Write each expression using a single exponent. x to the ninth over x squared

Answer:

[tex]P=0.735[/tex]

Step-by-step explanation:

Call A to the event in which Nathan is allergic to penicillin

So

[tex]P (A) = 0.75[/tex]

[tex]P (A') = 1-P (A) = 0.25[/tex]

Call B the event in which the skin test predicts correctly.

So:

[tex]P (B) = 0.98\\P (B ') = 1-P (B) = 0.02[/tex]

We look for the probability that Nathan is allergic to penicillin and the test predicts it.

This is [tex]P (A\ and\ B)[/tex].

[tex]P (A\ and\ B) = P (A)*P (B)\\\\P (A\ and\ B) = 0.75 * 0.98\\\\P (A\ and\ B) = 0.735[/tex]

ANSWER

260 miles

EXPLANATION

The equation that models the cost is

[tex]y = 35 + 0.25x[/tex]

If you have a maximum of $100 to spend for the car rental, then we can equation the cost function to

$100 to determine the maximum number of miles you could travel.

[tex]35 + 0.25x = 100[/tex]

[tex]0.25x = 100 - 35[/tex]

[tex]0.25x = 65[/tex]

[tex]x = \frac{65}{0.25} [/tex]

[tex]x = 260mi[/tex]

Therefore the maximum number of miles you can travel is 260 miles

The answer would be 2. Angle PQR = Angle SQT

Hope it helps :)

Answer is 2 for sure Goodluck.

Answer:

[tex]y=- 4x + 4[/tex]

Step-by-step explanation:

The slope formula for a straight line is:

[tex]y=mx+b[/tex]

Where, 'm' is the slope and 'b' is the y-intercept.

To find the x-intercept of a line, we need to equal 'y' to zero, and then solve for 'x'. In this case we know that the x-intercept is 1, so we have the point (x1, y1)=(1,0). We are given a second point which is: (x0, y0)=(-2, 12).

To find the slope, we use the following formula:

[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-12}{1-(-2)} = -4 [/tex]

Now, The equation of the line is: y - y0 = m(x-x0). Then, substituting the values of 'm', 'x0' and 'y0' we have that:

[tex]y - 12 = -4(x+2) ⇒ y = -4x-8 + 12 ⇒ y=- 4x + 4[/tex]

The equation of the line using the slope-intercept form is:

[tex]y=- 4x + 4[/tex]

Answer:

Step-by-step explanation:

The equation of a circle in the standard form:

[tex](a-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex]x^2+y^2-12y-15=0[/tex]

Convert into a standard form using

[tex](a-b)^2=a^2-2ab+b^2\qquad(*)[/tex]

[tex]x^2+\underbrace{y^2-2(y)(7)+7^2}_{(*)}-7^2-15=0\\\\(x-0)^2+(y-7)^2-49-15=0[/tex]

[tex](x-0)^2+(y-7)^2-64=0[/tex]           add 64 to both sides

[tex](x-0)^2+(y-7)^2=64[/tex]

The center (0, 7)

The radius: r = √64 = 8

Answer:

b

Step-by-step explanation:

Also got B if you it’s not right let me know send me a comment and I will try to help with the best of my ability

Answer:

The function is A = 10√r

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

  variables that can be expressed by an equation in which one

  variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

 constant of variation

* Now lets solve the problem

# A is varies directly with the square root of r

- Change the statement above to a mathematical relation

∴ A ∝ √r

- Chang the relation to a function by using a constant k

∴ A = k√r

- To find the value of the constant of variation k substitute A and r

 by the given values

∵ r = 16 when A = 40

∵ A = k√r

∴ 40 = k√16 ⇒ simplify the square root

∴ 40 = 4k ⇒ divide both sides by 4 to find the value of k

∴ 10 = k

- The value of the constant of variation is 10

∴ The function describing the relationship of A and r is A = 10√r

Answer:

A = 10[tex]\sqrt{r}[/tex]

Step-by-step explanation:

Given A varies directly with the square root of r then the equation relating them is

A = k[tex]\sqrt{r}[/tex] ← k is the constant of variation

To find k use the condition r = 16 , A = 40

k = [tex]\frac{A}{\sqrt{r} }[/tex] = [tex]\frac{40}{\sqrt{16} }[/tex] = [tex]\frac{40}{4}[/tex] = 10

A = 10[tex]\sqrt{r}[/tex] ← equation of variation

Answer: 2 pounds

Step-by-step explanation: There are 16 ounces in one pound. So when you divide 32 by 16, you get 2. Therefore your answer would be 2 pounds!

For this case we must make a conversion.

We know, by definition, that 1 ounce is equivalent to 0.0625 pounds.

We make a rule of three to determine how many pounds are 32 ounces.

1oz ---------------> 0.0625lb

32oz -------------> x

DOnde "x" represents the number of pounds

[tex]x = \frac {32 * 0.0625} {1}\\x = 2[/tex]

So, 32 ounces equals 2 pounds

Answer:

2 pounds

Answer:

x = 0, y = 7

Step-by-step explanation:

Solving a system of equations using substitution requires one side to be equal to a variable present in the equation, in this case x or y. We should simplify the equation using elimination before substituting to reduce the chance of error.

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. These equations arew already aligned for us.

                  3x - 10y=-70

             -   4x +9y = 63

                  -x + y = 7

Now, for substitution, the equation must be set to a variable.

                  -x + y = 7

                  y = x + 7

Next, plug the equation in where applicable in another equation.

                  4x +9(x + 7) = 63

                  4x + 9x + 63 = 63

                  13x = 0

                  x = 0

The final step of substitution is to plug the known variable into an equation to find the other variable.

                  3(0) - 10y=-70

                  0 - 10y = -70

                  10y = 70

                  y = 7

I guarantee you this answer is correct, I worked it out using other methods and graphing prior to submitting this answer.

Answer:

x = 0 , y = 7

Step-by-step explanation:

[tex]3x - 10y = - 70..............(1) \\ 4x + 9y = 63...................(2) \\ (1) \times 4 \\ 12x - 40y = - 280...........(3) \\ (2) \times 3 \\ 12x + 27y = 189...........(4) \\ (4) - (3) \\ 67y = 469 \\ \\ y = \frac{469}{67} \\ y = 7 \\ put \: y = 7 \: into \: (1) \\ 3x - 10(7) = - 70 \\ 3x - 70 = - 70 \\ 3x = - 70 + 70 \\ 3x = 0 \\ x = \frac{0}{3} \\ x = 0[/tex]

Option D. an isulator

Is the right answer i guess...

As The transfer of electrons increases The cunductivity also increases...

Hope it helps...

Regards,

Leukonov/Olegion.

Answer:

Insulator

Step-by-step explanation:

As insulators are meant to prevent the conduction of electricity.

so we know the point E is on the circle, thus the distance NE is really the radius of the circle hmmm what would that be?

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad E(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-1-(-6)]^2+[1-(-2)]^2}\implies r=\sqrt{(-1+6)^2+(1+2)^2} \\\\\\ r=\sqrt{5^2+3^2}\implies r=\sqrt{34}\implies r\approx 5.83 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad H(\stackrel{x_2}{-10}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NH=\sqrt{[-10-(-6)]^2+[-7-(-2)]^2} \\\\\\ NH=\sqrt{(-10+6)^2+(-7+2)^2}\implies NH=\sqrt{(-4)^2+(-5)^2} \\\\\\ NH=\sqrt{41}\implies NH\approx 6.4\impliedby \begin{array}{llll} \textit{units away from the center}\\ \textit{is outside the circle} \end{array}[/tex]

recall the radius is about 5.83, anything shorter than that is inside the circle, anything longer than that is outside it.

Answer:

outside the circle

Step-by-step explanation:

trust me. i did it on khan academy

Answer:

172.92 minutes

Step-by-step explanation:

Step 1: Write a proportion

33/5 = X/26.2

Step 2: Solve your proportion

X = 172.92

Find the rate for the number of minutes per mile. (# of minutes/mile)

33 minutes/5 miles = 6.6 minutes/mile

It takes him 6.6 minutes to run a mile, so you can multiply 26.2 miles by 6.6 minutes to find how long it takes him to run 26.2 miles.

26.2(6.6) = 172.92 minutes

Answer:

585$

Step-by-step explanation:

multiply 55 by 5, then multiply 20 by 8, last multiply 25 by 6 and add each of the totals to one another.

The mean ticket price is 5.85

This is the assumption method ;)

Take all tickets to be adult tickets

$9 x 553 = $4977

Then..... $4977 - $3936 = $1041

The difference between the child and adult ticket is $3, so divide $1041 by $3

$1041 divided by $3 = 347

347 is the number of child tickets sold

347 x $6 = $2082

So 553 - 347 = 206 ( no. of adult tickets )

206 x $9 = $1854

Child tickets sold : 347

Adult tickets sold : 206

:0 ITS MAGIC IM SO SMART

Answer:

347 child tickets and 206 adult tickets are sold

Step-by-step explanation:

Let x be the no. of child tickets sold

Let y be the no. of adult tickets sold

A ticket office sold 553 tickets one day.

Equation becomes : [tex]x+y=553[/tex] ---A

Cost of 1 child ticket = $6

Cost of x child tickets = 6x

Cost of 1 adult ticket= $9

Cost of y adult tickets = 9y

Now we are given that the receipts totaled $3936.

So, Equation becomes : [tex]6x+9y=3936[/tex] ---B

Plot A and B

[tex]x+y=553[/tex] ---Green

[tex]6x+9y=3936[/tex] ---Purple

Intersection point = (x,y)=(347,206)

Refer the attached figure

Hence 347 child tickets and 206 adult tickets are sold

Answer:

4 n - 7

Step-by-step explanation:

- 3 , 1 , 5 , 9

The difference between the terms is 4, so our multiplier is 4 n

4 , 8 , 12 , 16 ( The 4 times tables )

-3 , 1 , 5 , 9 ( The original sequence )

What are we doing to get from the 4 times tables to get to the original sequence?

4 - - 3 = 7

8 - 1 = 7

12 - 5 = 7

16 - 9 = 7

We are subtracting 7 so our complete general term is 4 n -7

Answer:

4.3 feet

Step-by-step explanation:

48 miles. If 1 inch means 12 miles you can multiply both sides by 4 to get "4 inches = 48 miles"

Answer:

  square

Step-by-step explanation:

A graph reveals all side lengths are the same and sides are perpendicular. The quadrilateral is a square.

Answer:

y-axis

Step-by-step explanation:

Step-by-step explanation:

[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\\dfrac{9!}{9-32}=\dfrac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{-23}=-\dfrac{362880}{23}[/tex]

In this Multiplication in Algebra question, The expression '80 (1/4) x' is equivalent to '20x'. When the constant 80 multiplies with the fraction 1/4, the product then multiplies with the variable 'x' resulting in a simplified expression '20x'.

The given mathematical expression 80 (1/4) x can be simplified using the rules of multiplication in algebra.

Here the number 80 multiplies with the fraction 1/4 and then by the variable 'x'.

To carry out this operation, first multiply 80 by 1/4 which equals to 20, and then multiply this by 'x', so your final result would be 20x. Hence, the expression 80 (1/4) x is equivalent to 20x.

Learn more about Multiplication in Algebra here:

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The probable question may be:

Which is equivalent to 80 (1/4) x

Answer:

z = [tex]-\frac{2}{5}[/tex] or - 0.4

Step-by-step explanation:

8+2z = 6 - 3z

2z = 6 - 8 - 3z

2z + 3z = - 2

5z = -2

z = [tex]-\frac{2}{5}[/tex] or - 0.4

Answer:

arithmetic

Step-by-step explanation:

The points fall on a straight line. They won't do that for a geometric sequence.

___

Normally the terms of either sort of sequence are numbered with counting numbers: 1, 2, 3, .... Your x-values are negative, so are obviously not term numbers of a sequence. The differences of x-values are 1, and the differences of y-values are 2.5, so we know the x- and y-values are linearly related. That relationship can be expressed in point-slope form by ...

y = 2.5(x +1) +12.5

which can be simplified to

y = 2.5x +15

__

The arithmetic sequence with first term 17.5 and common difference 2.5 would be described by this same equation.

Answer:

O.118 seconds will be taken for a radio signal to travel from a satellite to the surface of earth.

Step-by-step explanation:

We are given Speed = 3.00 · 10^8 meters per second.

And Distance = 3.54.10^7 metwers

We need to find time.

We know that,

Distance = Speed * Time

3.54.10^7 = 3.00 · 10^8 * Time

Time = 3.54.10^7 / 3.00 · 10^8

Time = 1.18 X 10^7-8

Time = 1.18 x 10^-1

Time = 0.118 seconds.

So, O.118 seconds will be taken for a radio signal to travel from a satellite to the surface of earth.

It would be A.

All of the others include “Natural Numbers” -5 is not a natural number. A natural number is a counting number like 1,2,3,4,5.

Answer: I believe your answer is A.

hope you get 100%! ^.^

move parentheses by 6. 12x+110=6x+600

move variable to its left side and change its term 12x+110-6x=100

collect like terms and subtract 12 the divide both sides by 6.

answer 81.666666666666

Answer:

[tex]x = 230/3\\[/tex]

Step-by-step explanation:

Step 1:  Distribute

12x + 110 = 6(x + 100)

12x + 110 = (6 * x) + (6 * 100)

12x + 110 = 6x + 600

Step 2:  Subtract 6x from both sides

12x + 110 - 6x = 6x + 600 - 6x

6x + 110 = 600

Step 3:  Subtract 110 from both sides

6x + 110 - 110 = 600 - 110

[tex]6x = 490[/tex]

Step 4:  Divide both sides by 6

[tex]6x / 6 = 490 / 6[/tex]

[tex]x = 490 / 6[/tex]

[tex]x = (460/2) / (6/2)[/tex]

[tex]x = 230/3[/tex]

Answer:  [tex]x = 230/3\\[/tex]

Answer:

The answer to the question

Check the picture below.

Answer:

The correct answer is last option.

m<AEB = 140

Step-by-step explanation:

From the figure we can see  rectangle.

It is given that, m<ADE = 70°

To find the value of m<AEB

From the figure we get Triangle ADE is isosceles triangle

<DAE = 70°

Therefore m<AED = 180 - (70 + 70) = 40°

<AED and <AEB  are linear pairs

Therefore m<AEB = 180 - m<AED

 = 180 - 40 = 140

The correct answer is last option

140

Answer:

2,160 [tex]ft^{3}[/tex]

Step-by-step explanation:

The formula is V = lhw

15 x 24 x 6 = V

15 x 24 = 360

360 x 6 = 2,160

2,160[tex]ft^{3}[/tex]

Answer: 180 ft³

Step-by-step explanation:

You can calculate the volume of a right rectangular prism with this formula:

[tex]V=lwh[/tex]

Where "l" is the length and "w" is the width.

You know that the height of that this right rectangular prism is 15 feet, its length is 24 inches and its width is 6 feet.

Then, you need to make the conversion from 24 inches to feet (1 feet=12 inches):

[tex]l=(24in)(\frac{1ft}{12in})= 2ft[/tex]

Then, susbtituting values, you get:

[tex]V=(2ft)(6ft)(15ft)=180ft^3[/tex]

Answer:

k = 3.

Step-by-step explanation:

If the 2 roots are A and B we have the relations:

AB = 8/k and A+B = -14/k.

We are given that A = 6B so

6B^2 = 8/k

B^2 = 8/6k = 4/3k

B = 2 /√(3k) ......(1)

Now A + B = -14/k so

6B + B = 7B = -14/k

B = -2/k..........(2)

Eliminating B from equations (1) and (2):

2 /√(3k) = -2/k

Cross multiply:

2k = -2√(3k)

Squaring both sides:

4k^2 = 4 * 3k

4k^2 = 12k

k^2 = 3k

k = 3.

To find the value of k, we first define the roots as p and 6p. We then use the properties of the sum and product of roots in a quadratic equation to form two equations. We can solve these equations to get the value of k.

The given quadratic equation is kx2 + 14x + 8 = 0. We are looking for the value of k for which one root of the equation is six times the other. Let's denote the roots by p and 6p (since one is 6 times the other).

For a quadratic equation ax2 + bx + c = 0, the sum of the roots is given by -b/a and the product of the roots is c/a. In this case, -b/a or -14/k is equal to the sum of the roots (p + 6p). The product of the roots, c/a or 8/k, is equal to p*6p.

From the sum of the roots equation, we can determine p = -14/7k and by substitifying p in the other equation we can solve for k.

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