The bases of the prism below are right triangles. If the prism's height measures 11 units and its volume is 130.9 units 3 3 , solve for x x.

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 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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Answer:

Step-by-step explanation:

Answer: I can’t find it please help

Step-by-step explanation:

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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Answer:

43 degrees.

Step-by-step explanation:

Since we have a box on the angle, we know that the sum of these angles is 90 degrees. These are complementary angles.

Here is a equation

x + 47 = 90

subtract 47

x = 43.

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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Answer: B $2,251.80

Step-by-step explanation:

:)

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:

The cost per T-shirt $5.

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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Step-by-step explanation:

calculate the tax on an item, we need to multiply the price by the tax rate as a decimal.

For the sneakers:

Tax on sneakers = 0.08 * $129.99 = $10.40

For the boots:

Tax on boots = 0.08 * $89.99 = $7.20

The difference between the tax on the sneakers and the tax on the boots is:

$10.40 - $7.20 = $3.20

Therefore, the correct answer is (A) The tax on the sneakers is $3.20 more than the tax on the boots

Answer: A. The tax on the sneakers is $3.20 more than the tax on the boots.

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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The student question is about calculating the statistics and probabilities for two different sample sizes of adolescent girls who are developmentally delayed, reaching their adult height.

For the sample size of 29 girls, the estimated standard error is 1.6337, and the statistic is 1.10. For the larger sample size of 91 girls, the new estimated standard error is 0.9222, and the new statistic is 1.95. As the sample size increases, the statistic becomes smaller.

Using the Distributions tool to determine the probability of getting the statistic or something more extreme for each sample size, you can find the probabilities (p) for each case. For the sample size of[tex]29 (n=29),[/tex] you will obtain a specific probability (p).

Similarly, for the sample size of[tex]91 (n=91)[/tex], you will get another probability (p). The distribution will change with larger sample sizes (n).

To observe the distribution changes, you can use the Degrees of Freedom slider in the tool and move it from the smallest value to the largest value. This will help you see how the shape of the distribution changes as the sample size increases.

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The inequality that represents the graph is Oys-3x+2. This inequality states that the y-value is greater than or equal to -3x+2.

Graph is a data structure that consists of nodes (also called vertices) and edges. Nodes represent entities such as people, places or objects, while edges represent the relationship between the nodes. Graphs are used to represent many different types of real-world relationships, such as social networks, transportation networks and communication networks. Graphs can also be used to solve complex problems in computer science, operations research and mathematics. Graphs provide an efficient way to store and manipulate data and can be used to represent both directed and undirected relationships.

This inequality can be interpreted as the solution set of all points that have a y-value that is at least -3x+2.

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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 engineered ACE2 immunoglobulin counters murine lethal SARS-CoV-2 infection through direct neutralization and Fc-effector activities".

What is  Immunoglobulin?

An Immunoglobulin is a blood protein that recognizes foreign molecules and signals the immune system to neutralize them.

Murine lethal SARS-CoV-2 is a laboratory-made strain of SARS-CoV-2 that can infect and kill mice. It is often used in research to study the virus and test potential treatments.

ACE2 is a protein found on the surface of cells that the SARS-CoV-2 virus uses to enter and infect cells.

An engineered ACE2 immunoglobulin is an artificially created version of ACE2 that is designed to bind to the virus and neutralize it. This is achieved through direct neutralization, where the ACE2 immunoglobulin binds to the virus and prevents it from entering cells.

Additionally, the ACE2 immunoglobulin has Fc-effector activities, which means it can activate other parts of the immune system to help fight the infection.

In summary, the engineered ACE2 immunoglobulin counters murine lethal SARS-CoV-2 infection through direct neutralization and Fc-effector activities. It is an artificially created protein that binds to the virus and signals the immune system to neutralize it.

Complete Question:

Does the engineered ace2 immunoglobulin counters murine lethal sars-cov-2 infection through direct neutralization and fc-effector activities?

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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:

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

A human organism developing in the uterus from the ninth week until birth is called a(n) fetus.

A fetus is the term used to describe a human organism that is developing in the uterus from the ninth week of gestation until birth. During this time, the fetus undergoes significant growth and development, as all of the major organs and body systems are formed and begin to function.

The ninth week of gestation is considered a significant milestone in fetal development, as most of the critical stages of organogenesis have been completed by this time. From this point onward, the fetus primarily grows and matures in preparation for life outside of the womb.

During the remaining weeks of gestation, the fetus undergoes a number of important developmental processes, including continued brain development, growth of the nervous system, and development of the lungs and other vital organs. At the same time, the fetus also gains weight and size, and begins to develop a layer of fat that will help to regulate body temperature after birth.

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Answer: there are 12 fruit centers and 15 caramel centers

Step-by-step explanation:

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:

$45.72

Step-by-step explanation:

16×3=48

48×0.0475(4.75%)=2.28. <----- tax

2.28+48=45.72

Answer:

Step-by-step explanation:

$105.20

Answer:

90, 86, and 92 are three options

Step-by-step explanation:

Step-by-step explanation:

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

The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.

The circumference of a circle is given as ;

C = 2πr

C = 9cm

therefore, 9 = 2× 3.14 × r

9 = 6.28r

r = 9/6.28

r = 1.43 cm

Area of circle = πr²

= 3.14 × 1.43²

= 6.42cm²( nearest hundredth)

therefore the area of the circle is 6.42cm²

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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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