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The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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The equation (i), (ii), and (v) are the equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

2 + x = 5

x + 1 = 4

9 + x = 6

x + (-4) = 7

-5 + x = -2

If we take x =3,

the sums would be true.

for the equation (i) take x = 3,

2 + x = 5

2 + 3 = 5

LHS = RHS = 5

for equation (ii) take x = 3,

x + 1 = 4

3 + 1 = 4

LHS = RHS = 4

for equation (iii) take x = 3,

9 + x = 6

9 + 3 = 6

12 ≠ 6

LHS ≠ RHS

for the equation (iv) take x = 3,

x + (-4) = 7

3 + (-4) = 7

-1 ≠ 7

LHS ≠ RHS

for the equation (v) take x = 3,

-5 + x = -2

-5 + 3 = -2

-2 = -2

LHS = RHS = -2

Hence, if If we take x =3, the sums would be true. the equation (i), (ii), and (v) are the equivalent.

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The maximum number of pens and pencils she can purchase is 10 pens and 30 pencils. The result is obtained by using substitution method on inequality problem.

The most important thing in inequality problem is the inequality symbol. The symbols are:

Teri wants to buy as many pencils and pens as possible by spending no more than $6.50. She wants three pencils for every pen. Each pencil costs $0.15 and each pen costs $0.20.

Find the maximum number of pens and pencils she can purchase?

Let's say:

The money spent is no more than $6.50. It means the maximum money spent is $6.50. We got the inequality.

0.15x + 0.20y ≤ 6.50

She wants 3 pencils for 1 pen. We have x = 3y.

Substitute x with 3y!

0.15(3y) + 0.20y ≤ 6.50

0.45y + 0.20y ≤ 6.50

0.65y ≤ 6.50

y ≤ 10

x = 3y = 3(10) = 30

Hence, Teri can purchase 10 pens and 30 pencils with the money she can spend.

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Answer:

0.0207 = 2.07% approximate probability of finding at least 157 defects

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\lambda\) is the mean in the given interval.

Normal Probability Distribution

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

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

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

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

n instances of a Poisson distribution can be approximated to a normal distribution, with \(\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}\)

The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.

This means that \(\lambda = 1.33\)

Suppose that we inspect 100 Volkswagen vehicles at random.

This means that \(n = 100\)

Mean and standard deviation:

\(\mu = n\lambda = 100*1.33 = 133\)

\(\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53\)

What is the approximate probability of finding at least 157 defects?

Using continuity correction(Poisson is a discrete distribution, normal continuous), this is \(P(X \geq 157 - 0.5) = P(X \geq 156.5)\), which is 1 subtracted by the p-value of Z when X = 156.5. So

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

\(Z = \frac{156.5 - 133}{11.53}\)

\(Z = 2.04\)

\(Z = 2.04\) has a p-value of 0.9793.

1 - 0.9793 = 0.0207

0.0207 = 2.07% approximate probability of finding at least 157 defects

Answer: 10+ 10 = 20

1+1= 2

Step-by-step explanation:

Answer:

The answer is 56°. Angle B is an exterior angle of triangle ABC, which means it is equal to the sum of the two remote interior angles (angles A and C). Angle A is 35°, angle C is 121°, so angle B is 56°.

Answer:

1050 miles

Step-by-step explanation:

velocity=distance/time

Distance=450 miles

Time=3 hours

Velocity=150 miles/hours

if time is 7 and velocity is 150 distance is 7x150=1050 miles

Answer:

Step-by-step explanation:

4/mx

Based on the information we can infer that 5/8 between 6 people is equal to 15/24.

To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.

5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder

So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:

(5/4) x 6 = 30/4 = 15/2 = 15/24

So each person would receive 15/24 of the original amount.

Note: Here is the question in English:

5/8 divided in 6 people

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The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Answer:

88%

Step-by-step explanation:

Triangles ABC and EDC are congruent triangles and this can be proven by:

Congruent triangles are those triangles that have the same lengths of their sides and the same angles. The orientation of the triangle does not matter so they can face in any direction.

With the midpoint of BD being C, we then know that line segments BC & DC are congruent as they meet at the same place. The same is true of line segments AC & EC are congruent.

The sides of the triangle are therefore the same so Triangles ABC and EDC are congruent.

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-6(1+7x)+7(1+6x)=-2​

This is False.

Use distributive property:

-6 -42x + 7 +42x = -2

Combine like terms to get:

1 = -2

Since 1 is not -2, it is false.

Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

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Answer: 3

Step-by-step explanation:

The tenths place in this number:

2 = tens place

1 = ones place

.

3 = tenths place

4 hundredths place

Answer is 3.

Look at each place value. The number shows you how much of each are there.

Tenths is the first column after the decimal point and it says 3.

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Two events, A and B, are independent if:

Let's define:

A: the baby has brown eyes

B: the baby has a fast heart rate

number of babies with brown eyes: 2 + 15 = 17

number of babies with fast heart rate: 15 + 24 + 22 + 14 = 75

number of babies with brown eyes and a fast heart rate: 15

total number of babies: 2 + 1 + 2 + 5 + 75 = 85

Then:

In conclusion, the events are independent

Answer:

Answer:

7

Step-by-step explanation:

If you use the pi button:

the radius is 7

154cm² ÷ pi = 49

Square root of 49 = 7

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

The relationships are illustrations of proportional equations

Machine D could pack 605 more candies than machine C in 11 minutes

The equation of machine C is represented by:

\(y = 75x\)

The equation of the graph of machine D is represented by:

\(y = 130x\)

Substitute 11 for x in both equations

\(y = 75 * 11 = 825\)

\(y = 130 * 11 = 1430\)

Calculate the difference (d)

\(d =1430 - 825\)

\(d =605\)

Hence, Machine D could pack 605 more candies than machine C in 11 minutes

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Answer: D

Step-by-step explanation:

When you convert the equation to y-intercept form it becomes y > \(\frac{1}{2}\)x +3 and the sign is > because the line is dotted and the shaded portion is above the graph.

Answer:

The car travels 25 miles per gallon of gas used

Step-by-step explanation:

Unit Rate

It's given a car uses 9.8 gallons of gas to travel 245 miles.

We have to calculate how many miles the car travels per gallon. The unit rate gives us that result by dividing the number of miles by the gallons used:

unit rate = 245 miles / 9.8 gallons = 25

The car travels 25 miles per gallon of gas used

Answer:

i think its A

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the measure of angle A