A disc has a diameter of centimeters while a mini disc has a diameter of centimeters. Write the ratio of the mini disc diameter to the disc diameter.

Answer:

a = 37

Step-by-step explanation:

the sum of any triangle angles is 180

then 62 + 81 + a = 180

a = 37

.. ..

Answer:

a = 37 degrees

Step-by-step explanation:

81+62 = 143

We know that all angles of a triangle = 180 degrees

180-143= 37 degrees

a = 37 degrees

Answer: E(X) = 4

              V(X) = [tex]\frac{16}{3}[/tex]

Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:

f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]  

The mean or expectation of an unifrom distribution is:

E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]

For the density function in interval [0,8], expectation value is:

E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]

E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]

E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]

E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]

E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]

E(X) = 4

Variance of a probability distribution can be written as:

V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]

For uniform distribution in interval [0,8]:

V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]

V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]

V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{64}{3}[/tex] - 16

V(X) = [tex]\frac{16}{3}[/tex]

The mean and variance are 4 and 16/3, respectively

Answer:

C. 15 centimeters

Step-by-step explanation:

The Triangle Midsegment Theorem

segment LM = 1/2 of AC

LM = 1/2 * 30

LM = 15 cm

Answer:

current population growth rate would be -3.1%

Step-by-step explanation:

We have to:

Growth rate = r * (1 - population / carrying capacity)

for 1960,

we have carrying capacity = 21 billion

population = 3 billion

r = Growth rate 1960 / (1 - population / carrying capacity)

replacing:

r = 0.021 / (1 - 3/21)

r = 0.0245

that is to say r = 2.45%

Now the current population would be:

= 0.0245 * (1 - carrying population / carrying capacity)

we replace:

= 0.0245 * (1 - 6.8 / 3)

= -0.031

current population growth rate would be -3.1%

The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.

Given :

The growth rate is given by the formula:

[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]

Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).

[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]

[tex]0.021=r\times \dfrac{18}{21}[/tex]

0.0245 = r

So, r = 2.45%.

Now, the growth rate of the current population is:

[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]

[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]

0.031 = Growth Rate

So, the growth rate is -3.1%.

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I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.

The only function there is the last one. (Right bottom)

Answer:

Step-by-step explanation:

Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...

  10x +5(10 -x) = 80

  5x +50 = 80

  5x = 30

  x = 6 . . . . . . . . pounds of chocolate

  10 -x = 4 . . . . . pounds of jelly candy

6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.

Answer:

Answer B) (2 times )

Step-by-step explanation:

Let's start with the person that shook hands more (Dora), so we already know how four of this connections took place See attached image.

step 1:

D is connected to A, B, C, and E

Step 2:

Now proceed with the connections for the second greatest (C who shook hands with 3 people). Notice that C is already connected with D, and can connect with B and with E, but NOT with A (since this person shook hands only once - with D. So C is connected to B, D, and E completing the three handshakes.

step 3: Now just corroborate that B is already connected to two people (C and D).  So just count the number of connections that E is left with: 2 handshakes.

Answer:

( E ) 0

Step-by-step explanation:

Solution:-

- There can be two ways in solving this question. Either we lay-out a map of every person ( Alan, Bella, Claire, Dora, and Erik ) shaking hands with each other.

- We will use an intuitive way of tackling this problem.

- We have a total of 5 people who greeted each other at the party.

- Each of the 5 people shook hands exactly " once "! We can give this a technical term of " shaking hands - without replacement ".

- We will define our event as shaking hands. It takes 2 people to shake hands.

- We will try to determine the total number of unique "combinations" that would result in each person shaking hands exactly one time.

- We have a total of 5 people and we will make unique combinations of 2 people shaking hands. This can be written as:

                            5C2 = 10 possible ways.

- So there are a total of 10 possible ways for 5 people to greet each other exactly once at the party.

- We are already given the data for how many handshakes were made by each person as follows:

                      Name                 Number of handshakes

                       Alan                                   1

                       Bella                                  2

                       Claire                                 3

                       Dora                                   4

               =======================================

                      Total                                  10

               =======================================

- So from the data given. 10 unique hand-shakes were already done by the time it was " Eriks " turn to go and greet someone. This also means that Erik has already met all 4 people in that party. So he doesn't have to approach anyone to shake hands and know someone. He is already been introduced to rest of 4 people in the group.

Answer: Erik does not need to shake hands with anyone! He is known and greeted rest of the 4 people on the group.

Answer:

[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]

Step-by-step explanation:

The expression, [tex] -6(4\frac{2}{3}) [/tex] , can be understood or interpreted as negative six multiplied by four and two-third.

Thus, it could be evaluated using distributive property of multiplication, as shown below:

[tex] (-6)(4) + (-6)(\frac{2}{3}) [/tex]

[tex](-6)(4) + (-6)(\frac{2}{3}) \\(-24) + (-2)(2)\\-24 + (-4)\\-24 - 4\\= -28[/tex]

Answer:

0.40

Step-by-step explanation:

The computation of the probability for the second student be sophomore and the first is a freshman is shown below:

Let us assume

Sophomore = S

Freshman = F

Based on this assumption, the probability is as follows

So,

[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]

= 0.40

Hence, the probability for the second student be sophomore and the first student be freshman is 0.40

Answer:

76°

Interior angle of a rhombus =360

104° +104° +76° +X =360

X= 360 - 284

X= 76°

We know that the value of ∠x in the given rhombus is 76°.

So, get the ∠x as follows:

Then,

Therefore, we know that the value of ∠x in the given rhombus is 76°.

Know more about rhombus here:

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Answer:

√96

Step-by-step explanation:

PQ is tangent to both lines, so PQ is perpendicular to PO and QO'.

The radius of the smaller circle is 3, and the radius of the larger circle is 8.

If we draw a line from O to O', and another line from point O to line QO' that is parallel to PQ, we get a right triangle where OO' is the hypotenuse, the short leg is 8−3=5, and the long leg is the same length as PQ.

Using Pythagorean theorem:

x² + 5² = 11²

x = √96

Answer:

-1

Step-by-step explanation:

If a line is parallel on a graph, then that means that they will descend/climb at the same rate. Therefore, the slope of this line is also -1.

Hope this helped!

Answer:If they are parallel,

Then their slope will be same...

Step-by-step explanation:

Answer:

[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]

Step-by-step explanation:

According to the Parallelogram definition, every Parallelogram have a pair of congruent sides.  In this case, Namely [tex]\overline{RS} \cong \overline{TQ}[/tex]  and [tex]\overline{QR} \cong \overline{TS}[/tex]

(not listed as an option)

And the opposite angles are congruent too.

So

[tex]\angle T \cong \angle R\\\angle S \cong \angle Q[/tex]

∠R≅∠T relationship is true for the RSTQ parallelogram

A quadrilateral is a polygon having four sides, four angles, and four vertices.

A parallelogram is a quadrilateral with four sides.

a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

In parallelogram the opposite sides have equal length.

The opposite sides are congruent and the opposite angles are also congruent.

SR=TQ

ST=RQ

These sides are equal and

∠R≅∠T

∠S≅∠Q

In the given options only ∠R≅∠T is given, so we can consider this.

Hence ∠R≅∠T relationship is true for the RSTQ parallelogram

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Answer:

20b^3+12b^2

Step-by-step explanation:

v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

y = 2666.67

Step-by-step explanation:

Well to solve this we can make a system of equations.

x = cost of car alone

y = cost of accesories,

[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]

So now we plug in 8y for x in x + y = 24000.

(8y) + y = 24000

9y = 24000

Divide both sides by 9

y = 2666.666666

or 2666.67 rounded to the nearest hundredth.

Now that we have y we can plug that in for y in x=8y.

x = 8(2.666.67)

x = 21,333.33 rounded to the nearest hundredth.

Thus,

accessories "y" cost around 2666.67.

Hope this helps :)

Answer:i explained it

Step-by-step explanation:

The total cost of the fence will be 30(2L + 2W) + 2*25 W <= 9000

60L + 110W <= 9000

60 L <= 9000 - 110W

L <= 150 - 11/6 W

For a given width, the maximum area will correspond to the maximum length, so we can just go ahead and say L = 150 - 11/6 W

A = LW = (150 - 11/6 W) W

A = 150 W - 11/6 W2

A' = 150 - 11/3 W = 0

150 = 11/3 W

W = 450/11

Answer:  4

Step-by-step explanation:

Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.

The attachment shows the graph rotated 1-turn to the left (90°).

Notice it is in the exact same position as #4.

Answer:

the answer is A) h=3V/(Pi*r^2)

Step-by-step explanation:

This question is asking to solve for h, the equation is allready solved for V.

to solve for h means to get h by itself on one side of the equation.

1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation

2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.

3) (3*V)/(pi*r^2)=h. Simplify.

4) 3V/(Pi*r^2)=h.

Answer:

120°

Step-by-step explanation:

Given that an angle = 240 less than 6 × its own supplement,

Let x = be the angle

Its supplement = (180 - x)

If the angle (x) is 240 less than 6 times its own supplement, (180 - x), we will have the following expression:

[tex] x = 6*(180 - x) - 240 [/tex]

Simplify the expression to solve for x

[tex] x = 1080 - 6x - 240 [/tex]

[tex] x = 1080 - 240 - 6x [/tex]

[tex] x = 840 - 6x [/tex]

Add 6x to both sides

[tex] x + 6x = 840 - 6x + 6x [/tex]

[tex] 7x = 840 [/tex]

Divide both sides by 7 to solve for x

[tex] \frac{7x}{7} = \frac{840}{7} [/tex]

[tex] x = 120 [/tex]

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.

