Rewrite the following without an exponent.

Answer:

[tex]\frac{2}{81}[/tex]

Step-by-step explanation:

Step 1

List the experimental probabilities of each color using the first letter of that color. The spinner is spun 18 times The probabilities are listed below. P(blue)=3/18, P(red=4/18), P(white) =3/18, P(yellow)=2/18, P(black)=5/18, P(purple)=1/18

Step 2

The second step is to calculate the required probability given the information in step 1. The probability that George will spin a red and then a yellow is obtained by multiplying the probability that he spins a red and the probability that he spins a yellow. This calculation is shown below,

[tex]P=P(red)\times P(yellow)=\frac{4}{18} \times \frac{2}{18} =\frac{8}{324} =\frac{2}{81}.[/tex]

The correct answer is  [tex]\frac{2}{81}[/tex]

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have m = -4 and the point (-2, 5). Substitute:

[tex]y-5=-4(x-(-2))[/tex]

[tex]y-5=-4(x+2)[/tex]      use distributive property

[tex]y-5=(-4)(x)+(-4)(2)[/tex]

[tex]y-5=-4x-8[/tex]      add 5 to both sides

[tex]\boxed{y=-4x-3}[/tex]

Answer:

all is work is shown and pictured

Answer: 145

3.7 x 60 = 222 (how far north she drove)

1.4 x 55 = 77 (how far south she drove)

222 - 77 = 145 (how far from home)

Expressing the equation in the form y = mx + b where m is slope and b is y-

intercept is represented as y = -4x - 3

The slope intercept form is represented as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

m = -4

using the coordinate (-2, 5) lets find b

y = -4x + b

5 = -4(-2) + b

5 = 8 + b

b = 5 - 8

b = -3

Therefore,

y = -4x - 3

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Answer:

(x - 3)² + (y - 2)² = 8

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre to a point on the circle

To find r use the distance formula

r = √(x₂ - x₁)² + (y₂ - y₁)²

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (5, 4)

r = [tex]\sqrt{(5-3)^2+(4-2)^2}[/tex] = [tex]\sqrt{4+4}[/tex] = [tex]\sqrt{8}[/tex]

(x - 3)² + (y - 2)² = ([tex]\sqrt{8}[/tex])²

(x - 3)² + (y - 2)² = 8 ← equation of circle

Answer:

B

Step-by-step explanation:

well plug in x and y

so if it says y=2x-3 put it as 7=(2x2)-3  and see if it gives u 7 and if it does di the next set of x and y numbers

Answer:

B  y=2x+3

Step-by-step explanation:

We need to find the slope of the relationship in the table

m = (y2-y2)/(x2-x1)

  = (13-7)/(5-2)

   = 6/3

  =2

The slope is 2

We can use point slope form to make an equation

y-y1=m(x-x1)

y-7 = 2(x-2)

Distribute the 2

y-7 =2x-4

Add 7 to each side

y-7+7 =2x-4+7

y = 2x+3

Answer:

9/20

Step-by-step explanation:

9/10 times 1/2 equals 9/20

Answer:

9/20

Step-by-step explanation:

Answer:

4617 yd

Step-by-step explanation:

30.5 ft make 1 roll of tape

Length of tape = 454 × 30.5/1

Length of tape = 13 847 ft

1 ft = 3 yd

Length of tape = 13 847 × 1/3

Length of tape = 4617 yd

Answer:

First one is wrong. x should be 16.

Second one is not completely visible, so cannot say.

Step-by-step explanation:

In the last step, the divison by 4 yields:

x/16 = 1, so x = 16

Answer:

Let y represents the ounces of first spice.

