Marie is choosing a bag of apples to make into a pie. She thinks the pie will be tastier if it has more apples. The bag of green apples weighs 4.75 pounds. The bag of red apples weighs 4.5 pounds.

The probability of getting exactly one head is 1/3.

To find the probability of getting exactly one head when tossing n coins after drawing a ball with number n from the box, we need to consider the possible values of n (0, 1, or 2) and calculate the probability for each case.

Case 1: n = 0

If the ball drawn has number 0, we toss 0 coins and the probability of getting exactly one head is 0 since there are no coins to toss.

Case 2: n = 1

If the ball drawn has number 1, we toss 1 coin and there is only one possible outcome to get exactly one head. The probability of this outcome is 1/2, as there are two equally likely outcomes (head or tail) for a single coin toss.

Case 3: n = 2

If the ball drawn has number 2, we toss 2 coins. There are two possible outcomes to get exactly one head: (head, tail) or (tail, head). Each outcome has a probability of 1/2 * 1/2 = 1/4. Since there are two such outcomes, the total probability is 2 * 1/4 = 1/2.

Therefore, to calculate the overall probability, we need to consider the probabilities for each case weighted by their respective probabilities. Since each case has an equal chance of occurring (1/3 for each case), the final probability is:

(1/3) * 0 + (1/3) * (1/2) + (1/3) * (1/2) = 1/6 + 1/6 = 1/3.

Hence, the probability of getting exactly one head is 1/3.

Learn more about probability here:

brainly.com/question/31828911

#SPJ11

Answer: It is B. RuthAnn will meet her annual goal of $32,523 for retirement with an excess of $20,791.60.

Step-by-step explanation:

Answer: 20%

Step-by-step explanation:

The expected value was 50, the value in reality was 60, so

(60 - 50) / 50

= 10/50

= 1/5

To convert to a percent we multiply by 100:

= 20%.

Answer: Another angle ϕ between 0∘ and 360∘ that has the same cosine as 71∘ is approximately 288.99∘.

Step-by-step explanation:

To obtain another angle ϕ between 0∘ and 360∘ that has the same cosine as 71∘, we can use the fact that the cosine function has a period of 360∘.

This means that the cosine of an angle and the cosine of that angle plus a multiple of 360∘ are equal.

To obtain ϕ, we can use the following formula: cos(ϕ) = cos(71∘ + 360∘k) where k is an integer.

We want to get the smallest positive value of k that gives an angle between 0∘ and 360∘.

Using a calculator, we can obtain the cosine of 71∘:cos(71∘) ≈ 0.309.

Now we can solve for ϕ:cos(ϕ) = cos(71∘ + 360∘k)ϕ = ±acos(cos(71∘ + 360∘k))

We want to get the value of k that makes ϕ between 0∘ and 360∘.

Since cos(71∘) is positive, we can take the positive value of the arccosine function:ϕ = acos(cos(71∘ + 360∘k))

We can use a table of cosine values to find the value of ϕ. Since cos(71∘) is positive, ϕ is either in the first or fourth quadrant. In the first quadrant, ϕ is equal to 71∘.

In the fourth quadrant, the cosine function is positive between 270∘ and 360∘, so we can add 360∘k to 71∘ to get a positive angle:ϕ = acos(cos(71∘ + 360∘k)) ≈ 288.99∘

Therefore, another angle ϕ between 0∘ and 360∘ that has the same cosine as 71∘ is approximately 288.99∘.

Learn more about angles here, https://brainly.com/question/25716982

#SPJ11

Answer:

\(276\) acres of old-growth trees are there.

Step-by-step explanation:

Given: A forest covers \(69,000\) acres. A survey finds that \(0.4\%\) of the forest is​ old-growth trees.

To find: How many acres of​ old-growth trees are​ there?

Solution:

We have,

A forest covers \(69,000\) acres.

Now, \(0.4\%\) of the forest covers old-growth trees.

So, old-growth trees covers \(=0.4\%\) of \(69,000\).

\(=\frac{0.4}{100} \times69,000\)

\(=\frac{4}{1000} \times 69,000\)

\(=276\)

Hence, \(276\) acres of old-growth trees are there.

Answer:

276 acres in the forest.

Step-by-step explanation:

Total area of the forest = 69000 acres

Old — grown trees = 0.4%

0.4% of 69000 = 69000× 0.4/100

= 69000×0.004= 276

Old grown trees are covered 276 acres in the forest.

Answer:

144.92

Step-by-step explanation:

32.11 = 032.11

3.67 = 003.67

032.11

109.14 +

003.67 +

______

144.92

______

Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:

Hello . ♡

The answer to your question is : −370 .

Step-by-step explanation:

Hope this helps u ;)

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

To know more about parameters refer here:

https://brainly.com/question/29911057#

#SPJ11

Answer:

3rd option

Step-by-step explanation:

The area (A) of a semicircle is calculated as

A = \(\frac{1}{2}\) πr² ( r is the radius )

Here diameter = 44, so r = 44÷ 2 = 22

Then

A = \(\frac{1}{2}\) π × 22² = \(\frac{\pi (22^2)}{2}\)

Answer:

C

Step-by-step explanation:

To solve for the area of a circle, you use the equation pi*r^2.

To solve for a half-circle, you divide by two.

Hope this helped! :)

The amount of buttermilk needed for the cake recipe, which is 170.0 mL, is approximately 0.72 cups.


To convert milliliters to cups, we need to use the given conversion factors. First, we convert milliliters to liters by dividing number by 1000 (since there are 1000 milliliters in a liter). Therefore, 170.0 mL is equal to 0.17 liters.

Next, we convert liters to quarts. Since 1 liter is approximately equal to 1.0567 quarts, we multiply 0.17 liters by 1.0567 to get 0.179939 quarts.

Finally, we convert quarts to cups. Since there are 4 cups in a quart, we multiply 0.179939 quarts by 4 to get approximately 0.72 cups.

Therefore, 170.0 mL of buttermilk is approximately equal to 0.72 cups.

Learn more about Number click here :brainly.com/question/3589540

#SPJ11

Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Answer:

658ft

Step-by-step explanation:

you first have to calculate the angle next to that 28°angle,if you look at the two they form a 90° so to find that angle you have to subtract 90-28=62

the x is the opposite of angle 62 and the 350 si the adjacent so you can use the tan ratio to find the answer

tan62=opposite/adjacent

tan62=y/350

y=tan62×350

=658ft

I hope this helps

When a sprinkler head is installed on a finished ceiling or wall, a(n) escutcheon is required and may be included as part of the listed assembly or as a decorative touch.

An escutcheon is a protective and decorative cover that is used when a sprinkler head is installed on a finished ceiling or wall. It is designed to conceal the gap between the sprinkler head and the surrounding surface, providing a neat and finished appearance. The installation of an escutcheon is necessary for several reasons. First, it helps to prevent the accumulation of dust, dirt, or debris around the sprinkler head, which could potentially interfere with its functions.

By covering the gap, the escutcheon acts as a barrier, keeping the area clean and maintaining the proper operation of the sprinkler system. Secondly, the escutcheon serves an aesthetic purpose. It enhances the overall appearance of the sprinkler head installation, making it visually appealing and blending it seamlessly with the surrounding ceiling or wall.

Learn more about functions here:

https://brainly.com/question/31062578

#SPJ11

Answer:

? = 64°

Step-by-step explanation:

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

The third angle in the triangle on the right is

third = 180° - (84 + 36)° = 180° - 120° = 60°

Thus the third angle in the triangle on the left is

third = 90° - 60° = 30° , then

? = 180° - (86 + 30)° = 180° - 116° = 64°

To solve this problem, we need to find the point along the string where it should be cut in order to minimize the total area of the circle and square formed. Let's denote this point as \($x$\) , which represents the length of the string used for the circle.

Given that the total length of the string is 100 cm, the length of the string used for the square would be \($(100 - x)$\) cm.

The formula for the area of a circle is \($A_{\text{circle}} = \pi r^2$\), where \($r$\) is the radius. Since the string length used for the circle is \($x$\), the radius would be \($\frac{x}{2}$\), and the area of the circle would be:

\(\[ A_{\text{circle}} = \pi \left(\frac{x}{2}\right)^2 = \frac{\pi x^2}{4} \]\)

The formula for the area of a square is \($A_{\text{square}} = a^2$\), where \($a$\) is the length of the side. Since the string length used for the square is \($(100 - x)$\), the length of the side would be \($\frac{100 - x}{4}$\), and the area of the square would be:

\(\[ A_{\text{square}} = \left(\frac{100 - x}{4}\right)^2 = \frac{(100 - x)^2}{16} \]\)

To minimize the total area, we need to find the value of \($x$\) that minimizes the sum of the areas:

\(\[ \text{Total Area} = A_{\text{circle}} + A_{\text{square}} = \frac{\pi x^2}{4} + \frac{(100 - x)^2}{16} \]\)

Now, let's find the derivative of the total area with respect to \($x$\) and set it to zero to find the critical points:

\(\[ \frac{d(\text{Total Area})}{dx} = \frac{\pi x}{2} - \frac{100 - x}{8} = 0 \]\)

Simplifying the equation:

\(\[ \frac{\pi x}{2} = \frac{100 - x}{8} \]\)

Solving for \($x$:\)

\(\[ 4\pi x = 200 - 2x \]\)

\(\[ 4\pi x + 2x = 200 \]\)

\(\[ x(4\pi + 2) = 200 \]\)

\(\[ x = \frac{200}{4\pi + 2} \]\)

Using a calculator to approximate the value of \($x$:\)

\(\[ x \approx 8.11 \text{ cm (rounded to two decimal places)} \]\)

Therefore, the string should be cut at approximately 8.11 cm from one end to minimize the total area of the circle and square.

To verify that this is indeed the minimum, we can take the second derivative of the total area with respect to \($x$\) and check its sign:

\(\[ \frac{d^2(\text{Total Area})}{dx^2} = \frac{\pi}{2} - \frac{1}{8} \]\)

Since the second derivative is positive \(($\frac{\pi}{2} - \frac{1}{8} > 0$)\), it confirms that the point \($x \approx 8.11$\)  cm is a minimum point.

To know more about representation visit-

brainly.com/question/32572476

#SPJ11

5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.

To convert atoms to moles we need a conversion factor: Avogadro's number. According to Avogadro's number: there are 6.02 × 10²³ calcium atoms in 1 mole of calcium atoms. The number of moles corresponding to 3.00 × 10²¹ atoms of calcium is:

Number of moles = 5.03 x 10²¹ /  6.02 × 10²³

Number of moles = 8.6 × 10⁻³ moles of calcium

5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.

You can learn more about Avogadro's number here: https://brainly.com/question/15524237

#SPJ1

Step-by-step explanation:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Answer:

turtle: 10 + 5 = 15

brother:  3 + 1 1/2 = 4 1/2

hamster: 6 1/2 + 3 1/4 = 9 3/4

Mom: x + 1/2x = 1 \(\frac{1}{2}\)x

Step-by-step explanation:

Answer:

12. 108 degrees

13. 150 degrees

15. 40 degrees

16. 30 degrees

Step-by-step explanation:

12. 540 is the total degrees inside a pentagon, and since it is regular (every side is equal) you divide 540/5 to get 108

13. 1800 is the total degrees inside a dodecagon, and since it is regular (every side is equal) you divide 1800/12 to get 150

15. 1260 is the total degrees inside a nonagon however since it is asking for the exterior angle you take 1260/9 to get 140 and since every straight line is 180 degrees you subtract 140 from 180 to get 40 degrees.

16. 1800 is the total degrees inside a 12-gon (dodecagon) however since it is asking for the exterior angle you divide 1800/12 to get 150 degrees which since every straight line is 180 you subtract 150 from 180 to get 30 degrees.

The true statement about the Internet connection cost is D. Any amount of time over an hour and a half would cost $10.

In this situation, the function is f (t), when t is a value between 0 and 30. The cost is $0 for the first 30 minutes

When t is a value between 30 and 90, the cost is US$ 5 if the connection takes between 30 and 90 minutes.

Here, the true statement about the Internet connection cost is D. Any amount of time over an hour and a half would cost $10.

Learn more about cost on:

https://brainly.com/question/13862342

#SPJ1

Based on the information provided, 2 is not a solution of x>5 because a possible solution requires a number greater than 5.

Inequalities include symbols such as >, ≤, ≥, among others that should be interpreted correctly to solve the inequality. In this case, the symbol in the inequality is >, which means greater than. Based on this, the value of x should be greater than 5, for example, 7, 19, 2948, etc.

Therefore, 2 is not a solution to the inequality x>5 because a number greater than 5 rather than less than 5 is required to solve this expression.

Note: This question is incorrect and incomplete; here is the complete question:

Explain why 2 is NOT a solution of x>5

Learn more about inequalities in https://brainly.com/question/30231190

#SPJ1

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

To learn more on word problems: https://brainly.com/question/15588055

#SPJ1

Answer:

.75

Step-by-step explanation:

sin is \(\frac{opposite side}{adjacent side}\)

The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.

This is because the sample means would be expected to be centered around the population mean.

The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

standard deviation of sample means = standard deviation of population / square root of sample size

In this case, the standard deviation of sample means would be:

6 / square root of 4 = 3

So the answer is 3.

So, the mean of the distribution of the sample means would be 3. Your answer: 3.

To learn more about mean : brainly.com/question/31101410

#SPJ11

Without knowing the size of the outer circle, it is impossible to determine the exact area of the shaded region. However, we can use the circumference of the inner circle (125.6 inches) to find its radius, and then use that to calculate the area of the shaded region as a fraction of the area of the outer circle.

The formula for the circumference of a circle is C = 2πr, where r is the radius. We can rearrange this formula to solve for r:

r = C/2π

Plugging in the given circumference of the inner circle, we get:

r = 125.6/2π
r ≈ 19.998 inches

Since both circles have the same center, we know that the radius of the outer circle must be at least 19.998 inches longer than the radius of the inner circle. Let's call the radius of the outer circle R. Then:

R = r + 19.998
R ≈ 39.996 inches

The area of a circle is given by the formula A = πr^2. So the area of the inner circle is:

A_inner = πr^2
A_inner ≈ 1256.64 square inches

And the area of the outer circle is:

A_outer = πR^2
A_outer ≈ 5023.27 square inches

The area of the shaded region is the difference between these two areas:

A_shaded = A_outer - A_inner
A_shaded ≈ 3766.63 square inches

So the area of the shaded region is approximately 3766.63 square inches, but this answer depends on the radius of the outer circle, which is not given in the problem.