Annual starting salaries for college graduates with degrees in business administration are generally expected to have a population standard deviation of $3,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. How large a sample should be taken if the desired margin of error is (a) [1 pt] $500

Answer:

x=13

Step-by-step explanation:

Side Splitter Theorem states that If a line is parallel to one side of a triangle and intersects the other two sides, it divides both sides proportionally.

21/14 =1.5

6x1.5 = 9

x-4=9

x=13

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

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ANSWER A

If two events is mutually exclusive, it means that they cannot occur at the same time. Coin tossing is an example of something being mutually exclusive, landing on heads and tails cannot happen at the same time; it's either one or the other! In our case, this is not the case. The pizza having mushrooms on it does not affect the type of crust. The crust type and mushrooms can happen at the same time; you can have both! Therefore, Thick Crust Pizza and Pizza with mushrooms are not mutually exclusive.

ANSWER B

ANSWER 1: We know that there are nine pizzas in the oven. Looking at the chart, we see that three total pizzas have thick crust. One of them has no mushrooms and two of them do have mushrooms. This probability is 3/9, or 1/3.

ANSWER 2: We want to find a pizza that has both mushrooms and a thick crust. As we saw when solving for Answer 1, we have that 2 pizzas have both thick crust and mushrooms. This probability is 2/9.

ANSWER C

A dependent event is one that will depend on the result before it. Thick crust pizza and mushrooms do not affect each other at all; they do not depend on each other. They both do their own thing. We need to justify with things we found in Answer B. Well, when we added the event of mushrooms our probability decreased. If one of the events depended on the other, the probability would have definitely increased.  Therefore, these events are both independent.

I hope that this helps you! Have a wonderful day!

Answer:

A=8

b=15

c=40

Step-by-step explanation:

5/8 as well as 10/16 = .625

a=8 blocks for 5 min given in question

b:24*0.625=15

c:25*40=.625 or 8 * 5=40 , since 5×5=25 taking 1st column times 5

Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.

Let's represent the total no of oranges by x.

Therefore ,

2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.

an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x

x = 12+4 or x-12 = 4

= 16

therefore amir got 16 oranges in all

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Answer:

0.2333 = 23.33% probability he passes exactly one test

Step-by-step explanation:

We have these following probabilities:

3/4 probability that he passes the first test.

If he passes the first test, 4/5 probability that he passes the math test.

If he does not pass the first test, 1/3 probability that he passes the math test.

What is the probability he passes exactly one test

Two scenarios:

Pass first(3/4 probability) and fails second(1/5 probability).

Fails first(1/4 probability) and passes second(1/3 probability). So

\(p = \frac{3}{4}*\frac{1}{5} + \frac{1}{4}*\frac{1}{3} = \frac{3}{20} + \frac{1}{12} = \frac{9 + 5}{60} = \frac{14}{60} = 0.2333\)

0.2333 = 23.33% probability he passes exactly one test

Answer:

No

Step-by-step explanation:

You can if you want, but there is a total of 6 on the dice. And there are 3 odds. Each odd you role you gain 10 cents, but each time a student roles a even they also get 10 cents. So you will get paid and in a game of chance and gambling. You won't gain anything if ALL of the students are together and going against you. Its like 1 vs 25 and you would have to pay a lot of students at one time to play this game. So logically no, because you won't gain money. But also you could if you always get odds, but again. That's a 3/6 or 1/2 each time you role to get a odd number.

Hope that helped, or even made sense xD

Answer:

m= 1

Step-by-step explanation:

find to ordered pair on the graph and \(y^{1} - y^{2} \\ x^{1} - x^{2}\)

Answer:

8a^5

Step-by-step explanation:

Well to start off 2*4=8

So the coefficent will be 8

and when multipling ezponents we add the exponents and 2+3=5 so the exponent will be 5.

So 8a^5 is the answer

Given:

The points A(-3, 3), B(0, 7), C(4, 10), D(1, 6) create parallelogram ABCD.

To find:

The perimeter of parallelogram ABCD.

Solution:

Distance formula is

\(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Using distance formula, find the side length of parallelogram.

\(AB=\sqrt{(0-(-3))^2+(7-3)^2}\)

\(AB=\sqrt{(3)^2+(4)^2}\)

\(AB=\sqrt{9+16}\)

\(AB=\sqrt{25}\)

\(AB=5\)

Similarly,

\(BC=\sqrt{\left(4-0\right)^2+\left(10-7\right)^2}=5\)

\(CD=\sqrt{\left(1-4\right)^2+\left(6-10\right)^2}=5\)

\(AD=\sqrt{\left(1-\left(-3\right)\right)^2+\left(6-3\right)^2}=5\)

Now,

Perimeter of ABCD is

\(P=AB+BC+CD+AD\)

\(P=5+5+5+5\)

\(P=20\)

Therefore, the perimeter of parallelogram ABCD is 20 units.

Volume of cylinder = πr^2h

400π = πr^2 *25

r^2 = 400/25

r ^2= 16

r =4 feet

radius = 4 feet

Answer:

a = 18 ft is the answer.

Step-by-step explanation:

a = ?

b = 24 ft

c = 30 ft

According to the Pythagoras theorem,

a² + b² = c²

a² + 576 = 900

a² = 900 - 576

a² = 324

a = 18 ft

∴ a = 18 ft is the length of the missing leg.

Answer:

18 feet

Step-by-step explanation:

The Pythagorean theorem is a formula that can be used to find the unknown side length of a right triangle when given the length of the other two sides. The general formula for the Pythagorean theorem is the following,

\(a^2 + b^2 = c^2\)

Where (a) and (b) are the legs of the right triangle, or rather the sides adjacent to the right angle of the right triangle. Additionally, (c) is the hypotenuse or the side opposite the right angle of the right triangle.

Substitute in the given values and solve, let parameter (a) represent the unknown side of the triangle,

\(a^2 + b^2 = c^2\\\)

Substitute,

\((24)^2 + a^2 = (30)^2\\\)

Simplify,

\(576 + a^2 = 900\)

Inverse operations,

\(576 + a^2 = 900\\-576\\\\a^2 = 324\\\sqrt{}\\\\a = 18\)

trapezoid, i got the last one wrong

Answer: Trapezoid

Step-by-step explanation:

A trapezoid is a quadrilateral with only one pair of parallel sides; the bases are parallel to each other. The legs don't have to be parallel (they're not).

Answer:

A

Step-by-step explanation:

Given statement solution is :-  For the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.

Regular Pay:

Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:

Regular Pay = Regular Hours x Hourly Rate

Regular Pay = 40 hours x $11.90/hour

Regular Pay = $476

Overtime Pay:

Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.

Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)

Overtime Pay = 13 hours x ($11.90/hour x 1.5)

Overtime Pay = 13 hours x $17.85/hour

Overtime Pay = $231.45

Gross Pay:

Gross Pay is the sum of Regular Pay and Overtime Pay.

Gross Pay = Regular Pay + Overtime Pay

Gross Pay = $476 + $231.45

Gross Pay = $707.45

Therefore, for the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

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Answer:

Step-by-step explanation:

15 gal/300 miles = 1 gal/20 miles

Answer:

1 24/25 or one and twenty-four twenty-fifths (in word form).

Step-by-step explanation:

This would be the answer since, we firstly have to convert the mixed fractions into improper fractions. 7/5*7/5, which equals to 49/25. In simplified form it would be 1 2/25.

1 2/5=7/5

7/5*7/5= 49/25 or 1 24/25.

Anyhow, the answer is 1 24/25

The simplified mixed fraction for the given fraction is  \(24\frac{1}{2}\)

A fraction represented with its quotient and remainder is a mixed fraction, a mixed fraction is a combination of a whole number and a proper fraction.

Given that a fraction \(1\frac{2}{5}\) × \(1\frac{2}{5}\)

We need to simply it in a mixed fraction,

\(1\frac{2}{5}\) × \(1\frac{2}{5}\)

= 7/2 × 7/2

= 49 / 2

= \(24\frac{1}{2}\)

Hence, the simplified mixed fraction for the given fraction is  \(24\frac{1}{2}\)

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Answer:  4 x 5 = 20 + 7= 27 subtracted from 40 = 13 dollars left that were not  used

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer: The surface area of the rectangular prism is approximately 4 square yards.

Step-by-step explanation: Given that the volume of the rectangular prism is 160 cubic yards, we can find the dimensions of the prism using the formula:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

So, we have:

160 = lwh

Now, we need to find two other measurements in order to calculate the surface area of the rectangular prism. However, we do not have enough information to find all three dimensions. Therefore, we will assume one dimension and find the other two.

