Joan is 5 years older than Ellen, and 3 years ago the sum of their ages was 17 years. In how many years will Joan be 21 years old?

Final answer:

The combined probability of scoring less than 200 or greater than 800 on a normally distributed college-entrance exam with mean 500 and standard deviation 100 is approximately 0.3%.

Explanation:

The probability that a randomly chosen exam score is less than 200 or greater than 800 in a normally distributed college-entrance exam can be found by using the properties of the normal distribution. Since the mean score is 500 and the standard deviation is 100, scores below 200 are three standard deviations below the mean, and scores above 800 are three standard deviations above the mean. Given the symmetry and the empirical rule of normal distribution, approximately 99.7% of values lie within three standard deviations from the mean, leaving roughly 0.3% of the values outside this range. Therefore, since both tails (below 200 and above 800) are considered, we need to split this percentage, which gives us approximately 0.15% (or 0.0015 in probability terms) for each tail. Thus, the combined probability of scoring less than 200 or greater than 800 is approximately 0.3% (or 0.003 in probability terms).

The cost of each bus for the school's field trip is approximately $192.20.

To calculate the cost of each bus, you first subtract the tip from the total expenses.

So, $1829.82 - $100 = $1729.82.

This is the total cost for the 9 buses without the tip.

Next, you divide this amount by the number of buses to find the cost per bus. $1729.82 / 9 = $192.20.

Therefore, each bus costs about $192.20.

Answer:

1)he maximum height your feet will be above the ground is 12

2)Will you be able to dunk the ball= yes

Step-by-step explanation:

Given:

In order to dunk the basket ball, height needed to jump= 2.5 feet

The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12

1) the maximum height your feet will be above the ground=?

Given function of height,h(x)=-16t^2+12

finding maximum of the above function

The maximum of any function written in form of ax^2+bx+c is given by

max= c - (b2 / 4a)

Putting values c=12, b=0 and a=16, we get

max= 12-(0^2/4(-16))

      = 12 -0

      =12 feet

he maximum height your feet will be above the ground is 12 feet.

2)  Will you be able to dunk the ball=?

As the maximum height the feet will be above the ground is 12 feet which is greater than the height needed to jump in the air to dunk the ball 2.5 feet  i.e.

12>2.25

hence yes you will not be able to dunk the ball !

Answer: - 2/5

Step-by-step explanation: Isolate the vcariable by divding each side by factors that don't contain the variable.

Exact Form: x = - 2/5

Deciaml form: x = -0.4

Hope this helps! :) ~Zane

Hello there! B. -2/5.

To solve for x, you want to get x alone and isolate all other terms.

2 = -6 – 20x  - Start by adding 6 to both sides of the equation.

2+6 = -6+6 – 20x ⇒ 8 = -20x

8 = -20x - Next, divide both sides of the equation by -20..

8/-20 = -20/-20x ⇒ -8/20 = x

Now, we have -8/20 as our value for x. The last step is to simplify. Since 8 and 20 are both divisible by 4, divide both sides of the fraction by 4.

x = -2/5. This is your final answer. I hope this helps and have a great day! ~ saturns

Edit: Sorry for the typos, i fixed them! You have to press suuuper hard to get the S key on my keyboard to work :)

Answer:

1395in^3

Step-by-step explanation:

First find the volume of the cuboid, 15in x 9in x 7in = 945in^3

Then find the volume of the rectangular pyramid using the formula V=lwh/3, the total height is 17in so subtract the height of the cuboid from the total height, giving you 10in.

V=(15in)(9in)(10in)/3 = 450in^3

450in^3 + 945in^3 = 1395in^3

Answer:

B) 5065

Step-by-step explanation:

100.5 times 5 = 502.5

502.5 times 100

+ 8 times 5 (commission)

The question asks for the total commission fee when buying five XYZ bonds. Each bond has $8 commission. Therefore, 5 bonds * $8 = $40.

To determine the total cost of purchasing five XYZ bonds with a commission fee of $8 each, you have to multiply the number of bonds by the commission fee. So, the calculation will be:

This means the total cost just for purchasing (not including the face value of the bonds themselves) is $40.

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source of answer

Answer:

D is the right answer

Step-by-step explanation:

Answer:

400 to 500

Step-by-step explanation:

The increase in the price from $400 to $500 has got the larger change, that is the change of 25%.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the data provided in the question,

Percentage change from $400 to $500

% change = (500 - 400)/400 × 100

% change = 25%

Percentage change from $500 to $600,

% change = (600 - 500)/500 × 100

% change = 20%

Therefore, $400 to $500 has the largest change.

To know more about Percentage:

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Answer:

Paul purchased 23 pieces of pepperoni pizza

Step-by-step explanation:

Let pepperoni pizza pieces = x

and plain pizza pieces  = y

So, the equations will be:

AS pepperoni pizza piece is sold for $1.15 and plain pizza is sold for $0.90 and Paul paid $39.05

1.15 x + 0.90 y = 39.05    eq(1)

Paul bought total 37 pieces of pizza so,

x + y = 37      eq(2)

Solving eq(1) and (2)  we can find the pieces of pepperoni pizza bought by Paul.

Multiplying equation (2) with 1.15 and subtracting eq(1) and eq(2)

1.15 x + 0.90 y = 39.05

1.15 x + 1.15 y = 42.55

-         -              -

__________________

0 x - 0.25 y = -3.5

y = -3.5/-0.25

y = 14

Putting value of y in equation(2)

x+y = 37

x + 14 = 37

x = 37 - 14

x = 23

So, Paul purchased 23 pieces of pepperoni pizza as x represents pepperoni pizza pieces.

By setting up and solving a system of linear equations, we determined that Paul purchased 23 pieces of pepperoni pizza for Pam's party.

To determine how many pieces of pepperoni pizza Paul purchased for Pam's party from Perry's pizza parlor, we can set up a system of equations based on the cost of each piece and the total amount spent. Let x represent the number of pepperoni pizzas at $1.15 each and y represent the number of plain pizzas at $0.90 each. We have the following equations based on the given information:

x + y = 37 (total pieces of pizza purchased)

1.15x + 0.90y = $39.05 (total amount spent)

By solving these equations simultaneously, we can find the exact number of pepperoni and plain pizzas that Paul purchased. Multiplying the second equation by 100 to clear the decimals, we get:

115x + 90y = 3905

Now, multiply the first equation by 90:

90x + 90y = 3330

Subtract the modified first equation from the modified second equation:

(115x + 90y) - (90x + 90y) = 3905 - 3330

25x = 575

x = 23

Paul purchased 23 pieces of pepperoni pizza.

The answer is 8 1/4 hope this helps

To find out how much flour is needed for three batches of rolls, you multiply 2 3/4 cups by three, resulting in 8 1/4 cups of flour.

Finding the Amount of Flour for Multiple Batches of Rolls

To calculate the amount of flour needed for three batches of rolls, we simply multiply the amount needed for one batch by three. The recipe states that you need 2 3/4 cups of flour for one batch. Thus, the mathematically formal way to find the amount for three batches is:

2 3/4 cups of flour × 3 = (2 × 3) + (3/4 × 3)

Now, solve the equation step by step:

Multiply the whole number: 2 × 3 = 6 cups of flour.

Multiply the fraction: 3/4 × 3 = 9/4, which can be simplified to 2 1/4 cups of flour by dividing 9 by 4.

Add the results from step 1 and step 2 together: 6 cups + 2 1/4 cups = 8 1/4 cups of flour.

Therefore, you would need 8 1/4 cups of flour to make three batches of rolls.

Answer:

petunias, snapdragons, then pansy

Step-by-step explanation:

Ok first, lets find the percentage of 18 out of 40: 18/40= 0.45

The 21 out of 50= 21/50= 0.42

Lastly, 12/30= 0.40

And its very simple to put from least to greatest:

0.40, 0.42, 0.45

Hope this helped ;)

The answer is petunias, snapdragons, then pansies.

Hope this helps!

Answer:

10^2

Step-by-step explanation:

10^2 = 10x10 = 100

100 x 9 = 900

Answer:  The correct option is (C) [tex]a^5.[/tex]

Step-by-step explanation:  We are given to choose the correct simplification for the following expression :

[tex]P=a^2.a^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property of exponents :

[tex]x^a.x^b=x^{a+b}.[/tex]

So, the simplification of expression (i) is as follows :

[tex]P\\\\=a^2.a^3\\\\=a^{2+3}\\\\=a^5.[/tex]

Thus, the correct simplification of the given expression is [tex]a^5.[/tex]

Option (C) is CORRECT.

Answer:

|x| + |y| = 29

Step-by-step explanation:

We have been given the expression;

|x| + |y|

We are required to evaluate the above expression if;

x = 16 and y = 13

The parallel vertical lines imply that we are dealing with the absolute value of x and y;

|x| + |y| = |16| + |13|

           = 16 + 13

           = 29

Answer:

The correct answer is 29

Step-by-step explanation:

Points to remember

|x| = x

|-x| = x

It is given an expression, |x| + |y|

To find the value of given expression

|x| + |y|  if x = 16 and y = 13

Substitute the value of x and y in the above expression,

|x| + |y| = |16| + |13|

 = 16 + 13 = 29

Therefore the correct answer is 29

Answer:

17

35

Step-by-step explanation:

Answer:

17

35

Step-by-step explanation:

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

[tex]x^{2}+y^{2}=4^{2}[/tex]

Is the equation of a circle with center at the origin and radius 4 units

so

the inequality

[tex]x^{2}+y^{2}< 4^{2}[/tex]

[tex]x^{2}+y^{2}< 16[/tex]

The solution is the shaded area inside the dashed line of the circle

using a graphing tool

see the attached figure

Answer:

See explanation

Step-by-step explanation:

Car A: Started at 0 and ended at 300, thus, car A travels 300 miles.

It travels 6 hours, so car A speed is [tex]\frac{300}{6}=50[/tex] mph.

Car B: Started at 100 and ended at 300, thus, car B travels 300-100=200 miles.

It travels 5 hours, so car B speed is [tex]\frac{200}{5}=40[/tex] mph.

Since 50>40, car A traveled faster than car B.

The graph for the car A is steeper than the graph for the car B.

Answer:

D. Cluster sampling

Step-by-step explanation:

Dealing with the whole population can be cumbersome, time-consuming and very expensive. In order to make it more feasible for researchers they can employ cluster sampling. In cluster sampling, the population are divided into precincts, or gropus. The researcher then selects the groups that will be included in the study through simple random samping or systematic sampling. The researcher can opt to choose let the whole cluster or group to participate in the study or they can randomly select the individuals within the groups.

Answer:

d

Step-by-step explanation:

Answer:

[tex]x\geq3[/tex]

[tex]12x+7y\leq63[/tex]

[tex]y\geq0[/tex]

Step-by-step explanation:

If we let x be the amount of live bait and y be the amount of natural bait, Then we can come up with the following inequalities;

We are told that John would like to get at least 3 pounds of live bait. At least 3 means 3 or more. Since x represents the amount of live bait, we have;

[tex]x\geq3[/tex]

Moreover,we are informed that;

The store sells live bait for $12 a pound and natural bait for $7 a pound. x pounds of live bait would cost 12x while y pounds of natural bait would cost 7y. The total cost would thus be;

12x + 7y

but John only has a budget of $63. This implies that he can spend $63 at most, thus;

[tex]12x+7y\leq63[/tex]

Finally we can have our last inequality as;

[tex]y\geq0[/tex]

Answer:

Part 1) The measure of angle PSL is 45°

Part 2) The measure of angle XYZ is 70°

Part 3) The measure of angle HJZ is 100°

Part 4) The measure of angle PHL is 120°

Part 5) The measure of angle WXZ is 140°

Part 6) The measure of angle UTG is 62°

Step-by-step explanation:

