What is the exact volume of the cylinder? Enter your answer, in terms of π, in the box. m³ $\text{Basic}$ $x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$ $x\frac{ }{ }$ $x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$ A cylinder that is 2.5 m tall with a radius of 1.5 m

Answer:

x = 43

Step-by-step explanation:

125^(3x+7)=25^(5x−11)

Rewriting the bases as powers of 5

125 = 5^3  and 25 = 5^2

5^3 ^ (3x+7) = 5^2^(5x-11)

We know a^b^c = a^ (b*c)

5^(3 * (3x+7)) = 5^(2*(5x-11))

Distribute

5^(9x+21) = 5^(10x-22)

The bases are the same so the exponents are the same

9x+21 = 10x-22

Subtract 9x from each side

9x+21 -9x = 10x-9x-22

21 = x-22

Add 22 to each side

21+22 = x-22+22

43 = x

Answer:

The painting is [tex]t = 10911.1 \ years \ old[/tex]

Step-by-step explanation:

From the question we are told that

    The amount of carbon present after t year is

           [tex]y(t) = y_o * e ^{-0.00012t}[/tex]    {Note ; This is the function }

Here  [tex]y(t)[/tex] is the amount of carbon-14 after time t

        [tex]y_o[/tex] the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

  Then it mean that

            [tex]y(t) = 0.27 y_o[/tex]

So the equation is represented as

       [tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]

=>    [tex]0.27 = * e ^{-0.00012t}[/tex]

=>    [tex]ln(0.27) = -0.00012t[/tex]

=>  [tex]- 1.30933 = -0.00012t[/tex]

=>  [tex]t = \frac{-1.30933}{-0.00012}[/tex]

=>   [tex]t = 10911.1 \ years[/tex]

Answer:

The volume of sphere is 267.95 units³.

Step-by-step explanation:

Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :

[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]

[tex]let \: r = 4[/tex]

[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times 64[/tex]

[tex]v = \frac{256}{3} \times 3.14[/tex]

[tex]v = 267.95 \: {units}^{ 3} [/tex]

Answer:

You need to use the AAS (angle angle side) congruency theorem

Step-by-step explanation:

youre welcome!!!

Answer:

The Angle-Angle-Side Postulate (AAS)

Step-by-step explanation:

It is given that angle 1 and 2 are equivalent so that is angle #1

It is given that angle 3 and 4 are also equivalent so that is angle #2

And finally, it is given that side TS and side TR are equivalent giving you that last side you need to prove the type of Postulate it is

If this helped, please consider giving me brainliest, it will help me a lot

Have a good day! :)

Answer:

when we add all the angles.

=58+94+15=167

so it's a 180..

180_167

=13

round to nearest tenth.

=10..

Step-by-step explanation:

(ax + b)² = a²x² + 2abx + b²

In this case, a = 1, so:

14 = 2b

b = 7

(x + 7)² = x² + 14x + 49

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------             The frequency is ~7.5*1014 Hz

Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.

Step-by-step explanation:

Speed = wavelength × frequency

3×10⁸ m/s = (400×10⁻⁹ m) f

f = 7.5×10¹⁴

Answer:

The  confidence interval is  [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]

Step-by-step explanation:

From the question we are told that

    The first sample size is  [tex]n_1 = 146[/tex]

    The second sample size is [tex]n_2 = 180[/tex]

    The first sample mean is [tex]\= x_1 = 51.6[/tex]

    The second  sample  mean is  [tex]\= x_2 = 62.7[/tex]

     The first standard deviation is  [tex]\sigma _1 = 9.42[/tex]

     The second standard deviation is  [tex]\sigma _2 = 14.5[/tex]

Given that the confidence level is  98% then the significance level is mathematically evaluated as

      [tex]\alpha = (100 -98 )\%[/tex]

       [tex]\alpha = 2 \%[/tex]

        [tex]\alpha = 0.02[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is  [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]

The reason we are obtaining critical value of  

 [tex]\frac{\alpha }{2}[/tex]

instead of  

[tex]\alpha[/tex]

is because  

 [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (

[tex]1-\alpha[/tex]

) did not cover which include both the left and right tail while  

 [tex]\frac{\alpha }{2}[/tex]

is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

      [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]

substituting values

      [tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]

substituting values

     [tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]

     [tex]E = 0.2405[/tex]

The 98% confidence interval is mathematically represented as

      [tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]

substituting values

      [tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]

     [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]

Answer: 23, 25, 27

Step-by-step explanation:

Let the 3 consecutive odd numbers be x, x+2 and x+4.

So

2x+(x+2)+3(x+4)=152

2x + x + 2 + 3x + 12 = 152

6x+14=152

6x = 152 - 14

x=138/6

x=23

So, the numbers are 23, 25 and 27.

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

A) 3x²c² + 5xc² - 2c²

Factor c² from all terms in the expression.

c²(3x² + 5x - 2)

Factor 3x² + 5x - 2

c²(3x-1)(x+2)

B) x² + 6x + 9

x² + 3x + 3x + 9

Factor common terms.

x(x+3)+3(x+3)

Take x+3 common.

