a school gives an entry exam for admission. suppose the score of this exam follows a normal distribution n(400, 60). this year, the school decides to admit students who score in the top 30%. suppose a student scored 428 on the test. will the student be admitted? explain your reasoning.

The height of a cone with a diameter of 12 m whose volume is 340 m^3 is 9m

The height of a cone is calculated using the formula:

h = 3V/πr 2

Where h = height of the cone

V = volume of the cone

r = Radius of the cone

But note that radius, r = diameter divided by 2

r = 12 ÷ 2 = 6m

Volume = 340 m^3

Substitute the values into the formula

h = 3 × 340 ÷ 3.14 × 6 × 6

h = 1020 ÷ 113.04

h = 9m

Therefore, the height of a cone with a diameter of 12 m whose volume is 340 m^3 is 9m

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The measure of angle B is in the given cyclic quadrilateral is 140 ⁰.

The measure of angle B is calculated by applying the principle of circle geometry for cyclic quadrilateral.

From the given figure, we will have the following equation;

angle D + angle B = 180 (opposite angles of a cyclic quadrilateral are supplementary)

x + ( 4x - 20 ) = 180

5x - 20 = 180

5x = 200

x = 200/5

x = 40

The measure of angle B is calculated as;

∠B = 4x - 20

∠B = 4 (40) - 20

∠B = 160 - 20

∠B = 140 ⁰

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Answer:

1/110

Step-by-step explanation:

Probability of selecting a rose is 3/12, probability of selecting a tulip is 4/11, and probability of selecting a carnation is 1/10.

[tex]\frac{3}{12} *\frac{4}{11} *\frac{1}{10} \\=\frac{1}{110}[/tex]

a) The probability that the demand will exceed 200 cfs during the early after- noon on a randomly selected day is 0.1353.

b)  The water-pumping capacity that the station should maintain during early afternoons is 460.52 cfs, so that the probability that demand will exceed capacity on a randomly selected day is only 0.01.

a) The given probability distribution of the demand for water during the early afternoon hours is given as exponentially distributed with a mean of 100 cfs. Therefore, the random variable X, representing the demand for water during early afternoon hours, follows exponential distribution with parameter λ = 1/100. We are required to find the probability that the demand will exceed 200 cfs during the early afternoon on a randomly selected day. By definition of probability density function of exponential distribution, the probability that the demand for water during early afternoon hours will exceed 200 cfs on a randomly selected day is:  

P(X > 200) = e-2  ≈ 0.1353

b) Given that the probability that demand will exceed capacity on a randomly selected day is only 0.01, we can write this in terms of the probability density function of exponential distribution as:

P(X > c) ≤ 0.01, where c is the water-pumping capacity that the station should maintain during early afternoons.

If X ~ Exponential distribution with parameter λ, the probability density function is given by:

f(x) = λ e-λx;  x > 0

For the probability P(X > c) ≤ 0.01, we have:

P(X > c) = e-λc ≤ 0.01 (probability distribution function of exponential distribution)

⇒ e-λc = 0.01

⇒ λc = ln(100) = 4.6052

⇒ c = 4.6052 * 100 = 460.52 cfs

Therefore, the station should maintain a pumping capacity of 460.52 cfs.

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A significant difference between the theoretical and experimental probabilities in this case may be due to the relatively small sample size of 25 spins.

According to the law of large numbers, as the sample size (the number of times the experiment is repeated) increases, the experimental probability of an event approaches its theoretical probability.

The law of large numbers can be expressed mathematically using the following formula:

P(E) ≈ n(E)/n

where P(E) is the experimental probability of event E, n(E) is the number of times event E occurs in the experiment, and n is the total number of trials (or spins, in this case).

As n (the sample size) increases, the experimental probability P(E) approaches the theoretical probability of the event, which we can represent as P'(E). Mathematically, we can write:

lim P(E) = P'(E)

n→∞

In other words, as the sample size approaches infinity, the experimental probability approaches the theoretical probability.

Therefore, if Jess had spun the pointer many more times, the experimental probability of the pointer landing on 3 would have approached the theoretical probability of 25%. On the other hand, the relatively small sample size of only 25 spins may have introduced some chance variation that caused the experimental probability of 16% to differ significantly from the theoretical probability.

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Polynomial functions can only have 2 terms which is true.

Monomials are polynomials that contain only one term. Examples: 15x 2, 3b, and 12y 4 Binomials are polynomials that contain only two terms. Examples: x + y, 4x – 7, and 9x + 2

Therefore, Polynomial functions can only have 2 terms which is true.

Answer:

False

Step-by-step explanation:

Polynomial functions contain two or more terms.

Hope this helps

Answer: To sketch all the possible rectangles that Kay could make with 16 small squares and 1 large square, we can arrange them in different configurations. For example:

One possible rectangle could have a length of 8 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

 8 small squares

8 small squares

1 large square

The area of this rectangle is (8)(2) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 17(1).

Another possible rectangle could have a length of 4 small squares and a width of 4 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

4 small squares 4 small squares

4 small squares 4 small squares

1 large square

The area of this rectangle is (4)(4) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 1(17).

A third possible rectangle could have a length of 8 small squares and a width of 1 small square. The large square would be used to fill in the empty space at one end of the rectangle.

8 small squares

1 large square

The area of this rectangle is (8)(1) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 9(1).

A fourth possible rectangle could have a length of 4 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

4 small squares 2 small squares

4 small squares 2 small squares

1 large square

The area of this rectangle is (4)(2) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 3(3).

So, there are four possible rectangles that Kay could make with 16 small squares and 1 large square, and the area of each rectangle can be expressed in both standard form and factored form as shown above.

Step-by-step explanation:

Each box weighs 11.5 pounds. The answer is option B.

Pound is a unit of measurement of mass or weight commonly used in the United States and some other countries, abbreviated as "lb".

To solve the problem, we need to use some basic algebraic equations. Let x be the weight of each box in pounds. Then, we can set up the following equation:

5x + 7.5 = 65

Simplifying this equation, we get:

5x = 57.5

Dividing both sides by 5, we get:

x = 11.5

Therefore, each box weighs 11.5 pounds. The answer is option B.

Pound is a unit of measurement of mass or weight commonly used in the United States and some other countries, abbreviated as "lb". One pound is equal to 16 ounces, and approximately 0.45 kilograms. It is commonly used to measure the weight of objects, such as people, animals, and goods.

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The area of the shaded region of the ring is approximately 1600.36 square feet.

A circle's size may be determined using both its radius and diameter. The circumference of a circle, measured from centre to centre, is its diameter. The radius is the separation between any point on a circle's perimeter and its centre. In other words, the diameter is equal to the radius's length times two. This connection may be mathematically expressed as d = 2r, where d is the diameter and r is the radius. While the radius is frequently employed in computations involving circles, such as determining the area or circumference, the diameter is frequently used to describe the size of a circle.

The area of the circle is given by the formula:

A = πr²

For the inner circle we have:

radius = 36/2 = 18

A = π(18)²

For the outer circle we have:

radius = 44/2 = 22 ft.

A = π(22)²

Now, the area of the shaded portion is:

A = π(22)² - π(18)²

A = π(484) - π(324)

Substituting 3.14 for π we have:

A = 1600.36 square feet

Hence, the area of the shaded region is approximately 1600.36 square feet.

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The complete question is:

The sales tax rate is 7% in Allegheny County. The sales tax rate in Warren County is 6%. And the book was bought in Allegheny County.

A math teacher bought a book for $ 24.99, and the sales tax on the book was $ 1.75. The teacher was able to determine whether the book was purchased in Allegheny County or Warren County by figuring out the sales tax rate. Because the total sales tax on the book was $1.75, which is equivalent to 7% of the purchase price of $24.99, the book was purchased in Allegheny County.

Sales tax rate = Total sales tax / Purchase price

Using the above formula,

Total sales tax = Sales tax rate * Purchase price

Let's calculate the sales tax using the above formula;

For Warren County, Sales tax rate = 6% = 0.06

Total sales tax = Sales tax rate * Purchase price= 0.06 * 24.99= $1.4994 ≈ $1.50

For Allegheny County,Sales tax rate = 7% = 0.07

Total sales tax = Sales tax rate * Purchase price= 0.07 * 24.99= $1.7493 ≈ $1.75

As we can see, the total sales tax on the book was $1.75, which corresponds to the sales tax rate of 7%. Therefore, the book was bought in Allegheny County.

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A motorboat with a speed of 10 km/hr in still water travels 35 km upstream on a river and 18 km up an adjacent stream for 8 hours. The speed of the river's current is approximately 5.55 km/hr.

Let's call the speed of the stream's current "v" km/hr, and the speed of the river's current "v - 1" km/hr (since it is 1 km/hr slower than the stream's current). Let's also call the speed of the motorboat in still water "s" km/hr.

When the motorboat is traveling upstream (against the current), its effective speed is:

s - (v - 1)

When the motorboat is traveling downstream (with the current), its effective speed is:

s + (v - 1)

Using the formula distance = speed x time, we can set up two equations based on the distances traveled upstream and downstream:

35 = (s - (v - 1))t1

18 = (s + (v - 1))t2

We also know that the total time spent on the trip is 8 hours:

t1 + t2 = 8

We can use the first equation to solve for t1:

t1 = 35 / (s - (v - 1))

We can use the second equation to solve for t2:

t2 = 18 / (s + (v - 1))

Substituting these expressions for t1 and t2 into the third equation, we get:

35 / (s - (v - 1)) + 18 / (s + (v - 1)) = 8

Multiplying both sides by (s - (v - 1))(s + (v - 1)), we get:

35(s + (v - 1)) + 18(s - (v - 1)) = 8(s - (v - 1))(s + (v - 1))

Expanding and simplifying, we get:

53s - 17v + 17 = 4s^2 - 4v^2 + 6s + 6v

Rearranging and simplifying, we get:

4s^2 - 47s + 4v^2 + 23v - 17 = 0

We have two unknowns (s and v), so we need another equation. We can use the fact that the speed of the motorboat in still water is 10 km/hr:

s - v = 10

We can solve this equation for s:

s = v + 10

Substituting this expression for s into the previous equation, we get:

4(v + 10)^2 - 47(v + 10) + 4v^2 + 23v - 17 = 0

Expanding and simplifying, we get:

4v^2 + 74v - 477 = 0

Solving this quadratic equation using the quadratic formula, we get:

v ≈ 5.55 km/hr (rounded to two decimal places)

Therefore, the speed of the river's current is approximately 5.55 km/hr.

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Answer:

234

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of circle: [tex](x-a)^2+(y-b)^2=r^2[/tex]  where (a,b) is center and r is radius.

This is a circle with center [tex](\frac{5}{2} ,4)[/tex] and radius [tex]\sqrt{60}[/tex].

Diameter [tex]=2 \times radius=2\sqrt{60} =4\sqrt{15}[/tex]

Ross's profit percentage is 17%.

How to calculate the percentages?

To calculate a percentage, you need to divide the part by the whole and then multiply the result by 100. The formula is:

Percentage = (part/whole) x 100

Let's work through the problem step by step:

Ross bought the chair for 1000.

1. He marked it up by 30%, which means he added 30% of 1000 to the original price:

[tex]1000 + 0.3 * 1000 = 1300[/tex]

2. He gave a discount of 10%, which means he subtracted 10% of the marked-up price:

[tex]1300 - 0.1 * 1300 = 1170[/tex]

3. The customer paid 1228.50 inclusive of a 5% tax, which means the original price before tax was:

1228.50 / 1.05 = 1170

4. Ross's profit was the difference between the price he sold the chair for and the price he bought it for:

1170 - 1000 = 170

5. To find the profit percentage, we divide the profit by the cost and multiply by 100:

[tex](170 / 1000) * 100 = 17%[/tex]

Hence, Ross's profit percentage is 17%.

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Answer:

Carl used a total of 3 liters of coffee in all.

Step-by-step explanation:

There are 1000 milliliters (mL) in a liter, so to convert from milliliters to liters, you need to divide by 1000.

To find the total amount of coffee used, you can multiply the number of mugs by the volume of each mug:

12 mugs x 250 mL/mug = 3000 mL

To convert this to liters, you divide by 1000:

3000 mL ÷ 1000 = 3 L

Therefore, Carl used 3 liters of coffee in all.

Answer:

Carl used 3 liters of coffee in all

Step-by-step explanation:

Step 1: multiply 12 by 250 to determine how mL are in all the mugs of coffee which gets you 3000

Step 2 convert: There are 1000 milliliters (mL) in a liter, so to convert from milliliters to liters, you need to divide by 1000. So divide 3000 by 1000 to find how much liters Carl uses in all. Which gets you 3

Therefore, Carl used 3 liters of coffee in all

The demeaned approach's advantages over the LSDV approach are it gives more accurate coefficient estimates, as it accounts for variations in the intercepts across different units because it can prevent multicollinearity, which is the correlation between two independent variables.

The demeaned approach refers to subtracting the unit means from every variable in the dataset. By subtracting the means from every variable in the dataset, this approach simplifies the regression model's interpretation and can enhance its estimation accuracy.

The LSDV approach involves adding a dummy variable for every single unit in the dataset. By adding a dummy variable for each unit, the LSDV approach keeps the data unaltered and estimates coefficients for each unit individually. However, this method can be inconvenient if the data includes many units.

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Step-by-step explanation:

BRO I USE TO DO THIS IN 7TH GRADE I GOT YOU.

Yes, there is a correlation between the number of hours per week a student works outside of school and how many units the student takes in a quarter.

The cluster sample of 482 students is chosen in order to examine the relationship between these two variables. The statistical relationship between two variables is known as correlation.

The correlation coefficient r is used to determine the degree and direction of the correlation between two variables. The correlation coefficient is a numerical value that ranges from -1 to +1.

A negative correlation exists when one variable decreases as the other variable increases. A positive correlation exists when both variables increase or decrease together.

In this case, if the number of hours per week a student works outside of school increases, the number of units the student takes in a quarter may decrease, indicating a negative correlation between the two variables. Similarly, if the number of hours per week a student works outside of school decreases, the number of units the student takes in a quarter may increase, indicating a positive correlation between the two variables.

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Answer: C

Step-by-step explanation:

To firgure out if a graph is a function, do the vertical line test. If the line ahs more than 1 intersection anywhere on the graph, it is not a function.

Answer:

[tex]y = - 3x {}^{ - 12x - 1} [/tex]

Step-by-step explanation:

Hope that's help your answer

The probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is 0.6747

When adults with smartphones are randomly selected, 53% use them during meetings or classes. You need to find the probability that fewer than five of the 11 selected adults use their smartphones during meetings or classes. Here's how to calculate the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Where X represents the number of smartphone users in the selected group who use their phones in meetings or classes. Using the binomial probability formula, you can calculate each of these probabilities separately.

[tex]P(X = 0) = (11C0)(0.53)^0(1 - 0.53)^11 = 0.0026\\P(X = 1) = (11C1)( 0.53)^1(1 - 0.53)^10 = 0.0247\\P(X = 2) = (11C2)(0.53)^2(1 - 0.53)^9 = 0.1012\\P(X = 3) = (11C3)(0.53) ^3(1 - 0.53)^8 = 0.2346\\P(X = 4) = (11C4)(0.53)^4(1 - 0.53)^7 = 0.3116\\[/tex]

Therefore, the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is:

[tex]P(X < 5) = 0.0026 + 0.0247 + 0.1012 + 0.2346 + 0.3116 = 0.6747[/tex]

Therefore, the probability is 0.6747.

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This equation involves a cosine function shifted to the right by pi/2 units [tex]y = cos(x - \pi /2) - 1[/tex]

Explain about cosine function ?

The cosine function is a mathematical function that describes the relationship between the angles and the adjacent sides of a right triangle. It is defined as the ratio of the adjacent side of a right triangle to its hypotenuse.

In trigonometry, the cosine function is often represented as cos(θ), where θ is the angle of interest. The value of the cosine function for a given angle θ can range from -1 to 1, depending on the angle's position relative to the x-axis.

According to the question:
Based on the description you provided, it seems like option (c) is the correct answer:

[tex]y = cos(x - \pi /2) - 1[/tex]

This equation involves a cosine function shifted to the right by pi/2 units, which causes the wave to start below the x-axis. The additional -1 at the end of the equation causes the entire graph to be shifted downward by one unit.

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Jake interpreted the mean as the mode. Half the cats weighed less than pounds and half weighed more.

What is mean and mode?

In statistics, mean and mode are two common measures of central tendency used to describe a set of data:

Mean: The mean, also known as the average, is calculated by adding up all the values in a data set and dividing the sum by the total number of values. It is a measure of the central location of the data, and it gives us an idea of the typical value of the data set. For example, the mean weight of a group of cats can tell us the typical weight of a cat in that group.

Mode: The mode is the value that appears most frequently in a data set. It is a measure of the most common value or values in the data, and it is useful for describing the shape of the distribution of the data. For example, the mode of the weights of a group of cats can tell us the most common weight among the cats in that group. It is possible for a data set to have more than one mode (bimodal or multimodal).

Jake's error is that he interpreted the mean as the mode, which is the most frequent value in a data set. The mean, however, is the average value of a data set and is calculated by adding all the values and dividing by the total number of values. Therefore, his interpretation that half the cats weighed less than the mean and half weighed more is incorrect. In reality, the mean only tells us the average weight of all the cats in the data set, but it does not indicate anything about the distribution of weights.

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Answer: When dividing a polynomial by a monomial, we can simply divide each term in the polynomial by the monomial.

So, dividing (8zy² - 28z¹y5 + 12z³y7) by (4z¹y³) gives:

(8zy²)/(4z¹y³) - (28z¹y5)/(4z¹y³) + (12z³y7)/(4z¹y³)

Simplifying each term by canceling out any common factors gives:

2y^(-1)z^(1-1) - 7y^(5-3)z^(1-1) + 3y^(7-3)z^(3-1)

which simplifies to:

2yz^0 - 7y^2z + 3y^4z^2

Therefore, (8zy² - 28z¹y5 + 12z³y7) ÷ (4z¹y³) = 2yz^0 - 7y^2z + 3y^4z^2.

Step-by-step explanation:

Answer: 70km

Step-by-step explanation: 280/4=70

Let's have a couple of examples:

You're going to drive at an average of 70km/h for 4 hours. Distance is speed multiplied by time, so: 70km/h * 4 hours = 280km.

You are going to run for 80km in 6 hours  80/6=13.33. You will run 13.33 km an hour 13.33x6= 80km

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If all three dimensions of a pyramid are multiplied by a factor of 2, the volume of the pyramid increases by a factor of 8, meaning the new volume is eight times the original volume.

If all three dimensions of a pyramid are multiplied by a factor of 2, the new pyramid will be twice as long, twice as wide, and twice as tall as the original pyramid. Therefore, the volume of the new pyramid will be 2 x 2 x 2 = 8 times the volume of the original pyramid.

In other words, if V1 is the volume of the original pyramid, and V2 is the volume of the new pyramid, we can write:

V2 = 8 x V1

So the volume of the pyramid increases by a factor of 8.

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The missing side of the right triangle is 12 feet

The Pythagorean theorem is a mathematical theorem that states that the length of the longest leg or side of a given triangle is equal to the sum of the squares of the other two sides.

The other two sides of the triangle are the opposite and the adjacent side.

From the information given in the diagram, we have;

Hypotenuse = 37

Opposite side = 35

Adjacent side = x

Substitute the values

37² = 35² + x²

find the squares

1369 = 1225 + x²

make 'x' the subject of formula

x² = 144

Find the square root

x = 12 feet

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Answer:

457

Step-by-step explanation:

220+237=457

Step-by-step explanation:

'x + 5' under the sqrt sign cannot be less than zero

so   x values (domain) must be greater than or equal to -5  to + inf

  the resulting y values (range)  will go from   0 to + inf

D    [-5, +∞)

R    [0, +∞)