:ARE X AND Y PROPORTIONAL? HOW
DO YOU KNOW? EXPLAIN.
A.
B.
35
х
3
6 | 9
12
30
25
у
1
2
3
4
1
20
15
10
5
0
0 1 2 3 4 5 6 7 x

Answer:

b(a+2)(a-1)

Step-by-step explanation:

b(2a+a^2-2-2-a)

Answer:

b (a + 2) (a - 1)

Step-by-step explanation:

1. First you need to factor out b from the equation because it is the one factor that they all have in common.

2ab + a²b - 2b - ab

b (2a + a² - 2 - a)

2. Then you just factor 2a + a² - 2 - a and remember the b

b (2a + a² - 2 - a)

b (a + 2) (a - 1)

check your answer:

b (a + 2) (a - 1)

b (a²- a + 2a - 2)

a²b - ab + 2ab - 2b

2ab + a²b -2b - ab

hope this helps!!

The half-life of this substance that weighs 32 mg and one year later, the sample weighs 25.5 mg will be 3.053 year.

The duration it takes for a given quantity to fall to half of its initial value is known as the half-life. The phrase can be used to refer to other types of decay, whether or not they are exponential, but it is most frequently used in connection with atoms going through radioactive decay. The amount of time needed for the reactant concentration to drop to half its initial value is known as the half-life of a reaction.

Here,

The initial weight of radioactive substance=32 mg

The final weight of radioactive substance=25.5 mg

Duration=1 year

The formula,

N(t)=N(0)*1/2^(t/t₁/₂)

25.5=32*1/2^(1/t₁/₂)

half-life, t₁/₂ = 3.053 year

The half-life of this substance, which weighs 32 mg, will be 3.053 years when the sample weighs 25.5 mg.

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Answer:

∠ EFH = 112°

Step-by-step explanation:

∠ ACD and ∠ EFH are Alternate exterior angles and are congruent, thus

11x - 20 = 9x + 4 ( subtract 9x from both sides )

2x - 20 = 4 ( add 20 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Thus

∠ EFH = 11x - 20 = 11(12) - 20 = 132 - 20 = 112°

The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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The width of the pool is approximately 4.01 feet.

Mrs. Sanford plans to build a rectangular pool in her backyard, which will hold 9,000 gallons of water. The pool's height is 15 feet and its length is 20 feet. To determine the width of the pool, we need to first convert gallons to cubic feet, as 1 gallon equals approximately 0.1337 cubic feet.

So, 9,000 gallons * 0.1337 = 1,203.3 cubic feet of water. Now, we know that the volume of a rectangular pool is calculated using the formula V = LWH (Volume = Length * Width * Height). We have the volume (1,203.3 cubic feet), the height (15 feet), and the length (20 feet), so we can solve for the width (W):

1,203.3 = 20 * 15 * W
1,203.3 = 300 * W
W = 1,203.3 / 300
W ≈ 4.01 feet

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The angles which are congruent are ∠1 and ∠5,∠6 and ∠4, and ∠8 and ∠2 thus options (A),(C), and (D) are correct.

The angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

As per the given parallel lines m and n and a transversal s shown below,

∠1 = ∠7 (alternative exterior angle)

Since ∠7 = ∠5 (opposite angles)

Therefore, ∠1 = ∠7.

∠6 = ∠4 (alternative interior angle)

∠8 = ∠2 (alternative exterior angle)

Hence "The angles which are congruent are ∠1 and ∠5,∠6 and ∠4, and ∠8 and ∠2".

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Answer:

A , B , and E (see the screenshot)

Step-by-step explanation:

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

The volume generated by rotating the region bounded by y=14√x, y=0, and x=1 about x=-2 is approximately 188.5 cubic units.

To use the method of cylindrical shells, we need to consider a vertical strip of width dx at a distance x from the axis of rotation. When this strip is rotated about the axis, it generates a cylindrical shell with radius (x+2) and height y = 14√x.

The volume of this cylindrical shell can be expressed as:

dV = 2π(x+2)(14√x)dx

Integrating this expression from x=1 to x=4 (the limits of the region), we get:

V = ∫1^4 2π(x+2)(14√x)dx

= 28π ∫1^4 (x+2)√x dx

= 28π (∫1^4 x√x dx + ∫1^4 2√x dx)

= 28π [2/5 x^(5/2) + 4/3 x^(3/2)]_1^4

= 28π [(2/5 4^(5/2) + 4/3 4^(3/2)) - (2/5 1^(5/2) + 4/3 1^(3/2))]

= 28π [(32/5 + 16/3) - (2/5 + 4/3)]

= 28π (102/15)

= 188.4955592

Therefore, the volume generated by rotating the region bounded by y=14√x, y=0, and x=1 about x=-2 is approximately 188.5 cubic units.

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Custard must contain 1.4% pasteurized egg yolk.

Custard is a sweet or savory dish made from milk, sugar, and eggs, often flavored with vanilla or other flavorings. In order to be considered custard, it must contain at least 1.4% pasteurized egg yolk, which acts as a thickening agent and gives custard its characteristic creamy texture.

