Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.

Answer:

see image...

the (x-h) shifts the curve left right (east west)

and the +k at the end shifts it up/down (north/south)

Step-by-step explanation:

Answer:

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The production manager claims they have a mean life of 83 months with a variance of 81.

This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]

Sample of 146:

This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]

What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?

This is 1 subtracted by the p-value of Z when X = 81.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

1 - 0.0078 = 0.9922.

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

That's a question about quadratic function.

Any quadratic function can be represented by the following form:

[tex]\boxed{f(x)=ax^2+bx+c}[/tex]

Example:

[tex]f(x)= -3x^2-9x+57[/tex] is a function where [tex]a=-3[/tex], [tex]b=-9[/tex] and [tex]c=57[/tex].

Okay, in our problem, we need to find the value of x when [tex]f(x)=0[/tex]. That's mean that the result of our function is equal to zero. Therefore, we have the quadratic equation below:

[tex]x^2+4x-5=0[/tex]

To solve a quadratic equation, we use the Bhaskara's formula. Do you remember the value of a, b and c? They going to be important right now. This is the Bhaskara's formula:

[tex]\boxed{x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} }[/tex]

So, let's see the values of a, b and c in our equation and apply them in the Bhaskara's formula:

In [tex]x^2+4x-5=0[/tex] equation, [tex]a=1[/tex], [tex]b=4[/tex] and [tex]c=-5[/tex]. Let's replace those values:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-4\pm \sqrt{4^2-4\times1\times(-5)} }{2\cdot1}[/tex]

[tex]x=\frac{-4\pm \sqrt{16-(-20)} }{2}[/tex]

[tex]x=\frac{-4\pm \sqrt{16 + 20)} }{2}[/tex]

[tex]x=\frac{-4\pm \sqrt{36} }{2}[/tex]

[tex]x=\frac{-4\pm 6 }{2}[/tex]

From now, we have two possibilities:

To add:

[tex]x_1 = \frac{-4+6}{2} \\x_1=\frac{2}{2} \\x_1=1[/tex]

To subtract:

[tex]x_2=\frac{-4-6}{2} \\x_2=\frac{-10}{2} \\x_2=-5[/tex]

Therefore, the result of our problem is: [tex]x_1 = 1[/tex] and [tex]x_2=-5[/tex].

I hope I've helped. ^^

Enjoy your studies.  \o/

Answer:

The maximum number of minutes to keep the cost at $50 or less is 110 minutes

Step-by-step explanation:

Given

[tex]C(x) = 30[/tex] ---- [tex]x < 60[/tex]

[tex]C(x) = 30 + 0.40(x - 60)[/tex] --- [tex]x \ge 60[/tex]

Required

[tex]C(x) = 50[/tex] ---- find x

We have:

[tex]C(x) = 30 + 0.40(x - 60)[/tex]

Substitute 50 for C(x)

[tex]50 = 30 + 0.40(x - 60)[/tex]

Subtract 30 from both sides

[tex]20 = 0.40(x - 60)[/tex]

Divide both sides by 0.40

[tex]50 = x - 60[/tex]

Add 60 to both sides

[tex]110 = x[/tex]

[tex]x =110[/tex]

Answer:

The height of the spanning tree is one by the breadth-first search at the central vertex of Wn.

Step-by-step explanation:

The graph is connected and has a spanning tree where the tree can build using a depth-first search of the graph. Start with chosen vertex, the graph as the root, and root add vertices and edges such as each new edge is incident with vertex and vertices are not in path. If all vertices are included, it will do otherwise, move back to the next level vertex and start passing. It is for depth-first search. For breadth-first search, start with chosen vertex add all edges incident to a vertex. The new vertex is added and becomes the vertices at level 1 in the spanning tree, and each vertex at level 1 adds each edge incident to vertex and other vertex connected to the edge of the tree as long as it does not produce.

Answer:

a) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.

b) 0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.

c) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Questions a/c:

Questions a and c are the same, so:

Event A: Brings lunch to work.

Event B: Is a woman.

Probability of a person bringing lunch to work:

9% of 15%(woman)

3% of 100 - 15 = 85%(man). So

[tex]P(A) = 0.09*0.15 + 0.03*0.85 = 0.039[/tex]

Probability of a person bringing lunch to work and being a woman:

9% of 15%, so:

[tex]P(A \cap B) = 0.09*0.15[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.039} = 0.3462[/tex]

0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.

Question b:

Event A: Woman

Event B: Brings lunch

15% of the employees are women.

This means that [tex]P(A) = 0.15[/tex]

Probability of a person bringing lunch to work and being a woman:

9% of 15%, so:

[tex]P(A \cap B) = 0.09*0.15[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.15} = 0.09[/tex]

0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.

The 2 men working for 2 hours per 2 days will complete 1/2 unit of work. This is calculated by using the proportions formula.

The formula for the given proportions is,

a: b = c: d

⇒ a/b = c/d

⇒ ad = bc

In this way, the required variable is calculated.

For the given question, the proportion we can write

M1 × H1 × D1: M2 × H2 × D2 = W1: W2

⇒ M1 × H1 × D1 × W2 = M2 × H2 × D2 × W1

Where M1 = 4; H1 = 4; D1 = 4; M2 = 2; H2 = 2; D2 = 2 and W1 = 4

We need to calculate W2 -  required units of work

So, on substituting,

M1 × H1 × D1 × W2 = M2 × H2 × D2 × W1

⇒ 4 × 4 × 4 × W2 = 2 × 2 × 2 × 4

⇒ 64 × W2 = 32

⇒ W2 = 32/64

∴ W2 = 1/2

Thus, the required units of work are 1/2.

So, 2 men working for 2 hours for 2 days will complete 1/2 unit of work.

Learn more about proportions here:

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Disclaimer: The given question is incomplete. Here is the complete question.

Question: If 4 men working for 4 hours for 4 days complete 4 units of work then how many unit of work will be completed by two men working for two hours per 2 days?​

Answer:

601 in²

Step-by-step explanation:

To obtain the amount of wrapping needed to cover the cube shaped gift box, including the bow

Area of bow = 115 in²

Surface area of cube shaped box = 6a²

a = side length of cube = 9

Hence,

Surface area of gift box = 6 * 9²

Surface area = 6 * 81 = 486 in²

Total wrapping required = area of gift box + area of bow = (486 in² + 115 in²) = 601 in²

Answer: SORRY NEED AN ACCOUNT ON - 10

Step-by-step explanation:

To resolve the proposed issue, an explanation is needed in which the subject is addressed

Answer:

0.2725

0.0431

Step-by-step explanation:

The distribution here is a poisson distribution :

λ = 1.3

The poisson distribution :

p(x) = [(e^-λ * λ^x)] ÷ x!

Expected probability of finding male with 0 accident ; x = 0

p(0) = [(e^-1.3 * 1.3^0)] ÷ 0!

p(0) = [0.2725317 * 1] ÷ 1

p(0) = 0.2725317

= 0.2725

2.)

P(x ≥ 4) = 1 - P(x < 4)

P(x < 4) = p(x = 0) + p(x. = 1) + p(x = 2) + p(x = 3)

p(x = 0) =  p(0) = [(e^-1.3 * 1.3^0)] ÷ 0! = 0.2725

p(x = 1) = p(1) = [(e^-1.3 * 1.3^1)] ÷ 1! = 0.35429

p(x = 2) = p(2) = [(e^-1.3 * 1.3^2)] ÷ 2! = 0.23029 p(x = 3) = p(3) = [(e^-1.3 * 1.3^3)] ÷ 0! = 0.09979

P(x < 4) = 0.2725 + 0.35429 + 0.23029 + 0.09979 = 0.95687

P(x ≥ 4) = 1 - 0.95687 = 0.0431

Explanation:

The rule is that if log(A) = log(B), then A = B

Using this idea, we can then say,

log(t - 3) = log(17 - 4t)

t - 3 = 17 - 4t

t+4t = 17+3

5t = 20

t = 20/5

t = 4

The solution to the logarithmic equation is t = 5

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

log ( t - 3 ) = log  (17 - 3t )   be equation (1)

On simplifying , we get

The bases of the logarithm are equal

So , the values are equal and therefore  

t - 3 = 17 - 3t

Adding 3t on both sides , we get

4t - 3 = 17

Adding 3 on both sides , we get

4t = 20

Divide by 4 on both sides , we get

t = 20 / 4

t = 5

Therefore , the value of t is 5

Hence , the logarithmic equation is solved

To learn more about logarithm click :

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Answer:

f(x) = 40(1 + 0.13)^x

Step-by-step explanation:

The general formula for an exponential growth function is;

f(x) = a(1 + r)^x

Where;

a= initial population of the city

r= population growth rate

x = number of years

Given that;

a= 40,000

r= 0.13

The population of the city in thousands of people in terms of x is;

f(x) = 40(1 + 0.13)^x

Answer:

15

Step-by-step explanation:

1-0 =1

3-1 =2

6-3=3

10-6=4

We are adding 1 more each time

10+5 = 15

Answer:

Step-by-step explanation:

The reasons for each statement are inside the parentheses

1. <1 and <2 are complementary (given)

2. m<1 + m<2 = 90° (definition of complementary angles)

3. m<2 = 74° (given)

4. m<1 + 74° = 90° (Substitution)

5. m<1 = 16° (Subtraction property of equality)

This is gotten by subtracting 74° from both sides as follows:

m<1 + 74° - 74° = 90° - 74°

m<1 = 16°

Answer:

x = 2     y = 3

Step-by-step explanation:

-2x + 7 = 5x - 7

-7x + 7 = -7

-7x = -14

x = 2

y = -2(2) + 7

y = -4 + 7

y = 3

Answer:

a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

Step-by-step explanation:

Question a:

The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.

At the null hypothesis, we test if this is the average resistance, that is:

[tex]H_0: \mu = 0.15[/tex]

We are interested in testing the hypothesis that the resistors conform to the specifications.

At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:

[tex]H_1: \mu \neq 0.15[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.15 is tested at the null hypothesis:

This means that [tex]\mu = 0.15[/tex]

Sample mean of 0.152, sample of 10, population standard deviation of 0.005.

This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]

[tex]z = 1.26[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.

Looking at the z-table, z = -1.26 has a p-value of 0.1038.

2*0.1038 = 0.2076

The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

Question b:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.

The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.

The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

Reflective symmetry over the line y = 4 is No

Reflective symmetry over the line y = 1/7x + 3 is Yes

Answer:

$92

Step-by-step explanation:

42 + 26 + 6 + 18 = 92

Answer:

25, 33

Step-by-step explanation:

let the length of the one with equal sides be x

third side = x+8

x+x+x+8 = 83

3x+8 = 83

3x = 75

x = 25

x+8 = 25+8 = 33

We have two lines from the same point.

These two lines are also tangents to same circle which implies that they are of the same length.

That is 2x - 1 = 9

2x = 9 +1 = 10

x =10/2

x = 5

Answer:

Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.

Answer:

[tex]-32^\frac{3}{5} = -8[/tex]

Step-by-step explanation:

Given

[tex]-32^\frac{3}{5}[/tex]

Required

The equivalent expression

We have:

[tex]-32^\frac{3}{5}[/tex]

Rewrite as:

[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]

Expand

[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]

Remove bracket

[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]

[tex]-32^\frac{3}{5} = -2^3[/tex]

[tex]-32^\frac{3}{5} = -8[/tex]

Answer:

Step-by-step explanation:

the mean is

{(12x1)+(13x1)+(14x2)+(15x2)+(17)+(18)+(19x2)+(20)+(21x2)+(22)+(24)}/11

mean=264/11

mean=24

Answer:

3.) A,B,AB,O

Step-by-step explanation:

Non-numeric data refers to categorical data, or data that is not expressed quantitatively. Answers (1) and (2) contain quantitative data, so they would be eliminated as potential answer choices and therefore (4) would also be eliminated. This leaves answer (3), which does not have quantitative data and is therefore non-numeric.

Answer:

N80

Step-by-step explanation:

One ruler is N60 and one pencil is N20.

Answer:

obtuse                    

aniuhafjhnfajfnha

Answer:

m = 12.5

Step-by-step explanation:

x = - 3

(3m - x) 2= 81

(3m - (-3)) 2= 81

(3m + 3) 2= 81

6m + 6  = 81

      - 6     - 6

6m = 75

[tex]\frac{6m}{6}[/tex] = [tex]\frac{75}{6}[/tex]

m = 12.5

hope this helps! if you have an questions, pls let me know!

Answer:

it is

[(2+3+4+6)-2*4]:4=1.75

I THINK

Step-by-step explanation: