Factor as the product of two binomials. 36+12x+x^2=

The given radical can be simplified as follows:

\($$\begin{aligned}\sqrt{a b^{2}} \sqrt{a}= a |b|\end{aligned}$$\)

Here, the given radical is simplified by first breaking down its terms into their respective factors. Then the terms are simplified by making use of the properties of radicals and elementary algebraic operations. Finally, the simplified terms are written in their equivalent forms.

Hence, the given radical can be simplified as follows:

\($$\begin{aligned}\sqrt{a b^{2}} \sqrt{a}&= b \sqrt{a} \sqrt{a} \\&= b (\sqrt{a})^{2} \\&= b a \\\sqrt{a b^{2}} \sqrt{a}&= a |b|\end{aligned}$$\)

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Answer: 4,280

Step-by-step explanation:

Hi

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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The SAS congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

First, let's take two triangles ABC and DEF. If the side lengths of both triangles are the same (AB = DE, AC = DF) and the included angle (angle A) is the same in both triangles (angle A = angle D) then the two triangles are congruent. This is known as the SAS congruence.

To prove the SAS congruence, we can use the Law of Congruent Triangles. This law states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

To prove this, we can use the Side-Angle-Side Postulate. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

This means that if the side lengths of both triangles are the same (AB = DE, AC = DF) and the included angle (angle A) is the same in both triangles (angle A = angle D) then the two triangles are congruent. This is known as the SAS congruence.

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Performance measures dealing with the number of units in line and the time spent waiting are called D. operating characteristics.

Operating characteristics are performance measures that provide information about the operational behavior of a system. In the context of queuing theory, operating characteristics specifically refer to measures related to the number of units in line (queue length) and the time spent waiting (queueing time) within a system. These measures help assess the efficiency and effectiveness of the system in managing customer or job arrivals and processing.

The number of units in line is an important indicator of how congested a system is and reflects the amount of work waiting to be processed. By monitoring the queue length, managers can determine if additional resources or adjustments to the system are required to minimize customer wait times and enhance throughput.

Similarly, the time spent waiting, often referred to as queueing time, measures the average or maximum amount of time a customer or job must wait before being serviced. This measure is crucial in assessing customer satisfaction, as excessive wait times can lead to dissatisfaction and potential loss of business.

Operating characteristics provide quantitative insights into these key performance indicators, allowing organizations to make informed decisions regarding resource allocation, process improvements, and service level agreements.

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Answer:

20.25?

Step-by-step explanation:

Answer:

the answer is 1 OK OK OK OK OK

Required value of ∠N is 19°.

What are complementary angles?

Angles are a type of angle that add up to a total of 90 degrees are called Complementary angles.

If two angles are complementary

then the sum of those angles equals 90 degrees.

All these angles are often denoted as "C" or "C-angle" in mathematical equations or diagrams.

For example if one angle is 30 degrees then its complementary angle is 60 degrees because 30 + 60 = 90.

If one angle is 45 degrees, then its complementary angle is 45 degrees because 45 + 45 = 90.

Complementary angles can be found in many geometric shapes such as triangles,squares, rectangles .

In a right triangle, the two acute angles are complementary because they add up to the right angle, which is always 90 degrees. In a rectangle or square, opposite angles are complementary because they add up to 180 degrees which is the sum of all angles in these shapes.

Here given that measure of ∠N is 71°.

Now ∠N and ∠M are complementary angles.

So, ∠N + ∠M = 90°

∠N = 90° - 71° = 19°

Therefore, required value of ∠N is 19°.

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Correct question is "The measure of ∠M is 71° and ∠N and ∠M are complementary angles.What is the measure of ∠N ?"

Therefore, the probability that you match on at least five of them is 0.376.

Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is approximately 0.5. Assume further that you discuss ten topics with the stranger. What is the probability that you match on at least five of them?

Given that we have discussed 10 topics with a stranger, and the probability that our details match for any given topic is approximately 0.5.

So the probability that they don't match is 1-0.5 = 0.5.

Now let X = number of topics out of 10 on which we match the stranger.

The distribution of X is Binomial with n=10 and p=0.5.i.e. X ~ B(10, 0.5)We are interested in P(X ≥ 5)P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Now, using the Binomial probability distribution formula,P(X = k) = (nCk)pk(1−p)n−k where nCk is the number of combinations of n things taken k at a time.

We use the formula as follows:

P(X = 5) = (10C5)(0.5)5(0.5)10−5

P(X = 6) = (10C6)(0.5)6(0.5)10−6

P(X = 7) = (10C7)(0.5)7(0.5)10−7

P(X = 8) = (10C8)(0.5)8(0.5)10−8

P(X = 9) = (10C9)(0.5)9(0.5)10−9

P(X = 10) = (10C10)(0.5)10(0.5)10−10

Now substituting values, P(X ≥ 5) = (10C5)(0.5)5(0.5)10−5 + (10C6)(0.5)6(0.5)10−6 + (10C7)(0.5)7(0.5)10−7 + (10C8)(0.5)8(0.5)10−8 + (10C9)(0.5)9(0.5)10−9 + (10C10)(0.5)10(0.5)10−10= 0.376

Let us write down the steps we have used to solve the problem:

Given that we have discussed 10 topics with a stranger, and the probability that our details match for any given topic is approximately 0.5. So the probability that they don't match is 1-0.5 = 0.5.

Let X = number of topics out of 10 on which we match the stranger. The distribution of X is Binomial with n=10 and p=0.5. i.e. X ~ B(10, 0.5). We are interested in P(X ≥ 5).

Using the Binomial probability distribution formula, P(X = k) = (nCk)pk(1−p)n−k, we calculate the probabilities of matching on 5, 6, 7, 8, 9, and 10 topics. We add these probabilities to get P(X ≥ 5) = 0.376.

Therefore, the probability that you match on at least five of them is 0.376.

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Answer:

A)0.4x-6=0.08x+2

Step-by-step explanation:

I'm pretty sure.

Answer:

x = 10

Step-by-step explanation:

3(3x+10) = 120

Expand: 9x + 30 = 120

Cross sides: 9x = 120-30

Simplify: 9x = 90

Divide : x = 90\9

just guess

jk i think the last one

Answer:

(6,8)

D

y-intercept (0,-6/5)

x-intercept (-3,0)

Step-by-step explanation:

Answer:

for first one

we have y=8

substituting value

2x+3×8=12

2x=12-24

x=-12/2=-6

x=-6 for first one

Step-by-step explanation:

for second one

let keep (2,2)

equation becomes

2×2+3×2=10

10=10 true

let keep (1,3)

equation becomes

2×1+3×3=10

11=10 false

so (2,2) is your answer for second one.

✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽

➷  \(x + 3 = 21\)

➷ \(x = 21 - 3\)

➷ \(x = 18\)

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ May ♡

Answer: There would be 17 Left-handed students

Step-by-step explanation: I know there's a common core way to do this by doing cross multiplication with 1/5 x "x"/85 (x being the answer) but this question is simple enough to just divide 85 by 5

According to the statement the distance from the plane to the top of the larger sphere is 3 + 2 = 5 units.

The distance from the plane to the top of the larger sphere can be found by considering the arrangement of the spheres.

We have three smaller spheres of radius 1 that are mutually tangent to each other and the plane.

On top of them, there is a larger sphere of radius 2.
Let's denote the distance from the plane to the center of the larger sphere as h.

Since the spheres are tangent to each other, the distance from the plane to the top of the larger sphere will be equal to the sum of the radii of the smaller spheres (3 x 1 = 3) plus the radius of the larger sphere (2).
Therefore, the distance from the plane to the top of the larger sphere is 3 + 2 = 5 units.

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When the number of people is multiplied by 4, the number of pizzas is also multiplied by 4. This relationship can be observed by examining the equivalent ratios shown in the table.

Equivalent ratios represent the same proportional relationship between two quantities. In this case, the quantities being compared are the number of people and the number of pizzas. The table displays different combinations of people and pizzas that maintain the same ratio.

Let's consider an example from the table. If we look at the first row, it states that when there are 2 people, there are 1 pizza. If we multiply the number of people by 4 (2 x 4 = 8).

This pattern holds true for all the equivalent ratios in the table. When the number of people is multiplied by 4, the number of pizzas is also multiplied by 4. This demonstrates a consistent and proportional relationship between the two quantities.

The concept of equivalent ratios is fundamental in understanding proportional relationships and scaling. It allows us to make predictions and calculations based on the established ratio.

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I have to stay on the surface (minimum surface interval) to do these two dives safely : 1:04-1:10 hours

You'll need a Recreational dive planner table, I annexed a copy, now you'll follow the next steps:

1. In the first part of your table, you'll look for the distance row (in feet) of your first dive, for this specific exercise you'll find 60, once you locate it you'll go down that column until you reach the time you'll dive, in this case, 45 (minutes) or the closest value (47).

2. You'll check and keep the letter in that 47 row (S) for future use.

3. Now you have to go to the second part of your table and look for the distance column, in feet, of your second dive. We find 60 and then going right in the blue row, we'll look for the time (35) or its closest value (36).

4. Finally, we have to check the letter for 36 minutes (F) and we'll make it met with the letter S in the first portion of your tables. This will give us an interval of time, 1:04-1:10 in this case.

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The scale on the map is 1 cm for 500 m.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, A man walks 1500 metres. on a map, this is shown as 3 cm.

3 cm = 1500 m

1 cm = 500 m

Hence, The scale on the map is 1 cm for 500 m.

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Answer:

\(\frac{2}{3}\)in

Step-by-step explanation:

4in is the total so if it takes 6 hours. divide 4 by 6 and you get \(\frac{2}{3}\).

Fast way to do this is to write out 4/6 and see they both can divide by 2. then you have the fraction in simplest form.

The volume V of the solid can be calculated as V = 5π cubic units using a double integral in polar coordinates, where the limits of integration are 1 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π.

The volume V of the solid can be found by integrating the given function z = 6 - \(x^{2}\) - \(y^{2}\) over the region R.

To find the limits of integration, we observe that the region R is defined in polar coordinates as 1 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π.

The volume can be calculated using a double integral in polar coordinates as: V =\(\int\int R(6-r^{2} ) r dr d\theta\)

Integrating with respect to r first, we have: V = \(\int\limits^0_{2\pi } \int\limits^1_2 (6-r^{2} ) r dr d\theta\). Evaluating the inner integral with respect to r, we get: V = \(\int\limits^0_{2\pi } {3r^{2}- \frac{r^{4} }{2} [1 to 2] } \, d\theta\)

Simplifying and evaluating the limits, we have:

V = \(\int\limits^0_{2\pi } {(6-8)- \frac{{3} }{2}-2 } \, d\theta\)

V = 5π

Therefore, the volume of the solid is 5π cubic units.

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Answer:

\(y = 3x + _ 2\)

Step-by-step explanation:

The graph of y = 3^x will pass through the point (0, 1).  This graph passes through the point (-3, 1); it has been shifted to the left 3 units.

A function can be translated, or shifted, to the left by adding a number to x before the function is applied; in this case, it means adding 3 to x before the base is raised to the power.  This gives us

This graph has also been translated, or shifted, down 2 units.  This can be done by subtracting a number from the end of the function; this gives us

Answer:

y÷8

Step-by-step explanation:

quotient is just a fancy word for division

a.It's true that P(X = k + 1) = p/1 - p n - k/k + 1 P(X = k), as desired.

b. The largest value when k is the largest integer less than or equal to (n + 1)p occur at an integer value of k.

(a) To show that P(X = k + 1) = p/1 - p n - k/k + 1 P(X = k), we can use the formula for the binomial probability mass function:

\(P(X = k) = (n choose k) p^k (1 - p)^{(n - k)\)

Then, using the identity (n choose k) = (n choose k + 1) (k + 1)/(n - k), we have:

P(X = k + 1) = (n choose k + 1)\(p^{(k + 1)} (1 - p)^{(n - k - 1)}\)

= (n choose k + 1)\(p^{(k + 1)\) (1 - p)ⁿ / (\((1 - p)^{(k + 1)\) (1 - p))

= [(n - k)/(k + 1)] p / (1 - p) P(X = k)

Therefore, P(X = k + 1) = p/1 - p n - k/k + 1 P(X = k), as desired.

(b) To find the value of k that maximizes P(X = k), we can take the ratio of consecutive probabilities:

P(X = k + 1)/P(X = k) = (1 - p)/(k + 1) * (n - k)/p

Setting this expression equal to 1 and solving for k, we get:

(n - k)/p = (k + 1)/(1 - p)

n - kp = pk + p

k = (n + 1)p - 1

Since k must be an integer, the largest integer less than or equal to (n + 1)p is the largest value of k that maximizes P(X = k). This is because P(X = k) is increasing for k < (n + 1)p and decreasing for k > (n + 1)p, so the maximum must occur at an integer value of k.

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Answer:

99/4 = 24 3/4

Step-by-step explanation:

25 1/2 = (25 x 2 + 1)/2 = 51/2 = 102/4

102/4 - 3/4 = 99/4 = 24 3/4

Step-by-step explanation:

Since 4104 students are employed sophomores, juniors, or seniors, the total number of unemployed students is 11,989 - 4104 = 7885.

And since 745 students are employed freshman, the number of unemployed freshman is 7885 - 745 = 7140.

So, the total number of freshman is 745 + 7140 = 7885.

The Venn diagram would look like this:

[ Freshmen ] [ Sophomores, Juniors, Seniors ]

[ 7885 ] __________ [ 4104 ]

| 745 |

__________

[ 7140 ]

So, there are 7885 freshman.

The critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.

When finding a 98% confidence interval for a normally distributed population with a sample size of 32, you will need to use a critical value from the standard normal (z) distribution.

To find the critical value, you can refer to a z-table or use a calculator with statistical functions. For a 98% confidence interval, you will need the z-score that corresponds to the middle 98% of the data, leaving 1% in each tail. This z-score is approximately 2.33.

So, the critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.

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Answer:

The anwser is A

Step-by-step explanation:

A is the best anwser choice given