If 9y – 5 = 22, find the value of 2y.

Answer:

red balls = 5

blue balls = 5

total balls = 5 blue+5 red

= 10

[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]

[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]

Answer:

Step-by-step explanation:

Total number of red balls = 5

Total number of blue balls = 5

Total number of balls in jar = 5 + 5

                                             = 10

Probability of the first ball being red = total number of the red ball/total number of balls in the jar

                                                             = [tex]\frac{5}{10}[/tex]

                                                             = [tex]\frac{1}{2}[/tex]

Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)

Answer:

x = -4

Step-by-step explanation:

A circle is 360 degrees.

Anyway, first add 85 + 35 + 115 and you will get 235.

Now subtract 235 from 360.

360 - 235 = 125 degrees

Now to find x, do

-32x - 3 = 125

-32x = 128

-32x/-32 = 128/-32

x = -4

Hope it helped! My answer is expert verified.

Answer:

A.

Step-by-step explanation:

If the results are similar (A) should be your answer!

Option A is correct.

Generalization is a process which leads to something more general and whose product consequently refers refers to an actual or potential manifold  in a certain way.

According to the given question

"At the end of the first day, the store found that twice as many shoppers select an apple"

So, the generalization can be made from the above result is " from the given choice of a banana or an apple, twice as many shoppers will select an apple".

Hence, option A is correct.

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Answer:

Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)

Step-by-step explanation:

The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:

If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].

Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.

Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].

That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].

The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:

Make use of a [tex]z[/tex]-table to find these two probabilities:

Calculate the probability that this question is asking for:

[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].

Answer:

The answer is 35%

Step-by-step explanation:

If we add together 35 and 65 we get 100.  This means altogether there are 100 kids in her school.  Out of those 100 kids, 35 like scary movies.  We can write this as the fraction 35/100.  This is equivalent to 0.35 or 35%.

Answer:

35%

Step-by-step explanation:

35+65

= 100

[tex]\frac{35}{100} * 100[/tex]

= 35%

Answer:

A) 6 Inches

Step-by-step explanation:

1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.

Conversion rate is 120 ÷ 10 which equals 12.

Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.

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Answer:

Fraction form: it snowed 2 1/10 inches in total, decimal form: in other words it snowed 2.1 inches.

Step-by-step explanation:

Answer:

0.27

Step-by-step explanation:

Greatest decimal value is 0.27

Decimals are based on the preceding powers of 10

Given decimal values are

0.2,0.27,0.029,0.231

Order the decimal numbers from low to high

0.029<0.2<0.231<0.27

Hence, the greatest decimal value is 0.27

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Answer:

60 years

Step-by-step explanation:

Given that :

Sarah's age = a

Assume Sarah is older than 44 ; then a > 44

64 = 4 times difference between a and 44

Expressing the problem mathematically ;

64 = 4 * (a - 44)

64 = 4a - 176

64 + 176 = 4a

240 = 4a

a = 240 / 4

a = 60

Hence, Sarah is aged 60

Answer:

60/2.5 = 24 cm

Step-by-step explanation:

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Answer:

The answer is 24 inches.

Step-by-step explanation:

Given:

1 inch = 2.5 cm

or, 1 cm = 1/2.5 inch............... eqn (i)

Now,

Wideness of envelope = 60 cm

= 60 (1/2.5) inches [From eqn (i)]

= 60/2.5 inches

= 24 inches Ans

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Step-by-step explanation:

y = x2 + 12x.

x= y2 + 12x           would also be 12 y

y2 = x - 12x               would be -x

y2=-11x  

y=[tex]\sqrt{-11x}[/tex], for x > 0    negative  square root not possible

Describe the three errors?

The three errors made in finding the inverse of y = x² + 12x are,

⇒ First mistake to write 12y in place of 12x.

⇒ Second mistake to write the expression y² = x - 12x.

⇒ Third mistake because it never possible negative square root for x > 0.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = x² + 12x

Here, The process are,

⇒ y = x² + 12x.

⇒ x = y² + 12x

There is first mistake to write 12y in place of 12x.

