Pran ran 29 miles less than Robin last week. Pran ran 19 miles. How many
miles did Robin run?

The algebraic expression for the sentence in this problem is given as follows:

n - (x + 8).

The sentence in this problem is given as follows:

"A number n minus the sum of the number and eight".

The sum of an unknown number x and eight is given as follows:

x + 8.

The subtraction of the number n by the expression is given as follows:

n - (x + 8).

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The amount that they have altogether is $ 76.8.

To convert mixed fractions to improper fractions, multiply the denominator with the whole number and add the numerator.  

For example,

1 (1/2) =  [ 2×1 + 1] /2 = 3/2

2 (2/5) = [ 5×2 + 2] /5 = 12/5    

Here we have

Andreas has $18

Bonnie has 1 2/3 times as much as Andreas.

Here 1 2/3 is a mixed fraction we need to convert to an improper fractions

=>  1 2/3 = (3+2)/3 = 5/3

=> The amount that Bonnie has = 5/3 of (18)

= \(\frac{5}{3} \times 18\) = 5 × 6 = $ 30

Cheryl has 1  3/5 times as much as Bonnie  

=> 1 3/5 = (5 + 3)/5 = 8/5

=> The amount that Cheryl has = 8/5 of 18

=> \(\frac{8}{5} \times 18\) = $ 28.8  

By the above calculations, they all together have

=> $ 18 + $ 30 + $ 28.8 = $ 76.8

Therefore,

The amount that they have altogether is $ 76.8

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Answer:

Answer:

A first of all because the sample involves only rock cods that voluntarily get hooked to the fishing rod, this is a major source of bias as the sample does not represent the whole general population.

Rather adopt stratified sampling stratified basing on Geographical location can be suggested for this study.

II. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias

Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study

To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted

Iii. this study is using convenient samples. and the effect of head ache medicine may be affected by other medicines too so the headache medicine cannot be the only reason for painrelief so it is better to sample rando amongst patients with headache

Answer:

One-third of the volume

Step-by-step explanation:

Volume of cylinder = πr²h

Volume of cone = (1/3)πr²h

Answer:n the metric system, "milli" means 1/1,000 and "kilo" means 1,000. This means that a milligram is 1/1,000 of a gram, and a kilogram is 1,000 grams. So a kilogram is much heavier than a milligram; in fact, a kilogra

Step-by-step explanation:

Answer:

44.59 divided by 5.25= 8.49

Hope this helps!!

Answer:

44.5÷56 that how you answer

Answer:

(3x+14°) + (7x-4)° = 180°

=> 10x + 10 = 180

=> 10x = 180 – 10

=> x = 170/10

=> x = 17

The value of x is 17

Answer:

Step-by-step explanation

p - the price of pizza

c- the price of a bottle of coke

p = c+3.2

3p + c=19.4

3* (c+3.2)+c=19.4

3*c+3*3.2+c=19.4

3c+c+9.6=19.4

4c+9.6=19.4

-9.6 -9.6

4c=9.8

:4. :4

c=2.45

p=2.45+3.2=5.65

verify : 3*5.65+2.45=16.95+2.45=19.40

Answer:

B is the answer

Step-by-step explanation:

For this case we have two points given:

(-4, -4) and (-4,4)

The third vertex for this case would be:

(4,-4)

And then the resulting base would be:

d= 4+4 = 8

correct answer:

8 units

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer: The answer is C

Step-by-step explanation:

Answer:

0.167

Step-by-step explanation:

the question says we won exactly twice, so the probability of winning on two consecutive days can be calculated as:

total number of 2 consecutive days(11) /total ways of picking 2 days out of 12 days (12C2)

12C2 = 66

11/66

= 1/6

= 0.167

so the probability of winning on two executive days is equal to 0.167

f(-5) = 15 (A)

f(x) = - 2x + 5

replace x = - 5

f(-5) = -2(-5) + 5

(-)(-) = +

f(-5) = 10 + 5

f(-5) = 15 (A)

f(-5) = -2(-5) + 5

(-)(-) = +

f(-5) = 10 + 5

f(-5) = 15 (A)

Answer:

Step-by-step explanation:

The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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If a plot of the residuals shows a curved pattern, it indicates that a straight line is not a good model for the data. This does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve.

When a least-squares regression line is fit to a set of data, it is used to determine the linear relationship between two variables. If a plot of the residuals (the difference between the observed values and the predicted values from the regression line) shows a curved pattern, it indicates that a straight line is not a good model for the data. This could mean that there is a nonlinear relationship between the two variables or that the data contains outliers that are not accounted for by the regression line. However, it does not necessarily mean that the correlation between the two variables must be 0 or positive, as the regression line might still be a good model for the data depending on the extent of the curve. To determine if the regression line is an accurate model for the data, it is important to visually inspect the plot of the residuals and assess whether the pattern is random or systematic. If the pattern is random, it indicates that the regression line is a good model for the data. If the pattern is systematic, it indicates that the regression line is not a good model for the data and alternative models should be considered.

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Answer:  60

-----------------

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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You have the maximum diameter, so with it you finde tghe maximum area

From the graph we can conclude it is an injective function or a one-to-one function, so, every element of the function's codomain is the image of at most one element of its domain.

Therefore, the answer is:

f(x) has an inverse function, because it's graph passes the horizontal line test ( since it is injective)

The solution to the triangle is: a ≈ 22.4, b = 4 , c ≈ 77.2 ,A = 27° ,B ≈ 42.5°

C ≈ 110.5°  we got the answer by using law of sine

what is  law of sine?

The Law of Sines, also known as the Sine Rule, is a mathematical formula used in trigonometry to relate the sides and angles of a non-right-angled triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

In the given question,

Using the law of sines and the fact that the angles of a triangle sum up to 180 degrees, we can solve for the missing parts of the triangle:

sin(A)/a = sin(B)/b = sin(C)/c

sin(27)/a = sin(B)/42 = sin(C)/72

We can use the first equation to solve for a:

a = b(sin(A)/sin(B)) = 42(sin(27)/sin(B)) ≈ 22.4161

Next, we can use the second equation to solve for sin(B):

sin(B) = b(sin(A)/a) = 42(sin(27)/a) ≈ 0.6822

Taking the inverse sine, we find that B ≈ 42.4827 degrees.

Now we can use the fact that the angles of a triangle sum up to 180 degrees to solve for C:

C = 180 - A - B ≈ 110.5173 degrees.

Finally, we can use the law of sines again to solve for the remaining side, c:

c = a(sin(C)/sin(A)) = 22.4161(sin(110.5173)/sin(27)) ≈ 77.2352

Therefore, the solution to the triangle is:

a ≈ 22.4

b = 42

c ≈ 77.2

A = 27°

B ≈ 42.5°

C ≈ 110.5°

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Answer:5 years is 650 10 years is 1300

Step-by-step explanation:

f EB = 6.2, CD = 3.3, and ED= 6.2, then the value of B is 6.6.

An isosceles triangle is a type of triangle with two sides of equal  length. Two opposite angles of an isosceles triangle with equal sides are equal in size. In geometry, a triangle is a three-sided polygon that is classified into three categories based on its sides, for example:

Properties of an isosceles triangle

Therefore,

EB = 6.2

ED = 6.2

So EB=ED

ΔEBD is  isosceles triangle and ∠BCE is right angle

so C is middle point of BD

Hence, BD = 2CD

                  = 2X 3.3

                  = 6.6

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(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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The force in the rod when the temperature is 150 °F is 718.72 pounds-force.

Let suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force (\(F\)), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.

Given simmetry considerations, we derive an expression for the spring force (\(F\)), in pounds-force,  as a sum of mechanical and thermal effects by principle of superposition:

\(F = k\cdot (\Delta x + 0.5\cdot \Delta l)\)   (1)

Where:

The rod elongation is described by the following thermal dilatation formula:

\(\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})\)   (2)

Where:

If we know \(k = 1000\,\frac{lb}{in}\), \(\Delta x = 0.7\,in\), \(\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}\), \(L_{o} = 48\,in\), \(T_{o} = 30\,^{\circ}F\) and \(T_{f} = 150\,^{\circ}F\), then the force in the rod at final temperature is:

\(F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right]\)

\(F = 718.72\,lbf\)

The force in the rod when the temperature is 150 °F is 718.72 pounds-force. \(\blacksquare\)

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The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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The probability of getting two correct answers will be 0.0625.

The probability of getting two correct answers will be:

Probability of getting the correct answer will be:

= 1/4 = 0.25

The probability of getting two correct answers will be:

= 0.25 × 0.25

= 0.0625

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