7) What is "$96 spent in 4 hours" written as a unit rate in minutes?
D) $1.60/minute
C) $0.53/minute
A) S0.40/minute
B) $0.30/minute

If 66 sixth graders are randomly selected, the probability that the sample mean would be greater than 92.25 wpm is approximately 0.2142 or 21.42%.

If the sample size is sufficient, we can apply the theorem of central limitation to determine the pattern of distribution of sample means. Since n = 66 is a big enough number in this situation, we may use a normal distribution to roughly comparable the distribution of the sample means.

The general population's mean, which is 89 wpm, is the same as the mean value of the sample means. The following formula can be used to identify the average deviation of the sample means, commonly referred to as the standard deviation or error of the mean:

Standard error is equal to standard deviation squared.(sample size) Standard deviation: 16 squared(66) standard deviation: 1.969 Using the following formula, we can now standardise the sample mean: The formula for z is (sample mean - population mean) / standard error. z = (92.25 - 89) / 1.969 z = 1.732

We may determine the probability when a standard normal random variable is greater than 1.732 using the standard normal distribution table or calculator. This likelihood is roughly 0.0429, or 4.29%. we must remember that rather than just looking for any random variable, we are seeking for the probability that a sample mean is higher than 92.25 wpm. As a result, we must use the sample mean distribution, which we roughly categorized as a normal distribution.

The z-score must then be converted using the following formula to its original units of measurement: Sample mean equals population mean plus z times the standard error. 89 + 1.732 * 1.969 is the sample mean.

92.25 is the sample mean.

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Answer:

f(x) = -5(2)-4     f(x) = -10-4      f(x) = -14

Step-by-step explanation:

You put in the number 2 for the variable x

Answer:

∠5

Step-by-step explanation:

If Im not mistaken with the order of angles, ∠5 is the answer because they are both angles in the middle of he transversal making them interior angles, then alternate is pretty self explanatory.

Overload Distortion (D_o) is then given by the sum of the squared errors weighted by their probabilities:

\(D_o = P(X = -Δ/2)(X + Δ/2)^2 + P(X = Δ/2)(X - Δ/2)^2\)

Given, X is a random variable with the probability density function (pdf) f\(_X(x) = (1/2)e^(-|x|/2),\)and we have a 2 bits/sample uniform quantization.

(a) Granular Distortion (D_g):

Granular distortion occurs when the input signal is closer to a quantization level than the midpoint between two adjacent quantization levels. It is given by the expected value of the squared error between the original signal X and its quantized value Q(X).

The quantization step-size is Δ, and since we have a 2 bits/sample quantizer, there are 4 quantization levels: -3Δ/2, -Δ/2, Δ/2, and 3Δ/2.

To find the granular distortion, we first need to calculate the quantized value for each quantization level and then find the expected value of the squared error.

For the quantization levels:

Q(-3Δ/2) = -Δ

Q(-Δ/2) = 0

Q(Δ/2) = 0

Q(3Δ/2) = Δ

The probability of each quantization level is given by the integral of the pdf f_X(x) over the range of each quantization level.

P(X = -Δ) = ∫[(-3Δ/2), (-Δ/2)] f_X(x) dx = ∫\([(-3Δ/2), (-Δ/2)] (1/2)e^(-|x|/2) dx\)

P(X = 0) = ∫[(-Δ/2), (Δ/2)] f_X(x) dx = ∫\([(-Δ/2), (Δ/2)] (1/2)e^(-|x|/2) dx\)

P(X = Δ) = ∫[(Δ/2), (3Δ/2)] f_X(x) dx = ∫\([(Δ/2), (3Δ/2)] (1/2)e^(-|x|/2) dx\)

Granular Distortion (D_g) is then given by the sum of the squared errors weighted by their probabilities:

\(D_g = P(X = -Δ)(X + Δ)^2 + P(X = 0)(X)^2 + P(X = Δ)(X - Δ)^2\)

(b) Overload Distortion (D_o):

Overload distortion occurs when the input signal is closer to the midpoint between two adjacent quantization levels than the quantization level itself. It is given by the expected value of the squared error between the midpoint and its quantized value.

The midpoint between -Δ and 0 is -Δ/2, and the midpoint between 0 and Δ is Δ/2.

Overload Distortion (D_o) is then given by the sum of the squared errors weighted by their probabilities:

\(D_o = P(X = -Δ/2)(X + Δ/2)^2 + P(X = Δ/2)(X - Δ/2)^2\)

Now that we have the expressions for granular distortion (D_g) and overload distortion (D_o) in terms of the step-size Δ.

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a. Fraction of earnings that Mariano put into each piggy bank  is 1/12

b. Mariano earns $28.8

Mariano divides his earnings into a saving account and 3 piggy banks.  

First,  we have to know the fraction that we divide in the 3 piggy banks.

Piggy banks =Total earning-Saving account

Saving account 3/4,  

Total earnings is 1

to rest both terms we have to get the same denominator, so we can say that the total earning is 4/4

Piggy banks =4/4-3/4=( 4-3)/4=1/4

Piggy banks =1/4

Each piggy bank will be 1/3 of that 1/4

1/3 x 1/4=

For fraction multiplication, multiply the numerators and then multiply the denominators to get

1×1/3×4=1/12

This fraction cannot be reduced.

b. Mariano adds $2.40

1/12 is 2.40

We use cross-multiplication

a/b=c/d  replacing   (1/12)/2.40 = 1/ ?

So,  the total earning (?) is 1 x 2.40/ (1/12)

= 2.40 x 12=$28.8

Complete question:

Mariano delivers newspapers. He always puts 3/4 of his weekly earnings in his savings account and then divides the rest equally into 3 piggy banks for spending at the snack shop, the arcade, and the subway.

a. What fraction of his earnings does Mariano put into each piggy bank?

b. If Mariano adds $2.40 to each piggy bank every week, how much does Mariano earn per week delivering papers?

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Mariano always puts 3/4 of his weekly earnings in his savings account and then 1/4 part  divides into 3 piggy banks and in each it has 1/12 .

Let the total income of Mariano who delivers newspaper be x.

He puts 3/4(x) of his total income of his weekly earnings in his savings account.

The remaining income be x/4 and it is divided into 3 piggy banks.

so the income divides into each piggy bank will be 1/3(x/4) = x/12

so, therefore the amount that Mariano puts in each piggy bank is 1/12 part of his weekly income.

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The confidence interval provides a range of values within which the true difference between the means is likely to fall. the critical t-value from the t-distribution table at the given level of significance (α = 0.05).

To test whether µ1 ≠ µ2 (the means of two populations are not equal) at the α = 0.05 level of significance, we can use a two-sample t-test.

The t-test compares the means of two independent samples and determines if there is enough evidence to reject the null hypothesis that the means are equal.

To perform the t-test, we need sample data from both populations. We calculate the test statistic t using the formula:

t = (X1 - X2) / √((s1^2/n1) + (s2^2/n2))

where X1 and X2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

The degrees of freedom for the t-test can be approximated using the formula:

df ≈ (s1^2/n1 + s2^2/n2)^2 / ((s1^2/n1)^2 / (n1 - 1) + (s2^2/n2)^2 / (n2 - 1))

We compare the calculated t-value with the critical t-value from the t-distribution table at the given level of significance (α = 0.05). If the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that µ1 ≠ µ2.

To construct a 95% confidence interval about µ1 - µ2, we use the formula:

(X1 - X2) ± tα/2 * √((s1^2/n1) + (s2^2/n2))

where tα/2 is the critical value from the t-distribution corresponding to the desired level of confidence (95% in this case). The confidence interval provides a range of values within which the true difference between the means is likely to fall.

It's important to note that the assumptions of normality and independence should be checked before performing the t-test and constructing the confidence interval.

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Answer:

  y = x³ +2x² +x -1

Step-by-step explanation:

The attachment shows the four points we can read from the graph and the cubic regression function that fits them.

  y = x³ +2x² +x -1

_____

Additional comment

It is useful to become familiar with the regression function capability of your graphing calculator or spreadsheet. Free or inexpensive apps are available for tablet or phone, and on the web.

The Fibonacci series in which 0 does not consider is 1,2,3,5,8,13,21,34,…

A series of numbers known as the Fibonacci sequence is one in which each succeeding number is created by adding the two numbers that came before it. The Fibonacci sequence is named for the Italian mathematician who created it.

The standard Fibonacci series

0,1,1,2,3,5,8,13,21,34,…

When 0 is not considered as Fibonacci number, the series can be rewritten as,

1,2,3,5,8,13,21,34,…

The Fibonacci series where number 0 is excluded is 1,2,3,5,8,13,21,34,…

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3/4 is the total.

See attached image for explanation.

Please consider marking "Brainliest".

Thanks <3

Answer:

this graph has an x-intercept values of -1 and 2

Answer:

0.41666666, to round up, the answer is 0.42

Step-by-step explanation:

\( \frac{3}{8} + \frac{1}{8} - \frac{1}{3} + \frac{1}{4} = \frac{4}{8} - \frac{1}{3} = \frac{4}{24} + \frac{1}{4} = \frac{10}{24} = \frac{5}{12} \)

The approximate values triangle for angle B, angle C, and side b are B ≈ 54.4 degrees, C ≈ 96.6 degrees, and b ≈ 36.8 units, respectively, rounded to the nearest 10th.

Given data:

Side a = 18

Side c = 27

Angle A = 29 degrees

Step 1: Find angle B using the law of sines:

sin(B)/c = sin(A)/a

sin(B)/27 = sin(29°)/18

sin(B) = (27sin(29°))/18

B = arcsin((27sin(29°))/18)

Step 2: Find angle C using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

C = 180° - 29° - B

Step 3: Find side b using the law of sines:

sin(C)/c = sin(A)/a

sin(C)/27 = sin(29°)/18

sin(C) = (27 × sin(29°))/18

b = (sin(C) × a)/sin(A)

Step 4: Substitute the given values into the equations and calculate the approximate values using a calculator:

B ≈ arcsin((27 × sin(29°))/18) ≈ 54.4 degrees

C ≈ 180° - 29° - 54.4° ≈ 96.6 degrees

b ≈ (sin(96.6°)*18)/sin(29°) ≈ 36.8

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The question is -

Solve the triangle. Angle A is opposite side a, Angle B is opposite side b and Angle C is opposite side c. Round final answers to the nearest 10th

Given data: side a = 18, side c = 27, angle A = 29 degrees.

The complement of an event is the probability of the event not occurring. In this case, if the probability of an event is 4/7, then its complement would be 1 - 4/7, which simplifies to 3/7.

The complement of an event A, denoted as A', is the probability of A not occurring. In this case, if the probability of an event A is 4/7, then the probability of A' is given by:

P(A') = 1 - P(A)

Substituting the value of P(A) as 4/7:

P(A') = 1 - 4/7

To subtract fractions, we need a common denominator:

P(A') = 7/7 - 4/7

Simplifying the expression:

P(A') = 3/7

Therefore, the complement of the event with a probability of 4/7 is 3/7.

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Line AB is neither a Median nor an Altitude.

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an item or a form into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

Given, A triangle in that there is an angle bisector AB.

Since,

Median:

A median of a triangle is a line segment that joins a vertex to the mid-point of the side that is opposite to that vertex.

In our case, it is not specified if AB bisects the opposite line

Altitude:

The altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side. Also, known as the height of the triangle, the altitude makes a right-angle triangle with the base.

In our case, it is not specified if AB makes a Right triangle or not.

Therefore, Line Ab is neither a Median nor an Altitude.

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Answer:

sinTheta = 24/25

cotTheta = 7/24

cscTheta = 25/24

Step-by-step explanation:

Use pythagorean thm or pythagorean triples to find the missing side of the triangle.

7^2 + x^2 = 25^2

49 + x^2 = 625

x^2 = 576

x = 24

The third side of the triangle is 24. We'll need this in a sec.

The marked angle is called theta. That 0 with a belt is greek letter theta. They could just call it angleA or angleB or whatever. Its name is just theta no big deal.

25 is the hypotenuse (longest side). The side that's 7 units long is one of the pieces that makes up AngleTheta. So the 7 is "adjacent" to theta. The other leg, 24, is "opposite" from theta.

sinTheta is a ratio. It is OPPOSITE/HYPOTENUSE

sinTheta = 24/25

cotTheta is tanTheta flipped over.

tanTheta is OPP/ADJACENT

so...

cotTheta =

ADJ/OPP

=7/24

Last, cscTheta is sinTheta flipped over.

We already found sinTheta, so flip it over.

cscTheta = 25/24

SOH-CAH-TOA is supposed to help you memorize the ratios for sine (opp/hyp), cos (adj/hyp), and tan (opp/adj).

The math word for "flipped over" is reciprocal.

csc is the reciprocal of sin

sec is the reciprocal of cos.

cot is the reciprocal of tan.

Good luck! Hope this helps!

The student should subtract the correct value, -2, instead of -3  is the answer.

The student made an error while performing synthetic division. To correctly divide x³-x²-2x by x+1 using synthetic division, we start by writing the coefficients of the polynomial in descending order, which in this case are 1, -1, and -2. Next, we write the opposite of the divisor, which is -1, on the left side.

We then bring down the first coefficient, 1, and multiply it by -1, which gives us -1. Adding this result to the second coefficient, -1, we get -2. We then multiply -2 by -1, which gives us 2, and add it to the last coefficient, -2. The result is 0.

The correct division would be x²-2. So, the student's error was in the second step of synthetic division, where they incorrectly added -1 and -2 to get -3 instead of the correct result, which is -2. To correct the error, the student should subtract the correct value, -2, instead of -3.

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Hyperkalemia is a medical condition that refers to an elevated level of potassium in the blood.

This condition can be caused by several factors, including kidney disease, certain medications, and hormone imbalances. Symptoms of hyperkalemia can range from mild to severe, depending on the level of potassium in the blood.

In a 60-year-old female diagnosed with hyperkalemia, the most likely symptom that would be observed is muscle weakness. This is because high levels of potassium can interfere with the normal functioning of muscles, leading to weakness, fatigue, and even paralysis in severe cases.

Other symptoms that may be observed in hyperkalemia include nausea, vomiting, irregular heartbeat, and numbness or tingling in the extremities. Treatment of hyperkalemia typically involves addressing the underlying cause of the condition, as well as managing symptoms through medication and lifestyle changes.

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Answer:

10sqrt3

Step-by-step explanation:

sqrt300

= sqrt(100*3)

=10sqrt3

Answer:

\(n=\frac{386x-75}{5}\)

Step-by-step explanation:

Add like terms

\(-35x+3\cdot \frac{3}{5}x-22\cdot \:2x-15=n\)

Add 15 on both sides

\(-35x+\frac{9}{5}x-44x-15+15=n+15\)

Simplify

\(-35x+\frac{9}{5}x-44x=n+15\)

Multiply sides by 5

\(-35x\cdot \:5+\frac{9}{5}x\cdot \:5-44x\cdot \:5=n\cdot \:5+15\cdot \:5\)

Simplify

\(-386x=5n+75\)

Divide both sides

\(\frac{-386x}{-386}=\frac{5n}{-386}+\frac{75}{-386}\)

You will get

\(x=-\frac{5n+75}{386}\)

Then you will solve for n using x

Multiply both sides by 386

\(\frac{386\left(5n+75\right)}{386}=386x\)

Simplify

\(5n+75=386x\)

Subtraction

\(5n+75-75=386x-75\)

Simplify

\(5n=386x-75\)

Divide by 5 to get n

\(\frac{5n}{5}=\frac{386x}{5}-\frac{75}{5}\)

\(n=\frac{386x-75}{5}\)

The standard deviation for the random variable X, the number of wins, is approximately 0.10341.

Probability of winning a certain lottery \(= 1/51,949\)

560 times were played overall.

Let X represent the random variable that represents the number of victories out of 560 plays.

The probability of winning in one play is \(p = 1/51,949\). The probability of not winning in one play is \(q = 1 - p\)

\(q = (51,949 - 1) / 51,949\)

\(q = 51,948 / 51,949.\)

What X should actually be is:

\(E(X) = np\)

\(E(X) = 560 * (1/51,949)\)

\(E(X) = 0.010793\)

The variance of X is:

\(Var(X) = npq\)

\(Var(X) = 560 * (1/51,949) * (51,948/51,949)\)

\(Var(X) = 0.010699\)

The value of X's standard deviation is

\(SD(X) = \sqrt{Var(X)}\)

\(SD(X) = \sqrt{0.010699}\)

\(SD(X) = 0.10341\)(approx)

Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.

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Together, it will take the two machines 102 minutes to produce 5100 cans.

To solve this problem, we will use the work formula,

which is Work = Rate × Time.

1. First, let's find the rate of each machine.

New machine rate: 5100 cans / 170 minutes = 30 cans/minute

Old machine rate: 5100 cans / 255 minutes = 20 cans/minute

2. Now, let's find the combined rate of both machines. Combined rate: New machine rate + Old machine rate = 30 cans/minute + 20 cans/minute = 50 cans/minute

3. Finally, we will use the combined rate to find the time it takes for both machines to produce 5100 cans together.

Time = Work / Combined rate = 5100 cans / 50 cans/minute = 102 minutes

Together, it will take the two machines 102 minutes to produce 5100 cans.

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The canoeing speed is 3.25 km/hr and the speed of the current is 0.75 km/hr

Given that,

Distance = 20 km

Time        = 5 hours

Since we know that,

distance = rate x time

For the downstream trip:

Since he's going with the current, then

⇒ rate = canoeing speed + speed of current

So, we can write:

⇒ 20 = (canoeing speed + speed of current) x 5

For the upstream trip:

Since he's going against the current, then

distance = 20 km

time = 8 hrs

⇒ rate = canoeing speed - speed of current

So we can write:

⇒ 20 = (canoeing speed - speed of current) x 8

Now we have two equations with two variables (canoeing speed and speed of current).

Solve for one variable in terms of the other and substitute into the other equation to solve for the other variable.

To solve the first equation for canoeing speed + speed of current:

⇒ (canoeing speed + speed of current) x 5 = 20

⇒ canoeing speed + speed of current = 4

Solve the second equation for canoeing speed - speed of current:

⇒(canoeing speed - speed of current) x 8 = 20

⇒canoeing speed - speed of current = 2.5

Now we have two equations:

⇒ canoeing speed + speed of current = 4

⇒ canoeing speed - speed of current = 2.5

Add these two equations to eliminate the speed of current:

⇒ 2 x canoeing speed = 6.5

⇒ canoeing speed = 3.25 km/hr

Substitute this value back into one of the original equations to solve for the speed of current,

⇒ (canoeing speed + speed of current) x 5 = 20

⇒ (3.25 + speed of current) x 5 = 20

⇒ 16.25 + 5 x speed of current = 20

⇒ 5 x speed of current = 3.75

⇒ speed of current = 0.75 km/hr

Hence the required speed of canoeing is 3.25 km/hr and speed of current is 0.75 km/hr.

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Answer:

m(Au)=45.6 [gr] ; m(Cu)= 10.8 [gr].

Step-by-step explanation:

the masses of gold (Au), copper (Cu) and aluminium (Al) are:

0.76*60=45.6 (gr); 0.18*60=10.8 (gr.) and 0.06*60=3.6 (gr).

Answer:

H0 : μ1 - μ2 = 0

H1 : μ1 - μ2 ≠ 0

-1. 34

0.1837

Step-by-step explanation:

Full time :

n1 = 125

x1 = 2.7386

s1 = 0.65342

Part time :

n2 = 88

x2 = 2.8439

s2 = 0.49241

H0 : μ1 - μ2 = 0

H1 : μ1 - μ2 ≠ 0

Test statistic :

The test statistic :

(x1 - x2) / sqrt[(s1²/n1 + s2²/n2)]

(2.7386 - 2.8439) / sqrt[(0.65342²/125 + 0.49241²/88)]

−0.1053 / sqrt(0.0034156615712 + 0.0027553)

-0.1053 /0.0785554

= - 1.34

Test statistic = - 1.34

The Pvalue :

Using df = smaller n - 1 = 88 - 1 = 87

Pvalue from test statistic score ;

Pvalue = 0.1837

Pvalue > α ; We fail to reject the null and conclude that the GPA does not differ.

At α = 0.01 ; the result is insignificant

Answer:

40

Step-by-step explanation:

4x2x5=40, the formula for volume is LxWxH=V length times width times height

Answer:

44

Step-by-step explanation:

it's adding one each time

Answer:

44 Its definitely this answer

Answer:

x=50

Step-by-step explanation:

This is a vertical angle, so the angle on top and the bottom are equal

[2(x+10)]=3x-30

2(x+10)=3x-30

2x+20=3x-30

50=x