Two friends compete with each other and five other, equally good, violinists for first and second chair in an orchestra, in a blind competition What is the probability that the two friends end up as first and second chair together?

The volume of the cone, when the base area is 12 ft² and the height is 6 ft, is approximately 24 ft³.

To find the volume of the cone when the base area is 12 ft² and the height is 6 ft, we need to first determine the variation constant relating the volume, base area, and height.

Let's denote the volume of the cone as V, the base area as A, and the height as h. According to the problem, the volume varies jointly with the base area and the height.

Therefore, we can write the following equation:

V = k * A * h

Here k is the variation constant we want to find.

Given one set of values: when A = 15 ft² and h = 2 1/2 ft, V = 12.5 ft³.

Substitute these values into the equation and solve for k:

12.5 ft³ = k * 15 ft² * (2.5 ft)

Now, we can solve for k:

k = 12.5 ft³ / (15 ft² * 2.5 ft)

k = 0.3333 ft

Now that we have the value of the variation constant (k), we can find the volume when A = 12 ft² and h = 6 ft:

V = k * A * h

V = 0.3333 ft * 12 ft² * 6 ft

V = 23.9996 ft³

Therefore, the volume of the cone is 24 ft³.

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The correct question is as follows:

The volume of a cone varies jointly with the base (area) and the height. The volume is 12.5 ft³ when the base (area) is 15 ft² and the height is 2 1/2 ft. Find the volume of the cone (after finding the variation constant) when the base (area) is 12 ft² and the height is 6 ft.

Answer:

  y = -4x -6

Step-by-step explanation:

The given segment has a rise if 1 for a run of 4, so a slope of ...

  m = rise/run = 1/4

The desired perpendicular has a slope that is the negative reciprocal of this:

  m = -1/(1/4) = -4

A point that has a rise of -4 for a run of 1 from the given midpoint is ...

  (-1, -2) +(1, -4) = (0, -6) . .  . . . . . the y-intercept of the bisector

So, our perpendicular bisector has a slope of m=-4 and a y-intercept of b=-6. Putting these in the slope-intercept form equation, we find the line to be ...

  y = mx +b

  y = -4x -6

The equation of the line in slope intercept form is y = -4x -6

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the y intercept.

Two lines are perpendicular of the product of the slope is -1

The line passes through the point (-5, -3) and (3, -1). Hence:

Slope = (-1 - (-3)) / (3 - (-5)) = 1/4

The slope of the line perpendicular to this line is -4 (-4 *  1/4 = -1).

The line passes through (-1, -2), hence:

y - (-2) = -4(x - (-1))

y + 2 = -4(x + 1)

y = -4x -6

The equation of the line in slope intercept form is y = -4x -6

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

-2a - 3

Step-by-step explanation:

bº equals 1 due to the zero exponent.

Thus, -2a-3 bº simplifies to -2a - 3.

Answer:

−2/a^3  

Step-by-step explanation:

Answer: B. This is sometimes true.

Step-by-step explanation:

A positive correlation between 2 variables means that they generally move in the same direction meaning that as one variable rises, the other rises as well and as the other falls, the other falls as well.

However, the correlation can be strong, weak or anything in-between. This means that just because one variable increases by 12 does not mean the other would as well. It could increase by 1 alone and still have a positive correlation albeit a small one.

Therefore, if the value of one variable is above the mean, it doesn't always follow that the other with a positive correlation will as well as they just might not have that strong a correlation.

Step-by-step explanation:

Hello, there!!!

It's so simple here,

Here,

we have is 1 angle is 120°and other is 3x°.

now,

3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}

so, 3x°=120

or, x=120°/3

=40°

Therefore, the value of x is 40°.

Hope it helps....

Answer:

420 miles

Step-by-step explanation:

60 ×7=420

thank

Answer:210 miles

Step-by-step explanation:because there is 7 hours so you need to multiply up to six hours so 60 x 3 = 180 or 6 hours + 1 hour = 30 miles so 180+30= 210

Answer:

A. The theoretical probability of spinning any one of the five colors is 20%.

C. The theoretical probability of spinning green is equal to the experimental probability of spinning green.

E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

These are the answers on edg 2020, just took the test.

Step-by-step explanation:

Answer:

a, c, e,

Step-by-step explanation:

:)

Answer:

101,000>1,100

Step-by-step explanation:

101,000>1,100

Answer:

101,000>1,100

Step-by-step explanation:

Answer:

174 cm²

Step-by-step explanation:

The figure given is a prism with isosceles trapezoid as base.

Its surface area can be calculating the area of each face that makes up the prism, and summing all together.

There are 6 faces. Their dimensions and areas can be calculated as follows:

2 isosceles trapezium:

It has 2 parallel bases, (a and b), of 4cm and 6cm,

Height (h) = 2.8cm

Area = ½(a+b)*h

Area = ½(4+6)*2.8

Area = ½(10)*2.8 = 5*2.8 = 14 cm²

4 rectangles of different dimensions:

Rectangle 1 (down face): l = 10cm, b = 4cm

Area = 10*4 = 40 cm²

Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm

Area = 2(l*b) = 2(10*3) = 60cm²

Rectangle 4 (top face) = l = 10cm, b = 6cm

Area = 10*6 = 60cm²

Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²

Answer:

y = 3 passes through (8, 3) and is therefore parallel to y = -2

Step-by-step explanation:

Any line parallel to y = -2 is a horizontal one, and it has the same slope (zero) as does y = -2.