From the given statements, we draw a table as shown below:

                          ounces of spice        Percentage          ounces of salt

First spice                 y                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          y + 175                         5%                        (x+15)(0.05)

Now, to solve for y

we have;

Final spice = First spice + second spice

[tex]0.03y + 175(0.06) = (y+175)(0.05)[/tex]

[tex]0.03y+ 10.5= 0.05y+ 8.75[/tex]

Subtract 10.5 on both sides we have;

[tex]0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5[/tex]

Simplify:

[tex]0.03y = 0.05y -1.75[/tex]

Subtract 0.05y on both sides

[tex]0.03y -0.05y= 0.05y -1.75-0.05y[/tex]

Simplify:

[tex]-0.02y = -1.75[/tex]

Divide both sides by -0.02, we get;

[tex]y = \frac{-1.75}{-0.02} = 87.5[/tex]

Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

It needs 87.5 ounces of spice that is 3% salt.

Order of Operations in Mathematics follow this following rule :

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem !

[tex]\texttt{ }[/tex]

Given:

175 ounces of a spice that is 6% salt

[tex]\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

x ounces of a spice that is 3% salt

[tex]\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

(175 + x) ounces of a spice that is 5% salt

[tex]\texttt{total mass of salt} = s_1 + s_2[/tex]

[tex]5\% \times ( 175 + x ) = 10.5 + 0.03x[/tex]

[tex]8.75 + 0.05x = 10.5 + 0.03x[/tex]

[tex]0.05x - 0.03x = 10.5 - 8.75[/tex]

[tex]0.02x = 1.75[/tex]

[tex]x = 1.75 \div 0.02[/tex]

[tex]x = 175 \div 2[/tex]

[tex]x = 87.5 \texttt{ ounces}[/tex]

[tex]\texttt{ }[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3

Answer:

The answer is 6

Step-by-step explanation:

What you do is this.  

3/9 times 18/1 because you need to make 18 a fraction and then multiply. And you will get 6

Answer:

4 heads

Step-by-step explanation:

Assuming the coins are properly weighted such that each side is equally likely, this means that getting heads is the same probability as getting tails. We're told that getting 2 heads and 4 tails is a 23.4% chance. If we somehow fool our brains into thinking heads and tails swap, then it would be 4 heads and 2 tails. The swap is simply changing the labels for each coin. It really doesn't matter. This symmetry is useful to help simplify larger problems.

If the coins were altered so that the chances of getting heads on any single coin toss was something like 60%, then swapping the labels wouldn't work because the two sides would be different.

Answer:

y ≤ -4x+25

Step-by-step explanation:

First we need to figure out the equation for the line

The y intercept is  25

Next figure out the slope

slope = (y2-y1)/((x2-x1)

      = (49-25)/(-6-0)

      = 24/-6

    = -4

The equation for a line in slope intercept form is y = mx+b

y = -4x+25

This is a solid line so our inequality will have an equals in it.

It is shaded below, so y is less than.

If it was shaded above, y would be greater than

y ≤ -4x+25

Answer:

C. 31

Step-by-step explanation:

3000 there are 3-4 errors

If we first divide 24,000 by 3,000, will get 8

then since there a error for each 3,000 books, we do 8 x 4 = 32 and 8 x 3 = 24

32 (8 x 4)  the max amount of printing errors

24 (8 x 3) the minimum amount of printing errors

So we should expect 24-32 printing errors

Only answer between the numbers is c. 31

Final answer:

The exact number of books that could have a printing error out of 24,000, given the rate of 3 to 4 errors per 3,000 books, can be calculated to be within a range, making 31 the only viable option provided.

Explanation:

The question is about determining the exact number of books that will have a printing error out of 24,000, given that there are between 3 and 4 printing errors per every 3,000 books. To find the possible number of errors, we multiply the number of books (24,000) by the rate of errors (3 to 4 per 3,000). This gives us a range of possible errors, from (24,000 / 3,000) * 3 = 24 to (24,000 / 3,000) * 4 = 32. Therefore, the only option within this range is 31.

Answer:

A) (1/9)^8

Step-by-step explanation:

9^-5 × 9^-3 =

Rule: a^m * a^n = a^(m + n)

= 9^-8

Rule: (a^m)^n = a^(mn)

= (9^-1)^8

Rule: a^-m = 1/a^m

= (1/9)^8

Answer: A) (1/9)^8

To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.

The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5). 

Expanding this, we have:

The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.

Answer:

Step-by-step explanation:

You just add and subtract

Answer:

x - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

A polynomial has the form

first term is the term of highest degree followed by term of second etc.

note that x = [tex]x^{1}[/tex] ← degree 1

x - [tex]\sqrt{7}[/tex]

fits this description and is a polynomial of degree 1

Answer:-11

Step-by-step explanation:

use -6 to represent losing 6 yards

use -5 to represent losing 5 yards

add these together

(-6) + (-5) = -11

when adding two negative values, make sure your sum is negative

Answer:

it is 9

Step-by-step explanation:

6 plus 3 is 9

I had this for homework so I know

Answer:

1+5*2 or simplified, 1+10= 11

Answer:

$.43 per pen

Step-by-step explanation:

To find the unit rate, we take the price of the pens and divide by the number of pens

$1.29/3

$.43 per pen

Answer: $0.43

Step-by-step explanation:

Unit rate is how much each pen costs.

If the total amount is $1.29 for all three pens, then the price for one pen should be calculated by 1.29/3, therefore, the answer is $0.43

Answer:

slope = 2.5 and the y intercept is 3

Step-by-step explanation:

To find the slope we can use the formula

m = (y2-y1)/(x2-x1)

I will use the point (2,8) (6,18)  We can pick any 2 point we want.

 = (18-8)/(6-2)

  = (10/4)

  = 2.5

To find the y intercept we need to find the equation of the line.

We will use the point slope form

y-y1= m(x-x1)

y-8 = 2.5(x-2)

Distribute the 2.5

y-8 = 2.5x-5

Add 8 to each side

y-8+8 = 2.5x-5+8

y = 2.5x+3

This equation is in slope intercept form  y = mx+b

where the slope is 2.5 and the y intercept is 3

Hi There!

-----------------------------------

Find The Slope:

[tex]m = \frac{13 - 8}{4 - 2} = \frac{5}{2} or 2.5[/tex]

-----------------------------------

Find The Y-Intercept:

Substitute using x = 2 and y = 8

Use y = mx + b

Substitute: 8 = 2.5(2) + b

Simplify: 8 = 5 + b

Subtract 5 too both sides: 8 - 5 = 5 + b - 5

Simplify: 3 = b

Y-Intercept = 3

-----------------------------------

Point Slope Form: y - 8 = 2.5(x - 2)

Slope Intercept Form: y = 2.5x + 3

-----------------------------------

Hope This Helps :)

Answer: 2.50

Step-by-step explanation: your answer is 2.50

Answer:

Constant of proportionality,  [tex]r = \frac{1}{10}[/tex]

Step-by-step explanation:

Constant of proportionality states that the constant value of the ratio of two proportional quantities x and y,

it is written in the form of y = kx, where k is the constant of proportionality.

Given the equation: [tex]y =rx[/tex]                        .....[1]

where r is the constant of proportionality.

From the table we consider

x = 14 and y = 1.4

Substitute these given values in [1] to solve for r;

[tex]1.4 = r(14)[/tex]

Divide both sides by 14 we get;

[tex]r = \frac{1.4}{14} = \frac{14}{140} = \frac{1}{10}[/tex]

therefore, the Constant of proportionality,  [tex]r = \frac{1}{10}[/tex]

The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x.

The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x. For example, in the equation y = rx, 'r' represents how much y changes for every unit change in x.

For instance, if the equation is y = 2x, then the constant of proportionality is 2. This means that for every unit increase in x, y increases by 2 units.

Keywords: constant of proportionality, linear equation, rate of change

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Answer:

The answer Is D

Step-by-step explanation: I looked it up on Google, next time just type it into Google because it will solve it on a calculator for you.

