suppose 37 students are enrolling in one of four courses. there will be at least one course that has at least how many students?

The answer is that 84% of women are taller than 62 inches .

The given problem is a problem of normal distribution in mathematical statistics. This distribution is a continuous univariate distribution. Its density function is given by -

f(x)= [tex]\frac{1}{σ\sqrt{2\pi } }[/tex][tex]e^{\frac{-1}{2} }[/tex]([tex]{\frac{x-u}{σ}}^{2}[/tex])

Now the actual question is  what proportion of women are taller than the height at one standard deviation below the mean since that is the first quartile range.  

Following the statistical rules of the normal distribution, we know that 50% of women are taller than the mean height of 64.5 inches.

In addition to this, we know that 34% of women will have heights of between minus 1 standard deviation and the mean (62 and 64.5 inches). Adding these percentages together, we can determine that 84% of women are taller than 62 inches or minus 1 standard deviation.

Hence, 84% of women are taller than 62 inches or minus 1 standard deviation.

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assume you want 15 participants in each condition of your experiment, which uses a 2x3 factorial design has total number of participants 15 x 3 = 45 participants

A 2x3 factorial design is composed of two independent variables and three levels for each variable. The number of participants required for each condition is equal to the number of levels in each variable (2 x 3 = 6). To determine the total number of participants required for the experiment, multiply the number of participants per condition by the number of conditions (15 x 6 = 90). If the experiment uses a repeated measures design, then the total number of participants required is half of this amount (90 / 2 = 45).

15 x 3 = 45 participants

assume you want 15 participants in each condition of your experiment, which uses a 2x3 factorial design has 15 x 3 = 45 participants

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Answer:

Step-by-step explanation:

f(x) = 8 sin [2(x+3)] + 9

x = 8 sin [2(y+3)] + 9

isolate y [tex](f^{-1}(x))[/tex]:

x/8 - 9 = sin[2(y+3)]

[tex]sin^{-1}(\frac{x}{8} - 9) = 2(y+3)[/tex]

                     =  2y + 6

[tex]sin^{-1}(\frac{x}{8} - 9) = 2y + 6\\sin^{-1}(\frac{x}{8} - 9) - 6 = 2y\\\frac{sin^{-1}(\frac{x}{8} - 9) - 6}{2} = y[/tex]

To find the difference in the number of items produced by the two plants, we can subtract the production level of the second plant from that of the first plant. This gives us:

Therefore, the first plant produces [tex]5x + 22[/tex] more items daily than the second plant.

Answer:

She walked 1.508 miles

Step-by-step explanation:

In 1 hour, Marta can walk 2.9 miles

In 0.52 hours, she can walk 2.9 x 0.52 = 1.508 miles

[tex]5x+10y=25[/tex]

Add -10y to both sides:

[tex]5x+10y+-10y=25+-10y[/tex]

[tex]5x=-10y+25[/tex]

Divide both sides by 5:

[tex]\dfrac{5x}{5} =\dfrac{-10y+25}{5}[/tex]

[tex]\fbox{y = -2y + 5}[/tex]

Answer:

-------------------------------------

The charge of $55 with error margin of  ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.

If 1000 people signed up for the service, then the least total amount is:

Correct choice is B.

the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot) with time.

To find the maximum altitude attained by the rocket, we need to find the vertex of the function h(t). We can do this by taking the derivative of the function and setting it equal to 0.

h'(t) = -32t + 300

Setting h'(t) = 0, we get

-32t + 300 = 0

32t = 300

t = 300/32

hence the time t ≈ 9.375

Now, we can substitute the value of t in the original equation h(t) to get the maximum altitude attained by the rocket.

h(9.375) = -16(9.375)2 + 300(9.375)

h(9.375) = 300 ft

Therefore, the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot).

The complete question is :

flight of a rocket the altitude in feet attained by a model rocket t time seconds into flight is given by the function h(t). find the maximum altitude (in ft) attained by the rocket. (round your answer to the nearest foot.) h(t)= -16t2 + 300t

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Answer:

22

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

[tex]\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22[/tex]

Answer:im guessing 1

Step-by-step explanation:

cuz the other ones dont make sense to be the answer

The simple interest implies that Lonzo owes $1513.5

The given variables can be represented as:

Loan amount P = $1500

Rate of interest, R = 1.2%

Time to pay back the loan, t = 9 months i.e. 0.75 year

The amount from a simple interest can be calculated using:

A = P(1 + RT)

Substitute the known values in the above equation, so, we have the following representation

A = 1500 * (1 + 1.2% * 0.75)

Evaluate

A = 1513.5

Hence, the amount owed is $1513.5

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Answer:The graph of the line shifts horizontally left 5 units.

Step-by-step explanation:

Answer:

252

Step-by-step explanation:

A car takes 4 hours to reach a destination travelling at the speed of 63 km/h.

Speed = distance / time

Distance = speed × time

Distance it took the car, travelling for 4 hours to a destination at a speed of 63 kilometers per hour would be

4 × 63 = 252 kilometers.

If the car travels at a different speed of 56 kilometers per hour and the distance remains 252 kilometers, the time it takes will be

Time = distance / speed

= 252/56 = 4.5 hours

The time varies inversely with the speed. The more the speed, the lesser the time and the lesser the speed, the more the time.

