If y varies jointly as x and z and inversely as the square of w, and y = 3 when x = 3, Z = 10, and w = 2, then y = 4 when x = 4, z = 20, and w= 4.

True or False ?

Answer:

The sample size required is, n = 502.

Step-by-step explanation:

The (1 - α)% confidence interval for population proportion is:

\(CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\cdot (1-\hat p)}{n}}\)

The margin of error is:

\(MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}\)

Assume that 50% of the people would support this political candidate.

The margin of error is, MOE = 0.05.

The critical value of z for 97.5% confidence level is:

z = 2.24

Compute the sample size as follows:

\(MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}\)

       \(n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\)

           \(=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502\)

Thus, the sample size required is, n = 502.

The exponential functions are f(x)=2(1/2)∧x

We should note that an exponential function is the type of function that is used to find the growth in a function.  A good example of an exponential function is the function f(x)=m×, where m>0 and m≠0 and x is a positive or negative integer.

The given parameters are

f(x)=2(1/2)^x

g(x)=3(−7)^x

j(x)=14(3)^x

k(x)=13(−2)^x

h(x)=9(6.7)^x

Among these parameters, the one that is a function is f(x)=2(1/2)∧x because it satisfies the condition of a function.

This function when simplified gives 1ˣ

Therefore f(x)=1ˣ

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Answer:

Plot the point at the minimum of the graph.

Step-by-step explanation:

If you keep moving the graph down, pick the point with the lowest y value that is still on the blue.

Answer:

last one

Step-by-step explanation:

The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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Answer:

y = 2sin(x/2 - pi/4) + 1

Step-by-step explanation:

The normal sine has a range of [-1, 1]. This one has a range of [-1, 3], so the amplitude is 2 times higher (4 vs 2).

After that, 2sin(x) has a range of [-2, 2], but this one has a range of [-1, 3], so we need to shift it upwards by 1.

We now know that the answer is 2sin(____)+1.

A normal sine has it's middle point while rising at x = 0, but this one has it at x = pi/2 - so we need to shift a sine to the right by pi/2.

Lastly, a sine has a cycle of length 2pi, but this one has a cycle of length 4pi. We can achieve that by dividing the argument 2.

We now know that the answer is 2sin(x/2 - pi/4) + 1. We can plot it to verify.

Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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The dimensions of the rectangle are 4 ft by 5 ft.

Given that the length of a rectangle is 3 ft less than twice the width, and the area of the rectangle is 44 sq.ft. We have to find the dimensions of the rectangle. Let's consider the width of the rectangle as x ft.Length of the rectangle = (2x - 3) ftArea of the rectangle = Length x Width44 = (2x - 3) x x44 = 2x^2 - 3x44 = x (2x - 3)2x^2 - 3x - 44 = 0To solve for x, we will factorize the equation by splitting the middle term.2x^2 - 8x + 5x - 20 = 0Factorize2x(x - 4) + 5(x - 4) = 0(x - 4) (2x + 5) = 0x = 4 ft (since the width of a rectangle can't be negative)or 2x = -5This gives us an invalid value, so x = 4 ftNow that we have the width of the rectangle, we can calculate the length as follows:Length of the rectangle = (2x - 3) ftLength of the rectangle = (2 * 4) - 3Length of the rectangle = 8 - 3Length of the rectangle = 5 ft.

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The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

According to the given information, the letter that comes next in the given alphanumeric series is "N".

What is alphanumeric series?

An alphanumeric series is a sequence of letters and/or numbers that follows a certain pattern or rule. For example, "A, B, C, D, E..." is an example of an alphabetical series, and "1, 3, 5, 7, 9..." is an example of a numerical series. An alphanumeric series may combine both letters and numbers, such as "A1, B2, C3, D4, E5...". The pattern or rule followed by an alphanumeric series may be based on numerical or alphabetical order.

The given series V, Q, M, J, H, ... follows a pattern where each letter is the 6th letter from the previous letter. So, the next letter in the series would be 6 letters after H, which is N.

Therefore, the letter that comes next in the given alphanumeric series is "N".

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The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.

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Answer:

x=7−√10 or x=7+√10

Step-by-step explanation:

−5(x−7)2+30=−20

Step 1: Simplify both sides of the equation.

−5x2+70x−215=−20

Step 2: Subtract -20 from both sides.

−5x2+70x−215−(−20)=−20−(−20)

−5x2+70x−195=0

For this equation: a=-5, b=70, c=-195

−5x2+70x+−195=0

Step 3: Use quadratic formula with a=-5, b=70, c=-195.

x=

−b±√b2−4ac

2a

x=

−(70)±√(70)2−4(−5)(−195)

2(−5)

x=

−70±√1000

−10

x=7−√10 or x=7+√10

Answer:

100 students selected randomly as their enter your middle school in the morning

Step-by-step explanation:

Answer:

C (100 students selected randomly from your middle school)

Step-by-step explanation:

The first one is wrong because its only 10 people from your homeroom.

The next one is also wrong sense its only 5 people who could also share the same interests as you.

The next one is wrong because its not from their middle school

That leaves us with the last one, its selected randomly with a lot of people involved from their middle school.

The measure of central angle DBC is 68 degree.

Hence, option C is correct.

In the given figure,

Measure of intercepted arc = 68 degree,

We have to find the measure of central angle DBC

We know that,

When two circle radii intersect in the center of a circle, they produce a vertex. These circle arms may begin at two distinct positions along the arc of such a circle. The two radii cross to produce a central angle, which serves to divide a circle into separate sectors.

A central angle is generated in the center of a circle when two radii within the circle overlap. As previously stated, a central angle in geometry is one whose vertex forms at the canter of the circle and whose arms cross the circle at two separate positions.

By connecting these two locations, an arc on the circle is formed. As a result, a central angle is the angle formed by an arc in the center of a circle.

Thus by property of central angles,

central angle = measure of intercepted arc

Hence,

⇒ m ∠DBC = 68 degree.

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Answer:

x=63/8

Step-by-step explanation:

9/8=x/7

or, 9*7=x*8

or, 63=8x

x=63/8

Answer:

C

Step-by-step explanation:

the function calculates the number of pages left to print. that means for every minute it subtracts a number of pages from the total of pages (that total being 152 pages).

the colored print only manages 30 pages per minute, while the pure black ink printing manages 33 pages per minute.

The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.

What is increasing function?

⇒ The function is said to be increasing if the y value increases as the x value increase over a given range

What is average rate of change?

⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another

As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)

And it is true for the interval [0,2]

The faster the growth rate higher the average rate of change

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Answer:

C.

Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.

Answer:

70m-175=6m-12

70m-6m=175-12

64m=163

m=163/64

Answer:

7 (x-7) or 7x-49

Answer:

\(\(1450\)\)

Step-by-step explanation:

Based on the given conditions, formulate: \(\frac{1160}{0.8}\)

Convert decimal to fraction:\(\(\dfrac{1160} {\dfrac{8}{10}}\)\)

Divide a fraction by multiplying its reciprocal:\(\(1160 \times \dfrac{10}{8}\)\)

Cross out the common factor: \(\(145 \times 10\)\)

Calculate the product or quotient: \(\(1450\)\)

get the result: \(\(1450\)\)

Answer: \(\(1450\)\)

Answer:

DCB = 44 degree

Step-by-step explanation:

DAB (given = 100

(180-100 ) / 2 = 40

ADB = ABD = 40 degree   (each)

ADC (given =  108

BDC =  DBA =  108-40 = 68 degree;

(subtracting angle inscribed within another triangle)

Triangle DBC =   180- 68+68 = 180 - 136 = 44 degree

Find DCB We have found BDC and DBA by deducting ADB from ADC

to get  BDC

Then we deduct BDC from ADC to get DCB

Answer:

It has letters

Step-by-step explanation:

Answer:

Step-by-step explanation:

2. ∠K≅∠L and ∠M≅∠N

3. Definition of similar triangles

4. ΔJKL ≈ ΔJMN

5. Addition Property

Step-by-step explanation:

1 week = 7 days

given 7 days = 14 hours of practice

and let x be the number of hours spent on practicing and y the number of days.

from the above expression we can have the equation,

\(y = \frac{x}{2} \)

using the equation when y = 10,

\( \frac{x}{2} = 10 \\ x = 2(10) \\ = 20\)

Answer:

3

Step-by-step explanation:

-2=0+x

x¹=-2 (purple one)

4=2x-2

2x=6

x²=3 (green one)