Roselyn is driving to visit her family, who live 150150150 kilometers away. Her average speed is 606060 kilometers per hour. The car's tank has 202020 liters of fuel at the beginning of the drive, and its fuel efficiency is 666 kilometers per liter. Fuel costs 0.600.600, point, 60 dollars per liter.
What is the price for the amount of fuel that Roselyn will use for the entire drive?

Answer:

y = -1x + 1

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y = -1x + 1

Answer:

AB-46 cm

Step-by-step explanation:

Use law of cosines

AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134

AB= 46 cm

The value of x is 4.

Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.

The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.

In the given figure ABCD is a rectangle.

OA=2x+1 and OD=x+5             [Given]

AC and BD are diagonals of a rectangle.

As we know that the diagonals of a rectangle are always equal.

So, AC = BD

We can also write it as,

2×OA=2×OD

2×(2x+1) =2×(x+5)

Apply the distributive property a(b+c)=ab+ac, we get

4x+2=2x+10

Subtract 2x from both sides, we get

4x+2-2x=2x+10-2x

2x+2=10

Subtract 2 from both sides, we get

2x+2-2=10-2

2x=8

Divide both sides by 2, we get

2x/x=8/2

x=4

Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.

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Answer:

404 inches

Step-by-step explanation:

Since a room of 2cm is to be left of either side of the TV, thus, the permissible required length of the TV is 136-2 = 134cm

Use Pythagoras Theorem,

h² = 134² + 86² = 17956 + 7396 = 25352

h = √25352 = 159.22 ≈ 159cm = 404.41 inches ≈ 404 inches.

The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let the number of half page ads be represented by h

Let the number of full page ads be represented by f.

Total number of advertisements = 15

h + f = 15 ....... (i)

h = 15 - f

Therefore, the system of equations to represent the situation will be:

60h + 100f = 1340 ........ (ii)

Put the value of h into equation (ii)

60(15 - f) + 100f = 1340

[tex]\Rightarrow[/tex]  900 - 60f + 100f = 1340

Collect like terms

    100f-60f  = 1340-900

[tex]\Rightarrow[/tex]              40f = 440

[tex]\Rightarrow[/tex]                   f = 11

The number of full-page advertisements that Michael purchased is 11.

Since h + f = 15

[tex]\Rightarrow[/tex]    h + 11 = 15

[tex]\Rightarrow[/tex]       h = 15 - 11

[tex]\Rightarrow[/tex]      h = 4

The number of half page advertisements that Michael purchased is 5.

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The sample size needed to obtain a margin of error of 0.05 for the estimation of a population proportion is 384.

Given margin of error of 0.05 and confidence interval of 95%.

We have to find the sample size needed to obtain a margin of error of 0.5 with confidence level of 95%.

Margin of error is the difference between real values and calculated values.

The formula of margin of error is as under:

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where

z is the critical value of z for given confidence level

n is sample size

σ is population standard deviation

We have not given population standard deviation so we will use the following formula:

Margin of error=z*[tex]\sqrt{p(1-p)}[/tex]/[tex]\sqrt{n}[/tex]

We have to find z value for 95% confidence level.

z value=1.96

We know that [tex]\sqrt{p(1-p)}[/tex]<=1/2

put [tex]\sqrt{p(1-p)}[/tex]=1/2

Margin of error=1.96*1/2/[tex]\sqrt{n}[/tex]

0.05=1.96*0.5/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=0.98/0.05

[tex]\sqrt{n}[/tex]=19.6

squaring both sides

n=384.16

After rounding off we will get

n=384.

Hence the sample size needed to obtain a margin of error of 0.05 is 384.

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Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

The relations in a right triangle are given as follows:

In this problem, we have that:

Hence:

[tex]\sin{\alpha} = \frac{10}{12}[/tex]

[tex]\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}[/tex]

[tex]\alpha = 56.4^\circ[/tex].

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Stratified random sampling is used to subdivided into groups by volume of sales.

According to the statements

Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.

Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.

Thus, Stratified random sampling is used to subdivided into groups by volume of sales.

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No digit with the format 90x0y07 is divisible by 2017

The given parameters are:

Dividend = 90x0y07

Divisor = 2017

The dividend is a 7-digit number, and the divisor is a 4-digit number

So, the quotient must be 3 to 4 digits.

Comparing the first and last digits of 90x0y07 and 2017;

The first and last digits of the quotient must be 4 and 1, respectively

So, we have:

90x0y07 = 2017 * 4a1

Assume a = 9.

So, we have:

90x0y07 = 2017 * 491

90x0y07 = 990347

The above is 6-digit.

So, we make use of a 4-digit quotient

This gives

90x0y07 = 2017 * 4ab1

Next, we make use of trial by error.

After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017

The closest attempt is

90x0y07 = 2017 * 4471

90x0y07 = 9018007

Where:

x = 1, y = 0 and the digit between x and y is 8, not 0

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Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

This question is incomplete, the missing diagram is uploaded along this answer below.

Area of a rectangle is expressed as; A = l × b

Given that;

A = l × b

180in² = 20in × x

x = 180in² / 20in

x = 9in

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

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Answer:

6.45

Step-by-step explanation:

I am not staring at zero.  I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.

6.4 + 1/2(6.5-6.4)  Combine in the parentheses

6.4 + 1/2(.5)  Take half of .5

6.4 + .05  add

6.45

50^99 is greater than 99!

The numbers are given as:

99! and 50^99

When the above numbers are estimated using a calculator, we have:

99! = 9.332622e+155

50^99 = 1.577722e+168

Next, we compare the exponents

168 and 155

168 is greater than 155

Hence, 50^99 is greater than 99!

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By using mind ig -,-

Hope Helpful ~

Answer:

  A.  The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.

Step-by-step explanation:

Reflection is a rigid transformation. It preserves both angles and side lengths. Dilation preserves angles, but changes all lengths by the same scale factor.

The described triangle was subject to reflection, which preserves angles and lengths. It was also subject to dilation, which preserves angles, but not lengths.

The appropriate description is that of choice A.

The correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

From the given steps, we can see that when a scatter plot is constructed,  the independent variable is the input variable and should be represented by the x-axis.

Hence, the correct statement about when a scatterplot is constructed is  the independent variable is the input variable and should be represented by the x-axis. Option A

The complete question is;

Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.

The independent variable is the input variable and should be represented by the y-axis.

The dependent variable is the input variable and should be represented by the x-axis.

The dependent variable is the input variable and should be represented by the y-axis.

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Answer: A; The independent variable is the input variable and should be represented by the x-axis.

Step-by-step explanation:

I just know

The graph of the rational function is shown below

From the question, we are to graph the given rational function

To determine the graph that corresponds to the given rational function,

First, we will graph the given rational function.

The given rational function is

x²+3x-1/x+1

The graph of the rational function is shown below

Now, we will compare each of the rational graphs in the provided options with the attached graph

The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.

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The area of the actual building lot is 5040 square ft

This factors are used to enlarge or diminish the given figure. Given the  scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, the new length and width is expressed as:

Length = 12 * 7 = 84ft

Width = 5*12=60 ft

Determine the area

Area = 84 * 60

Area = 5040 square feet

Hence the area of the actual building lot is 5040 square ft

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Answer:

y =x - 2

Step-by-step explanation:

If the slope of the line is  'm', then the slope of the perpendicular to the given line = [tex]\sf \dfrac{-1}{m}[/tex]     (opposite reciprocal)

    y = -x - 3

Compare with equation of line in slope y-intercept form: y = mx +b

 m = -1

[tex]\sf \text{Slope of the perpendicular line = $-(\dfrac{1}{-1})= 1$}[/tex]

This line passes through (2, 0);

Equation of the line in slope - point form:

        [tex]\sf y - y_1 = m(x - x_1)[/tex]

       y  - 0   = 1 (x - 2)

            y = x - 2

Answer:369

Step-by-step explanation:

all you have to do is multiply 18 and 22 its easy

18 x 22 = 369.

Answer:

The correct answer is 15.

Step-by-step explanation:

We are given that the original sides BC is 5.  To find the length of B'C' we take the side of BC and multiply it by the scale factor.

5 (original BC) x 5 (the given scale factor) = 15

Answer:

15

Step-by-step explanation:

correct on edge 2023

Using the t-distribution, the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight is of 69.06 ounces.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]\voerline{x} = 66, t = 2.0154, s = 10.2, n = 45[/tex]

Hence the upper bound of the interval is:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 66 + 2.0154\frac{10.2}{\sqrt{45}} = 69.06[/tex]

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Based on the given polynomial, the degree of the polynomial can be calculated to be 1.

the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.

from the above, we see that the highest power is 1 from 8x¹.

the degree of the polynomial is therefore 1.

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Answer:

4ft^3

Step-by-step explanation:

1.333333*3*1^3=4

To start finding the volume of this sphere, we get the following data:

To find the volume we apply the following formula:

We substitute our data in the formula and solve:

Substituting values into the equation

Calculate exponent cubed

Multiplying

Therefore, the volume of the sphere is 32 ft³.

The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.

The real rate of return exists at 2.926%.

The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.

The formula for the real rate of return:

R = (1+N)/(1+i) - 1

Where, N exists the nominal rate and i exists the inflation rate, as decimals.

A certificate of deposit offers a nominal interest rate of 5.5 percent annually.

This means that N = 0.055

Inflation exists 2.5 percent

i = 0.025

Substitute the values in the above equation, we get

[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]

= [1.055/1.025] - 1

= 1.02926 - 1

= 0.02926

0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%

The real rate of return exists at 2.926%.

Therefore, the correct answer is option D. 3%.

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In data analytics, a population refers to all possible data values in a certain dataset

Data analysis is a systematic computer-aided analysis of data or statistics. [1] It is used to discover, interpret, and convey meaningful patterns in the data. It also includes applying data patterns for effective decision-making.

It may be useful in areas where there is a lot of recorded information. The analysis relies on the simultaneous application of statistics, computer programming, and operations research to quantify performance.

Organizations can apply analytics to business data to describe, predict, and improve business performance. Areas within the analysis include descriptive analysis, diagnostic analysis, predictive analysis, prescriptive analysis, and cognitive analysis in particular. [2] Analysis can be applied in various fields such as marketing, management, finance, online systems, information security, and software services.

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Using linear functions, the cost will be the same, of $70, when there are 5 students.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the functions are:

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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Answer:

2x - 5 < -8 or 2x - 5 > 8

Step-by-step explanation:

|2x - 5| > 8

2x - 5 < -8 or 2x - 5 > 8

The two inequalities that can be written from the |2x - 5| > 8 are:

2x - 5 > 8

-2x + 5 > 8

We have,

To split the inequality |2x - 5| > 8 into two separate inequalities, we consider both the positive and negative cases for the absolute value expression.

Positive case:

When 2x - 5 is positive, we have:

2x - 5 > 8 _____(1)

Negative case:

When 2x - 5 is negative, we have:

-(2x - 5) > 8

Simplifying the negative case:

-2x + 5 > 8 ______(2)

Now, we have two inequalities:

2x - 5 > 8

-2x + 5 > 8

These are the two inequalities resulting from the given inequality

|2x - 5| > 8.

Thus,

The two inequalities that can be written from the |2x - 5| > 8 are:

2x - 5 > 8

-2x + 5 > 8

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Answer:

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m represents the slope and b represents the intercept.

x - 3y = 6

3y = x - 6

y = [tex]\frac{1}{3}[/tex]x - 2

4x - y = 1

y = 4x - 1

6x + 5y = -15

5y = -6x - 15

y = -[tex]\frac{6}{5}[/tex]x - 3

13x - 11y = -12

11y = 13x + 12

y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]

The answers to the questions are:

1. x = 4

2.  x = 1.5

3. x = 1.875

4. x = 1

1. 4x + 3 = 19

4x = 19 - 3

4x = 16

divide by 4

x = 4

(4/3)x + 5 = 17

= 1.33x + 5 = 7

Take like terms

1.33x = 7-5

1.33x = 2

divide through by 1.33x to get 2

x = 2/1.33

x = 1.5

4x(6 - 2) - 10 = 20

Multiply and open the bracket

24x - 8x - 10 = 20

Take like terms

16x = 20+10

16x = 30

x = 30/16

= 1.875

4.3x + 0.7 = 5

4.3x = 5 - 0.7

4.3x = 4.3

x = 1

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Answer: All real numbers

Step-by-step explanation:

The domain is the set of inputs.