The probability that an adult is actively looking for a job is 0.18. The probability of an adult being unemployed and actively looking for a job is 0.04. What is the probability of an adult being unemployed given that they are actively looking for a job?

Answers

Answer 1

The probability of an adult being unemployed given that they are actively looking for a job is 0.22.

How to calculate the probability?

It should be noted that probability gas to do with the likelihood that something will occur.

Remember the multiplication rule for conditional probability:

P(B AND A)=P(B|A)P(A)

Rearranging, we see thatP(B|A)=P(B AND A)P(A)

So if we think of A as being the event that an adult is actively looking for a job and B as the event that an adult is unemployed, then we can plug in the known information to find

P(B|A)=0.04 + 0.18

≈0.22

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Related Questions

Find all X such that -13 < 5x - 3 ≤ 17.

Answers

Answer:

-5  < x < 17/5

Step-by-step explanation:

add three onto all sides -10 < 5x < 17

then divide all sides by -5  < x < 17/5

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 17.6 inches, andstandard deviation of 3.3 inches.If 37 items are chosen at random, what is the probability that their mean length is greater than 18.9 inches?(Round answer to four decimal places)Question Help: D VideoSubmit Question

Answers

Answer:

The probability is 0.9999

Explanation:

Given that the mean is 17.6 inches

standard deviation is 3.3/37 = 0.089

We have:

z(18.9)

[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\frac{18.9-17.6}{0.089}=14.6067[/tex]

Now, we have

P(x > 18.9) = P(z > 14.6067)

= 0.9999

z(0.394) = 0.6532

True or false?
Raising prices is the quickest way to resolve excess demand.

Answers

Answer:

this is true

Step-by-step explanation:

diagram 10 shows a straight line PQ with point P(-4,9) and Q(12,1).

Answers

We have a line defined by two points, P(-4,9) and Q(12,1).

Knowing two points of the line, we can calculate the slope with the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In this case, the slope will be:

[tex]\begin{gathered} m=\frac{y_Q-y_P}{x_Q-x_P} \\ m=\frac{1-9}{12-(-4)}=\frac{-8}{12+4}=-\frac{8}{16}=-\frac{1}{2} \end{gathered}[/tex]

With the slope and one point we can express the equation in slope-point form:

[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-y_Q=m(x-x_Q) \\ y-1=-\frac{1}{2}(x-12) \\ y=-\frac{1}{2}x+\frac{12\cdot1}{2}+1 \\ y=-\frac{1}{2}x+6+1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]

The x-intercept is the value of x that makes the function f(x) become 0.

In this case, we have to find x so that y = 0.

We can replace y in the equation and calculate x as:

[tex]\begin{gathered} y=0 \\ -\frac{1}{2}x+7=0 \\ -\frac{1}{2}x=-7 \\ x=-7\cdot(-2) \\ x=14 \end{gathered}[/tex]

Then, for the x-intercept is x = 14.

Answer:

a) The equation of the line is y = (-1/2)*x+7

b) The x-intercept is x = 14.

customer account “numbers” for a certain company consists of 4 letters followed by 2 single digit numbers. how many different account numbers are possible if repetitions of letters and digits are allowed?

Answers

[tex]26^4\cdot\: 10^2=26^4\cdot\: 100=45697600[/tex]

On a recent trip, Carol's car used 7/8 of a tank of gasoline. Which decimal and percentrepresents this amount?

Answers

The fraction of gasoline used is:

[tex]\frac{7}{8}[/tex]

We need to convert this fraction to decimal and to percentage to find the answer.

Converting 7/8 to decimal:

For this we have to do the division between 7 and 8:

Thus, the decimal form of 7/8 is 0.875

Converting 7/8 to percentage:

we use the result that we previously get of 7/8 as a decimal: 0.875, and to convert it to percentage we multiply it by 100:

[tex]0.875\times100=87.5[/tex]

7/8 to percentage is equal to 87.5%

Answer: 0.875 and 87.5%

can somebody please help me with this question

Answers

Answer:

  U'(12, 15)

Step-by-step explanation:

Given point U(4, 5) is part of figure STUVW that is dilated by a factor of 3 about the origin, you want the coordinates of U'.

Dilation

Dilation about the origin multiplies each coordinate value by the scale factor:

  U' = 3U

  U' = 3(4, 5) = (12, 15)

The coordinates of U' are (12, 15).

A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after 5 years?Use the calculator provided and round your answer to the nearest whole number.

