please check image regarding rational exponents

Based on the provided lines and angles;

Let's discuss each problem we have:

Problem 2: Parallel lines m and n are cut by transversal l

Statement A: ∠1 = ∠5 is correct because both are corresponding angles and congruent.

Statement B: ∠2 = ∠4 is correct because both are vertical angles and congruent

Statement C: ∠2 = ∠7 is incorrect because ∠7 is the corresponding angle of ∠3 which is the supplementary angle of ∠2

Statement D: ∠3 and ∠6 form a linear pair is correct because both are consecutive interior angles and supplementary

Statement E: ∠4 and ∠5 are supplementary is correct because both are consecutive interior angles.

Problem 3: Parallel lines a and b are cut by transversal c and d

∠1 = 115°

∠8 = 105°

∠5 is adjacent and the supplementary angle of ∠8, then:

∠5 + ∠8 = 180°

∠5 + 105° = 180°

∠5 = 75°

∠11 is the alternate exterior angle of ∠5 and both are congruent, then:

∠11 = ∠5 = 75°

∠16 is the corresponding angle of ∠4 and congruent. ∠4 is the adjacent and supplementary of ∠1, then:

∠16 = ∠4

∠4 + ∠1 = 180°

∠16 + ∠1 = 180°

∠16 + 115° = 180°

∠16 = 65°

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Connection between normal probabilities and empirical rule links to an external site probability is 0.95 probability is 0.02.

The parts from a supplier in an average  have a mean value  of 31.8 inches and a standard deviation value  of 2.4 inches. Probability is 0.02, which is inconsistent with the.

Probability is basically the chances of something happening . The theoretical probability is the form of probability that is  based on the reasoning behind probability. For example, if a coin is tossed than the theoretical probability of the chance or outcome of getting a head will be ½.

Probability is the branch of mathematics that basically deal for outcome of something or the chances of getting the favorable outcome four main types of probability exist: classical, empirical, subjective and axiomatic.

Probabilities always range between 0 and 1. The formula to find the  probability can be expressed as: Probability =Favorable number of Outcomes / Total Number of Outcomes. or. P(A) = f / N.

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The values of the probabilities are 4/7, 2/7 and 5/7

p(the trip will take 25 minutes)

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

25 minutes = 8

Total = 14

So, we have

P(25 minutes) = 8/14 = 4/7

p(the trip will take 20 minutes)

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

20 minutes = 4

Total = 14

So, we have

P(20 minutes) = 4/14 = 2/7

p(the trip will take atleast 25 minutes)

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

At least 25 minutes = 8 + 2 = 10

Total = 14

So, we have

P(At least 25 minutes) = 10/14 = 5/7

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Answer: 101/20, 5 1/11, 5.57, 5.576

Step-by-step explanation:

I hope this is correct :D

Answer:

Kendall must have 5 dimes in her pocket.

Step-by-step explanation:

First, let's write down all the information that is given to us:

q = number of quarters   ["q, the number quarters"]

d = number of dimes     ["d, the number of dimes"]

q = 4     ["Kendall has 4 quarters in her pocket"]

25q + 10d = 150

Since the value of q is given to us, our equation now has one unknown variable, d, and we can solve for it.

25q + 10d =      150 [Plug in q]

25(4) + 10d =      150 [Simplify]

100 + 10d =      150 [Subtract 100 from both sides]

10d = 50     [Divide both sides by 10]

d = 5

So, since d=5, Kendall must have 5 dimes in her pocket.

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The probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

The probability of selecting exactly one defective calculator out of the 6 sent to the local high school can be calculated using the binomial probability formula. The binomial probability formula is [tex]P(x) = nCx * p^x * q^(n-x)[/tex]. For this problem, n = 6 (the number of calculators sent to the local high school), x = 1 (the number of defective calculators selected), p = 4/12 (the probability of selecting a defective calculator from the shipment of 12 calculators), and q = 8/12 (the probability of selecting a non-defective calculator from the shipment of 12 calculators). Plugging these values into the formula gives [tex]P(x) = 6C1 * 4/12^1 * 8/12^5[/tex], which simplifies to 0.29166. This means that the probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

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a) The probability that all three family members are assigned to the same station is  1/27.

b) The probability that at most two family members are assigned to the same station is 11/27.

c) The probability that every family member is assigned to a different station is 2/9.

For (a), there is only one way for all three family members to be assigned to the same station, and there are 3 stations, so the probability is 1/3^3 = 1/27.

For (b), there are three ways for two family members to be assigned to the same station, either A and B, B and C, or A and C. The probability of two family members being assigned to the same station is (1/3)^2 (2/3). There are three ways for this to occur, so the probability is (3) (1/9) (2/3) = 2/3. There is also one way for all three family members to be assigned to the same station, so the probability is (1/3)^3 = 1/27. Adding these two probabilities gives 11/27.

For (c), there are 3! = 6 permutations for the family members to be assigned to different stations. Each family member can be assigned to any of the 3 stations, so the probability is (3!) (1/3)^3 = (6) (1/27) = 2/9.

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Complete Question:

A family consisting of three persons-A, B, and C-goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that (a) All three family members are assigned to the same station? (Round your answer to three decimal places.) (Ne Responseberse ssigd tah ni sation number tor each (b) At most two family members are assigned to the same station? (Round your answer to three decimal places.)  (c) Every family member is assigned to a different station? (Round your answer to three decimal places.)

The number of fish that were between 30 cm and 40 cm long is equal to 0.8.

In Mathematics, a histogram can be defined as a type of chart that is used to graphically represent a group of data points (statistical information) into user-specified ranges through the use of rectangles or rectangular bars.

Based on the information provided in the histogram (see attachment), the number of fish that were between 30 centimeters and 40 centimeters long can be calculated based on the frequency density as follows;

Number of fish = 1/5 × 4

Number of fish = 0.2 × 4

Number of fish = 0.8

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Answer:

Timmy has been working at Monster Burger longer than Susie, which explains why he earns more money. Monster Burger employees are given a 50 cent raise each year, so Susie's salary will likely increase over time as she continues to work there.

Step-by-step explanation:

It is possible to determine how long Susie has been working at Monster Burger by using the information given. Since Timmy makes 720 dollars working 40 hours and Susie makes 600 dollars working the same hours, we can calculate their hourly wages:

Timmy's hourly wage: 720 / 40 = 18 dollars

Susie's hourly wage: 600 / 40 = 15 dollars

Since Monster Burger employees are given a 50 cent raise a year, this means that Susie's hourly wage has increased by 50 cents * x years, where x is the number of years Susie has been working there. Thus, we have:

15 + (0.50 * x) = 18

Solving for x, we get:

x = (18 - 15) / 0.50 = 6 years

Therefore, Susie has been working at Monster Burger for 6 years.

The cost per square inch is $0.16 per square inches ( nearest hundredth)

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

The area of a circular pie = πr²

= 3.14 × (10/2)² since r = d/2

= 3.14 × 5²

= 78.5 square inches

apple pies are sold for a cost of $12.85

Therefore the cost per square inches

= 12.85/78.5

= $0.16(nearest hundredth) per square inches

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The amount of money Gabriela paid for the pair of glasses after the discount is $50.4

Regular price of the pair of glasses= $72

Percentage discount= 30%

Amount Gabriela actually paid= Regular price of the pair of glasses - (Percentage discount of Regular price of the pair of glasses)

= 72 - (30% × 72)

= 72 - (0.3 × 72)

= 72 - 21.6

= $50.4

Therefore, Gabriela paid $50.4 for the pair of glasses after deducting discount.

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Answer:

y=1 x=5

Step-by-step explanation:

from the second equation

x=5y

then,when we substitute the equation

4(5y)+3y=23

20y+3y=23

23y=23

y=1

if and only if,x=5y and y=1

then x=5

Step-by-step explanation:

a)

-sin(2x) = cos(2x)

sin(2x) = cos(2x)

2sin(x)cos(x) = cos(2x)

2sin(x)cos(x) = 1 or -1

sin(x) = +/-√(1/2) or sin(x) = 0

x = (2n+1)π/4 or x = nπ

b)

3 tan(x) = 2 sin(2x)

tan(x) = 2/3 sin(2x)

sin(2x) = 3 tan(x)/2

cos^2(x) = (1 - sin^2(x)) = (1 - (3 tan(x)/2)^2)/4

x = nπ/2 + arctan(2√(2)/3) or x = nπ/2 + arctan(-2√(2)/3)

c)

sec(x) cos(3x) = 0

cos(x) = 0 or cos(3x) = 0

x = nπ/2 or x = (3n+1)π/6

d)

1 - cos(x) = 2 - 2sin^2(x)

cos(x) = 2sin^2(x) - 1

2sin^2(x) = cos(x) + 1

sin^2(x) = (cos(x) + 1)/2

sin(x) = +/- √((cos(x) + 1)/2)

e)

4cos^4(x) - 5cos^2(x) + 1 = 0

cos^2(x) = (1 ± √(5))/2

x = arccos(±√((1 + √(5))/2)) or x = arccos(±√((1 - √(5))/2))

Note: n is any integer in the given domain.

Answer:

(3.369, 4.071)

Step-by-step explanation:

Miguel finish an 800-meter race first.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Miguel ran 80 meters in 20 seconds while Trina ran 40 meters in 15 seconds.

Hence, The speed of Miguel is,

⇒ Speed = Distance / Time

⇒ Speed = 80 / 20

⇒ Speed = 4 m/s

And, The speed of Trina is,

⇒ Speed = Distance / Time

⇒ Speed = 40/15

⇒ Speed = 2.67 m/s

Cleary, The speed of Miguel is faster than Trina.

Hence, Miguel finish an 800-meter race first.

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The probability that x is greater than 75 from a normal distribution with a mean of 100 and a standard deviation of 10 is 0.9151.

The formula for calculating the probability that x is greater than 75 from a normal distribution with a mean of 100 and a standard deviation of 10 is P(x>75)=1-P(x<75). The probability can be calculated using the cumulative distribution function of the normal distribution. The cumulative distribution function of the normal distribution is given by

F(x)=1/2[1+erf((x-mean)/(standard deviation*sqrt(2))]

Where erf is the error function defined by erf(x)=2/sqrt(pi)*∫x^0 e^-t^2 dt

Therefore, the probability that x is greater than 75 is

P(x>75)=1-1/2[1+erf((75-100)/(10*sqrt(2))]

=1-1/2[1+erf(-1.25)]

=1-1/2[1-0.1151]

=0.9151

The probability that x is greater than 75 from a normal distribution with a mean of 100 and a standard deviation of 10 is 0.9151.

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The number of 2/3 parts in the number 4 will be 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The number of 2/3 parts in the number 4. Then the expression is given as,

⇒ 4 ÷ (2/3)

⇒ 4 x (3/2)

⇒ 2 x 3

⇒ 6

The number of 2/3 parts in the number 4 will be 6.

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The solution is, Their rate of change is respectively 0.5.

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The slope-intercept form of the equation of a straight line is:

y=mx+c

where, m= rate of change.

From the given equations, the two that have the same rate of change are:

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

Their rate of change is respectively 0.5.

The correct choices are A and D.

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The graph of the linear function y = -1/3x + 8 is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function for this problem is defined as follows:

y = -x/3 + 8.

Meaning that:

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The gray squirrel population t years after introduction is P(t) = [tex]340 x 2^(t/9).[/tex]

The formula for the gray squirrel population, p, t years after the introduction of the population is [tex]P(t) = P0 x 2^(t/9)[/tex], where P0 is the initial population. We can use this formula to answer both (a) and (b). For (a), we can substitute t = 0 and P(t) = 680, to solve for P0. This gives us that the initial population of gray squirrels was 340. For (b), we can substitute t = 27 (the number of years since introduction) and P(t) = 680, to solve for P(27). This gives us that the expected population of gray squirrels t years after introduction is 1360. Therefore, the formula for the gray squirrel population t years after introduction is [tex]P(t) = 340 x 2^(t/9)[/tex].

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Answer: They make the same amount of money

Step-by-step explanation:

Divide 36 by 4

Divide 63 by 7

You get 9 each time.

Answer:

They make the same amount of money

Divide 36 by 4

Divide 63 by 7

You get 9 each time.

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

The solution is Option B.

The pressure at the ocean's surface is given by the equation A = 14.7 pounds per square inches

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

P = 14.7 + ( f/22.5 )   be equation (1)

where P is the total pressure in pounds per inch²

And , f is the height in feet below the ocean's surface

Now , pressure at the ocean's surface is when f = 0

Substitute the value of f = 0 in equation (1) , we get

P = 14.7 + ( 0/22.5 )

On simplifying the equation , we get

P = 14.7 pounds/inch²

Hence , the equation is P = 14.7 pounds/inch²

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Answer:B

Step-by-step explanation:

If you simplify 3/6 you will get 1/2

The expression of the area of the barrel is 14π(h + 7)

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

The DIAMETER of the barrel is 14.

This means that the radius is 7 units

The area of the barrel is calculated as

Area = 2πr(h + r)

Substitute the known values in the above equation, so, we have the following representation

Area = 2π * 7(h + 7)

Evaluate

Area = 14π(h + 7)

Hence, the area is 14π(h + 7)

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Answer:

the answer is in the picture.. if you have any questions feel free to ask