Solve the system of equations
3x + y = 3
x + y = 2

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

24

Step-by-step explanation:

From the table given, at Mimi's Bakery, 1 X-Large sheet cake size will give us a number of servings of 120.

To find out how many X-Large cake size the school should order, simply divide the number of expected expected guests by the number of servings the X-Large cake will do.

Given that the score is expecting 2,889 guests, the school should order for:

2,889 ÷ 120 = 24.075 X-Large cakes.

Let's just say, an estimated 24 X-Large size cake should be ordered.

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the confidence coefficient.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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Since A and B are mutually exclusive, the probability of A occurring given that B has already occurred is 0. This means that P(A | B) = 0.

P(A ∩ B) = 0, since the events are mutually exclusive.

P(A | B) = 0, since the probability of A given B is 0 when A and B are mutually exclusive.

Since A and B are mutually exclusive, they cannot both occur at the same time. This means that the probability of them both happening at the same time is 0. As a result, P(A ∩ B) = 0.

Since A and B are mutually exclusive, the probability of A occurring given that B has already occurred is 0. This means that P(A | B) = 0.

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Answer:

Step-by-step explanation:For any shape it’s always true that for volume

V

the surface area is:      =2‾‾‾√3

for some constant   depending on the shape. So to work out the surface area from the volume we just need to know the value of   for the shape in the question.

For a cube for example we have that  =6, assuming consistent units i.e.: unit 2 for area and unit 3

3

 for volume.

More generally if we have formula for both volume and surface area in terms of a particular one dimensional measurement  

d

 of the shape then we can always write these formula in the form:

=13

=12

for constants  constants   1  and  1

. Then we have:

=1‾‾‾√3

=1(1)2‾‾‾‾‾‾√3

=121‾‾‾√32‾‾‾√3

and therefore:

=121‾‾‾√3

For example for a sphere we have that   that  =42  and  =433 and therefore:

=4(43)2‾‾‾‾‾‾√3

=36‾‾‾‾√3

So if a particular sphere has volume   =8  then we can calculate its surface area to be:

=36‾‾‾‾√382‾‾√3=436‾‾‾‾√3 m2

Answer:

Step-by-step explanation:

I think that<,> help show the relationship because you are comparing the 2 numbers by stating which is bigger than or smaller than the other.

HOPE IT HELPED

the answer is >,< because it is saying which number is bigger and which is snaller

Answer:5 and 1/16

Step-by-step explanation:

Answer:

n - 3

Step-by-step explanation:

Decreased always mean subtraction.

Solution for 80000 is what percent of 800000:

80000:800000*100 =

(80000*100):800000 =

8000000:800000 = 10

Now we have: 80000 is what percent of 800000 = 10

Answer:

30.5 hours

Step-by-step explanation:

444-78=366

366/12=30.5

30.5 x 12= 366

Answer:

She worked 30 1/2 hours last week

Step-by-step explanation:

Look at the picture

Hope this helps:)))

The actual area of her office is 50 square feet.

The scale used for the blueprint of the office is the scale of reduction.

Also, the scale of reduction is uniform for the overall drawing.

We are given,

The blueprint for Zahra's new office measures 4 cm long and 2 cm wide.

The scale for the blueprint is 6 cm to 15 ft.

Let's find the actual length and width by unitary method;

Since 6 cm of the drawing denotes the actual size of 15 ft.

So, 1 cm of the drawing denotes the actual size of 15 ft./6 cm.

So, 4 cm of the drawing denotes the actual size of 15 ft./6 cm * 4 cm = 10 ft.

So, 2 cm of the drawing denotes the actual size of 15 ft./6 cm * 2 cm = 5 ft.

So, the actual length of the office will be 10 ft. and the actual width of the office will be 5 ft.

Now,

Area of the office = length * width = 10 * 5 = 50 square feet.

Thus, the actual area of her office is 50 square feet.

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There are 28 days in 4 weeks.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

There are 7 days in a week, so to convert weeks to days, we multiply the number of weeks by 7. For example, if we have 2 weeks, we would multiply 2 by 7 to get 14 days.

In this case, we are given 4 weeks and asked to convert it to days. So we multiply 4 by 7 to get:

4 x 7 = 28

Therefore, there are 28 days in 4 weeks.

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We need to find the vertex of the quadratic equation -0.001x² + 8x - 7000. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.001 and b = 8. Plugging in the values, we get x = -8/(2*(-0.001)) = 4000. the value of x that maximizes the manufacturer's profit is 4000 cases (option b).

Therefore, the value of x that maximizes the manufacturer's profit is 4000 cases. Option (b) is the correct answer. It's worth noting that we can also verify that this is a maximum by checking the sign of the leading coefficient (-0.001) - since it is negative, the quadratic opens downwards, meaning that the vertex represents a maximum point.
The manufacturer's profit is given by the equation P(x) = -0.001x^2 + 8x - 7000. To find the value of x that maximizes the profit, we need to determine the vertex of the parabola. The x-coordinate of the vertex is found using the formula x = -b/(2a), where a and b are the coefficients of the quadratic term and the linear term, respectively.

In this case, a = -0.001 and b = 8. Plugging these values into the formula, we get:

x = -8 / (2 * -0.001) = 4000

Therefore, the value of x that maximizes the manufacturer's profit is 4000 cases (option b).

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The point of intersection is the point where two or more lines meet.

Noah's claim is incorrect

The given parameters are:

Line l, line m and point of intersection p

See attachment for illustration of the perpendicular lines l and m.

Using the attachment as a guide, we can see that both transformations do not have the same effect on the points on both lines.

This is so because, figures 2 and 3 can be transformed to one another by reflecting across line l.

Hence, Noah's claim is incorrect

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The complete question is

"The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. Which statement is correct?

a. The domain of this function represents the total cost for a job

b. H is a function of C

c. The painter charges a $35 service fee in addition to an hourly rate

d. The painters hourly rate is $35.00"

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours. So, the correct option is D. The painters hourly rate is $35.00

Function is a type of relation, or rule, that maps one input to specific single output.

The equation c = 35h + 60 describes a plumber's charges, c, for a job that takes h hours.

The fixed fee, or service fee, is $60.

$35 is the hourly fee since in the function, it is 35 that is multiplied by the number of hours.

So, the correct option is D. The painters hourly rate is $35.00

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The probability on a particular day that all machines will break down is 0.00060840. So the option b is correct.

In the given question,

A company has four photocopy machines A, B, C and D.

The probability that a given machine will break down on a particular day is;

P(A) = 13⁄100

P(B) = 9⁄50

P(C) = 1⁄5

P(D) = 13⁄100

We have to find the probability on a particular day that all machines will break down.

The required probability = P(A∩B∩C∩D)

The required probability = P(A)∙P(B)∙P(C)∙P(D)

The required probability = 13⁄100 × 9⁄50 × 1⁄5 × 13⁄100

The required probability = 1521/2500000

The required probability = 0.00060840

Hence, the probability on a particular day that all machines will break down is 0.00060840. So the option b is correct.

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Answer:

$5

Explanation:

If 48 ÷ 12 = 4

Then $1.25 * 4 = $5

Answer:

$5

Step-by-step explanation:

48÷12=4

$1.25×4=$5

The absolute value of -2784.75 is 2784.75.

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The most direct way to measure how dispersed a set of scores is, is by using the range. The range is calculated by subtracting the lowest score from the highest score in the dataset, which gives a quick and easy measure of the spread of the scores.

However, the range can be influenced by extreme scores and may not provide a complete picture of the variability. Other measures of variability, such as the standard deviation and variance, take into account the variability of all scores in the dataset and provide a more robust measure of variability.

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Answer:

Three solutions were found :

x = 3/2 = 1.500

x = 2

x = -1

Step-by-step explanation:

Answer:

The ratio between A and B is 30/1.

Step-by-step explanation:

In math, ratios are the relationships between two quantities using division. They want us to find the ratio of A (3 * 10^-6) to B (0.0000001). While the quantity of A is in scientific notation, the quanitity of B is in decimal notation.

Scientific notation is a way to notate very large or very small numbers in the form of a * 10^m, where 1 ≤ a < 10.

Decimal notation is the regular notation we use for rational numbers that are not fractions or percentages.

I will do the math in scientific notation. First, I will convert B from decimal notation to scientific notation. To do this, I must first find the decimal point in B.

0.0000001

Then, I move the decimal place right until the a number is between 1 and 10.

1

But we can't just make such a small number into 1 like nothing! I have to notify the change in a using powers of 10. SInce I moved the decimal place 7 places and the number got smaller, I will say that 1 can be multiplied by 10^-7

1 * 10^-7.

Now I can find the ratio between A and B. First, I write the ratio as is.

(3 * 10^-6)/(1 * 10^-7)

Next, I can rearrange the a number and the powers of 10 with each other.

= (3/1)(10^-6/10^-7)

Simplify.

= (3)(10)

= 30

The ratio between A and B is 30/1.

If a certain taxi driver charges a rate of r cents per person per mile. It would cost (3rx)/200 dollars .So the correct answer is option D.

If the taxi driver is charging r cents per person per mile, then the total cost for 3 people to travel x miles without the discount is 3rx cents. To give a 50% discount, the total cost would be reduced by 50%, or divided by 2.

Therefore, the total cost for 3 people to travel x miles with the 50% discount is (3rx)/2 cents. To convert this to dollars, we need to divide by 100 cents per dollar, giving us:

(3rx)/200 dollars.

It's important to pay attention to units and conversions when working with rates and percentages. In this case, we needed to convert from cents to dollars to get the final answer. Additionally, it's helpful to double-check the algebraic manipulation to ensure that the answer makes sense in the context of the problem.

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Complete question is:

A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. 3xr/2

B. 3x/200r

C. 3r/200x

D. 3xr/200

E. xr/600.

2.76 would be the necessary value for her f statistic.

Given that,

A psychopathology expert evaluates the prevalence of depression among people living in five different climate zones. She gathers information from 15 randomly chosen individuals in each area. If she uses a between-groups, one-way anova to compare her groups with a 0.05 p-value

To find :  The critical value for her f statistic

We have here,  k = 4, N= 16*4 = 64

Degree of freedom for between groups = k - 1 =  4 - 1 = 3

Degree of freedom for error  = 64-4 = 60

F critical value  = 2.76.....by using F critical value table or Excel command =FINV(0.05,3,60)

Therefore, 2.76 would be the necessary value for her f statistic.

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Answer:\(\color{yellow}{}\)

\(\color{iron}{{-1, 0, 4}}\)

\(\color{iron}{{-3, 1, 2}}\)

Domain is 5 and the range is 4 so the Function is 1.25

Answer:

20 and 10

These are the only two possible numbers who match those descriptions.

The Pearson correlation coefficient for the given data set is 0.5 (option a).

To calculate the Pearson correlation coefficient,

1: Calculate the mean of x and y.

Mean of x: (2 + 1 + 3) / 3 = 2

Mean of y: (6 + 2 + 4) / 3 = 4

2: Calculate the deviation of each value from the mean for both x and y.

x deviation: (2 - 2), (1 - 2), (3 - 2) = 0, -1, 1

y deviation: (6 - 4), (2 - 4), (4 - 4) = 2, -2, 0

3: Calculate the product of the deviations for each pair of values.

Product of deviations: (0 * 2), (-1 * -2), (1 * 0) = 0, 2, 0

4: Calculate the squared deviation for each value of x.

x squared deviation: \((0^2), (-1^2), (1^2)\) = 0, 1, 1

5: Calculate the squared deviation for each value of y.

y squared deviation: \((2^2), (-2^2), (0^2)\) = 4, 4, 0

6: Sum up the products of the deviations and divide by the square root of the product of the squared deviations of x and y.

Pearson correlation coefficient: (0 + 2 + 0) / sqrt((0 + 1 + 1) * (4 + 4 + 0))

Pearson correlation coefficient: 2 / sqrt(2 * 8)

Pearson correlation coefficient: 2 / sqrt(16)

Pearson correlation coefficient: 2 / 4

Pearson correlation coefficient: 0.5

Therefore, the Pearson correlation coefficient for the given data set is 0.5, which corresponds to option a.

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Considering the expression of a line, the equation of the line that passes through the pair of points (35, -30) and (-12, 34) is y=-4/3x +18.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of said line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope and the value of one of the points in the expression of a line, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (36, -30) and (x₂, y₂)= (-12, 34), the slope m can be calculated as:

m= (34 - (-30))÷ (-12 - 36)

m= (34+30)÷ (-12 - 36)

m= 64÷ (-48)

m= -4/3

Considering point 2 and the slope m, you obtain:

34= -4/3×(-12) + b

34= 16 +b

34 -16= b

18= b

Finally, the equation of the line is y=-4/3x +18.

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Answer:

353,760 feet per hour

Step-by-step explanation:

multiply 5280 by 67.

Answer:

353760

Step-by-step explanation: