The price of a cake plus 11% delivery charge comes to a total cost of $19.98. What was the price of the cake?

Step 1 of 2 : Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity. Enter the equation in the box below:

Answer:

the simplified expression is negative twelve sevenths

Step-by-step explanation:

To simplify the expression, we can start by applying the rules for combining like terms:

(-7) * 2 - (3 * sqrt(64)) = (-14) - (3 * sqrt(64))

Next, we can use the fact that the square root of 64 is 8 to simplify the expression further:

(-14) - (3 * sqrt(64)) = (-14) - (3 * 8) = (-14) - 24 = -38

Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common factor:

-38 / 5 = (-38 / 2) / (5 / 2) = -19 / 2 = negative twelve sevenths

Therefore, the simplified expression is negative twelve sevenths.

Answer:

the simplified expression is negative twelve sevenths

Step-by-step explanation:

The required rate of change is given as [tex]C=\frac{-2t^4-2t^3+200t+50}{\left(t^3+50\right)^2}[/tex].

Given that,
To determine the rate of change in the function of the bloodstream,

C(t) = [tex]\left(\frac{\left[2t^{2\:}\:+\:t\right]}{\left[t^{3\:}\:+\:50\right]}\right)[/tex]

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

Here,
C(t) = [tex]\left(\frac{\left[2t^{2\:}\:+\:t\right]}{\left[t^{3\:}\:+\:50\right]}\right)[/tex]

Apply the rule of ,[tex]\left(\frac{f}{g}\right)'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]
[tex]dC/dt=\frac{\frac{d}{dt}\left(\left[2t^2+t\right]\right)\left[t^3+50\right]-\frac{d}{dt}\left(\left[t^3+50\right]\right)\left[2t^2+t\right]}{\left[t^3+50\right]^2}[/tex]

[tex]C =\frac{-2t^4-2t^3+200t+50}{\left(t^3+50\right)^2}[/tex]
For the value so of the t substitute t in the above expression,

Thus, the required rate of change is given as [tex]C=\frac{-2t^4-2t^3+200t+50}{\left(t^3+50\right)^2}[/tex].

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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:

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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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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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 equation of the line of best fit, rounded to the nearest integer, is y = 381x - 566.

What does "Line of Best Fit" mean?

The trend line sometimes referred to as the line of best fit in statistics, uses a straight line on the scatter plot to best depicts the given data points. All of the points, part of the points, or none may be traversed by a straight line. In the statistical approach, it is regarded as one of the significant results of regression analysis.

Given values of x and y, we will use the graphing calculator to find the line of Best Fit, we will get an equation in linear form as:

or, y = 381x - 566

Hence, the equation of the line is y = 381x - 566.

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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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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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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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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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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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Independent Variable: 30 pieces of gum

Dependent Variable: 2 pieces of gum

We predict that independent variables will affect dependent variables. What transpires as a result of the independent variable is known as a dependent variable.

The variable you change or manipulate in an experimental study to examine its effects is known as an independent variable. Because it is unaffected by any other study variables, it is referred to as being "independent."

The variable that alters as a result of the modification of the independent variable is known as a dependent variable. The result that interests you is what you're measuring, and it "depends" on your independent variable.

He has 30 pieces of gum which is the independent, 2 would be the dependent.

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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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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]x=5t-3[/tex]

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

Step-by-step explanation:

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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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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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

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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Answer:

Commutative Property Addition

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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The  samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center are:

Sample can be defined as the way  of randomly collecting data or information from a group of population so as to draw or reach a conclusion.

Most researcher tend to collect sample when carrying out a survey in which they will then examine, analyze and evaluate the sample they collected before reaching a conclusion.

When a researcher want to carryout survey so as to know how the  resident of a city feel about building a new youth center. The researcher has to collect the survey sample from :

Therefore the correct option is B,D,E.

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The complete question is:

Which are samples that are appropriate to survey regarding how the city’s residents feel about building a new youth center? Select all that apply.

10 names selected from the city phone book.

100 residents who live near the proposed site for the youth center.

100 tourists at the city park last Friday.

50 children at each of the city’s four elementary schools.

100 parents of children at each of the city’s four elementary schools.

The system has one solution. Option A

The substitution method of solving simultaneous equations involving substituting the value of one variable I to a given equation.

Given the equation;

10x - y = 1    (1)

5x -4y = -3   (2)

Make 'y' the subject from equation (1)

-y = 1 - 10x

y = -1 + 10x

Substitute the value into equation(2)

5x - 4(-1 + 10x) = -3

expand the bracket

5x + 4 - 40x = -3

collect like terms

-35x = -7

x = 1/5

Now, substitute the value of x as 1/5

y = -1 + 10(1/5)

y = -1 + 2

y = 1

Hence, the values are 1/5 and 1

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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)

The forecast for the first week of June is 206.40.

The forecast for for the first week of June will be based on the five-week moving average.

Five-week moving average: (applications of (week 1 + week 2 + week 3 + week 4 +week 5)) / 5

For first 5 week: (238 + 199 +215 +212 +207)/5 = 214.20

For second 5 week: (199 + 215+ 212+ 207+ 211)/5 = 208.80

For third 5 week : (215 + 212 + 207 + 211 + 196)/5 = 208.20

For the fourth 5 week or the first week of June:

(212 + 207 + 211+ 196 + 206)/5 = 206.40

The question is incomplete, the complete question is:

Exhibit 17-5 State Division of Motor Vehicles (DMV) statistics show the rate of new driver's license applications to be as shown below.

Month  Week Application

April  

               1       238

               2        199

               3        215

               4        212

May         1         207

               2         211

               3          196

               4          206

Refer to Exhibit 17-5. Using a five-week moving average, what is the forecast for the first week in June?

a. 198.45

b. 202.83

C. 206.40

d. 200.20

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