What is another way of writing the following expression?
3(7 + 4)

A (3 × 7) + (3 × 4)

B (3 + 7) × (3 + 4)

C 3 × 7 × 4

D 7(3 + 4)

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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Answer:

A and F

Step-by-step explanation:

Answer:

Step-by-step explanation:

Assuming the colon between 40 and 8 is a mistype...

PEMDAS(Parenthesis, Exponents, Multiplication + Division, Addition + Subtraction)

\(40-8+3^2+(15-7)*2\\\\Parenthesis\\\\40-8+3^2+8*2\\\\Exponents\\\\40-8+9+8*2\\\\Multiplication\\\\40-8+9+16\\\\Subtraction\\\\32+9+16\\\\Addition\\\\41+16\\\\Addition\\\\57\)

Hope it helps <3

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▹ Answer

57

▹ Step-by-Step Explanation

You need to follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

40 - 8 + 3² + (15 - 7)* 2

40 - 8 + 9 + (15 - 7) * 2

40 - 8 + 9 + 8 * 2

40 - 8 + 9 + 16

= 57

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

A. The 99% confidence interval for the difference in the proportion of all dinner customers and all lunch customers who are served within 2 minutes is between -0.195 and 0.289. (0.714 - 0.667) ± 2.576*(√0.714(1- 0.714)/35 + 0.667(1- 0.667)/75).

B. Since the confidence interval contains 0, we cannot conclude that the proportion of customers served within 2 minutes of placing their order is greater during lunch hours than during dinner hours.

Step-by-step explanation:

got this off chegg.

Answer:

Step-by-step explanation:

I can cover this, so a math book is a rectangle, I hope you knew that, there is the front, back, and sides of a math book, given 2 faces and 4 sides of a book, there will be 6 faces, now for the vertices, there are 6 faces, so the edges will make 8 vertices, a vertex is where 2 or more edges meet, so now we will count the edges, given the 6 faces, we can count all of the edges and end up with 8 edges, I hope this helped you

Answer:

Step-by-step explanation:

As per steps given the congruent pairs are:

So two sides and included angle - it represents side-angle-side or SAS congruency theorem

The solution to the equation in this problem is given as follows:

x = 7.

The equation in the context of this problem is defined as follows:

7x - 15x - 16 = -72.

Then we combine the like terms, as follows:

-8x = -72 + 16

-8x = -56

8x = 56.

Then we apply the division operation to obtain the value of x as follows:

x = 56/8

x = 7.

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The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

a.

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

b.

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

c.

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

d.

P(\(A^c\) ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

\(P(A^c)\) is the probability that the first component drawn is not defective:

\(P(A^c)\) = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P(\(A^c\) ∩ B) = P(\(A^c\)) * P(B) = 0.65 * (350/999) ≈ 0.228

e.

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

f.

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

g.

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

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Answer:

hes

56 inches

hope it helps

Answer:

16y+(-4x)+(-3/4)

Step-by-step explanation:

i don't have a step by step explanation but I hope this helps!

We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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Answer:

14

Step-by-step explanation:

Step 1:

6 - ( 5x - 9 ) 2       Equation

Step 2:

6 - ( 5 ( 1 ) - 9 ) 2     Input x

Step 3:

6 - ( 5 - 9 ) 2      Multiply

Step 4:

6 - ( - 4 ) 2        Subtract

Step 5:

6 - ( - 8 )      Multiply

Answer:

14        Add

Hope This Helps :)

Answer:

14

Step-by-step explanation:

1) 6-(5[1]-9)2

2) 6-(5-9)2

3) 6-(10-18)

4) 6-(-8)

5) 14

It should be noted that the power that the volunteers use to pushe the van is 200 watts.

From the information, they used a total force of 1,200 newtons and ater pushing the Van for 15 minutes, they were able to move the van 150 meters away from your house.

It should be noted that power is calculated as:

Power = Force × Displacement / Time

Force = 1200 Newton

Displacement = 150 meters

Time = 15 minutes = 15 × 60 = 900 seconds.

Therefore, the power that the volunteers use to pushe the van is:

Power = Force × Displacement / Time

=(1200 × 150) / 900

= 200 Watt.

Therefore, it should be noted that the power that the volunteers use to pushe the van is 200 watts.

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Answer:

80 possible connections

Step-by-step explanation:

Let the constant k = change in possible connection/number of computers

change in possible connections = 10 - 6 = 4

change in number of computers = 5-4 = 1

k = 10-6/5-4

k = 4/1

k = 4

Since k = possible connections/number of computers:

4 = possible connections/20

possible connections = 4 * 20

possible connections = 80

Hence the possible number of connections with 20 computers are 80 connections

Answer:

A. \(60 ft^3\)

Step-by-step explanation:

So to find the volume of a single box, we can determine that by multiplying the width by the height by the length. So:

2.5 × 2.4 × 2 = 12

Now because we have 5 of these boxes, and we know each box has a volume of 12, all we have to is multiply 12 by 5 to get 60.

Answer:

60 cubic feet

Step-by-step explanation:

Total volume of boxes = Number of boxes × Volume of I box

                                      = 5 × (Length × Width × Height)

                                     = 5 × (2 feet × 2.5 feet × 2.4 feet)

                                     = 60 cubic feet

∴Option A

Answer:

the answer

1000000002

Answer: 17th percentile

Step-by-step explanation: i say this because it falls before the 50 percentile

The measure of ∠A is 123 degrees.

The angle made between the radius and the tangent at the point of contact on a circle is 90°.  

Therefore,

∠D = 90 degrees

∠E = 90 degrees

The diagram ACDE forms a quadrilateral. The sum of angles in a quadrilateral is 360 degrees.  Therefore, we have to equate the sum of the quadrilateral angles to 360 degrees.

Hence,

90 + 90 + 2x + 7 + 5x - 2 = 360

180 + 7x + 5 = 360

7x = 360 - 180 - 5

7x = 180 - 5

7x = 175

x = 175 / 7

x = 25

Therefore,

∠A = 5(25) - 2 = 125 - 2 = 123 degrees.

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Answer: D

Step-by-step explanation:

Since it is subtracting x from 20. D tells the change from 20 dollars after buying the notebook or x.

A is 20 + x

B is 20/x

C is 20x or 20 * x

D is 20 - x

Answer:

B

Step-by-step explanation:

you can see the words cut and smaller so that indicates subtraction

Answer:

15*8*10-7*8*11=584

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 0.86

Step-by-step explanation:

The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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Answer:

1 and 4

Step-by-step explanation:

because the square roots are always irrational. however, a rational number can be expressed as a decimal, fraction, and others...

Hope that helped

Answer:

the answer would be a or b

Step-by-step explanation:

because they both can be written as fraction

hope this helps you!

To find the limit of a convergent sequence, we can simply take the limit as n approaches infinity. Let's calculate the limits for each of the given sequences:

A. \(\sf\:\lim_{n \to \infty} \frac{5n}{n+7} \\\)

To find the limit, we divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{5n/n}{(n+7)/n} = \frac{5}{1} = 5 \\\)

Therefore, the limit of the sequence A is 5.

B. \(\sf\:\lim_{n \to \infty} \frac{4-7n}{8+n} \\\)

Again, divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{4/n - 7}{8/n + 1} = \frac{0 - 7}{0 + 1} = -7 \\\)

So, the limit of sequence B is -7.

C. \(\sf:\lim_{n \to \infty} \frac{8n - 500\sqrt{n}}{2n + 800\sqrt{n}} \\\)

Divide the leading terms by n:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500\sqrt{n}/n}{2 + 800\sqrt{n}/n} \\\)

As n approaches infinity, the terms involving \(\sf\:\sqrt{n}/n \\\) tend to 0:

\(\sf\:\lim_{n \to \infty} \frac{8 - 500(0)}{2 + 800(0)} = \frac{8}{2} = 4 \\\)

Therefore, the limit of sequence C is 4.

To summarize:

A. The limit of sequence A is 5.

B. The limit of sequence B is -7.

C. The limit of sequence C is 4.

Answer:

ok so from looking at this if he earns 14 dollars he saves 5 so he saves

5/14 so lets just multiply this by the 56

56*5/14=20

so he saves 20

20

Hope This Helps!!!

Based on a system of equations, a pound of apples costs $0.89.

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

A system of equations is also referred to as simultaneous equations.

                    Apples     Pears     Total Cost

Janice              2              3             $3.85

Lisa                  4              2             $4.94

Let the cost of a pound of apples = x

Let the cost of a pound of pears = y

2x + 3y = 3.85 ... Equation 1

4x + 2y = 4.94 ... Equation 2

Multiply Equation 1 by 2:

4x + 6y = 7.7 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 6y = 7.7

-

4x + 2y = 4.94

4y = 2.76

y = 0.69

Substitute y = 0.69 in Equation 1 or 2:

4x + 2y = 4.94

4x + 2(0.69) = 4.94

4x + 1.38 = 4.94

4x = 3.56

x = 0.89

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