A football team consists of 18 freshmen and 18 sophomores, 15 juniors, and 12 seniors. Four players are selected at random to serve as captains. Find the probability that at least 1 of the students is a senior.

Answer:

-6ab^3sqrtac^2 option b

Step-by-step explanation:

i just did it

Answer:

Step-by-step explanation:

Answer:

2.08 x 10^11

Step-by-step explanation:

To put a number into scientific notation you move the decimal to the spot right after the first digit. To figure out what the power is you count how many digits you moved it past in order to get to the spot you want it (right after the first digit; in this case the 2)

So in this case you would move the decimal from the end of the number backwards past 9 zeros, the 8, and another zero, which is a total of 11 digits.

From there you take the number with the new decimal place and multiply by 10 to the power of the number you counted earlier, which for this example is 11

So the final answer is 2.08 x 10^11

Answer:

  5.972 cm

Step-by-step explanation:

Using implicit differentiation, we have ...

  0 = (2πr +π(√(r^2+h^2) +r^2/√(r^2+h^2))·dr/dh +πrh/√(r^2+h^2)

For the given values of r and h, this is ...

  0 = (12π +π(10 +36/10))dr/dh +48π/10

  dr/dh = -4.8/(12+13.6) = -0.1875

Then the tangent line is ...

  r = -0.1875(h -8) +6

__

For a height of 8 +15/100 = 8.15, the estimated value of r is ...

  r = -0.1875(8.15 -8) +6 = -0.1875(0.15) +6 = 5.971875

The estimated value of r is 5.972 cm.

Answer:

Step-by-step explanation:If you choose any 3 of the 7 vertices, you can connect them with lines to create a unique triangle.

So, the question becomes "In how many different ways can we select 3 vertices from 7 vertices?"

Since the order in which we select the 3 vertices does not matter, we can use COMBINATIONS.

We can select 3 vertices from 7 vertices in 7C3 ways.

Two shaped are merged so

One is square and the other is trapezoid so,

AREA OF SQUARE=4*4

=16

AREA OF TRAPEZOID=(2+4)x4/2

So,rhe answer will be

12+16=28

HOPE IT IS HELPFUL

Answer: 28 units^2

Step-by-step explanation:

You basically have a square and a trapezoid merged together

4*4=16 for the square

(2+4)*4/2=12 for the trapezoid

so

12+16=28 is your answer

Answer:

a) margin of error ME = 5.77

b) Margin of error becomes smaller

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

a)

Given that;

Mean = x

Standard deviation r = 25

Number of samples n = 72

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

ME = 1.96(25/√72)

ME = 1.96(2.946278254943)

ME = 5.774705379690

ME = 5.77

b)

For n = 89

ME = 1.96(25/√89)

ME = 1.96(2.649994700015)

ME = 5.193989612031

ME = 5.19

5.19 is smaller than 5.77 in a) above. So,

Margin of error becomes smaller

Answer:

22 is the answer but which country are you from

Answer:

22

Step-by-step explanation:

Answer:

  (x, y, z) = (1, -3, 1)

Step-by-step explanation:

Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:

  (x, y, z) = (1, -3, 1)

__

Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.

Using the first equation to write an expression for z, we have ...

  z = 4x +3y +6

Substituting that into the second and third equations gives ...

  6x -y +3(4x +3y +6) = 12   ⇒   18x +8y = -6

  8x +2y +4(4x +3y +6) = 6   ⇒  24x +14y = -18

Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:

  3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)

  10y = -30

  y = -3

Substituting into the first equation (of the equations in x and y), we have ...

  18x +8(-3) = -6

  18x = 18

  x = 1

Finally, substituting into the equation for z gives ...

  z = 4(1) +3(-3) +6 = 1

The solution is (x, y, z) = (1, -3, 1).

___

The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.

Answer:

XY = 5268

Step-by-step explanation:

XY = XZ (originating from the same point)

85b+83=91b-283

85b-91b=-283-83

-6b=-366

Dividing both sides by -6

b = 61

Now

XY = 85b+83

= 85(61)+83

= 5268

Answer:

by finding something to factor it by

Answer:

1) first eliminate constant (number without variable) you eliminate constant by doing the inverse operation (if constant is being added, then subtract) (if constant is being subtracted, then add it)

ex: if  x+9=32

subtract 9 from both sides to get rid of it

x=23

2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it

you could multiply by 3 on both sides:

x+9=69

x=60

Answer:

[/tex]y2=e^(-x)[/tex]

Step-by-step explanation:

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION

Answer:

24?

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

[tex] a = 1 - \sqrt{2} [/tex]

[tex] (a - \dfrac{1}{a})^3 = [/tex]

[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]

[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]

[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]

[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]

[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]

[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]

[tex] = 2^3 [/tex]

[tex] = 8 [/tex]

Answer:

It's B I think.

Step-by-step explanation: If they the lines intersected then it'd mean they crashed.

The graph below shows a recent 10-meter race between two remote-control automobiles. The racial assertions in A, B, and C are true.

A graph that shows the relationship between two or more variables, each of which is measured along one of two axes that are at right angles to one another.

At 6 meters into the race, the blue car overtook the red car because, at that moment, the blue car had a bigger distance than the red car.

Due to the greater slope of the blue vehicle's path compared to the red car's line, the blue car is faster.

Because the blue car's x-intercept is at (3, 0), where x stands for time and y for distance from the starting line, it began 3 seconds later than the other cars.

Hence Statements B, C, and D about race are true.

Q.The graph below represents a recent 10-meter race between two remote control cars.

A graph titled Remote Control Car Race has seconds after the race starts on the x-axis and distance from the start line (meters) on the y-axis. A line labeled red car goes through (3, 2) and (6, 4). A line labeled blue car goes through (3, 0) and (5, 2).

Which statements about race are true? Check all that apply.

The red car won the race because it started above the blue car.

The cars crashed 9 seconds into the race because that is the point of intersection, and neither car continued on after that point in time.

The blue car passed the red car at 6 m into the race because that is the point of intersection, and the blue car has a greater distance than the red car after that time.

The blue car is faster because the slope of its line is steeper than the slope of the line representing the red car.

The blue car started 3 seconds late because it has an x-intercept of (3, 0) and x represents the time and y represents the distance from the starting line.

learn more about graphs here :

https://brainly.com/question/10712002

#SPJ6

Answer: [tex]x = \frac{35}{2}[/tex] or [tex]x = 17.5[/tex]



Step-by-step explanation:

[tex]\frac{4}{7} = \frac{10}{x}[/tex]

[tex]\frac{4x}{4} = \frac{70}{4}[/tex]

[tex]x = \frac{35}{2}[/tex]

or [tex]x = 17.5[/tex]

Answer:

1 hour

Step-by-step explanation:

From Distance = speed × time

time = Distance/ speed

=66/66 = 1 hour

Answer: Infintely many

Step-by-step explanation:

5(x + 10) - 25 = 5x + 25

5x +50 - 25 = 5x + 25

5x +25 = 5x + 25

Same equation

this one is kinda Hard ill do sum research and help

Answer:

hope

this

is

correct

Answer:

  D.  129°

Step-by-step explanation:

Angles XZY and XZV form a linear pair, so are supplementary.

 angle XZV = 180° -51° = 129°

Answer:

The best estimate would be around 10-16

Step-by-step explanation:

The think is that they can be in many orders and since there is four of them it would be more orders.

Hope this helps

Answer:

1/8

Step-by-step explanation:

Answer:

When you simplify it, you get the answer of 1.

Step-by-step explanation:

Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.

So, simplify 2/3 / (-4) first, obtaining -1/6.

Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.

Answer:

my butt

Step-by-step explanation:

my poop

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Answer:

(A)129 Pounds

Step-by-step explanation:

Let x be the number of 23% zink alloy

Therefore:

Since the total result is 516 pounds

The number of pounds of 42% zink alloy =516-x pounds

We then have the resulting equation:

0.23x+0.42(516-x)=0.3725*516

0.23x+216.72-0.42x=192.21

Colect like terms

0.23x-0.42x=192.21-216.72

-0.19x=-24.51

Divide both sides by 129

x=129 pounds

Therefore, the number of pounds of 23% zink alloy that must be mixed is 129 pounds.

Answer:

y = x/6 - 17/6

Step-by-step explanation:

     x - 6y = 17

<=>6y = x - 17  

<=> y  =x/6 - 17/6

Hope this helps!

Answer:

7

Step-by-step explanation:

∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹)

This is the sum of the first 3 terms of the sequence.

The first 3 terms are:

4 × (½)¹⁻¹ = 4

4 × (½)²⁻¹ = 2

4 × (½)³⁻¹ = 1

So the sum is:

∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹) = 4 + 2 + 1 = 7

Answer:

Step-by-step explanation:

(a)

The number of receivers is 5.

The number of CD players is 4.

The number of speakers is 3.

The number of cassettes is 4.

Select one receiver out of 5 receivers in [tex]5C_1[/tex] ways.

Select one CD player out of 4 CD players in [tex]4C_1[/tex] ways.

Select one speaker out of 3 speakers in [tex]3C_1[/tex] ways.

Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.

Find the number of ways can one component of each type be selected.

By the multiplication rule, the number of possible ways can one component of each type be selected is,

The number of ways can one component of each type be selected is

[tex]=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240[/tex]

Part a

Therefore, the number of possible ways can one component of each type be selected is 240.

(b)

The number of Sony receivers is 1.

The number of Sony CD players is 1.

The number of speakers is 3.

The number of cassettes is 4.

Select one Sony receiver out of 1 Sony receivers in ways.

Select one Sony CD player out of 1 Sony CD players in ways.

Select one speaker out of 3 speakers in ways.

Select one cassette out of 4 cassettes in [tex]4C_1[/tex] ways.

Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.

By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,

Number of ways can one components of each type be selected

[tex]=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12[/tex]

Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.

(c)

The number of receivers without Sony is 4.

The number of CD players without Sony is 3.

The number of speakers without Sony is 3.

The number of cassettes without Sony is 3.

Select one receiver out of 4 receivers in 4C_1 ways.

Select one CD player out of 3 CD players in 3C_1 ways.

Select one speaker out of 3 speakers in 3C_1 ways.

Select one cassette out of 3 cassettes in 3C_1 ways.

Find the number of ways can components be selected if none is to be Sony.

By the multiplication rule, the number of ways can components be selected if none is to be Sony is,

[tex]=4C_1*3C_1*3C_1*3C_1\\\\=108[/tex]

[excluding sony from each of the component]

Therefore, the number of ways can components be selected if none is to be Sony is 108.

(d)

The number of ways can a selection be made if at least one Sony component is to be included is,

= Total possible selections -Total possible selections without Sony

= 240-108

= 132  

Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.

(e)

If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,

[tex]= \text {Total possible selections with at least one Sony} /\text {Total possible selections}[/tex]

= 132  / 240

= 0.55

The probability that the system selected contains exactly one Sony component is,

[tex]= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}[/tex][tex]\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125[/tex]

Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.

If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.

Answer:

The temperature difference in 5 minutes will be 12.38ºC

Step-by-step explanation:

The difference in temperature after t minutes is given by the following equation:

[tex]T(t) = T(0)(1-r)^{t}[/tex]

In which T(0) is the initial temperature and r is the decrease rate, as a decimal.

Decreases by 5% every minute.

This means that [tex]r = 0.05[/tex]

What will the temperature difference be in 5 minutes if it is currently 16°C

This is T(5) when [tex]T(0) = 16[/tex]

So

[tex]T(t) = T(0)(1-r)^{t}[/tex]

[tex]T(t) = 16(1-0.05)^{t}[/tex]

[tex]T(t) = 16*(0.95)^{t}[/tex]

[tex]T(5) = 16*(0.95)^{5} = 12.38[/tex]

The temperature difference in 5 minutes will be 12.38ºC

Answer:

a) [tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]

[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]

Now we just take square root on both sides of the interval and we got:

[tex] 19.08 \leq \sigma \leq 66.56[/tex]

b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]

On this case we need to find the sample standard deviation with the following formula:

[tex]s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}

And in order to find the sample mean we just need to use this formula:

[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}[/tex]

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

[tex]df=n-1=9-1=8[/tex]

The Confidence interval is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and the critical values are:

[tex]\chi^2_{\alpha/2}=20.09[/tex]

[tex]\chi^2_{1- \alpha/2}=1.65[/tex]

And replacing into the formula for the interval we got:

[tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]

[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]

Now we just take square root on both sides of the interval and we got:

[tex] 19.08 \leq \sigma \leq 66.56[/tex]

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Answer:

Domain: [-3, 5]

Range: [-5, 4]

Step-by-step explanation:

The first thing is to define what is the domain and the range. The domain of a function f (x) is the set of all the values for which the function is defined, and the range of the function is the set of all the values that f takes.

In other words, the domain is the value on the "x" axis and the range is the value on the "y" axis.

In this case, both are an interval, the domain would be from -3 to 5 and in the case of the range it would be from -5 to 4.

Domain: [-3, 5]

Range: [-5, 4]