At one university, the mean distance commuted to campus by students is 19.0 miles, with a standard deviation of 4.2 miles. Suppose that the commutedistances are normally distributed. Complete the following statements.(a) Approximately 95% of the students have commute distances between ? milesand ? miles(b) Approximately ? of the students have commute distances between 6.4 miles and 31.6 miles.

Answer:

x = 61

Step-by-step explanation:

sqrt = square root

sqrt(x + 20) = 9 square both sides to cancel out sqrt

x + 20 = 81 subtract 20 to get x alone

x = 61

The proportion of the ore's composition that is neither silver nor copper is  99.9536 %.

What is percentage ?

Percentage , which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

The ore is found to be 0.0094 % silver and 0.037 % copper.

The percentage of matter in the ore that is

neither silver nor copper is = 100% - 0.0094 % - 0.037 %

= 99.9536 %

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As y varies directly with x, the numerical value of x when y = 55 is 5.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A direct variation equation is a linear equation in two variables.

It is expressed as;

y ∝ x

Hence,

y = k(x)

Where k is proportionality constant.

Given that;

First, we determine the proportionality constant of the direct variation.

y = k(x)

77 = k(7)

Divide both sides by 7

77/7 = k(7)/7

k = 77/7

k = 11

Now, we find the value of x when y = 55

y = k(x)

55 = 11(x)

Divide both sides by 11

55/11 = 11(x)/11

x = 55/11

x = 5

Therefore, the numerical value of x is 5.

Option D)5 is the correct answer.

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Answer:

  y = x³ -2x² -13x -10

Step-by-step explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

  p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

  p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

  y = x³ -2x² -13x -10

A turkey casserole (30 servings) uses 3.75 pounds of the turkey breast. To scale the recipe for 50 servings we need 6.75 pounds turkey.

The currency of the United Kingdom and nine of its affiliated territories is called sterling (stg; ISO code: GBP). The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.

The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, the euro, and the Japanese yen, it is currently the fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with other three currencies and the renminbi. Midway through 2021, sterling is also fourth most-held reserve currency in global reserves.

if 30 servings uses = 3.75 pounds

then, 1 serving = 3.75 pounds/ 30

50 servings = [tex]\frac{3.75}{30} * 50[/tex]= 6.25 pounds

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(x+18)° is vertical opposite 112° and vertical opposite angles are equal meaning

⇒(x+18)°=112°

x+18°=112°

x=112°-18°

∴x=94°

(2y)° is in a straight line with 112° meaning their sum is 180°

[tex]2y+112=180\\2y=180-112\\2y=68\\\frac{2y}{2} =\frac{68}{2} \\y=34[/tex]

∴y=34°

Answer: 47

Step-by-step explanation:

answer: solutions is x = - 2

Answer:

[tex]{ \tt{ {x}^{2} + 2 = 0 }} \\ \\ { \tt{ {x}^{2} = - 2 }} \\ \\ { \tt{x = \sqrt{ - 2} }}[/tex]

- At this point, we can't operate the square root. Let's introduce the imaginary part of a value

From complex numbers;

[tex]{ \boxed{ \tt{{ \red{note} \: {\rightarrow{i \times i = - 1 = {i}^{2} }}}}}}[/tex]

Therefore;

[tex]{ \tt{x = \sqrt{2 \times {i}^{2} } }} \\ \\ { \boxed{ \rm{ \: x = i \sqrt{2} \: \: }}}[/tex]

C) Triangle ABC is equilateral.

E) Segment AB is the same length as segment AC because they are both radii of the same circle centered at point A.

F) Segment AB is the same length as segment BC because they are both radii of the same circle centered at point B.

In the given figure,

A and B are the centres of the two intersecting circles.

In a circle having centre at A, we have

AC = AB = radius

In a circle having centre at B, we have

BC = BA = radius

According to Euclid's first axiom, things that are equal to the same thing are equal to one another.

Therefore, AC = AB = BC

Hence, the triangle is an equilateral triangle.

