What is 4 less than the quotient of x and 3?

The average speed of the family during their walk  over a time period of 1.35 hours is 1.407 km/hr

Let us say that the distance covered by the family is x

so , according to the formula of average speed

Average speed = total distance covered/total time taken

Hence,

average speed = \(\frac{0.75+1.15}{1.35} km/hr\)

                          = \(\frac{1.9}{1.35} km/hr\)

                          = 1.407 km/hr

therefore, the average speed of the family is 1.407 km/hr

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The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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To find the number of yellow cupcakes that do not have vanilla icing, we need to determine the total number of yellow cupcakes and subtract the number of yellow cupcakes with vanilla icing.

Given that there are 24 cupcakes in total, and 1/4 of them are red velvet, we can calculate the number of yellow cupcakes as follows:

Number of yellow cupcakes = Total cupcakes - Red velvet cupcakes

= 24 - 1/4 * 24

= 24 - 6

= 18

Now, since 2/3 of the yellow cupcakes have vanilla icing, we can find the number of yellow cupcakes with vanilla icing:

Number of yellow cupcakes with vanilla icing = 2/3 * Number of yellow cupcakes

= 2/3 * 18

= 12

Finally, to find the number of yellow cupcakes without vanilla icing, we subtract the number of yellow cupcakes with vanilla icing from the total number of yellow cupcakes:

Number of yellow cupcakes without vanilla icing = Number of yellow cupcakes - Number of yellow cupcakes with vanilla icing

= 18 - 12

= 6

Therefore, there are 6 yellow cupcakes that do not have vanilla icing.

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Divide by 5 both sides

3^x=60/5

3^x=12

Apply log both sides

log(3^x)=log(12)

xlog(3)=log(12)

x=log(12)/log(3)

using a calculator

If both the corresponding angles and sides are congruent and proportional, respectively, you can state that the triangles are similar.

To determine if two triangles are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.

To state if the triangles in each pair are similar, follow these steps:

1. Identify the corresponding angles: Compare the angles of one triangle to the angles of the other triangle. If all the corresponding angles are congruent, then the triangles are similar.

2. Check for proportional sides: Compare the lengths of the corresponding sides of the two triangles. If the ratios of the corresponding sides are equal, then the triangles are similar.

3. If both the corresponding angles and sides are congruent and proportional, respectively, you can state that the triangles are similar.

For example, consider two triangles with angles A, B, and C, and sides a, b, and c. If you find that angle A of one triangle is congruent to angle A of the other triangle, angle B is congruent to angle B, and angle C is congruent to angle C, and the ratios a/b, b/c, and a/c are all equal, then you can conclude that the two triangles are similar.

Remember, similarity is not the same as congruence. Similar triangles have the same shape but can differ in size.

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Answer:

this is my best awnser

Step-by-step explanation:

It represents a linear function and there will be 216 ants after 1 year

Answer:

b

Step-by-step explanation:

Answer:

B) (x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

(a) P(all three flights full) = 0.012 or 1.2%

(b) P(at least one flight not full) = 0.988 or 98.8%

(c) P(Only Atlanta full) = 0.042 or 4.2%

(d) P(Exactly two full) = 0.378 or 37.8%.

(a) The probability that all three flights are full can be calculated by multiplying the probabilities of each individual flight being full since the events are assumed to be mutually independent. Therefore, P(A∩B∩C) = P(A) × P(B) × P(C) = 0.4 × 0.3 × 0.1 = 0.012 or 1.2%.

(b) The probability of at least one flight not being full can be found by calculating the complement of the event that all three flights are full. So, P(at least one flight not full) = 1 - P(A∩B∩C) = 1 - 0.012 = 0.988 or 98.8%.

(c) To find the probability that only the Atlanta flight is full, we need to consider two cases: (i) Atlanta flight is full while New York and Los Angeles flights are not full, and (ii) Atlanta flight is full while New York and Los Angeles flights are full. These two cases are mutually exclusive, so we can sum their probabilities.
P(Only Atlanta full) = P(A'∩B'∩C) + P(A∩B∩C) = (1 - P(A)) × (1 - P(B)) × P(C) + 0.012 = 0.6 × 0.7 × 0.1 + 0.012 = 0.042 or 4.2%.

(d) To calculate the probability that exactly two of the three flights are full, we consider three mutually exclusive cases: (i) New York and Atlanta flights are full while Los Angeles flight is not full, (ii) New York and Los Angeles flights are full while Atlanta flight is not full, and (iii) Atlanta and Los Angeles flights are full while New York flight is not full. We sum the probabilities of these three cases.
P(Exactly two full) = P(A∩B'∩C') + P(A∩B∩C') + P(A'∩B∩C) = P(A) × (1 - P(B)) × (1 - P(C)) + P(A) × P(B) × (1 - P(C)) + (1 - P(A)) × P(B) × P(C) = 0.4 × 0.7 × 0.9 + 0.4 × 0.3 × 0.9 + 0.6 × 0.3 × 0.1 = 0.378 or 37.8%.

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Answer:

Let's denote the GEE score before as X and the GEE score after as Y.Original Data:- Sample size: n = 10

- GEE scores before taking the training session (X): X1, X2, ..., X10

- GEE scores after taking the training session (Y): Y1, Y2, ..., Y10

i. Sample variance of the difference between GEE scores before and after taking the training session:

To calculate the sample variance of the difference, we need to compute the differences (Xi - Yi) for each individual and then calculate the variance of those differences.

Compute the differences: D1 = X1 - Y1, D2 = X2 - Y2, ..., D10 = X10 - Y10

Sample variance of the differences: s^2 = [Σ(Di - D)^2] / (n - 1)

where D is the sample mean of the differences.

ii. 95% confidence interval for the difference between GEE scores before and after taking the training session:

To construct a confidence interval for the difference, we can use the formula

where CI is the confidence interval, D is the sample mean of the differences, t is the t-score corresponding to the desired confidence level and degrees of freedom, s is the sample standard deviation of the differences, and n is the sample size.

Additional Supplementary Data:

If we have additional supplementary data, we need to combine the original and supplementary data to calculate the sample variance and construct the confidence interval.

iii. Sample variance of the difference (with original and supplementary data):

We include the additional supplementary data in the differences calculation and then compute the sample variance using the updated differences.

iv. 95% confidence interval for the difference (with original and supplementary data):

Similarly, we use the updated sample variance and the combined data to calculate the confidence interval.

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The total number of hours Josh worked during the week is 44.7 hours.

We first need to calculate his regular pay by dividing his weekly gross earnings by his hourly rate:

$487.29 / $10.95 = 44.7 hours

Since the company pays time-and-a-half for any hours worked exceeding 40 in one week, we need to determine if Josh worked more than 40 hours during the week. If he did, we'll calculate his overtime pay by multiplying his regular pay by 1.5.

If Josh worked 44.7 hours, then he worked 44.7 - 40 = 4.7 hours of overtime.

His overtime pay would be 4.7 hours * $10.95 * 1.5 = $81.48

His regular pay would be 40 hours * $10.95 = $438.00

So his total weekly pay would be $438.00 + $81.48 = $519.48

The total number of hours Josh worked during the week is 44.7 hours.

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The average speed for the first part of the trip is 60 miles.

Given:

1st leg DATA:

distance = 120 miles ;

rate = x mph ;

time = d/r = 120/x hrs

2nd leg DATA:

distance = 220 miles ;

rate = x-5 mph ;

time = 220/(x-5) hrs

hence the equation we frame is:

Equation:

120/x + 220/(x-5) = 6

120(x-5) + 220x = 6x(x-5)

120x - 600 + 220x = 6x² - 30x

-6x² + 340x + 30x - 600 =0

-6x² + 370x - 600 = 0

-3x² - 185x + 300 = 0

(3x-5)(x-60)

3x = 5 or x-60=0

x = 5/3 or x = 60

hence x-5 = 60-5

= 55 miles per hour.

Hence we get the answer as 60 miles.

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The interval estimate is approximately 0.95 to 1.59. This means that, with a given margin of error, exposure to tears is estimated to lower males' self-rated sexual arousal by 0.95 to 1.59 points.

The interval estimate, based on the information provided, can be calculated by subtracting the margin of error from the observed effect to obtain the lower bound, and adding the margin of error to the observed effect to obtain the upper bound.

Subtracting:

Lower bound = Observed effect - Margin of error

Lower bound = 1.27 - 0.32 = 0.95

Adding:

Upper bound = Observed effect + Margin of error

Upper bound = 1.27 + 0.32 = 1.59

The researchers found that exposure to tears resulted in a decrease in self-rated sexual arousal by an average of 1.27 points. However, it is important to note that this estimate comes with a margin of error of 0.32 points.

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Karen has made 76 calls today to secure donations at the call center.

Let's assume that Karen has made x calls so far today. According to the information given, she has convinced 18% of the people she has called to donate. This means that 18% of x calls have resulted in successful donations, which can be written as 0.18x.

Karen wants to be just over the 25% mark by convincing 12 out of the next 30 people she calls to donate. This means that the total number of successful donations should be slightly more than 25% of the total number of calls made. Representing this mathematically, we have (0.18x + 12)/(x + 30) > 0.25.

Simplifying the inequality, we have 0.18x + 12 > 0.25(x + 30). Solving for x, we find that x > 76.

Therefore, Karen has made 76 calls so far today to secure donations at the call center in order to be just over the 25% mark by convincing 12 out of the next 30 people she calls to donate.

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Answer:

16

Step-by-step explanation:

The number of more students who choose pizza rather than students who choose salad is 16.

It is given that

total number of students=80

It is value per hundred.

number of students who choose salad= 10% of 80=8

number of students who choose Sandwich=20% of 80=16

number of students who choose Hamburger = 15% of 80 = 12

number of students who choose Hot Dog=25% of 80 = 20

number of students who choose Pizza = 30% of 80 = 24

so,

Number of more students who choose pizza rather than students who choose salad  = Number of students who choose pizza - Number of students who choose Salad = 24-8 =16

Therefore,

the number of more students who choose pizza rather than students who choose salad is 16.

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Answer:

Step-by-step explanation:

C the probability that a customer buys a hat given that the customer has bought a sweater.

Answer:

$14

Step-by-step explanation:

After Shanice spent half of her allowance and earned $7, she is left with $14.

This means the remaining of her weekly allowance is $7, This can be derived by subtracting $7 from 15 - $14 - $7 = $7

This means that it is $7 that remains after spending half of her weekly allowance

her weekly allowance = $7 x 2 = $14

The line plot shows the favorite color of the students in the class. Option A, 9 students liked red or blue.

The line plot presents four columns with red, blue, orange, and yellow colors at the bottom. The number of students liking the color is represented by the x variable. The line plot presents five x in the column of red and four x in the column of blue. Therefore, a total number of students liking the color red and blue are option 9.

A line plot or line chart presents a chart along the number line. Line dots are often used in the line chart but variables can be presented by alphabet as well. It presents the frequency of the number of times the variable is presented in the data. If the data is big in numbers, the legend is used to present the variable. For instance, the legend of the line plot is x. Therefore, x = 5 students.

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Answer:

A

Step-by-step explanation:

Answer:

32.50

Step-by-step explanation:

times it all be 5 than you will get your answer

Answer:

$81.25

Step-by-step explanation:

A = l * w

5 (times longer) * 5 (times wider) = 25 (times longer & wider)

25 * cost

25 * $3.25 =

$81.25

\(1-2+3-4+5-\ldots+2019-2020+2021=1+2021+(-2-2020)+3+2019+\ldots+(-1010-1012)+1011=2022-2022+2022-\ldots-2022+1011=1011\)

Answer:

2) 4,2

Step-by-step explanation:

Factor by grouping:

\(x^2-6x+8\\\\x^2-4x-2x+8\\\\x(x-4)-2(x-4)\\\\(x-2)(x-4)\)

Setting the expression equal to 0 and using the Zero Product Property, \(x=2\) and \(x=4\), which are the factors of the original polynomial.

Answer:

The factors are x-2 and x-4.

Step-by-step explanation:

x^2 - 6x + 8

= (x - 2)(x - 4)

It sounds like you may be experiencing a bug with your Alexa device. This is likely due to a software update or miscommunication between the device and the server.

To resolve this issue, you may need to restart your device by unplugging it from the power source and plugging it back in. You can also try clearing the cache of your device. Additionally, you may need to update the software of your device by visiting the Amazon website and downloading the most recent version of the software. If the issue persists, you may need to contact Amazon customer service for further assistance.

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Answer:

(A)Each triangle has two congruent angles: Angle M is congruent to angle O and Angle R is congruent to angle S.

Step-by-step explanation:

In Triangle MNO

\(\angle M = 54.4$ degrees, \angle N = 71.2$ degrees\\\angle M+\angle N+\angle O=180^\circ\\54.4^\circ+71.2^\circ+\angle O=180^\circ\\\angle O=180^\circ-(54.4^\circ+71.2^\circ)=54.4^\circ\)

In Triangle RST

\(\angle R = 54.4$ degrees, \angle T = 71.2$ degrees\\\angle R+\angle T+\angle S=180^\circ\\54.4^\circ+71.2^\circ+\angle S=180^\circ\\\angle S=180^\circ-(54.4^\circ+71.2^\circ)=54.4^\circ\)

Therefore:

Triangle NMO is congruent to triangle TSR; and

Triangle NMO is congruent to triangle TRS

This is because

\(\angle M \cong \angle O =54.4^\circ; and\\ \angle R \cong \angle S =54.4^\circ .\)

The correct option is A.

Answer:

A

Step-by-step explanation:

Just did the test.

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207

finding the percentage of 65 of 330 individuals

65 / 330 * 100 = 19.697% = 0.19697

number of samples, n = 330

standard deviation, σ   is calculated from

= √{(p(1 - p)) / n}

= √{(0.197 * (1 - 19.7)) / 330}

= √{(0.197 * (0.803)) / 330}

= 0.022

Margin of error, E

= Z(0.95) * σ/√(n)

= 0.171 * 0.022/√(330)

= 0.171 * √(0.022²/330)

= 0.000207

= 0.021%

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Answer:

13

Step-by-step explanation:

85 + (180 - 98) = 167

180 - 167 = 13

9514 1404 393

Answer:

Step-by-step explanation:

The midpoint formula is useful here. For midpoint M, we have ...

  M = (C + D)/2

  2M = C + D

  2(10, 10) = (15, s) +(t, 3)

  (20, 20) = (15+t, s+3)

  t = 20 -15 = 5

  s = 20 -3 = 17

__

Check

  (C +D)/2 = ((15, 17) +(5, 3))/2 = (20, 20)/2 = (10, 10) . . . checks OK

Answer:

no hdjsjfjabjsjfbsbajdisjsb

The triangle can be a right triangle

The side lengths are given as:

3, 3 and 3√2

If the triangle is a right triangle, then the following must be true

a^2 = b^2 + c^2

Where a is the longest side.

So, we have:

\((3\sqrt 2)^2 = 3^2 + 3^2\)

Evaluate the expressions

18 = 18

Both sides of the equation are equal

Hence, the triangle can be a right triangle

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