⇒ y² = x - 12x

There is second mistake.

⇒ y² = -11x

⇒ y = √-11x, for x > 0

There is third mistake because it never possible negative square root for x > 0.

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Answer:

Step-by-step explanation:

You know the total will be $70.

She bought food, let's call that "F"

She spent $26 more on clothes than food. So her clothes purchase is "F+26".

So let's set-up the equation this way:

food + clothing = Total Spent

F + F + 26 = 70

2F + 26 = 70 (subtract 26 from both sides of the = sign)

2F = 44 (Divide both sides so you find out how much was spent on "F" or food.)

F = 22 (But the question doesn't stop there.)

Deborah spent $22 on food. (Remember, she spent $26 more on clothes, so we have to use our "clothes" equation? ) Deborah spent $48 on clothes. She spent a total of $70 on her purchases.

Answer:

K = 56

Step-by-step explanation:

Subtract 9

k/2 = 28

multiply by 2

k = 56

Answer:

pfft no lol

Step-by-step explanation:

yeah no

have a good day!  :)

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Answer:

yes

Step-by-step explanation:

i think,because it goes past the center it all

Answer:

x = 26

Step-by-step explanation:

m<B = m<E = (x + 17)°

180 - (25 + 112) = (x + 17) (sum of ∆)

180 - 137 = x + 17

43 = x + 17

Subtract both sides by 17

43 - 17 = x

x = 26

Answer:

sure easy man the carrot is blue and green and orange there naswer soled

Step-by-step explanation:

We have,

[tex]f(x) = - 2 \sqrt[3]{x + 7} [/tex]

Taking limit,

[tex] \lim _{x \rarr \infty } f(x) \\ = \lim _{x \rarr \infty } - 2 \sqrt[3]{x + 7} [/tex]

If x approaches to positive infinity,

this implies f(x) approaches to negative infinity

Answer:

11:10 am.

Step-by-step explanation:

The first thing I'm going to do is to add all the given time together

Total time = time spent at Willis tower + time spent at Navy Pier + time spent shopping

Total time = 1 HR and 10 minutes + 3 HR and 10 minutes + 1 hour and 15 minutes

Total time = (1 + 3 + 1) hr + (10 + 10 + 15) minutes

Total time = 5 hours + 35 minutes

The question doesn't make mention of how long they spent making the journey so, I'm assuming they spent 35 minutes driving around from Willis to the Pier and finally while shopping

Time = total time + time spent driving

Time = 5 hours 35 minutes + 35 minutes

Time = 6 hours and 10 minutes

Now, this time we've calculated, is what we're going to subtract from the dinner time to get our final answer

Needed time = dinner time - time

Needed time = 5:10 pm - 6:10

Needed time = 17:10 - 6:10

Needed time = 11:10

This means that they ought to start their tour by 11:10 am, so that they can meet their dinner

Answer:

11 sqrt(2)

Step-by-step explanation:

We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)

the length of x is 11

so the lengths of the sides are 11, 11, 11 sqrt(2)

The hypotenuse is 11 sqrt(2)

Answer:

C.  G' (4,-7), R' (2,-3), T'(6,-4)

Step-by-step explanation:

Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.

Answer:

the GCF would be 22 this is because that is 88 and 66 greatest common factor (gcf)

Step-by-step explanation:

have a good day!!

Answer:

A, 2 5/8 cups

Step-by-step explanation:

Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.

Answer:

yes 40

Step-by-step explanation:

she got it correct

Answer:

To know what the answer is

Step-by-step explanation:

clearly I do not know, but I can say that we do need to know the mass bc in the future there will be more and more androids on the rising making human interaction bad.

Answer:

Step-by-step explanation:

Answer:

10 + w = -2.6

Step-by-step explanation:

Answer:

x=-5/2,0

Step-by-step explanation:

It is solved by first factorizing it

10x²+25x=5x(2x+5)=0

Finding the zeros

5x=0x=0/5=0

2x+5=0

x=-5/2

Therefore x is -5/2 or 0

Answer:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.

Step-by-step explanation:

Theorem 60: If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.