We could invent the horizontal line y = 3 (which comes from the point (8, 3) and surmise that it is parallel to the given line y = -2.

Thus, y = 3 passes through (8, 3) and is therefore parallel to y = -2.

In the future, please share any answer choices that are give you.  Thank you.

Answer:

[tex]log_{10}[/tex] 10000 = 4

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Here b = 10, n = 4 and x = 10000, thus

[tex]log_{10}[/tex] 10000 = 4 ← in logarithmic form

that is [tex]10^{4}[/tex] = 10000 ← in exponential form

Answer:

  3.48%

Step-by-step explanation:

Interest rate is the one variable in the amortization formula that cannot be solved for directly. An iterative or graphical approach is needed. There is no formula. Financial calculators, financial apps, and spreadsheets are all able to do this calculation.

__

In the attached, we have used a graphing calculator to find the value of interest rate (in %) that makes the loan payment be $200 for a loan of $11,000. It shows us the rate is 3.48%. (A financial calculator confirms this value.) The x-intercept in the graph is the interest rate that makes the difference between the payment and $200 be zero. In our formula for the payment, we have used t for years. 60 monthly payments is 5 years.

-4x^2-28x-68

hope this helped!

Step-by-step explanation:

Hello, there!!!

The answer is: -4x^2-28x-68.

See explanation in picture.

Hope it helps...

Answer:

The 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Step-by-step explanation:

To solve the above question, we would be making use of the confidence interval formula:

Confidence Interval = Mean ± z score × σ/√n

In the above question,

Mean = 40

σ = Standard deviation = 5

n = number of samples = 81

Confidence Interval = 95%

The z score for a 95% confidence interval = 1.96

Therefore, the confidence interval =

= 40 ± 1.96 (5/√81)

= 40 ± 1.96(5/9)

= 40 ± 1.0888888889

Confidence Interval

a)40 + 1.0888888889

= 41.0888888889

Approximately = 41.089

b ) 40 - 1.0888888889

= 38.911111111

Approximately = 38.911

Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Answer:

11811 feet

Step-by-step explanation:

Hope it helps!

There are about 11,812 feet in 3.6 kilometers.

To convert kilometers to feet, we need to use the conversion factor:

1 kilometer = 3,280.84 feet.

Now, to find how many feet are in 3.6 kilometers,

we can multiply 3.6 by the conversion factor:

So, 3.6 kilometers x 3,280.84 feet/kilometer

= 11,811.504 feet.

Thus, Rounded to a whole number, there are about 11,812 feet in 3.6 kilometers.

Learn more about Unit Conversion here:

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Answer:

a. 3.35

Step-by-step explanation:

Given that :

an experiment with 3 groups  consist of 10 participant in each group.

This implies that:

number of group k = 3

number of participants n = 10

N = nk

N =  10 × 3 = 30

The degree of freedom within can be calculate as:

dfw = N - k

dfw = 30 - 3

dfw = 27

The degree of freedom for the critical value

dfc = n- 1

dfc = 3 - 1

dfc = 2

At the level of significance ∝ = 0.05

The F critical value from the standard normal F table

i.e

[tex]F_{critical { (2, 27)}=[/tex] 3.35

Answer:

Step-by-step explanation:

Hello, just apply the instructions as below.

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

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4.5 cm

Step-by-step explanation:

a^2+b^2=c^2

A represents the leg we already know, which has a length of 4 cm. C represents the hypotenuse with a length of 6 cm:

4^2+b^2=6^2, simplified: 16+b^2=36

subtract 16 from both sides:

b^2=20

now find the square root of both sides and that is the length of the other leg.

sqrt20= 4.4721, which can be rounded to 4.5

Answer:

4.5 cm

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse.

One leg is unknown and the other is 4 cm. The hypotenuse is 6 cm.

[tex]a=a\\b=4\\c=6[/tex]

Substitute the values into the theorem.

[tex]a^2+4^2=6^2[/tex]

Evaluate the exponents first.

4^2= 4*4= 16

[tex]a^2+16=6^2[/tex]

6^2=6*6=36

[tex]a^2+16=36[/tex]

We want to find a, therefore we must get a by itself.

16 is being added on to a^2. The inverse of addition is subtraction. Subtract 16 from both sides of the equation.

[tex]a^2+16-16=36-16\\\\a^2=36-16\\\\a^2=20[/tex]

a is being squared. The inverse of a square is a square root. Take the square root of both sides.

[tex]\sqrt{a^2}=\sqrt{20} \\\\a=\sqrt{20} \\\\a=4.47213595[/tex]

Round to the nearest tenth. The 7 in the hundredth place tells us to round the 4 in the tenth place to a 5.