Pasteurized egg yolk is used to ensure the safety of the dish, as it has been treated to eliminate any potential bacterial contamination. This requirement is often enforced by food regulatory agencies to ensure that custard products are safe for consumption.

Therefore, any product that is labeled as custard must meet this standard in order to be sold to the public.

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Answer:

58°

Step-by-step explanation:

A + B + C = 180 °

The smallest value of C is 91.

A + B = 89

A = 2B - 4

2B - 4 + B = 89

3B - 4 = 89

3B = 93

B = 31

A + 31 = 89

A = 58

Answer:

1. 279,936

2. 727

4. 4,096

9!

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

2! x 2! x 2!

An estimator is Unbiased if the Expected Value of the estimator is exactly equal to the parameter that it is estimating.

The correct answer is A.

An "estimator" or "point estimate" is a statistic (that is, a function of the data) that is used to infer the value of an unknown parameter in a statistical model. A common way of phrasing it is "the estimator is the method selected to obtain an estimate of an unknown parameter".

An estimator is a statistic used to estimate an unknown population parameter, such as the mean or variance. An unbiased estimator is one that, on average, produces estimates that are equal to the true value of the population parameter being estimated. This means that the expected value of the estimator is exactly equal to the parameter it is estimating.

Unbiasedness is an important property for an estimator to have because it ensures that the estimator is not systematically overestimating or underestimating the population parameter.

An estimator that is biased will tend to consistently overestimate or underestimate the true value of the parameter, which can lead to incorrect conclusions or decisions based on the estimates.

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Elena was running at 2.5 miles per hour

Form the question it can be deduced that the the running track is 1/4 mile long . this is equivalent to 0.25 mile.

A lap of a mile is equivalent to a quarter of a mile which is same as 1/4 mile or 0.25 mile

Hence we can solve the number of miles per hour using the formula

= number of miles covered by Elena / time take to complete the mileage

= 0.25 miles / 1/10

= 2.5 miles per hour

Hence Elena was running at 2.5 miles per hour

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To have $3,793,695.00 in his retirement account when he retires, Derek would need the rate on the account to be approximately 5.89%.

To calculate the required rate on Derek's retirement account, we can use the formula for the future value (FV) of an annuity:

\(FV = P * [(1 + r)^n - 1] / r\)

Where:

FV is the desired future value

P is the amount deposited on each birthday

r is the interest rate per period

n is the total number of periods (number of birthdays)

In this case, the desired future value (FV) is $3,793,695.00, the amount deposited on each birthday (P) is $14,455.00, and the total number of periods (n) is the difference between Derek's final and initial birthday, which is 68 - 27 = 41.

We need to solve for the interest rate (r). Rearranging the formula:

\(r = [(FV / P) / [(1 + r)^n - 1]]\)

Substituting the given values, we have:

\(r = [(3,793,695.00 / 14,455.00) / [(1 + r)^{41} - 1]]\)

We can use numerical methods or trial and error to find the value of r that satisfies the equation. By using these methods, the approximate value of r is found to be 0.0589 or 5.89%.

Therefore, Derek would need the rate on his retirement account to be approximately 5.89% for him to have $3,793,695.00 in it when he retires.

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After 3 days, Emilio will have collected 28 + 8(3) = 52 signatures, and Belle will have collected 25 + 9(3) = 52 signatures as well.

To determine the number of signatures both Emilio and Belle will have, we can set up an equation:

28 + 8x = 25 + 9x

where x is the number of days it takes for both of them to collect the same number of signatures.

Simplifying the equation, we get:

3x = 3

x = 1

So it will take them one more day for Belle to collect the same number of signatures as Emilio.

To find out how many signatures they will both have, we can substitute x=1 into either of the equations and solve for the number of signatures. Let's use Emilio's equation:

28 + 8(1) = 36

Therefore, both Emilio and Belle will have 36 signatures.

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Answer:

10 + 5x ≤ 25

Step-by-step explanation:

The combination that is not a valid proposed set of quantum numbers is b.

The valid range of values for the quantum numbers are:
- n can be any positive integer (1, 2, 3, ... )
- l can be any integer from 0 to n-1
- ml can be any integer from -l to +l
- ms can be either +1/2 or -1/2
The valid ranges for each quantum number are as follows:

n (principal quantum number): Any positive integer

l (azimuthal quantum number): 0 to (n - 1)

ml (magnetic quantum number): -l to l

ms (spin quantum number): -1/2 or 1/2

Let's check each proposed set of quantum numbers:

a. 3; 2; 1; -1/2 - This set is valid. The values for n, l, ml, and ms are within the valid ranges.

b. 4; 3; 3; 1/2 - This set is not valid. The value of l (azimuthal quantum number) cannot be greater than n - 1. In this case, l is 3, which is greater than n - 1 (4 - 1 = 3). Therefore, this set is not valid.

c. 1; 0; 0; -1/2 - This set is valid. The values for n, l, ml, and ms are within the valid ranges.

d. 2; 0; 0; 1/2 - This set is valid. The values for n, l, ml, and ms are within the valid ranges.

e. 2; 0; 1; 1/2 - This set is valid. The values for n, l, ml, and ms are within the valid ranges.
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Answer:

13.9 ft

Step-by-step explanation:

Answer:

46655

Step-by-step explanation:

\(75250 \cdot \frac{62}{100} = 46655\)

Given:

A storeowner made a list of number of greeting cards sold last month.

The store sold 167 thank-you cards, 285 birthday cards and 56 blank cards.

Required:

What is the probability that the next customer will buy a blank card expressed as a percent?

Explanation:

We will find total number of cards sold as:

167 + 285 + 56 = 508

Now we will find percentage of each type of card sold as:

Percentage of blank cards sold

Answer:

Hence, in percent probability of sold blank card is 11%.

rd

Sangeetha got Rs. 412, Manish got Rs. 103 and the difference is Rs. 309

Data;

To calculated the amount Sangeetha got, let's solve the ratio

\(4 + 1 = 5\\\frac{4}{5} * 515 = 412\)

Sangeetha got Rs 412.

To calculate the amount Manish got we can either subtract 412 from 515 or we find 1/5 of 515

\(\frac{1}{5} * 515 = 103\)

The difference in the amount is calculated by subtracting 412 from 103

\(412 - 103 = 309\)

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Answer:

a=8/2

a=4

Step-by-step explanation:

Answer:

\(a = 4\)

Step-by-step explanation:

\((2a) = 8\)

\(a = \frac{8}{2} \)

\(a = 4\)

Answer:

34.06°

Step-by-step explanation:

25 is the length of the hypotenuse side and 14 is the length of the opposite side.

Therefore, you will need to use sine to work out the missing angle.

sinx = opp / hyp

sinx = 14 / 25

x = sin ^ -1 (14 / 25)

= 34.06°

The Solution to the given questions are:

A central angle is an angle whose vertex is at the centre of a circle and whose sides intersect the circle at two distinct points. The measure of a central angle is equal to the measure of the arc intercepted by the angle, where the arc is the portion of the circle between the two points of intersection.

An intercepted arc is a segment of a circle's circumference that is bounded by two points on the circle and contains all the points of the circle's circumference that lie between those two points. In other words, it is the portion of the circle that is "cut out" or intercepted by two points on the circle.

In this given question,

The circumscribed angle can be measured by dividing the central angle by 2.

Hence,

112°/2= 56°.

Therefore, the measurement of circumscribed angle is 56°.

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Answer:

$80 original price

Step-by-step explanation:

If 45% of an item is $36 what is the original price?

40% = 0.4

36/0.4 = $80 original price

Answer:

$80

Step-by-step explanation:

45/100=36/x

Cross multiply

45x=100(36)

45x=3600

/45.   /45

x=80

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Answer:

A) sin θ = 3/5

B) tan θ = 3/4

C) csc θ = 5/3

D) sec θ = 5/4

E) cot θ = 4/3

Step-by-step explanation:

We are told that cos θ = 4/5

That θ is the acute angle of a right angle triangle.

To find the remaining trigonometric functions for angle θ, we need to find the 3rd side of the triangle.

Now, the identity cos θ means adjacent/hypotenuse.

Thus, adjacent side = 4

Hypotenuse = 5

Using pythagoras theorem, we can find the third side which is called opposite;

Opposite = √(5² - 4²)

Opposite = √(25 - 16)

Opposite = √9

Opposite = 3

A) sin θ

Trigonometric ratio for sin θ is opposite/hypotenuse. Thus;

sin θ = 3/5

B) tan θ

Trigonometric ratio for tan θ is opposite/adjacent. Thus;

tan θ = 3/4

C) csc θ

Trigonometric ratio for csc θ is 1/sin θ. Thus;

csc θ = 1/(3/5)

csc θ = 5/3

D) sec θ

Trigonometric ratio for sec θ is 1/cos θ. Thus;

sec θ = 1/(4/5)

sec θ = 5/4

E) cot θ

Trigonometric ratio for cot θ is 1/tan θ. Thus;

cot θ = 1/(3/4)

cot θ = 4/3

Answer: A

Step-by-step explanation:

Step-by-step explanation:

We need to find the value of x for all problems if Y is between X and Z.

For all cases, XZ = XY+YZ

4. XY = 5x, YZ=x, and XZ=25

Putting all values

25 = 5x + x

25 = 6x

\(x=\dfrac{25}{6}\)

5. XY = 12, YZ=2x, and XZ = 28

28 = 12 + 2x

x = 8

6.  XY = 4x. YZ=3x, and XZ = 42

XZ = XY+YZ

42 = 4x + 3x

42 = 7x

x = 6

7. XY=2x + 1. YZ = 6x, and XZ=81

XZ = XY+YZ

81 = 2x + 1 + 6x

80 = 8x

x = 10

Answer:

8, -5, -4, 6

Step-by-step explanation: