There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 6 or a multiple of 4?

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

When lines are parallel, their slopes have to be the SAME.

Since the given line's slope is -1/2, the parallel line's slope is also -1/2

y = -1/2x + b

To find "b", plug in the point (2, -2) into the equation

y = -1/2x + b

-2 = -1/2(2) + b

-2 = -1 + b     Add 1 on both sides

-1 = b

y = -1/2x - 1

The caloric content of the pan pizza is 1110 calories and the caloric content of the beef burrito is 1230 calories.

Let's assign variables to the caloric content of the items. Let x represent the caloric content of the pan pizza and y represent the caloric content of the beef burrito. We can form two equations based on the given information:

x + 2y = 3570

2x + y = 3450

To solve this system of equations, we can use either substitution or elimination method. Let's use substitution method:

y = 3450 - 2x

x + 2(3450 - 2x) = 3570

x + 6900 - 4x = 3570

-3x = -3330

x = 1110

2(1110) + y = 3450

2220 + y = 3450

y = 1230

Therefore, the caloric content of the pan pizza is 1110 calories and the caloric content of the beef burrito is 1230 calories.

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Answer:

x = 17.5 and y = 35

Step-by-step explanation:

2x + 10 = y + 10 ( alternate angles )

subtract 10 from both sides

2x = y ⇒ 6x = 3y → (1)

the sum of the 3 angles in the triangle = 180°

6x + y + 10 + 30 = 180 ( replace 6x by 3y )

3y + y + 40 = 180

4y + 40 = 180 ( subtract 40 from both sides )

4y = 140 ( divide both sides by 4 )

y = 35

substitute y = 35 into (1)

2x = 35 ( divide both sides by 2 )

x = 17.5

Answer:

So, total gallons were made in all =9.31 gallons

Step-by-step explanation:

We are given

A scientist repeated an experiment three times, making 1.42, 3.81, and 4.08 gallons of a new product

so,

first experiment =1.42 gallons

Second experiment =3.81 gallons

Third experiment =4.08 gallons

now, we can find total gallons

total gallons = first experiment + second experiment + third experiment

total gallons =1.42 gallons + 3.81 gallons +4.08 gallons

total gallons =9.31 gallons

Final answer:

Tonya ran the race approximately 6.13 seconds faster than Jada.

Explanation:

To find out how much faster Tonya ran the race, we need to calculate the difference between their race times.

Tonya's race time is 69.07 seconds, while Jada's race time is 75.2 seconds.

To calculate the difference, we subtract Jada's race time from Tonya's race time: 69.07 - 75.2 = -6.13 seconds.

Therefore, Tonya ran the race approximately 6.13 seconds faster than Jada.

Answer:

You are going to line up the decimal points to each other and add a zero to the end of the shortest decimal.

3.99+39.9=43.89

Step-by-step explanation:

You are going to take the 3.99 and add that to the 39.9 like normal but you are first going to line up the decimals.

Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = [tex]7^{\circ}[/tex]

[tex]\angle CAB = \angle DCA = 7^{\circ}[/tex]       [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

[tex]\tan (\theta) = \frac{Opposite side}{Adjacent Base}[/tex]

[tex]\tan (\angle CAB) = \frac{BC}{AB}[/tex]

Here, BC = 50 foot and [tex]\angle CAB =7^{\circ}[/tex]

then;

[tex]\tan (7^{\circ}) = \frac{50}{x}[/tex]

or

[tex]x = \frac{50}{\tan 7^{\circ}}[/tex]

[tex]x = \frac{50}{0.1227845609}[/tex]

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'

Using the tangent of the angle of depression, the distance from the boat to the base of the lighthouse is calculated to be approximately 407 feet.

To solve this problem, we need to use trigonometry. The angle of depression from the observer at the top of the lighthouse to the boat is the same as the angle of elevation from the boat to the observer because these angles are alternate interior angles formed by parallel lines (the water's surface and the height level at the observer's eyes) and a transversal (the line of sight from the observer to the boat).