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Answer:

[tex]\frac{81}{241}[/tex]

Step-by-step explanation:

multiply both numbers by 100.  241 is prime so you cannot reduce it further.

Answer:

384x² - 486xy²

Step-by-step explanation:

I think this is the answer all I did us first i solved the brackets then I multiplied them by 6x

Answer:

P' (- 5, 3 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x , - y ) , then

P (- 5, - 3 ) → P' (- 5, 3 )

The entered points (6,4) and (6,-7) belong to a vertical line, There is no slope and The entered points (-9,-5) and (-9,5)belong to a vertical line. There is no slope.

          Formula: x = 6.

       Angle (θ)=90°

       Location (d) = 11

       (x)=0 Distance between x's

       d = (y2 + x2) = (-112 + 02) = 121 = 11 is the distance between y's (y)=11.

        Formula: x = -9.

       Location (d) = 10

        (x)=0 Distance between x's

        Distance between y's (d) = y2 + x2 = 102 + 02 = 100 = 10

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The simplified inequality is x > 7.

What is an inequality?

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: (i)The symbol a b indicates that an is less than b. (ii)A > b indicates that an is greater than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed. In contrast to rigorous inequalities, there are two forms of non-strict inequality relations.

The given inequality -3 < x - 10

or, -3 + 10 < x

or, 7 < x

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The slope of the new road is zero.

The slope of a line is the change in y with respect to the change in x.

In other words, the slope of a line is rise over run.

Therefore, the new road the city planner wants to build is perpendicular to the the D street.

(5, 1)(5, 4)

slope of D street = 4 - 1 / 5 - 5

slope of D street = 3 / 0

slope of D street = infinity

An infinite slope is simply a vertical line. Therefore, it is only perpendicular to a horizontal line which will have a slope of 0. Hence, the new road should have a slope of 0.

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How are the given functions ordered based on their slopes?

1.  y = -2x+ 3

slope = m= -2  

tanФ = -2                 -----(1) Least steep slope

Ф = -63.4°  

2. y= 3/4x-3

slope = m = 3/4      ------(3)

tanФ = 3/4

Ф= 36.9°

3. y= 4x+0.5

slope = m = 4          ------(5) Steepest

tanФ = 4

Ф = 75.9°

4. y= x+42

slope = m= 1            ------(4)

tanФ= 1

Ф= 45°

5. y = - 0.5x+ 7

slop = m= -0.5         -----(2)

tanФ = -0.5  

Ф = -26.56°

What is a slope?

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4408 books must to be produced so that production costs is equal to sales money.

Production costs refers to the direct and indirect costs that come from manufacturing a product. Production costs usually include expenses, such as labor, raw materials and manufacturing supplies. Cost of products sold are the production costs incurred on goods that is actually sold in a certain specified period

Let the no. of books= X

Cost = 9.25X + 49590

revenue = 20.50X

20.50X = 9.25X+ 49590

20.50X - 9.25X = 49590

11.25X = 49590

X = 4408

4408 books must to be produced so that production costs is equal to sales money

We can Check by:

cost = 9.25(4408) + 49590

        = 40774+ 49590

cost = 90364

revenue = 20.5(4408)

revenue = 90364

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The point is located at 3 1/2 points to the left of the origin and 1 1/4 points below the origin

The coordinate of the point on a coordinate plane is given as

Point = (-3 1/2, -1 1/4)

Rewrite the above coordinate as follows:

(x, y) = (-3 1/2, -1 1/4)

Split the coordinates into x and y coordinates

So, we have the following equations

x = -3 1/2

y = -1 1/4

The above means that:

Next, we plot the points

See attachment for the plot of the points on a coordinate plane

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1) Given this equality,

15x = 75 Divide both sides by 15

x=5

2) Then we can write that since x = 5 and 15x = 75 we have here is the Division Property of Equality.

Because in this case, we divided both sides by 15, which is different from zero to find equivalent equality.

3) So

Given

Answer

The graph (g-f)(x)=-4x complies with the query.

An edge denotes the connection between the x and y vertices and is represented by the pair (x ,y). In the examples that follow, circles stand in for vertices and lines for edges.

The graph indicates that line generated by function f(x) passes through the points (1,-3) and (0,0) and that line similarly passes through the points (1,1) and (0,0).

With the use of the formula Y-Y1 = y2-y1/x2-x1, we can thus determine the equation of the lines (x-x2)

Therefore, the equation of the line produced by the function f(x) y+3= 3-0/0-1 (x-1)

Function f(x) Equals 3x since y+3=-3x+3 y=-3x.

the line drawn by the function g(x) has the equation y=x, hence function g(x)=x.

We now need to figure out, (g-f) (x) = g(x)- f(x) = -3x-x = -4x

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Answer:

536

Explanation:

rom the given table:

If an individual and spouse enroll in the low deductible plan, the monthly premium will be $536.

It should be emphasized that a relationship is proportional if its graph is a line that passes through its origin.

If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to do this, the ratio is not proportional. The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.

If the graph of a relationship is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional. Additionally, if anything is not linear, it is not proportionate.

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The equation of the polynomial is P(x) = 6.86(x + 5) (x + 3) (x - 1)

Given,

x intercepts which the polynomial passes though = (-5, 0), (-3, 0), and (1, 0).

Point = (3, 14).

We have to find the polynomial equation;

A polynomial is defined as;-

P(x) = a(x - c₁) (x - c₂)....(x - cₙ)

Here,

a is a constant

c₁, c₂,...cₙ are the zeros of the polynomial

Here,

-5, -3 and 1 are the zeros of the given polynomial

(x + 5), (x + 3) and (x - 1) are the factors of the given polynomial.

Then the equation of polynomial be like;

P(x) = a(x + 5) (x + 3) (x - 1)

This polynomial passes through point (3, 14)

That is,

14 = a(3 + 5) (3 + 3) (3 - 1)

14 = a x 8 x 6 x 2

14 = 96a

a = 96/14

a = 6.86

Substitute this in equation of polynomial;

That is,

P(x) = 6.86(x + 5) (x + 3) (x - 1)

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Answer: its 243

Step-by-step explanation:

The condition "two more than the quotient of a number and 4 is equal to 9"  gives the number 28.

Each component of a division equation has its own name.

The following describes the relationship between such four parts:

Dividend = Divisor x Quotient + Remainder

For the given problem;

Two more than the quotient of a number and 4 is equal to 9.

Let the number be n;

n/4 + 2 = 9

Simplifying;

n/4 = 9 - 2

n/4 = 7

n = 7×4

n = 28

Thus, the value of the number is found as 28.

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Answer:

(-40)

Step-by-step explanation:

therefore, 3x0=0

(6x8)+k=0

40+k=0

k=0-40

k=(-40)

The water pressure on a submerged object is given by P = 64d, then the

a. The answer to the subject of the formula, "d," is d = P/64.

b.  The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

Given the role as;

P = 64d

Where;

P stands for pounds per square foot of pressure.

d represents the object's depth in feet.

Let's now make the variable "d" the focus of the formula.

The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.

(a) We get,

P/64 = 64d/64

d = P/ 64

(b) P equals 672 pounds per square foot if there is pressure.

When the variable's value is substituted into the formula, we get;

d = P/64

Then,

d = 672/64

Discover the quotient,

d = 10. 5 ft.

The value is 10.5 feet .

Therefore,

a. The answer to the subject of the formula, "d," is d = P/64.

b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet.

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To find the x-intercept, simply but y=0 in the equation given and solve for x

That is;

3x - 4y = 12

3x - 4(0) = 12

3x = 12

Divide both-side of the equation by 3

x= 4

The x-intercept is;

(4, 0)

To find the y-intercept, simply put y=0 in the equation given and then solve for y

That is;

3x - 4y = 12

3(0) - 4y = 12

-4y = 12

Divide both-side of the equation by -4

y = -3

The y-intercept is (0, -3)

Hence, the correct option is B.

x-int: (4,0)

y-int: (0, -3)