choose a number between 67 and 133 that is a multiple of 2,8 and 16 .

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be \(h(t) = -16\cdot t^{2} + 128\cdot t + 320\), the first and second derivatives are, respectively:

First Derivative

\(h'(t) = -32\cdot t +128\)

Second Derivative

\(h''(t) = -32\)

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

\(-32\cdot t +128 = 0\)

\(t = \frac{128}{32}\,s\)

\(t = 4\,s\) (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

\(h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320\)

\(h(4\,s) = 576\,ft\)

The highest altitude that the object reaches is 576 feet.

Answer:

1/64

Step-by-step explanation:

4x4^3/4^7

4^-3

1/4^3

1/64

Answer:an isosceles triangle with PQ=QR (option C)

Step-by-step explanation:

Answer:

A. a right tringle with PQ ⊥ QR

Step-by-step explanation:

If you plot the points on a graph you'll notice that the triangle formed is not an isosceles triangle and is in fact a right triangle with PQ being perpendicular to QR.

Answer:

54

Step-by-step explanation:

63x 6/7

Answer:

a

Step-by-step explanation:

because all top numbers can go into bottom numbers.

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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2/3 is the correct answer

Answer: b is the answer

Step-by-step explanation:

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:  population mean μ = 37.40 mm; population std dev σ ≈ 7.57 mm

Step-by-step explanation:

The first group of numbers is the set of ranges for the categories (or 'classes') we will use. The second group of numbers is how many observations (frequency) for each category.

If the categories were just single numbers, we would get the total category values by multiplying the frequency times the category value. But the categories are each a range of values. What we do here is we take the midpoint of each range, and use that.

So we have range midpoint values of 22, 27, 32, 37, 42, 47, and 52.

We get the population mean by multiplying each class midpoint times its frequency, and then summing up all the products, and then dividing by the total number of observations, 'N'.

N = 6+10+18+25+22+15+4 = 100

For frequency * class midpoint, we have ...

6 * 22 = 132

10 * 27 = 270

18 * 32 = 576

25 * 37 = 925

22 * 42 = 924

15 * 47 = 705

4 * 52 = 208

If we add these up, we get 3740

(a.) population mean μ = 3740/N = 3740/100 = 37.4 mm

The population standard deviation is the square root of the population variance, so we must get the variance first.

variance is the average of the squared differences from the mean.

We take each data point (midpoint of its class), subtract the mean, then square that difference. Then we multiply that squared difference by the frequency for that class. Then we add all those products together.

This takes some time to do manually, but here goes. ( If you have Microsoft Excel, the program can be used to do a lot of this.)

For Class 1 (midpt 22): 6 * (37.4 - 22)^2 = 1422.96

For Class 2 (midpt 27): 10 * (37.4 - 27)^2 = 1081.60

For Class 3 (midpt 32): 18 * (37.4 - 32)^2 = 524.88

For Class 4 (midpt 37): 25 * (37.4 - 37)^2 = 4.00

For Class 5 (midpt 42): 22 * (37.4 - 42)^2 = 465.52

For Class 6 (midpt 47): 15 * (37.4 - 47)^2 = 1382.40

For Class 7 (midpt 52): 4 * (37.4 - 52)^2 = 852.64

If we add all the products together, we get 5,734.00

Divide by N = 100

5734/100 = 57.34

The population variance is 57.34 mm squared

The population standard deviation is Greek letter sigma (lower case) σ and is the square root of the variance, so

(b.)  σ = \(\sqrt{57.34}\) ≈ 7.57 mm

Notice that when we get to the std dev, we are back at the original unit of measure, not its square

I hope this helps.

Answer:

A

Step-by-step explanation:

Khan Academy

Answer:

10 cups of milk

Step-by-step explanation:

First, we know that the ratio for flour to milk is 3:2, so if you are making 5 cakes, you need to multiply the ratio by 5.

So, 2 x 5 = 10, which is your answer

Hope this helps!

Answer:

−12\(x^{2}\)+3x+9

Step-by-step explanation:

=(3)(3x)+(3)(3)+−12x2+−6x

=9x+9+−12x2+−6x

Combine Like Terms:

=9x+9+−12x2+−6x

=(−12x2)+(9x+−6x)+(9)

=−12\(x^{2}\)+3x+9

Tan(x/2) = (1 + cosx)/sinx is equivalent to the trigonometric identity cscx

An equation is an expression that can be used to show the relationship between variables and numbers.

Trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent.

It is given as:

tanФ = sinФ/cosФ, cotФ = 1/tanФ = cosФ/sinФ, cosecФ = 1/sinФ and secФ = 1/cosФ

According to half angle formula:

tan(x/2) = (1 + cosx)/sinx

Hence:

tan(x/2) + cotx = [(1 - cosx)/sinx] + (cosx/sinx)

tan(x/2) + cotx = (1 - cosx + cosx)/sinx

= 1/sinx

= cscx

Therefore tan(x/2) = (1 + cosx)/sinx is equivalent to cscx

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The required probability for purchasing more than one costume is 0.03.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The given problem can be solved as follows,

The number of visitors purchasing no costume, exactly one and more than one costumes are given as 81, 6 and 3 respectively.

