The figure shown represents a roof truss
design. Based on the markings on the figure,
which of the triangles can you prove are
congruent?

Answer:

5

Step-by-step explanation:

3-(-2) will become positive 5. so number line will go towards positive 5.

Answer:

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large shipment of televisions contained 9% defectives

This means that [tex]p = 0.09[/tex]

Sample of size 393

This means that [tex]n = 393[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.

X = 0.12

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812

X = 0.06

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

[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Answer:

To divide a decimal by another decimal:

Move the decimal point in the divisor to the right until it is a whole number.

Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.

Then divide the new dividend by the new divisor

Step-by-step explanation:

see in the example

Answer:

x = 69

Step-by-step explanation:

m<M = x

From the triangle we know that

m<M + m<MNQ + m<MQN = 180

From the parallel lines we know that

m<MNQ = m<UQN = x

x + x + 42 = 180

2x + 42 = 180

2x = 138

x = 69

Answer:

xlog(64)−xlog(2)−2

Step-by-step explanation:

Simplify 6log(2) by moving 6 inside the logarithm.

log(2^6)x − log(2)x − 2

Raise 2 to the power of 6.

log(64)x − log(2)x − 2

Reorder factors in log(64)x − log(2)x −2.

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2[tex]\pi[/tex]r             ( Calculate the total circumference)    

C = 2(8)[tex]\pi[/tex]

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

The arc length in approximate form is 33.49 radians.

[tex]s = r\times \theta[/tex]

where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.

Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]

For given question,

We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.

[tex]r=8~cm,~\theta=240^{\circ}[/tex]

First we convert angle in radians.

[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]

Using the formula of the arc length,

[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]

The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]

Substitute the value of [tex]\pi = 3.14[/tex]

So, the arc length would be,

[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians

Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

the arc length in approximate form is 33.49 radians.

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Answer:

Step-by-step explanation:

We will work in the y-dimension only here. What we need to remember is that acceleration in this dimension is -9.8 m/s/s and that when the projectile reaches its max height, it is here that the final velocity = 0. Another thing we have to remember is that an object reaches its max height exactly halfway through its travels. Putting all of that together, we will solve for t using the following equation.

[tex]v=v_0+at[/tex]

BUT we do not have the upwards velocity of the projectile, we only have the "blanket" velocity. Initial velocity is different in both the x and y dimension. We have formulas to find the initial velocity having been given the "blanket" (or generic) velocity and the angle of inclination. Since we are only working in the y dimension, the formula is

[tex]v_{0y}=V_0sin\theta[/tex] so solving for this initial velocity specific to the y dimension:

[tex]v_{0y}=35sin(35)[/tex] so

[tex]v_{0y}=[/tex] 2.0 × 10¹ m/s

NOW we can fill in our equation from above:

0 = 2.0 × 10¹ + (-9.8)t and

-2.0 × 10¹ = -9.8t so

t = 2.0 seconds

This is how long it takes for the projectile to reach its max height. It will then fall back down to the ground for a total time of 4.0 seconds.

Answer:

45 km por galón

60 galones en 2700 Km

Step-by-step explanation:

180 / 4

45 km por galón

900 / 45

20 galones

2700 / 45

60 galones en 2700 Km

9514 1404 393

Answer:

Step-by-step explanation:

Each image point has its signs reversed from the pre-image point.

  (x, y) ⇒ (-x, -y) . . . . describes the rotation

Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.

Answer:

3rd and 2nd option

Step-by-step explanation:

Answer:

243.125

Step-by-step explanation:

First do the integral part

11110011

1. From left to right, starting with a zero,

2. add the digit, double, move on to the next digit and repeat step 2 until digits are exhausted.

The successive results are

1

3

7

15

30

60

121

243

For the decimal part, we proceed similarly but

1. From the right-most digit proceed to the left, start with a zero.

2. Add the digit, halve, move on to the next digit and repeat step 2 until the decimal is reached.

Successive results are:

0.5

.25

.125

So the final result is 11110011.001 binary is 243.125 decimal

9514 1404 393

Answer:

  assumed accuracy from overly precise numbers

Step-by-step explanation:

Except when counting large sums of money or considering definitions, most real-world numbers are not accurate beyond about 6 significant figures. When considering survey or sample results, the accuracy can be considerably less than that, often not even good to 3 significant figures. (Margin of error is usually some number of percentage points greater than 1.)

Expressing the given ratios to 10 significant figures substantially misstates their accuracy. (10^-9 television is less than 1 day's accumulated dust).

9514 1404 393

Answer:

  5/8

Step-by-step explanation:

The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.

Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.

The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.

Step-by-step explanation:

this is a relatively easy function. Just plug in the value for x

Answer:

I'm pretty sure it's 8x^2+20xy-12y^2

Answer:

pff don't know .  sssory

Step-by-step explanation:

Answer:

The margin of error for her confdence interval is of 0.3757.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Standard deviation of 0.55 meters.

This means that [tex]s = 0.55[/tex]

What is the margin of error for her 99% confidence interval?

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]

[tex]M = 0.3757[/tex]

The margin of error for her confdence interval is of 0.3757.

Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.

Suppose that we have:

Sample size n  < 30

Then the margin of error(MOE) is obtained as

Margin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]

where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance

For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.

Then, by the given data, we get:

[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18

The degree of freedom is n-1 = 17

Level of significance = 100% - 99% = 1% = 0.01

The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)

Thus, margin of error for 99% confidence interval for considered case is:

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]

Thus, the margin of error for the given condition is 3.28 approximately.

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Answer:

I have not been able to answer it sorry

Answer:

Bob had 25 cars

Step-by-step explanation:

10+15=25

Answer:

$40,000

Step-by-step explanation:

this the workings above

Answer:

The price elasticity of demand is -10

Step-by-step explanation:

Given

[tex]p_1,p_2 = 50,40[/tex]

[tex]q_1,q_2 = 400,500[/tex]

Solving (a): The coefficient of price elasticity of demand (k)

This is calculated as:

[tex]k = \frac{\triangle q}{\triangle p}[/tex]

So, we have:

[tex]k = \frac{500 - 400}{40 - 50}[/tex]

[tex]k = \frac{100}{-10}[/tex]

[tex]k = -10[/tex]

Because |k| > 0, then we can conclude that the company made a wise decision.

Answer:

310/[tex]3^{3}[/tex] = 310/27 =11.48

Step-by-step explanation:

Answer:

310/ = 310/27 =11.48

Step-by-step explanation:

Answer:

b= 5i square root of 3

b = -5i square root of 3

Step-by-step explanation:

4b^2+300=0

4b^2 = -300

b^2 = -75

b = square root of -75

b = -75^1/2

^1/2 means square root

b = 25^1/2 * 3^1/2 * i

b= 5i square root of 3

b = -5i square root of 3

Answer:

Step-by-step explanation:

21,753

at unit place=3 not an even number,not equal to 5 and not equal to 0

so 21,753 is not divisible by 2,5 and 10

again

2+1+7+5+3=18 divisible by 3 and 9.

so 21,753 is divisible by 3 and 9.

Answer:

See below

Step-by-step explanation:

Hi there!

We're given that ΔABC≅ΔXYZ

When two triangles are congruent, their corresponding parts are congruent

Because of that, it means vertex A in ΔABC is congruent to vertex X in ΔXYZ, vertex B is congruent to vertex Y, and vertex C is congruent to vertex Z

Since we don't have a picture of the triangles given, we can use the names of the triangles to find the corresponding parts

so, to find the corresponding congruent angle to <BCA:

B is the first letter in the angle, and the corresponding letter in ΔXYZ is Y.

C is the second letter in the angle, and the corresponding letter is Z.

A is the last letter in the angle, and the corresponding letter is X

so that means <YZX is congruent to <BCA

now let's do the same for <ZYX

Z is the first letter in the angle, and the corresponding letter that's in the same place in ΔABC is C

Y is the second letter in the angle, and the corresponding letter is B

X is the last letter in the angle, and the corresponding letter is A

So that means <CBA is congruent to <ZYX

Now to find corresponding sides:

We can still use the names of the triangles, ΔABC and ΔXYZ

so to find the corresponding side to AB,

in ΔABC, AB makes up the first and second letter of the name of the triangle

The corresponding side must also make up the first and second letter of the name of the triangle

in ΔXYZ, the letters X and Y make up the first and second letter

so that means XY must be corresponding to AB

finally,

we need to find the segment congruent to YZ

in ΔXYZ, YZ makes up the second and third letter of the name of the triangle

the corresponding side must also make up the second and third letter of the name of the triangle

in ΔABC,  the letters B and C make up the second and third letter in the triangle

So that means BC must be congruent to YZ

Hope this helps!

Answer:

C

Step-by-step explanation:

p=20+1

The number of new professors needed to hire to keep the ratio of students and professors the same is 16.66  professors.

Given,

A small college has 1200 students and 80 professors.

The college is planning to increase enrollment to 1450 students next year.

We need to find how many new professors should be hired to keep the

ratio of students to professors the same.

If the two ratios are the same then we called it that they are in proportion.

Example:

4/6 = 10/15

2/3 = 2/3

Find the ratio between the students and professors before the increase in enrollment.

= Number of students / Number of professors

= 1200 / 80

Dividing by 8

= 150 / 10

= 15 / 1

This means one professor for 15 students.

Find the number of students after the increase in enrollment.

= 1450

Find the number of new students enrolled.

= 1450 - 1200

= 250

Since the ratio between the students and professor is 15 students for one professor.

For 250 new students, the number of new professors we need is:

= 250 ÷ 15

= 16.66

This means we need around 16.66 new professors.

Thus the number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.

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Answer:

BC = 28

Step-by-step explanation:

The midsegment DF is half the measure of the third side BC , then

BC = 2 × DF = 2 × 14 = 28

Answer:

- 3.027

Step-by-step explanation:

First price = 10000 ; second price = 700

Number of tickets sold = 11000

Ticket cost = $4

Probability that a ticket wins grand price = 1 / 11000

Probability that a ticket wins second price = 1 / 11000

X ____ 10000 _____ 700

P(x) ___ 1 / 11000 ___ 1/11000

Expected winning for a ticket buyer :

E(X) = Σx*p(x)

E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost

E(X) = 0.9090909 + 0.0636363 - 4

E(X) = - 3.0272728

E(X) = - 3.027

Answer: 0.108

Step-by-step explanation:

Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:

= 1 - 21.6%

= 78.4%

The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:

= 5% × 21.6%

= 0.05 × 0.216

= 0.108

9514 1404 393

Answer:

  22

Step-by-step explanation:

For calculators without a cube root key, you can use the 1/3 power. The attached shows the quotient to be about 22.

Answer:

B

Step-by-step explanation:

Let the base of the triangle be b and the height be h.

The sum of the base and height is 14. Thus:

[tex]b+h=14[/tex]

Recall that the area of a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

From the first equation, solve for either variable:

[tex]h=14-b[/tex]

Substitute:

[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]

Distribute:

[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]

Distribute:

[tex]\displaystyle A=-0.5b^2+7b[/tex]

Let b = x. Hence:

[tex]A=-0.5x^2+7x[/tex]

Therefore, our answer is B.