two containers designed to hold water are side by side, both in the shape of a cylinder. container A has a diameter of 32 feet and a height of 16 feet. container B has a diameter of 30 feet and a height of 18 feet. container A is full of water and the water is pumped into container B until container B is completely full.After the pumping is complete, what is the volume of water remaining in container A to the nearest tenth of a cubic foot?

Answer:

Step-by-step explanation:

So you know that some number of nickels, dimes and quarters will add up to 490 cents. Every nickel is worth 5 cents, so some number of nickels can be 5n. In the same way, some number of dimes can be 10d, and some number of quarters can be 25q. So the general equation is going to be 5n + 10d + 25q = 490 But since the dimes and quarters are also explained in relation to the number of nickels, think of everything as nickels: the number of dimes (d) = the number of nickels + 7, so d = n + 7 And in the same way, you can arrive at the number of quarters (q) is nickels + 4, so q = n + 4 So re-write the equation, but each time you see d, write n + 7 instead and each time you see q, write n + 4. you'll end up with lots of chunks of n: 5n + 10(n + 7) + 25(n + 4) = 490 when you do all the multiplying, you get: 5n + 10n + 70 + 25n + 100 = 490 combine all those terms and you get 40n + 170 = 490. Subtract 170 from both sides and you get 40n = 320. Divide both sides by 40 and you get n = 8. Which means you have 8 nickels, then add 7 to get 15 dimes, and for the quarters it was the nickels plus 4, so you have 12 quarters. When you double check by multiplying out how much each pile of coins is worth, it will add up to 490 cents, or $4.90

Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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Answer: 15

Step-by-step explanation:

In my opinion it's 15 because calculators

Answer:

15

Step-by-step explanation:

10 can be written as 5 + 5

5 + 10

= 5 + 5 + 5

= 5 x ( 1 + 1 + 1 )

= 5 x 3

= 15

Solution

-

Question A:

The pair of dice has a total space f

- For the dice to give a total of at least 5, the possible combinations are:

- Thus, we have the probability of choosing at least 5 as follows:

Question B:

- A total of at lest 10 ihas the following possibilities:

- Thus the probability of the second roll being a total of at least 10 is

The $7,000 worth of purchase and payment of $5,000 before the three months deadline gives the amount owed at 2.49% monthly compound interest rate as $2,153.15

Owed: $2,153.15

Compound interest accounts for the interest that is earned on an interest, such that the interest rate is compounded on an initial amount.

The given parameters are;

The amount of the items purchased from the store = $7,000

The amount of down payment required = 10%

The amount paid in three months = $5,000

Monthly interest on amount owed after three months = 2.49%

Required;

The amount owed after payment of $5,000 before three months

Solution;

Using the compound interest formula, we have;

\( \displaystyle{A = P \cdot \left(1 + r \right)^{n} }\)

Where;

A = The amount owed

P = The amount loaned = $7,000 - $5,000 = $2,000

r = Monthly interest rate = 2.49%

n = The number of months = 3 months

Which gives;

\( \displaystyle{A = 2000 \times \left(1 + 0.0249 \right)^{3} \approx 2153.1509}\)

The amount owed (for the 3 months period) is approximately $2,153.15

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0.012 is the answer!

I hope this helps you out! :D

\(\\ \sf\longmapsto \dfrac{12}{1000}\)

\(\\ \sf\longmapsto 0.012\)

More:-

\(\\ \sf\longmapsto \dfrac{1}{10}=0.1\)

\(\\ \sf\longmapsto \dfrac{1}{100}=0.01\)

Answer:

\(f(x) = cos(x - \frac{\pi }{4} ) -1\)

Step-by-step explanation:

In this graph, we have the coordinate point (\(\frac{\pi }{4} , 0\)). Without translations, cos(0) = 0, which means that the graph is shifted to the right by \(\frac{\pi }{4}\). We also know that the graph is shifted down by 1 because we have the point

(\(\frac{5\pi }{4} , -2\)), but accounting for the right shift, this point should really by (\(\pi , -2\)). cos(\(\pi\)) = -1, but on the graph it is -2, meaning that it is shifted down by 1.

Therefore, accounting for the right shift by \(\frac{\pi }{4}\) and the shift down by 1, our equation is \(f(x) = cos(x - \frac{pi}{4} ) - 1\).

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

-36

Step-by-step explanation:

Step-by-step-explanation

The first thing you would do is multiply both numbers inside the parenthesis by -3.

You would get -21 + (-15) or you could just wrtie -21 - 15, whichever is easier for you.

Then you'd simply add both -21 and -15 together, and you get -36. :D

Answer:

0.0369

Step-by-step explanation:

normalcdf (1220,1320,900,200) is 0.0369

The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.

Answer:

3.053

Step-by-step explanation:

Based on the pattern of the sequence, we can reasonably infer that the missing decimal is 0.053, which would fit the pattern of increasing by 0.001 from 3.052 to 3.053, and then increasing by 0.010 from 3.053 to 3.063.

Answer:

A car travels at average speed of 4m/s and covers a distance of 2.4km calculate the time take help me

Answer:

\(y=\frac{1}{6}x+6\)

Step-by-step explanation:

Let \((x_1,y_1)\rightarrow(-6,5)\) and \((x_2,y_2)\rightarrow(6,7)\)

Determine slope

\(m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}\)

Use either ordered pair to find the y-intercept

\(y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b\)

Final equation

\(y=\frac{1}{6}x+6\)

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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The second location result in the largest area of grass that Jaeger can eat, which is approximately 353.57 square meters.

We may infer from the facts provided that Jaeger the goat will be confined to a 10- by-16-meter rectangular shelter by means of a 15-meter chain. All of the grass along the chain may be consumed by Jaeger. At three separate points in the shed, we are instructed to locate the patch of grass that Jaeger can eat.

Let's consider the three different locations as follows:

Attach the chain to a corner of the shed.

Jaeger can only eat as much grass as is contained inside a quarter-circle with a radius of 15 meters (the length of the chain) if the chain is fastened to a shed corner. This quarter-circle's area is:

Area = (1/4) x π x (15 meters)²

Area = 176.71 square meters (approx)

Affix the chain to the middle of one of the shed's longer sides.

This semicircle's area is:

Area = (1/2) x π x (15 meters)²

Area = 353. 57 square meters (approx)

To the center of one of the shed's shorter sides, fasten the chain.

This circular sector's area will be as follows:

Area = (90/360) x π x (15 meters)²

Area = 176.71 square meters (approx)

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The answer of the given question based on the finding the value of x and y from the triangle given the answer is (a) the values of x and y are approximately 25.98 cm and 15 cm, respectively , (b) the value of y is 18√3.

An angle is  geometric figure formed by two rays that share  common endpoint, called  vertex. The rays are also called  sides or legs of angle. Angles are typically measured in degrees or radians, and they are used to describe  amount of rotation between two rays.

Angles can be classified based on their degree of rotation. A right angle is  angle that measures exactly 90° degrees, while  acute angle measures <90° degree. Obtuse angle measure > 90° degrees but < 180° degrees. straight angle is  angle that measures exactly 180° degrees, and full rotation or revolution is equivalent to  angle of 360° degrees.

Using the given information, we can start by drawing a triangle ABC where angle B is 60° degrees, angle C is 30° degrees, and BC is 30 cm.

Next, we can use the fact that the sum of angles in a triangle is 180° degrees to find angle A:

angle A = 180° degrees - angle B - angle C

angle A = 180° degrees - 60° degrees - 30° degrees

angle A = 90° degrees

So angle A is 90° degrees, which means triangle ABC is a right triangle.

We can now use the trigonometric ratios of sine, cosine, and tangent to find the values of x and y. Let's choose to use sine and cosine:

sin 60° degrees = opposite / hypotenuse = x / 30

x = 30 sin 60° degrees

x ≈ 25.98 cm

cos 60° degrees = adjacent / hypotenuse = y / 30

y = 30 cos 60° degrees

y ≈ 15 cm

Therefore, the values of x and y are approximately 25.98 cm and 15 cm, respectively.

(B) We can use the trigonometric ratio of tangent to find the value of y:

tan 60° degrees = opposite / adjacent = y / x

y = x tan 60° degrees

y = 18 tan 60° degrees

y = 18 (√3)

Therefore, the value of y is 18√3.

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Answer:

See below

Step-by-step explanation:

The number you described is the same as \(sin(60^{\circ})=\frac{\sqrt{3}}{2}\) where the sine of an angle is the ratio between a right triangle's opposite side to the angle and the hypotenuse. So, in this case, if we had a right triangle with a height of \(\sqrt{3}\) units and a hypotenuse of 2 units, the ratio between the two sides will result in the value you provided. This right triangle in particular would be a 30-60-90 triangle.

In the case of a unit circle, it’s the y-coordinate of the point where a 60° angle in the standard position intersects a unit circle and a right triangle is created from that.

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

a. The initial quantity of radioactive material is 0.68 g.

b. It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

a. In order to find the initial quality of radioactive material, we will use the formula:

Initial Quality = Final Quantity * (1 - Reduction Rate)^Years

We know that -

the final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.

Initial Quantity = 1.52 g * \((1 - 0.18)^4\)

Initial Quantity = 1.52 g * 0.452

Initial Quantity = 0.68 g

Hence, the initial quantity of the radioactive material is 0.68 g.

b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:

Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)

We know that -

the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).

Years = log(0.2 / 0.0.68) / log(1 - 0.18)

Years = 7.15

Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.

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Answer:

13/12=37

Step-by-step explanation:

Answer:

282.463

Step-by-step explanation:

Answer: 282.436

Step-by-step explanation:

281.7

+   0.736

282.436

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

The equation of the polynomial in vertex form is \(y +8= (-2)\cdot (x-3)^{2}\), its vertex is \((h,k) = (3, -8)\).

The expression of the axis of symmetry is \(x = 3\).

The y-intercept of the function is -26.

Step-by-step explanation:

The vertex form of the second order polynomial is defined by the following expression:

\(y-k = C\cdot (x-h)^{2}\)  (1)

Where:

\(x\) - Independent variable, dimensionless.

\(y\) - Dependent variable, dimensionless.

\(h,k\) - Coordinates of the vertex, dimensionless.

\(C\) - Vertex constant, dimensionless.

Let \(y = -2\cdot x^{2}+12\cdot x - 26\), then we proceed to present the produre for the determination of the vertex form:

1) \(y = -2\cdot x^{2}+12\cdot x - 26\) Given

2) \(y = (-1)\cdot (2\cdot x^{2})+(-1)\cdot (-12\cdot x) + (-1)\cdot (26)\) \((-a)\cdot (-b) = a\cdot b\)/\((-a)\cdot b = -a\cdot b\)

3) \(y = (-1)\cdot (2\cdot x^{2}-12\cdot x +26)\) Distributive property

4) \(y = [(-1)\cdot (2)]\cdot (x^{2}-6\cdot x +13)\) Associative and distributive properties

5) \(y = (-2)\cdot [(x^{2}-6\cdot x+9)+4]\) \((-a)\cdot b = -a\cdot b\)

6) \(y = (-2) \cdot [(x-3)^{2}+4]\) Perfect square trinomial

7) \(y = (-2)\cdot (x-3)^{2}+4\cdot (-2)\) Distributive property

8) \(y = (-2)\cdot (x-3)^{2}+(-8)\) \((-a)\cdot b = -a\cdot b\)

9) \(y +8= (-2)\cdot (x-3)^{2}\) Compatibility of addition/Existence of the additive inverse/Modulative property/Result.

The equation of the polynomial in vertex form is \(y +8= (-2)\cdot (x-3)^{2}\), its vertex is \((h,k) = (3, -8)\).

The axis of symmetry is a line perpendicular to axis in which the square component of the vertex form is set. The expression of the axis of symmetry is \(x = 3\).

The y-intercept is the value of the polynomial when \(x = 0\), then, the value is:

\(y = -2\cdot (0)^{2}+12\cdot (0) -26\)

\(y = -26\)

The y-intercept of the function is -26.

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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