Answers

Answer:

The population after 5 years is approximately 337,465 people

Explanation:

The population of the city is 250,000

Annual growth rate is 6%

The population after t years is:

[tex]P=P_oe^{rt}[/tex]

After 5 years, t = 5 and the population becomes:

[tex]\begin{gathered} P=250000e^{\frac{6}{100}\times5} \\ \\ =250000e^{0.3} \\ \\ \approx337465 \end{gathered}[/tex]

The population after 5 years is approximately 337,465 people

Given a pair of points on each line. use the slope formula to determine whether AB and CD are para el perpendicular, or neither. GH: G(14, 13) and H(-11,0) RS: R(-3, 7) and S(-4,-5)

Answers

1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula

And R(-3,7) , S(-4,-5)

Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that neither that line is parallel nor perpendicular.

3) So the answer is GH is not parallel nor perpendicular.

Part A find the value of each variable
x=14, y=15
x=14, y=-5
x=24, y=-10
x=24, y-5
Part B
the angle measures?
100°
50°
80°
130°

Answers

Answer:

Part A:

Option 1

3x + 8 = 5x - 20 (vertically opposite angles)

2x = 28

x = 14

3x + 8 + 5x + 4y = 180° (adjacent angles on a straight line)

8x + 4y = 172

Substitute x = 14 into equation to find y.

8(14) + 4y = 172

4y = 60

y = 15

Hence, x = 14 and y = 15.

Part B:

Option 4

Unlabeled angle = 5x + 4y (vertically opposite angles)

Substitute x and y to find angle measure.

5(14) + 4(15) = 130°

Hence, measure of unlabeled angle is 130°.

A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?

Answers

A bird is flying above a tree. You are standing 40 feet away from the tree. The angle of elevation to the top of the tree is 32°, and the angle of elevation to the bird is 42°. What is the distance from the bird to the top of the tree?​

Let

A -----> you

B-----> a bird

C-----> top of the tree

see the following image

step 1

In the right triangle ABD

tan(42)=BD/AD

substitute given values

tan(42)=BD/40

BD=40*tan(42)

BD=36 ft

step 2

In the right triangle ACD

tan(32)=CD/AD

CD=AD*tan(32)

CD=40*tan(32)

CD=25 ft

step 3

Find the difference BD-CD

36-25=11 ft

therefore

the answer is 11 ft

what is the derivative of sqrt(9x^2-1)​

Answers

Answer:

900

Step-by-step explanation:

because I know answer

The answer would be 900

dentashboard/home
Town policy requires that a certain number of trees be planted for every tree that is cut down.
For example, if 8 trees are cut down, 48 trees will be planted. A homeowner is going to cut down
5 trees on his property.
Solve Problems with Ratios and Unit Rates-Instruction-Level F
How many trees will be planted when 5 are cut down?
Trees Planted
Trees Cut Down
48
8
5

Answers

This can be solved using ratio and proportions.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A ratio in mathematics illustrates how many times one number contains another.

First, we find the ratio of trees planted to trees cut

= 48/8 = 6

So, no. of trees to be planted when 5 trees are cut = 5x6 = 30

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A committee of 6 is to be chosen from the 28 students in a class. If there are 10 males and 18 females in the class, in how many ways can this be done if there must be at least three females on the committee? A: 339864B: 816720C: 3060D: 18564

Answers

Hello! First, let's write some important information contained in the exercise:

committee = 6 students

class: 28 students:

- 10 males

- 18 females

Let's consider the rule: At least three females must be on the committee, so we have some cases, look:

_F_ * _F_ * _F_ * __ * __ * __

1st option:

3 females and 3 males

_F_ * _F_ * _F_ * _M_ * _M_ * _M_

2nd option:

4 females and 2 males

_F_ * _F_ * _F_ * _F_ * _M_ * _M_

3rd option:

5 females and 1 male

_F_ * _F_ * _F_ * _F_ * _F_ * _M_

4th option:

6 females and 0 male

_F_ * _F_ * _F_ * _F_ * _F_ * _F_

Now, we have to use the formula below and find the number of possible combinations:

[tex]C_{n,p}=\frac{n!}{p!\cdot(n-p)!}[/tex]

Let's calculate each option below:

1st:

3 females:

[tex]C_{18,3}=\frac{18!}{3!\cdot(18-3)!}=\frac{18\cdot17\cdot16\cdot15!}{3\cdot2\cdot1\cdot15!}=\frac{4896}{6}=816[/tex]

3 males:

[tex]C_{10,3}=\frac{10!}{3!\cdot(10-3)!}=\frac{10\cdot9\cdot8\cdot7!}{3\cdot2\cdot1\cdot7!}=\frac{720}{6}=120[/tex]

3 females and 3 males: 816 * 120 = 97920

2nd option:

4 females:

[tex]C_{18,4}=\frac{18!}{4!\cdot(18-4)!}=\frac{18\cdot17\cdot16\cdot15\cdot14!}{4\cdot3\cdot2\cdot1\cdot14!}=\frac{73440}{24}=3060[/tex]

2 males:

[tex]C2=\frac{10!}{2!\cdot(10-2)!}=\frac{10\cdot9\cdot8!}{2\cdot1\cdot8!}=\frac{90}{2}=45[/tex]

4 females and 2 males: 3060* 45 = 137700

3rd option:

5 females:

[tex]C_{18,5}=\frac{18!}{5!\cdot(18-5)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13!}{5\cdot4\cdot3\cdot2\cdot1\cdot13!}=\frac{1028160}{120}=8568[/tex]

1 male:

[tex]C_{10,1}=\frac{10!}{1!\cdot(10-1)!}=\frac{10!}{1\cdot9!}=\frac{3628800}{362880}=10[/tex]

5 females and 1 male = 8568 * 10 = 85680

4th option:

6 females and 0 male:

[tex]C_{18,6}=\frac{18!}{6!\cdot(18-6)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13\cdot12!}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot12!}=\frac{13366080}{720}=18564[/tex][tex]C_{10,0}=\frac{10!}{0!\cdot(10-0)!}=\frac{10!}{10!}=1[/tex]

6 females and 0 male: 18564 * 1 = 18564

To finish the exercise, we have to sum the four options:

97920 + 137700 + 85680 + 18564 = 339864

So, right answer A: 339864.

Function g is a transformation of the parent function f(x) = x2. The graph of fis reflected across the x-axis, and then translated left 4 units anddown 2 units to form the graph of gWrite the equation for g in the form y = ax2 + bx + cO A. y = -x2 + 8x + 14O B. y = -x2 - 8x - 18O C. y = x2 - 8x + 18O D. y = -x2 - 8x + 14

Answers

The parent function is given as:

f(x) = x²

y = x²

The graph is reflected across the x - axis

The x axis remains the same but the y axis is negated

g(x) = -x²

It is translated 4 units left

The function g(x) becomes

g(x) = -(x - 4)²

It is the translated 2 units down

g(x) = -(x - 4)² - 2

Simplifying the above equation:

g(x) = - (x² - 8x + 16) - 2

g(x) = -x² + 8x - 16 - 2

g(x) = -x² + 8x - 18

The line of best fit is given as y = 9 - 3x. Find the value of y when x = -3.091827

Answers

Solution

We are given the equation

[tex]y=9-3x[/tex]

We want to find y when x = -3. We only need to put x = -3

[tex]\begin{gathered} y=9-3x \\ y=9-3(-3) \\ y=9+9 \\ y=18 \end{gathered}[/tex]

Therefore, the answer is

[tex]\begin{equation*} 18 \end{equation*}[/tex]

MATHEMATICAL PHRASES_____5. the quatient of y and seven is eight_____6. thrice a number is eighteen_____7. the sum of twice a number and five is nine_____8. a number decreased by seven is twenty-eight

Answers

Explanation

Part A: The quotient of y and seven is eight.

Answer: y/7 =8

Part B: Thrice a number is eighteen

Answer: 3x = 18

Part C: The sum of twice a number and five is nine

Answer: 2x+5 =9

Part D: A number decreased by seven is twenty- eight

Answer: x-7 =28

Colleen truman earns 5% commission on all sales in june her sales totaled 54,000$ how much did she earn in commission?

Answers

The amount earned as commission in the month of June is $2700

How to determine the amount earned as commission?

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

Commission percentage = 5%

Total sales in the month of June = $54000

The amount earned as commission in the month of June is then calculated as

Amount = Commission percentage x Total sales in the month of June

Substitute the known values in the above equation

So, we have

Amount = 5% x 54000

Evaluate

Amount = 2700

Hence, the commission amount is $2700


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A model of Spaceship Earth, a major tourist attraction at Epcot Center in Florida, is a sphere whose diameter is approximately 5 inches.The volume of the model sphere is approximately ___ cubic inches.Use 3.14 for pi. Round only your final answer to the nearest hundredth.

Answers

The Volume of the model sphere is given as

[tex]V_{\text{sphere}}=\frac{4}{3}\pi r^3[/tex]

Given that the diameter is 5inches, the radius will be

[tex]\begin{gathered} \text{diameter,d}=2\times radius \\ r=\frac{d}{2}=\frac{5}{2}\text{inches} \\ r=2.5\text{inches} \end{gathered}[/tex]

substituting r in the formula will give

[tex]\begin{gathered} V_{\text{sphere}}=\frac{4}{3}\times3.14\times(2.5)^3 \\ =\frac{4}{3}\times3.14\times76.765625 \\ =\frac{964.17625}{3} \\ =321.3922\text{cubic inches} \end{gathered}[/tex][tex]V_{\text{sphere}}=321.39\text{cubic inches}[/tex]

Hence, the volume of the model sphere is approximately 321.39 cubic inches

Two motorcycle dealers sell the same motorcycle for the same original price. Dealer A advertises that the motorcycle is on sale for 7.5% off the original price. Dealer B advertises that it is reducing the motorcycle’s price by $599. When Bonnie compares the sale prices of the motorcycles in both dealers, she concludes that the sale prices are equal.
Let p represent the motorcycle’s original price.

Which equation models this situation?

0.075p = p − 599

0.925p = p + 599

0.075(p−599) = p

0.925p =

AND NO SPAM I WILL REPORT YOU AND BAN YOU IMMEADIATLEY AND HELP THIS IS DUE TODAY!! SO FAST PLS

Answers

Considering the definition of an equation, the equation 0.925p= p - 599 models the following situation: the sale prices of the motorcycles in both dealers are equal.

Definition of equation

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:

When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

Equation in this case

Being "p" the motorcycle’s original price, you know that:

Dealer A advertises that the motorcycle is on sale for 7.5% off the original price  → Sale price A= 100%×p - 7.5%×p → Sale price A= (100% - 7.5%)× p → Sale price A= 92.5%p → Sale Price A= 0.925p (expressed as decimals)Dealer B advertises that it is reducing the motorcycle’s price by $599. → Sale price B=p - 599

If the sale prices are equal, the equation in this case is:

Sale price A= Sale price B

0.925p= p - 599

Finally, the equation 0.925p= p - 599 represent the situation.

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The table and graph show the population or Oregon

Answers

From the given table, it is found that:

a. The average population decline was of 2,250 deer a year.

b. The population would have reached 225 thousand deer during the years of 2017 and 2018.

What is the average rate of change of a function?

The average rate of change of a function is given by the change in the output divided by the change in the input of the function. Hence, over an interval [a,b], the average rate of change is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In 1984 and 2018, the populations are given as follows:

1984: 250 thousand.2018: 173.5 thousand.

Hence the rate of change is given as follows:

r = (173.5 - 250)/34 = -2.25.

(2.25 thousand = 2,250).

For item b, the following linear function is built:

y = 230.5 - 1.45x.

The amount would be of 225 when:

230.5 - 1.45x = 225

1.45x = 5.5.

x = 5.5/1.45

x = 3.79.

Hence between the years of 2017 and 2018.

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Type the correct answer in type the answer in the box.Consider functions fand g.f(x)=(x+1)^3g(x) = 3sqrtx + 1Evaluate the function composition.(fg)(-64) = _

Answers

f(x) = (x + 1)^3

g(x) = cubic root x + 1

f(g)(x) =

[tex]\begin{gathered} f(g(x))\text{ = (3}\sqrt[]{x}+2)^3 \\ f(g(x))\text{ = x + 6(3}\sqrt[]{x})^2\text{ + 12(3}\sqrt[]{x})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(3}\sqrt[]{-64})^2\text{ + 12(3}\sqrt[]{-64})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(16) - 48 + 8} \\ f(g(-64))\text{ = -64 + 96 - 48 + 8} \\ f(g(-64))\text{ = 104 - 112} \\ f(g(-64))\text{ = -8} \end{gathered}[/tex]

result

f(g(-64)) = -8

What is the measure of a?
In the figure below, C D bisects ∠A C B
AB=B C
∠ B E C=90° and
∠D C E=42°
Find the measure of ∠A

Answers

The measure of "a" in the above-given right-angled triangle is 32°

What is a triangle?

Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Key properties of a right-angled triangle to note are:

One angle is always 90° or a right angle.The side opposite angle of 90° is the hypotenuse.The hypotenuse is always the longest side.The sum of the other two interior angles is equal to 90°.The other two sides adjacent to the right angle are called base and perpendicular.The Sum of all three interior angles is equal to 180°

To solve for "a" recall the following. It is given that:

AB = BC

∠BEC=90°

∠DCE=42°

Because CD bisects ∠ACB, Hence,

∠ACD = ∠DCB = x.............................1

∠DCE= ∠BCE + ∠DCB .....................2

= ∠BCE + x = 42° ................................3

To find  ∠A, we use deductive reasoning to state:

∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)

Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:

∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°

Recall equation 2, where ∠DCB = x, hence

∠A +∠E +x + x + ∠BCE = 180°

Recall equation three where 3 where  ∠BCE + x = 42°, hence

∠A +∠E +x + (x + ∠BCE) = 180°

⇒ ∠A +∠E + x + 42° = 180°

Recall that ∠E = 90° so

⇒ ∠A +90° + x + 42° = 180° (Collect like terms)

⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence

∠A + x = 48°...........................4

Recall that in Δ ABC

AB =  BC (given)  

Hence, ABC is an Isosceles triangle. Since this is true, then

⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)

Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°

3x = 48

x = 48/3

x = 16°

Recall that

∠A = 2x...........equation 5, hence,

∠A = 2 * 16

∠A = 32°

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(4b) If you know that you can drive 230 miles withthat much gas, how many miles per gallon doesyour bus get?Round your answer to the nearest tenth of a mile.The bus gets miles per gallon,

Answers

Given the following question:

Part A:

75 dollars to spend on gaS

Gas per gallon costs $2.80

[tex]\begin{gathered} 75\div2.80=26.7857143 \\ 26.7857143 \\ 8>5 \\ 26.8\text{ gallons of gas} \end{gathered}[/tex]

With 75 dollars you can buy "26.8 gallons of gas."

Part B:

We know we can travel 230 miles with 26.8 gallons of gas, now we have to find out how many miles can we travel PER gallon of gas.

[tex]\begin{gathered} 230\div26.8=10.4477612 \\ 10.4477612 \\ 4<5 \\ 10.4\text{ miles per gallons} \end{gathered}[/tex]

"10.4 miles" per gallon

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

Answers

For the description "The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations." Graphing method for solving systems is in play. Option A

This is further explained below.

What is Graphing method for solving systems?

Generally, Construct a graph using the first equation.

Create a graph using the same rectangular coordinate system for the second equation.

Find out whether the lines overlap, if they run parallel to one another, or if they are the same line.

In conclusion, Find a solution to the problem that we are having. In the event that the lines meet, locate the location where they do so.

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CQ.

Identify which method for solving systems is being described by this fact:

The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

answer choices

Graphing

Substitution

Elimination (adding or multiplying)

Henry purchased compact disks for $112. The compact discs cost $16 each.Which of the following equations could you use to find how many compact disks, x, Henry purchased?$16 = $112xO $112 = $16xXO $112=16$112 = x - $16

Answers

Problem

Henry purchased compact disks for $112. The compact discs cost $16 each.

Which of the following equations could you use to find how many compact disks, x, Henry purchased?

Solution

We can set up the following notation:

x= number of disks

total cost = (number of disks)* (unitary price)

Total cost = $112

number of disks =x

unitary price = $16

Replacing we got:

112 = x*16

For this case the correct equation would be given by:

$112 = $16x

When do you know you can stop the long division process when converting a fraction to a decimal number?

Answers

Division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

What is Division?

a division is a process of splitting a specific amount into equal parts.

We can stop the long division process when converting a fraction to a decimal number.

There can be two situations in converting fractions to decimals:

When division stops after a certain number of steps as the remainder becomes zero.

When division continues as there is a remainder after every step.

Hence When division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.

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The sides of a scalene triangle have measures that are consecutive even integers. If the perimeter of this
triangle is 60 inches, what is the length of the longest side of the triangle?

Answers

Answer: 22

Step-by-step explanation:

Let the sides have lengths [tex]x-4, x-2, x[/tex]. Since the perimeter is 60,

[tex]x-4+x-2+x=60\\\\3x-6=60\\\\3x=66\\\\x=22[/tex]

So, the length of the longest side is 22 units.

i need help with this pls

Answers

Hello!

What is an x-intercept:

 ⇒ value of x when the value of y equals '0'

       [tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]

  x-intercept is 25/8

What is a y-intercept:

 ⇒ value of y when the value of x equals '0'

       [tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]

   y-intercept is 5

Hope that helps!

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 6​% rate of​ defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be​ accepted, or will many be​ rejected?

Answers

The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.

By Binomial probability distribution,

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,

[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!

n=42, as 42 tablets are tested.

p=0.06 as 6% is defective.

If at most there is 1 defective piece then it will be accepted.

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074

P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047

Thus,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.074 + 0.0047

P(X ≤ 1) = 0.0787

The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.

Learn more about the Binomial probability distribution at

https://brainly.com/question/15061169?referrer=searchResults

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