Find the measure of the missing angle.

A searchlight is shaped like a paraboloid of revolution. if the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across, 2.5 feet deep should the searchlight be.

As per the given information,

A searchlight is shaped like a paraboloid of revolution. If the light source is located 2 feet from the base along the axis of symmetry and the opening is 5 feet across.

Here we have to Find: How deep should the searchlight be.

First of all, we need to find the equation of the paraboloid of revolution.

Let's assume that the axis of the paraboloid is along the y-axis and the vertex is at the origin (0, 0, 0).

So, the equation of the paraboloid is given by:

y² = 4ax

Where, a = 2 feet (distance of light source from vertex)

So, the equation of the paraboloid is:

y² = 8x ..... (1)

The opening of the paraboloid is given to be 5 feet across.

We know that the diameter of a circle is equal to twice the radius. Hence, the radius of the opening is 2.5 feet.

The vertex is the point (0, 0, 0). We need to find the depth of the searchlight. The depth is nothing but the perpendicular distance from the vertex to the plane of the opening. The plane of the opening is given by the equation x = -2.5 (since the opening is along the yz-plane)

The equation of the plane is given by x = -2.5

Now, we need to find the coordinates of the point where the paraboloid intersects the plane of the opening.

We can substitute x = -2.5 in equation (1) to get:

y² = -20

Squaring both sides, we get:

y = ±√(-20)

Since y can only be positive (since we are considering the upper half of the paraboloid),

y = √(-20) = i√20 = 2√5 i

So, the point where the paraboloid intersects the plane of the opening is (-2.5, 2√5 i, 0)

The depth is nothing but the perpendicular distance from the vertex (0, 0, 0) to the point (-2.5, 2√5 i, 0). Hence, the depth is given by:√((-2.5 - 0)² + (2√5 i - 0)² + (0 - 0)²)= √(6.25 + 20 - 0) = √26.25 = 2.5 feet

Hence, the depth of the searchlight should be 2.5 feet.

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The probability that the duration for complete the task of framing a building will be done within 22 days is equals to the 0.32.

The normal distribution shapes like mount, therefore, it is also known as the mounted-shaped distribution. There is only one peak of the mount, that lies at the center because the distribution belongs to the family of symmetric distributions. We have a task of framing a building has been estimated.

Average or mean, μ = 25 days

standard deviations, σ = 5 days

we have to determine the probability that the duration will be done within 22 days, P( X= 20). Assuming a normal distribution, first we determine the Z-statistic or Z-Score value. Formula for Z-score is written as, Z = ( X− μ)/σ

here, X = 20, so plug all known values

=> Z = ( 20 - 25)/5

=> Z = -5/5 = - 1

The P value is defined as the probability under the assuming that no effect or no difference (null hypothesis). Using the normal distribution table, for Z = -1 , the p value, P( Z = - 1) = P( X= 20) = 0.317311.

Hence, required probability is 0.32.

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Answer:

2/9yd²

Step-by-step explanation:

We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.

1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D

Answer: B $2,251.80

Step-by-step explanation:

:)

After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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Answer:

Step-by-step explanation:

We simply have to divide 900 by 50 to get us 18. Now multiply 18 by 0.5 to get an answer of 9 inches. Hope this helped!

It is not possible to get a score of 9 because 9 is an odd number.

What are numbers?

Numbers are mathematical symbols used to represent values or quantities. They are classified into different types based on their properties and can be used in different areas for counting, measuring, and solving problems.

What is meant by odd numbers?

Odd numbers are integers that are not evenly divisible by 2. They are characterized by having a remainder of 1 when divided by 2. They are expressed as 2n+1, where n is an integer. Examples are 1, 3, 5, 7, 9, etc.

Possibilities:

1.All three pennies score 1: total score is 3.

2.Two pennies score 1 and one penny scores 0: total score is 2.

3.Two pennies score 0 and one penny scores 1: total score is 1.

4.All three pennies score 0: total score is 0.

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Yes, the study group can claim a normal distribution of the sample means.

This is because when a group takes random samples from a population that has a normal distribution, the means of those samples will also follow a normal distribution. The reason for this is due to the Central Limit Theorem, which states that when a large enough number of samples are taken from a population, the distribution of the sample means will become more and more normal.

Since the study group is taking 20 random samples of 15 from a population with a normal distribution, it can be assumed that the means of the sample will have a normal distribution.  Therefore, when the study group draws 20 random samples of 15 from a population that has a normal distribution, they can be certain that the sample means will also follow a normal distribution.

