Lara asked 20 people how many coins each person had in his or her pockets. She used this data to calculate the measures of central tendency shown below.
• mean: 8.4
• median: 3.5
Which statement about the people Lara surveyed is most likely true?

A. Nobody had more than 12 coins in his or her pockets.

B. Exactly 10 people had more than 8 coins in their pockets.

C. The person who had the most coins in his or her pockets had at least 14 coins.

D. The same number of people had exactly 3 coins in their pockets as had exactly 4 coins in their pockets.

The number that belongs in the green box is 57.8 degrees.

We are given that;

The triangle sides 11 12 20

Now,

The interior angles of a triangle always add up to 180 degrees. To find the interior angles of a triangle whose sides are 11 cm, 12 cm and 20 cm, we can use the law of cosines1.

Let’s call the angle opposite the side of length 11 cm as A, the angle opposite the side of length 12 cm as B, and the angle opposite the side of length 20 cm as C. Using the law of cosines, we can find that:

\(cos(A) = (b^2 + c^2 - a^2) / (2bc) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) = 0.55cos(B) = (a^2 + c^2 - b^2) / (2ac) = (11^2 + 20^2 - 12^2) / (2 * 11 * 20) = 0.6cos© = (a^2 + b^2 - c^2) / (2ab) = (11^2 + 12^2 - 20^2) / (2 * 11 * 12) = -0.45\)

We can then use inverse cosine function to find the angles:

\(A = cos^-1(0.55) ≈ 57.8 degreesB = cos^-1(0.6) ≈ 53.1 degreesC = cos^-1(-0.45) ≈ 129.1 degrees\)

The interior angles of this triangle are approximately 57.8 degrees, 53.1 degrees, and 129.1 degrees.

Therefore, by the angle answer will be 57.8 degrees.

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The 164° and 81° located with the angle x at a point indicates that the size of the angle x is 115°

The angles that are arranged around a point add up to 360°. The angles at a point are the angles which together, produce a rotation of 360°.

The sum of angle at a point can be used to find the measure of the angle x as follows;

The addition of angles at a point = 360°

Therefore; 164° + 81° + x = 360°

Therefore; x = 360° - (164° + 81°) = 115°

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Answer:

you find the slope by using this equation = y2 - y1 / x2 - x1.

For example, if you had two points, (2,4) and (3,6)

2 will be x1 because it's your first x. 3 will be x2 because it's your second x.

So with that pattern, 4 will be y1 and 6 will be your y2.

So the equation will be 6-4 / 3-2. That will equal 2/1 so the slope is 2.

Hope this helped.

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°.

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

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

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

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

\( \boxed{ \bold{z \: = \: 72°}}\)

Answer:

a. y= 16+ 7x

b. y=19+9x

c. y= 10+5x

Step-by-step explanation:

a.) adds 7 each time

b.) adds 9 eah time

c.) adds 5 each time

Answer:

hope it helps you......

Answer:

the last one

Step-by-step explanation:

Answer:

111 miles

Step-by-step explanation:

Youngstown, Prairieville; and Dorchester, in respective order, lie approximately in a straight line.

Total distance from Youngstown to Dorchester = 213 miles.

Youngstown to Prairieville = 102 miles

Find Prairieville to Dorchester.

Distance from Prairieville to Dorchester = Total distance - distance from Youngstown to Prairieville

= 213 miles - 102 miles

= 111 miles

Therefore, distance from Prairieville to Dorchester = 111 miles

Based on the relative frequency table that compares nonfiltered and filtered cigarettes, we can infer that cigarette filters are effective because they reduce larger tar amounts.

Tar (mg)                     Relative Frequency            Relative Frequency  

                                        (nonfiltered)                              (filtered)

6 - 11                                 0/ 25 = 0%                             1 / 25 = 4%

12 - 17                                0/ 25 = 0%                             1 / 25 = 4%

18 - 23                                2/ 25 = 8%                            5 / 25 = 20%

24 - 29                              1/ 25 = 4%                             18 / 25 = 72%

30 - 35                               13/ 25 = 52%                          0 / 25 = 0%

36 - 41                               6/ 25 = 24%                         0 / 25 = 0%

42 - 47                              3 / 25 = 12%                         0 / 25 = 0%

Total                                 25 / 25 = 100%                     25 / 25 = 100%

From the table, we can see that the unfiltered cigarette has higher tar amounts which means that cigarette filters are effective in reducing tar content.

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Using the future value formula, it is found that:

a) You will have $301,355 in the account after 30 years.

b) You will have put $108,000 in the account.

c) You will have earned $193,355 in interest.

The future value formula  is given by:

\(V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right]\)

In which the parameters are described as follows:

Considering the $300 deposits, the interest rate of 6% and the monthly compoundings for 30 years, the values of the parameters are given as follows:

P = 300, r = 0.06/12 = 0.005, n = 12 x 30 = 360.

Hence the balance of the account after 30 years will be given by:

\(V(30) = 300\left[\frac{(1.005)^{360} - 1}{0.005}\right]\)

V(30) = $301,355.

The amount placed into the account is given by:

360 x 300 = $108,000.

The remaining amount is earned in interest, hence:

301355 - 108000 = $193,355.

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Answer:

The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.

Step-by-step explanation:

A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000.

At the null hypothesis, we test if the mean is of at least $1000, that is:

\(H_0: \mu \geq 1000\)

At the alternative hypothesis, we test if the mean is less than $1000, that is:

\(H_1: \mu < 1000\)

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used.

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

1000 is tested at the null hypothesis:

This means that \(\mu = 1000\)

To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245.

This means that \(n = 47, X = 941, s = 245\)

Value of the test statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{941 - 1000}{\frac{245}{\sqrt{47}}}\)

\(t = -1.65\)

P-value of the test and decision:

The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with t = -1.65 and 47 - 1 = 46 df.

Using a t-distribution calculator, the p-value is of 0.053.

The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.

The result of the calculation of the expression is 39.6, to three significant figures.

option B.

Simplification of an algebraic expression or any mathematical expression can be defined as the process of writing an expression in the most efficient and compact form without changing the actual meaning of the expression.

The given expression is;

(6.45) (4.89) + 8.1

The given expression is simplified as follows;

(6.45) (4.89) + 8.1

solve the bracket first;

= ( 6.45 x 4.89) + 8.1

= 31.54 + 8.1

now, do the addition operation;

= 31.54 + 8.1

= 39.64

The original numbers were given in three significant figures, so our final answer must be in 3 significant figures as well.

= 39.6 ( 3 s.g.f)

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Using the simple interest formula it is seen that Mrs Jo saves an amount of $180 when she chooses option B over option A.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

To determine which option is better, we need to compare the total amount of interest paid for each option.

Option A -

The principal amount is $900 and the interest rate is 8%. The term is 5 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.08 × 5

Interest = $360

Total amount paid = Principal + Interest

Total amount paid = $900 + $360

Total amount paid = $1260

Option B -

The principal amount is $900 and the interest rate is 10%. The term is 2 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.10 × 2 = $180

Total amount paid = Principal + Interest

Total amount paid = $900 + $180

Total amount paid = $1080

Therefore, option B is the better option because it has a lower total amount paid by choosing option B.

Mrs. Jo will save -

$1260 - $1080 = $180

Therefore, Mrs. Jo will save $180 by choosing option B instead of option A.

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Answer: The correct formula for the sequence -1, -5, -9, ... is an = -4 + (-1) n - 1). This formula uses the common difference of -4 and the first term of -1 to calculate the value of the nth term in the sequence.

Answer:

v=-7

Step-by-step explanation:

2(v-8)-8v=26

2v-16-8v=26

-6v-16=26

     +16  +16

-6v=42/-6

v=-7

The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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Answer:

1 3/4 cups of wheat flour is in the bowl

Step-by-step explanation:

x + 2/3 = 2 5/12

First, convert the 2/3 to 12ths by multiplying numerator and denominator by 4 = 8/12

Then convert the 2 5/12 to an improper fraction 29/12

x + 8/12 = 29/12

subtract 8/12 from both sides

x = 21/12 = 1 9/12 = 1 3/4

Answer:

Option B: 3:8 is the right answer.

Step-by-step explanation:

Given that:

There are a total of eight circles.

The number of black circles is three.

Ratio is defined as quantitative relationship between two quantities.

As the statement demands ratio of black circles to total number of circles,therefore,

Ratio of black circles to total circles is 3:8

Hence,

Option B: 3:8 is the right answer.

Let's investigate whether two pairs of corresponding angles in two triangles having equal angle measures is necessary and sufficient to prove that the triangles are similar.

Let's first create a random triangle ABC:

From triangle ABC, we have:

m∠ABC = 88 degrees

m∠CAB = 32 degrees

Apply the Triangle Angle Sum to find m∠ACB:

180 - 88 - 32 = 60 degrees

Hence, we have:

m∠ACB = 60 degrees.

Now, for triangle DEF, we have:

m∠DEF = 88 degrees

m∠FDE = 32 degrees

Also, the measure of angle EFD will be:

180 - 88 - 32 = 60 degrees

m∠EFD = 60 degrees

Part C.

We can see the corresponding angles of ∆DEF and ∆ABC are congruent, although the corresponding side lengths of not equal.

Part D.

We have the measures of the correspoding angles:

m∠ABC = m∠DEF = 88 degrees

m∠CAB = m∠FDE= 32 degrees

The angles we did not set in triangle DEF is:

m∠EFD = 60 degrees

Now, the corresponding angle to angle EFD is:

Angle ACB = 60 degrees.

Part E.

With the two angles, fixed, we can see that using the two angles fixed and completing the triangles, both triangles have similar shapes.

Part F. Since the corresponding angles of the triangles are congruent, the corresponding side lengths will be the proportion.

The ratios of the corresponding sides will be equal.

Part G:

Let:

AC = 8

AB = 6

BC = 4

DF = 4

DE = 3

EF = 2

Let's dilate using scale factor = 2

AC = 8 * 2 = 16

Ab = 6 * 2 = 12

BC = 4 * 2 = 8

Now, let's compare the corresponding sides:

We can see that after dilating ABC about the origin, the ratio of the corresponding sides are constant.

This means the corresponding sides of ABC and DEF are still in proportion.

Part H.

Based on their lengths and angle measures, we can say the triangles are Similar triangles.

Similar triangles have corresponding congruent angles and the corresponding sides are in proportion.

Part I.

The sequence of transformation that can be used here is the dilation, rotation, and translation.

Part J.

Both triangles are similar.

Part K.

Yes, knowing two pairs of corresponding angles are equal is enough to know to decide that two triangles are similar.

Answer:

Yes, since log(2) and log(5) both exist as valid values for the logarithm.

didnt check if ur equation is correct though

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

okay i'll keep this in mind

Step-by-step explanation:

The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.

Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.

Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.

Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $30,000*120% = $36,000.

Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.

-Direct labor cost as allocation base:

The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $20,000*120% = $24,000.

Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Direct labor hours as allocation base:

The actual direct labor hours used in job 201 is 400 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.

Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.

-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.

The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.

The applied overhead cost for job 201 is $24*240 hours = $5,760.

Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.

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Integrate:

\(\displaystyle\int_{-2}^3((x+6)-x^2)\,\mathrm dx = \int_{-2}^3(6+x-x^2)\,\mathrm dx\)

\(=\left(6x+\dfrac{x^2}2-\dfrac{x^3}3\right)\bigg|_{-2}^3\)

\(=\left(18+\dfrac92-9\right) - \left(-12+2+\dfrac83\right)\)

\(=\boxed{\dfrac{125}6}\)

Answer: so are you saying that 8+14x because I don’t know what you write so here the answer

Step-by-step explanation: Hope this help :D

Evaluate for x=10

8+(14)(10)

8+(14)(10)

=148

But if you don’t want that then I will guess the answer is C.11

The value of x is 8

Given: 8, 14, x

Average = 10

Then,

(8 + 14 + x) / 3 = 10

Cross product

(8 + 14 + x) = 3 × 10

22 + x = 30

x = 30 - 22

x = 8

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Answer:

The jumping dolphin is approx. 6 meters under sea level

The flying seagull is approx. 8 meters under sea level

The mobula ray is approx. 2 meters under sea level

The clownfish is approx.t 4 meters under sea level

The octopus is approx.  8 meters under sea level

The jumping dolphin: The mobula ray is 9 meters lower than the jumping dolphin.

The flying seagull: The mobula ray is 11 meters lower than the flying seagull.

The octopus: The mobula ray is 11 meters higher than the octopus.

The jumping dolphin: The albatross is 1 meter lower than the jumping dolphin.

The flying seagull: The albatross is 3 meters lower than the flying seagull.

The octopus: The albatross is 13 meters higher than the octopus.

The jumping dolphin: The clownfish is 8 meters lower than the jumping dolphin.

The flying seagull: The clownfish is 10 meters lower than the flying seagull.

The octopus: The clownfish is 6 meters higher than the octopus.

If the new dolphin is above the dolphin in the picture, then its distance from the surface of the ocean is 6 - 3 = 3 meters.

If the new dolphin is below the dolphin in the picture, then its distance from the surface of the ocean is 6 + 3 = 9 meters.

✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧

Answer:

-30

Step-by-step explanation:

2|y|-x^2

=2|-3|-6^2

=6-36

=-30

The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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Answer:

Step-by-step explanation: