Please answer this correctly

The type of triangle drawn is an isosceles triangle.

Base angles ∠ACB and ∠CAB are equal.

This is a type of triangle with base angles and opposite sides equal.

Analysis:

∠DCA = ∠CAB ( alternate angles are equal)

∠CAB + ∠ACB + ∠CBA = 180°( sum of angles in a triangle)

50 + ∠ACB + 80 = 180

130 + ∠ACB = 180

∠ACB = 180 - 130 = 50°

Since ∠ACB = ∠CAB = 50°. The triangle drawn is an isosceles triangle.

In conclusion, the triangle is isosceles because the base angles are equal.

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Answer:

At least 8.96 hours of sleep to be in the top 1%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 7.45, \sigma = 0.65[/tex]

How many hours of sleep to be on the top 1%?

The top 1% is the 100 - 1 = 99th percentile, which is X when Z has a pvalue of 0.99. So X when Z = 2.327. Then

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

[tex]2.327 = \frac{X - 7.45}{0.65}[/tex]

[tex]X - 7.45 = 0.65*2.327[/tex]

[tex]X = 8.96[/tex]

At least 8.96 hours of sleep to be in the top 1%.

Answer:

2.31

.12

7.73

Step-by-step explanation:

σx¯=0.653–√0=0.12

By plugging all the numbers into the formula z=x¯−μσx¯ we find that

2.31=x¯−7.450.12

0.28=x¯−7.45

7.73=x¯

Answer:

The length of the first piece = 41 cm

Step-by-step explanation:

Let the length of the first piece = a

Let the length of the second piece = b

Let the length of the third piece = c

we are given the following:

b = 3a . . . . . (1)     (The 2nd piece is 3 times as long as the 1st piece)

c = 6 + a  . . . . (2)    (the 3rd piece is 6 centimeters longer than the 1st piece)

a + b + c = 211 . . . . . (3)    (  the yarn has a total length of 211 centimeters)

Next, let us eliminate two variables, and this can easily be done by substituting the values of b and c in equations 1 and 2 into equation 3. this is done as follows:

a + b + c = 211

a + (3a) + (6 + a) = 211       ( remember that   b = 3a; c = 6 + a)

a + 3a + 6 + a = 211

5a + 6 = 211

5a = 211 - 6 = 205

5a = 205

∴ a = 205 ÷ 5 = 41 cm

a = 41 cm

Therefore the length of the first piece (a) = 41 cm

now  finding b and c

substituting a into equation 1 and 2

b = 3a

b = 3 × 41 = 123

∴ b = 123 cm

c = 6 + a

c = 6 + 41 = 47

∴ c = 47 cm

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?

Solution:

Probability = number of favorable outcomes/number of total outcomes

From the information given,

The probability that respondents did not provide a response, P(A) is 4/100 = 0.04

The probability that a respondent said that their experience fell short of expectations, P(B) is 26/100 = 0.26

The probability that a respondent said that their experience met expectations, P(C) is 65/100 = 0.65

A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95

Therefore, the probability,P(D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05

B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P(C) × P(D) = 0

Therefore, the probability of P(C) or P(D) is 0.65 + 0.05 = 0.7

Answer: true

Step-by-step explanation: reciprocal of 3/4 is 4/3

Hence, 2/3 × 4/3 = 8/9

Answer:

40200

Step-by-step explanation:

(8x7x6x5x4x3x2x1) - (5x4x3x2x1)

Or simply plug 8! - 5! into the calc.

Answer:

Step-by-step explanation:

40200

Answer:

False.

Step-by-step explanation:

This statement is false, for any value of F because the power function with an even exponent is always positive or 0.

Answer:

B and E

Step-by-step explanation:

A: 3 + 6 < 4 + 3 and 6 > 4

9 < 7 is false so A is not the answer.

B: 1 + 5 < 4 + 3 and 5 > 4

6 < 7 and 5 > 4 are true so B is an answer.

C: 2 + (-1) < 4 + 3 and -1 > 4

-1 > 4 is false so C is not an answer.

D: 1 + 1 < 4 + 3 and 1 > 4

1 > 4 is false so D is not an answer.

E: 2 + 8 > 4 + 3 and 8 > 4

10 > 7 and 8 > 4 are both true so E is an answer.

F: -1 + 8 > 4 + 3 and 8 > 4

7 > 7 is false so F is not an answer.

Answer:

[tex]\mathbf{E(p) = 1 - 3p}[/tex]

the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%

Step-by-step explanation:

Given that:

the number of units demanded [tex]q = pe^{-3p}[/tex]

Taking differentiations ; we have,

[tex]\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})[/tex]

[tex]\dfrac{dq}{dp}=(1-3)e^{-3p}[/tex]

Now; the price elasticity of demand using the differentials definition of elasticity  is:

[tex]E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}[/tex]

[tex]E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}][/tex]

[tex]\mathbf{E(p) = 1 - 3p}[/tex]

(b)   Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.

The estimate of the percentage change in price is :

[tex]=\dfrac{2.10-2.00}{2.00}*100 \%[/tex]

= 5%

From (a)

[tex]\mathbf{E(p) = 1 - 3p}[/tex]

Now at p = $2.00

E(2) = 1 - 3 (2.00)

E(2) = 1 - 6

E(2) = -5

The percentage change in q = -5 × 5%

The percentage change in q = -25%

Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%

Answer: . x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. ... sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 105 miles). and the fastest spaceship goes 153,454 miles per hour

Step-by-step explanation:

The number of hours that should be taken to fly to the moon from Earth is 7 hours.

Given that

Now we know that

[tex]Time = \frac{Distance}{Speed} \\\\= \frac{2.4 \times 10^5 }{3.6 \times 10^4} \\\\= \frac{240}{36}[/tex]

= 6.66 hours

= 7 hours

Therefore we can conclude that The number of hours that should be taken to fly to the moon from Earth is 7 hours.

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Answer:

840 cm

Step-by-step explanation:

From the diagram attached, the 3 by 3 grid is made up of nine 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of four rows each row having a length of 3 cm and four columns with each column having a length of 3 cm.

The length of wire required by the 3 by 3 grid = 4 column (3 cm / column) + 4 row (3 cm / row) = 12 cm + 12 cm = 24 cm

The 20 by 20 grid is made up of twenty 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of twenty one rows each row having a length of 20 cm and twenty columns with each column having a length of 20 cm.

The length of wire required by the 20 by 20 grid = 21 column (20 cm / column) + 21 row (20 cm / row) = 420 cm + 420 cm = 840 cm

An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made so, to take the balance to $282 requires 6.4 years and this can be determined by using the simple interest formula.

Given :

SImple interest formula can be used to determine the total number of years will it take for the balance to be $282.

The formula of simple interest is given by:

[tex]\rm A = P(1+rt)[/tex]

where A is the final amount, P is the initial principal balance, r is the annual interest rate and t is the time in years.

Now, put the known values in equation (1).

[tex]\rm 282 = 250(1+0.02t)[/tex]

[tex]\rm 282=250+5t[/tex]

32 = 5t

t = 6.4 years

So, 6.4 years will it take for the balance to be $282.

So, the graph correct graph is shown by option D).

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Answer:

D

Step-by-step explanation:

Answer:

We have 20% fruit juice and 70% fruit juice.

We need 60 pints of 35% fruit juice.

We set up 2 equations where t is 20% and s is 70%

t + s = 60 pints

.20t + .70s = (.35 * 60)

We solve for both unknowns

t = 42  s = 18

We need 42 pints of 20% and 18 pints of 70 %

**** DOUBLE CHECK *******************************

42 pints of 20% = 8.40 pints of juice 33.6 pints water

18 pints of 70% = 12.60 pints of juice 5.40 pints water

TOTAL mixture = 21 pints juice 39 pints water = 60 total pints

21 pints juice / 60 = .35 (or 35% fruit juice)

Correct !!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome of event

Given 5 individuals with 4, 6, 7, 10, and 15 years of teaching experience.

Since two of these 5 individuals are randomly selected to serve on a personnel review committee, total possible outcome = 5C2 (randomly selecting 2 personnel out of 5 )

5C2 = [tex]\frac{5!}{(5-2)!2!}[/tex]

[tex]= \frac{5!}{3!2!}\\ = \frac{5*4*3!}{3!*2} \\= 10\ possible\ selections\ can\ be\ done[/tex]

To get the probability that the chosen representatives have a total of at least 16 years of teaching experience, first we need to find the two values that will give a sum of years greater that or equal to 16 years. The possible combination are as shown;

4+15 = 19years (first reps)

6+10 = 16years (second reps)

6+15 = 21years (third reps)

7+10 = 17 years (fourth reps)

7+15 = 22 years (fifth reps)

10+15 = 25 years (sixth reps)

This shows that there are 6 possible ways to choose the representatives that have a total of at least 16 years of teaching experience

Total outcome = 10

expected outcome = 6

Probability that the chosen representatives have a total of at least 16 years of teaching experience = [tex]\frac{6}{10} = \frac{3}{5}[/tex]

Answer:

There is not enough evidence to support the claim that the chance of this cross to be blue-flowering is significantly smaller than 0.75 (P-value = 0.11).

Test statistic z=-1.225.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the chance to be blue-flowering is significantly smaller than 0.75.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.75\\\\H_a:\pi<0.75[/tex]

The significance level is 0.05.

The sample has a size n=200.

The sample proportion is p=0.71.

[tex]p=X/n=142/200=0.71[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.75*0.25}{200}}\\\\\\ \sigma_p=\sqrt{0.000938}=0.031[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.71-0.75+0.5/200}{0.031}=\dfrac{-0.038}{0.031}=-1.225[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.225)=0.11[/tex]

As the P-value (0.11) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the chance to be blue-flowering is significantly smaller than 0.75.

Answer:

8x + 6 + 4 = 3x - (2x + 4)

Step-by-step explanation:

When Gio applies the distributive property, the equation above is the result. Naturally, I look at the 1st parenthesis I see and start the 1st distributive property there first. The 2nd distributive property would be the other parenthesis where you multiply by -1, so you would get 8x + 6 + 4 = 3x - 2x - 4

Answer:

A or 8x + 6 + 4 = 3x - (2x + 4)

Step-by-step explanation:

The length of wire used for the square in order to minimize the total area is 9.42m.

We are given that;

Length of wire= 30m

Now

Let the length of the wire used for the square x. The length of the wire used for the circle is 30-x.

The perimeter of the square is 4x and the perimeter of the circle is 2πr=2π(30-x)/(2π)=15-x/π.

The area of the square is [tex]x^2/16[/tex] and

the area of the circle is π(15-x/π)2/4π=225/π-(15x)/π2+[tex]x^2[/tex]/4π.

The total area is A=x2/16+225/π-(15x)/π2+[tex]x^2[/tex]/4π.

To maximize A, we take its derivative with respect to x and set it equal to zero: d[tex]A/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]

Solving for x, we get x=120/(8+4π).

Therefore, 30-x=120/(8+4π)(3-π).

To minimize A, we take its derivative with respect to x and set it equal to zero:

[tex]dA/dx=x/8-15/π^2+1/(4π)(x)=0[/tex]

Solving for x, we get x=120/(8+4π)(3+π).

So, 30-x=120/(8+4π)(3-π).

Therefore, by area the answer will be approximately 9.42 m.

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Answer:

46

Step-by-step explanation:

Azman=35+amin

Aziz=3×amin

therefore;35+amin+2amin+amin/3=73

219=35+4amin

219-35=4amin

184=4amin

Amin's mark=184÷4

=46

Answer:

correct option: 2 -> It would decrease.

Step-by-step explanation:

If the amount of gas is the same, the following relation needs to be constant:

[tex]Pressure * Volume / Temperature[/tex]

So, If the pressure is constant, the volume and the temperature are directly proportional (if one increases, the other also increases).

Then, an decrease of 3 times in the volume would cause an decrease of 3 times in the temperature.

So the correct option is 2.: It would decrease.

Answer:

  y = 4x +16

Step-by-step explanation:

The given equation is in "point-slope" form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The slope of the given line is m=4. This is the same slope as any parallel line.

__

The line you want can be written in the same point-slope form as ...

  y -32 = 4(x -4)

Rearranging, we have ...

  y = 4x -16 +32 . . . . . add 32, eliminate parentheses

  y = 4x +16 . . . . . . . . collect terms

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

The question is incomplete:

Recorded here are the germination times (in days) for ten randomly  chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.

We start calculating the sample mean M and standard deviation s:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\[/tex]

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\[/tex]

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075[/tex]

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=3.25 \cdot 1.075=3.49[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3[/tex]

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Answer:

128 kg/m^3

[tex]solution \\ \: mass = 512 \: kg \\ volume = 4 {m}^{3} \\ now \\ density = \frac{m}{v} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{512}{4} \\ \: \: \: \: \: \: \: \: \: = 128 \: kg/ {m}^{3} [/tex]

hope this helps...

Good luck on your assignment

Answer:

1

Step-by-step explanation:

4^3 × 4^-3

Apply the law of exponents.

4^(3+-3)

4^(0)

Any base with the exponent of 0 is equal to 1.

= 1

Answer:

1

Step-by-step explanation:

the exponents cancel out to 0, and an exponent of 0 is always 1

Answer:

C. ± 2.326 years.

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

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

[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.326/tex]

Now, find the width of the interval

[tex]W = 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.

In this question:

[tex]\sigma = 5, n = 25[/tex]

So

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

[tex]W = 2.326*\frac{5}{\sqrt{25}}[/tex]

The correct answer is:

C. ± 2.326 years.

Answer:

m = -3

Step-by-step explanation:

Slope Formula: [tex]m = \frac{y2-y1}{x2 - x1}[/tex]

All you have to do is plug in 4 for x1, 0 for x2, 0 for y1, and 12 for y2 and you should be able to calculate your answer!

Answer:

-3

Step-by-step explanation:

→ Utilise the gradient formula

[tex]\frac{y2-y1}{x2-x1}[/tex]

→ Substitute in the values from the coordinates (4,0) and (0,12)

[tex]\frac{12-0}{0-4}=\frac{12}{-4} =-3[/tex]

→ The gradient of the line is -3

Answer:

9

Step-by-step explanation:

5≤n≤12

List all the even integers

6,8,10,12

Then find the mean

(6+8+10+12) /4

36/4

9

The mean is 9

Answer:

49/99

Step-by-step explanation:

I'm assuming you want to find the fraction that gives the decimal 0.494949...

If that is the case, the 49/99 is your answer.

Answer:

4

Step-by-step explanation:

Cos(angle) = adjacent/hypotenuse

Cos(angle) = 1.5/10

Angle = arccos(1.5/10)

Angle = 81.37 degrees

Although the angle is close, it is over the 80 degrees, so the inspector should be concerned.