The probability that a grader will make a marking error on any particular question of a multiple-choice exam is 0.10. If there are ten questions and questions are marked independently, what is the probability that no errors are made

The 4 angles need to add to 360.

2 of them are 70

The other two need to equal 360-140 = 220

They are both the same so one angle needs to equal 220/2 = 110

Now find x:

X + 60 = 110

Subtract 60 from both sides:

X = 50. The answer is D

Answer:

2m + 1

Step-by-step explanation:

Simply combine like terms. m terms go with m terms and constants go with constants.

Answer:

2m + 1

Step-by-step explanation:

3m + 1 - m =

= 3m - m + 1

= 2m + 1

Answer:

Answer C

Step-by-step explanation:

You are balancing this equation out by subtracting 7x from both sides. This means you are using the subtraction property of equality.

Answer:

-3+(-5)

Checking our answer:

Adding this does indeed give -8

Answer:

3ab

Step-by-step explanation:

area = length * width

width = area/length

width = (12ab^2)/(4b)

width = 3ab

Answer:

  -5

Step-by-step explanation:

The value of x that gives f(x) = 3 is -5.

  [tex]f^{-1}(3)=-5[/tex]

Answer:

0.56

Step-by-step explanation:

What is the probability that his mother returns just in time to catch Gabe stealing a cookie?

The probability of this is the same as 1 minus the probability that Gabe is NOT caught.

- Judy could return at anytime in the next 90 seconds

- Gabe spends the first 40 seconds pondering... time wasted=40secs

- It takes 30 seconds (out of the remaining 50secs) to finish eating a cookie without a trace

- The question says that Gabe was going to do it, so he probably did

Now we're looking for the probability that he gets caught. That is, probability that he does not "successfully" complete the 30secs task within the remaining 50secs.

Remember that each second has an equal probability of being the second that Judy comes back in. The latter of the 90 seconds does not carry a higher probability!

So the probability of catching Gabe (despite the 30secs it takes to complete his task) is 50/90 which is equal to 0.56

The value of the expression when simplified is -13

It is important to note:

PEDMAS is a mathematical acronym that representing;

Also, we should note that absolute value of a number is the non-negative value of that number. It s the value of a number irrespective of its direction from zero.

It is denoted with the symbol '| |'

Given the expression;

|2-5|-(12 ÷4-1)^2

Solve the bracket

|-3| - (12 /3)^2

Solve further

|-3| - 4^2

Find the absolute value

3 - 4^2

Find the square

3 - 16

-13

The value is - 13

Thus, the value of the expression when simplified is -13

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Answer:

15

Step-by-step explanation:

PEMDAS

3x3 = 9

3+3 = 6

9+6 = 15

By the BODMAS rule we get, 3 + 3 × 3 + 3 =​ 15

The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).

3 + 3 × 3 + 3 =​

3 × 3 = 9

3 + 9 + 3 = 15.

Therefore, the correct answer is 15.

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Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]

The critical t-value for a 99% confidence interval is t=2.678.

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

[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]

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

[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]

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

[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

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Answer:

segment I'm and segment ad

Answer:

The answer is B

Step-by-step explanation:

Answer:

2317.44

Step-by-step explanation:

Solution for What is 408 percent of 568:

408 percent *568 =

(408:100)*568 =

(408*568):100 =

231744:100 = 2317.44

Answer:

2317.44

Step-by-step explanation:

Answer:

a) 26.33 kg/d and 29.67 kg/d

b) 94.5%

Step-by-step explanation:

a. Find a 99% confidence interval for the true mean milk production.

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{1-0.99}{2} = 0.005[/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]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

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 = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d

The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d

b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?

We need to find z initially, when M = 1.25.

[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]2.25z = 1.25\sqrt{12}[/tex]

[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]

[tex]z = 1.92[/tex]

When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.

1 - 2*(1 - 0.9725) = 0.945

So we should use a confidence level of 94.5%.

For the ODE

[tex]ty'+2y=\sin t[/tex]

multiply both sides by t so that the left side can be condensed into the derivative of a product:

[tex]t^2y'+2ty=t\sin t[/tex]

[tex]\implies(t^2y)'=t\sin t[/tex]

Integrate both sides with respect to t :

[tex]t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C[/tex]

Divide both sides by [tex]t^2[/tex] to solve for y :

[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}[/tex]

Now use the initial condition to solve for C :

[tex]y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}[/tex]

[tex]\implies9=\dfrac4{\pi^2}(1+C)[/tex]

[tex]\implies C=\dfrac{9\pi^2}4-1[/tex]

So the particular solution to the IVP is

[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}[/tex]

or

[tex]y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}[/tex]

Answer:

its its 12.

Step-by-step explanation:

=8÷4×6+2-2

=2×6+2-2

=12+2-2

=14-2

=12 is answer..

Answer:

12

Step-by-step explanation:

8÷4×6+2-2

=2×6+2-2

=12+2-2

14-2

=12

Answer:

3.025

Step-by-step explanation:

3.4-1/2(0.75)

3.4-0.375

3.025

Answer:

48.3 cm²

Step-by-step explanation:

Let A be the area of the yellow region

A= the area of the square - the area of the quarter square

A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.

Answer:

Sample size = n = 150

Step-by-step explanation:

Recall that the margin of error is given by

[tex]$ MoE = z \cdot (\frac{\sigma}{\sqrt{n} } ) $\\\\[/tex]

Re-arranging for the sample size (n)

[tex]$ n = (\frac{z \cdot \sigma }{MoE})^{2} $[/tex]

Where z is the value of z-score corresponding to the 98% confidence level.

Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.

The z-score for a 98% confidence level is 2.326

So the required sample size is

[tex]n = (\frac{2.326 \cdot 10,500 }{2,000})^{2}\\\\n = (12.212)^{2}\\\\n = 149.13\\\\n = 150[/tex]

Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.

Answer:

27% of the possible Z values are greater than 0.613

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 = 0, \sigma = 1[/tex]

27% of the possible Z values are greater than

The 100 - 27 = 73rd percentile, which is X when Z has a pvalue of 0.73. So X when the z-score is 0.613.

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

[tex]0.613 = \frac{X - 0}{1}[/tex]

[tex]X = 0.613[/tex]

27% of the possible Z values are greater than 0.613

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]

I hope this helps!

Answer:

Step-by-step explanation:

5x(x + 3) + 6(x + 3)

The final answer is

( 5x + 6 ) ( x + 3 )

Hope this helps you

Answer:

20% jumped the turnstile

80% paid

Step-by-step explanation:

We can calculate the percent of people that jumped it by dividing the number that did by the total:

12/60 = 0.2, which is 20%

If 20% jumped it, then this means 80% paid.

Answer:

jumped= 20%

paid= 80%

Step-by-step explanation:

[tex]\frac{12}{60}[/tex]×100 = 20%

[tex]\frac{48}{60}[/tex]×100 = 80%

Answer:

(A) 1199.168

(B) 1503.372

(C) 159.17728

Step-by-step explanation:

(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.

Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 30th percentile,

X = 1261 + (-0.524)(118)

X = 1261 - 61.832 = 1199.168

(B) The number of chocolate chips that make up the middle 98% of chips in the bag is

X = 1261 + (2.054)(118)

X = 1261 + 242.372 = 1503.372

(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.

This is within 1.34896 standard deviations of the mean.

IQR = (1.34896)(118)

IQR = 159.17728

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In the absence of answer choices, let's find the expression for the volume.

Given: Volume = length×width×height

V = lwh

length =(2a + 11)

width =(5a – 12)

height= (a + 6)

V =  (2a + 11)(5a – 12) (a + 6)

Expand the first two brackets using distributive property

V = (10a² -24a +55a - 132)(a + 6)

Collect like terms

V = (10a² + 31a -132)(a + 6)

Expand the two brackets using distributive property

V = 10a³ + 31a² - 132a + 60a² + 186a - 792

Collect like terms

V = 10a³ + 91a² + 54a - 792

The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

Answer:

if the order of the digit matters, we have:

options: 1, 2, 3, 4.

We want to select two digits.

First selection: we have 4 options

Second selection: we have 3 options (because we already selected one in the first selection)

The total number of elements in the sample space, or the total number of combinations, is equal to the product of the number of options in each selection, this is:

P = 4*3 = 12

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

u/4 - 4 = -20

Add 4 to both sides:

u/4 = -16

Multiply both sides by 4:

u = -64

Answer:

u=-64

Step-by-step explanation:

u/4 -4 = -20

First add 4 to both sides.

u/4=-16

Now multiply both sides by 4

u=-64

Answer:  x = -10

Step-by-step explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90°  --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180°  --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180°  --> ∠2 = 109°

Solve for x:

109° = x + 119

 -10  = x

Answer:

x = -10

Step-by-step explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

Answer:

[tex]x = 9\ or\ x = 1[/tex]

Step-by-step explanation:

Given

[tex]x = 5 + \sqrt{16}[/tex]

Required

Find the value of x

[tex]x = 5 + \sqrt{16}[/tex]

We start by taking the square root of 16; Square root of 16 is +4 or -4; So, we have:-

[tex]x = 5 \±4[/tex]

The expression above can be split into two; This is as follows

[tex]x = 5 + 4\ or\ x = 5 - 4[/tex]

[tex]x = 9\ or\ x = 1[/tex]

Hence, the solution to [tex]x = 5 + \sqrt{16}[/tex] is B. 1 and C. 9

Answer:

its b and c

Step-by-step explanation:

the guy who answered first said so

also i just did it