Geometry: Explaining Volume Formulas

Answer:

he is more likely incorrect.

Step-by-step explanation:

Z = (ps - p0)/sqrt(p0(1-p0)/n)

ps = proportion sample

p0 = proportion null hypothesis (NCAA)

n = sample size

ps = 17 / 36/100 = 17/1 / 36/100 = 1700/36 =

= 47.22222222...%

Z = (0.47222... - 0.575)/sqrt(0.575(1 - 0.575)/36) =

= -0.10277777... /sqrt(0.244375 / 36) =

= -0.10277777... / 0.0823905... =

= -1.247446952... ≈ -1.25

p(-1.25) = 0.10565

0.10565 > 0.05

the null hypothesis is therefore likely, or at least cannot be rejected.

so, his claims are not supported, as surprising as this might feel given that the sample result itself is 10 points off the NCCA result, which feels to be a solid difference.

Answer:

20

Step-by-step explanation:

u add 13+7 and that gives you 20, so if you subtract 20 and 7 that gives you 13

The least number of colors needed to correctly color in the sections of the given picture so that no two touching sections have the same color is 5.

Let's say we begin with a single triangle. This triangle will be the first of a series of seven subsequent triangles, none of which will have any portions contact. If a square were the initial shape, then there are five shapes—three of which are squares and the other two are triangles—that don't have any touching portions. Given that a square takes up twice as much room, this value is probably lower, but location also matters. Therefore, for the given figure, the least number of colored areas you can color in that yet meet the required criteria is 5.

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The linear equation that represents the relationship between earnings and tips will be y = 0.75x + 50.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Working as a waitress is Amanda. She receives $50 every day in addition to 75% of the tips her clients leave.

Let 'x' be the tip amount and 'y' be the total earning.

y = 0.75x + 50

Check:

At (20,65), then we have

65 = 0.75(20)+50

65 = 15+50

65=65

At (50,87.5), then we have

87.5 = 0.75(50)+50

87.5 = 37.5+50

87.5=87.5

At (100,125), then we have

125 = 0.75(100)+50

125 = 75+50

125=125

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The sum of normally distributed random variables is also a normally distributed random variable.

Given [tex]n[/tex] random variables with [tex]X_i\sim\mathrm{Normal}(\mu_i,\sigma_i^2)[/tex], their sum is

[tex]\displaystyle\sum_{i=1}^n X_i \sim \mathrm{Normal}\left(\sum_{i=1}^n \mu_i, \sum_{i=1}^n \sigma_i^2\right)[/tex]

i.e. normally distributed with mean and variance equal to the sums of the means and variances of the [tex]X_i[/tex].

In this case, each of [tex]X_1,X_2,X_3[/tex] are normally distributed with [tex]\mu=4[/tex] and [tex]\sigma^2[/tex] = ... I'm not sure what you meant for the variance, so I'll keep it symbolic. Then

[tex]V = X_1+X_2+X_3 \sim \mathrm{Normal}(12, 3\sigma^2)[/tex]

The sum of the first 7 terms of the geometric series is 15.180

The formula for calculating the sum of geometric series is expressed according to the formula. below;

GM = a(1-r^n)/1-r

where

r is the common ratio

n is the number of terms

a is the first term

Given the following parameters from the sequence

a = 1/36

r = -3

n = 7

Substitute

S = (1/36)(1-(-3)^7)/1+3
S = 1/36(1-2187)/4
S = 15.180

Hence the sum of the first 7 terms of the geometric series is 15.180

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The total number of common tangents that can be drawn to the circles is 1

The tangent lines of a circle are the lines drawn, that touch the circle at only one point

The complete question is added as an attachment

From the attached figure, we have the following highlights:

The one point of intersection is the only point where both circles can have common tangents

Since there is only one point of intersection, then the number of common tangents on the circles is 1

Hence, the total number of common tangents that can be drawn to the circles is 1

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Answer:

1/6

Step-by-step explanation:

You have six choices and you want to pick only 1 of those choices.

1/6

[tex]\displaystyle\frac{1}{6}[/tex]

Probability explains the likelihood of an event occurring. The outcome you are finding the probability for is the successful outcome. The sample size is the total number of possible outcomes.

Simple Probability

Simple probability is when there is only one single event. In this situation, the cube is only being rolled once, so it's a simple probability question. To solve this question as a fraction, the numerator should be the number of successful outcomes and the denominator should be the sample size.

Solving for P(B)

Since there are 6 sides with 6 letters, the sample size is 6. So, 6 should be the denominator. We are finding the probability of "B", which means there is 1 successful outcome. Thus, the numerator should be 1.

This means as a fraction the probability is [tex]\frac{1}{6}[/tex].

Answer:

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

Step-by-step explanation:

Slope/Gradient = [tex]\frac{y1-y2}{x1-x2}[/tex]

P = (-8 , 3) (x1, y1)

Q = (-6 , 2) (x2, y2)

Slope = [tex]\frac{3-2}{-8-(-6)}[/tex] =[tex]\frac{1}{-8+6}[/tex] = [tex]\frac{1}{-2}[/tex] = [tex]-\frac{1}{2}[/tex]

Answer:

-1/2

Step-by-step explanation:

The formula for the slope is (change in y)/(change in x) or Rise/Run.

The change in y for the two points is: 3 --> 2 which is -1

The change in x for the two points is: -8 --> -6 which is +2

If we input these numbers in the slope equation, we end up with -1/2.

Since we cannot simplify -1/2 further, that is our final answer.

Answer:

13

Step-by-step explanation:

→ Substitute 3 into 2x

2 × 3

→ Evaluate

f ( x ) = 6

→ Substitute x = 3 into 3x - 2

3 × 3 - 2

→ Evaluate

7

→ Find the sum of the 2 results

13

When x = 3, the value of (f + g)(x) is 13.

To evaluate (f + g)(x) when f(x) = 2x and g(x) = 3x - 2, we substitute the given functions into the expression (f + g)(x).

(f + g)(x) = f(x) + g(x)

Substituting the given functions:

(f + g)(x) = 2x + (3x - 2)

Simplifying the expression:

(f + g)(x) = 2x + 3x - 2

Combining like terms:

(f + g)(x) = 5x - 2

Now, to find the value of (f + g)(x) when x = 3, we substitute x = 3 into the expression:

(f + g)(3) = 5(3) - 2

Simplifying further:

(f + g)(3) = 15 - 2

(f + g)(3) = 13

Therefore, when x = 3, the value of (f + g)(x) is 13.

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The initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

From the information given, we have the function to be;

a(t)=2400(1/2)^t/14

Where

To determine the initial amount, we have that t = 0

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{0}{14}[/tex]

[tex]A (t) = 2400[/tex]  × [tex]\frac{1}{2} ^0[/tex]

[tex]A (t) = 2400[/tex]

The initial amount is 2400 grams

For the amount remaining after 40 years, t = 40 years

A(t)=2400(1/2)^t/14

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{40}{14}[/tex]

[tex]A(t) = 2400[/tex] × [tex](0. 5) ^2^.^8^5^7[/tex]

[tex]A(t) = 2400[/tex] × [tex]0. 1380[/tex]

A(t) = 331. 26

A(t) = 331 grams in the nearest gram

Thus, the initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

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Check the picture below.

Answer: 28 [tex]units^{2}[/tex]

Step-by-step explanation:

The probability that the person selected is 40 years old or younger is 0.61.

Probability determines the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the person selected is 40 years old or younger = number of people 40 years or younger / total number of people at the movie theatre = (6 + 17 + 18 + 10 + 4 + 6) / (6 + 17 + 18 + 10 + 4 + 6 + 16 + 3 + 20)

61 / 100 = 0.61

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Answer:

[tex] \frac{27}{8} cm {}^{3} [/tex]

Is the volume of this right rectangular prism.

Step-by-step explanation:

Rectangular prism volume formula is:-

Answer:

[tex]V=\frac{27}{8}\: cm^3[/tex]

Step-by-step explanation:

The formula to find the volume of a rectangular prism is:

V = length × height × width

Let us find now.

[tex]V = length \:* height \:* width\\\\V =\frac{3}{2} *\frac{3}{2} *\frac{3}{2} \\\\V=\frac{9}{4}*\frac{3}{2} \\\\ V=\frac{27}{8}\: cm^3[/tex]

Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.

Primero, vamos a definir la superficie del agua como el 0 metros.

Sí sabemos que primero el buzo se sumerge 4 metros, entonces en este punto la posición del buzo es:

P = 0m - 4m = -4m

Luego el buzo sube 2 metros, entonces la nueva posición será:

P = -4m + 2m = -2m

Finalmente, el buzo desciende otros 5 metros, entonces la posición final del buzo será:

P = -2m - 5m = -7m

Así, concluimos que la posición final del buzo será 7 metros bajo la superficie del agua.

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The ODE is separable.

[tex]\dfrac{dy}{dx} = xy \iff \dfrac{dy}y = x\,dx[/tex]

Integrate both sides to get

[tex]\displaystyle \int\frac{dy}y = \int x\,dx[/tex]

[tex]\boxed{\ln|y| = \dfrac12 x^2 + C}[/tex]

But notice that replacing the constant [tex]C[/tex] with [tex]-C[/tex] doesn't affect the solution, since its derivative would recover the same ODE as before.

[tex]\ln|y| = \dfrac12 x^2 - C \implies \dfrac1y \dfrac{dy}{dx} = x \implies \dfrac{dy}{dx} = xy[/tex]

so either of the first two answers are technically correct.

Answer:

-20

Step-by-step explanation:

Use the distributive property to get [tex]2xy-14[/tex] (you multiply both xy and -7 by 2.) Now plug in the x and y values to get: [tex]2(-1)(3)-14[/tex]. This gets you [tex]-6-14[/tex] which is [tex]-20[/tex].

Applying the initial conditions, the specific solution is:

[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]

The general solution is given by:

[tex]y = e^{-2x}(C_1\sin{3x} + C_2\cos{3x})[/tex]

We apply the initial conditions to find the specific solution.

First, we have that y(0) = 4, then:

[tex]4 = e^{-2(0)}(C_1\sin{3(0)} + C_2\cos{3(0)})[/tex]

Since cos(0) = 1, we have that:

[tex]C_2 = 4[/tex]

Then:

[tex]y = e^{-2x}(C_1\sin{3x} + 4\cos{3x})[/tex]

The derivative is:

[tex]y^\prime(x) = -2e^{-2x}(C_1\sin{3x} + 4\cos{3x}) + e^{-2x}(3C_1\cos{3x} - 4\sin{3x})[/tex]

Since y'(0) = -17, then:

[tex]-17 = -8 + 3C_1[/tex]

[tex]3C_1 = -9[/tex]

[tex]C_1 = -3[/tex]

Then the specific solution is:

[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]

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Answer:

  c > 5

Step-by-step explanation:

The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.

We can subtract 3 from both sides to solve this.

  c +3 > 8 . . . . . . given

  c +3 -3 > 8 -3 . . . . subtract 3 from both sides

  c > 5 . . . . . . . . . simplify

The solution is c > 5.

__

Additional comment

Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.

Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.

Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)

As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.

The expected value for the drilling company, using a discrete distribution, is of -$9,125, that is, a loss of $9,125.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Considering the cost that it takes to sink a test well, and the probabilities of each outcome, the discrete distribution is given by:

Hence the expected value is given as follows:

E(X) = 300000 x 0.025 + 130000 x 0 .05 - 25000 x 0.925 = -$9,125.

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Answer:

YES! it's one-to-one function.

Step-by-step explanation:

One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then f is one to one.

Thus, when we look at this given function

X Y

[tex] - 2 \: \: \: \: \: \: 1 \\ - 5 \: \: \: \: \:- 1 \\ 3 \: \: \: \: \: \: - 5 \\ 1 \: \: \: \: \: \: - 2 \\ 0 \: \: \: \: \: \: 5 \\ - 1 \: \: \: \: \: \: 6 \\ - 6 \: \: \: \: \: \: \: 7 \\ \: \: 7 \: \: \: \: \: \: - 6[/tex]

So, when you look at each value of x is attaches with different value of y and there is no repetition of elements means that one element of x is directly attached to one element of y.

Hope it helps!

Answer:

  x = {π/6, π/2, 5π/6, 3π/2}

Step-by-step explanation:

The equation can be solved using a double-angle trig identity and factoring.

Dividing the equation by 7 and substituting for sin(2x), we have ...

  7sin(2x) = 7cos(x)

  sin(2x) = cos(x)

  2sin(x)cos(x) = cos(x)

  2sin(x)cos(x) -cos(x) = 0

  cos(x)(2sin(x) -1) = 0

The product of factors is zero when one or more of the factors is zero.

  cos(x) = 0   ⇒   x = {π/2, 3π/2}

  2sin(x) -1 = 0   ⇒   x = arcsin(1/2) = {π/6, 5π/6}

Solutions in the given interval are ...

  x = {π/6, π/2, 5π/6, 3π/2}

__

Additional comment

When the equation is of the form f(x) = 0, then the x-intercepts of f(x) are its solutions. We can rearrange this one to ...

  sin(2x) -cos(x) = 0

The solutions identified above match those shown in the graph.

6 decks of cards = 60 cards

---> 60/8 = 15/2 = 7.5

7.5 cards = 0.75 decks of cards

Therefore, each student will get 0.75 decks of cards.

Answer:

1

Step-by-step explanation:

Everyone gets 1 and there's 2 left over

Given that the graph shows P as a function of n, we have:

a. The more hot dogs that is sold, his profit increases.

b. Jimmy sells the hot dog for $1 each.

c. Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. He would make a profit of $7.

e. The number of hot dogs he needs to sell is: 20.

A linear  function is expressed as, y = mx + b, where y is a function of x, m is the unit rate, and b is the starting value or initial value of the function.

We are given that profit, P, is a function of the number of hot dogs sold, n.

a. The graph of the function slopes upwards, so this means that the more hot dogs that is sold, his profit increases.

b. Cost of 1 hot dog = Unit rate = change in y / change in x = 2 units/2 units

Cost of 1 hot dog = Unit rate = 1

Thus, Jimmy sells the hot dog for $1 each.

c. If you trace profit (P) on the graph when it is $8, the corresponding number of hot dogs, n, would be 16.

So, Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. When n = 15, P, from the graph would be 7.

Thus, if Jimmy sells 15 hot dogs, he would make a profit of $7.

e. When P = 12, from the graph, the corresponding n value is 20.

Therefore for Jimmy to make $12, the number of hot dogs he needs to sell is: 20.

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The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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Answer:

3

Step-by-step explanation:

A + B is calculated by adding the same positions in both matrices.

and position (2, 3) in A+B is therefore the sum of position (2, 3) in A plus the position (2, 3) in B, which is then

-4 + 7 = 3

Answer: They are the same

Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.

Answer:

y=-1/2n+44

Step-by-step explanation:

The number of bean stalks, n, represents the x values

The yield, y, represents the y values

After reading the problem, we have two coordinates: (30,29) and (32, 28) Because this problem is asking for y=mn+b, we have to find the slope. How do we find the slope? We do so by using the slope formula y2-y1/x2-x1. Now let's input the coordinates into this formula.

1.) 28-29/32-30 = -1/2

Let's plug -1/2 into y=mn +b

2.) y=-1/2n+b

Now we have to find what b ( y intercept) equals. To find B, we plug a coordinate into x and y. Let's use (30,29)

3.) 29 = -1/2(30)+b

29 = -15 +b

44 = b

We have now found the linear relationship form for this problem: y=-1/2n +44

Answer:

3:26 to be on time!

Step-by-step explanation:

If you leave your house at 3:26 am and then walk 34 minutes it will be 4 am

once you get to work.

Answer:

Step-by-step explanation:

Comment

I can't be sure what you mean by 2001/2. I will interpret it the way it is written.

1 hour produces 2001/2

8 hours produces x

What you have is a proportion.

Solution

1/8 = 2001/2 // x                       Cross multiply

1*x = 2001/2 *  8                       Combine

x = 8004

Answer

The printer will produce 8004 printed pages.