500 ft from the intersection of two roads. She has carefully

measured the angles of the lines of sight to points A and B as

shown in the drawing. If a car passes from A to B in 1.75 sec

and the speed limit is 55 mph, is the car speeding?

HINT Find the distance from B to A and use R = D/T.

The **Distance** between A, B based on the information will be 28.705 feet

From the information, the **policewoman** has positioned herself 500 ft from the intersection of two roads and she has carefully measured the angles of the lines of sight to the points.

**Distance** between A, B will be:

= 500 tan(15.4) - 500 tan(12.3)

= 500 (tan 15.4 - tan 12.3)

= 500(0.0574)

= 28.705 feet

The **speed** will be:

= 28.705 / 1.75

= 16.403 ft/s

= 12.3 mph

Learn more about **distance** on:

brainly.com/question/26550516

#SPJ1

the weights of medium oranges packaged by an orchard are normally distributed with a mean of 14 oz and a standard deviation of 2 oz. 1 orange is randomly selected. what is the probability that this orange weighs more than 17 oz?

The** probability** that an orange **weighs** more than 17 oz is 0.1587.

The **probability **that an orange weighs more than 17 oz is 0.1587. This value can be calculated using the Z-score formula, which is used to calculate the probability of an** event occurring.** The formula is as follows:

Z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

In this case, the **Z-score** is (17 - 14) / 2 or 1.5. We can find the probability using the Z-score table, which gives us 0.1587, the probability that an orange weighs more than 17 oz.

The Z-score formula is useful for determining the probability of an event occurring when the data follows a normal distribution. Knowing the mean and** standard deviation**, we can calculate the likelihood of a certain outcome occurring. In this case, the probability that an orange weighs more than 17 oz is 0.1587.

Learn more about ** probability **here;

https://brainly.com/question/11234923

#SPJ4

Find the value of X:

A. 24

B. 48

C. 40

D. 960

**Answer:**

B

**Step-by-step explanation:**

given a line parallel to a side of a triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

[tex]\frac{32}{x}[/tex] = [tex]\frac{20}{30}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2x = 3 × 32 = 96 ( divide both sides by 2 )

x = 48

What is (1/243) ^-x/3 = 4

Using the **log**, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

The power to which a number must be increased in order to obtain another number is known as a **logarithm**.

For instance, the logarithm of 100 in base ten is 2, since ten **multiplied **by two equals 100: log 100 = 2, since 102 = 100.

So, solve using a log as follows: (1/243) ^-x/3 = 4

[tex]\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}[/tex]

Therefore, using the **log**, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

Know more about **logarithms **here:

**https://brainly.com/question/25710806**

#SPJ1

I nee help with this

**Answer: MHT = 125; AHM = 55**

**Step-by-step explanation:**

(2x + 11) + (6x - 7) = 180 since they are supplementary angles

8x + 4 = 180 ---- subtract 4 on both sides

8x = 176 ---- divide by 8 on both sides

x = 22

MHT = 6x - 7

6(22) - 7 = 132 - 7 = 125

AHM = 2x + 11

2(22) + 11 = 44 + 11 = 55

The planet Neptune orbits the Sun. Its orbital radius is 30.1 (AU)

Assuming Neptune's orbit is circular, what is the distance it travels in a single orbit around the Sun?

Give your answer in terms of π

Answer:The distance that Neptune travels in a single orbit around the Sun is approximately 188.49 AU

Step-by-step explanation:To calculate the distance that Neptune travels in a single orbit around the Sun, we can use the formula for the circumference of a circle, which is given by 2 * π * r, where r is the radius of the circle.

In this case, the radius of Neptune's orbit is 30.1 AU, so the circumference of the circle can be calculated as follows:

2 * π * 30.1 = 188.49

To learn more about Distance,

https://brainly.com/question/12006508

Step-by-step explanation:To calculate the distance that Neptune travels in a single orbit around the Sun, we can use the formula for the circumference of a circle, which is given by 2 * π * r, where r is the radius of the circle.

In this case, the radius of Neptune's orbit is 30.1 AU, so the circumference of the circle can be calculated as follows:

2 * π * 30.1 = 188.49

To learn more about Distance,

https://brainly.com/question/12006508

Teresa volunteers 0.9 hours each day. If she volunteered for a total of 27.9 hours, for how many days did she volunteer?

**Answer:**

31

**Step-by-step explanation:**

27.9/0.9 = 31

If Teresa volunteers 0.9 hours each day, we can find the number of days she volunteered by dividing the total number of hours by 0.9:

number of days = 27.9 hours / 0.9 hours/day = 31 days

So Teresa volunteered for 31 days

number of days = 27.9 hours / 0.9 hours/day = 31 days

So Teresa volunteered for 31 days

ABCD is a kite with AB = BC and AD = DC = AC, the size of

The **size** of **angle** BCA is 45 **degrees**

A **quadrilateral **called a kite has two pairs of **sides **that are each the same **length** and are next to one another.

Where the **two uneven** sides **meet**, the two **angles** are **equal**. It can be thought of as two congruent triangles sharing a base. It has two diagonals that right-angle intersect with one another.

Given:

From the Figure we can see that

AB = BC and AD = DC = AC

and, ABC = 90 **degrees**

Now, In triangle ABC using** Angle sum Property**

A + B + C = 180

So, A + 90 + C = 180

A + C = 90

As, AB = BC

Then, 2C = 90

C = 45

Hence, the **angle **is 45 degrees

Learn more about **Kites **here:

https://brainly.com/question/30680165?

#SPJ9

The Question attached here seems to be incomplete/ inappropriate. The complete Question is:

ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle BCA

Melody had 120 stamps more than Jeremy. After Melody gave 30 stamps to Jeremy, she had twice as much as him. How many stamps do they have altogether?

melody had 120 stamps.

and she gave Jeremy 30 stamps .

so she had 90 stamps now.

after she gave Jeremy 30 stamps,she had twice as much as him.

so 90 is 45+45 .other way 45 is half of 90.

so Jeremy had 45 stamps now.

they have altogether 90+45=135 stamps.

the answer is 135

Final answer:

By creating and solving an algebraic equation, we learn that Jeremy started with 60 stamps and Melody started with 180 stamps. Therefore, they originally had 240 stamps combined.

Explanation:We'll use algebra to solve this. Let's let Jeremy's number of stamps be represented by **J**. According to the information, Melody had 120 more stamps than Jeremy before she gave him 30, so she had **J + 120** stamps. After transferring the 30 stamps, she has **J + 120 - 30** stamps, which simplifies to **J + 90** stamps. According to the problem, this amount is twice the amount Jeremy has after receiving the 30 stamps (**J + 30**). So, we can set up this equation: 2(J + 30) = J + 90.

Solving this equation gives **J = 60**. That means Jeremy started with 60 stamps. Therefore, Melody started with 60 + 120 = **180 stamps**. The total number of stamps both had originally is 60 + 180 = **240 stamps**.

https://brainly.com/question/32436021

#SPJ2

For an experiment, the temperature of a liquid must stay above 60°F . The starting temperature of the liquid is 90°F . It is placed in a cooler, which lowers its temperature 3°F each minute.

The liquid should be in the cooler less than 10 **minutes**. Therefore, option C is the correct answer.

A thermometer can be used to measure the degree of hotness or coolness that is present. It also expresses the **rate** of motion of a substance's atoms and molecules. The Fahrenheit, Celsius, and Kelvin thermometers measure temperature in degrees.

Given that, the **temperature** of a liquid must stay above 60° F.

The starting temperature of the liquid is 90° F.

Difference in temperature = 90-60

= 30

It is placed in a cooler, which lowers its temperature 3° F each minute.

= 30/3

= 10° F

Therefore, option C is the correct answer.

Learn more about the **temperature** here:

https://brainly.com/question/21031825.

#SPJ9

"Your question is incomplete, probably the complete question/missing part is:"

For an experiment, the temperature of a liquid must stay above 60°F. The starting temperature of the liquid is 90°F . It is placed in a cooler, which lowers its temperature 3°F each minute. Let m represent the number of minutes the liquid is in the cooler. Which statement determines how many minutes the liquid can stay in the cooler?

A) The liquid must be in the cooler fewer than 10 minutes.

B) The liquid must be in the cooler fewer than 15 minutes.

C) The liquid must be in the cooler fewer than 30 minutes.

D) The liquid must be in the cooler fewer than 60 minutes.

Given the expression: 10x2 + 25x − 15

Part A: What is the greatest common factor? Explain how to find it. (3 points)

Part B: Factor the expression completely. Show all necessary steps. (5 points)

Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)

Part A: The **greatest common factor** of [tex]10x2 + 25x − 15[/tex] is 5.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex].

Part C: The factoring from Part B is correct, as **multiplying** the two binomials in the parentheses yields [tex]2x2 + 5x − 3[/tex].

Part A: The **greatest common factor** of [tex]10x2 + 25x − 15[/tex] is 5. The greatest common factor (GCF) of a set of numbers is the largest number that is a factor of all numbers in the set. To find the GCF, first list all the factors of each number. The common factors among the numbers are the ones that are found in each **list of factors**. The largest number in the list of common factors is the GCF.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex]. To factor this expression, first identify the GCF, which is 5. Then divide the expression by 5 and factor the result. Since the result is a binomial, use the difference of squares formula, (x + a)(x − a). The resulting expression is then[tex]5(2x2 + 5x − 3[/tex]).

Part C: To check the factoring from Part B, multiply the two binomials in the **parentheses**. The result is [tex]2x2 + 5x − 3[/tex], which is the same as the original expression. To multiply, use the FOIL method. Multiply the First terms [tex](2x2 and 2x2)[/tex], the Outer terms[tex](2x2 and -3)[/tex], the Inner terms (5x and 2x), and the Last terms [tex](5x and -3)[/tex]. The resulting expression is [tex]2x2 + 5x − 3.[/tex]

Learn more about **greatest common factor **here:

https://brainly.com/question/11221202

#SPJ1

A daycare center in Burlington

currently has 8 assistant caregivers

and 5 senior caregivers. Since demand

is high, the owner is going to be hiring

3 assistant caregivers per month and

4 senior caregivers per month. Her

goal is to have a larger staff, including

an equal number of assistant

caregivers and senior caregivers. How

long will that take? How many of each

type will there be?

The** number of months** it will take to have same number of caregivers is 3 **months** .And there will be of 17 caregivers of each type.

**What is an equation?**

An **equation** is an **expression** with **variables** and **constant** having an **equality sign**. The **degree** of equation can be one or more than one.

We are given that initially there are 8 assistant caregivers

and 5 senior caregivers.

And the owner is going to be hiring 3 assistant caregivers per month and

4 senior caregivers per month.

Hence the number of total assistant caregivers after n months will be

3n +8

And the number of senior caregivers after **n** months will be 4n+ 5

To find n we **equate** the two

3n + 8 = 4n+5

n =3

Hence after 3 months there will be same number of assistant and senior caregivers

And the total number of assistant and senior caregivers is 3(3)+8 = 17

The number of months it will take to have same number of caregivers is 3 months .And there will be of 17 caregivers of each type.

Given below is a sample of **equation** please refer the link

https://brainly.com/question/17145398

#SPJ1

Lina is older than her cousin Sarika. This year the sun or their ages is 31, and the difference between their ages is 5. Which system of equations correctly represents the situations where L represents Linas age and S represents sarikas age

The **system of equations** that correctly represents the situation of Lina and Sarika's ages are:

A **system of equations** is two or more **equations** solved concurrently or at the same time.

A system of equations is called **simultaneous equations**.

The sum of Lina and Sarika's ages = 31

Lina's age > Sarika's by 5 years

Let Lina's age = L

Let Sarika's age = S

L + S = 31... Equation 1

L - S = 5... Equation 2

2L = 36

L = 18.

**Substituting** L = 18 into either **Equation** 1 or 2:

18 + S = 31

S = 31 - 18

S = 13

Learn more about **simultaneous equations** at https://brainly.com/question/148035.

#SPJ1

Sophie needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $127 for parts. The total was $227. Write and solve an equation which can be used to determine

x, the cost of the labor per hour.

**Answer:**

**Step-by-step explanation:**

(227-127)/4=x

"/" means divide.

90 points for helping! Need a explanation as well.

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]2y+3x=1\implies 2y=-3x+1\implies y=\cfrac{-3x+1}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+\cfrac{1}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3} \implies \cfrac{2}{ 3 }}}[/tex]

so we're really looking for an equation whose slope is 2/3

[tex]{\Large \begin{array}{llll} y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+\cfrac{5}{2} \end{array}} \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

the number of students enrolled at a college is 15 000 and grows 3% each tear. what will be the estimated population of the school in 6 yeears

The expected student **population** of the school will be N(t) = 15000*(1+3%)6=17910.78.

The term "**population"** refers to all citizens who are either permanently residing in a country or who are just passing through. Growth rates are the **population **changes that occur each year as a result of births, deaths, and net **migration. **The world population clock maintained by the US Census Bureau indicated that there were 7,922,312,800 people on the planet as of September 2022, and that number would rise to 8 billion by mid-November. **China **and India will have the two largest populations in the world in 2022, followed by the **United States,** the European Union, Indonesia, and **Pakistan**.

Learn more about **population** from

brainly.com/question/29885712

#SPJ4

90% of 40 is

О 24

О 20

О 35

О 36

The answer is 36 because if u take what 90% of 40 is then u get 36! Hope this helped

Answer: 36

Explanation: 90/100 * 40

3600÷ 100=36

Explanation: 90/100 * 40

3600÷ 100=36

Pls show your work thank you will mark the Brainliest

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

According to given information ~

[tex]\qquad \sf \dashrightarrow \: g(x) = 11(1.2) {}^{x} [/tex]

if x = 1;

[tex]\qquad \sf \dashrightarrow \:g(1) = 11(1.2)[/tex]

[tex]\qquad \sf \dashrightarrow \:g(1) = 11(1 + 0.2)[/tex]

[tex]\qquad \sf \dashrightarrow \:g(1) = 11 + (0.2 \times 11)[/tex]

[tex]\qquad \sf \dashrightarrow \:g(1) = 11 + ( \frac{20}{100} \times 11)[/tex]

[tex]\qquad \sf \dashrightarrow \:g(1) = 11 + ( {20}\% \: \: of \: \: 11)[/tex]

So, there's an increase of 20% in insect population each month.

What is the probability of choosing a green in 4 red marbles, 10 blue marbles, 7 green marbles, 6 yellow marbles

What is the probability of me choosing a green???

The probability of choosing a green marble out of the 4 red marbles, 10 blue marbles, 7 green marbles, and 6 yellow marbles is 7/27 or 0.25925925925925924.

1000m divide by 100n written in form of 10z

The **expression** 1000m ÷ 100n in the **form** of 10z is 10m/10n, which **simplifies** to m/10n.

**What is an expression?**

In **mathematics**, an **expression** is a **combination** of one or more **numbers, variables**, and **operations** such as **addition**, **subtraction**, multiplication, division, exponentiation, and so on.

We can simplify the expression 1000m ÷ 100n as follows:

1000m ÷ 100n = (1000 ÷ 100) × (m ÷ n)

= 10 × (m ÷ n)

= 10m/n

To write this in the form of 10z, we need to find a value of z that makes 10z equal to 10m/n. Since 10z is equal to 10 times z, we can set 10 times z equal to 10m/n and solve for z as follows:

10z = 10m/n

Dividing both sides by 10, we get:

z = m/10n

Therefore, the **expression** 1000m ÷ 100n in the **form** of 10z is 10m/10n, which **simplifies** to m/10n.

To learn more about the **expression**, visit:

https://brainly.com/question/723406

#SPJ1

2. Find x in the triangle below

We can see that the **triangle is equilateral**, thus, the value of x is 13.

We can see that it is a **right triangle**, and we know the value of one of the catheti and one of the angles.

Remember that the sum of the interior angles must be equal to 180°.

So if we have a right angle and a 45° angle, then the measure of the remaining angle is:

a = 180° - 90° - 45° = 45°

So we have an **equilateral triangle**, thus, the measure of x must be 13 units.

Learn more about **equilateral triangles** at:

https://brainly.com/question/17264112

#SPJ1

**Answer: 13 **

**Step-by-step explanation: Just took the test**

hich statements describe the length of the sides of an isosceles right triangle if one leg is 6√2 feet? Select all that apply.

The length of the other leg is 6 feet.

The length of the hypotenuse is 12 feet.

The length of the hypotenuse is 6 feet.

The length of the other leg is 6√2 feet.

The **correct statements **are:

The **length **of the other leg is 6√2 feet.

The length of the **hypotenuse **is 12 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the **square **of the **hypotenuse** is equal to the **sum **of the **squares **of the other two sides of a triangle.

Given:

One leg of an isosceles triangle is 6√2 feet.

As, we know **isosceles **triangle two of its **sides** **equal **in length then the other side can be 6√2 feet.

Now, using **Pythagoras theorem**

H² = P² + B²

H² = (6√2)² + (6√2)²

H² = 72 + 72

H² = 144

H= 12 units

The statements that applies here are:

The **length **of the other leg is 6√2 feet.

The length of the **hypotenuse **is 12 feet.

Learn more about **Pythagoras theorem** here:

https://brainly.com/question/343682

#SPJ1

**Answer:**

The answer is B and D

**Step-by-step explanation:**

I took the test.

let me know if you would like an explanation down in the comments!

the blood pressure in millimeters was measured for a large sample of people. the average pressure is 140 mm, and the sd of the measurements is 20 mm. the histogram looks reasonably like a normal curve. use the normal curve to estimate the following percentages.

The **percentage **of people with **blood pressure** between 115 and 165 mm is 68.27% (closest to option e). The percentage of people with blood pressure between 140 and 165 mm is 89.4% (closest to option b). The percentage of people with blood pressure over 165 mm is 10.6% (closest to option a).

To solve this problem, we can use the properties of the **normal distribution**, which is a continuous probability distribution that is often used to model real-world data. In particular, we can use the **empirical rule** (also known as the 68-95-99.7 rule) to estimate the percentages of people with blood pressure within certain ranges. The **empirical rule** states that, for a normal distribution:

Approximately 68% of the **data **falls within one **standard deviation** of the mean. Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard deviations of the mean. Using this rule, we can estimate the following percentages: The percentage of people with blood pressure between 115 and 165 mm: First, we need to find the **z-scores** for the lower and upper limits of the range: z_lower = (115 - 140) / 20 = -1.25.

z_upper = (165 - 140) / 20 = 1.25

We can then use a **standard normal distribution** table or a calculator to find the areas under the **curve corresponding** to these z-scores:

P(-1.25 < Z < 1.25) = 0.7887 - 0.1056 = 0.6831

So, approximately 68.31% of people have blood pressure between 115 and 165 mm.

The percentage of people with blood pressure between 140 and 165 mm: In this case, the lower limit is equal to the mean, so we only need to find the z-score for the upper limit: z_upper = (165 - 140) / 20 = 1.25

Using the same approach as before, we get:

P(Z < 1.25) = 0.8944

So, approximately 89.44% of people have blood pressure between 140 and 165 mm. The percentage of people with blood pressure over 165 mm:

In this case, we only need to find the area to the right of the **upper limit**:

P(Z > 1.25) = 0.1056

So, approximately 10.56% of people have blood pressure over 165 mm.

To learn more about **normal distribution** click here

brainly.com/question/29509087

**#SPJ4**

Complete Question

The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.

a. 10.6%

b. 89.4%

c. 39.4%

d. 78.8%

e. 68.27%

___ The percentage of people with blood pressure between 115 and 165 mm.

___ The percentage of people with blood pressure between 140 and 165 mm.

___ The percentage of people with blood pressure over 165 mm.

sita had 4^x . she want to buy a copy at (3*2^x+3) .she needed rs 128 more than how muc she had at the beggning

In the **beginning**, Sita had Rs. 64 to start with.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the **same base **value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

From the given information the equation can be formed as,

4ˣ + 128 = 3.2⁽ˣ⁺³⁾.

2²ˣ + 2⁷ = 3.2⁽ˣ⁺³⁾.

Putting some **arbitrary **values of 'x' we gey at x = 3,

64 + 128 = 3.64.

So, In the beginning, she had 4³ rs which is 64 rs.

learn more about **exponents **here :

https://brainly.com/question/5497425

#SPJ9

in a sequence the first term is 4 and the common difference is 3

**Answer:a=3, d=common difference=3, a2=7, ****a3=9**

**Step-by-step explanation:**

firstly we have given a,d (using the arithmetic progression formula)

( an=a+(n-1) )

so we have made a sequence a2=a+d=7

a3=a+2d=9

Please help me it’s a drag and drop

**Answer:**

1. identify the constant you will need to multiply each equation by to eliminate x

2. multiply all terms by -3 in equation 1

3. multiply all tems by 5 in equation 2

4. add the sum of the equation together to eliminate x

Explanation:1. identify the constant you will need to multiply each equation by to eliminate x

2. multiply all terms by -3 in equation 1

3. multiply all tems by 5 in equation 2

4. add the sum of the equation together to eliminate x

According to a recent study, 21% of peanut M&M's are brown, 13% are yellow, 3% are red, 24% are blue, 16%

are orange, and 24% are green. Assume these proportions are correct and suppose you randomly select four

peanut M&M's from an extra-large bag of the candies. Calculate the following probablities. Also calculate

the mean and standard deviation of the distribution. Round all solutions to four decimal places, if

necessary.

Compute the probability that at most two of the four M&M’s are yellow

P(x<=2)=

The **probability** that at most four of the M&M are yellow is 0.3357 and the **probability** that at least two of the four of the M & M are yellow is 0.6622

The** probability **that at most two of the four M&M's are yellow can be calculated using the cumulative distribution function (CDF) of the binomial distribution. The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. In this case, the number of trials is 4, and the probability of success (getting a yellow M&M) is 0.13.

The cumulative distribution function of the **binomial distribution** can be expressed as:

P(X <= k) = SUM[i=0 to k] (n choose i) * p^i * (1-p)^(n-i)

Where n is the number of trials, k is the value we want to find the probability for, p is the probability of success, and (n choose i) is the number of combinations of n items taken i at a time, which can be calculated as n! / (i! * (n-i)!).

For this problem, we want to find the sum of probabilities for X = 0, 1, and 2, so we have:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (4 C 0) * (0.13)^0 * (0.87)^4 + (4 C 1) * (0.13)^1 * (0.87)^3 + (4 C 2) * (0.13)^2 * (0.87)^2

= 0.3357

NB: "C" represent combination.

So the probability that at most two of the four M&M's are yellow is approximately 0.3357.

b. The probability that at least two of the four M&M's are yellow can be found by subtracting the probability of getting 0 or 1 yellow M&M's from 1. So:

P(X >= 2) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((4 C 0) * (0.13)^0 * (0.87)^4 + (4 C1) * (0.13)^1 * (0.87)^3)

= 0.6622

So the probability that at least two of the four M&M's are yellow is approximately 0.6622.

The mean of the distribution is given by n * p = 4 * 0.13 = 0.52, and the standard deviation is given by sqrt(n * p * (1-p)) = sqrt(4 * 0.13 * 0.87) = 0.9304.

learn more on** binomial distribution** here;

https://brainly.com/question/9325204

#SPJ1

What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails? (1 point)

• a

• b

The experimental probability is closer to the theoretical probability for group Y than group X.

The experimental probability and the theoretical probability for group X is the same.

• с

• d

The experimental probability and the theoretical probability for group Y is the same.

The experimental probability is closer to the theoretical probability for group X than group Y.

The correct statement regarding the **probabilities **is given as follows:

**d.** The experimental probability is closer to the theoretical probability for group X than group Y.

A probability is calculated as the **division **of the **desired **number of outcomes by the **total **number of outcomes.

For the **theoretical **probability, a coin is equally as likely to be heads or tails, hence for each group they are given as follows:

p = 1/2 = 0.5 = 50%.

The **experimental **probabilities for obtaining heads in each group are given as follows:

More can be learned about **probability **at https://brainly.com/question/24756209

#SPJ1

two dice are rolled in a random experiment. (a) what is the probability that at most one is a six? (1 point) (b) if the two faces are different, what is the probability that at most one is a six?

a) The probability that at most one is a six is **5/6.**

b) The **probability** that at most one is a six is** 2/3.**

In the question two dice are rolled in a** random experiment **and we have to find what is the probability that at most one is a six and if the two faces are different, what is the probability that at most one is a six.

a) The probability that at most one is a six is** 5/6**. There are only 6 possible outcomes when rolling two dice, and 5 of those outcomes involve at most one six: (1,2), (1,3), (1,4), (1,5), (2,5).

b) The probability that at **most one **is a six is 2/3. If the two faces are different, there are only 3 possible outcomes: (1,2), (2,3), (3,4). 2 of those outcomes involve at most one six: (1,2), (2,3). Thus, the **probability **is 2/3.

To learn more about **probability **link is here:

brainly.com/question/30034780

#SPJ4

Find the value of x. Round to the

nearest tenth.

X

12

x= [?]

Enter

**Answer: 2x + 12 **

**Step-by-step explanation:**

How do you find the measure of each angle indicated? m

10x+9x-9+6x-11+10x-5 = 360

19x-20+16x-5 = 360

35x-25=360

Divide by 5

7x-5=72

7x=77

X=11

Then just plug in x for each angle! Hope this helps!

19x-20+16x-5 = 360

35x-25=360

Divide by 5

7x-5=72

7x=77

X=11

Then just plug in x for each angle! Hope this helps!

which of the following statements are true about interscholastic athletics? (select all that apply.) interscholastic athletics should be part of the educational mission of the school the teacher/coach is the most influential person in the lives of many students it is important to be professional in all aspects of your coaching the teacher/coach has a responsibility to maximize the physical, social, personal and psychological development and competitive success of his/her students
This next question is a little bit tricky, but keep in mind the Disney World / Bush Gardens example from the lectures. What is the probability that someone uses a cell phone while driving or had no speeding violation? Find the probability that someone uses a cell phone while driving, add to that the probability that someone did not receive a speeding violation, then subtract the value in the square where those two overlap. Round your answer to the hundredths place.
on sundays tucker pickes up donuts for his family.he take $25 with him and a box of dozen donuts cost $6.50 fill in the equation thats represent the relationship between how much money tucker brought and how many boxes of donuts (d) he can buy
Whats the correct answer answer asap for brainlist
the attraction of a person's body toward earth is called weight. the reaction to this force is the earth's surface pushing against the person's body. the person's body pushing against earth's surface. the person's body pulling on the earth. none of these
1. if you want to measure voltage across on a resistor connected to a 5v dc power supply, which two jacks of the dmm should be used? where do you set the function/range knob? which voltage range should be selected?
select the correct answer. which markup language is useful to create cross-platform mobile applications and is flexible to run on tables, smart phones, and computer? a. html5 b. xml c. html d. xhtml
henderson air used to source all of their supplies from three suppliers. however, to remain competitive in recent years, henderson has started to source supplies from more suppliers in order to obtain the best prices. some of these suppliers are overseas. as a result, the firm's inventory levels:
which one of the following energy conversion devices has the highest energy efficiency? group of answer choices incandescent light bulb automobile engine steam turbine generator
the bilingual brain may provide some resistance to . group of answer choices autism spectrum disorders neurocognitive disorder due to alzheimer's disease depression and anxiety learning disabilities like dyslexia
A function is given.g(x) = 1 34x; x = 4, x = 3(a) Determine the net change between the given values of the variable.(b) Determine the average rate of change between the given values of the variable.
excavation costs are based on theA. amount of earth removedB. depth of the frost line in the areaC. time involved multiplied by a standard rateD. sophistication of the machinery necessary
PLEASE HELP WILL GIVE BRAINLIEST!!!!!Decisions made about quantities are:a/ best made using the marginal principle.b/ optimal when costs equal benefits.c/ the same as making either/or decisions.d/ best made when comparing prices and costs.
in the vector diagram below, the magnitude of A is 15m, the magnitde of B is 18m and the magnitude of C is 6m. Find the resultant vector using component method. Angle A = 35 Angle B = 30 Angle C = 50.
Select the best translation for the following term or phrase:There was a farmer.Haba un perro.La planta est madura.Y brill el sol.Haba un campesino.
The given tessellation formed by two or more regular polygons is shown.
Which of the following is the clearest example of a question that might be found on a push poll?a. Are you familiar with Rosemary Austin's voting record on tax subsidies for energy producers?b. Would you approve or disapprove of the job that Rosemary Austin is doing if you knew that she never even reads the legislation before voting to spend your tax dollars?c. Do you plan to vote for Rosemary Austin for the House of Representatives this November?d. Do you approve or disapprove of the job that Rosemary Austin is doing?
you wish to retire a millionaire in 40 years. you invest in small cap stock expecting to earn 16% per year compounded monthly. what amount must you invest per month to reach one million dollars in 40 years?
What can you say about the heat flow based on the diagram above between the mug of hot chocolate and hand? What about heat flow from the hand to the ice cube? Where is the heat released and absorbed ? Which object releases and absorbs heat? what arrow best represents this heat flow?
Please answer all questions