For #'s 11 - 13, match the real-life problem with the correct equation.
A) x + 15 = 7
B) 15 - x = 7
C) 15 + 7 = x
11) You own 15 DVDs. You buy 7 more. How many DVDs do you own now?
12) There are 15 members of a high school band brass section. After graduation there are only 7
members. How many members graduated?
13) The temperature rose 15 degrees to 7°F. What was the original temperature?

Answer:3

Step-by-step explanation:

Just count from -1 to positive 2 the dot doesn’t move

The bias that is taken care of here is that; Some of the population may not have access to other types of phones. Option A

When we talk about a bias in research we mean the kind of scenario that is able to cause the result of a research to become lobe sided. In other words, it is that which introduces inaccuracy to a research.

A lot of people if not everyone has access to a mobile phone and this would help more people to be able to participate in the interview. Some of these people may not have any of the other kinds of phone.

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Answer:

A

Step-by-step explanation:

took the test

Answer:

260.42 you add them because it want the total time of all of them

Step-by-step explanation:

Answer:

75,000

Step-by-step explanation:

I wish I were those kids

Probability of defect: 0.0027. Probability of defect: 0.00006.  Advantage of reducing process variation is that it results in a larger distance between the mean and the control limits, which makes it easier to identify and correct issues.

Using the normal distribution with a mean of ounces and a standard deviation of , the probability of a defect is the area under the curve outside the control limits, which is approximately 0.0027 or 0.27% (to 4 decimals). The number of defects in a production run would depend on the sample size and the proportion of defective items in the sample.

With a reduced standard deviation of , the probability of a defect is now approximately 0.00006 or 0.006% (to 4 decimals). In a production run of parts, the number of defects would be expected to be much lower than in part a, again depending on the sample size and the proportion of defective items in the sample.

The advantage of reducing process variation is that it allows for greater control limits, which means that more items can be produced within the control limits and fewer will be classified as defects. This can lead to higher quality products, lower production costs, and greater customer satisfaction.

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The probability that you are correct by making a random guess is 1/5.

According to the given question.

On a multiple choice test, each question has 5 possible answers.

As we know that probability, is a measure of the likelihood of an event to occur. It is calculated by taking the ratios of favorable outcomes to the total number of outcomes.

Here, it is given that there are 5 possible answers of one question.

⇒ Total number of outcomes = 5

Also, only one answer will correct out of 5 possible answers.

Which means, total number of favorable outcomes = 1

Therefore, the probability that you are correct by making a random guess

= favorable outcomes/total number of outcomes

= 1/5

Hence, the probability that you are correct by making a random guess is 1/5.

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Anwser:

180/3=60

60/12=5

3x(12x5)=180

b=5

Step-by-step explanation:

Answer: should be -6

Step-by-step explanation:

Set the expression to equal zero

z+6

Solve the equation

z+6+0

State the root

z+-6

Step-by-step explanation:

x = speed of hiker1

because they meet, between the 2 of them, together they cover 15 miles in 2 hours.

2×x + 2×(x + 2.7) = 15

2x + 2x + 5.4 = 15

4x = 9.6

x = 2.4 mph

so one hiker was going 2.4 mph,

the other 2.4 + 2.7 = 5.1 mph.

The relationship between j and k can be expressed as j = k^(-3) * C, where C is a constant. To find the value of C, we can use the initial condition j = 3 when k = 6:

3 = 6^(-3) * C

C = 3 * 6^3 = 648

So the relationship is j = 648 / k^3. To find another possible value for j and k, we can simply plug in a different value for k:

For option A:

j = 648 / 2^3 = 81

For option B:

j = 648 / 3^3 = 24

For option C:

j = 648 / 2^3 = 81

For option D:

j = 648 / 81^3 = 0.0008

For option E:

j = 648 / 2^3 = 81

Therefore, the only option that is another possible value for j and k is (A) j = 18, k = 2.

Bayes' rule, also known as Bayes' theorem or Bayes' law, is a mathematical formula used in probability theory and statistics. It provides a way to update our belief or probability of an event occurring, given new evidence.

The formula for Bayes' rule is:

P(A|B) = (P(B|A) * P(A)) / P(B)

where P(A|B) is the probability of event A occurring given that event B has occurred, P(B|A) is the probability of event B occurring given that event A has occurred, P(A) is the prior probability of event A occurring, and P(B) is the prior probability of event B occurring.

An example of how Bayes' rule can be used is in medical diagnosis.

Let's say a patient has a positive test result for a certain disease.

The probability of having the disease (event A) can be calculated using Bayes' rule, taking into account the sensitivity and specificity of the test.

The sensitivity is the probability of a positive test result given that the patient has the disease, and the specificity is the probability of a negative test result given that the patient does not have the disease.

By applying Bayes' rule, we can update the probability of having the disease based on the test result and the sensitivity and specificity values.

In short, Bayes' rule is a useful tool for updating probabilities based on new evidence. It is commonly used in various fields, including medicine, finance, and machine learning.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

Given the information on the problem, we can draw the following right triangle:

we can find how high the ladder reach using the pythagorean theorem:

therefore, the ladder reaches 21 ft high up on the wall

Answer:

Step-by-step explanation:

See image

Answer:

i think the last one

Step-by-step explanation:

Let the area of the curve be A. The Simpson's rule gives us the following:A = (b-a)/6 (f(a) + 4f((a+b)/2) + f(b)) = 12Also, the trapezoidal rule gives us the following:

A = (b-a)/2 (f(a) + f(b)) = 8.

Now, we know that (b-a)/h is equal to 2 in the trapezoidal rule and 4 in the Simpson's rule. This gives us 2h = b-a in the trapezoidal rule and 4h = b-a in the Simpson's rule.

By dividing the two formulas, we get:

(f(a) + 4f((a+b)/2) + f(b))/(b-a) = 12/(b-a) ...(1)and(f(a) + f(b))/(b-a) = 8/(b-a) ...(2).

Multiplying equation 2 by 4, we get:(4f(a) + 4f(b))/(b-a) = 32/(b-a) ...(3).

Now, adding equations 1 and 3, we get:5f(a) + 4f((a+b)/2) + 5f(b) = 44 ... (4).

Dividing equation 4 by 10, we get:f(a) + f((a+b)/2) + f(b) = 4.4 ... (5).

Again, from equation 1:(f(a) + 4f((a+b)/2) + f(b))/(b-a) = 12/(b-a).

Multiplying both sides by (b-a)/3, we get:(b-a)/3 * (f(a) + 4f((a+b)/2) + f(b))/(b-a) = 4 ...(6).

Simplifying equation 6, we get:(f(a) + 4f((a+b)/2) + f(b))/3 = 4 ...(7).

By subtracting equation 5 from equation 7, we get:2f((a+b)/2) = 0.4f(a) + 0.4f(b) + 0.4 ...(8).

Dividing equation 8 by 2, we get:f((a+b)/2) = 0.2f(a) + 0.2f(b) + 0.2 ...(9).

Therefore, applying Simpson's rule to sf(x)dx gives the value 12 and the trapezoidal rule gives the value 8, so f((a+b)/2) = 0.2f(a) + 0.2f(b) + 0.2.

/(3) cannot be calculated with the given data.

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There are 24 ways for the vote of the favorite, second favorite, and third favorite band to be cast.

The list contains 4 bands.

Out of these 1 band is Alonzo's favorite, 1 is his second favorite and another is his 3rd favorite

Now to choose his favorite Alonzo has 4 choices. Hence there are 4 ways to cast this vote.

Now since one band has been chosen, Alonzo is left with 3 bands on the list, hence he has 3 ways to cast the vote for the second favorite.

For the last vote of 3rd favorite, there are2 options available, hence this can be done in 2 ways.

Hence we get the total number of ways to be

4 X 3 X 2 ways

= 24 ways

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Answer:5800

Step-by-step explanation:

Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation:

The interval is (0 < x < 4) where both functions are increasing on the number line provided.

What is the interval of a function?

The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.

We have given,

f(x) = |3x| + 3

g(x) = –x^2 + 8x – 5

f(x) is increasing for x > 0.

g(x) is increasing for x < 4.

Both functions are increasing on the open interval (0, 4).

It will be graphed with a solid line between 0 and 4, and with open circles at 0 and 4.

See the black line on the x-axis of the attachment for an example of such a graph.

Hence, the interval is (0 < x < 4) where both functions are increasing on the number line provided.

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Answer:

Step 3

Step-by-step explanation:

4x - 8 < 6x + 18

4x - 6x < 18 + 8

- 2x < 26

The steps in the solution that follows correctly from the previous steps are:

Step 1

Step 2

Step 3

Step 4

All the options are correct.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

4(x - 2) < 6(x+3)

Removing the parenthesis.

Step 1:

4x - 8 < 6x + 18

Subtracting -6x on both sides.

4x - 8 - 6x < 6x + 18 - 6x

Step 2:

-2x - 8 < 18

Add 8 on both sides.

-2x < 18 + 8

Step 3:

-2x < 26

Divide both sides by 2.

-x < 13

Multiply - on both sides.

The sign will change.

Step 4:

x > -13

We see that,

All the steps are given correctly.

Thus,

The steps in the solution that follows correctly from the previous steps are:

Step 1

Step 2

Step 3

Step 4

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Answer:

Multiply 3 times 5.25

Answer:

its A

Step-by-step explanation:

The length of AB is 12 units. The two smaller triangles formed, namely ABD and BCD, are similar to the original triangle ABC.

In a right triangle ABC, with the altitude BD drawn to the hypotenuse AC, we can use the property of similar triangles to find the length of AB.Let x be the length of AB. Since the triangles ABD and ABC are similar, we can set up a proportion:

AB/AD = AC/AB+BC

Substituting the given values, we have:

x/12 = 27/(x + BC)

Cross-multiplying, we get:

27x = 12(x + BC)

Simplifying further:

27x = 12x + 12BC

Combining like terms:

15x = 12BC

Dividing both sides by 15:

x = (12/15)BC

Since BD is the altitude, we know that BD + DC = AC. Substituting the values:

12 + BC = 27

Simplifying:

BC = 15

Substituting BC = 15 back into the equation for x, we find:

x = (12/15)(15)

x = 12

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Answer:

See Explanation

Step-by-step explanation:

\(

\because \sin\bigg(\frac{\pi}{2} + x\bigg)= \cos x\\

\&\: \sin (\pi - x) = \sin x\\\\

Now,

\frac{\sin\bigg(\frac{\pi}{2} + x\bigg)}{\sin (\pi - x)} = \cot x\\\\

LHS

= \frac{\sin\bigg(\frac{\pi}{2} + x\bigg)}{\sin (\pi - x)} \\\\

=\frac{\cos x}{sinx} \\\\

= \cot x\\\\

= RHS\\\\

Hence\: Proved

\)

The correct answer is as follows: a) The data set that has the greatest sample standard deviation is Data set (ii).

b) Data set (ii) has the largest mean and mode, but the smallest median and the largest standard deviation.

(a) The data set that has the greatest sample standard deviation is Data set (ii).

The sample standard deviation is a measure of the amount of variation or dispersion of a set of data values.

In this case, Data set (ii) has more entries that are farther away from the mean, which results in a larger standard deviation.

(b) The data sets are the same in terms of containing the same numbers (11, 12, 13, 14, 15, 16, and 17).

However, they differ in terms of the order in which these numbers are arranged.

In addition, they differ in terms of the mean, median, mode, and standard deviation.

For example, Data set (ii) has the largest mean and mode, but the smallest median and the largest standard deviation.

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Answer: 24 inches

Step-by-step explanation:

Answer: sara is 60

Step-by-step explanation: 64 divided by 4 equals 16. 16 plus 44 equals 60

Answer:

When rotating any polygon 90 degrees, each vertice/point of the polygon should be changed from (x, y) to (y, -x). Because of this, E(-7, -4) should be E'(-4, 7), F(-2, -1) should be F'(-1, 2), and G(-5, -8) should be G'(-8, 5) after the rotation.

Step-by-step explanation:

Like I explained above, when rotating a shape 90 degrees clockwise on a plane, the points change from (x, y) to (y, -x). The student changed each point from (x, y) to (-y, x), which is a 90 degree counterclockwise rotation. That is why the student is incorrect.

I hoped this helped! Sorry, I am terrible at explaining things. :)

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Let's simplify step-by-step.

5x^3 + 3 + 2x^3 − x^2 + 1

= 5x^3 + 3 + 2x^3 + −x^2 + 1

Combine Like Terms:

= 5x^3 + 3 + 2x^3 + −x^2 + 1

= ( 5x^3 + 2x^3 ) + ( −x^2 ) + ( 3 + 1 )

= 7x^3 + −x^2 + 4

Answer:

= 7x^3 − x^2 + 4

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