A Banks loan officer rates applicants for credit the ratings can be described by a normal model with a mean of 200 and a standard deviation of 50. If an applicant is selected what percentage can be between 200 and 275?

The slope of 2 and passes through the point (-8,1)  :  y-1 = 2(x+8)

what is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The standard equation of a line in point slope form is expressed as;

so ,

y-y0 = m(x-x0)

m is the slope

(x0, y0) is the point

Given

Slope m = 5 (assumed value)

Point (-8,1)

Substitute the given data's into the formula

y -1 = 5(x-(-8))

y-1 = 5(x+8)

Hence the required equation is y-1 = 5(x+8)

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Based on the triangle inequality theorem, the set of side measurements that could be used to form a triangle is: D. 5, 11, 8.

The triangle inequality theorem states that three set of side measurements, a, b, and c would form a triangle if a + b > c, that is, the sum of any of two sides should be greater than the third side.

The set of side of measurements 5, 11, 8 will form a triangle because:

5 + 11 > 8 ⇒ 16 > 8

5 + 8 > 11 ⇒ 13 > 11

8 + 11 > 5 ⇒ 19 > 8

The other set of side of measurements do not conform to this criterion set by the triangle inequality theorem, therefore, the only set of side measurements that will form a triangle is: D. 5, 11, 8.

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Answer:

D.

5, 11, 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

the angles in a triangle add up to 180

2x + 3x + 4x = 180

(combine like terms)

9x = 180

(divide both sides by 9 to find out what x is)

x = 20

so now we know

(2x)° = 40°

(3x)° = 60°

(4x)° = 80°

What is the measure of the largest angle in the triangle shown above?

Given,

angle I = 54 degrees

angle FBC = 44 degrees

Recall, the sum of the angles in a triangle is 180 degrees. This means that for triangle BIC,

angle B + angle I + angle BCI = 180 degrees

54 + 44 + angle BCI = 180

angle BCI + 98 = 180

angle BCI = 180 - 98 = 82(sum of angles in a triangle)

Since lines AD and EH are parallel,

angle BCI and angle FGI are corresponding angles(They have similar positions and lie on the same side of the transversal, CI)

Thus,

angle FGI = 82(corresponding angles)

angle CGH and angle

angle CGH and angle FGI are vertically opposite angles. Vertically opposite angles are equal. Thus,

angle CGH = 82 degrees

The reason is 'vertically opposite angles'

Answer:20%

Step-by-step explanation:

1500/75=20(%)

Answer:   The average rate of change is −3.

Step-by-step explanation:

The average rate of change f(x) on the interval [a,b] is (f(b)−f(a))/(b−a)

a=−5 , b=5, f(x)=3x2−3x+1.

(f(b)-f(a))/(b-a)= (1-3(5)+3(5)^2-(1-3(-5)+3(-5)^2)) / (5-(-5)) = -3

Answer:

c

Step-by-step explanation:

c

The graph of the proportional relationship between the two quantities is attached below.

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we have that

35,867 ------> represents 100%

Applying proportion

Find out how much percentage represents 13,232

100/35,867=x/13,232

solve for x

x=(100/35,867)*13,232

x=36.89% ------> 37%

Sherry has $112.

bo              

Answer: Sherry has $112

Answer:

7(1 + 6)

Step-by-step explanation:

Solution:

Note that Mikayla has three savings accounts that she distributes her money into each paycheck. Now, let us denote by x the money in the accounts, thus if she wishes to put at least $80 into each account this paycheck, this means that the total amount of money must be greater than or equal to 3(80). This is equivalent to say:

this is equivalent to:

so that, we can conclude that the correct answer is:

Answer:

3.20611579...

Step-by-step explanation:

1.26

1) We can calculate that by writing out this algorithm:

We proceed normally as if we had two whole numbers. Multiplying 7 by each number.

Note that since there are two decimal places in the factor 0.18 we count two decimal places from the left to the right in the product.

2) Thus the answer is 1.26

Given

coordinates (2, 3) and centre points (0,0)

Find

Equation of a circle

Explanation

As we know the standard equation for a circle with centre (h , k ) and r is a radius

since, center is (0 , 0) , the equation becomes

Now, we find the value of radius , it is can find by using the pythagoras theorem,

so,

Final Answer

The equation for a circle passing through (2, 3) is

Answer:

Step-by-step explanation:

distance between the two points:

[tex]\sqrt{ (x_2-x_1)^{2} +(y_2-y_1)^2[/tex]

[tex]\sqrt[/tex](13-6)²+(28-23)²

√(7)²+(5)²

√49+25

√74

distance: 8.6cm

midpoint=

[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]

(6+3/2,23+28/2)

(19/2,51/2)

(9.5,25.5)

Therefore, number of bundles of tomatoes which was sold as selling price are: 225.5

What is selling price or sale?

In mathematics, the term selling price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called selling price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.

According to the question, the organic producer sells bundle of tomatoes as the selling price of $8 and the bunches of green beans as $5.

Total sales amount is: $464

In this, people bought three times more tomatoes as green bean bunches.

Let us assume tomatoes be 'x' and green beans be 'y'

3x + y = $464

x + y = $13

⇒ 2x = 451

⇒ x = 225.5 dollars

Therefore, number of bundles of tomatoes which was sold as selling price are: 225.5 dollars

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slope = (change in y)/ change in x

Answer: 3 Vans are needed.

Step-by-step explanation:

There are 30 students so already you need 3 vans, if you only have 2 vans, you will be leaving behind 10 students so regardless you need a 3rd van. with 3 vans you can hold 33 people. 30 students+ 3 drivers=33 people.

The inequality that represents the number of vans for the given case is V ≤ 30/11.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

Suppose the number of vans be V.

The number of students for each van is 11.

And, the total number of students is 30.

Now, the inequality for the number of vans can be written as,

11V ≤ 30

⇒ V ≤ 30/11

Hence, the inequality for the number of vans is given as  V ≤ 30/11.

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to find the x intercept, we need to replace y by 0, so we get

to find the y-intercept we need to replace x by 0

(9x² + 8x) - (2x²+ 3x)  = 7x² + 5x .

By simplifying we get x( 7x + 5) .

Consider two polynomials,

(9x² + 8x) and (2x² + 3x)

The difference of polynomials is,

(9x² + 8x) - (2x²+ 3x)  

9x² + 8x - 2x²+ 3x

= 7x² + 8x - 3x

= 7x² + 5x

Simplifying we get ,

taking x common,

= x( 7x + 5) .

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The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.

The given polynomial expression is 3x² + 3bx - 6x - 6b.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factors of given polynomial can be find using grouping method, that is

(3x² + 3bx) - 6x - 6b

=3x(x+b)-6(x+b)

=(x+b)(3x-6)

=3(x-2)(x+b)

The factors of the given polynomial is 3(x-2)(x+b). Therefore, option C is the correct answer.

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To determine which option is a representation of the graph we need to make the numer line analysis; to make it we need to notice that the functions has zeros at the points:

once we know this we divide the number line in the following intervals:

now we need check the sign of the function in each interval, to do this we choose a value in them.

For the first interval let's take x=-4, then we have:

From the last expression we notice that the value of the function is positive at this point. Hence the firts interval have positive values for the function.

For the second interval let's take x=-1, then we have:

From the result we conclude that the function is negative in this interval.

For the third interval, let's take x=1, we have:

From the result we conclude that the function is positive in this interval.

For the fourth interval, let's take x=3. then we have:

Then the function is positive in this interval.

Finally, for the fifth interval let's take x=5, then we have:

Then the function is negative in the last interval.

Hence the line analysis is:

The y-intercept of the function happens when x=0, then we have that:

Therefore the y-intercept of the function is 0.

Once we know the information from the line analysis and the y-intercept of the function we conclude that the sketch of the graph is option B.

Two graphs of the function (with different values for the y-axis) are shown below:

This graphs confirm that option B is an approximate sketch of the graph.

Given:

A third-degree polynomial function with a negative leading coefficient not appropriate for modeling non-negative real-world phenomena over a long period of time.

Explanation:

Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.

That is, the end behavior of the graph will always be negative on the right.

Final Answer:

Because a third-degree polynomial function with a negative leading coefficient is always going to turn negative as the independent variable increases.

That is, the end behavior of the graph will always be negative on the right.

A. The corresponding angles of triangles are coungrent (YES)

B. The triangles have the same shape (YES)

C. The triangles have the same size (YES)

D. The corresponding sides of the triangles are congruent (YES)

For the given expression √25 = ∛125. As, 5 is equal to 5.

For the given question;

Square root of 25 i.e, √25

To identify the square root of 25, determine the number because when multiplied by itself yields 25. The square root of 25 is thus 5.

To find the cube root of 125, determine the number that when multiplied on its own twice yields 125.

The cube root of 125 is thus 5, because 5×5×5 = 125.

The radical sign with such a small three (named the index) above and on the left is the symbol for cube root.

Thus, both the values are equal.

√25 = ∛125.

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Kali will have to work a minimum of 10 hours and a maximum of 22 hours to earn between 200 and 400. The inequality representing the solution will be 9 ≤ 15.75x ≤ 22.

In the question, it is stated that Kali earns $15.75 and a flat fee 0f 50. She wants to maintain her earnings between 200 and 400. Potential earning will be 'x'. The equation representing the earnings is 200 ≤ 15.75x + 50 ≤ 400. We will have to solve the inequality and find out the value for x.

=> 200 ≤ 15.75x + 50 ≤ 400

Subtracting 50 from the equation,

=> 150 ≤ 15.75x ≤ 350

Dividing the equation by 15.75

=> 9.52 ≤ x ≤  22.22

So, here x lies between 9.52 and 22.22. After rounding off we get range 10 and 22.

Hence, the solution for the inequality is 9.52 ≤ x ≤  22.22

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Answer: 2 kg

Step-by-step explanation:

If you are an apprentice plumber earning an annual salary of $21,060, and you lay claim to 3 allowances, the amount that will be withheld from your weekly pay for federal income tax is: $7.

To obtain the correct amount to be paid, we need to use the table provided by the IRS. First note that there are 52 weeks in a year, so we need to divide your annual earnings by the total number of weeks in a year.

So, 21060/52 = $405

When we look at the table to see the chart for a person who has a weekly wage of 400 - 410, and lays claim to three allowances, we will see that the right amount that such an individual is meant to pay is $7.

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