Answer: It is choice D

Step-by-step explanation: To figure out 25% of 1,200, multiply 1,200 by 0.25. 1,200 x 0.25 = 300

Answer:

AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent

In triangle RAS and triangle QAT

[tex]\angle R =\angle Q[/tex]   [Angle]

[tex]AS =AT[/tex]    [Side]                                       [Given]

By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.

⇒ [tex]\angle 5= \angle 6[/tex]      [By base ∠'s of isosceles triangle are equal]

By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.

[tex]\angle 4[/tex], [tex]\angle 5[/tex] are supplementary and [tex]\angle 6[/tex], [tex]\angle 7[/tex] are supplementary.

⇒[tex]\angle 4+ \angle 5 =180^{\circ}[/tex] and

[tex]\angle 6+ \angle 7 =180^{\circ}[/tex]  

Two [tex]\angle 's[/tex] supplementary to equal [tex]\angle 's[/tex]

[tex]\angle 4+ \angle 5 =\angle 6+ \angle 7[/tex]

Since,  [tex]\angle 5 =\angle 6[/tex]  

then, we get;

[tex]\angle 4 =\angle 7[/tex]  [Angle]

then, by AAS postulates,

[tex]\triangle RAS \cong \triangle QAT[/tex]

By CPCT[Corresponding Part of Congruent Triangles are equal]

[tex]RS = QT[/tex]              Hence Proved!

Answer:

for pluto answer is 451

Step-by-step explanation:

Answer:

width = 4.16 meter

length = 6.49 meter

Step-by-step explanation:

Area of the rectangle =27 m²

Let the width of the rectangle be x meter

So, Length = 3 * width - 6

                  = 3*x - 6

                  = 3x-6 meter

Area of the rectangle = length * width

27 = (3x-6)*x

Flipping the sides of the equation, we have

(3x-6)*x =27

Distributing the left side, we get

(3x)*(x) - (6)*(x) = 27

=> 3x² - 6x = 27

Subtract 27 from both sides,

3x² - 6x -27 = 27 - 27

=> 3x² - 6x -27 = 0

Factoring out 3 from all the terms on the left side, we have

3(x² - 2x -9) = 0

Dividing both sides by 3, we have

[tex]\frac{3(x^{2}-2x-9) }{3}[/tex] = [tex]\frac{0}{3}[/tex]

Cancelling out the 3's on the left, we get

x² - 2x -9 = 0

We'll use the quadratic formula to solve for the x,

x = [tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]

Comparing the quadratic equation x² - 2x -9 = 0 with ax² + bx + c = 0, we get

a = 1 (as x² has no coefficient)

b = -2

c = -9

Plugging in the values of a, b, and c into the quadratic formula, we get

x = [tex]\frac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-9) } }{2(1)}[/tex]

=> x = [tex]\frac{2\pm\sqrt{4+36 } }{2}[/tex]

=> x = [tex]\frac{2\pm\sqrt{40}}{2}[/tex]

=> x = [tex]\frac{2\pm2\sqrt{10}}{2}[/tex]

Factoring out 2 from the top, we get

x = [tex]\frac{2(1\pm\sqrt{10})}{2}[/tex]

Canceling out the 2's from the top and bottom, we have

x = [tex]1\pm\sqrt{10}[/tex]

Either x = [tex]1+\sqrt10[/tex] or x= [tex]1-\sqrt10[/tex]

=> x = 1 + 3.162 or x = 1 - 3.162

=> x = 4.162 (possible) or x = -2.162 (not possible as width can't be negative)

So, width = 4.16 meter (rounded off to the nearest hundredth)

Now,

Area of the rectangle = length * width

27 = length * 4.16

Flipping the sides of the equation,

length * 4.16 = 27

Dividing both sides by 4.16, we get

[tex]\frac{length * 4.16}{4.16} = \frac{27}{4.16}[/tex]

Cancelling out 4.16 from the top and bottom of the left side, we get

length = 6.490

=> length = 6.49 meter (rounded off to the nearest hundredth)

Answer:

The domain is {3,4,5,6}

Step-by-step explanation:

Because all your x - values is ur domain and ur y - values is ur range