Let's assume that the height of the rectangular prism is 10 yards. Then, we can rearrange the formula for the volume to solve for the product of the length and width:

lw = V/h = 160/10 = 16

Now, we have two equations:

lw = 16

wh = 160/10 = 16

Solving for w in the first equation, we get:

w = 16/l

Substituting this expression for w in the second equation, we get:

l(16/l)h = 16

Simplifying, we get:

h = 1

Therefore, the dimensions of the rectangular prism are:

length = l

width = 16/l

height = 10

Now, we can calculate the surface area of the rectangular prism using the formula:

SA = 2lw + 2lh + 2wh

Substituting the values we found, we get:

SA = 2(l(16/l)) + 2(l(10)) + 2((16/l)(10))

SA = 32/l + 20l + 160/l

To find the minimum value of this expression, we can take its derivative with respect to l and set it equal to zero:

dSA/dl = -32/l^2 + 20 + (-160/l^2)

0 = -32/l^2 + 20 - 160/l^2

52/l^2 = 20

l^2 = 52/20

l ≈ 1.44

Substituting this value of l back into the expression for SA, we get:

SA ≈ 4 square yards

Therefore, the surface area of the rectangular prism is approximately 4 square yards.

Answer: Answer:

The perimeter of the polygon are

PQ = 5

RS = 5

PR = √74 = 8.60

QS = √74 = 8.60

QR = 7

Step-by-step explanation:

To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula

d = √(x _2 - x_1)^2 + (y_2 - y_1)^2

Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)

x_1 = 0

y_1 = 4

x_2 = 5

y_2 = 4

PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2

= √ 5^2 + 0^2

= √ 25

= 5

Between R( 5 , -3) and S ( 0 , -3)

x_1 = 5

y_1 = -3

x_2 = 0

y_2 = -3

RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2

= √( -5)^2 + ( -3 + 3)^2

= √ 25 + 0

= √ 25

= 5

Between P( 0 , 4) and R (5 , -3)

x_1 = 0

y_1 = 4

x_2 = 5

y_2 = -3

PR = √( 5 - 0)^2 + ( -3 - 4)^2

= √ 5^2 + (-7)^2

= √ 25 + 49

= √ 74

= 8.60

Between Q ( 5 , 4) and S(0 ,-3)

x_1 = 5

y_1 = 4

x_2 = 0

y_2 = -3

QS = √ ( 0 - 5)^2 + ( -3 - 4)^2

= √ -5^2 + -7^2

= √ 25 + 49

= √ 74

= 8.60

Between Q( 5,4) and R(5 , -3)

x_1 = 5

y_1 = 4

x_2 = 5

y_2 = -3

QR = √ (5 - 5)^2 + ( -3 - 4)^2

= √ 0^2 + (-7)^2

= √ 0 + 49

= √ 49

= 7

Step-by-step explanation:

Answer:

1 --- The cyclist's average speed was 18 miles per hour.

2 --- I would travel 280 miles far.

3 --- Your average speed was 52.5 miles per hour.

4 --- You should expect to arrive in Leeds at 11:50 AM.

5 --- The athlete will run 2000 m in 8 minutes and 20 seconds.

6A --- The average speed of the journey is 48 miles per hour.

6B --- It will take him 6 hours and 40 minutes.

Step-by-step explanation:

1) 90 / 5 = 18

2) 70 x 4 = 280

3) 315 / 6 = 52.5

4) 210 / 90 = 2.3333

   0.333 = 0:20

   9:30 + 2:20 = 11:50

5) 2000 / 4 = 500

   500 / 60 = 8.3333

   0.3333 = 0:20

   8.3333 = 8:20

6A) 0:45 = 0.75

     420 / 8.75 = 48

6B) 420 / 63 = 6.666

      6.6666 = 6:40

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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The error interval for the time spent to complete the race is 12.305 ≤ t < 12.315

From the question, we have the following parameters that can be used in our computation:

Distance = 100 m

Time = 12.31 seconds

From the question, we understand that

Time = rounded to the nearest hundredth of a second.

The highest number that can be rounded to 12.31 to the nearest hundredth is 12.314

While the least is 12.305

When represented as an interval, we have

12.305 ≤ t < 12.314

Add/subtract the error

So, we have

12.305 - 0.001 ≤ t < 12.314 + 0.001

Evaluate

12.305 ≤ t < 12.315

Hence, the error interval is 12.305 ≤ t < 12.315

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Answer:

There are 750 more drama movies that children's movies.

Step-by-step explanation:

There are 1003 drama movies, and 253 children's movies.

1003 - 253 = 750