone is upside-down compared to the larger one.

And (h = 2m, d = 0)

If you plot these points, they form a line with a slope of -√(3/π) and a d-intercept of 2m√(3/π). Therefore you get a line of d = -√(3/π)h + 2m√(3/π).

We know the radius will always be half of this, to give us: r = (-h/2)√(3/π) + m√(3/π) = (-h/2 + m)√(3/π)

We plug this back into our volume formula:

v = (1/3)π[(-h/2 + m)√(3/π)]2h

v = (1/3)π(-h/2 + m)2√(3/π)2h

v = (-h/2 + m)2h as the constant factors cancel

v = (h2/4 - mh + m2)h

v = h3/4 - mh2 + m2h

Now we take the dv/dh

dv/dh = (3/4)h2 - 2mh + m2

Here, I personally decided to plot this (letting m = 1) just to confirm that the derivative after h = 0 is at first positive, then it passes zero, then it's negative before reaching h = 2 (which is the tallest height possible 2m, m = 1). This is to make sure that the height that gives the optimal volume is at that h-intercept, which it is.

So we just set dv/dh = 0 and solve for h:

0 = (3/4)h2 - 2mh + m2 Here, I suggest we use the quadratic formula

h = [2m ± √(4m2 - 3m2)]/(3/2)

h = (2/3)[2m ± √(m2)]

h = (2/3)(2m ± m)

Try both options:

h = (2/3)(2m + m)

h = (2/3)(3m) = 2m

We know a height of 2m yields a diameter of 0, so this is one is incorrect.

h = (2/3)(2m - m)

h = (2/3)m = 2m/3

Therefore, The value of h is equals to 2m/3 .

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Answer:

answer

A) 11.7²+X.6²

B) 7²+10² 0²

Answer:

a. = 3

b. = 141

c. = -12

Step-by-step explanation:

a.

2a - 3b if a = 2, and b = 1

2(2) - 3(1) = 4 - 1 = 3

b.

6d - w² if d=25 and w = 3

6(25) - 3² = 150 - 9 = 141

c.

8b/p-2 if b = -3 and p = 4

8(-3)/4-2 = -24/2 = -12

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The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.

A linear function containing one dependent and one independent variable.

It can be represented using the equation,

y = mx + c

where m is the slope

It is given in the question that,

Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.

After 4 seconds of driving, she was 70 meters away from the safe zone.

Let, D(t) be the distance to the safe zone (measured in meters) and t be the  time (measured in seconds)

After 4 seconds of driving, she was 70 meters away from the safe zone.

⇒ This means that at t = 4 seconds, D(4) = 70 meters

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative

⇒ m = - 24

y = mx + c

⇒ D(t) = (-24)t + c

Put t = 4,

D(4) = (-24)4 + c

70 = -96 + c ⇒ c = 166

⇒ D(t) = 166 - 24t

Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.

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The percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

The normal distribution is an illustration of a continuous distribution of probabilities in which most data points are grouped in the middle of the range and the remaining ones taper off equally to either extreme. The middle of the range is sometimes referred to as the distribution's mean.

The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed. A normal distribution is perfectly symmetrical on both sides.

Percentage of data points with z=a and b between two supplied data points

Add the a% sign and subtract the table percentile for z=a from the table percentile for z=b.

The percentile for the data table for z=-0.5 is 30.85.

the percdentile is 69.15 for z=0.5.Next, take the two percentiles apart.

69.15-30.85= 38.3%

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Approximately 38.30% of data points in a normal distribution fall between z = -0.5 and z = 0.5.

A special kind of normal distribution called a "standard normal distribution" has a mean () of 0 and a standard deviation () of 1.

When comparing alternative normal distributions with arbitrary mean and standard deviation, the standard normal distribution is frequently used as a reference distribution in statistics and probability theory.

We employ a procedure called standardisation, which entails dividing by the standard deviation and removing the mean from any normal distribution to get a standard normal distribution.

The percentage of data items in a normal distribution that lie between z = -0.5 and z = 0.5 can be found using a standard normal distribution table or a calculator with normal distribution capabilities.

Using a standard normal distribution table, the value for z = -0.5 is 0.3085, and the value for z = 0.5 is 0.6915. Subtracting these values gives:

0.6915 - 0.3085 = 0.3830

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Answer:

wouldnt it be 13? and do you have have ps3

Answer:

x = 6.24

Step-by-step explanation:

x =

Tan32° = OPP/ADJ

Tan32° = x/10

0.624 = x/10

cross-multiply

x = 6.24

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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"This is nonresponse bias because many customers may choose to not fill out the cards"
Not everyone will chose to leave a review when leaving the store, and those that do were probably in some way inconvenienced, and felt inclined to leave one, while the others left and went about their day.

Answer:

original: -5, 1

Final: 2, 1

Here, m∠GHI=72° and m∠LMN=108°. Therefore, option B is the correct answer.

Given that, m∠GHI=6x° and m∠LMN=9x°.

We need to find the measure of each angle.

Supplementary angles are thus a set of angles that complete each other to form 180°. Supplementary angles are those angles that sum up to 180°.

Now, 6x°+9x°=180°

⇒15x°=180°

⇒x°=12°

Thus, m∠GHI=6×12°=72° and m∠LMN=9×12°=108°.

Therefore, option B is the correct answer.

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Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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Answer:

I'm sorry hindi ko po alam