The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:

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

a) For x < 33.2 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]

From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%

b) For x > 46.6 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]

From the normal distribution table,  the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%

c) For x = 35.5 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]

For x = 42.8 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]

From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%

d) A probability of 75% = 0.75 corresponds to a z score of 0.68

[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]

75% of all students finish the activity in less than 37.3 seconds

Answer:

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Step-by-step explanation:

The amount of Carbon-14 after t years is given by the following equation:

[tex]A(t) = A(0)e^{-rt}[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.

This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]

How many years will it take for carbon–14 to decay to 10 percent of its original amount?

This is t for which:

[tex]A(t) = 0.1A(0)[/tex]

So

[tex]A(t) = A(0)e^{-rt}[/tex]

[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]

[tex]e^{-0.000124t} = 0.1[/tex]

[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]

[tex]-0.000124t = \ln{0.1}[/tex]

[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]

[tex]t = 18569.2[/tex]

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Answer:

Mean = 16.5

Variance = 35.55

Step-by-step explanation:

           x      P(x)        x. P(x)     x²            x². P(x)

          6      0.10          0.6      36            3.6

         12     0.35          4.2       144           50.4

        18     0.25           4.5       324            81

        24     0.30          7.2        576         172.8

                  ∑x P (x)  16.5         ∑x² P (x) 307.8

The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.

Mean is given by  E(X)=  ∑x P (x) =  16.5

Similarly the variance is also calculated using the expected value of X and X².

Variance is given= E(X)²-  [E(X)]²= 307.8- (16.5)²=  307.8-272.25 = 35.55

Answer:

It should be 10 for the first box, 1000 for the second box and 100 for the third box.

Step-by-step explanation:

Each extra decimal place value added, u have to multiply it by the next value place such as tenths/hundreths/thousandths

Question

Combine like terms to create an equivalent expression.

-3.6-1.9t+1.2+5.1t

Answer:

3.2t - 2.4

Step-by-step explanation:

Given;

-3.6 - 1.9t + 1.2 + 5.1t

Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e

=> − 1.9t + 5.1t - 3.6 + 1.2

=> 3.2t - 2.4

Therefore, the equivalent expression is;

3.2t - 2.4

Answer:

3.2t - 2.4

Step-by-step explanation:

right on khan

Answer:

A = 0.507 or 29 degrees

Step-by-step explanation:

5 = tanA * 9

inv tan = 5/9

angle A = 0.507

angle A = 29 degrees

Answer:

A=1,728

Step-by-step explanation:

To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.

The width is 12, the hight is 12, and the depth is 12 so you can write

A=12*12*12

Multiply 12 by 12

A=144*12

Multiply 12 by 144 to get your final total area

A=1,728

Hope this helps, feel free to ask follow-up questions if confused.

Have a good day! :)

Answer:

[tex]75[/tex]

Step-by-step explanation:

[tex]\frac{d}{dx}\left(x^3\right)[/tex]

[tex]=3x^{3-1}[/tex]

[tex]=3x^2[/tex]

[tex]3\left(5\right)^2[/tex]

[tex]=3\cdot \:25[/tex]

[tex]=75[/tex]

Question:

Diners frequently add a​ 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is ​$20.70? How much was the​ tip?

Answer:

Price of meal = $18

Tip price = $2.70

Step-by-step explanation:

Let the price of the meal be y;

Let the tip be t

From the question;

15% of y is the tip charge (t). i.e

t = 15%y

=> t = 0.15y          --------(i)

The total amount charged is $20.70  (This means that the sum of the price of the meal and the tip is $20.70)

=> y + t = 20.70            [substitute the value of t=0.15y from equation (i)]

=> y + 0.15y = 20.70

=> 1.15y = 20.70

=> y = [tex]\frac{20.70}{1.15}[/tex]

=> y = $18

Therefore the price of the meal, y, is $18.

From equation (i),

t = 0.15y           [substitute the value of y = $18]

t = 0.15(18)

t = $2.70

Therefore the tip was $2.70

Answer:

Step-by-step explanation:

The formula for calculating the standard error of the mean is expressed as shown below;

Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]

[tex]\sigma[/tex] is the standard deviation and n is the sample size.

Given [tex]\sigma[/tex] = 14 and n = 100

Substituting this values into the formula fr calculating the standard error of the mean;

[tex]SE = \frac{14}{\sqrt{100} } \\\\SE = \frac{14}{10} \\\\SE = 1.4[/tex]

Hence, standard error of the mean is 1.4