Then, the total number is 81 + 6 + 3 = 90

Now, the probability of purchasing more than one costume is given as,

P(More than one costume) = 3/90

                                            =  1/30

                                            = 0.03

Hence, probability that the next person will purchase more than one costume is 0.03.

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Answer:

x = 19

Step-by-step explanation:

By the Supplementary Angle Theorem we can say that;

123 + 3x = 180

3x = 57

x = 19

Hope this helps!

Answer: 56.52mm

Step-by-step explanation:

First, you have to find the circumference of the wheel and divide it by 25 since the spokes are equally spaced.

The equation for the circumference of a circle is:

C = 2πr

C = 2 x π x 225

C = 1413

Then, you divide it by 25

1413/25 = 56.52

Answer:

(4,2.5)

Step-by-step explanation:

Answer:

The answer is 21

Step-by-step explanation:

2 pounds = 32

32+3 = 35

35+21=56

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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\(\begin{aligned}\\&f(x)=\log_4\left(\dfrac{x^2(x+9)^3}{(x-1)^8}\right)\\&f(x)=\log_4(x^2(x+9)^3)-\log_4{(x-1)^8\\&f(x)=\log_4x^2+\log_4(x+9)^3-8\log_4{(x-1)\\&f(x)=2\log_4x+3\log_4(x+9)-8\log_4{(x-1)\end{aligned}\)

second option

Answer:

\(f(x) = 2\log_4x + 3\log_4(x + 9) - 8\log_4(x - 1)\)

Step-by-step explanation:

In the following answer I'll use the following logarithm laws:

\(\log_m(a \times b) = \log_ma + \log_mb\\\\\log_m(\frac ab) = \log_ma - \log_mb\\\\\log_m(a^b) = b \times \log_ma\)

Now for the answer:

\(f(x) = \log_4\left(\frac{x^2(x + 9)^3}{(x - 1)^8}\right)\\\\\to f(x) = \log_4\left(x^2(x + 9)^3\right) - \log_4\left((x - 1)^8\right)\\\\\to f(x) = \log_4\left(x^2\right) + \log_4\left((x + 9)^3\right) - \log_4\left((x - 1)^8\right)\\\\\to f(x) = 2\log_4x + 3\log_4(x + 9) - 8\log_4(x - 1)\)

Answer: It's 11.5

Explanation ( took so long)

\(C = \sqrt{a^{2} + b^{2} }\\14 = \sqrt{8^{2} + b^{2} }\\14 = \sqrt{64 + b^{2} }\\14^{2} = 64 + b^{2} \\196 = 64 + b^{2} \\64 +b^{2} = 196\\b^{2} = 196 - 64\\b^{2} =132\\b = \sqrt{132} \\b = 11.48\)

Answer:

106

Step-by-step explanation:

this question represents an arithmetic sequence problem where you can use this formula: a(n) = a(1) + d(n-1)  where 'n' is value you're solving for, a(1) is the initial value, and 'd' is the common difference

a(20) = 49 + 3(20-1)

= 49 + 3(19)

= 49 + 57

= 106

Answer:

C

Step-by-step explanation:

Non proportional graphs are non-linear and don’t go (necessarily) through 0,0

Proportional graphs are linear and always (eventually) cross through with 0,0

The shaded area represents the solution of the inequalities. Hence, points A, C, D and K are the solution of the system.

Get y first when graphing a linear inequality with two variables, such as x and y alone on one side. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.

The last step is to choose a point that is not on either line (usually (0, 0) is the simplest) and determine whether or not these coordinates satisfy the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.

Create a comparable graph for each of the system's inequalities. The place where all of the system's solutions overlap is known as the system's solution.

Given that, the inequality is:

y ≤ −2x + 10 & y > 1/(2x − 2)

The given points: A(-5,4), B(4,7), C(-2,7), D(-7,1), E(4,-2), F(1,-6), G(-3,-10), H(-4,-4), I(9,3), J(7,-4) and K(2,3).

The shaded area represents the solution of the inequalities.

Hence, points A, C, D and K are the solution of the system.

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The complete question is:

\(\tt Step-by-step~explanation:\)

We could see that the size of both images does not change, so it is not a dilation. The image is not mirrored either, so it is not a reflection. Finally, the image does not seem to change place that much from the preimage, so it should not be a translation, either. That means our answer is a rotation, because the image rotated about 180º.

\(\large\boxed{\tt Our~final~answer:~Rotation}\)

The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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The total number of shirts in the dresser is 4y + ×. The correct option is A

We need to add up the number of shirts on each shelf.

The first shelf's shirt count is indicated with the number x.

y indicates how many shirts are present on each of the four remaining shelves.

We may add up the shirts on each rack to determine the overall number of shirts:

Total = x + y + y + y + y

Simplifying the expression, we have:

Total = x + 4y

Therefore, The total number of shirts in the dresser is 4y + ×.

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Answer:

Step-by-step explanation:

Step one:

given

We are told that 3 apples seels for $5

let us first find the selling price of 1 apple

an apple = 5/3

=$1.6

Required

Step two:

The selling price of 8 apples

if 1 apple sells for $1.6

then 8 apples will sell for

=8*1.6

=$13.30