An industrial machine is able to make 8 cups in 4 seconds. What is the rate made per second?

Answer:

Step-by-step explanation:

First you take the 142+B=180

because those 2 are supplementary

B=38

and you see the 2 lines on the 2 sides that means those two sides are equal to each other and the angles corresponding with them are also equal to each other.  

and a triangle=  180 degrees

A and E are the same so A=E

180-B(38)= 142

and because A=E you do 142/2= 71

and now that you have A and E you don't need A or B for the last part so

E+(x)=180 because those two angles are supplementary.

and E is 71 so...

71+(x)=180  ---------180-71=x

X=109

The volume of the triangular prism is 198 cubic units.

To find the volume of a triangular prism, we need to multiply the area of the base triangle by the height of the prism.

In this case, the base of the triangular prism is a triangle with a base of 11 units and a height of 6 units, so the area of the base is:

Area of base = (1/2) × base × height

Area of base = (1/2) × 11 units × 6 units

Area of base = 33 square units

The height of the prism is given as 6 units.

Therefore, the volume of the triangular prism is:

Volume of prism = Area of base × Height

Volume of prism = 33 square units × 6 units

Volume of prism = 198 cubic units

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The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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Answer:

y2- y1

x2- x1

which would be,

-1 - 7

7- (-3)

Steps:

(-3, 7)        (7, -1)

(x1,y1)       (x2,y2)

Answer:

slope is delta y over delta x. In other words change in y over change in x. so if you take -3 (this is x) and 7 (this is also x) and you find the change. in this example it is positive 10. now you set that number aside and work on y now. so you now take 7 (this is y) and -1 (this is also y) and you find the change. It is -8. Finaly, since slope is delta y over delta x your answer is -8/10. -8/10 is your slope.

Hope this helped!

Null Hypothesis (H₀): The mean amount of time statistics students spend doing homework each night is greater than or equal to one hour.

Alternative Hypothesis (H₁): The mean amount of time statistics students spend doing homework each night is less than one hour.

The appropriate hypotheses for this scenario can be stated as follows:

Null Hypothesis (H₀): The true mean amount of time that statistics students spend doing statistics homework each night is equal to or greater than one hour.

Alternative Hypothesis (H₁): The true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.

In symbols:

H₀: μ ≥ 1

H₁: μ < 1

Here, μ represents the population mean amount of time spent doing statistics homework each night by statistics students.

The student wants to investigate if the data provide convincing statistical evidence to reject the null hypothesis and support the alternative hypothesis, suggesting that the true mean amount of time spent is less than one hour.

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Answer:

it is 12 - 8

Step-by-step explanation:

The absolute value of -12 is 12. The absolue value of 8 is 8.

12 - 8 = 4.

Answer:

=/-12/-/8/ [modulus od negative 12 is positive 12 ] and 8 is 8

=12-8

=4

Answer:

9

Step-by-step explanation:

The mean is calculated by adding up the scores and dividing the total by the number of scores.

A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.

The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.

This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.

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Answer:

1. -1

2.-4

3. 2

4.10

Answer:

$375

Step-by-step explanation:

$13,500÷36=$375

Hope this helps! :)

Answer:

Step-by-step explanation:

13500 divided by 36

By using Euclid's first book, we can prove that the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. In this case, the two pairs of adjacent sides are formed by the diagonals bisecting the quadrilateral into four smaller triangles with equal areas.

According to Euclid's first book, when two lines intersect at a right angle (perpendicular), they form four right angles. In the case of a quadrilateral with perpendicular, unequal, bisecting diagonals, the diagonals intersect at a right angle and divide the quadrilateral into four smaller triangles with equal areas.

1. Draw a quadrilateral with perpendicular, unequal, bisecting diagonals.
2. Label the points where the diagonals intersect as A, B, C, and D.
3. Label the point where the diagonals intersect as E.
4. Use Euclid's first book to prove that the angles at E are all right angles.
5. Use Euclid's first book to prove that the four triangles formed by the diagonals are congruent (equal in area).
6. Use the definition of a kite to prove that the quadrilateral is a kite (two pairs of adjacent sides are equal in length).
7. Therefore, the quadrilateral produced by perpendicular, unequal, bisecting diagonals is a kite.

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SOLUTION

Step 1 :

In this question, we are meant to consider the following:

Tyson has a game board that is made of 64 congruent sections.

Each section is a square with 2.5-inch sides.

We are to find the area of the game board in square inches.

Step 2:

CONCLUSION:

The area of the game board = 160 - inch -square ( OPTION B )

Step-by-step explanation:

Identify the cost of 125 miles;

\(125 \times 0.12 = 15\)

$15 for 125 miles.

Subtract 150 and 15;

\(150 - 15 = 135\)

(Money remaining)

Divide 135 by 25 to identify how many days she can rent the car;

\(135 \div 25 = 5 \frac{2}{5} \)

5 2/5 decreases to 5 as you can't rent a car for 5 2/5 days.

Answer: She can drive 125 miles and rent the car for 5 days.

Step-by-step explanation:

Given

\( {a}^{5} . {a}^{ - 3} \\ = {a}^{5 - 3} \\ = {a}^{2} \)

Hope it will help :)❤

Answer:

=a^5 - a^-3

=a^ 5 -3

= a^2.

Answer:

1) 2/5

2) 4/13

3) 1/8

4) 25/4 or 6 + 1/4

Step-by-step explanation:

1) 5/2 * x = 1

x = 1 / (5/2)

x = 2/5

2) (3 + 1/4) * x = 1

13/4 * x = 1

x = 1 / (13/4)

x = 4/13

3) 8 * x = 1

x = 1/8

4) (2/5)^2 * x = 1

2^2 / 5^2 * x = 1

4/25 * x = 1

x = 1 / (4/25)

x = 25/4

x = 6 + 1/4

The machine required at least 12 hours and 45 minutes to complete the hole on schedule.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, a special machine is used to construction site to dig holes.

And the depth of hole must be at least \(12\frac{1}{2}\) feet at the end of day.

After 4.75 feet, digging speed slows to the rate of 3/5 feet per hour.

In order to solve the problem:

First, we convert mixed fraction to decimal form,

\(12\frac{1}{2}\) feet  = 25 / 2

               = 12.5 feet

Digging speed slows,

12.5 - 4.75 = 7.75 feet.

To find the minimum amount of the time:

Time = 7.75 feet divided by the present rate of feet per hour.

Time = 7.75 ÷ 3/5

Time = 7.75 / 0.6

Time = 12.90

Converting  12.92 to hours and minutes.

0.90 is 90 percentage of 60 minutes,

90 x 60 / 100 = 45.

Time = 12 hours and 45 minutes.

Therefore, at the end of day to slay on the time machine needs to dig at least 12 hours and 45 minutes.

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The equation of the circle centered at the origin with a radius of 12 is x² + y² = 144.

In order to find the equation of a circle centered at the origin with a radius of 12, we need to use the standard form equation of a circle, which is:

(x - h)² + (y - k)² = r²

Where (h,k) represents the center of the circle, and r represents the radius.

In this case, since the circle is centered at the origin, h = 0 and k = 0. Also, since the radius is 12, we can substitute r = 12 in the above equation to get:

x² + y² = 12²

Simplifying further, we get:

x² + y² = 144

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Answer: 200m^3

Step-by-step explanation:

Rectangular prism (Cuboid) formula - L * W * H Length × Width × Height

10m(5m)(4m) = 200m^3

The implied cash price of the vehicle, considering a 5-year lease with $400 monthly payments and a 1.9% monthly interest rate, is approximately $39,919.35, including the residual value.



To find the implied cash price of the vehicle, we need to calculate the present value of the lease payments and the residual value at the end of the lease.First, we need to calculate the present value of the lease payments. The monthly lease payment is $400, and the lease term is 5 years, so there are a total of 5 * 12 = 60 monthly payments. We'll use the formula for the present value of an ordinary annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r,

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of periods.Using the given values, the monthly interest rate is 1.9% / 100 / 12 = 0.0015833, and the number of periods is 60. Plugging these values into the formula, we find:

PV = 400 * (1 - (1 + 0.0015833)^(-60)) / 0.0015833 ≈ $21,919.35.Next, we need to add the residual value of $18,000 at the end of the lease to the present value of the lease payments:

Implied Cash Price = PV + Residual Value = $21,919.35 + $18,000 = $39,919.35.Therefore, the implied cash price of the vehicle is approximately $39,919.35.

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lm pretty sure the answer is d

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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I will have 11 cookies remaining.

The expression will be; Y = 33 - X

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

For the first batch

Total = 36 - 33 (collected by dad)

Total = 33

Second batch

Let remainder = Y

Y = 33 - X

where X = teachers part

To find the remainder, X = 2/3 x Total

X = 2/3 x 33

X = 22

Therefore;

Y = 33 - 22

Y = 11

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The population in 10 years will be approximately 358,528.

I'm making a table where it shows the population every year. To find how much there is that year, I multiply the previous step by 1.02, which is 102%.

(I'm multiplying by 1.02 (102%) rather than 0.02 (2%) because the population is the previous year's population plus 2%. The previous year's population is 100%, then I'm adding 2%.)

Here's what it would look like:

year 0: 300,000 (this is how the city starts)

year 1: 306,000

year 2: 312,120

year 3: 318,362.4

year 4: 324,729.648

year 5: 331,224.24096

year 6: 337,848.7257792

year 7: 337,848.7257792

year 8: 344,605.700294784

year 9: 351,497.8143006797

year 10: 358,527.7705866933

However, having 0.7705866933 of a person isn't possible, so now, you round to the nearest whole number. The number 358,527.7705866933 rounds up to 358,528 (because the decimal place is greater than 4).

And there you have your answer :) Hopefully this helps!

The triangle is an isosceles triangle so remaining side less than 2.

What is an isosceles triangle ??

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

The length of one of the congruent sides is 5

The total length of two congruent sides is 10

The perimeter at the most is 12 (meaning the maximum length of the perimeter is 12)

The third side of the triangle must be 12-10 = 2 at the most

So the length of a remaining side is less than 2.

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The value of the side x for the given similar triangle will be 12 units.

The three-sided shape known as a triangle is sometimes used to allude to it. Every triangle has three sides and three angles, some of which might be the same.

The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.

As per the given both triangle,

The one angle of both triangles is 90° and one angle is the common angle.

Since the two angles are the same thus the third angle will be the same thus by the AAA postulate both triangles will be similar.

By a similar triangle rule,

20/x = 25/(√(25² - 20²))

x = 20/25 (15)

x = 12

Hence "The value of side x will be 12 units by AAA postulate".

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Answer:

$26

Step-by-step explanation:

10/5=2

That means that it costs $2 for each guest.

So 13x2=26

It will cost Sandra $26 if she invites 13 guests to her party.

Answer:

the real answer is c

Step-by-step explanation:

Answer: C) The amount of blue paint he will need

Step-by-step explanation:

Got 100%, have a good day:)

Answer:

\(\dfrac{5}{2}\pi\)

Step-by-step explanation:

Rotation about the y-axis

\(\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y\)

where:

Given function of y:  \(y = 3x^2\)

Rewrite the given function as a function of y:

\(\implies x^2=\dfrac{1}{3}y\)

Substitute the values into the formula:

\(\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y\)

\(\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}\)

\(\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}\)

Take out the constant and integrate:

\(\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}\)

Therefore, the exact value of the volume of revolution is:

\(\dfrac{5}{2}\pi\)

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Answer: the answer is D

Step-by-step explanation:

2=5-3