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Answer:

297

Step-by-step explanation:

5.5x4.5x12=297

Answer:

volume of the cube=15×15×15

=3375 in³

volume of the cylinder=πr²h

=π×7²×14

=686π

volume of the figure=3375+686π

the answer is first option

Answer:

2

Proof:

x^2 + 6x + 7 + 2 = x^2 + 6x + 9 = x^2 + 6x + 3^2 = (x + 3)^2

The value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2

"It is a polynomial which consists of three terms."

"A square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac"

For given question,

We have been given a square trinomial.

[tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex]

We need to find the number in the blank space, so that the given trinomial would be complete square.

Let 'm' be the required number.

So, the trinomial would be [tex]x^2 + 6x + (7 +m)[/tex]

Comparing above square trinomial with [tex]ax^{2} +bx+c[/tex],

we have a = 1, b = 6, c = 7 + m

We know, a square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac

⇒ b² = 4ac

⇒ 6² = 4 × 1 × (7 + m)

⇒ 36 = 4 × (7 + m)

⇒ 9 = 7 + m

⇒ m = 2

This means, we need to add 2 in the blank space.

So, the square trinomial would be,

[tex]x^2 + 6x + 7 + \underline {2}\\\\= x^2 + 6x + 9\\\\= (x + 3)^2[/tex]

Therefore, the value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex]  to complete the square is 2

Learn more about perfect square trinomial here:

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Answer:

The equation of the parallel line will be y = -2.5x - 8.

Step-by-step explanation:

First things first, let's rearrange the line equation provided into a more standard form:

[tex]5x + 2y = 14[/tex]

[tex]5x - 14 = -2y[/tex]

[tex]\frac{5x - 14}{-2} = y[/tex]

[tex]y = -2.5x + 7[/tex]

Therefore, we can see that this line has a slope (the coefficient preceding x) of -2.5. The parallel line must therefore also have a slope of -2.5.

Now, let us set the y-intercept of the parallel line to be (0, a) (since it must be on the y-axis).

If we factor in all of this, we get the equation:

[tex]\frac{a-(-3)}{0-(-2)} = -2.5[/tex]

Remember, the slope is found by dividing the vertical difference with the horizontal difference.

[tex]a - (-3) = -2.5(0+2)[/tex]

[tex]a + 3 = -5[/tex]

[tex]a = -8[/tex]

Hence, the equation of the parallel line will be y = -2.5x - 8.

Hope this helped!

Answer:

49

81

Step-by-step explanation:

Probability = number of possible outcome.

number of total outcome.

= orange counters = 81 - 32 = 49

49

81

Answer:

the function g because the graphs the graphs of f and g are symmetrical about the line y=x

Step-by-step explanation:

Inverse functions are symmetrical to each other about the line y=x. This means that if you flip a function over y=x, that will be its inverse function. It makes sense because inverse functions turn the input of the original function (x) into the output of the inverse function (y), so y=x and x=y. Take the point (-6,0) on f, it becomes (0,-6) on g.

Answer:

16% of GMAT scores are 647 or higher.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

This means that [tex]\mu = 547, \sigma = 100[/tex]

What percentage of GMAT scores are 647 or higher?

The proportion is 1 subtracted by the p-value of Z when X = 647. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{647 - 547}{100}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84.

1 - 0.84 = 0.16

0.16*100% = 16%

16% of GMAT scores are 647 or higher.

Answer:

The probability of getting an even number on a number cube is 1/2

The probability of getting the heads on a dime is 1/2

Step-by-step explanation:

A number cube has six numbers

And three of those numbers are even numbers.

Therefore;

Probability = 3/6

= 1/2

A dime has two faces, heads and tails

One of them is heads

Therefore;

Probability = 1/2

9514 1404 393

Answer:

 2 + 0.49x

Step-by-step explanation:

The total monthly cost is the sum of the fixed cost ($2) and the message charges ($0.49 × number of messages).

The monthly cost of x messages is 2+0.49x dollars.

Step-by-step explanation:

thats true

Answer:

Answer B

Step-by-step explanation:

Answer:

Let's define A as the area given by the integral:

[tex]\int\limits^1_{-1} {3x^4} \, dx[/tex]

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

[tex]\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}[/tex]

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536

Answer:

[tex]x \approx 2.278863[/tex]

Step-by-step explanation:

Required

The positive root of [tex]3\sin(x) = x[/tex]

Equate to 0

[tex]0 = x -3\sin(x)[/tex]

So, we have our function to be:

[tex]h(x) = x -3\sin(x)[/tex]

Differentiate the above function:

[tex]h'(x) = 1 -3\cos(x)[/tex]

Using Newton's method of approximation, we have:

[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]

Plot the graph of [tex]h(x) = x -3\sin(x)[/tex] to get [tex]x_1[/tex] --- see attachment for graph

From the attached graph, the first value of x is at 2.2; so:

[tex]x_1 = 2.2[/tex]

So, we have:

[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]

[tex]x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}[/tex]

[tex]x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641[/tex]

The process will be repeated until the digit in the 6th decimal place remains unchanged

[tex]x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654[/tex]

[tex]x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627[/tex]

[tex]x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627[/tex]

Hence:

[tex]x \approx 2.278863[/tex]

Answer:

At this pace the country will have only 237.6 million acres of forest left in 44 years.

Step-by-step explanation:

Given that a certain country has 586.08 million acres of forest, and every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes, to determine, if this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left, the following calculation must be performed:

Current amount - (amount lost per year x number of years) = 237.6

586.08 - (7.92 x X) = 237.6

586.08 - 7.92X = 237.6

-7.92X = 237.6 - 586.08

-7.92X = -348.48

X = -348.48 / -7.92

X = 44

Therefore, at this pace the country will have only 237.6 million acres of forest left in 44 years.

Answer:

200000%

Step-by-step explanation:

.

Answer:

59.44

Step-by-step explanation:

Nine employees If an electronic company retired last year

The retirement ages are listed below

56, 65, 62, 53, 68, 58, 65, 52, 56

The mean retirement age can be calculated as follows

= 56+65+62+53+68+58+65+52+56/9

= 535/9

= 59.44

Hence the mean retirement age is 59.44

Answer:

[tex]65.4[/tex]

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

[tex]\cos 61^{\circ}=\frac{y}{135},\\t=135\cos 61^{\circ}=65.4492987333\approx \boxed{65.4}[/tex]

Answer:

(examples) n = 2

n = 3

n = 4

Step-by-step explanation:

to demonstrate, all you do is select a number to represent 'n' and plug it in.

so for example, n = 2:

2(2) + 3(2) = 5(2)

4 + 6 = 10, which is true.

Answer:

Step-by-step explanation:

Answer:

option4 : 0.4

Step-by-step explanation:

[tex]Sin N = \frac{Opposite}{hypotenuse}[/tex]

[tex]sin 7 = \frac{x}{3.4}\\\\3.4 \times sin 7 = x \\\\3.4 \times 0.122 = x \\x = 0.41[/tex]

Answer:

2018 =2(2017)

Step-by-step explanation:

2018 = 2(πr²h)

Answer:

37.7

Step-by-step explanation:

EF and ED define the Tangent of D

Tan(37) = side opposite D / side adjacent to D

Opposite means a line (FE) that is not connected to the angle. It is never the longest line (hypotenuse) in a Right Triangle

Adjacent means the leg that is connected to the angle, but is not the hypotenuse.

Tan(D) = opposite over adjacent

Opposite = x

Adjacent = 50

Tan(37) = 0.7536 rounded to 4 places, but I've kept the exact value in my calculator.

0.7536 = x / 50     Multiply both sides by 50

0.7536*50 = x

x = 37.6777

The nearest 1/10 is 37.7

Answer:

eeeeeee

Step-by-step explanation:

xdddddddudjdjdjdjdjdjsjsjsjsjsjsjsjjsjsjsjsjsjsjsjsjsjsjjs

Answer:   [tex]\frac{3}{2} e-\frac{3}{4} f-\frac{3}{16}[/tex]

Step-by-step explanation: Everything in the parenthesis has to be multiplied by one fourth so we can do something like this: [tex](\frac{1}{4} )(6e)-(\frac{1}{4} )(3f)-(\frac{1}{4} )((\frac{3}{4} )[/tex]

That's distrubiting the one fourth into all of them

Now we simplify

[tex]\frac{3}{2} e-\frac{3}{4} f-\frac{3}{16}[/tex]

Answer:

The area of the circle in terms of π is:

Step-by-step explanation:

To find the area of that circle, you can use the equation:

Where:

Now, we can replace the given measurement in the equation:

That result is the same that to write:

By this reason, the result is 9/64 π in^2, giving the result in terms of π.

Answer:

1/6

Step-by-step explanation:

10x = 1.6666....

100x =16.6666...

90x = 16.6666... - 1.6666...

90x = 15

x = 15/90

x = 1/6

Answer:

16/33

Step-by-step explanation:

Tổng của cả 4 tấm thẻ là một số lẻ khi:

Có 1 thẻ là lẻ, 3 thẻ còn lại là chẵn, có: 6C1.5C3=60 cách

Có 3 thẻ là lẻ, 1 thẻ là chẵn, có: 5C1.6C3=100 cách

Suy ra có 160/11C4=16/33 cách

Answer:

the answer is 84.... .....