Jacob bought 13 packs of gum to add to the 5 pieces he already had. He then shared all of his pieces of gum with six friends. If Jacob and his six friends each revived 27 pieces of gum, how many were in each pack

Answer:

The z-score = -3.7 and p (-3.7) = 0.00011 or 0.011%

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean of time to finish a test = 60 minutes

Standard deviation of time to finish a test = 10 minutes

Time that a student finishes the test = 23 minutes

2. What is the z-score for the student?

z-score = (Time that a student finishes the test - Mean of time to finish a test)/Standard deviation of time to finish a test

Replacing with the real values:

z-score = (23 -60)/10 = -37/10 = -3.7

z-score = -3.7 and p (-3.7) = 0.00011 or 0.011%

Olivia should cut off an additional 19/16 inches of string.

We have,

Total length to be cut off: 3 3/4 inches

Length already cut off: 2 9/16 inches

First, let's convert the mixed numbers to improper fractions:

3 3/4 = (4 x 3 + 3)/4 = 15/4

2 9/16 = (16 x 2 + 9)/16 = 41/16

Now, subtract the length already cut off from the total length to be cut off:

3 3/4 - 2 9/16

= 15/4 - 41/16

= (60 - 41)/16

= 19/16

Therefore,

Olivia should cut off an additional 19/16 inches of string.

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Olivia needs to cut off another 1 3/16 inches of string. We found this by converting the mixed numbers to improper fractions, finding a common denominator, then subtracting and converting the result back to a mixed number.

In this mathematics problem, Olivia wants to cut 3 3/4 inches from a piece of string but she has already cut off 2 9/16 inches. To find out how much more she should cut, we subtract the amount she has already cut from the total amount she wants to cut.
Here's the process: 3 3/4 - 2 9/16

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Answer:

P1A2= 0.001

P1A'2=0.999

Step-by-step explanation:

Probability = number of ways A occurs/ number of different simple events

P1(A2) =1/1000=0.001

P1A2 = 1-(1/1000)= 999/1000 = 0.999

Probabilities are used to determine the outcome of an event.

The probability of winning is 0.001

Given

[tex]n = 1000[/tex] --- ways

Only one of the 1000 digits is a winning digit.

So, the probability of winning, P(A) is:

[tex]P(A) = \frac{1}{n}[/tex]

So, we have:

[tex]P(A) = \frac{1}{1000}[/tex]

Express as a decimal

[tex]P(A) = 0.001[/tex]

Hence, the probability of winning is 0.001

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Answer:

Perimeter of the model is approximately 1 m.

Step-by-step explanation:

Given:

Scale factor = [tex]\frac{1}{32}[/tex]

Actual base length of the sailboat (b) = 8 m

Actual hypotenuse length of the sailboat (h) = 13 m

Using Pythagoras theorem, we can find the third side of the right angled sailboat. Let the third side be 'l' m. So,

[tex]h^2=b^2+l^2\\\\13^2=8^2+l^2\\\\l^2=169-64\\\\l=\sqrt{105}=10.25\ m[/tex]

Now, actual perimeter of the sailboat = Sum of all the 3 sides

Actual perimeter = 13 m + 8 m + 10.25 m = 31.25 m

Now, we know that,

Scale factor = Model dimensions ÷ Actual dimensions

So, in terms of perimeter,

Scale factor = Model perimeter ÷ Actual perimeter

[tex]\frac{1}{32}=\frac{Model\ perimeter}{31.25}\\\\Model\ perimeter=\frac{31.25}{32}=0.97\approx1\ m[/tex]

So, perimeter of the model is approximately 1 m.

Final answer:

3-day Simple Moving Averages are computed by taking the average of three consecutive closing prices. The process is repeated for each set of three days within the ten-day period, resulting in a smoothed series of averages.

