Lamark goes to a bowling alley to test his belief that rolling a bowling ball slowly will result in knocking down more pins. He gently rolls his bowling ball towards the bowling pins lined up at the end of the lane. The bowling ball stops in the middle of the lane without striking the pins. Which statement below best explains what happened?

Answer:

a) The sample proportion is 0.06.

b) The test statistic is z = -1.89.

c) 0.0294

d) 0.294 < 0.05, which means that there is enough evidence that p is less than 0.1, which means that we reject the null hypothesis, and accept the shipment.

Step-by-step explanation:

The null hypothesis is:

\(H_{0} = 0.1\)

The alternate hypotesis is:

\(H_{1} < 0.1\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

a. Calculate the sample proportion p.

200 potatoes, 12 defective.

This means that \(p = \frac{12}{200} = 0.06\)

The sample proportion is 0.06.

b. Calculate the test statistic.

For a proportion p, we have that:

\(\sigma = \sqrt{p(1-p)}\)

In this question, since \(\mu = 0.1\)

\(\sigma = \sqrt{0.1}{0.9}\)

SRS of 200 means that \(n = 200\)

\(H{0} = 0.1\) means that \(\mu = 0.1\). So

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.06 - 0.1}{\frac{\sqrt{0.1*0.9}}{\sqrt{200}}}\)

\(z = -1.89\)

The test statistic is z = -1.89.

c. Find the p-value.

Looking at the z-table, \(z = -1.89\) has a pvalue of 0.0294, which is the pvalue of this hypothesis test.

d. Given α=0.05 what is your conclusion? Should he reject the shipment?

0.294 < 0.05, which means that there is enough evidence that p is less than 0.1, which means that we reject the null hypothesis, and accept the shipment.

Answer: A

Step-by-step explanation:

Answer: the answer is b. 6

Step-by-step explanation:

An interpretation of the relationship between the variables in this graph is that: C. you leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally, you continue at a slower (but constant) speed than before.

A graph can be defined as a type of chart which is used to graphically represent the relationship between the variables in a data set, on both the horizontal and vertical lines of a cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph attached in the image below, we can infer and logically deduce that an interpretation of the relationship between the variables in this graph is that you drove at a constant speed for 2 hours, and then stopped for 1 hour. Finally, you continued at a slower, but constant speed than before.

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\(20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5\)

Answer:

\(800\sqrt{5}\)

Step-by-step explanation:

Given: \(\large (20)^\text{$ \dfrac{5}{2} $}\)

Properties of Exponents:

Rational Exponent Property: \(\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}\)

Product of Powers Property:

1. Convert into a radical:

\(\sqrt[2]{20^5} \implies \sqrt{20^5}\)

2. Simplify the expression:

\(\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}\)

3. Evaluate the power:

\(20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}\)

4. Multiply:

\((400\times2)\sqrt{5}\\\\\implies800\sqrt{5}\)

Answer:

x > -3

Step-by-step explanation:

4 - 4x < 16

- 4x < 16 - 4

- 4x < 12 (note that both can be divided by -4)

x > -3

That's the final answer.

AND if you're co fused about why the sign changed, you should always remember this

By negative num I mean any number that starts with a minus for example -2, -3, -5, -100

The area of the new rug in factored form is 2(9x + 19x) square units

Given:

Area of blue rug = 8(x + 1)

Area of red rug = 10 (x+3)

Total area = blue + red

= 8(x + 1) + 10 (x+3)

= 8x + 8 + 10x + 30

= 8x + 10x + 8 + 30

= 18x + 38

= 2(9x + 19x)

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The distance covered in 2.6 days will be 637 miles. The correct option is D.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that the riders were able to cover about 245 miles per day before they would stop and rest. The trip between San Francisco and Denver takes 2.6 days.

Distance will be calculated by the formula below:-

Distance = Speed x time

Distance = 245 x 2.6

Distance = 637 miles

Therefore,  the distance covered in 2.6 days will be 637 miles. The correct option is D.

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The formula for the volume(V) of the rectangular prism is,

Where,

Therefore,

Hence,

The inequality on the number line is 5x -2 > -22 or 6x-7 < 11.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The open circles on the number line shows that it does not include those value i.e., the values have less than and greater than.

So, from the number line the inequality is -4 < x < 3.

Now, 5x -2 > -22 and 6x-7 < 11

5x > -20 and 6x < 18

x > -4 and x<3.

x+5 >8 and 3+ 2x < -5

x >3 and x < -4.

so, the inequality is 5x -2 > -22 or 6x-7 < 11.

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Answer:

There are no equations that we can see but send me a screen shot in discord of it and I will help, my discord is Mousycritter#2842

Step-by-step explanation:

x²/2 - 2x

(25/2 - 10) - (0)

12.5 - 10 = 2.5= 5/2

The surface area of the complex solid is 530 square yards.

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

I think x=  -1

Step-by-step explanation:

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

C

Step-by-step explanation:

Since the exponent on the 10 is negative, we need to move the decimal point to the left instead of the right. After moving the decimal point on the 2.5 to the left 4 places, we see that the answer is 0.00025.

The value of the resistor needed in this scenario is approximately 1.2 ohms.

To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.

Using Ohm's Law, we have the formula:

V = I * R

Where:

V is the voltage across the resistor (12 volts in this case),

I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),

R is the resistance of the resistor (which we need to find).

Rearranging the formula, we have:

R = V / I

Plugging in the values:

R = 12 volts / 10 amps

R = 1.2 ohms

Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.

It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.

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Answer:

1320 ways

Step-by-step explanation:

To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!

12! is the same as 12x11x10x9x8... etc

But in this problem, we are only looking for the top 3.

We can set up a formula

\(\frac{n!}{(n-r)!}\)

N is the number of options that are available and r represents the amount we are choosing

In this case, we have 12 teams so n=12

We are looking for the top 3 so r=3

\(\frac{12!}{(12-3)!}\)

\(\frac{12!}{9!}\)

We expand the equation and cancel out

\(\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}\)

Notice how both sides can cancel out every number 9 and below

That leaves us with 12x11x10

1320 ways

The possible ways for the gold, silver, and bronze medals to be awarded is 1320

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.

We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,

Using the concept of permutation, to find the number of ways

ⁿPₓ = n!/(n-x)!

= 12! / (12-3)!

= 12! / 9!

= 1320

Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320

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Answer:

The answer is B. they are congruent because they are a pair of corresponding angles.

Answer:

B)

Step-by-step explanation:

Angles 1 and two are corresponding angles, because if you were to move the top line down, the two angles would be in the exact same spot.

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

Step-by-step explanation:

The sum of supplementary angles is 180°.

5x+95 = 180

5x = 85

x = 17°

Answer: 36 combinations

Step-by-step explanation:

Since you have 4 toppings, 3 bases and 3 sauces, you can just multiply them to get the different combos.

4 * 3 * 3

= 36

here's the answer to your question

Answer:

500 students

Step-by-step explanation:

40% = 200 students

divide both by 4 to 10%

10% = 50

multiply both by 10 to get 100%

100% = 500

or the quicker way,

200 x 2 = 400 (80%) + 100 (20%) = 500 (100%)

Answer:

Step-by-step explanation:

x=2

so 7*2= 14

therefore the answer is 14

Answer:

x=27x

Step-by-step explanation:

x=27.x

find- x-?

x=27x

Answer:

Step-by-step explanation:

The average speed is 6 yards in 1 second!

GO CHEIFS!

Hope it helps

Answer:

6

Step-by-step explanation:

To find the average speed which is also the unit rate you simply need to divide the two numbers.

54 ÷ 9 = 6

So, 6 yards is your average speed.

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