a ladder is leaning against a wall. the ladder touches the wall 15 feet above the ground. how far is the bottom of the ladder from the wall if the length of the ladder is one foot more than twice its distance from the wall

The centre of the rotation is A

The line of the reflection is Y

Vertex A of the triangle ABC when rotated by 90° counterclockwise about the origin,

Rule to be followed,

A(x, y) → P(-y, x)

Therefore, A(1, 1) → P(-1, 1)

Similarly, B(3, 2) → Q(-2, 3)

C(2, 5) → R(-5, 2)

Triangle given in second quadrant will be the triangle PQR.

If the point P of triangle PQR is reflected across a line y = x,

Rule to be followed,

P(x, y) → X(y, x)

P(-1, 1) → X(1, -1)

Similarly, Q(-2, 3) → Y(3, -2)

R(-5, 2) → Z(2, -5)

Therefore, triangle given in the fourth quadrant is triangle XYZ.

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Answer:

33.94 cms of ribbon

Step-by-step explanation:

Because you need two diagonals to form the x, therefore the amount  of ribbon needed is the sum of the distance of both diagonals.

When crossing the diagonal, a rectangular angle is formed, where the diagonal would be the hypotenuse, we know that the distance of the hypotenuse can be calculated by means of the legs, which we know its value (12):

d ^ 2 = a ^ 2 + b ^ 2

a = b = 12

d ^ 2 = 12 ^ 2 + 12 ^ 2

d ^ 2 = 288

d = 288 ^ (1/2)

d = 16.97

16.97 cm is what it measures, a diagonal, therefore tape is needed:

16.97 * 2 = 33.94

A total of 33.94 cms of ribbon is needed

Answer from jmonterrozar

Answer:

Because is said

Step-by-step explanation:

C

The value of GI is approximately B. 77. Hence, the correct answer is B. 77.

Based on the given information and the similarity of triangles ^GHI and ^JKL, we can use the concept of proportional sides to find the value of GI.

We have the following information:

JP = 35

MH = 33

PK = 15

Since the triangles are similar, the corresponding sides are proportional. We can set up the proportion:

GI / JK = HI / KL

Substituting the given values, we get:

GI / 35 = 33 / 15

Cross-multiplying, we have:

GI * 15 = 33 * 35

Simplifying the equation, we find:

GI = (33 * 35) / 15

GI ≈ 77

Therefore, the value of GI is approximately 77.

Hence, the correct answer is B. 77.

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We can be 99.7% confident that the true proportion of individuals with schizophrenia in the population lies between 0.44 and 0.62.

In our schizophrenia model, the rough 99.7% certainty stretch can be determined utilizing the point gauge and standard blunder of the extent. With a point gauge of 0.53 and a standard blunder of 0.03, we can involve the equation for a certainty stretch, which is point gauge ± z* (standard mistake), where z* is the z-score related with the ideal certainty level.

For a 99.7% certainty stretch, the z-score is roughly 3. Consequently, the certainty span would be:

0.53 ± 3(0.03) = (0.44, 0.62)

This implies that we can be 99.7% certain that the genuine extent of people with schizophrenia in the populace lies somewhere in the range of 0.44 and 0.62.

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The number that is  2/3 of the way between 7 and 8 is, 16/24, 21/24.

a.

First step is to rewrite the fraction as an equivalent fraction in order for  both fractions to have the same denominator.

2/3=16/24

7/8=21/24

Hence:

2/3=0.66 and 16/24=0.66

7/8=0.875 and 21/24=0.875

b. The rational number in between  2/3 and 7/8 is  19/24

Therefore the number that is  2/3 of the way between 7 and 8 is, 16/24, 21/24.