[tex]a=4.5[/tex]

Add appropriate units. In this case, centimeters.

a= 4.5 cm

The length of the other leg is about 4.5 centimeters.

Answer:

[tex]\huge\boxed{7^{\frac{2}{15}}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\sqrt[3]7}{\sqrt[5]7}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{7^\frac{1}{3}}{7^\frac{1}{5}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=7^{\frac{1}{3}-\frac{1}{5}}\qquad\text{find the common denominator (15)}\\\\=7^{\frac{(1)(5)}{(3)(5)}-\frac{(1)(3)}{(5)(3)}}=7^{\frac{5-3}{15}}=7^{\frac{2}{15}}[/tex]

Answer:

D. 7 to the power of two fifteenths

Step-by-step explanation:

Answer:

2,044

Step-by-step explanation:

S9=G1 (1r^n)/1-r

G9=G1r^8, r=2

S9=(4)(-511)/-1=2,044

Answer: 2,044

Step-by-step explanation:

I just took the quiz!

Answer:

I was surprised that a plane parallel to the vertical axis creates a rectangular cross-section. I guess I was expecting to always see a circle or a circular shape in the cross-section, not purely straight edges as seen in a rectangle.

Step-by-step explanation:

edmentum answer

Answer:

The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising because I have not seen geometric figures like those before.

Step-by-step explanation:

Answer:

1 dz  to make 12 muffins

1 7/24 dz to make 15.5 muffins

Step-by-step explanation:

How many dozen (dz) eggs are needed to make 12 muffins?

See answer options, we are looking for an option with dz indicated along with the number:

The correct option is:

So 1 dozen of eggs required for 12 muffins, that is 12 eggs for 12 muffins or 1 egg for 1 muffin or 1/12 dz per muffin

To get 15.5 muffins:

Or in dozens:

Answer:

[tex] b = 2.7 [/tex]

Step-by-step explanation:

Given:

< C = 53°

< B = 80°

a = 2

Required:

Find b

Solution:

The question given suggests we are given measures for a ∆.

To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.

=> A = 180 - (53 + 80) = 47°

Law of Sines: [tex] \frac{a}{sin(A} = \frac{b}{sin(B} [/tex]

Plug in the values into the formula

[tex] \frac{2}{sin(47} = \frac{b}{sin(80} [/tex]

Cross multiply

[tex] 2*sin(80) = b*sin(47) [/tex]

Divide both sides by sin(47) to make b the subject of formula

[tex] \frac{2*sin(80)}{sin(47} = b [/tex]

[tex] 2.69 = b [/tex]

[tex] b = 2.7 [/tex] (nearest tenth)

Answer:

C) 640 strands of bacteria

Step-by-step explanation:

We are told in the question that the population doubles every 4 hours

Hence, formula to solve this question =

P(t) = Po × 2^t/k

From the question, we have the following information:

Beginning amount (Po) = 20 strands of bacteria

Rate(k) = 4 hours

Time(t) = 20 hours

Ending time (P(t)) = unknown

Ending amount = 20 × 2^20/4

= 20 × 2^5

= 20 × 320

= 640 strands of bacteria.

Therefore, the number of strands left after 20 hours is 640 strands of bacteria.

Answer:

the line of best fit can be approximated to:

y = -1.560 x + 22.105

Step-by-step explanation:

You are most likely expected to use a graphing tool are statistical program to calculate this. So enter the list of x-values separate from the list of y values and run the tool in linear regression mode.

Look at the attached image with the actual results including the line of best fit.

The equation can be written (rounding slope and y-intercept to 3 decimals) as:

y = -1.560 x + 22.105

Answer:

One half, or 1/2.

There are an equal amount of odd numbers as there are even numbers on the spinner.

Answer:

C. 1/2

One-half

Answer:

x = 0.09

Step-by-step explanation:

[tex] {3}^{x + 2} = {2}^{3} [/tex]

Taking Logarith both sides, we get :

Using the properties of Logarithms:

[tex](x + 2) log(3) = 3 log(2) [/tex]

[tex](x + 2) = 1.91[/tex]

(taking log2= 0.3 and log3= 0.47)

x = 0.09

A certain​ animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.

a. 93.52 °F  b. 95.22 °F      c. 94.72 °F

Answer:

a. z = - 2.1053

b. z = 0.87719

c. z = 0

Step-by-step explanation:

Given that :

The population mean μ = 94.72

The standard deviation σ = 0.57

the formula for calculating the standard normal z score, which can be represented as:

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

For  a.

The sample mean [tex]\bar x[/tex] = 93.52

The z score can be computed as follows:

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

[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{-1.2}{0.57}[/tex]

z = - 2.1053

For  b.

The sample mean [tex]\bar x[/tex]  =  95.22    

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

[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{0.5}{0.57}[/tex]

z = 0.87719

For  c.

The sample mean [tex]\bar x[/tex]  = 94.72

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

[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{0}{0.57}[/tex]

z = 0

Answer:

(0,2)

Step-by-step explanation:

the point where Oy intercepts the graph has x=0 and y= f(0)

so this is (0,2)

Answer:

5

Step-by-step explanation:

Answer:

B

Step-by-step explanation: