Select the correct answer.
Which statement about the inequality 2 1/5< 2 3/5 is true?
A. On the vertical number line, 2 1/2 is located below 2 3/5
B. On the vertical number line, 2
3/5 is located below 2 1/5 C. On the vertical number line, 2 3/5 and 2 1/5 are located at the same point
D. On the vertical number line, 2 1/5 and 2 3/5 are both located
is located below 0

Answer:

a=3.63

Step-by-step explanation:

Isolate the variable by dividing each side by factors that contain the variable.

Answer: 231/10

Step-by-step explanation: 11/5 x 21/2

= (11 x 21) = 231  

= 231/5 x 2

=  231/10

Answer:

3 hours

Step-by-step explanation

It would be easier to convert your fractions into decimals.

1/5 is the same as 2/10.  Since the denominator was multiplied by 2 then the numerator must be multiplied by 2 also.

2/10 in decimal form is 0.2

He would practice 1.2 hours per day on school days

On Saturday his practice is 2 1/2 times longer than 1.2 hours.

Convert 1/2 into decimal form. 1/2 is the same as 0.5.

So 2 1/2 is the same as 2.5

If you multiply the original time (1.2 hours) by 2.5, you'll know how long he practices on Saturday.

1.2 x 2.5  = 3 hours.

    1.2

 x 2.5

  -------

     60

   24  

------------

   300          

since you have 1 decimal place in the top number and 1 decimal in the bottom number, you must move your decimal 2 places to the left on your answer.  Instead of 300, your answer becomes 3.00

The standard error of estimate can be used for constructing a confidence interval about a value.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.

The size of a 90% confidence interval for a given estimate is one method to gauge how "good" it is; the greater the range, the more care must be used when utilizing the estimate. A crucial reminder of the limits of the estimations is provided by confidence intervals.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the expression :

Jacob's yearly income :

2000x + 3000 ; x = number of hours worked per week.

Carlos income :

3800x - 40000

Managers prediction = 35

Jacob.: 2000(35) + 3000 = 73000

Carlos : 3800(35) - 40000 = 93000

Carlos will earn more than Jacob given the manager's prediction.

Number of hours required so they can earn the same amount :

2000x + 3000 = 3800x - 40000

3000 + 40000 = 3800x - 2000x

43000 = 1800x

x = 43000/1800

x = 23.88

x = 24 hours

Answer:

a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°

QC ≅ Q'C'  and ∠AQC  is a right angle.

What is the transformation?

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or a geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given: A reflection is a transformation that maps point Q in a figure over a line, AB, such that for point C at the intersection of AB and QQ'.

We know that reflection creates an image equidistant from the line of reflection.

Thus,  QC ≅ Q'C'

Also in reflection, a line drawn from the point is perpendicular to the line of reflection.

Therefore,  ∠AQC is a right angle.

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According to the given information, the value(s) of x for which\($f(G(x)) = g(f(x))$\) is x = 1 or x = -2/3.

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

\(To find the inverse of $G(x)$:Replace $G(x)$ with $y$: $y = x - x^2 + 1$Solve for $x$: $x^2 - x + (1 - y) = 0$Apply the quadratic formula: $x = \frac{1 \pm \sqrt{1 - 4(1)(1-y)}}{2} = \frac{1 \pm \sqrt{-3 + 4y}}{2}$The inverse of $G(x)$ is therefore: $G^{-1}(x) = \frac{1 \pm \sqrt{-3 + 4x}}{2}$To find the value of $x$ for which $f(G(x)) = g(f(x))$:Start with $f(G(x))$: $f(G(x)) = f(x^2 - x + 2)$\)

\(Replace $f(x)$ with $3 - 2x$: $f(G(x)) = 3 - 2(x^2 - x + 2) = -2x^2 + 2x - 3$Replace $G(x)$ with $y$: $y = x^2 - x + 2$Replace $g(y)$ with $y - x^2 + 1$: $g(y) = y - x^2 + 1$Set $f(G(x))$ equal to $g(f(x))$ and solve for $x$:$-2x^2 + 2x - 3 = (3 - 2x) - x^2 + 1$Simplify and solve for $x$: $x = 1$ or $x = -\frac{2}{3}$\)

Therefore, according to the given information, the value(s) of x for which \($f(G(x)) = g(f(x))$\)is x = 1 or x = -2/3.

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Answer:

\( \boxed{\sf Mass \ (M) \ of \ the \ round \ ball = 10 \ grams} \)

Given:

Volume (V) = 10 millilitres

Density (\( \sf \rho \)) = 1 gram/millilitre

To Find:

Mass (M) of the round ball

Step-by-step explanation:

Formula:

\( \boxed{ \bold{Density \: ( \rho) = \frac{Mass \ (M)}{Volume \ (V)} }}\)

\( \sf \implies Mass \ (M) = Density \ (\rho) \times Volume \ (V)\)

Substituting value of density (\( \sf \rho \)) & volume (V) in the equation:

\( \sf \implies M = 1 \times 10 \\ \\ \sf \implies M = 10 \: grams\)

\( \therefore\)

Mass (M) of the round ball = 10 grams

Answer:

£885

Step-by-step explanation:

(11-7)x15x13+7x15

=

4x15x 13+105

=

780+105

=

885

{ Arithmetic}

The total amount of money that Tom earned on Monday is £885.

Based on the information given in the question, the calculation to solve the question goes thus:

= [(11 - 7) × 15] × 13 + (7 × 15)]

= (4 × 15 × 13) + 105

= 780 + 105

= £885

Therefore, the total amount of money that Tom earned on Monday is £885.

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Answer:

\(x=-8\)

Step-by-step explanation:

→All you need to do for this equation is, divide both sides by -300. You do this to get "x," by itself:

\(2400=-300x\)

\(\frac{2400}{-300} =\frac{-300x}{-300}\)

\(-8 = x\)

The percentage decrease from the August price to the September price = 20%

Here, In July the price of a holiday is £500.

And in August the price increases by 25%.

Let 'p' represents the price of a holiday.

First we need to find the value of the 25 percent of £500.

25% of £500

= 500 × (25/100)

= £125

so, the value of p would be,

p = £500 + 25% of £500

p = £500 + £125

p = £625

In September the price drops to £500 again.

i.e., p = 500

So, the decrease in price is: 625 - 500 = 125

Now we find the percentage decrease from the August price to the September price.

(125/625) × 100 = 20%

the percentage decrease in price = 20%

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The tangent ratio for the ΔABC is tanФ = 1.

Some of the trigonometric ratios are-

For the given right angles triangle ABC.

The sides AC = CB = 15

As, the angle ACB is the right angle i.e, ∠ACB = 90°, so, AB is the hypotenuses of the triangle.

For finding the value of tangent ratio;

tan = perpendicular/base

tan B = AB/ CB

tan B = 15/15

tan B = 1/1

tan B = 1

Thus, the value of tangent ratio = 1.

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According to the information, we can infer that A. 1: Real, Rational, Integer, Whole, Natural, B. 5.1: Real, Rational, C. √(-142): Non-real, D. \(\pi\) (Pi): Irrational, Real, E. 2/3: Rational, Real, F. ∛(-27): Non-real, G. 0.671: Real, Rational, H. 3√7: Irrational, Real, I. 0: Real, Rational, Integer, Whole, Natural, J. -√16: Real, Rational.

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To find a parametric equation of the line of intersection between the planes x+y=4 and 2x-y-z=2, we can set up a system of equations with the variables x, y, and z. Answer : The parametric equations x = 4 - t, y = t, z = -6 + 3t represent the line of intersection between the planes x+y=4 and 2x-y-z=2, where t is a parameter.

1. Start by solving one of the equations for one variable. Let's solve the first equation, x+y=4, for x in terms of y: x=4-y.

2. Substitute this expression for x into the second equation: 2(4-y)-y-z=2. Simplify: 8-2y-y-z=2.

3. Rearrange the equation to isolate z: -3y-z=-6. Solve for z: z=-6+3y.

4. Now we have expressions for x and z in terms of y. We can write the parametric equations using the parameter t:

  x = 4-t

  y = t

  z = -6+3t

The parametric equations x=4-t, y=t, z=-6+3t represent the line of intersection between the planes x+y=4 and 2x-y-z=2, where t is a parameter that varies along the line.

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a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

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When the area under the standard normal curve from 0 to z is 0.3508 and z is positive, the value of z is approximately 1.04 which can be found by using the z-table.

To find the value of z when the area under the standard normal curve from 0 to z is 0.3508 and z is positive, you can use the z-table or a standard normal distribution table.

1. Since the area from 0 to z is 0.3508, you need to find the total area to the left of z, which is the sum of the area from the left tail to the mean (0.5) and the area from the mean to z (0.3508). So, the total area to the left of z = 0.5 + 0.3508 = 0.8508.

2. Look up the closest value to 0.8508 in the standard normal distribution table (also known as the z-table), which shows the cumulative probability (area) for a given z-score.

3. Locate the row and column that corresponds to the value closest to 0.8508. In this case, the closest value is 0.8508 itself, located at the intersection of the row with 1.0 and the column with 0.04.

4. Combine the row and column values to find the corresponding z-score. In this case, the z-score is 1.04.

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False. In order to collect a systematic sample, you don't necessarily need to know the exact number in the population, nor do you need a sampling frame.

A systematic sample is a type of probability sampling method in which every nth item in the population is selected for inclusion in the sample.

To use this method, you need to have a sampling frame, which is a list of all the items in the population that you want to sample from.

However, you don't necessarily need to know the exact number of items in the population in order to use systematic sampling.

For example, if you are conducting a survey of households in a neighborhood, you can use systematic sampling by selecting every 10th house on a street.

You don't need to know the exact number of households in the neighborhood, as long as you have a sampling frame (e.g. a list of all the houses on the street) and a sampling interval (e.g. every 10th house).

So, to summarize, you don't necessarily need to define the number in the population to collect a systematic sample, but you do need a sampling frame.

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Sum of two angles that are supplementary = 180°

Let the first angle be x .

Then the other angle = x + 40

Measure of each angle =

\(x + x + 40 = 180\)

\(2x + 40 = 180\)

\(2x = 180 - 40\)

\(2x = 140°\)

\(x = \frac{140}{2} \)

\(x = 70°\)

Which means :-

The first angle:-

\(= x = 70°\)

The second angle :-

\(x + 40\)

\(70 + 40\)

\( = 110°\)

Therefore , the two supplementary angles are 70° and 110° .

Answer:

65 and 25

Step-by-step explanation:

The last set should not be the angle of the measurements of triangle ABC i.e. Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees

If we add the three sides of triangle so its total should be 180 degrees

So

= 55 + 65 + 60

= 180

Now

= 60 + 60 + 60

= 180

Now

= 57 + 58 + 65

= 180

And,

= 61 + 57 + 61

= 181

Therefore, The last set should not be the angle of the measurements of triangle ABC i.e. Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees

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Answer: its A

Step-by-step explanation:

if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.

How to solve investment?

If you invest $2,500 at a 4.5% weekly compounding rate, it will grow to a considerable amount in 4 years. To calculate this, we need to use the compound interest formula:

A = P(1 + r/n)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $2,500

r = 4.5% = 0.045

n = 52 (since compounding is weekly)

t = 4 years

Plugging in these values, we get:

A = $2,500(1 + 0.045/52) in power (52*4) = $3,157.22

So, if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.

It's important to note that this calculation assumes that the investment vehicle will have a steady and reliable return rate for the entire 4 years. There is always some level of risk involved with investing, so it's important to do your research and make informed decisions about where to put your money.

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Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.

Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.

However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.

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Answer:

The answer to this linear system is 7,-1

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

A 1/2

Step-by-step explanation:

Its still a 50% chance even though it landed on heads 60 times

Answer:

B

Step-by-step explanation:

If a merchant sells 1800 bags of oranges at a profit of Rs. 6/bag and 2500 bags of grapes at a loss of Rs. 4/bag, he made a loss of Rs. 800.

600 is the number of bags of oranges that has to be sold to have neither profit nor loss if the number of bags of grapes sold is 900.

A merchant makes a profit of Rs 6/bag of oranges sold and a loss of Rs. 4/bag of grapes.

In the given question,

Number of bags of oranges = 1800

Number of bags of grapes = 2500

Total outcome = Profit of oranges - loss of grapes

Profit of orange = 1800 * 6

= Rs. 10,800

Loss of grapes = 2500 * 4

= Rs. 10,000

Total outcome = 10,000 - 10,800

= - Rs. 800

Thus, he makes a loss of Rs. 800.

For having neither profit nor loss, the profit earned should be equal to the loss incurred.

Therfore, Profit = Loss

Let the number of bags of orange be x

Profit of oranges = 6x

Loss of grapes = 900 * 4

= Rs. 3600

Profit = Loss

6x = 3600

x = 600

Thus, 600 bags of oranges are sold in order to have neither profit nor loss if we sell 900 bags of grapes.

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The number of combination 6-letter words using five vowels in alphabetical order,

5*4*3*2*1*21=2520

Permutation and combination are methods for representing a collection of objects by selecting them from a set and forming subsets. It specifies the various ways to arrange a specific set of data. Permutations are when we select data or objects from a specific group, whereas combinations are the order in which they are represented.

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.

We have five vowels: a, i, e,0, and u.

make the 6-letter word using five vowels in alphabetical order,

5*4*3*2*1*21=2520

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