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Answer:

7 x 2.6

Step-by-step explanation:

the square root of 7 is exactly 2.645751311064591, so in this case I converted it to a smaller number, using tenths place.

solution:

7 x 2.6 = 18.2

Answer:

\( {7}^{ \frac{3}{2} } \)

Step-by-step explanation:

\( \sqrt{7} \: can \: also \: be \: written \: as \: {7}^{ \frac{1}{2} } \)

We can use this information to rewrite the original expression:

\(7 \times {7}^{ \frac{1}{2} } \)

7 can also be written as

\( {7}^{1} \)

Remember that when multiplying exponents, if they have the same base, we can add the exponents. Therefore:

\( {7}^{1} \times {7}^{ \frac{1}{2} } \\ {7}^{1 + \frac{1}{2} } \\ {7}^{1 \frac{1}{2} } \\ {7}^{ \frac{3}{2} } \)

This form of number of trade illustrates an example of comparative advantage, where each country specializes in the production of goods that they are more efficient at producing and then trading those goods with each other.

Comparative advantage is a concept in economics that states that countries that specialize in goods they are more efficient at producing will be able to produce those goods at a lower cost than countries that do not specialize in that good. In this form of trade, China specializes in the production of silk, while Germany specializes in the production of automobiles. By trading these goods with each other, both countries are able to benefit from the number of  specialization of each other, as they can produce silk or automobiles more efficiently and at a lower cost than the other country.

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Answer:

a)4/10

b)5/100000000000೦

c)6

Answer:

2 13/50

Step-by-step explanation:

gogle

On solving the expression 2 + (4/5) - (3/20), we get 53/20.

Given is the expression -

2 + (4/5) - (3/20)

The given expression is -

2 + (4/5) - (3/20)

Now, solving further, we get -

2 + (4/5) - (3/20)

2 + 4/5 - 3/20

(40 + 16 - 3)/20

53/20

Therefore, the given expression 2 + (4/5) - (3/20) is equivalent to 53/20.

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Answer:

EF is parallel to HG or EH is parallel to FG. EF to HG is correct I think.

Step-by-step explanation:

Look at the markings on the lines.

Answer:

option (e) 8

Step-by-step explanation:

using identity

==>1/(a^(-x))=a^x()

=(1/2)^(-3)

=(2)^3

=2*2*2=8

option (e)

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Answer:

12

Step-by-step explanation:

To find range, you subtract the largest and smallest number :)

It will take 11 posts for the number of followers to be equal

They will have 255 folllowers each on the 11th post

Here, we want to get the number of posts that would make them both have the same number of followers

For the first person, her number of followers after n post will be;

For the second person, her number of follwers after n post will be;

Since we have that, after n posts, the number of followers will be equal; we simply go on to equate the two

Thus, we have this as;

So after 11 posts, the number of follwers they each have will be the same

Now, we want to calculate the number of followes they have at the 11th post

We just need to substitute for n in any of the equations

Thus, we have that, the number of followers is';

The machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test using the normal distribution.

What is Normal Distribution?

The Normal Distribution, often known as the Gaussian Distribution, is the most important continuous probability distribution in probability theory and statistics. It is also referred to as a bell curve on occasion. In every physical science and in economics, a huge number of random variables are either closely or precisely described by the normal distribution. Additionally, it may be used to roughly represent various probability distributions, reinforcing the notion that the term "normal" refers to the most common distribution.

Let X denotes the scores.

In the question, It is given that:

Normal distribution with p=400 and 60.

\(X \sim N(\mu=400, \sigma=60)\\$$$\frac{X-\mu}{\sigma}(=Z) \sim N(0,1)$\\i.e. $P(Z \leq z)=\Phi(z)$\)

Let 'a' be the score to be in the top 10% of all machinists.

\(\begin{aligned}&P(X \leq a)=1-0.10=0.90 \\&\text { or, } P\left(\frac{X-\mu}{\sigma} \leq \frac{a-400}{60}\right)=0.90 \\&\text { or, } \Phi\left(\frac{a-400}{60}\right)=0.90=\Phi(1.282) \\&\text { or, } \frac{a-400}{60}=1.282 \\&\text { or, } \mathbf{a}=\mathbf{4 7 6 . 9 2}\end{aligned}\)

So,

The score a machinist need in order to be in the top 10% is 476.92.  

Hence,

a machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test.

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Step-by-step explanation:

\( = \frac{20}{5} . {2}^{ - 3} \)

\( = 4. \frac{1}{ {2}^{3} } \)

\( = \frac{4}{2 \times 2 \times 2} \)

\( = \frac{4}{8} \)

\( = \frac{1}{2} \)

The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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Answer:

A postulate :)

Step-by-step explanation:

This is because a postulate is a statement that is assumed true without proof, while a theorem is a true statement that can be proven.