Part 1) Find the measure of angle PSL

we know that

∠PSL+∠LSM=90° -----> by complementary angles

we have

∠LSM=45°

substitute

∠PSL+45°=90°

∠PSL=45°

Part 2) Find the measure of angle XYZ

we know that

∠WYX+∠XYZ=180° -----> by supplementary angles

we have

∠WYX=110°

substitute

110°+∠XYZ=180°

∠XYZ=70°

Part 3) Find the measure of angle HJZ

we know that

∠HJZ=∠HJK+∠KJZ

we have

∠HJK=20°

∠KJZ=80°

substitute

∠HJZ=20°+80°=100°

Part 4) Find the measure of angle PHL

we know that

∠PHL=∠PHS+∠SHL

we have

∠PHS=46°

∠SHL=74°

substitute

∠PHL=46°+74°=120°

Part 5) Find the measure of angle WXZ

we know that

∠WXZ=∠WXY+∠YXZ

we have

∠WXY=15°

∠YXZ=125°

substitute

∠WXZ=15°+125°=140°

Part 6) Find the measure of angle UTG

we know that

∠UTG=∠ATG-∠ATU

we have

∠ATG=120°

∠ATU=58°

substitute

∠UTG=120°-58°=62°

Answer:

(x - 3)(x + 1)(x + 5)

Step-by-step explanation:

I'd use synthetic division instead.  If we were to find the roots of the given polynomial, we could from them write the factors as well.

The divisor x + 5 corresponds to root x = -5.  Setting up synthetic div.,

-5   )   1    3    -13    -15

               -5     10    +15

      -----------------------------

           1   -2     -3      0

Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor.  Moreover, we know that the coefficients of the quotient are 1, -2 and -3.

1x² - 2x - 3 can be factored:  the factors are (x - 3) and (x + 1).

So the end result for this problem is (x - 3)(x + 1)(x + 5).

Answer:

Total amount that Matthew's bank will receive is $10099.81.

Step-by-step explanation:

We need to find the amount Matthew's bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually.

The formula for compound interest is:

[tex]A=P(1+r)^n[/tex]

Where A = future value

P= Principal Amount

r = interest rate

and n= time

So in the question we are given:

P= $8000

r = 6% or 0.06

t = 4 (since 4 yeras compounded annually)

A= 8000*(1+0.06)^4

A= 8000*(1.06)^4

A= 10099.81

So, total amount that Matthew's bank will receive is $10099.81.

Answer:

the answer is 10,099.80

Step-by-step explanation:

Answer:

It is 525

Step-by-step explanation:

Answer:

Look below

Step-by-step explanation:

SOH CAH TOA

We are using sine

sin(75) = x/150

x=sin(75)*150

x=0.9659258263*150

x=144.8888739

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

- 6

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ - 7, - 1 ]

f(b) = f(- 1) = (- 1)² + 2(- 1) - 8 = 1 - 2 - 8 = - 9

f(a) = f(- 7) = (- 7)² + 2(- 7) - 8 = 49 - 14 - 8 = 27

Hence

average rate of change = [tex]\frac{-9-27}{-1-(-7)}[/tex] = [tex]\frac{-36}{6}[/tex] = - 6

Answer:

Line B

Step-by-step explanation:

It is the line that most of the dots surround

Answer:

Line b

Step-by-step explanation:

Line b has the most black dots positioned close to it, and therefore is the best fit line.

Answer:

5

Step-by-step explanation:

There are 6 numbers on a die, one of them is 5 so we expect to get a five one of six times

P (5) = 1/6

If we roll the die 30 times, we expect to get a five 30 * 1/6 = 5 times

For this case we must factor the following expression:

[tex]-13m-m ^ 2 = 0[/tex]

We have a common factor "m" because it is the common term, so we have:[tex]m (-13-m) = 0[/tex]

Finally, the factorized expression of [tex]-13m-m ^ 2 = 0[/tex] is:[tex]m (-13-m) = 0[/tex]

ANswer:

[tex]m (-13-m) = 0[/tex]

Option B

Answer: -14

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-7)2

-7 • 2

-14