We have a right triangle where the lighthouse height is the opposite side to the angle of elevation, and the distance from the boat to the lighthouse is the adjacent side. Using the tangent function, which relates the opposite side to the adjacent side in a right angle triangle, we can set up the following equation:

tangent(7°) = opposite/adjacent or tan(7°) = 50/adjacent

So the adjacent side, which is the distance to the boat, is:

adjacent = 50 / tan(7°)

Using a calculator we find:

adjacent ≈ 50 / 0.1228 ≈ 407.2 feet

Thus, to the nearest foot, the boat is approximately 407 feet away from the base of the lighthouse.

Final answer:

Jim can rent the car for a maximum of 4 whole days with his budget of $115, as the inequality 21d + 0.10(250) <= 115 reveals that he doesn't have enough funds to cover the fifth day.

Explanation:

To determine the maximum number of days Jim can rent a car, we can set up an inequality. The cost per day to rent the car is $21.00, and he will be charged $0.10 for every mile he drives. Jim will travel 250 miles in total. Jim has a budget of $115.00 to spend.

Let d represent the number of days Jim can rent the car for. The inequality would be:

21d + 0.10(250) ≤ 115

To solve for d, you would perform the following steps:

Solving the inequality:

21d ≤ 90

d ≤ 90 / 21

d ≤ 4.2857

Since Jim can only rent the car for a whole number of days, the maximum number of days he can rent the car is 4 days.

Therefore, Jim's belief that he can rent the car for a maximum of 5 whole days is incorrect because he does not have sufficient funds for the fifth day.

Answer:

X = 73

Step-by-step explanation:

X - 3 = 53 + 17

Add 53 and 17

It gives you 70

Add 3 to boths sides

you get 73 on right side

Cancels out the negative 3 on left side and gives you 73 for final answer

X = 73

Answer:

N=3.24

Step-by-step explanation:

$3.00-n=0.24           Subtract $3

-n= -3.24               Divide by -1 to make the variable positive

n=3.24

Answer:

The total pennies in Russell's collection dated after 2000 is 800

Step-by-step explanation:

Given

Total Pennies: 1,200

Pennies before 1980: 25%

Pennies between 1980 and 2000: 35%

Required

Number of pennies in Russell’s collection are dated after 2000

Let P1 represent pennies dated before 1980

Let P2 represent pennies dated between 1980 and 2000

Let P3 represent pennies dated after 2000

To calculate the number of pennies dated after 2,000. you have to understand that his total collection of pennies is 100%

This means that

P1 + P2 + P3 = 100%

Where P1 = 25% and P2 = 35%.

So, we're solving for P3

By substituting, P1 = 25% and P2 = 35%, we have

25% + 35% + P3 = 100%

60% + P3 = 100%

Make P3 the subject of formula

P3 = 100% - 60%

P3 = 40%

The quantity of pennies dated after 2,000 is then calculated by P3 * Total.

i.e. 40% * 2000

= 0.4 * 2000

= 800

Hence, the total pennies in Russell's collection dated after 2000 is 800

Answer:

The second one that starts with 3

Step-by-step explanation:

To know if it's a function , check all the domains and make sure there are no repeating ones, if there is a repeating domain , it's not a function

Volume: πr^2h (where h = height and r = radius)

Radius: 12

Height: 24

12^2 * pi * 24 = 10,857.34 cubic centimeters

Answer:

A.Integers

Step-by-step explanation:

We are given that a diagram that represents the relationship of  a number sets.

We have to find that which describes the best set of numbers in block B

In block B

{....,-2,-1,0,1,2,....}

{0,1,2,3,...}

{1,2,3,...}

Integers:{...,-3,-2,-1,0,1,2,...}

Whole numbers:{0,1,2,...}

Natural numbers :{1,2,3,...}

Rational number: That number which can be written in the form of [tex]\frac{p}{q}[/tex] where q is not equal to zero , p and q are integers.

Hence, block B represent the set of integers.

Answer:A.Integers

Answer:

The correct answer is 49.

Step-by-step explanation:

We are given the following expression and we are supposed to evaluate it:

– (31 + 2) + 72 – (–5) 2

Solving the terms inside the brackets first, following the order of operations to solve a mathematical expression to get:

= - (33) + 72 - (-5) 2

Then we will do the multiplications to get:

= - (33) + 72 - (-10)

Further adding and subtracting the terms:

= 39 - (-10)

= 39 + 10

= 49

Answer:

D. -9

Step-by-step explanation:

-33 +49 -25 = -9

Answer:

18.1 million

Step-by-step explanation:

12.1 - 4.9 = 7.2 million increase in 6 years

7.2 / 6 = increase of 1.2 million a year

1.2 x 5 years = 6 million

12.1 million + 6 million = sales of 18.1 million in 2001

Based on linear growth from 1990 to 1996, ABC Electronics can expect total sales of approximately $18.1 million in 2001.

To predict sales for ABC Electronics in 2001 based on a linear growth pattern from 1990 to 1996, we first calculate the annual increase in sales over that period. In 1990, sales were $4.9 million and in 1996, sales were $12.1 million. This is an increase of $12.1 million - $4.9 million = $7.2 million over 6 years, which gives us an annual increase of $7.2 million / 6 years = $1.2 million per year.

Since we're assuming linear growth, we can extend this annual increase to predict sales for subsequent years. From 1996 to 2001 is 5 years, so we calculate the expected sales for 2001 by adding 5 times the annual increase to the 1996 sales figures: $12.1 million + (5 × $1.2 million) = $12.1 million + $6.0 million = $18.1 million.

Therefore, we can expect ABC Electronics to have total sales of approximately $18.1 million in the year 2001 if the linear growth trend continues.

Answer:

The probability that Mario will randomly catch the right goldfish on the first 5 attempts = 0.069

Step-by-step explanation:

From geometric distribution.

If the probability of success on each trial = P,

then the probability that the Nth trial is the first success

                    Pr (X = N) = [tex](1 - P)^{N - 1}[/tex] P

Now,

        P = [tex]\frac{1}{70}[/tex]

        Maximum attempt = 5

Probability that Mario will randomly catch the right goldfish on the first 5 attempts

= [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{1}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](1 - \frac{1}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]

= [tex]\frac{1}{70}[/tex] + [tex]\frac{69}{70}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{2}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{3}[/tex] [tex]\frac{1}{70}[/tex] + [tex](\frac{69}{70} )^{4}[/tex] [tex]\frac{1}{70}[/tex]

= 0.069

Answer: 1. A) 0.14

2. C) 46%

3. D) 86%

4. B) 0.513

5. A) 0.003

6. C) 0.069

7. C) 0.25%

8. D) 0.03

9. C) 71%

10. A) 10%

Step-by-step explanation: 100% :)

Answer:

8/25

Step-by-step explanation:

Steps:

1. First you count how many number are divisible by three. The numbers are 3, 6, 9, 12, 15, 18, 21, and 24, which is a total count of 8 numbers.

2. Then you count the numbers of slips of paper, which you know is 25.

3. Finally, put the number of numbers that are divisible by three or the total slips of paper to find your answer.

Answer:

[tex]\sqrt{274}[/tex]

Step-by-step explanation:

Given [tex]z_1=-8+3i,\ z_2=7-4i.[/tex]

1. Find the difference [tex]z_1-z_2:[/tex]

[tex]z=z_1-z_2=-8+3i-(7-4i)=-8+3i-7+4i=(-8-7)+(3i+4i)=-15+7i.[/tex]

This complex number has real part [tex]Rez=-15[/tex] and imaginary part [tex]Imz=7.[/tex]

2. The modulus of complex number z is

[tex]|z|=\sqrt{Re^2z+Im^2z}=\sqrt{(-15)^2+7^2}=\sqrt{225+49}=\sqrt{274}.[/tex]

The distance between [tex]z_1\ \text{and}\ z_2[/tex] is:

                        16.5529 units

We know that the difference between two complex numbers:

[tex]z_1=a_1+ib_1\ \text{and}\ z_2=a_2+ib_2[/tex] is given by:

[tex]|z_1-z_2|=|(a_1+ib_1)-(a_2+ib_2)|\\\\i.e.\\\\|z_1-z_2|=|(a_1-a_2)+i(b_1-b_2)|\\\\|z_1-z_2|=\sqrt{(a_1-a_2)^2+(b_1-b_2)^2}[/tex]

Here we have:

[tex]z_1=-8+3i\ \text{and}\ z_2=7-4i[/tex]

i.e.

