Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. q^2+7q

It would take a total of 20 days to produce the batch of pens.

Let's calculate the work done by the 3 machines for the first 8 days:

Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work

The remaining work that needs to be done by all 12 machines is:

Remaining work = 1 - (2/20) = 0.9

Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:

Total work = 0.9

Work done by 12 machines in one day = 12/20 = 0.6

Total number of days needed = 0.9/0.6 = 1.5

Therefore, the total number of days needed to produce the batch of pens is:

8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days

However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:

10.5 + 9.5 = 20 days

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Answer:

9 a^2 + 30 a + 25 the anwser is A

Step-by-step explanation:

Expand the following:

(3 a + 5)^2

(3 a + 5) (3 a + 5) = (3 a) (3 a) + (3 a) (5) + (5) (3 a) + (5) (5) = 9 a^2 + 15 a + 15 a + 25 = 9 a^2 + 30 a + 25:

Answer: 9 a^2 + 30 a + 25

The central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

what is normal distribution?

A normal distribution is a bell-shaped probability distribution that is symmetrical and characterized by its mean (μ) and standard deviation (σ). It is also known as a Gaussian distribution, after the mathematician Carl Friedrich Gauss.

However, for smaller sample sizes, the distribution of sample means may still resemble the shape of the population distribution.

Here are some more specific descriptions of the distribution of sample means for different population distributions:

1. Rectangular distribution: The distribution of sample means will approach a normal distribution as the sample size increases, with the mean and median at the center of the distribution.

2. Uniform distribution: The distribution of sample means will also approach a normal distribution as the sample size increases, with the mean at the center of the distribution.

3. Normal distribution: The distribution of sample means will be a normal distribution regardless of sample size, with the mean and median at the center of the distribution.

4. Positively skewed distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the mean will be higher than the median.

5. Nonmodal distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the exact shape will depend on the specifics of the nonmodal distribution.

6. Multimodal distribution: The distribution of sample means will also approach a normal distribution as the sample size increases, but the exact shape will depend on the specifics of the multimodal distribution.

7. Negatively skewed distribution: The distribution of sample means will approach a normal distribution as the sample size increases, but the mean will be lower than the median.

Therefore, central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

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Answer:

f(2) =  18

Step-by-step explanation:

Put '2' into the equation where 'x' is to get :

f(2)  =  2 (2^2) + 5 (sqrt(2+2)

        =  8        + 5 (2)   =  18

Variance  of customers who pay by card = 16

Mean number of customers = 20

Given that,

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with

P(A)=0.4,

P(B)=0.2,

and

P(C)=0.4

Because we are interested in whether or not a debit card was used, we can use the binomial distribution.

Let X= the number of customers who use a debit card.

Here, probability of customers who pay with debit card (or success) is

p=0.2

(a) Mean and variance of the number of customers who pay with a debit card:

The mean number of customers who pay with a debit card can be calculated as given below:

μ=np =100×0.2

=20

The variance of the number of customers who pay with a debit card can be calculated as given below:

σ²=np(1−p) =100×0.2(1−0.2)

=16

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Answer:

3927

Step-by-step explanation:

This is the answer my teacher gave me, I promise.

The four-digit passcode is 3927 and this can be determined by using the given data and by using the hit and trial method.

Given :

Let the four digits passcode be 'abcd'. Then mathematical expression that represents "The second digit to the left is 3 times the first (left most) digit" is given below:

b = 3a   --- (1)

The mathematical expression that represents "the sum of the digits is 21" is given below:

a + b + c + d = 21    --- (2)

So, let a = 3, then b = 9, and the last two digits are 27. So, the number becomes 3927.

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My own multi-step combination problem is given below:

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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The length of the pendulum is 7 ft, the period is approximately 1.86 seconds.

The problem states that the period of a pendulum varies directly as the square root of its length. This means that as the length of the pendulum increases, so does its period. In mathematical terms, we can express this relationship as:

p ∝ √L

where p is the period of the pendulum and L is its length. The symbol "∝" means "is proportional to."

To find the period of a pendulum when its length is 7 ft, we can use the given information that the period is 1.1 s when the length is 2 ft. We can set up a proportion using the formula above:

p₁/√L1 = p₂/√L2

where p₁ = 1.1 s, L1 = 2 ft, p₂ = the unknown period we want to find, and L2 = 7 ft.

Plugging in the values we know, we get:

1.1/√2 = p₂/√7

To solve for p₂, we can cross-multiply and simplify:

1.1 x √7 = p₂ x √2

p₂ = (1.1 x √7) / √2

p₂ ≈ 1.86 s

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Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

The balance in the account after the given period is \(\$6,872.74\)  

we know that

The compound interest formula is equal to  

\(\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}\)

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

\(\text{t}= 8 \ \text{years}\)

\(\text{P}=\$4,000\)

\(\text{r}=0.07\)

\(\text{n}=1\)

substitute in the formula above

\(\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74\)  

Answer:

f(x) = 6ˣ⁻⁷-3

Step-by-step explanation:

The basic transformations of an exponential function from the parent function can be given by the equation:

f(x) = b^x [parent exponential function]

f(x) = ab^((x/c)-h) + k [transformation of parent exponential function]

Where b is the parent growth or decay, a is the vertical stretch or compression, c is the horizontal stretch or compression, h is the horizontal translation, and k is the vertical translation.

Given a translation down 3 units, and another translation right 7 units, we are only using h, and k.

Given that our original function is g(x) = 6ˣ. We know our parental growth or b is 6. So just substitute our quantities and solve:

f(x) = g(x-7) - 3 → (1)6^((x/1)-7) - 3 → 6^(x-7) - 3 → 6ˣ⁻⁷-3.

Answer:

f(x) = 6ˣ⁻⁷-3

Step-by-step explanation: I took the test

Answer:

3/10

Step-by-step explanation:

Take the number of pizzas and divide by the number of people

3 pizzas / 10 people

Each person got 3/10 of a pizza

Answer:

\( \frac{3}{10} \)

Step-by-step explanation:

\( \frac{pizza}{number \: \: of \: \: \: people} \\ \frac{3}{10} \)

Each person received 3/10 of pizza

Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

that they both have right angles and have a leath of 5

Step-by-step explanation:

Answer:

a ≤ 2

Step-by-step explanation:

Simplify both sides of the inequality

42a + 48 ≤ 132

Subtract 48 from both sides

42a + 48 − 48 ≤ 132 − 48

42a ≤ 84

Divide both sides by 42

42a/42 ≤ 84/42

a ≤ 2

Answer:

8

Step-by-step explanation:

if you divide 32 by 4 its 8

Answer:

8 dollars a game

Step-by-step explanation:

divide 4 into 32 and you get 8

Answer:

alternative hypothesis test

Explanation:

Remember, the alternative hypothesis test usually suggests that there is a chance of variation (difference) in the data observed.

Hence, since we are told the "real estate agent believes that the values of houses in the neighborhood she works in have increased (the chance of variation) from last year," and that "each difference is calculated by subtracting the market value of the previous year from the market value of the current year," we can reach the conclusion that this is an example of an alternative hypothesis test.

In linear equation, 11.6 is  the cost of 300ml.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations whose variables have a power of one are called linear equations. A single variable example with real values for a and b and x as the variable is ax+b = 0.

100ml is equal to 1 liter.

300/100 = 3

 35/3= 11.6

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Answer:

0.8

Step-by-step explanation:

(2 x 10^-4)

= 0.0002

(4x10^3)

= 4000

0.0002 x 4000 = 0.8

The hours 1,100 hours on Saturn is equivalent to 100 days on Earth and Mars

From the question, we have the following table of values that can be used in our computation:

Planet      Length of one day (hours)

Earth                24

Mars                25

Saturn               11

Also, we have

Number of hours on Saturn = 1100

So, we can represent the table of values as a ratio

Earth : Mars : Saturn = 24 : 25 : 11

Substitute Number of hours on Saturn = 1100 in the ratio

Earth : Mars : 1100 = 24 : 25 : 11

Multiply the ratio by 100

So, we have

Earth : Mars : 1100 = 2400 : 2500 : 1100

This means that

Earth = 2400 hours

Mars = 2500 hours

Divide by 24 and 25

Earth = 100 days

Mars = 100 days

Hence, the number of days on Earth is 100 days

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The number of days that are equal to 1,100 hours on Saturn is given as follows:

100 days.

A proportion is a fraction of a total amount, which is used along with the basic arithmetic operations such as multiplication and division to find the desired measures in the context of a problem.

The length of one day in Saturn, from the table, is given as follows:

11 hours.

Hence the following rule of three models the situation, considering that we want the number of days for 1,100 hours, hence:

1 day - 11 hours

x days - 1100 hours.

Then the number of days equivalent to 1100 hours on Saturn is obtained applying cross multiplication, as follows:

11x = 1100

x = 1100/11

x = 100 days.

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A predicate nominative is a noun or a pronoun which follows the verb and describes the subject.

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Answer:

Luis.

Step-by-step explanation:

180-90-20-40= 30

A triangle's angles have to make up 180 degrees, thus Luis is correct.

Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Answer:

hi jjojnbpoinopino

Step-by-step explanation:

0ionoujniuiuninioujnoinjnuioulij

9514 1404 393

Answer:

  2 < x < 15

Step-by-step explanation:

The triangle inequality requires all of ...

  (x +11) +(2x +10) > (5x -9)   ⇒   30 > 2x

  (2x +10) +(5x -9) > (x +11)   ⇒   6x > 10

  (5x -9) +(x +11) > (2x +10)   ⇒   4x > 8

The solutions to these are ...

  x < 15

  x > 5/3

  x > 2

So, the final requirement that has x satisfying all of these is ...

  2 < x < 15

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

A function is composite when the co- domain of the first mapping is the domain of the second mapping

Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:

a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13

(f + g)(-2) = 4 + 8 - 2 + 13

(f + g)(-2) = 23

b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13

(f - g)(-2) = 4 + 8 + 2 - 13

(f - g) (-2) = 1

c). f(x) - g(x) = x² - 4x - x - 13

f(x) - g(x) = x² - 5x - 13

Therefore, the domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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