Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Answer:

area = base x height

Step-by-step explanation:

You multiply the base of the square and the height of the square and you get the area of it.

Answer:

  b. Square -2

Step-by-step explanation:

You want to know the first step in evaluating 1/2 |2x² - 3| for x = -2.

The Order of Operations tells you the first step is to evaluate expressions inside the innermost grouping symbols. Here, that means you want to evaluate the expression 2x² - 3.

Once you have identified that expression, you start by evaluating terms with exponents. That term here is x². When x=-2, the first step is to square -2.

__

Additional comment

After you get x² = 4, then you evaluate the product 2(4) = 8, and then the difference 8 -3 = 5. Then the absolute value is determined |5| = 5, and finally the product with 1/2: (1/2)(5) = 5/2.

The correct option is option b. It can be obtained by following the order of operation BODMAS.

What is the order of operation?
To solve any mathematical expression, the BODMAS rule is used. The full form of BODMAS is Bracket Order DIvision Multiplication Addition Subtraction. It can be simplified as, to solve the Mathematica expression first open all brackets, then powers, then division, then multiplication, then addition, and finally subtraction.

Now, consider the following expression:

1/2 |2x² - 3|

Now, substitute -2 for x in the above expression.

1/2 |2(-2)² - 3|

In the above expression there is no bracket hence the next step is solve power of -2.

Hence, the first step of solving the above expression is square -2.

Hence, the correct option is b. It can be obtained by following the order of operation BODMAS.

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From given report, on average college women gain more weight than college men during their first year of college.

In this question, we ahve been given a study is conducted to show that college women, on average, gain more weight than college men during their first year of college.

The study is completed and reports a p-value of 0.001

We need to write the conclusion for above situation.

We can see that the results are statistically significant.

And from given p-value, we can say that on average college women gain more weight than college men during their first year of college.

Therefore, on average college women gain more weight than college men.

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No. of concert the stadium host to  earn the revenue of 200000 is 8.

acc to our question-

hence,No. of concert the stadium host to  earn the revenue of 200000 is 8.

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Answer: -8

Step-by-step explanation:

The line has a slope of 1/8, so the x increases by 8 for every 1 the y increases, and vice versa for a decrease.

The difference between the x coordinates 8 and -8 is 16. We then need to divide this by 8, because the x increases by 8 for every 1 the y increases, and we need to find the increase/decrease in y.

16/8 = 2

We need to subtract 2 from -6, giving us our answer, -8.

600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.

Given:

standard deviation σ = 0.01

margin of error e = 0.0008

For 95% confidence interval:

z value = 1.96

we know that:

e = z * σ/[tex]\sqrt{n}[/tex]

0.0008 = 1.96*0.01/[tex]\sqrt{n}[/tex]

0.0008 = 0.0196/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex] = 0.0196/0.0008

= 24.5

n = 24.5^2

n = 600.25

Therefore 600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.

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The given statement is false.

Statistics is a science concerned with developing and studying methods of collecting, analyzing, interpreting, and presenting empirical data. Statistical research is applicable to virtually all scientific disciplines, and research challenges in various scientific disciplines motivate the development of new statistical methods and theories. Statisticians use a variety of mathematical and computational tools to develop methods and study the theory behind methods.

The given statement is false: A p-value is the probability of obtaining a sample statistic less extreme than the one observed under the assumption that the statement in the null hypothesis is true.

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Answer: C / .33

Step-by-step explanation:

There are ΔABC and ΔXYZ triangles that are congruent due to the SAS congruence postulate.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given question,

In ΔABC and ΔXYZ,

Side BC = Side YZ

m∠C = m∠Z

Side AC = Side XZ

According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Thus, both triangles are congruent.

Hence, there are ΔABC and ΔXYZ triangles congruent due to the SAS congruence postulate.

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[tex]\tan \theta=\frac{7}{16} \\ \\ \theta=\arctan(7/16) \approx 24^{\circ}[/tex]

Y in the expression represents the range of the function. Option A is correct.

Given that,
In the expression y = 12- 4x, what y = 3 represents in the function, is to be determined.

Range, it is the set of values that come out to an outcome for a certain mathematical operation.

here,
y = 12 - 4x
where, 12 = intercept , -4 = rate,
when y = 3 implies that, at the value of x, the outcome of the equation is 3 or it is said to be range.

Thus, Y in the expression represents the range of the function. Option A is correct.

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Answer:

v=53 degrees

Step-by-step explanation:

So since 180 degrees in tri, v-23+2v+v-9=180

Plus 23 and 9: 4v=212

v=53 degrees

Answer:

$8551.56

Step-by-step explanation:

In the equation

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

P is the principal (in this case, the amount loaned to Erica), r is the interest rate, n is the number of times compounded per year (12 in the problem since there are 12 months in a year), and t is the time in years.

By plugging in our principal, rate (converted to a decimal), compounding periods and time, we have:

[tex]A=5300(1+\frac{0.08}{12})^(12*6)\\ A=5300(\frac{151}{150})^(72)\\ A=8551.561=8551.56[/tex]

The probability of getting 2 white balls is 2/11.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.

Probability(Event) = Favorable Outcomes / Total Outcomes

Main body:

total balls = 5+6 =11

1st try:

P(white balls) = 5/11

2nd try:

as there is no replacement,

no. of white balls = 4

total balls =10

P( white ball) = 4/10

Now multiplying both the result = (5/11)*(4/10)

P( WHITE BALLS) = 2/11

Hence answer is 2/11.

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The equivalent equation of the given equation 3(x-4) = 18+2x-11 is given by,

x=19.

Given the mathematical equation is,

3(x-4) = 18+2x-11

Evaluating the equation we get,

3x-12 = 18+2x-11

3x-2x = 18-11+12, separating the variable and numbers

x = 19

Hence the equivalent equation of the given equation is x=19.

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The.maximum number of gigabytes Meena can use while staying within her budget is 5 gigabytes

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.

They are denoted by the symbols ≥ < > ≤.

Let the maximum gigabytes be x.

The inequality to illustrate the information will be:

38 + 3x < 55

Collect like terms

3x < 55 - 38

3x < 17

Divide

x < 17/3

x < 5 2/3

The maximum gigabytes is 5.

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The fifth number is 120

the fifth number can be calculates as follows

mean = [tex]\frac{sum of each value in the population}{number of values in the population}[/tex]

so the sum of the number is mean x number of values

sum of the 4 number = 70 x 4 = 280, while,

sum of the 5 number = 80 x 5 = 400

so the fifth number = 400 - 280 = 120

so, the fifth number is 120

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Answer:

One Solution

Step-by-step explanation:

5(3x+2)-2=4(4x-3)

15x + 10 - 2 = 16x - 12

15x + 8 = 16x - 12

15x = 16x - 20

-x = -20

x = 20

Step-by-step explanation:

8m + 20 - 6m - m + 7

We combine 8m and -6m to get 2m. Now we combine 2m and -m to get m.

This gives us:

m + 20 + 7.

We combine 20 and 7 to get 27.

This gives us the answer of

m + 27

Answer:

B)  f(5) = 8

Step-by-step explanation:

Remainder Theorem

When a polynomial f(x) is divided by (x − c) the remainder is f(c).

Therefore, if f(x) is divided by (x - 5) the remainder is f(5).

As the remainder is 8, then f(5) = 8.

The first figure is an example of a solid polyhedron,

Name of the bases: PONMQ, KJIHL

Name of the faces: HINM, IJON, JKPO, KPQL, LNMQ.

Name of the edges: HI, IN, MN, MH, LH, LQ, QM, LK, KP, PQ, KJ, JO, OP, JI, IN, ON

Name of the vertices: H, I, J, K, L, M, N, O, P, Q.

what is a solid polyhedron?

If all of the sides of a 3-dimensional solid are flat, it is a polyhedron. Soccer balls, prisms, bricks, houses, and pyramids are all real-world polyhedrons. These shapes all have flat sides. If a shape has any curved sides, it is no longer a polyhedron.

As the definition of the solid polyhedron says that if any shape has any curved sides, then it cannot be a solid polyhedron.

The second figure has curved surface, so it can't be a solid polyhedron.

Hence, the first figure is an example of a solid polyhedron,

Name of the bases: PONMQ, KJIHL

Name of the faces: HINM, IJON, JKPO, KPQL, LNMQ.

Name of the edges: HI, IN, MN, MH, LH, LQ, QM, LK, KP, PQ, KJ, JO, OP, JI, IN, ON

Name of the vertices: H, I, J, K, L, M, N, O, P, Q.

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Melitta found out that if she walks really fast during her morning exercise, she can cover 2 1/4 miles in 3/4 of an hour.

Mellita is walking with a coverage of 2.8  miles per hour. We simply need to know how far she covers in an hour to calculate her walking speed in miles per hour.

Time taken to complete 2~1/4 miles is 3/4 of an hour. This is the time she can beat, so we have to find for the remaining 1/4th half of 2~1/4 miles i.e

Miles she can cover in 1/4 of hour = 1/4 * 2~1/4

    = 1/4  * 9/4

    = 9/16 miles.

Now, Add this to the miles that she can cover, i.e 2~1/4

= 2~1/4 + 9/16

= 9/4 + 9/16

= (36+9)/16

= 45/16

= 2.8 miles.

Hence, Melitta can walk 2.8 miles per hour.

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The problem and solution are:

(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) The person will have $33 after 6 months.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation is y = 5x + 3.

(a) Problem: I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) Solution: The person gets $5 every month, therefore, he will have $5x after x month.

The person has $3 initially, therefore, the total money he will have after x month is:

y = 5x + 3

To find how much money will the person have after 6 months, substitute x=6 into the above equation:

y = 5(6) + 3

y = 30 + 3

y = 33

The person will have $33 after 6 months.

Hence, the problem and solution are:

(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) The person will have $33 after 6 months.

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Table C, which depicts the link between the quantity of books and the overall cost, is therefore the appropriate table.

Given,

7 books cost $89.25 in a bookstore.

Here, we need to locate the table that shows how the quantity of books and the overall cost relate to one another.

We must first determine the price of one book in order to determine the cost of the specified number of books.

To do that, we must divide the sum by the total number of books, from which we may calculate the price of a single book.

That works out to $89.25 for 7 books.

Consequently, the price of one book is,

=> $89.25/7

=> $12.75.

Consequently, based on the provided tables,

Cost of 8 books =  $102 (8 x 12.75).

Cost of 9 books =  $114.75 (9 x 12.75).

Table C, which depicts the link between the quantity of books and the overall cost, is therefore the appropriate table.

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The base of the Eiffel Tower in Frank's model is 4 inches.

A ratio indicates the number of times one number contains another.

Given, the height of the Eiffel Tower is 984 feet and the width at its base is 328 feet.

The ratio of height to base of the Eiffel Tower is given by:

984/328

=3

Therefore, the ratio of height to base for Frank's model should also be 3, Which is given by:

12/(base)=3

12/3=base

4 = base

Hence, the base of the Eiffel Tower in Frank's model is 4 inches.

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Using linear regression, it is found that:

a) The equation is: y = -0.00408x + 16.

b) The interpretation of each coefficient is:

The linear regression equation is obtained inserting the points given on the table at the end of the answer in a linear regression calculator.

Then the equation will have the following format of a linear function:

y = mx + b.

In which the coefficients are as follows:

The points are given as follows:

(0, 16), (242, 14.8), (519, 14.1), (698, 13.5), (825, 12.7), (1009, 11.6).

Using the calculator, the equation is:

y = -0.00408x + 16.

The problem is given by the image at the end of the answer.

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The missing length indicated for 3 and 4 are The value of x is 28, the value of x is 18

What is triangle similarity rule?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal, and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "~"

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose shapes are similar to one another.

1. As we can see all the sides belongs to the same right-angled triangle

Therefore, ratio of similar sides will be equal

i.e.

[tex]\frac{12}{15} = \frac{x}{35}\\\\x=\frac{12}{15}(35)[/tex]

x=28

2. As we can see all the lines with red arrows are parallel to each other

Therefore, the corresponding angles will be equal

i.e.

[tex]\frac{8}{24}=\frac{x}{54}[/tex]

[tex]x=\frac{8}{24}(54)[/tex]

x = 18

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The angle of elevation is 18. 43 degrees

Angle of elevation can be described as an angle formed between a horizontal line and the line of sight above the line.

From the information given, we have that;

Using the tangent identity, we have;

tan θ = opposite/ adjacent

tan  θ = 1/ 3

Divide the values

tan θ =0. 3333

Find the tan inverse of the value to determine  θ

θ = tan^-1(0. 3333)

θ = 18. 43 degrees

Hence, the value is 18. 43 degrees

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The cost of one knife is £ 5.52.

Given, one knife is equal to three times spoon.

Let the cost of knife be x, and cost of spoon be y.

x=3y. ------(1)

9 spoons and 12 knives costs £82. 80, which can be written as

9(spoons)+12(knife)=£82. 80

9y+12x=£82. 80

9y+12(3y)=£82. 80

9y+36y=£82. 80

45y=£82. 80

y=£82. 80/45

y=£ 1.84

The cost of one spoon is £1.84.

We have to find the cost of one knife, we can substitute the value of y in equation 1 to get the cost of one knife.

x=3(1.84)

x=5.52.

Therefore, the cost of one knife is £5.52.

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Corrected Question

A knife is three times the cost of a spoon.  9 spoon and 12 knives cost £82. 80 work out the cost of one knife.

Answer:

f(5) = 22; f(9) = 34

Step-by-step explanation:

f(5) = 3(5) +7

f(5) = 22

f(9) = 3(9) +7

f(9) = 34