(x+3)(x+3)

C) x² - 9

x² -3²

Apply formula : a² - b² = (a+b)(a-b)

(x+3)(x-3)

Answer:

A) [tex]c^2(3x-1)(x+2)[/tex]

B) [tex](x+3)(x+3)[/tex]

C) [tex](x+3)(x-3)[/tex]

Step-by-step explanation:

Part A:

[tex]3x^2c^2+5xc^2-2c^2[/tex]

Taking [tex]c^2[/tex] common

[tex]c^2(3x^2+5x-2)[/tex]

Using mid term break formula

[tex]c^2 (3x^2+6x-x-2)[/tex]

[tex]c^2[3x(x+2)-1(x+2)][/tex]

[tex]c^2(3x-1)(x+2)[/tex]

Part B:

[tex]x^2 + 6x + 9.[/tex]

[tex](x)^2+2(x)(3)+(3)^2[/tex]

[tex](x+3)^2[/tex]

[tex](x+3)(x+3)[/tex]

Part C:

[tex]x^2-9[/tex]

[tex](x)^2-(3)^2[/tex]

[tex](x+3)(x-3)[/tex]

Answer:

[tex] \sqrt{392 {x}^{7} } [/tex]

Simplify

that's

[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]

Hope this helps you

​Answer:

14.29cm

Step-by-step explanation:

Height of the building=10cm

Angle of depression=60°

We are therefore asked to find the distance from the stone to the

the foot of the building;Therefore we use Tan ratio which is opp/adj;

Let the distance from the stone to the foot of the building be x;

10/x=Tan60°

10/x=1.7/1

We then cross multiply to get 1.7x=10

x=10/1.7

=10*10/1.7*10

=100/17

=14.29cm.

Answer:

The probability is  [tex]P(X > x) = 0.0013499[/tex]

Step-by-step explanation:

From the question we are told that

     The mean is  [tex]\mu = 25[/tex]

      The standard deviation is [tex]\sigma = 5 \ minutes[/tex]

      The random number  [tex]x = 40[/tex]

Given that the time taken is  normally distributed  the probability is mathematically represented as

     [tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]

Generally the z-score for the normally distributed data set is mathematically represented as

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

So  

     [tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]

    [tex]P(X > x) = 0.0013499[/tex]

This value is obtained from the z-table

Answer:

I think D

Step-by-step explanation:

Verticle or horizontal line test, it would be a function either way

Answer:

hope this is right y=74

Step-by-step explanation:

have not done this since two years ago so...

but anyway 148-180 = 32

32 is that angle

if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.

The correct answer is 90.

Answer:

answer there

Step-by-step explanation:

hope it. was. helpful

Answer:

The probability that only one candidate is hired is 0.10.

Step-by-step explanation:

The probability of event E occurring is the ration of the favorable number of outcomes to the total number of outcomes.

[tex]P(E)=\frac{n(E)}{N}[/tex]

It is provided that N = 10  candidates are presented in a random order.

Compute the probability that only one candidate is hired as follows:

[tex]P(\text{Only 1 Hire})=\frac{1}{10}=0.10[/tex]

Thus, the probability that only one candidate is hired is 0.10.

Answer:

18

Step-by-step explanation:

Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.

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           Hi my lil bunny!

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The statement for [tex]6x - 3 = 9[/tex] is :

[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

[tex]\huge\boxed{(6;\ -31)}[/tex]

Step-by-step explanation:

Let: [tex]f(x)=ax^2+bx+c[/tex].

The coordinates of the vertex:

[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]

We have

[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]

Substitute:

[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]

The vertex form of an equation of a quadratic function:

[tex]f(x)=a(x-h)^2+k[/tex]

We have:

[tex]f(x)=x^2-12x+5\to a=1[/tex]

Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]

[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]

for labor. Joni paid $85 less per hour for labor. explanation:

The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.

It refers to the total amount of the expenditure done on a product in manufacturing or procuring.

It refers to the expenditure done on procuring labor for the work.

In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,

labor cost Shannon Paid=339.50-112

=$227.50

labor cost per hour=227.50/3.5

=$6.5 per hour

Joni paid total $455 in which the cost of spare parts is $310 and rest is labor

labor cost paid by Joni=455-310

=$145

labor cost per hour=145/2.5

=$58 per hour

So by doing comparing we found that Shannon had paid $6 per hour extra for labor.

Learn more about cost at https://brainly.com/question/1153322

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Answer:

C. It is an angle that has its vertex at the center of a circle.

Step-by-step explanation:

That's the definition.

A. is wrong. An angle with a measure greater than 180° is an obtuse angle,

B. is wrong. An angle that has its vertex on the circle is an inscribed angle.

D. is wrong. Part of the circumference of a circle is an arc.

Answer:

1.2 miles

Step-by-step explanation:

5.3 - 4.1 = 1.2 miles

Answer:

Step-by-step explanation:

5.3 - 4.1 = 1.2

1.2 miles difference.

This is because from Washington to Lanberry it is 4.1 miles. From Washington to Newberry it is 5.3., SO, if you subtract it you will get 1.2 miles difference.

Hope this helped,

kavitha

Answer:

For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81

Step-by-step explanation:

ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...

3^-6

using law of indices x^-a = 1/x^a

So 3^-6 = 1/3^6

Now find the power of 3^6

which is the same as 3×3×3×3×3×3 = 729

therefore 1/3^6 = 729

For 3^-4

using the above method

3^-4 is same as 1/3^4

which is equal to

finding the nominator

3×3×3×3 = 81

so the answer is 81

Answer:

A

Step-by-step explanation:

First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.

So, let's apply this pattern to find the next number in this series.

2, 2 1/2, 1 1/2, 2, 1

The next number in this series is 1.

Hope this helps!! :)

Answer:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

Step-by-step explanation:

Part a

We want to find:

[tex] P(X<6.4)[/tex]

And we just need to find the area below the curve until x=6.4, since we have a triangle we can do this:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

Part b

For this case we want to find this probability:

[tex] P(X>4.8)[/tex]

And we can use the complement rule and we got:

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]