Hope this helps!

To determine the minimum sample size needed to estimate the mean number of hours worked per week by college graduates employed full-time, while ensuring that our estimate is within a certain margin of error.

We can use the formula for sample size calculation.

The formula is:
\(n = (Z * σ / E) ^ 2\)

Where:
n = minimum sample size needed
Z = Z-score corresponding to the desired confidence level (e.g., for 95% confidence level, Z ≈ 1.96)
σ = standard deviation of the population (given as hours per week)
E = maximum margin of error (given as hours per week)

Plugging in the given values, let's say we want the estimate to be within 2 hours per week:

\(n = (1.96 * σ/ 2) ^ 2\)
Since the standard deviation (σ) is not given in the question, we cannot calculate the exact sample size.

However, once the value of σ is known, you can substitute it into the equation to find the minimum sample size needed for your desired margin of error.

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Answer:

2. All reals

Step-by-step explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

Answer:

(x-6) (x+5)

Step-by-step explanation:

x^2 - x - 30

What two terms multiply to -30 and add to -1

-6 *5 = -30

-6+5 = -1

(x-6) (x+5)

Answer:

A) The expressions for the Perimeter of the garden =

Perimeter = (x + 12)ft + (x +12)ft + (x + 8)ft + (x + 8)ft

Perimeter = 4x + 40 ft

B) The expressions for the Area of the garden =

Area = (x + 12)ft + (x + 8)ft

Area = (x² + 20x + 96)ft²

Step-by-step explanation:

A garden is 12 feet long by 8 feet wide. The length and width of the garden will each be increased by the same number of feet.

The expressions below represent the new length and width of the larger garden Length = (x + 12) ft; width = (x + 8)

A) Perimeter of the Garden

Let us assume that the Garden is rectangular

The formula for Perimeter of the Garden = 2L + 2W

Length = (x + 12)ft

Width = (x + 8)ft

Perimeter = 2(x + 12) ft + 2(x + 8)ft

Perimeter = (x + 12)ft + (x +12)ft + (x + 8)ft + (x + 8)ft

Perimeter = (2x +24 + 2x + 16)ft

Perimeter = (2x + 2x + 24 + 16)ft

Perimeter = 4x + 40 ft

B) The Area of the Garden

The formula for Area of the Garden = L × W

Length = (x + 12)ft

Width = (x + 8)ft

Area = (x + 12)ft + (x + 8)ft

Area = (x² + 8x + 12x + 96)ft²

Area = (x² + 20x + 96)ft²

Purpose of having a supplier scorecard A supplier scorecard is a tool that is used to evaluate the performance of suppliers and to monitor their progress. It helps in the assessment of how well the suppliers are meeting the needs of the buyers and it helps the buyers to decide which suppliers they should continue to work with in the future.

The purpose of having a supplier scorecard is to evaluate the suppliers' performance in terms of quality, delivery, price, and customer service, and to monitor their progress over time. The scorecard can be used to identify areas where suppliers are excelling and areas where they need to improve. Analysis of the current scorecard and concerns Emily’s concern is that the current scorecard is too simplistic and does not provide enough information to make informed decisions about suppliers. The concerns with the current scorecard are that it is too simplistic and does not provide enough information about the supplier's performance. Analysis of the proposed scorecard and its adequacy The proposed scorecard addresses Emily's concerns by providing more detailed information about the supplier's performance in specific areas.

It also includes more metrics for evaluating the supplier's performance. Differences between the current scorecard and the proposed scorecard The proposed scorecard is more detailed and includes more metrics than the current scorecard. It provides more information about the supplier's performance in specific areas. How suppliers will react to the proposed scorecard and the dynamics of the buyer-supplier relationship Suppliers may react negatively to the proposed scorecard if they feel that it is too strict or unfair. The scorecard may change the dynamics of the buyer-supplier relationship by putting more pressure on suppliers to meet certain standards. Potential options, recommendations, and actionSome potential options and recommendations for improving the scorecard include adding more metrics, providing more detailed feedback to suppliers, and revising the scoring system to make it more accurate and fair.

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Answer:

x=8, y=4

(8,4)

Step-by-step explanation:

y = x - 4

y = -0.5x + 8

x - 4 = -0.5x + 8

x = -0.5x + 12

1.5x = 12

15x = 120

x = 8

plug x back into one of the first equations, and you get

y = 4.

(8,4)

Midpoint is (5, 4)

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#1

-6-3-5

Hence inequality will be

\(\\ \sf\longmapsto -6\leqslant 5\)

#2.

3<5

But we need inequality

\(\\ \sf\longmapsto 3\leqslant 5\)

#3

The inequality given by

\(\\ \sf\longmapsto -6\leqslant 3\leqslant 5\)

Answer:

1. Inequality

\( \hookrightarrow \: { \rm{ - 6 < 0 < 3}}\)

2. Inequality

\( \hookrightarrow \: { \rm{3 < 0 < 5}}\)

3. Inequality

\( \hookrightarrow \: { \rm{ - 6 < 0 < 3 < 5}}\)

Answer:

-----------------------

Use the principle of inclusion-exclusion.

Substitute values and find the number of Both:

Find out how many read only one newspaper:

So, 30 people read both newspapers, and 70 people read only one newspaper.

a)The two way table is shown in figure,

b)The success rate of the three treatments in preventing cardiac arrests are 90.91% , 79.41% and 70%.

c)The expected cell count are as shown in the figure,

d)No. There is no difference among the treatments.

e) The brief summary is mentioned below.

Given,

The total number of people is 107.

33 people are enrolled in a stress management programme.

3 people had cardiac events as a result of the stress management programme.

34 people are in the exercise group.

The number of cardiac events in the exercise group was 7 people.

40 people receive routine care.

12 people had cardiac events while receiving standard care.  

a)

The two-way table for the given information is shown in the figure

b)

During the same time period, 7 of the 34 people in the exercise group and 12 of the 40 patients in usual care experienced such events.Success rate can be determined by,

\(Success=\frac{no.\ of\ people\ who\ did not\ suffered\ in\ group}{Total\ number\ of people\ in\ group}\)

For stress management:-

\(Success\ rate = \frac{30}{33}=0.9091=90.90\%\)

For exercise program:-

\(Success\ rate = \frac{27}{34}=0.7941=79.41\%\)

For usual care:-

\(Success\ rate = \frac{28}{40}=0.7=70\%\)

c)

Expected cell count can be calculated by formula,

\(Expected\ value=\frac{row\ total*column\ total}{table\ total}\)

then,

Expected value for the people who suffered cardiac arrest,

Under stress management:-

\(E= \frac{22*23}{107}=6.79\)

Under exercise group:-

\(E=\frac{22*34}{107}=6.99\)

Under usual care:-

\(E=\frac{22*40}{107}=8.22\)

Expected value for the people who did not suffered cardiac arrest :-

Under stress management:-

\(E=\frac{85*33}{107}=26.21\)

Under exercise group:-

\(E=\frac{85*34}{107}=27.01\)

Under usual care:-

\(E=\frac{85*40}{107}=31.78\)

The expected cell count is mentioned in the table

d)

The null and alternate hypothesis are

\(H_0\) :There is no difference in the actual success rates of the three treatments.

\(H_1\) :The three treatments differ in terms of actual success rates.

The test statistic can be calculated by

\(x^2=\sum \frac{(O-E)^2}{E}\)

Where,

O=observed value

E=Expected value

Under null hypothesis,

\(x^2=\frac{(3-.679)^2}{6.79}+\frac{(7-6.99)^2}{6.99}+\frac{(12-8.22)^2}{8.22}+\frac{(30-26.21)^2}{26.21}+\frac{(27-27.01)^2}{27.01}+\frac{(28-31.78)^2}{31.78}\\\\=4.8514\)

The p-value for the test is \(P(x_2 > 4.8514)=0.0884\)

There is no statistically significant difference in the success rates of the three treatments.

e)

Because the p-value is greater than 0.05 (at the 5% level of significance), there is insufficient evidence to reject the null hypothesis and conclude that there is no difference in the actual success rates for the treatments.

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