Explanation:

The 3-day simple moving average (SMA) of a series of stock prices is calculated by taking the sum of three consecutive closing prices and dividing by three. For the input series 7.78, 7.90, 8.00, 7.97, 7.86, 7.67, 7.60, 7.65, 7.65, 7.70, we perform the following steps:

For days 1, 2, and 3, the SMA would be (7.78 + 7.90 + 8.00) / 3.

For days 2, 3, and 4, the SMA would be (7.90 + 8.00 + 7.97) / 3.

Continue this process until you calculate the SMA for the last three days in the series.

Here is how they are actually calculated:

Day 1-3: (7.78 + 7.90 + 8.00) / 3 = 7.8933

Day 2-4: (7.90 + 8.00 + 7.97) / 3 = 7.9567

Day 3-5: (8.00 + 7.97 + 7.86) / 3 = 7.9433

Day 4-6: (7.97 + 7.86 + 7.67) / 3 = 7.8333

Day 5-7: (7.86 + 7.67 + 7.60) / 3 = 7.7100

Day 6-8: (7.67 + 7.60 + 7.65) / 3 = 7.6400

Day 7-9: (7.60 + 7.65 + 7.65) / 3 = 7.6333

Day 8-10: (7.65 + 7.65 + 7.70) / 3 = 7.6667

These averages help show the trend by smoothing out fluctuations in the data.

Answer:

The answer to your question is 90 dB

Step-by-step explanation:

Data

I = 10⁻³

I⁰ = 10⁻¹²

Formula

     Loudness = 10log ([tex]\frac{I}{Io}[/tex])

Process

1.- To solve this problem, just substitute the values in the equation and do the operations.

2.- Substitution

     Loudness = 10 log [tex](\frac{10^{-3}}{10^{-12}} )[/tex]

3.- Simplify

      Loudness = 10log (1 x 10⁹)

      Loudness = 10(9)

      Loudness = 90

Answer:

  232°

Step-by-step explanation:

There are a couple of ways to find the desired direction. Perhaps the most straightforward is to add up the coordinates of the travel vectors.

  30∠270° +50∠210° = 30(cos(270°), sin(270°)) +50(cos(210°), sin(210°))

  = (0, -30) +(-43.301, -25) = (-43.301, -55)

Then the angle from port is ...

  arctan(-55/-43.301) ≈ 231.79° . . . . . . . 3rd quadrant angle

The bearing of the ship from port is about 232°.

_____

Comment on the problem statement

The term "knot" is conventionally used to indicate a measure of speed (nautical mile per hour), not distance. It is derived from the use of a knotted rope to estimate speed. Knots on the rope were typically 47 ft 3 inches apart. As a measure of distance 30 knots is about 1417.5 feet.

Answer:

The answer is A B C

I just took the test

Step-by-step explanation:

Answer:

ABC

Step-by-step explanation:

AB is parallel to A'B'.

DO,1/2(x, y) = (one-half x, one-half y)

The distance from A' to the origin is half the

After calculating the initial velocity with which the ball was thrown upwards, the time taken for the ball to reach its peak and fall back to earth was calculated to be approximately 38 seconds.

In order to find out how long the ball will be in the air, we are essentially dealing with an example of free fall in Physics. When the ball reaches its maximum height, its velocity will be zero and it will have spent a certain amount of time t to reach there. But the total time it will be in the air is twice this amount, as it will take the same amount of time to go up and come back down.

Using the second equation of motion, v = u + gt (where v = final velocity, u = initial velocity, g = acceleration due to gravity and t = time), when the ball reaches maximum height, its final velocity (v) is zero. If we rearrange this equation, we get t = (v - u) / -g.

As the problem doesn't state the initial velocity with which the ball is thrown upward, we need to find it first. We can do this by applying the equation of motion: v² = u² + 2gs, where s = displacement. If we set v = 0 at maximum height, the equation becomes u = √(2gs). Given s = 178 m and g = 9.8 m/s², we find u ≈ 186.26 m/s. Substituting these values into our time equation, we get t ≈ 19 seconds for the time to reach maximum height. As mentioned, the ball will take the same time to fall back, hence the total time in air will be around 38 seconds.

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The expression that represents the total cost of the baseball game will be 5t + 2h.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

An expression or formula is a finite collection of signs and is well thus according to context-dependent norms.

A gathering of 5 companions goes to a ball game. Every individual purchases a ticket for the game and 2 hotdogs. Allow t to address the expense of a ticket and h to address the expense of hotdogs.

Then the expression of the total cost is given as,

⇒ 5t + 2h

The expression that represents the total cost of the baseball game will be 5t + 2h.

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Answer:

$1510.32 (Select option closest to this)

Step-by-step explanation:

Given:

-  Siding material cost = $18.50 per square yard

- installation cost = $12.40 per square yard

- width of one side = 22 ft

- height of one side = 10 ft

Find:

- How much should you charge to put siding on the ends of the house

Solution:

- Assuming the the cost of material is also borne by you. Summing the rate of material and installation for both sides for you per square yard:

Total rate for both side = 2*($18.50 per square yard + $12.40 per square yard

 Total rate for both side = $ 61.8 per square yard

- Area covered by a side is:

  Area covered = 10 * 22 = 220 ft^2 * (yard^2 / 9 ft^2) = 24.44 yard^2

- Total amount you will be charging is:

   Total amount = Total rate for both side * Area covered

   Total amount = $ 61.8 per square yard * 24.44 yard^2 = $1510.32

Answer:

Alex can do the job in 60 days alone.

Step-by-step explanation:

Alex and Brandon working together, they can finish the job of cleaning the school in 15 hours. Brandon alone in 20 hours can finish the job.

So, Brandon can complete [tex]\frac{1}{20}[/tex] part of the job in one hour.

Let, Alex alone can finish the same job in x hours.

So, Alex can complete [tex]\frac{1}{x}[/tex] part of the job in one hour.

So, working together they do [tex](\frac{1}{20} + \frac{1}{x}) = \frac{x + 20}{20x}[/tex] part of the whole job in one hour.

Hence, from the conditions given we can write

[tex]\frac{x + 20}{20x} = \frac{1}{15}[/tex]

⇒ 15x + 300 = 20x

⇒ 5x = 300

⇒ x = 60 days.

Therefore, Alex can do the job in 60 days alone. (Answer)

Answer:

The information given is not enough to determine their ages explicitly, so, here their ages are given in terms of Anna's age, which is the best that could be determined.

Anna's age = x years

Robert's age = (x - 11) years

Sara's age = (x - 9) years

David's age = (x - 1) years

Step-by-step explanation:

Let Anna be x years old.

Anna's age = x

Because Anna is 11 years older than Robert, we can say Robert's age is Anna's age minus 11.

Robert = x - 11

But Robert is 2 years younger than Sara, we can say Sara's age is Robert's age plus 2

Sara = (x - 11) + 2

= x - 9

David is 8 years older than Sara, we can say David's age is Sara's age plus 8.

David = (x - 9) + 8

= x - 1

Answer:

Step-by-step explanation:

I'm not quite sure what the question is.

64% + 28% = 92%

100% - 92% = 8%

If 8% = 50

100% = x

8x = 5000

x = 625 pairs of shoes at the beginning

Answer:

The equation for this trend line is N = -2/1 + 110

Step-by-step explanation:

We are able to find this answer through the equation used to find m

[tex]\frac{y2-y1}{x2-x1}[/tex]

We plug in our selected points

[tex]\frac{70-50}{20-30}[/tex]

From this, we get -2/1

Our y intercept is equivalent to 110 due to the point in which it crosses the y-axis

Hope this helps

Answer:

( 1, 7.5 )

Step-by-step explanation:

First I found the midpoint of the G and H coordinates. Then I found the midpoint of that new coordinate and G.

