Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran charged $450 and paid $150 of that in his billing cycle. Which expression will find the amount of interest Tran will be charged after the first month?

Answer:

7 software packages

Step-by-step explanation:

Given,

Signing amount = $ 225,

Additional amount for each software package = $ 25

Thus, the total amount for x software packages = signing amount + additional amount for x packages

= 225 + 25x

If total amount ≥ $ 400

225 + 25x ≥ 400

25x ≥ 400 - 225

25x ≥ 175

[tex]\implies x \geq \frac{175}{25}=7[/tex]

Hence, the minimum number of software packages that she must sell would be 7.

Final answer:

Alison needs to sell at least 7 software packages this week on top of her base salary to earn at least $400.

Explanation:

Alison wants to earn at least $400 this week by selling software packages. She earns a base $225 per week plus $25 for each software package sold. To determine the minimum number of software packages Alison must sell, we subtract her base salary from her desired earnings for the week:

Required earnings (>=$400) - Base salary ($225) = Sales required from software packages

$400 - $225 = $175

Now divide the sales required from software packages by the amount earned per package:

$175 / $25 = 7

Therefore, Alison needs to sell at least 7 software packages to meet her goal of $400

Answer:

$1000

Step-by-step explanation:

quarterly is 1/4

12/4 is 3

so every 3 months you pay $250

annually is the whole year so 250*4

Answer:

1000

Step-by-step explanation:

Answer:

Step-by-step explanation:

232/2=116

so 116,116 has maximum product

Keisha bought 15 science fiction novels.

Step-by-step explanation:

Given,

Number of novels bought by Keisha = 24

Mystery novels = 3/8 of total novels

Mystery novels = [tex]\frac{3}{8}*24=\frac{72}{8}[/tex]

Mystery novels = 9

Let,

x represent the number of science fiction novels.

Mystery novels + Science fiction novels = Total novels

[tex]9+x=24\\x=24-9\\x=15[/tex]

Keisha bought 15 science fiction novels.

Keywords: fraction, addition

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Answer:

w=1.5t+12

Step-by-step explanation:

that's the right answer

The equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t

We can make use of the given data.

The infant gained weight at a pace of 1.5 pounds each month, reaching 16 pounds at the end of 4 months. With this knowledge, the equation can be written as follows:

W(t) = Initial weight + (Rate of weight gain per month) * (Number of months)

W(t) = 16 + (1.5 * t)

So, the equation for the function W(t) representing the weight of the newborn baby t months after birth is W(t) = 16 + 1.5t

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To find the number of students who played soccer but not baseball or tennis, we need to analyze the given information and use the formula A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C). Substituting the given values, we find that 32 students played soccer but not baseball or tennis.

To determine how many students played soccer but not baseball or tennis, we need to analyze the information given in the Venn diagram provided. Let's label the regions of the Venn diagram:

A represents the set of students who played soccer.

B represents the set of students who played baseball.

C represents the set of students who played tennis.

From the given information, we know that:

To find the number of students who played soccer but not baseball or tennis, we need to calculate the value of A without the intersection of the other sets. Using the formula:

A = (A ∩ B) + (A ∩ C) + (A - A ∩ B ∩ C),

we can substitute the given values:

A = 4 + 3 + (25 - 1)

A = 32

Therefore, 32 students played soccer but not baseball or tennis.

Answer:

a. Discrete

b. Discrete

c. Not a random variable

d. Continuous

e. Discrete

f. Continuous

Step-by-step explanation:

The discrete random variable is countable while continuous random variable is measurable.

a. The number of fish caught is a discrete random variable because these are countable.

b. The number of text book authors are also countable so it is a discrete random variable.

c. The political party affiliation of adults is not a random variable because the political party affiliation depends on person's interest and it cannot be randomly assigned to person. Also random variable is the numerical outcome of random experiment whereas political affiliation is the categorical variable that results in non numerical responses such as Democrat, Republicans etc.

d. The square footage of a house is measurable and so it is a continuous random variable.    

e. The number of free dash throw attempts are countable so it is a discrete random variable

f. The weight of Upper T dash bone steak is measurable and so it is a continuous random variable.

The number of fish caught during a fishing tournament is a discrete random variable, while the square footage of a house is a continuous random variable. The other examples are not random variables.

a. The number of fish caught during a fishing tournament is a discrete random variable. The values of the variable are obtained by counting the number of fish caught.

b. The number of textbook authors now sitting at a computer is not a random variable. It is a fixed number and does not vary.

c. The political party affiliation of adults in the United States is not a random variable. It can be determined by surveying adults or analyzing existing data.

d. The square footage of a house is a continuous random variable. The values of the variable are obtained by measuring the size of the house.

e. The number of free-throw attempts before the first shot is made is a discrete random variable. The values of the variable are obtained by counting the number of attempts.

f. The weight of an Upper T-bone steak is a continuous random variable. The values of the variable are obtained by measuring the weight of the steak.

The sum of the given series [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex]  is 130.

Step-by-step explanation:

The sum of series need to be found is [tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] .

Apply sum rule,

[tex]\sum x_n+y_n=\sum x_n+\sum y_n[/tex]

[tex]\sum _{a=1}^{10}\:\left(2a+2\right).[/tex] =[tex]\sum 2a+\sum 2[/tex].

Apply the constant multiplication rule,

[tex]\sum c\cdot a_n=c\cdot \sum a_n[/tex] .

[tex]\sum 2\cdot a=2\cdot \sum a[/tex].

[tex]\sum _{a=1}^{10}n[/tex] = 1+2+3+4+5+6+7+8+9+10.

[tex]\sum _{a=1}^{10}n[/tex] = 55.

[tex]\sum 2\cdot a[/tex]=2×55.

[tex]\sum 2\cdot a [/tex]=110.

To find [tex]\sum _{a=1}^{10}2[/tex],

Apply sum rule, [tex]\sum _{k=1}^n\:a\:=\:a\cdot n[/tex] ,

[tex]\sum _{a=1}^{10}2[/tex] =2×10.

[tex]\sum _{a=1}^{10}2[/tex] = 20.

[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] = 110+20.

[tex]\sum _{a=1}^{10}\:\left(2a+2\right)[/tex] =130.

Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

[tex]\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}[/tex]

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

In the right triangle XYZ

Find the tangent of angle X

[tex]tan(X)=\frac{YZ}{XZ}[/tex] ---> opposite side angle X divided by adjacent side angle X

substitute the given values

[tex]tan(X)=\frac{9}{12}[/tex]

Simplify

[tex]tan(X)=\frac{3}{4}[/tex]

Remember that

∠Q≅∠X

so

[tex]tan(Q)=tan(X)[/tex]

therefore

[tex]tan(Q)=\frac{3}{4}[/tex] ---->Three-fourths

Answer:

Step-by-step explanation:

The initial height of the snowman is 85 cm. snowman melts and loses 3cm in height for every hour the sun shine and the sun shine only 6.5 hours a day. This means that the height that the snowman loses in a day would be

3 × 6.5 = 19.5 cm

Therefore, in a day, the snowman loses 19.5 cm in height. Therefore,

the number of days that it will take the snowman to melt would be

85/19.5 = 4.36 days

4 hours ago = 1,000

2 hours ago = 2,000

Now = 4,000

In 2 hours = 8,000

In 4 hours = 16,000

In 6 hours = 32,000

In 8 hours = 64,000

In 10 hours = 128,000

In 12 hours = 256,000

The answer would be D. 12 hours.

Answer: 84

Step-by-step explanation:

K=28

O=2K=2*28=56

O+K=56+28=84

The total number of boxes that Kyle and Omar sold is 84.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

Multiplication = to multiply any two or more numbers or variables called multiplication.

As per the given,

Kyle sold 28 boxes of fruit.

Omar sold 2 times,

28 x 2 = 56 boxes

Total boxes = 56 + 28 = 84 boxes

Hence "The total number of boxes that Kyle and Omar sold is 84".

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Answer:

Median = 45

Step-by-step explanation:

We are given the following data set:

21, 23, 76, 47, 55, 135, 45, 30, 17

Median is the number that divides the data into two equal parts.

Formula:

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

Sorted data:

17, 21, 23, 30, 45, 47, 55, 76, 135

Sample size = 9, which is odd

Median =

[tex]\dfrac{9+1}{2}^{th}\text{ term} = \dfrac{10}{2}^{th}\text{ term} = 5^{th}\text{ term}\\\\= 45[/tex]

The median of given set of numbers is 45.

Answer:

n=7

Step-by-step explanation:

let n be number of sides.

(n-2)180=900

n-2=900/180=5

n=5+2=7

Answer:

B. 33

Step-by-step explanation:

Let the number of Fuji trees be F, the number of gala be G and the total number of trees be x.

10% cross pollinated, this means 1/10 cross pollinated or 0.1x

Number of Fuji plus cross pollinated is 187.

And cross pollinated is 3/4 of total or let’s say 0.75 of total which is 0.75x

Now, adding 0.1x + 0.75x would equal 187

0.85x = 187

x = 187/0.85 = 220 trees

The total number of trees is 220.

The number of gala trees is thus 220 - 187 = 33 trees

Answer:

Each of the three friends will get one-sixth of the Thomas's enitre marble collection.

Step-by-step explanation:

Fraction of the total marble collection brought by Thomas = [tex]\frac{1}{2}[/tex]

Now, Thomas divides these marbles equally among his three friends. So, each of the three friends will get one-third of the total marble collection brought by Thomas.

Fraction of total marble collection got by each friend = [tex]\frac{1}{3} \;of\;fraction\;of\;total\;marble\;collection\;brought\;by\;Thomas[/tex]

= [tex]\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}[/tex]

∴ Each of the three friends of Thomas will get one-sixth of his entire collection of marbles.

Answer:

C. 2.0 < t < 2.5

Step-by-step explanation:

Diameter of track (D) = 2 miles, Average rate (A) = 3 miles per hour

A = distance/ time

time (t) = distance/A

distance around the track (circumference) = πD = 3.142 × 2 miles = 6.284 miles

t = 6.284miles/3miles/hour = 2.1 hour

Therefore, 2.0 < t < 2.5

Answer:

Option C. Residual

Step-by-step explanation:

Residuals are defined as:

Thus,

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residuals.

Option C. Residual

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the residual.

The following information should be considered:

Therefore we can conclude that option c is correct.

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Answer:

DE=10

Step-by-step explanation:

Given that in triangle ABC, $BC = 20 \sqrt{3}$ and $\angle C = 30^\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$,

To find length of DE

Please refer to the attachment for solution

Since perpendicular bisector we have DC = 1/2 BC = 10 sqrt 3

Using right triangle CDE, we get DE = 10

Final answer:

When a positive integer x, which leaves a remainder of 5 when divided by 9, is multiplied by 3, the remainder when 3x is divided by 9 is 6.

Explanation:

When the positive integer x is divided by 9, the remainder is 5. To determine the remainder when 3x is divided by 9, we should remember that when two positive numbers multiply, the result has a positive sign. So multiplying x by 3, we get 3x. The initial information tells us that x = 9n + 5 for some integer n. Thus, 3x equals 3(9n + 5), which simplifies to 27n + 15. This expression can be further broken down as 27n + 9 + 6, which is the same as 9(3n + 1) + 6. Therefore, when 3x is divided by 9, it is the same as dividing this expression by 9, which leaves us with a remainder of 6. Hence, the remainder when 3x is divided by 9 is 6.

Answer:

a ) P₈  =  40320

b) P = 576

c) P =   1440

d) P =  24

Step-by-step explanation:

a )  8 people sitting in a row without restrictions

simple  Total ways  =  P₈  =  8!

P₈  =  8*7*6*5*4*3*2*1

P₈  =  40320

b) There are 4 men and 4 women  and no two men or 2 women can sit next to each other

Let  letters e women  and numbers  be men we have something like this

1  a  2  b  3  c  4  d

So we have the permutations of the four digits (men)

P₄  =  4!  

P₄  =  4*3*2*1   =  24

And the permutations of the 4 women too  equal to 24

Then total ways of sitting in a row in this case is

P = 24*24  = 576

c) There are 5 men and they have to sit next to each other

In this case we have 2 groups:  

Group 1    5 men                        Group  2    3  women

We have two groups and the ways are

group men first                group of women second         1  way

group of women first       group of  men second             2  way

Permutations within men group

P₅  =  5!    =  5*4*3*2*1    

P₅  =   120

Permutations within the women group

P₃  = 3!     =  3*2*1  

P₃  = 6

Total ways case c)   T = 6*120*2  =

P(c)  =  1440

d) There are four couples and each couple must be together

P₄ =  4!  =  4*3*2*1

P₄ =  24

Answer:the approximate amount that he will have to set aside each month to reach his goal is $162

Step-by-step explanation:

Total amount of bill that John wants to pay off js $2,100. $2,100 bill in the next 13 months. To determine the amount that he will have to set aside each month to reach his goal, we would divide the total bill by the number of months. It becomes

2100/13 = 161.538

The approximate amount is $162

Answer:

$162

Step-by-step explanation:

$2,100/13

Answer:

Z value for the first  pump = -0.68

Z value for the second pump = 0.45

Step-by-step explanation:

Data provided in the question:

Mean labor cost to repair a heat pump = $90

Standard deviation = $22

Labor cost for the first, X₁ = $75

Labor cost for the Second, X₂ = $100

Now,

Z value for the first  pump = [X₁ - Mean] ÷ Standard deviation

thus,

Z value for the first  pump = [ $75 - $90] ÷ $22

= - 0.68

Z value for the second pump = [X₁ - Mean] ÷ Standard deviation

thus,

Z value for the second pump = [ $100 - $90] ÷ $22

= 0.45

Answer:

z1= -0.6818

z2= 0.45

Step-by-step explanation:

Mean labor cost to repair the heat pump is μ= $90

standard deviation σ= $22

Labor cost for the first heat pump X_1= $75

labor cost for the second heat pump is X_2= $100

z value for the first heat pump

[tex]z_1= \frac{X_1-\mu}{\sigma}[/tex]

⇒ [tex]z_1= \frac{75-90}{22}[/tex]

= -0.6818

z value for the second heat pump

[tex]z_2= \frac{X_2-\mu}{\sigma}[/tex]

⇒[tex]z_2= \frac{100-90}{22}[/tex]

= 0.45

Answer: The number is 12.

Step-by-step explanation:

Since we have given that

Sum of two digits = 12

Let the one's digit be 'x'

Let the ten's digit be '12-x'

So, Original number would be

[tex]x+10(12-x)\\\\=x+120-10x\\\\=-9x+120[/tex]

If 16 is added to the number, then one of the digit is four times the value of the other.

According to question, we get that

[tex]-9x+120+16\\\\=-9x+136[/tex]

so, the one's digit be 'x'.

Let the ten's digit be '4x'.

so, New number would be

[tex]10x+4x=14x[/tex]

According to question, it becomes,

[tex]14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=\dfrac{136}{23}=12[/tex]

So, the number would be

[tex]-9x+120=-9\times 12+120=-108+120=12[/tex]

Hence, the number is 12.

Answer:

66

Step-by-step explanation:

Brute force:

2 digit numbers that has sum of 12:

39, 48, 57, 66

Add 16 to the numbers:

55, 64, 73, 82

Find the number that shows a digit is 4 times the value of other:

82 (2x4 =8)

Answer:

Case 1: As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) decreases.

It is an 'odd' function with 'positive' a.

Case 2: As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) decreases.

It is an 'even' function with 'negative' a.

Case 3: As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) increases.

It is an 'even' function with 'positive' a.

Case 4: As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) increases.

It is an 'odd' function with 'negative' a.

Step-by-step explanation:

Let us consider a monomial function:

             f(x) = axⁿ

Case 1:

As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) decreases.

This happens only if a is 'positive' and n is 'odd'.  So, it is an 'odd' function with 'positive' a.

Case 2:

As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) decreases.

This happens only if a is 'negative' and n is 'even'. So, it is an 'even' function with 'negative' a.

Case 3:

As x > 0 increases, f(x) increases.  As x < 0 decreases, f(x) increases.

This happens only if a is 'positive' and n is 'even'. So, it is an 'even' function with 'positive' a.

Case 4:

As x > 0 increases, f(x) decreases.  As x < 0 decreases, f(x) increases.

This happens only if a is 'negative' and n is 'odd'. So, it is an 'odd' function with 'negative' a.

Keywords: monomial function, odd function, even function

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Identify the monomial function described as odd or even, and indicate whether a is positive or negative.

Step-by-step explanation:

987 → 789

987 - 789 = 198

876 → 678

876 - 678 = 198

765 → 567

765 - 567 = 198

654 → 456

654 - 456 = 198

543 → 345

543 - 345 = 198

432 → 234

432 - 234 = 198

321 → 123

321 - 123 = 198

Generally it is always like that:

3 ≤ x ≤ 9

100x + 10(x-1) + (x - 2) → 100(x - 2) + 10(x - 1) + x

(100x + 10(x - 1) + (x - 2)) - (100(x-2) + 10(x-1) + x)

= 100x + 10(x - 1) + (x - 2) - 100(x - 2) - 10(x - 1) - x   cancel 10(x - 1)

= 100x + x - 2 - 100x + 200 - x     cancel 100x and x

= 100 - 2

= 198

Answer:

3,000 people

Step-by-step explanation:

Total number of people larger stadium can hold equals 4.5 times [tex]10^{4}[/tex] people,

which equals 45,000 people.

Now,

it is given that larger stadium can hold 15 times more people than small stadium .

So, smaller stadium will hold  15 times less people than the larger stadium ,

Which equals , [tex]\frac{45000}{15}[/tex] = 3,000 people.

Thus ,

Smaller stadium can hold a total of 3,000 people.

Answer:

The answer is 35.

35% of the class had scores that were greater than 70 but less than 85.

Step-by-step explanation:

Let's assume the number of students in the class =100

If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70

In other words, 25 scores were less than or equal to 70.

If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85

Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.

We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70 and 85.

Answer:

The answer is 35.

35% of the class had scores that were greater than 70 but less than 85.

Step-by-step explanation:

Let's assume the number of students in the class =100

If 75% of the class scored greater than 70, then, it means 25% (100-75) of the scores were less than or equal to 70

In other words, 25 scores were less than or equal to 70.

If 60% of the class had scores that were less than 85, then, it means 40%(100-60) of the scores were greater than or equal to 85

Therefore, of the 100 scores, 25 scores were LESS THAN OR EQUAL to 70, and 40 scores were GREATER THAN OR EQUAL to 85.

We've now accounted for 65 (25+40) scores, which means the remaining 35 (100-65) scores must be between 70

Answer:

The answer to your question is letter B

Step-by-step explanation:

Process

1.- Find two points of each line

Line A    (-2, 0)   (-1, 2)

Line B    (-1. - 5)   (-6, 0)

2.- Find the slope and equation of each line

Line A

             [tex]m = \frac{2 - 0}{-1 + 2}[/tex]

             [tex]m = \frac{2}{1}[/tex]

                    m = 2

             y - 0 = 2(x + 2)

            y = 2x + 4

Line B

             [tex]m = \frac{0 + 5}{-6 + 1}[/tex]

             [tex]m = \frac{5}{-5}[/tex]

                    m = -1

             y - 0 = -1(x + 6)

             y = -x - 6

3.- Find the inequalities

Line A, we are interesteed in the lower area of the line, so the inequality is

                      y ≤ 2x + 4

Line B, we are also interested in the lower area of the line so the inequality is

                      y ≥ - x - 6

Answer:B

Step-by-step explanation:

Answer:

8.65%

Step-by-step explanation:

Given information:

Recession Return = 13%

Normal Return = 6%

Boom  Return = -4%

Probability of a recession = 45 %

Probability of a boom = 5 %

Probability of a normal = 100 - 45 - 5 = 50%

We need to find the expected rate of return on this stock.

Expected rate of return is the sum of products of probability and returns of each state of economy.

Expected rate of return [tex]=13\%\times 45\%+6\%\times 50\%+(-4\%)\times 5\%[/tex]

                                       [tex]=5.85\%+3\%-0.2\%[/tex]

                                       [tex]=8.65\%[/tex]

Therefore, the expected rate of return on this stock is 8.65%.