The ratio of boys to girls in Ms. Graham’s class is 3 to 5. There are 20 girls in the class.

What is the total number of students in Ms. Graham's class?

Answer:

y=12, x=6

Step-by-step explanation:

y+3=15

3x-6=12

Step-by-step explanation:

y = 2/5 x - 9/5

when x = -1,

the value of y = 2/5(-1) - 9/5

= -2/5 - 9/5 = -11/5

Answer:

39

Step-by-step explanation:

B is a right angle, so it is 90°

90 - 51 = 39

Answer:

\(let \: that \: angle \: be \: x \\ x + 51 \degree = 90 \degree \\ x = 90 \degree - 51 \degree \\ x = 39 \degree\)

Answer:

8.15% probability your hand contains exactly 3 hearts

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the cards are chosen is not important, so we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

What is the probability your hand contains exactly 3 hearts (out of 5 cards)?

We have 52 cards in total.

13 are clubs, 13 are spades, 13 are hearts, 13 are diamonds.

Desired outcomes:

3 hearts, from a set of 13.

Other 2 cards, from a set of 52-13 = 39.

So

\(D = C_{13,3}*C_{39,2} = \frac{13!}{3!(13-3)!}*\frac{39!}{2!(39-2)!} = 211926\)

Total outcomes:

5 cards, from a set of 52. So

\(T = C_{52,5} = \frac{52!}{5!47!} = 2598960\)

Probabilities:

\(p = \frac{D}{T} = \frac{211926}{2598960} = 0.0815\)

8.15% probability your hand contains exactly 3 hearts

Given data:

The given graph is shown.

The location of point P lies in fourth coordinate in which x is positive and y is negative.

Thus, the coordinate of P is (3,-2), so option (D) is correct.

so, we know the diameter is 8, so that means its radius is half that, or 4.

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2\)

Answer:

The answer is 20 hours

Step-by-step explanation:

20x60=1200

1200÷60=20

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

One way to solve

1 car = 20 minutes

3*(1 car) = 3*(20 minutes) multiply both sides by 3

3 cars = 60 minutes

3 cars = 1 hour

20*(3 cars) = 20*(1 hour) ... multiply both sides by 20

60 cars = 20 hours

-------------------

Another way to solve

(1 car)/(20 minutes) = (60 cars)/(x minutes)

1/20 = 60/x

1*x = 20*60 ... cross multiply

x = 1200 minutes

x = (1200 min)*( (1 hr)/(60 min) )

x = (1200/60) hr

x = 20 hours

Finn would run 18 miles after 6 track practices.

We have,

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Answer:

Step-by-step explanation:

To simplify the expression 3 x (3/4) whole to a unit fraction, we can start by multiplying the whole number 3 by the denominator of the fraction, which is 4:

3 x (3/4) = (3 x 4)/4 x (3/4) = 12/4 x 3/4

We can simplify the fraction 12/4 by dividing both the numerator and denominator by 4:

12/4 = 3

Substituting this back into the expression, we have:

3 x (3/4) = 3/1 x (3/4) = 9/4

Therefore, 3 x (3/4) whole is equal to the unit fraction 9/4.

Answer:

-9

Step-by-step explanation:

\(f(-2)=2(-2)=-4 \\ \\ g(-2)=|-2-3|=5;\\ \\ (f-g)(2)=-4-5=-9\)

A function that has a greater maximum include the following: A. Function 1 has a larger maximum at (4, 1).

In order to determine the maximum value of function 2, we would have to take the first derivative with respect to x and then, substitute this x-value into the original function while equating it to zero (0), and then evaluate as follows;

f(x) = −x² + 2x - 15

f(x) = −2x + 2

0 = −2x + 2

2x = 2

x = 2/2

x = 1

For the maximum value of function 2, we have:

f(1) = −(1)² + 2(1) - 15

f(1) = -14

For the maximum value of function 1, we can logically deduce that it is equal to 1 based on the graph in image attached above.

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The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.

Answer:

D: <K = 35°

Step-by-step explanation:

<E = 55

<L = 90°

Now

<LKE = 180-90-55

<K = 35°

Answer:

\(\fbox{\begin{minipage}{8.8em}Option D is correct\end{minipage}}\)

Explanation:

Here, we state again the definition of inscribed angle in circle:

(1) An inscribed angle has the vertex on the circle and the sides are chords.

=> In the picture shown, angle ELK is inscribed angle with vertex L and LE and LK are chords.

(2)An inscribed angle also creates an intercepted arc whose endpoints are on the angle.

=> Inscribed angle ELK creates intercepted arc EK.

(3) According to the Inscribed Angle Theorem, the measure of intercepted arc is twice as the measure of its inscribed angle.

=> Angle ELK = (1/2) arc EK

Arc EK, whose EK is diameter, is equal to measure of half of circle, or 180 degree, in other words.

=> Angle ELK = (1/2) x 180 = 90 deg

(4) As the property of sum of 3 angles inside a triangle, this sum is equal to 180 degree.

=> Considering triangle ELK:

ELK + LEK + LKE = 180 deg

or

90 + 55 + LKE = 180 deg

or

LKE = 180 - 90 - 55 = 35 deg

Hope this helps!

:)

Answer:

LCM of 30 and 45 is 90

They will leave together after 90 minutes, which is 8:30 am

Answer:

Where is the graph?

Step-by-step explanation:

Answer:

1. neither. the slopes are not negative reciprocals of each other, or are they equal.

2. perpendicular. the slopes are negative reciprocals of each other.

Step-by-step explanation:

you're welcome

Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

The counting principle says that we multiply the number of ways for each of these events together to get the total number of ways to get a license plate. Hence, there are \(158184000\) ways to create a license plate.

What is the counting principle?

The fundamental counting principle states that if there are \(p\) ways to do one thing and \(q\) ways to do another thing, then there are \(p\)×\(q\) ways to do both things.

So,

The number of ways to count the first number are \(9\) ways.

The number of ways to count the first letter are \(26\) ways

The number of ways to count the next letter are \(26\) ways

The number of ways to count the third letter are \(26\) ways

The number of ways to count the next number are \(10\) ways

The number of ways to count the next number are \(10\) ways

The number of ways to count the next number are \(10\) ways

So, the total number of ways to get a license plate is:-

\((9).(26).(26).(26).(10).(10).(10)=158184000\).

Hence, there are \(158184000\) ways to create a license plate.

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All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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Answer:

The best model is hypergeometric distribution.

Step-by-step explanation:

The probability would be best modeled with hypergeometric distribution.

Hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws, without replacement, which is often employed in random sampling for statistical quality control.

The hypergeometric distribution differs from the binomial distribution in the lack of replacements.

Thus, the best model is hypergeometric distribution.

ANSWER:

4 CDs

STEP-BY-STEP EXPLANATION:

According to the statement we can propose the following equation

Solving for x:

Which meanshe he buy 4 CDs

Answer:

0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Standard deviation of 2 and a mean diameter of 200 inches.

This means that \(\sigma = 2, \mu = 200\)

83 shafts

This means that \(n = 83, s = \frac{2}{\sqrt{83}}\)

What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches?

Mean between 200 - 0.2 = 199.8 inches and 200 + 0.2 = 200.2 inches, which is the p-value of Z when X = 200.2 subtracted by the p-value of Z when X = 199.8.

X = 200.2

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{200.2 - 200}{\frac{2}{\sqrt{83}}}\)

\(Z = 0.91\)

\(Z = 0.91\) has a p-value of 0.8186

X = 199.8

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{199.8 - 200}{\frac{2}{\sqrt{83}}}\)

\(Z = -0.91\)

\(Z = -0.91\) has a p-value of 0.1814

0.8186 - 0.1814 = 0.6372

0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.

The measure for the exterior angle to the angle X of the triangle XYZ is 112.55°

In any triangle, an exterior angle is equal the sum of its two opposite interior angles is equals.

For the triangle XYZ, the exterior angle to the angle X is equal to the sum of the two opposite interior angles Y and Z

angle Y = 38.25° and angle Z = 74.3°

exterior angle to X = 38.25° + 74.3°

exterior angle to X = 112.55°

This implies that the angle X = 180° - 112.55° = 67.45°

and 67.45° + 38.25° + 74.3° = 180° which is true for the sum of interior angles of a triangle.

Thus, exterior angle to the angle X that is derived to be 112.55° is true for the triangle XYZ.

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Answer:

112.55

Step-by-step explanation:

i got it right

Answer:

8,12 and 16

Step-by-step explanation:

Answer:

76ft^3

Step-by-step explanation:

Volume of a cube is Length x Width x Height, basically: 4 x 4 x 4 which is 64 ft^3. Add that to the small box gives you 64 + 12 or just 76 ft^3

Answer:

(2x + 3)3

Step-by-step explanation:

Simplify:  (2x+3)(3)

Answer: (2x + 3)3

Hope this helps.

The z-score for the given normally distributed data of typing test is 3.33 and its left and right p -value is equal to 0.9996 and 0.00043 respectively.

As given in the question,

Mean of the typing test 'μ' = 60 words per minutes

Standard deviation of the typing test 'σ' = 6 word per minutes

Number of words per minutes 'X' = 80

z- score = ( X - μ ) / σ

             = ( 80 - 60 ) / 6

             = 20 /6

             = 3.33

z-score graph for the given data indicates the left tailed p -value .

Using table:

left tailed p -value = 0.9996

Right tailed p - value = 0.00043

two tailed p- value = 0.00086

Two tailed confidence level is given by 0.9991

Therefore , the z-score of the given mean and standard deviation is equal to 3.33 and left and right p -value is 0.9996 and 0.00043 respectively.

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Answer:

50.

Step-by-step explanation:

.