)A bag contains 20 marbles of the same size that are blue, green, and red. The probability of picking a blue marble is 20%. The probability of picking a green marble is 50%. Determine the probability of picking a red marble from the bag and then classify the probability of picking a red marble as likely or not likely to occur.

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

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Answer:

0.25 miles per minute

Explanation:

In order to find speed from table, find the gradient from the given values.

\(\sf speed: \dfrac{change \ in \ distance}{change \ in \ time}= \dfrac{rise}{run}\)

Take two points: (4.25, 4), (3.25, 0)

\(\sf \rightarrow speed: \dfrac{4.25-3.25}{4-0}\)

\(\sf \rightarrow speed: \dfrac{1}{4}\)

\(\sf \rightarrow speed: 0.25\)

To find Brian's speed, calculate the slope of the linear function represented by the table of values. This means that Brian's speed is 20 miles per hour.

To determine Brian's speed, we need to find the slope of the linear function represented by the table of values. The slope represents the rate at which the number of miles on the odometer is changing per unit of time.

In this case, the slope can be calculated by taking the difference in miles between any two points on the table and dividing it by the difference in time.

For example, if we take the first two points on the table (0 miles at 0 hours and 20 miles at 1 hour),

the slope would be (20 - 0) / (1 - 0) = 20 miles/hour.

This means that Brian's speed is 20 miles per hour.

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After calculating we found that: a) 95% of widget weights lie between 42 and 54 ounces.b) 97.35% of widget weights lie between 39 and 54 ounces and c) 0.3% of widget weights lie above 45 ounces.

a) Since the distribution is bell-shaped and the mean is 48 ounces with a standard deviation of 3 ounces, we can use the 68-95-99.7 Rule to determine that 68% of the widget weights lie within one standard deviation of the mean, 95% lie within two standard deviations of the mean, and 99.7% lie within three standard deviations of the mean. Thus, we know that 95% of the widget weights lie between:

48 - 2(3) = 42 ounces and 48 + 2(3) = 54 ounces.

b) To find the percentage of widget weights that lie between 39 and 54 ounces, we need to determine how many standard deviations away from the mean these values are.

39 ounces is 9 ounces below the mean, so it is (9/3) = 3 standard deviations below the mean.

54 ounces is 6 ounces above the mean, so it is (6/3) = 2 standard deviations above the mean.

Using the 68-95-99.7 Rule, we know that 99.7% of the widget weights lie within three standard deviations of the mean. Since 39 ounces is three standard deviations below the mean, we can conclude that 0.15% (or 0.003 x 100) of the widget weights lie below 39 ounces.

Likewise, since 54 ounces is two standard deviations above the mean, we know that 2.5% of the widget weights lie above 54 ounces. Thus, the percentage of widget weights that lie between 39 and 54 ounces is:

100% - 0.15% - 2.5% = 97.35%

c) We need to find the percentage of widget weights that lie above 45 ounces. Since 45 ounces is three standard deviations below the mean, we know that 99.7% of the widget weights lie above 45 ounces. Therefore, the percentage of widget weights that lie above 45 ounces is:

100% - 99.7% = 0.3%.

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Answer:

Step-by-step explanation:

Let the five courses with their corresponding credit hours be represented as shown;

FST 201 = 4

FST 203 = 5

FST 112 = 1

FST 219 = 5

FST 223 = 4

If a student earned grades of​ B, B,​ A, C, and D respectively in those courses with the following grading system  A =​4, B =​3, C =​2, D =​1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.

Credit point for each course = Number of credit hour * point for each grade

FST 201 = 4 * 4 = 16points (A)

FST 203 = 5 * 4 = 20points (A)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 4 = 20points (A)

FST 223 = 4 * 4 = 16points (A)

Total credit point = 16+20+4+20+16 = 76points

Total credit point gotten by the student is calculated as thus;

FST 201 = 4 * 3 = 12points (B)

FST 203 = 5 * 3 = 15points (B)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 2 = 10points (C)

FST 223 = 4 * 1 = 4points (D)

Total credit point gotten by the student = 45points.

student's Grade Point Average​ (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)

Combining like terms yields 7x⁵ - x³ - x² + 4x.

Answer:

a

Step-by-step explanation:

Answer:

180-(60+70)=50

180-50=130 so a

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/x = sin45

x = 3/sin45

x = 3 / ½(√2)

x = 3(2/√2)

x = 3((2√2)/2)

x = 3√2

The value of x from the give triangle is 3√2 units. Therefore, option D is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, we have opposite = 3 units and hypotenuse = x units.

We know that, sinθ=Opposite/Hypotenuse

sin45°=3/x

1/√2 =3/x

x=3√2 units

Therefore, option D is the correct answer.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

the slope would be 17

Step-by-step explanation:

he earns $17 per hour

you find this by dividing the amount earned by the hours worked

102 / 6 = $17 per hour

187 / 11 = $17 per hour

According to the given percentage, the shipping and handling fee that Elizabeth will pay is $16.6

Percentage:

Percentage refers one-hundredth (1/100) of something. And it refers to the rate or proportion of that one hundred.

Given,

Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of the price.

Here we need to find the shipping and handling will Elizabeth paid.

We know that, the price of the product is $83.

And the charges for the shipping and handling is 20%.

So, it can be written as the following form,

=> Additional charges = 20% of 83

=> Additional charges =  20/100 x 83

=> Additional charges = 20 x 0.83

=> Additional charges = 16.6

Therefore, the shipping and handling charges is $16.6

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Answer:

○ \(\displaystyle [\frac{1}{2}, ∞[\)

Step-by-step explanation:

All you want to do is set the radical equal to zero to determine your domain, and sinse substituting \(\displaystyle \frac{1}{2}\) in for \(\displaystyle x\) would make this 0, it would be the INCLUDED endpoint, so your bracket faces \(\displaystyle \frac{1}{2},\) then continues on infinitely.

I am joyous to assist you at any time.

**The ONLY time this is not the case is when you have a rationale-radical function, in which you must never have 0 in the denominatour.

Answer:

The attached graph shows my answer.

Step-by-step explanation:

The graph has to start at the top because the number of carrots has to decrease and the graph slants down to the right because the time has to increase. Then the situation says that he eats one carrot at a time until half are eaten. The graph shows the line going down until approximately half. Then he doesn't eat any more, so the line is horizontal until the end of the graph to show no change.

Answer:

(-8, 12)

Step-by-step explanation:

Dilation of point (-4, 6) about point (0, 0)

Scale factor = 2

Image coordinate:

(-8, 12)

hope this helps and is right!! p.s. i really need brainliest :)

The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x-4) + 2(x-4)

= (5x+2)(x-4)

Hence, the factored form is (5x+2)(x-4).

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The expression for the perimeter of a rectangle as required to be written is; P = 2 (l + w).

Recall, the perimeter of a rectangle is the sum total of all its side lengths.

Since a rectangle has 2 length and 2 width measures, the perimeter is therefore given as;

P = 2l + 2w.

P = 2 (l + w)

Hence, if the length = x + 4 and width = x + 3 for instance; we have that;

P = 2 (x+4 + x+3)

P = 4x + 14.

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As per the result received by solving the equation  PV = C the rate at which the volume is decreasing at this instant is (-)30 cm3/min. The negative sign is to denote the decrement of volume with respect to time.

Robert Boyle investigated the connection between a confined gas's volume V and pressure p in the middle of the 16th century. Boyle noted that the relationship between pressure and volume is seen to be almost constant. For a perfect gas, the result of pressure and volume is a precise constant.In his honor, the relationship between pressure and volume is known as Boyle's Law.

Boyle's law may be used in everyday life while adding fluid to a syringe. The syringe's internal volume and pressure rise when the plunger is pulled back. Until the pressure within and outside the barrel are equal, the fluid outside the syringe is drawn into the barrel.

The rate at which the volume is decreasing at the given instant can be found by taking the first derivative of the equation PV =C and substituting the respective values as shown below.

P*dV/dt + V*dP/dt = 0

which gives dV/dt = -30 cm3/min

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Answer:

Correct option:

"The total cost of renting a jet ski for $25 per hour plus a fee of $50."

Step-by-step explanation:

Proportional relationships are associations between two variables where the ratio of these two variables are correspondent. Or, in a proportional relationship, one variable is a constant value times the other variable. This constant is known as the "constant of proportionality".

The first three options represents a proportional relationship.

But the last option does not.

"The total cost of renting a jet ski for $25 per hour plus a fee of $50."

That is,

TC = 25·h + 50

The relationship is linear not proportional.

The exact value of sin theta in simplest form is \(-\frac{\sqrt{35} }{6} .\)

The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions.

Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.

Since cos theta is negative and angle theta is in Quadrant III, we can use the fact that in Quadrant III, both sin and cos are negative.

We can use the Pythagorean identity to find the value of sin theta:

\(Sin^{2}+ cos^{2} = 1\)

sin² θ+ (-1/6)² = 1

sin² θ + 1/36 = 1

sin² θ = 1 - 1/36

sin² θ = 35/36

We take the square root of both sides, remembering that sin theta is negative in Quadrant III:

sin θ = \(-\frac{\sqrt{35} }{6} .\)

Therefore, the exact value of sin theta in simplest form is -sqrt(35)/6.

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Answer:

120

Step-by-step explanation:

we know if the arc measures 120, we know that its 1/3 of the circle, so ABC will also be 120

Answer:

x= 3/2

Step-by-step explanation:

3/x=2

Multiply x both sides so,

3 =2x

Divide 2 to get the value of x so,

x= 3/2

Answer:

\(P(n>55)=0.1357\)

Step-by-step explanation:

From the question we are told that:

Sample size n=100

Sample space n'=36

Generally the equation for the mean number of times odds appears is mathematically given by

\(\=x_o=hp\)

\(\=x_o=100*0.5\)

\(\=x_o=50\)

Generally the equation for standard deviation is mathematically given by

\(\sigma=(hp(1-p))^{1/2}\\\sigma=(50(0.5))^{1/2}\)

\(\sigma=5\)

Therefore probability to make wrong decision P(n>55)

\(P(n>55)=1-P(z<50.5/5)\\P(n>55)=1-P(z<1.1)\\P(n>55)=1-0.86\)

\(P(n>55)=0.1357\)

An approximation for the probability that you will make the wrong decision is 0.1587.

S=Number of time that the result was odd

n=100

p=0.5

Hence:

E[S]=100×0.5

E[S]=50

Standard deviation=√100×0.5×0.5

Standard deviation√25

Standard deviation=5

Using normal approximation to the binomial

P(S≥55)=P(S-50/5 ≥ 55-50/5)

P(S≥55)=1-P(z ≤ 1)

P(S≥55)=1-0.8413

P(S≥55)= 0.1587

Inconclusion  an approximation for the probability that you will make the wrong decision is 0.1587.

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The unlabeled side length for this problem has the measure given as follows:

13.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The sides for this problem are given as follows:

5 and 12.

Hence the measure of the hypotenuse is obtained as follows:

h² = 5² + 12²

h² = 169

h = 13.

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Answer:

6

Step-by-step explanation:

Add all the numbers together and divide by the amount of numbers

6+9+3+8+9+3+4= 42

42/7 = 6

Answer:

6

Step-by-step explanation:

To find the mean or the average of the data set, you add all the numbers together and then divide the sum by the number of numbers in the data set.

6+9+3+8+9+3+4 =42

Then divided by the # of terms.

42/7= 6

Answer:

$2.50X > $25

Step-by-step explanation:

the cost times the unknown will be less or equal to$25

The inequality function to  represent the relationship between the amount of money should be considered as the $2.50X > $25.

Since

Jinan has $25 dollars to spend on drinks for the class party.

And, A case of drinks cost $2.50.

So here the inequality function should be $2.50X > $25

Here the cost should be less or equivalent to 25.

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Answer:

None

Step-by-step explanation:

Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.

Answer:

One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.

Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.

One way to construct a confidence interval for a proportion is to use the formula:

p ± z * sqrt(p * (1 - p) / n)

where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:

0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)

which simplifies to:

0.6 ± 0.22

or:

(0.38, 0.82)

This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.

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Answer:

-5 and -3

Step-by-step explanation:

Answer:

given a number x, negative 3 times that number is -3x. If this has to be at least 57, it means that -3x must be greater than or equal to 57:

\(-3\geq 57\) Dividing both sides by -3 solves the equation, but we have to switch the inequality sign because we're dividing by a negative number:

\(x \leq \frac{57}{3} =19\)

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

Explanation:

Check out the diagram below. I've added in the label (4x+13) degrees to the angle adjacent to the (9x-2) degree angle. This is valid due to corresponding angles being congruent when we have parallel lines like this.

The two angles form a 180 degree straight angle

(4x+13) + (9x-2) = 180

4x+13 + 9x-2 = 180

(4x+9x) + (13-2) = 180

13x + 11 = 180

13x+11-11 = 180-11 .... subtracting 11 from both sides

13x = 169

13x/13 = 169/13 .... dividing both sides by 13

x = 13

We can verify this by noticing that

4x+13 = 4*13+13 = 65

9x-2 = 9*13-2 = 115

So, (4x+13)+(9x-2) = (65)+(115) = 180, showing the two angles are supplementary.

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

The angles (9x-2) and (6y-1) are also a linear pair. They are adjacent and supplementary

Let's use x = 13 to find the value of y

(9x-2) + (6y-1) = 180

9x-2+6y-1 = 180

9x+6y-3 = 180

9*13+6y-3 = 180 .... plug in x = 13

117+6y-3 = 180

6y+114 = 180

6y+114-114 = 180-114 .... subtract 114 from both sides

6y = 66

6y/6 = 66/6 ...... divide both sides by 6

y = 11

To help confirm,

6y-1 = 6*11-1 = 65

which adds onto the (9x-2) = 115 degree angle to get 180.

-----------

Side note: as an alternative, you can solve 4x+13 = 6y-1 to get the same y value. This is because alternate exterior angles are congruent when we have parallel lines like this.