Let speed = s and let time = t

s varies inversely with t

Introducing constant of inverse variation k, it becomes

s = k/t

When s = 56, t = 4.5

56 = k/4.5

k = 4.5 × 56 =252

This is the distance

Hope this helps!!! :)

Since the line is linear, the sum of the angles should be 180 degrees

x + 28 + 73 = 180

x = 180 - 28 - 73

x = 79 degrees

Hope this helped :)

Answer:

C - 52.50

Step-by-step explanation:

49 Euros To dollars

Answer:

C) 52.50

Step-by-step explanation:

[tex]\frac{15}{14}[/tex] = [tex]\frac{x}{49}[/tex]  Cross multiply and solve for x

14x = 15(49)

14x = 735  Divide both sides by 14

[tex]\frac{14x}{14}[/tex] = [tex]\frac{735}{14}[/tex]

x = 52.50

Answer:

x = 20

y = 70

Step-by-step explanation:

It's rather difficult to explain since nothing is labeled but those are the answers

Answer: c) sphere's radius

Step-by-step explanation:

formula for volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

formula for surface area of sphere = 4πr²

we need to know the radius of sphere to find both

62/87,21

y = x + 5

3x + y = 25

Substitute x + 5 for y in the second equation.

Substitute the solution for x into either equation to find y.

The solution is (5, 10).

Answer:

Step-by-step explanation:

Answer:

20% decrease

Step-by-step explanation:

[tex]\frac{75-60}{75}[/tex]

[tex]\frac{15}{75}[/tex] = .2  to make a percent, multiply by 100 = 20%

Answer:

4

Step-by-step explanation:

√64 = 8

√4 = 2

8/2 = 4

Answer:4

Step-by-step explanation:

[tex]\sqrt{64[/tex] = 8

[tex]\sqrt{4[/tex]  = 2

8÷2=4

The augmented matrix for the system of equations 3x + 4y = 23, 5x - y = 23 is [tex]\left[\begin{array}{ccc}3&4&|23\\5&-1&|23\end{array}\right][/tex].

A new matrix, referred to as an augmented matrix, is produced by combining the columns of two existing matrices. The augmented matrix is a crucial component when employing matrices to resolve straightforward linear equations. The number of rows in the augmented matrix is equal to the number of variables in the linear equation. The augmented matrix can be defined as the union of two straightforward matrices along the columns. If the first matrix has m columns and the second matrix has n columns, the augmented matrix will have m + n columns.

The given system of equations is

3x + 4y = 23

5x - y = 23

We can write the system as an augmented matrix:

[tex]\left[\begin{array}{ccc}3&4&|23\\5&-1&|23\end{array}\right][/tex]

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To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:

Sin (A-B) = Sin A Cos B - Cos A Sin B

This formula is derived from the identity:

Sin (A-B) = Sin A Cos B - Cos A Sin B

which can be derived by using the double angle identities for sine and cosine:

Sin (2A) = 2 Sin A Cos A

Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A

Substituting these identities into the identity above, we get:

Sin (A-B) = Sin A Cos B - Cos A Sin B

Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.

Therefore, Sin (A-B) = sinAcos B - Cos Asin B.

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The solution is Option D.

The minimum number of trips of buses to carry 420 people is 5 trips

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

The number of people the tour bus can carry = 72 people

The total number of people who want to go sightseeing = 420 people

So , the equation will be

The number of trips of bus to carry 420 people =  total number of people who want to go sightseeing / number of people the tour bus can carry

Substituting the values in the equation , we get

The number of trips of bus to carry 420 people = 420/72

The number of trips of bus to carry 420 people = 5.8

The number of trips of bus to carry 420 people = 5 buses

Therefore , the minimum number of buses is 5 buses

Hence , The minimum number of trips of buses to carry 420 people is 5 trips

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Answer:

234.833333.

Step-by-step explanation:

To get this answer, you need to add 7000, which is the amount of the loan, by 1.35%. Which is the interest. You get 7095.4. Then divided that by 30, you get 234.833333.

After 7 hours, the population of bacteria is obtained as 418544.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The initial population of bacteria is given as 37000.

And, the doubling time is 2 hours.

Then, the formula for the population of bacteria at t hour can be given as,

P(t) = P₀ × [tex]2^{t/2}[/tex] where P₀ is the initial population.

Substitute t = 7 and P₀ = 37000 to get,

P(7) = 37000 × [tex]2^{7/2}[/tex]

⇒ P(7) = 418544

Hence, the population of bacteria after 7 hours is 418544.

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Answer:

Negative seven and seven sixteenths

Step-by-step explanation:

2⅛ x (-7) x 5/10

= 17/8 x (-7) x 1/2

= - 119/16

= - 7 7/16

Answer:

25x^2√(2x)

Step-by-step explanation:

2√(50x^5) + 5x√(18x^3) =

2√((2*25) * x^(4+1)) + 5x√((2*9) * x^(2+1)) =

2√(2 * 5^2 * x^4 * x^1) + 5x√(2 * 3^2 * x^2 * x^1) =

5*2√(2 * 1 * x^(2^2) * x) + 3*5x√(2 * 1 * x^2 * x) =

10√(2 * x^(2^2) * x) + 15*x*x√(2 * 1 * x) =

10√(2x * (x^2)^2) + 15*x^2√(2x) =

10x^2√(2x) + 15x^2√(2x) = 25x^2√(2x)

The point difference between Huskies and Bobcats are 3 x + 4.

Given data :

Difference = Huskies - Bobcats

Hence,

( 5x - 3 ) - ( 2x - 7 )

= 5x - 3 - 2x + 7

= 3x + 4

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Step-by-step explanation:

f(x) = 3(x - 5) + 8

f-1(x) = -1(3(x - 5) + 8)

= -3(x - 5) - 8

= -3x + 15 -8

= -3x + 7