assume that for a particular group of students, the events is a senior and is female are independent. If 30% of the students are seniors and 54% of the students are female, what is the probability of being a female senior?​

Answer:

(3s-2)°+(4s-6)°=90

3s-2+4s-6=90

7s-8=90

7s=90+8

7s=98

Dividing both sides by 7

S=98/7

S=14

Answer:

40 degrees

Step-by-step explanation:

A full triangle is 180 degrees

85+55=140

180-140=40

The polynomial is not a perfect square trinomial. This is false..

It should be noted that a perfect squares trinomial is the algebraic expression which has the form of ax² + bx + c.

The equation given is 9x² - 30x + 25. This will be expanded as:

9x² - 30x + 25.

9x² - 15x - 15x + 25

3x(3x - 5) - 5(3x - 5)

= (3x - 5)(3x - 5)

In this case, 9x² - 30x + 25 is a perfect square binomial of 3x - 5 and not a trinomial.

Therefore, the correct option is false.

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The highest possible value of x in millions of dollars is approximately 76.4 million.

To find the highest possible value of x in millions of dollars, we need to determine the value of x that will allow the fund to last forever.

The value of the fund in year t can be expressed as:

V(t) = x + 1.045x + (1.045^2)x + ... + (1.045^(t-1))x

This is a geometric series with a common ratio of 1.045. The sum of a geometric series is given by the formula:

S = a * (1 - r^t) / (1 - r)

where a is the first term, r is the common ratio, and t is the number of terms.

In this case, a = x, r = 1.045, and we want the sum to be infinite (to last forever). Therefore, we can set up the following equation:

V = x / (1 - 1.045) = 80 million

Simplifying this equation, we get:

x / (0.955) = 80 million

x = 80 million * 0.955

x ≈ 76.4 million

So, the highest possible value of x in millions of dollars is approximately 76.4 million.

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The highest possible value of x in millions of dollars is approximately 76.4 million.

To find the highest possible value of x in millions of dollars, we need to determine the value of x that will allow the fund to last forever.

The value of the fund in year t can be expressed as:

V(t) = x + 1.045x + (1.045^2)x + ... + (1.045^(t-1))x

This is a geometric series with a common ratio of 1.045. The sum of a geometric series is given by the formula:

S = a * (1 - r^t) / (1 - r)

where a is the first term, r is the common ratio, and t is the number of terms.

In this case, a = x, r = 1.045, and we want the sum to be infinite (to last forever). Therefore, we can set up the following equation:

V = x / (1 - 1.045) = 80 million

Simplifying this equation, we get:

x / (0.955) = 80 million

x = 80 million * 0.955

x ≈ 76.4 million

So, the highest possible value of x in millions of dollars is approximately 76.4 million.

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Answer:

A C and A F

Step-by-step explanation:

A C goes from A to C

A F goes from A to F

Answer:

P=22.6, T=67.4

Step-by-step explanation:

\(sin(P)=\frac{5}{13}\\ P= 22.6\\\\tan(T)=\frac{12}{5}\\ T=67.4\\\\cos(T)=\frac{5}{13} \\T=67.4\)

Answer:

Step-by-step explanation:

a. 50x+200

b. 200

c. 50

d. y intercept - the cost to buy the phone

e. slope represents number of months that you have the phone plan

If there is a 93% chance of it being cloudy in the afternoon, the odds of it not being cloudy can be calculated as 7:93.

To determine the odds of an event, we divide the probability of the event not occurring by the probability of the event occurring. In this case, the probability of it being cloudy is 93%, which means the probability of it not being cloudy is 100% - 93% = 7%.

To express the odds, we use a ratio. The odds of it not being cloudy can be represented as 7:93. This means that for every 7 favorable outcomes (not cloudy), there are 93 unfavorable outcomes (cloudy).

It's important to note that the odds are different from the probability. While probability represents the likelihood of an event occurring, odds compare the likelihood of an event occurring to the likelihood of it not occurring.

In this case, the odds of it not being cloudy are relatively low compared to the odds of it being cloudy, reflecting the high probability of cloudy weather as announced by the meteorologist.

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Answer:

2/9 or 22%

Step-by-step explanation:

probability would be 4/18 = 2/9 = 22.2%

Answer:

0.99925077115

Answer:

44

Step-by-step explanation:

4+8(5)

Multiply 8 by 5

4+40=44

Add 4 to the product (40) to get the final answer of 44

Remember PEMDAS

Step-by-step explanation:

just as the graph shows.

no trick or hidden meaning or whatever.

#1

0 seconds to 5 seconds.

0 meters to 3 meters.

traveled 3-0 = 3 meters in 5-0=5 seconds

#2

0 seconds to 8 seconds.

0 meters to 5 meters.

traveled 5-0=5 meters in 8-0=8 seconds.

White color has the same frequency as the distribution of colors in the bag.

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
in the bag, there are 100 cards, and an equal number of cards in colors blue, red, white, and yellow.
Frequency of each color card in bag = 100 / 4 = 25

Now,
if 20 colors have been drawn, the equally distributed frequency of each color,
= 20 / 4 = 5 card,
So from the table, the white color has a frequency of 5.

Thus, the white color has the same frequency as the distribution of colors in the bag.

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Answer:

Equal volumes

Step-by-step explanation:

Given

\(h \to\) height of cone

\(d \to\) diameter of cone

\(H \to\) height of cylinder

\(D \to\) diameter of cylinder

Such that:

\(d = 2D\)

\(h =\frac{3}{4}H\)

Required

The relationship between the volumes

The volume of a cylinder is:

\(V_1 = \pi R^2H\)

Where

\(R = 0.5D\)

So:

\(V_1 = \pi (0.5D)^2H\)

\(V_1 = \pi *0.25*D^2H\)

\(V_1 = 0.25\pi D^2H\)

The volume of the cone is:

\(V_2 = \frac{1}{3}\pi r^2h\)

Where

\(r =0.5d\)

\(r = 0.5 * 2D\)

\(r = D\)

and

\(h =\frac{3}{4}H\)

So, we have:

\(V_2 = \frac{1}{3}\pi * D^2 * \frac{3}{4}H\)

\(V_2 = \frac{1}{4}\pi * D^2H\)

\(V_2 = 0.25\pi * D^2H\)

\(V_2 = 0.25\pi D^2H\)

So, we have:

\(V_1 = 0.25\pi D^2H\)

\(V_2 = 0.25\pi * D^2H\)

\(V_1 = V_2\)

Answer: : When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

Step-by-step explanation:

Answer:

x should equal 16

Step-by-step explanation:

Raina can run any number of laps (n) less than 8 to ensure her total running time is less than 48 minutes.

To find the possible numbers of laps Raina will run today, we can set up an inequality based on the given information.

Let's assume Raina will run n laps today, and each lap takes 6 minutes. Therefore, the total time she will take to run n laps is 6n minutes.

The problem states that Raina will run less than 48 minutes today. Therefore, we can write the inequality as:

6n < 48.

To solve this inequality for n, we need to isolate n on one side of the inequality.

Dividing both sides of the inequality by 6, we get:

n < 48/6

Simplifying the right side, we have:

n < 8

Therefore, the inequality solved for n is:

n < 8

This means that the possible numbers of laps Raina will run today are any positive integer value less than 8.

Since the number of laps cannot be negative or zero, the feasible values for n are 1, 2, 3, 4, 5, 6, and 7.

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Answer: 14

Step-by-step explanation: I am guessing that you wrote the "c" incorrectly and that meant to be an "e". All you really need to do is replace the letters with the numbers that equal the letters, which would be:

(15) - 1/2(2)

1/2 * 2 = 1

15 - 1 = 14

Answer:

C

Step-by-step explanation:

The graphs are reflected across the y-axis.

Answer:

True

Step-by-step explanation:

A reflecrion always is the sam edustance because then it makes it look like they are reflecting each other.

Well visualize a 10 foot ladder leaning on a wall and how the space from the distance of the wall are gonna form an angle in this question it tells you it forms a 30 degree angle so your gonna go up 10 feet and out how much the angle is on a slant and multiply the two numbers?

the space between is what your determining.

     /l

   /  l < that is the wall

 /    l

/      l

^that is the ladder

Answer:

55w + 145

Step-by-step explanation:

Total = all accounts, so you have to add 10w to 45w, and 120 to 25

10w + 45w = 55w

120 + 25 = 145

So the answer is 55w + 145

Answer: a) Let Q be an orthogonal matrix and let λ be an eigenvalue of Q. Then there exists a non-zero vector v such that Qv = λv. Taking the conjugate transpose of both sides, we have:

(Qv)^T = (λv)^T

v^TQ^T = λv^T

Since Q is orthogonal, we have Q^TQ = I, so Q^T = Q^(-1). Substituting this into the above equation, we get:

v^TQ^(-1)Q = λv^T

v^T = λv^T

Taking the norm of both sides, we have:

|v|^2 = |λ|^2|v|^2

Since v is non-zero, we can cancel the |v|^2 term and we get:

|λ|^2 = 1

Taking the square root of both sides, we get |λ| = 1.

b) Let Q1 and Q2 be orthogonal matrices. Then we have:

(Q1Q2)^T(Q1Q2) = Q2^TQ1^TQ1Q2 = Q2^TQ2 = I

where we have used the fact that Q1^TQ1 = I and Q2^TQ2 = I since Q1 and Q2 are orthogonal matrices. Therefore, Q1Q2 is an orthogonal matrix.

here this probally will help

Answer:

5, 3

Step-by-step explanation:

Answer: squared

Step-by-step explanation:

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

2x² - xy - 15y²

Step-by-step explanation:

(2x + 5y)(x - 3y)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x - 3y) + 5y(x - 3y) ← distribute parenthesis

= 2x² - 6xy + 5xy - 15y² ← collect like terms

= 2x² - xy - 15y²