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Answer: there are 12 fruit centers and 15 caramel centers

Step-by-step explanation:

Answer:

1 1/3 pounds of American cheese is equivalent to 4/3 pounds of American cheese.

2 1/4 pounds of turkey is equivalent to 9/4 pounds of turkey.

2/3 pound of cheddar cheese is equivalent to 0.67 pounds of cheddar cheese.

So the cost of each item is:

American cheese: (4/3) x $6.99 = $9.32 (rounded to the nearest cent)

Turkey: (9/4) x $5.99 = $13.48 (rounded to the nearest cent)

Cheddar cheese: 0.67 x $3.99 = $2.67 (rounded to the nearest cent)

To find the total cost, we add up these amounts:

$9.32 + $13.48 + $2.67 = $25.47

Therefore, the customer paid $25.47 for all the items.

The transformation rule to show dilating the dog to one-half its size and moving it to the location of the smaller puppy on the graph is:

1. Dilate the dog by a scale factor of 1/2 with respect to the center of dilation.

2. Translate the dilated dog by a vector that moves it to the location of the smaller puppy on the graph.

The mathematical expression of this rule is:

(x', y') = 1/2(x - h, y - k) + (a, b)

Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade.

To calculate Serena's overall grade, we need to first determine the weight of the final exam. We know that the assignments are worth 45% and the quizzes are worth 40%, which leaves 100% - 45% - 40% = 15% for the final exam.

Next, we can calculate Serena's grade for each component of the course. Her grade for assignments is 78% and her grade for quizzes is 65%. We can calculate her grade for the final exam by multiplying her score of 96% by the weight of the final, which is 15%:

Final grade = (0.45 * 78%) + (0.4 * 65%) + (0.15 * 96%)

Final grade = 35.1% + 26% + 14.4%

Final grade = 75.5%

Therefore, Serena's overall grade in the course is 75.5%. It's important to note that in a weighted grading system like this, the final exam is often a major determinant of the final grade. In this case, Serena's strong performance on the final exam helped to boost her overall grade, even though her scores on the assignments and quizzes were not as high. It's also worth noting that this calculation assumes that all assignments, quizzes, and the final exam were weighted equally within their respective categories (i.e., each assignment was worth the same percentage of the assignment grade).

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The height of the image after being scaled down by 80% three times is 76.8mm, which is not within the required range for a U.S. passport photo.

Scaling is the process of increasing or decreasing the size of a picture by dividing or multiplying its dimensions. An picture is expanded when it is scaled up, and its size is decreased when it is scaled down. An picture is affected by scaling when its size and, consequently, appearance, are altered. An picture may become pixelated or fuzzy if it is scaled up or down excessively, and information may be lost if it is scaled down too much. The aspect ratio of an image—the proportion of its width to its height—can also be impacted by scaling. The picture could look stretched or squished if the aspect ratio is modified.

Given that the image is 150 mm in height.

Thus, 80% of the image is:

150mm x 0.8 = 120mm

The scaling is performed 3 times, thus:

120mm x 0.8 = 96mm

96mm x 0.8 = 76.8mm

Hence, the height of the image after being scaled down by 80% three times is 76.8mm, which is within the required range for a U.S. passport photo.

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The complete question is:

The Critical value to be used to gain the 98 confidence interval for the population mean is2.508 and can be determined using the t- distribution table.

critical value is the value of a test statistic that defines the upper and lower bounds of the confidence interval or determines the position of statistical significance in a statistical test.

Given

The following way can be carried out to determine the critical value

Step 1-First determine the degrees of freedom using the following formula

degrees of freedom = n- 1

where n is the sample size.

Step 2- Replace" n" in the below formula.

degrees of freedom = 23- 1

= 22

Step 3- Now you can use the t- distribution table to determine the critical value to get a 98 confidence interval.

critical value = 2.508

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The 4 in the hundredths place has a smaller value than the 4 in the tens place.

In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.

In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.

Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.


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Answer:

Step-by-step explanation:

$105.20

Answer:

≈283,39 mm^2

Step-by-step explanation:

The diameter is 19 mm, so the radius is half diameter (9,5 mm)

[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]

By reducing −16/5 ⋅ (−15/56) in lowest term, the answer is 6/7.

To perform the indicated operation and reduce the result to lowest terms, we need to multiply the two fractions:

(-16/5) x (-15/56) = (16 x 15) / (5 x 56)

(when we multiply two negative numbers, the result is positive)

= 240 / 280

Now we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 40:

240 / 280 = (240 ÷ 40) / (280 ÷ 40) = 6/7

Therefore, -16/5 ⋅ (-15/56) = 6/7 in lowest terms.

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Probability of selecting a black marble is 1/23.

There are a total of 23 marbles in a bag, each with a different color. Among these marbles, there is only one black marble. If one wants to find the probability of selecting a black marble from this bag, they would have to divide the number of black marbles by the total number of marbles.

The formula for probability is as follows:P (A) = number of favorable outcomes/number of possible outcomes. In this case, the probability of selecting a black marble is: 1/23.The denominator is 23 because there are 23 marbles in the bag, and the numerator is 1 because there is only one black marble among these marbles.

Thus, the probability of selecting a black marble from this bag is 1/23.

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Answer: The cost of each small candle is $3 and the cost of each large candle is $6.

Step-by-step explanation:

Let's use variables to represent the cost of each small candle and each large candle. Let's call the cost of each small candle "x" and the cost of each large candle "y".

We can set up two equations based on the information given:

4x + 1y = 18 (equation 1)

5x + 2y = 27 (equation 2)

We can solve for one variable in terms of the other by using one equation to eliminate one variable. Let's solve for "y" in terms of "x" by multiplying equation 1 by 2 and subtracting it from equation 2:

5x + 2y = 27

(8x + 2y = 36)

-3x = -9

Dividing both sides by -3, we get:

x = 3

Now that we know the cost of each small candle is $3, we can substitute that value into one of the equations to solve for the cost of each large candle. Let's use equation 1:

4x + 1y = 18

4(3) + 1y = 18

12 + y = 18

y = 6

Therefore, the cost of each small candle is $3 and the cost of each large candle is $6.

The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.

This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.

Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.

It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.

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Part A: The theoretical probability of drawing a red card is 0.32 or 32%.

Part B: The experimental probability of drawing a red card is 0.38 or 38%, and it is 6% greater than the theoretical probability.

Part A: The theoretical probability of drawing a red card from the hat is the number of red cards divided by the total number of cards in the hat:

[tex]P_{red}[/tex] = 8 ÷ (8 + 6 + 7 + 4)

= 8 ÷ 25

= 0.32 or 32%.

Part B: The experimental probability of drawing a red card can be calculated by dividing the number of times a red card was drawn by the total number of trials:

[tex]P_{red}[/tex] = 437 ÷ 1150

= 0.38 or 38%.

The difference between the experimental probability and the theoretical probability can be calculated as follows:

0.38 - 0.32

= 0.06 or 6%

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Answer:

90, 86, and 92 are three options

Step-by-step explanation:

Lila's height is 0.89 + 0.19 = 1.08m.

What is height ?

Height typically refers to the measurement of an object or person from the base to the top, usually measured vertically. It is often used in reference to the physical dimension of a person or object, such as the height of a building, tree, or individual.

According to the question:

In the context of the given problem, height refers to the height of Fatima, Charlotte, and Lila.

Fatima is 1.27 meters tall, Charlotte is 0.89 meters tall, and Lila is taller than Charlotte by half the difference between Fatima's height and Charlotte's height.
The difference between Fatima's height and Charlotte's height is 1.27 - 0.89 = 0.38m.

Half of that difference is 0.38/2 = 0.19m.

So, Lila is taller than Charlotte by 0.19m.

Therefore, Lila's height is 0.89 + 0.19 = 1.08m.

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Answer:

$45.72

Step-by-step explanation:

16×3=48

48×0.0475(4.75%)=2.28. <----- tax

2.28+48=45.72

Step-by-step explanation:

find the inverse of the following functions. the domain and range of the iverse a) f(x) = x

Answer:

Step-by-step explanation:

Answer: I can’t find it please help

Step-by-step explanation:

The correct response is: The anticipated temperature in Fahrenheit if the cricket has not yet chirped once every minute.

Each term in the algebraic equation is either a constant or the result of a constant and one variable. Y = mx + b, where x is the independent variable, m is the slope, and b is the y-intercept, is the general form of a linear equation. Several real-world phenomena, like as the link between speed and time in a moving object and the relationship between price and quantity in economics, are modeled using linear equations.

given

The correct response is: The anticipated temperature in Fahrenheit if the cricket has not yet chirped once every minute.

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