The coordinate of point J is given by the section formula with ratio 1: 3 is (1, 7.5).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.

Segment GH has endpoints at G(-2,9) and H(10,3). Point J lies on GH between G and H such that GJ: GH is 1: 3.

Let the coordinate of the J be (x, y).

We know that the section formula is given as

[tex]\rm (x, y) = ( \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}, \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2})\\\\(x, y) = ( \dfrac{1*10+3(-2)}{1+3}, \dfrac{1*3+ 3*9}{1+3})\\\\(x, y) = ( \dfrac{4}{4}, \dfrac{30}{4})\\\\(x, y) = (1, 7.5)[/tex]

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Answer:

m<BCD is equivalent to 148*

Step-by-step explanation:

We know this due to the inscribed angle always being congruent to the angle that it inscribes. Hope this helps

Answer:

106°

Step-by-step explanation:

m arc BCD=148

∠A=1/2*148=74°

∠BCD=180-74=106°

Answer: the explicit formula is

Tn = 3 + 5(n - 1)

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 3

d = 8 - 3 = 13 - 8 = 18 - 13 = 5

The explicit formula for the arithmetic sequence is

Tn = 3 + 5(n - 1)

Answer: The answer in simplest form is [tex] -6(1/4) [/tex]

Step-by-step explanation:

In Wyatt's method I observed the mixed fraction was converted to simple fraction in the second step.

Therefore Wyatt's solution will be:

[tex] 2/5 * -15(5/8) = 2/5 * -125/8 = -25/4 [/tex]

Distributive property was used in Abigail's method.

The solution would be:

[tex] 2/5 * -15(5/8) = 2/5(-15 -5/8) = 2/5(-15) + 2/5(-5/8) = -6(-1/4) [/tex]

Note: Complete question is contained in the image

Answer:

2/5

Step-by-step explanation:

Answer:

STANDARD FORM PEOPLE Ax + By =C

so

find slope

m=-3

then plug that and one of the two points into the equation

y - y1 = m(x - x1)

y-1= -3(x-6)

y-1=-3x + 18

y + 3x = 19

so your answer is

3x + y = 19

Answer:

The bus left New York city at 5:10pm

Step-by-step explanation:

First, we need to calculate the total number of hours the bus used to travel from New York to Washington.

Total number of hours traveled

= 2 1/3hr + 1 3/4hr + 5/6hr

= 7/3+7/4+5/6

=28+21+10/12

=59/12

= 4 11/12hours

Converting 11/12hours to minutes we will have 11/12×60 = 55minutes

Therefore the bus traveled for 4hours 55minutes.

If the bus arrived in Washington at 10:05 pm and the bus left New York 4hours 55minutes ago, this means that the bus did left New York at (10.05-4.55)pm i.e 5:10pm

4hours past 10:05pm will be 6:05pm

55minutes past 6:05pm will be 5:10pm

This means that the bus left New York city at 5:10pm

A - B = 4

A + B = 64

__________ +

A - B + A + B = 64 + 4

2A = 68

A = 34

B = 34 - 4

B = 30

Answer:

7

Step-by-step explanation:

Regular polygons have the same number of lines of symmetry as they do sides.

Polygons with an even number of sides have a line of symmetry for each pair of opposite vertices, as well as a line of symmetry through midpoints of opposite sides.

Polygons with an odd number of sides have a line of symmetry for each vertex, passing through the midpoint of the opposite side.

A heptagon has 7 vertices, and therefore has 7 lines of symmetry.

Answer:

true

Step-by-step explanation:

it is possible through thorough work out and exercises

and secondly a numbers of diets has to be avoided such starchy foods and junks

Answer:

42 and 63

Step-by-step explanation:

I think you mean the ratio is 2/3 instead of 23

Then the answer is 42/63 = (2 x 21) / ( 3 x 21) = 2/3

Answer:

5.4

Step-by-step explanation:

Surface area of the large 16 in diameter pizza is

[tex]A = \pi(d/2)^2 = \pi8^2 = 64\pi[/tex]

Cost per unit surface area is

[tex]c = \frac{9.6}{64\pi} = \frac{0.15}{\pi}[/tex]

Surface area of the small 12-in diameter pizza is

[tex]a = \pi(12/2)^2 = \pi6^2 = 36\pi[/tex]

So the total cost for that much surface area of pizza is

[tex]ac = 36\pi*\frac{0.15}{\pi} = 5.4[/tex]

Answer:

Conclusion: The proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.

Step-by-step explanation:

To test the claim made by the CEO of a large electric utility company the newspaper must conduct a hypothesis test for one proportion.

Assumption:

The significance level (α) of the test can be assumed to be 5%.

Hypothesis:

[tex]H_{0}:[/tex] The proportion of customers satisfied with the service they receive is 0.80, i.e. [tex]p=0.80[/tex]

[tex]H_{a}:[/tex] The proportion of customers satisfied with the service they receive is different from 0.80, i.e. [tex]p\neq 0.80[/tex]

Decision Rule:

If the p-value of the test is less than the significance level (α) then the null hypothesis may be rejected. But if the p-value  is more than the significance level (α) then we cannot reject the null hypothesis.

Test Statistics:

As the sample size is large, i.e.n = 100 > 30, then according to the central limit theorem sampling distribution of sample proportion will follow the normal distribution.

The test statistic used is:

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

Given:

The p-value of the hypothesis test is computed to be 0.894.

That is:

[tex]p-value=0.894>\alpha =0.05[/tex]

This implies that we fail to reject the null hypothesis at 5% level of significance.

Conclusion:

The null hypothesis was failed to be rejected at 5% level of significance.

Thus, concluding that the proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.

Step-by-step explanation:

The integral is the area under the curve.  When the curve is above the x-axis, the area is positive.  When the curve is below the x-axis, the area is negative.  The integral equals 0, so we want to find the value of b such that the area of the quarter circle is canceled out by the area of the triangle.

Area of the quarter circle is:

A = π/4 r²

A = 9/4 π

Area of the triangle is:

A = ½ bh

9/4 π = ½ (b − 3) (b − 3)

9/2 π = (b − 3)²

b − 3 = 3√(π/2)

b = 3 + 3√(π/2)

b = 6.760

Answer:

The repulsive force is [tex]3.067\times10^{-4}N[/tex].

Step-by-step explanation:

Consider the provided information.

The coulomb's law to calculate the repulsive force: [tex]F=\frac{kQ_1Q_2}{r^2}[/tex]

Where the value of k is 9.00×10⁹ Nm²/C²

Substitute the respective values in the above formula.

[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{[(13 cm)(\frac{1m}{100cm} )]^2}[/tex]

[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{(0.13 m)^2}[/tex]

[tex]F\approx0.0003067N[/tex]

[tex]F=3.067\times10^{-4}N[/tex]

Hence, the repulsive force is [tex]3.067\times10^{-4}N[/tex].

Time required for the pendulum to swing from its position furthest to the right to its position furthest to the left: 1.25 seconds

Step-by-step explanation:

A pendulum is a system consisting of a rod/string connected to a mass which is left free to oscillate back and forth around its equilibrium position, straight vertical.

The period of a pendulum is the time the pendulum takes to complete one full oscillation, that means it is the time the pendulum takes to go from its furthest position on the left to the same position again. It is calculated as

[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]

where L is the length of the pendulum and g the acceleration of gravity.

The figure in this problem represents the position of the pendulum. We observe that the time it takes for the pendulum to do one complete oscillation is 2.5 seconds.

The time it takes for the pendulum to swing from its position furthest to the right to its position furthest to the left is half the period: therefore, it is

[tex]\frac{T}{2}=\frac{2.5}{2}=1.25 s[/tex]

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