[tex]a_1=-8\ ,\ b_1=3,\ a_2=7\ \text{and}\ b_2=-4[/tex]

i.e. we have:

[tex]|z_1-z_2|=\sqrt{(-8-7)^2+(3-(-4))^2}\\\\|z_1-z_2|=\sqrt{15^2+7^2}\\\\|z_1-z_2|=\sqrt{225+49}\\\\|z_1-z_2|=\sqrt{274}\\\\|z_1-z_2|=16.5529[/tex]

Look at the picture.

[tex]A(3,\ 2)\to A'(2,\ 3)\\\\B(-4,\ 1)\to B(1,\ -4)\\\\C(-3,\ -2)\to C'(-2,\ -3)[/tex]

Answer:

a. -2

Step-by-step explanation:

3¾ ≈ 4

-⅖≈ -½

4 × (-½) = -2

A reasonable estimate is -2.

Answer:

Step-by-step explanation: -2

Answer:4 • (2x + y)

Step by step solution :

Step  1  :

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  4x + 2y  =   2 • (2x + y)

Final result :

 4 • (2x + y)

Step-by-step explanation:

The expression 2(4x+2y) is equivalent to 8x + 4y.

The expression 2(4x + 2y) can be simplified using the distributive property, also known as the distributive law or the distributive property of multiplication over addition.

This property allows you to distribute the factor outside the parentheses to each term inside the parentheses. Here are some equivalent expressions:

Distributing the 2:

2(4x + 2y) = 2 * 4x + 2 * 2y = 8x + 4y

Using the distributive property in reverse:

2(4x + 2y) = 4x(2) + 2y(2) = 8x + 4y

Factoring out a common factor:

2(4x + 2y) = 2 * (2 * 2x + 2 * y) = 2 * 2(2x + y) = 4(2x + y)

Learn more about Equivalent Expressions here:

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Answer:

i squared + 5

Step-by-step explanation:

Answer:

7(x + 2)

Step-by-step explanation:

7x + 14 =

7 can be factored out of each term.

= 7 * x + 7 * 2

= 7(x + 2)

Answer:

2A/b =h

Step-by-step explanation:

A = 1/2bh

Multiply each side by 2

2*A = 2*1/2bh

2A = bh

Divide each side by b

2A/b = bh/b

2A/b =h

Answer:

1890, thats the cost per week to replace them.

Step-by-step explanation:

Answer:

They will meet at 3836 meters

Step-by-step explanation:

Maya is at 7832 meters

Juan is at -160 meters  ( below sea level)

If they are meeting at the midpoint, we add them together and divide by 2

Midpoint = (7832 + -160)/2

               = (7672)/2

               =3836 m

Answer:

The midpoint elevation will be 3,836 meters.

Step-by-step explanation:

Maya's elevation of 7832 can be represented by the positive integer +7832 since she is above sea level.  Sea level would represent 0 on our number line.  However, Juan is below sea level, so we can represent his distance at -160.  When we add these two integers together +7832 + (-160) = 7672 meters above sea level.  Since Maya and Juan are going to meet at the midpoint, we would divide our overall distance (7672) by two to get 3836 meters.  

Answer: 1,596 cubic cm. To find the volume, you need to multiply all the three sides given.

Step-by-step explanation:

12cm * 7 cm* 19cm = 1596 cm^3

The volume of the box given the length, width and height is 1,596 cm³

Given:

Length of the box = 12cm

Width of the box = 7 cm

Height of the box = 19 cm

Volume of the box = length × height × width

= 12 cm × 7 cm × 19 cm

= 1596 cm³

Therefore, the volume of the box is 1,596 cm³

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