Yesterday, Jack drove 39 1/2 miles. He used 1 1/4
gallons of gasoline. What is the unit rate for miles per gallon?

The amount that Casey invested in the savings account is $10,000 and the amount Casey invested in the certificate of deposit is $60,000.

0.01c -  0.02s = $800 equation 1

c + s = $70,000 equation 2

Where:

Multiply equation 2 by 0.01:

0.01c + 0.01s = 700 equation 3

Subtract equation 3 from equation 1:

0.01s = 100

Divide both sides of the equation by 0.01:

s = 100 / 0.01

s = 10,000

Substitute for s in equation 2:

c + 10,000 = 70,000

c = 70,000 - 10,000

c = 60,000

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Step 1

The distribution given is a binomial distribution with following data:

[tex]n=25, \quad p=0.25[/tex]

Step 2:

(a) Probability of at most 6 calls involving a fax message:

We have to add probabilities for x=0 to x=6

[tex]\begin{aligned}& P(X \leq 6)=\sum_{x=0}^6{ }^{25} C_x(0.25)^x(1-0.25)^{25-x} \\& =\left(\begin{array}{l}{ }^{25} C_0(0.25)^0(1-0.25)^{25-0}+{ }^{25} C_1(0.25)^1(1-0.25)^{25-1} \\+{ }^{25} C_2(0.25)^2(1-0.25)^{25-2}+{ }^{25} C_3(0.25)^3(1-0.25)^{25-3} \\+{ }^{25} C_4(0.25)^4(1-0.25)^{25-4}+{ }^{25} C_{5 x}(0.25)^5(1-0.25)^{25-5} \\+{ }^{25} C_6(0.25)^6(1-0.25)^{25-6}\end{array}\right)\end{aligned}[/tex]

[tex]\begin{aligned}& =\left(\begin{array}{l}{ }^{25} C_0(0.25)^0(0.75)^{25-0}+{ }^{25} C_1(0.25)^1(0.75)^{24} \\+{ }^{25} C_2(0.25)^2(0.75)^{23}+{ }^{25} C_3(0.25)^3(0.75)^{22} \\+{ }^{25} C_4(0.25)^4(0.75)^{21}+{ }^{25} C_{5 x}(0.25)^5(0.75)^{20} \\+{ }^{25} C_6(0.25)^6(0.75)^{19}\end{array}\right) \\& =\left(\begin{array}{l}0.0007525+0.006271+0.02508+0.06410 \\+0.1175+0.003171+0.182819\end{array}\right) \\& =0.5611\end{aligned}[/tex]

Therefore,

[tex]P(X \leq 6)=0.5611[/tex]

Step 3:

(b) Probability of exactly 6 calls involving a fax message:

We have to find probabilities for x=6[tex]\begin{aligned}& P(X=6)={ }^{25} C_6(0.25)^6(1-0.25)^{25-6} \\& ={ }^{25} C_6(0.25)^6(0.75)^{19} \\& =0.182819\end{aligned}[/tex]

Therefore,

P(X=6)=0.182819

Step 4:

(c) Probability of at least 6 calls involving a fax message:

We have to add probabilities for x=0 to x=5 and subtract from 1[tex]\begin{aligned}& P(X \geq 6)=1-(P(X < 6)) \\& =1-(P(X \leq 6)-P(X=6)) \\& =1-(0.5611-0.1828) \\& =0.6217\end{aligned}[/tex]

Therefore,[tex]P(X \geq 6)=0.6217[/tex]

Step 5:

(d) Probability of more than 6 calls involving a fax message:

We have to add probabilities for x=0 to x=6 and subtract from 1[tex]\begin{aligned}& P(X \geq 6)=1-(P(X \leq 6)) \\& =1-(0.5611) \\& =0.4389\end{aligned}[/tex]

Therefore,

[tex]P(X \geq 6)=0.4389[/tex]

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He need to pay $245 per month .

How is the amount of interest you will pay calculated?

Past due bill = $585

Now  just made payment arrangements for the next 3 months to keep my account from being suspended

So, Payment each month of past bill = 585/3 = 195

His normal monthly bill is $50.00 per month.

So, I need to pay per month = $50+$195

= $245

Hence ,He need to pay $245 per month .

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The interval notation of domain and range is (-∞, ∞).

Interval notation:

In algebra, interval notation refers the way to describe continuous sets of real numbers by the numbers that bound them.

Given,

Here we need to write the interval notation of domain and range.

In order to find the interval notation, first we have to know the definition of domain and range.

In math domain refers the domain of a function is the set of values that we are allowed to plug into our function. Basically, this set is the x values in a function such as f(x).

And where as the range of a function is the set of values that the function assumes. And it is the values that the function shoots out after we plug an x value in.

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If 3x – y = 5 and 2x + y = 15  then evaluation of  x^2 + 2y is equal to 72.

What is evaluation ?

Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.

3x-y=5 and 2x+y= 15

Add the two equations together to eliminate y

3x-y=5

2x+y= 15

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

5x = 20

Divide by 5

5x/5 = 20/5

x = 4

Now we can find y

2x+y = 15

2(4) +y = 15

8+y =15

Subtract 8 from each side

8+y-8 = 15-8

y =7

We want to find

x^2+2xy

(4)^2 +2(4)(7)

16+56

72

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Answer:

The babysitter earns $66 babysitting for 9 hours a day.

Step-by-step explanation:

1. First, you need to find the amount of money they make babysitting for 3 hours, since 9 and 6 are divisible by 3.

2. Then you divide $44 by 2, to find that they make $22 babysitting for 3 hours.

3. Then you multiply $22 by 3 to get your answer of $66.

The population be 12 years from now is 6.612.

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

Population after n years = Present Population = (1 + (r/n))ⁿ

Population after 12 years = 5000 ( 1 + (15/100))²

= 5000(115/100)²

= 5000 (115/100)*(115/100)

= 6.612.5

Hence, the population be 12 years from now is 6.612.

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Answer:

Option 2

Step-by-step explanation:

The greater than sign with the line under it means greater than/less than or equal to. So -2.4 is less than or equal to -2.40.

-Hope this helped

The Principal when calculated quarterly will give a sum of 2900 + (2.525)^4t at a rate of 6.1% interest

What is Compound Interest?

Compound interest is usually referred to as "interest on interest." Compound interest can work in your favour as your assets increase over time, but it can also work against you if you're paying off debt, such as credit cards. A calculator can assist in estimating how much money compound interest will generate over time.

Given that the Principal amount is $2900

and the Rate of Interest is 6.1%

Since, the interest is calculated quarterly

Amount = Principal * (1 + Rate/4)^4*Time

Amount = 2900 + (1 + 6.1/4)^4t

Amount = 2900 + (10.1/4)^4t

Amount = 2900 + (2.525)^4t

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Step-by-step explanation:

When an article is sold for 1200 there is 10% profit at what price should it be sold to gain 20%​.

find the base price without any profit:

$1,200/1.1 = $1,090.9090901

to gain 20%:

$1,090.9090901 * 1.2 = $1,309.09 (rounded)

Answer:

[tex]x=5t-3[/tex]

[tex]y=3t^2-5[/tex]

Step-by-step explanation:

The amount will be $1,730.21 in the account after 11 years if  quarterly payments of $ 650 into an annuity paying 9% interest compounded.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

P = 650

r = 9% = 0.09

t = 11 years

n = 4

Plug all the values in the formula, we get:

A = $1,730.21

Thus, the amount will be $1,730.21 in the account after 11 years if  quarterly payments of $ 650 into an annuity paying 9% interest compounded.

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Answer:

Lyric ran faster.

Step-by-step explanation:

When you plot y = 5x, you can trace a certain point to see which value is higher.  When I plotted y = 5x and chose the point when x = 8, y = 40 for Kira, and for Lyric, at x = 8, y = 80.  Since the y coordinate (distance) is higher, Lyric ran faster.

Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.

You may use the following logic to analyze this situation. Theoretically, the faster runner will have traveled a longer distance at any given point in time different than 0 when comparing to the other runner. Therefore, let's randomly pick a point in time to see who had traveled the longer distance.

The time we'll evaluate will be 4 seconds.

For this, simply substitute the "x" by the number "4" in the given equation for Kira:

[tex]y=5(4)\\ \\y=20[/tex]

Conclusion: Kira had traveled a total distance of 20 yards, 4 seconds after starting the race.

To evaluate the graph, we'll have to draw a line where x=4 sits and then find the value of "y" the function returns. Check the attached images in order to see this process.

Conclusion: Lyric had traveled a total distance of 40 yards, 4 seconds after starting the race.

After 4 seconds Kira traveled 20 yards;

After 4 seconds Lyric traveled 40 yards.

Conclusion: Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.

To express the amount of parcels Joshua must transport in order to earn more than $20 per day, we can use the inequality 5x + 10 > 20.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1]

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities[1]. Equivalence is not considered.

There are two form of inequality relations that are not strict, in contrast to strict inequalities:

The indication of an or b denotes that.

According to our question-

x stands for every delivery he makes:

.5x + 10 > 20

This demonstrates that in order for the inequality to exist, it must exceed $20.

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The graph in the figure is not a direct variation

From the question, we have the graph that represents the given parameters that can be used in our computation

By definition, the graph of a direct variation represents a straight line that passes through the origin

Also, from the graph, we can see that:

The line on the graph is not a straight line. In fact, the line is a curve

A curve does not represent any type of variation

Hence. the graph is not a direct variation

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Answer:

Below

Step-by-step explanation:

5 1/2 = 11 / 2

11/2  ÷  3/4   = 11/2  x 4/3  = 44/6 = 7  1/3

Using system of linear equation, the store sold 240 chemistry books and 189 biology books

A system of equations is a set or collection of equations that you deal with all together at once. The general representation of linear equations are given as y = mx + c

Let set our variables as;

x + y = 429 ...eq(i)

x = 51 + y ...eq(ii)

Put eq(ii) into (i)

(51 + y) + y = 429

51 + 2y = 429

2y = 429

y = 189

x = 51 + 189

x = 240

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The rational function that has a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = -3 is:

f(x) = 3 / (x - 4)(x + 3)

What is  horizontal asymptote?

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Answer: B

Step-by-step explanation: B. So that people would keep buying new things

Goods are often planned to become obsolete in order to encourage people to continue buying new things. This can be done by intentionally designing products with a limited lifespan or by using materials that are prone to wear and tear. Companies may also release new versions of products or discontinue support for older models in order to encourage consumers to upgrade to the latest version. By making their products become obsolete, companies can create a sense of urgency for consumers to keep buying new things and maintain their sales.

The value of the given polynomial x² - 3xy + 1/2y² if x = 12 and y = 2/3 is; -19 / 36.

It follows from the task content that the value of the polynomial be determined for the given polynomial expression.

As evident in the task content; the given expression is;

x² - 3xy + 1/2 y².

Hence, since the given values of x and y are: 1/2 and 2/3 respectively.

On this note, we have that;

( 1/2 )² - ( 3 × 1 / 2 × 2 / 3 ) + ( 1 / 2 × (2 / 3)² )

= 1/4 - 1 + ( 2 / 9 )

= -3 / 4 + 2 / 9

= -19 / 36

On this note, the value of the given polynomial is; -19 / 36.

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If the distances form a geometric sequence, the total distance Mr. Meyering jumps if he completes infinitely many jumps is equal to 40 inches.

In Mathematics, a geometric sequence can be defined as a series of real and natural numbers that are calculated by multiplying the next number by the same number (common ratio) each time.

Mathematically, the sum of an infinite geometric sequence can be calculated by using this mathematical expression:

S = a₁/(1 - r)

Where:

First of all, we would determine the common ratio between the distances he jumped as follows;

Common ratio, r = a₂/a₁

Common ratio, r = 10/20

Common ratio, r = 0.5.

For the total distance, we have;

S = a₁/(1 - r)

S = 20/(1 - 0.5)

S = 20/0.5

S = 40 inches.

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Using the percentage increase formula, we know that the median monthly rent increase from 1987 to 1995 is 31%.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

So, we know that:

The median monthly rent in 1987 was $399.

The median monthly rent in 1995 was $523.

Percentage increase formula: C = x2 - x1/x1 * 100

Where c is the relative change, x1 is the initial value and x2 is the final value.

Now, insert the values in the formula as follows:

C = x2 - x1/x1 * 100

C = 523 - 399/399 *  100

C = 124/399 *  100

C = 31.07

Round off: 31%

Therefore, using the percentage increase formula, we know that the median monthly rent increase from 1987 to 1995 is 31%.

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Answer:

[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the slope formula to find the slope of the line:

[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-3, -1) into the point-slope formula:

[tex]\implies y-(-1)=2(x-(-3))[/tex]

[tex]\implies y+1=2(x+3)[/tex]

Substitute the found slope and point (2, 9) into the point-slope formula:

[tex]\implies y-9=2(x-2)[/tex]

Therefore, the correct answer option is:

[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]

Answer:-6.5

Step-by-step explanation:

Answer:

Step-by-step explanation

Use pemdas.

P- Parenthesis

e- Exponents

m- Multiplication

d- Division

a- Additon

s-Subtraction

5÷10+2-9

=5÷12-9

=5÷3

=1.666666666667

Answer:

Commutative Property Addition

Answer:

1

Step-by-step explanation:

Number of roots = number of real roots + number of non-real roots

The graph intersects the x-axis 3 times

4 = 3 + x

x = 1

Answer: place points at (0,3) and (5,5)

Step-by-step explanation: the formula for a line is y = mx + b, where m is the slope and b is the y-intercept (the point where the line meets the y-axis). Since b is positive 3, place a point at (0,3).

m = 2/5, and since slope is rise over run (distance traveled in y axis over distance traveled in x axis) and it is positive, your next point is 2 up and 5 right, which is (5,5). You could also place a point at (-2,-2).

Answer:

Step-by-step explanation: