A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes. How much commission does she earn for selling each suit and each pair of shoes? Solve by substitution.

After subtracting the principal and two counselors from the 83-person room capacity, dividing the remaining space by two shows that a maximum of 40 student-athletes can attend the meeting with their parents.

The maximum number of student-athletes that can attend a meeting in a conference room that has a capacity of 83 people while also accounting for their accompanying parents. Given that the principal and two counselors will also be in attendance, we need to subtract three from the total capacity to accommodate them, leaving us with 80 seats available. Since each student will bring a parent, we divide the remaining seats by two. Therefore, the maximum number of student-athletes that can attend each meeting is 40 students, with each accompanied by a parent.

Answer:

Step-by-step explanation:

To get the amount of paper required to cover the box, we find the area of the box. The dimensions of the box are as follows:length=21/2 ftwidth=11/2 ftheight=4 ftArea of the box is given by the formula:SA=2lw+2lh+2hwSA=2(21/2×11/2)+2(21/2×4)+2(11/2×4)SA=2(231/4)+2(42)+2(11/2×4)SA=115.5+84+44SA=243.5 ft²Stella will need 243.5 ft²

Final answer:

Jenya has 2 $1 bills, 4 $5 bills, and 6 $10 bills, which all adds up to her total of $82.

Explanation:

Jenya has a combination of $1, $5, and $10 bills in her wallet adding up to $82. To find out how many of each she has, we need to set up a system of equations based on the information provided:

Now we can form two equations:

Simplifying the equations gives us:

Further simplification and solving for x yields:

This means Jenya has 2 $1 bills, 2*2 = 4 $5 bills, and 2*2 + 2 = 6 $10 bills.

Answer:

368

Step-by-step explanation:

The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).

This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).

To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).

By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.

Therefore, the limit of the sequence as n tends to infinity is 0.

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Answer:

[tex](x+60)=y[/tex] and [tex]1.05x+0.90(60)=1.00y[/tex]

Step-by-step explanation:

Let

x-----> pounds of hamburger worth [tex]\$1.05[/tex] per pound

we know that

The equation that represent the situation is

[tex]1.05x+0.90(60)=1.00(x+60)[/tex] ------> equation A

Let

[tex]y=(x+60)[/tex] -----> equation B

substitute equation B in equation A

[tex]1.05x+0.90(60)=1.00y[/tex]

The better deal is the loan with the 600% APR.

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum).

Given that, Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.

There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.

600/365 = 1.643

The daily interest rate of the loan will be 1.643%.

The following equation is used to find the total interest payment:

[tex]A = P(1+\frac{r}{365} )^{t} -P[/tex]

A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.

Plug in your values into the equation.

P = 380 r = 1.643 and t = 7

380(1+1.643/365)^7 - 380 = 12.136

Rounded to the nearest hundredths value, the total interest paid will be $12.14.

Compare the total amounts paid for both loans.

$12.14 < $45

Hence, The better deal is the loan with the 600% APR.

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The correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.

To convert 5.5 pounds to ounces, we need to use the conversion factor that relates pounds to ounces. We know that there are 16 ounces in 1 pound. Therefore, to convert pounds to ounces, we need to multiply the number of pounds by 16.

The appropriate ratio to use for this conversion would be option A : 16 ounces per 1  pound, or [tex]\( \frac{16 \text{ ounces}}{1 \text{ pound}} \).[/tex]

This ratio tells us that for every 1 pound, there are 16 ounces. Using this ratio, we can convert pounds to ounces by multiplying the number of pounds by 16.

Therefore, to convert  5.5  pounds to ounces, we would use the following calculation:

[tex]\[ 5.5 \text{ pounds} \times \frac{16 \text{ ounces}}{1 \text{ pound}} = 88 \text{ ounces} \][/tex]

So, the correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.

The complete question is:

Choose the ratio that vou would use to convert 5.5 pounds to ounces Remember that there are 16 ounces in 1 pound.

A. 88 ounces/1 pound

B. 16 ounces/1 pound

C. 1 pound/16 ounces

D. 1 ounce/88 pounds

A circle with an area of 254.47 square inches is given.

We have to determine the circumference of the circle.

Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.

[tex] \Pi r^{2}=254.47 [/tex]

[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]

[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]

[tex] r^{2}=80.97 [/tex]

[tex] r=\sqrt{80.97} [/tex]

r = 8.99

Therefore, r = 9 inches (approximately)

Circumference of a circle = [tex] 2\Pi r [/tex]

= [tex] 2 \times \frac{22}{7} \times 9 [/tex]

= 56.57 inches

= 56.6 inches (approximately).

Therefore, the circumference of the circle is 56.6 inches.

B. 22 : 2. 22 : 2 is equivalent to 11 : 1.

C. 55 : 5. 55 : 5 is equivalent to 11 : 1.

E. 110 : 10. 110 : 10 is equivalent to 11 : 1.

In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective common multiple (numerator or denominator):

For 22 : 2, we would divide all through by 11;

22 : 2 = 11 : 1

For 55 : 5, we would divide all through by 5;

55 : 5 = 11 : 1

For 110 : 10, we would divide all through by 10;

110 : 10 = 11 : 1

Complete Question:

Select three ratios that are equivalent to 11 : 1.

Choose 3 answers:

1 :11

22 : 2

55 : 5

9 : 99

110 : 10

Answer:

30°C

Step-by-step explanation:

The following expression can be used to convert Farenheit degrees (°F) to Celsius degrees (°C).

°C = 5 . (°F - 32) / 9

If the temperature in Centerville is 86°F, we can replace this value in the previous expression to find its value in the Celsius scale.

°C = 5 . (°F - 32) / 9

°C = 5 . (86 - 32) / 9

°C = 5 . (54) / 9

°C = 270 / 9

°C = 30°C

Answer:

C

Step-by-step explanation:

If youre doing the test ;)

Using the correlation coefficient, mean test scores, and mean GPA, we can predict that a freshman with a GPA of 2.9 would have an approximate combined test score of 1260.71.

Since we know the mean combined application test score is 1225, the standard deviation is 120, the mean GPA is 2.64, and the standard deviation for GPA is 0.58, we can use this information to predict scores.

First, we will use the correlation coefficient (r), which in this case is 0.44, to calculate the slope (b) of the best-fit line. The slope (b) is calculated by dividing the product of the standard deviations by the mean test score, and then multiplying by the correlation coefficient.

b = r * (Sy / Sx)
b = 0.44 * (0.58 / 120)
b = 0.44 * 0.0048333
b ≈ 0.0021

Next, we need to find the intercept (a) of the best-fit line, which can be calculated using the means of the two variables (mean test score and mean GPA).

a = mean of GPA - b * mean of test scores
a = 2.64 - 0.0021 * 1225
a ≈ 0.10

With the slope (b) and the intercept (a), we can now predict the combined test score for a student with a GPA of 2.9.

Predicted Test Score = a + b * GPA
Predicted Test Score = 0.10 + 0.0021 * 2.9
Predicted Test Score ≈ 1260.71

Thus, for a freshman with a first-semester GPA of 2.9, the predicted combined test score would be approximately 1260.71.

Answer:

b

Step-by-step explanation:

To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.

To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps: