A 16-ft ladder leans against a building, as shown. To thenearest foot, how far is the base of the ladder from the building?8 feet22 feet4 feet11 feet

Answer:

B. Six inches less than her brothers

Answer: B.

Step-by-step explanation:

The exponents' best option will be determined by

a + b's value is seven.

How often a number is multiplied by itself is indicated by the exponent.

For instance

In this case, 2 is multiplied by 4

Now in ( m times)

The base is designated as a, and the power is designated as m.

There are some indexing laws.

\(1)a^m \times a^n = a^{m+n}\\2)\frac{a^m}{a^n} = a^{m-n}\\3) (a^m)^n = a^{mn}\\4) (ab)^m = a^mb^m\\5) a^0 = 1\\6) a^{-m} = (\frac{1}{a})^m\)

Here,

\((2^a)(2^b) = 128\\\)

\(2^{a+b} =2^7\) [According to laws of indices]

\(a + b = 7\)

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Complete Question

If \((2^a)(2^b) = 128\\\), then a  + b is equal to?

According to the above, the point s coincides with number -5, the point t coincides with number -8.24 and the point u coincides with number 6.28.

To identify the points that coincide with the expressions we must perform the mathematical operations shown. In this case, we must find the roots and multiply the 2 by the number pi as shown in the expressions column.

An important point is that we must do these operations in the positive form and then put the negative symbol because it is not possible to find the root of a negative number.

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The quantity of lemonade that Regan sold on saturday given the amount sold by Mark is 1 11/12 gallons.

Fractions are non-integers that consist of a numerator and a denominator. A proper fraction is a fraction in which the numerator is less than the denominator. e.g. 2/3. A mixed fraction is made up of a whole number and a proper fraction. An example is 2 7/8.

2 7/8 x 2/3

23/8 x 2/3 = 23/12 = 1 11/12 gallons

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I hope this helps you, I just took this quiz so it is correct.

Answer:

11.66 per week

Step-by-step explanation:

alex gets 11.66

dann gets 23.32

eva gets 16.66

By using the Concept of Permutations,There are 59,280 different ways to choose the president, vice president, and secretary from a class of 40 students.

To determine the number of different ways people can be chosen as president, vice president, and secretary from a class of 40 students:

You can use the concept of permutations.

Step 1: Choose the president. There are 40 students in the class, so there are 40 choices for the president position.

Step 2: Choose the vice president. Since the president has been chosen, there are now 39 remaining students to choose from for the vice president position.

Step 3: Choose the secretary. After selecting the president and vice president, there are 38 remaining students to choose from for the secretary position.

Now, multiply the number of choices for each position:

40 (president) x 39 (vice president) x 38 (secretary) = 59,280 different ways to choose the president, vice president, and secretary from a class of 40 students.

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The calculations are

a) 4.5 × 0.03060 × 0.421 = 0.0570

b) (7.290 × 10^11) ÷ (6.7100 × 10^4) = 1.09 × 10^7

c) 87.6 + 9.988 + 2.2 + 10.87 = 110.6

d) (25.1 + 273.15) ÷ 2.67410 = 108.1

a) To determine the correct number of significant figures, we multiply the numbers and then round to the least number of significant figures involved, giving the answer of 0.0570.

b) The division of two numbers in scientific notation involves dividing the coefficients and subtracting the exponents. After performing the calculation and rounding to the correct number of significant figures, we get the answer of 1.09 × 10^7.

c) Adding the given numbers, we obtain the sum of 110.6. Since all the numbers provided have three significant figures, the answer also has three significant figures.

d) First, we perform the addition of 25.1 and 273.15, giving us 298.25. Then, we divide this result by 2.67410, rounding to the correct number of significant figures, resulting in the answer of 108.1.

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Answer:

1 kilometer east

Step-by-step explanation:

if you subtract 2 from 3 you get one, plus it's east with the bigger number, so that's why it's one kilometer east

The displacement from his starting point at home is 1 km.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

A man drives 3 km east from home to the store and then 2 km west to a friend’s house.

The term "displacement" refers to a shift in an object's location. It is a vector quantity with a magnitude and direction.

The displacement from his starting point at home is calculated as,

Displacement = 3 - 2

Displacement = 1

The displacement from his starting point at home is 1 km.

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1) 180 square cm

Answer:

2) 41 cubic cm

Step-by-step explanation:

1)

Area of pool = 12 * 15 = 180 square cm

2) Volume of water = 1/3 * Volume of pool

= 1/3 *123

= 41 cubic cm

Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)

Where, x represent the number of totts.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

My friend Raw has either no more than 5 toots and more than 10 toots.

Now, Let number of toots = x

Hence, We get;

⇒ x < 5

And, x > 10

Thus, The solution of the inequality is,

⇒ x ∈ (- ∞, 5) ∪ (10, ∞)

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Answer: 1+17r is your answer

Step-by-step explanation: Combine like terms

Answer:

1+17r

Step-by-step explanation:

The linear approximation of the function at the indicated point is as follows: F(x,y) = x -5y - 1

The linear approximation of a function is nothing more than estimating the value of the function at a location using a line. When we see a curve (of a function) with a point on it, we recall the idea of the tangent line. If we determine the equation of the tangent line at the given position, the value of the function at any location extremely near to the given point can be estimated using the equation of the tangent line. Since the tangent line is used in this process, the idea is also referred to as the "tangent line approximation" or "linear approximation."

How to solve?

In this case, our goal is to locate the linear approximation of the provided function at the stated location.

We start by replacing the values, then determine the partial derivative with regard to x and finally y.

We now sum these values, having first substituted the x and y values into the differentiated partial equation. The findings are then added up.

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a. To find the direction of the vector p1p2⇀, we subtract the coordinates of p1 from the coordinates of p2: (x2 - x1, y2 - y1, z2 - z1).

For the given points:

1. p1(-1, 1, 5), p2(2, 5, 0): The direction of p1p2⇀ is (2 - (-1), 5 - 1, 0 - 5) = (3, 4, -5).

2. p1(1, 4, 5), p2(4, -2, 7): The direction of p1p2⇀ is (4 - 1, -2 - 4, 7 - 5) = (3, -6, 2).

3. p1(3, 4, 5), p2(2, 3, 4): The direction of p1p2⇀ is (2 - 3, 3 - 4, 4 - 5) = (-1, -1, -1).

4. p1(0, 0, 0), p2(2, -2, -2): The direction of p1p2⇀ is (2 - 0, -2 - 0, -2 - 0) = (2, -2, -2).

b. To find the midpoint of the line segment p1p2⇀, we take the average of the coordinates of p1 and p2: ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2).

For the given points:

1. p1(-1, 1, 5), p2(2, 5, 0): The midpoint of p1p2⇀ is ((-1 + 2)/2, (1 + 5)/2, (5 + 0)/2) = (0.5, 3, 2.5).

2. p1(1, 4, 5), p2(4, -2, 7): The midpoint of p1p2⇀ is ((1 + 4)/2, (4 + (-2))/2, (5 + 7)/2) = (2.5, 1, 6).

3. p1(3, 4, 5), p2(2, 3, 4): The midpoint of p1p2⇀ is ((3 + 2)/2, (4 + 3)/2, (5 + 4)/2) = (2.5, 3.5, 4.5).

4. p1(0, 0, 0), p2(2, -2, -2): The midpoint of p1p2⇀ is ((0 + 2)/2, (0 + (-2))/2, (0 + (-2))/2) = (1, -1, -1).

a. To find the direction of a vector, we subtract the coordinates of its initial point from the coordinates of its terminal point. This gives us a vector that represents the change in position from the initial point to the terminal point. In this case, we subtract the coordinates of p1 from the coordinates of p2. The resulting vector represents the direction of movement from p1 to p2.

b. To find the midpoint of a line segment, we take the average of the coordinates of its

two endpoints. This gives us a point that lies exactly halfway between the two endpoints. In this case, we add the coordinates of p1 and p2 and divide each sum by 2 to find the average. The resulting point represents the midpoint of the line segment p1p2⇀.

By finding the direction and midpoint of a line segment, we can gain insight into its geometric properties. The direction vector provides information about the orientation and magnitude of the line segment, while the midpoint gives us a central reference point. These calculations are fundamental in geometry and can be applied in various contexts, such as determining the slope of a line or finding the center of a line segment.

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The point that should an open circle be drawn exists (0, 0).

The first equation in the system is f(x) = -x, for x < 0.  

This means when x=0, f(x) = f(0) = 0.

Since we have the inequality x<0, this means at the point (0, 0),

the point will be open and not filled in.

Therefore, the correct answer is option b) (0, 0).

The complete question is:

The function f(x) is to be graphed on a coordinate plane

At what point should an open circle be drawn?

a) (–1, 0)

b) (0, 0)

c) (0, 1)

d) (1, 0)

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Using permutations, the word CAMPFIRE can be arranged in 40,320.

A permutation is the number of ways in which a data set can be arranged or ordered.

Order is important in permutations, unlike in combinations.

The word to be arranged in different ways = CAMPFIRE

The number of letters in CAMPFIRE = 8

The formula for permutations is: n! / (n - r)!.

In this formula:

n is the number of letters in the word

r is the number of letters to be arranged

n = 8

r = 8

8! / (8 - 8)!

= 8! / 0!

= 8! / 1 = 8!

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40,320

Thus, the word CAMPFIRE can be arranged in 40,320 ways based on the permutation formula.

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The maximum number of mites in the peach orchard are 1564

Given that,

There are found to be mites in a peach orchard. According to research conducted by the Department of Agriculture, the number of mites t hours after the orchard has been sprayed is roughly represented by the equation N(t)=1600-3tln(0.07t)-t

To find : What is the maximum number of mites in the peach orchard? Round to the nearest whole number.

N(t)=1600-3tln(0.07t)-t

N(19)=1600-3(19)ln(0.07(19))-(19)

N(19)=1600- 16.255 - 19

N(19)=1564.74

N(19)≈1564

Therefore, the maximum number of mites in the peach orchard are 1564

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In June, Guillermo's Oil and Lube performed a total of 980 oil changes for automobiles and light trucks.

1. Calculate the total time spent on oil changes:

  Since a typical oil change takes 24 minutes, multiply 24 by 980: 24 * 980 = 23,520 minutes.

2. Determine the total amount of oil used:

  On average, 6.2 quarts of oil are used per oil change. Multiply 6.2 by 980: 6.2 * 980 = 6,076 quarts.

Therefore, in June, Guillermo's Oil and Lube performed 980 oil changes, which took a total of 23,520 minutes.

They used a total of 6,076 quarts of oil for these oil changes.

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The value of the constant k that makes the differential equation (6zy-ey)dr = (et - kr?)dy exact is k = 3. The homogeneous equation can be converted to a separable dc y equation by using the substitution y = ur.

To find the value of k, we need to check if the differential equation is exact. A differential equation is exact if the following condition holds:(6zy-ey)_y = (et - kr?)_x

In this case, we have:

(6zy-ey)_y = 6z - e

and:

(et - kr?)_x = e - 2kr

Equating these two expressions, we get:

6z - e = e - 2kr

Solving for k, we get:

k = 3

Now, to convert the homogeneous equation to a separable dc y equation, we use the substitution y = ur. This gives us the following equation:

(6zu - eu)dr = (et - 3r^2)du

Dividing both sides of this equation by u, we get:

6z - e = et/u - 3r^2/u

Multiplying both sides of this equation by u, we get:

6zu - eu = et - 3r^2

This is a separable dc y equation.

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We can conclude that C. the neighborhood is significantly less likely to be Democrat.

The null hypothesis was that there is no difference between the proportion of Democrats in the sample and the population. Since the null hypothesis has been rejected, it means that there is a significant difference between the sample and the population proportions. In this case, 60% of the respondents in the random sample are Democrats, which is lower than the 75% Democrat proportion in the community as a whole. Therefore, we can conclude that the neighborhood from which the sample was drawn is significantly less likely to be Democrat compared to the overall community.

The other options are not supported by the given information:

A type I error might or might not have occurred. We cannot determine this based on the information provided. A type I error refers to the incorrect rejection of a true null hypothesis. Without knowing the true proportions of the neighborhood, we cannot determine if a type I error has been committed. Whether a one-tailed test or a two-tailed test was used is not specified in the question.

However, the conclusion that the neighborhood is significantly less likely to be Democrat can be derived from either type of test. Therefore, the correct option is C.

The question was incomplete, Find the full content below:

sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one:

a. a type i error has been committed

b. a one-tailed test has definitely not been used

c. the neighborhood is significantly less likely to be democrat

d. the difference is not significant

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Sipho made two misconceptions in his calculation. Firstly, he incorrectly calculated 35 ÷ 14 as 5/2 instead of 2.5. Secondly, he subtracted a fraction from a whole number instead of converting the fraction to a decimal first.

Sipho was given the sum 4310− 35÷14 to calculate. Let's analyze each step that Sipho did and identify any misconceptions:

Step 1: 35 ÷ 14 = 5/2

Misconception: Sipho seems to have divided 35 by 14 and obtained the result as a fraction of 5/2. However, this is incorrect. The correct result is 2.5. It appears that Sipho made a mistake while dividing 35 by 14.

Step 2: 4310 - 5/2

Misconception: Sipho subtracted the result of 35 ÷ 14 from 4310. However, since he obtained the result as a fraction, he should have converted it to a decimal first before subtracting. The correct calculation would have been 4310 - 2.5 = 4307.5.

Therefore, Sipho made two misconceptions in his calculation. Firstly, he incorrectly calculated 35 ÷ 14 as 5/2 instead of 2.5. Secondly, he subtracted a fraction from a whole number instead of converting the fraction to a decimal first.

It is essential to understand the basic principles and operations of Mathematics to avoid such errors. Careful attention to detail, practice, and clarification of doubts can help in avoiding such misconceptions.

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Answer:

\(\boxed {\boxed {\sf \ \frac {17}{77}}}}\)

Step-by-step explanation:

The experimental probability is the probability of an event occurring in an experiment that was conducted. It is the ratio of the times an event occurred to the total trials.  

\(P(event)= \frac{ number \ of times \ event \ occurs} {total \ number \ of \ trials}\)

We are trying to find the experimental probability of landing on green.

\(P(green)= \frac{17}{77}\)

This fraction cannot be simplified any further, so the experimental probability of landing on the color green is 17/77

Answer:

dicailmal 4.6  and ratioal 4:6                dont add this but this will also work 4/6

Step-by-step explanation:

Answer: don’t know the “following probabilities but I have included answers below

Step-by-step explanation:

4 blue + 6 green = 10 total

probability of getting green once and blue next: 6/10*4/9 = 24/90 or about 0.27

probability of green both times: 6/10*6/9 = 36/90 or 0.4

probability of blue first then green next: 4/10*6/9 = same as first answer (about 0.27)

probability of blue both times: 4/10*4/9 = 16/90 or about 0.18

Yes, it is possible for a process to pass through the 2nd or 4th quadrant. The 2nd quadrant is characterized by negative values of work done and positive values of heat added.

This could happen in a scenario where a gas is compressed at a constant temperature, which results in negative work done, but heat is added to the gas to maintain its temperature. The 4th quadrant is characterized by negative values of both work done and heat added. This could happen in a scenario where a gas is expanded at a constant temperature, which results in negative work done and no heat is added or removed from the gas.

As for the effect of a negative value of the polytropic index 'n', it indicates that the process is non-adiabatic and not reversible. A negative value of 'n' means that the process is not able to maintain constant heat transfer or constant entropy. This could result in energy losses and a decrease in the efficiency of the process. It could also indicate that the process is not in equilibrium and is being driven by external forces. Overall, a negative value of 'n' can have negative effects on the performance and stability of a process.

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There is a 50-50 chance that John gets to the airport before Jane. Therefore, the chance that John gets to the airport before Jane is 1/2.

Suppose John takes the shuttle van directly from Berkeley to the airport, and Jane drives from Berkeley and takes the parking shuttle. They leave at the same time, and their travel times are independent. The chance that John gets to the airport before Jane is 1/2.Solution:

Since the travel times of John and Jane are independent and given that they leave at the same time, the chance that John gets to the airport before Jane is equal to the probability that Jane arrives at the airport after John.

There are two possible outcomes, either John arrives first or Jane arrives first. Both of these outcomes are equally likely.

Since the probability of two mutually exclusive events happening is equal to the sum of their probabilities, and we know that the probability of both John and Jane arriving at the same time is 0, the probability that John gets to the airport before Jane is:1/2

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We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,(\(H_{0}\)):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,(\(H_{A}\)) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ \(\sqrt{p'(1-p')/n}\) ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ \(\sqrt{0.231( 1- 0.231)/ 273}\)

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

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The minimal cost of the box is $96.

Given data;

The volume of the box (v) = x²y

Given that, volume = 16 m³

So, 16 = x²y

y = 16/x² → (I)

Material for the base costs $8 per square meter, and material for the sides costs $2 per square meter.

Total cost (C) = 8 (x²) + 2*(xy)(4)

                      = 8x² + 8xy

Using (I),

C(x) = 8x² + 8x(16/x²)

C (^) = 8x² + 128/x

Now find critical points from

∴ \(\frac{d}{dx} = [8x^2+\frac{128}{x} ]=0\)

  x³ = 8

  x = 2

So, the minimal cost will be given by x= 2,

Now, y = 16/x²

            = 16/4

            = 4

Dimension of the box that minimizes the cost is;

height = 4m, width=2m and breadth = 12m

Now,

Minimum cost = 8 (2)² + 128/2 = 32 + 64

                        = 96

Hence, The minimal cost of the box is $96.

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Answer:

π is an irrational number which has value 3.142…and is a never-ending and non-repeating number.

I am going to say no simply bc pi itself can't be multiplied by 0 whatever times 0 going to be 0 and so 0 is rational

Answer:

Step-by-step explanation:

Volume of cylinder=pir^h

420={22/7×6×6]h=792/7h=113.14h

h=420/113.14

h=3.712