(PLEASE ANSWER ASAP I JUST NEED TO CHECK MY ANSWER PLEASE EXPLAIN ALSO)

(PLEASE ANSWER ASAP I JUST NEED TO CHECK MY ANSWER PLEASE EXPLAIN ALSO)

Answers

Answer 1
2.just subtract one from morning and half a hour is 30 minutes so it would be 2 hours left
Answer 2

Answer:

1 hour and half an hour

Step-by-step explanation:

cause 3 hours minus 1 hour minus half an hour equal to 1 hour and half, hope this help u


Related Questions

an analysis was made of the number of students who dropped general psychology during the fall semester--the number that were observed dropping is shown in the table below which shows the drops classified by four majors. the records office tells us that for the university as a whole there are 8% of the students majoring in education, 28% majoring in business, 42% in arts and sciences, and 22% undecided. if the university expected that there should be no difference among the different majors in dropping this class, what would be the expected percent of business majors who dropped in this sample.

Answers

The expected percent of business majors who dropped in this sample would be 28%.

To find the expected percent of business majors who dropped in this sample, we need to first calculate the total number of students in the sample. From the table below, we see that a total of 250 students dropped general psychology during the fall semester.

| Major              | Number of Students Dropping |
|--------------------|-----------------------------|
| Education          | 20                          |
| Business           | 70                          |
| Arts and Sciences  | 120                         |
| Undecided          | 40                          |
| **Total**             | **250**                        |

Next, we need to calculate the expected number of students who would have dropped from each major if there were no difference among the majors. To do this, we can multiply the total number of students who dropped (250) by the percentage of students in each major:

Education: 0.08 x 250 = 20
Business: 0.28 x 250 = 70
Arts and Sciences: 0.42 x 250 = 105
Undecided: 0.22 x 250 = 55

So, if the university expected that there should be no difference among the different majors in dropping this class, the expected percent of business majors who dropped in this sample would be:

Expected percent of business majors who dropped = (Expected number of business majors who dropped / Total number of students who dropped) x 100
= (70/250) x 100
= 28%

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Please help find f(-3)

Please help find f(-3)

Answers

Answer: 0

Step-by-step explanation:

f(-3) = |(-3) ^ 2 - 9|

f(-3) = |9 - 9|

f(-3) = 0

how many ways are there to put $4$ balls in $3$ boxes if two balls are indistinguishably green, two are indistinguishably red, and the boxes are distinguishable?

Answers

36 different ways to arrange the four balls.

We will treat this as a combination of two issues involving two indistinguishable balls and three different boxes.

We can put two identical green balls in a box together or in separate boxes if they are not identifiable.

There are three ways to set them up together (in boxes 1, 2, or 3), and three ways to set them up independently (nothing in boxes 1, 2, or 3). Thus, there are six different ways to arrange identical green balls.

The identical red balls can be placed in 6 different ways, giving a total of 6*6=36 different ways to arrange the four balls.

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A company has improved its production process. Under the old process, 11 workers could produce 4,873 units per hours and the materials cost $56 per unit of output. Workers are paid $17 per hour and the finished product is sold for $102 per unit. After the improvement, materials costs have been reduced by $14 per unit of output and it now takes 3 fewer workers to make the same amount of output. What is the percentage change in multifactor productivity? (do not use a \% sign, e.g. enter 50% as .5)

Answers

The percentage change in multifactor productivity is approximately 36.15%.

To calculate the percentage change in multifactor productivity, we need to compare the productivity before and after the improvement in the production process. The multifactor productivity is calculated by dividing the output value by the input value.

Given data for the old process:

Number of workers: 11

Output per hour: 4,873 units

Materials cost per unit: $56

Worker wage per hour: $17

Selling price per unit: $102

Given data for the improved process:

Materials cost reduction per unit: $14

Workers reduced: 3

Let's calculate the multifactor productivity before and after the improvement:

Before the improvement:

Output value = Output per hour * Selling price per unit = 4,873 * $102 = $497,046

Input value = (Number of workers * Worker wage per hour) + (Materials cost per unit * Output per hour) = (11 * $17) + ($56 * 4,873) = $5,661 + $272,488 = $278,149

Multifactor productivity before = Output value / Input value = $497,046 / $278,149 ≈ 1.785

After the improvement:

Output value remains the same = $497,046

Input value = [(Number of workers - Workers reduced) * Worker wage per hour] + [(Materials cost per unit - Materials cost reduction per unit) * Output per hour]

= [(11 - 3) * $17] + ($42 * 4,873) = $119 + $204,666 = $204,785

Multifactor productivity after = Output value / Input value = $497,046 / $204,785 ≈ 2.43

Now, let's calculate the percentage change in multifactor productivity:

Percentage change = ((Multifactor productivity after - Multifactor productivity before) / Multifactor productivity before) * 100

= ((2.43 - 1.785) / 1.785) * 100

= (0.645 / 1.785) * 100

≈ 36.15

Therefore, Multifactor productivity has changed by about 36.15 percent.

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each of two pesticide brands is applied to 100 containers of fire ants. brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours.

Answers

The pValue is 0.15625 > 0.05 when  brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.

Let A represent the new pesticide and B be the Ant Killer. Then, you are given that

Brand1 kills ants in 65 of 100 containers:

Xa = 65/100 = 0.65

Brand2 kills ants in 58 of 100 containers:

Xb = 58/100 = 0.58

You know need to find sample variance for both,

s²A =∑(Xi - Xa)

= 65(1-0.65)² + 35(0 - 0.65)²

= 22.7

s²B =∑(Xi - Xb)²

= 59(1-0.59)² + 41(0 - 0.59)²

= 24.19

You can know do a test for significance

t = (Xa - Xb) / √(sA /nA) +(sB/nB)

and derive the conclusion from there

Here, Null and alternative hypothesis are generally,

Alternative hypothesis

Here, there are three samples are assumed. They are:

i) Samples are taken independently

ii) Samples must be selected randomly

iii) n₁p₁ ≥ 5 , n₁q₁ ≥ 5, n₂p₂ ≥ 5, n₂q₂ ≥ 5

i.e., p₁ = 0.65 ; p₂ = 0.58 , n₁= 100

q₁ = 0.35 ; q₂ = 0.42 , n₂=100

Corresponding p-value at Z = 1.01722

p-value = 0.15625 > 0.05

Hence, the pValue is 0.15625 > 0.05 when  brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.

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The average cost of gas in 2015 was $3.40. The average cost of gas in 2018 was $2.35. What is the percent decrease in the cost?

Answers

Step-by-step explanation:

100% = $3.40

1% = 100%/100 = 3.4 / 100 = 0.034

the price difference between 2015 and 2018 is

3.4 - 2.35 = 1.05

how many % of the original price in 2015 is this ?

1.05 / 0.034 ≈ 30.88

so, the price decrease was about 30.88%

On march 24, 1989, the exxon valdez oil tanker ran aground and leaked millions of gallons of oil into prince william sound. the spill covered approximately 11,000 square miles of ocean. the oil spread out in a circular pattern and the radius increased by 0.10 mph. use π = 3.14. at this rate, how many hours did it take for oil to cover the area? 187 hours 592 hours 1,871 hours 5,917 hours

Answers

hours did it take for oil to cover the area  = 592

The correct option is B.

What is geometrical figure?

Geometrical shapes are the shapes that depict the shapes of various items. Various figures have two dimensions, while others have three. Only the x and y axes are used for two-dimensional figures, whereas the x, y, and z axes are used for three-dimensional shapes.

According to the given information:

Given,

Area = 11000m²

Radius = .10m/h

We know the area of the circle:

Area = πr²

The relation between parameter:

Area = πr²

11000 = 3.14 * (0.10t)²

Dividing both side by 3.14

11000/3.14 = (3.14 * (0.10t)²)/3.14

by solving this we get:

(.10t)² = 3503.184

.10t = 59.187

dividing both side by 0.10

t  = 59.187/.10

t =  591.877

t = 592

hours did it take for oil to cover the area  = 592

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What is the value of the expression

What is the value of the expression

Answers

Answer:1.345299 = -1/3

Step-by-step explanation:

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Answers

I’ll answer right now let me get a paper real quick

Answer:

0-0

Step-by-step explanation:

oof- hard stuff

round off 2371 +1625 to the nearest hundred​

Answers

Answer:

2000 + 2000 = 4000

Step-by-step explanation:

2371 is rounded to 2000

1625 is rounded to 2000

2000 + 2000 = 4000

Hope this helps!

2400 + 1600 = 4000

2371 is rounded to the nearest hundred which is 2400
1625 is rounded to the nearest hundred which is 1600
If you add the all together you get 4000

Convert 35 pounds of candy to stones. (1 stone = 14 pounds)

Answers

Answer:

2.4 stone

Step-by-step explanation: i think i did it in my head

Answer:

2.4

Step-by-step explanation:

33-(2c + 4) = 2(c + 7) +C​

Answers

Answer:

c=3

Step-by-step explanation:

C=3 ///////////// (ignore these bars pls XD)

The product of two of three numbers is 7.8. if one number is 3/5, find the other number ( if you don't know please don't answer)​

Answers

Answer: 13,I

Step-by-step explanation:

set the 3 number is 3/5, x,y

product of them

3 /5 xy = 7:6

xy = 7:6 x 5 /3

Xy = 13

So the two number is 13, 1

Step-by-step explanation: hope this helped, Meow!

Office Supplies: The Office Supplies account started the year with a $4,000 debit balance. During the year, the company purchased supplies for $13,400, which added to the Office Supplies Account. The inventory of supplies available at the end of the year totaled $2,554.1. The beginning balance of Office Supplies: 2. The amount to be adjusted (show your calculation): 3. The ending balance of the account after the adjustment (show your calculation):4. Adjusting Journal Entry (please include description): Date Account Debit Credit

Answers

1.The beginning balance should be $4,000

2.The amount to be adjusted is $2554

3.The ending balance of the account after the adjustment $2554

4. Office Supplies Account is $14846

Adjusting entry:

An adjusting entry is an additional journal entry that is made at the end of the month or year. When any financial transaction is incurred for which the amount is not accrued yet or no financial transaction incurred for the accrued amount and in such case the adjusting entry is made to know the actual amount accrued in the month or year.

The adjustment entries are the additional entries to the recorded journal entries.

"Information available from the question"

The Office Supplies account started the year with a $4,000 debit balance

The company purchased supplies for $13,400,

The inventory of supplies available at the end of the year totaled $2,554.

Now, According to the question:

1. The beginning balance should be $4,000

2.The adjusted amount is

Opening balance = 4000

Add: New purchases = 13400

Balance after Purchase = 17400

Less: Year end balance = 2554

3. The ending balance is $2,554

4. The adjusting journal entry is

Dr. Supplies Expense Account is 14846

Adjustment in the year = Cr. 14846 (subtracted from the balance)

Office Supplies Account is 14846

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The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.
The number of times one needs to use the completely filled cone to completely fill the cylinder with water is

Answers

Well, we would find the volume of both the cylinder and the cone.

The formula to find the volume of a cylinder is V =  \pi  r^{2} h.

The formula to find the volume of a cone is V =  \frac{1}{3}  \pi  r^{2} h.

Now, when using pi (the symbol  \pi ), if the problem asks to use the approximate value of pi as 3.14, we'll use 3.14 to represent pi. If the problem asks for the exact answer, then we'll just put the pi sign next to our final answer we've gotten.

We can do both ways to solve with pi. Tho let's solve using the approximate value of pi.

One more thing. When there's an exponent in the problem, (such as  r^{2}  in the problem), that just means you would multiply the base, (which is r in  r^{2} ), by itself the number of times the exponent, (which is the number 2 in  r^{2} ), shows. For example, if it was  3^{2} , that would just mean we would multiply 3 times itself twice. So  3^{2}  would be the same as 3 times 3, which is 9. When you deal with variables in a problem, (the letters used to represent a value in the equation, such as a, b, c, d, etc.), they're solved in multiple ways. If a number is next to a variable, (for example, 3b), it would mean you are supposed to multiply the number times the variable. If a number is next to parenthesis, that would mean you would multiply the number times the answer from the parenthesis. In formulas, when all the letters and numbers are squished together in one line, that means you would multiply all of them times each other after they're individually solved. In this problem, r = radius and h = height.

So without further-a-do, let's begin! :)

So the question says that the radius of the cylinder is 10 centimeters, and the height is 20 centimeters. According to the formula given above, we would multiply the radius times itself twice, which would be 10 times 10, which equals 100, then multiply it by the height which is 20, so 100 times 20 = 2,000. If we were to find the exact volume, it would be 2,000 with the pi sign next to it, which would be 2,000 \pi . Though, let's find the volume with the approximate value of pi, 3.14. So 2,000 times 3.14 is 6280. The exact volume of the cylinder is 2,000 \pi and the approximate volume is 6280.

Now after we find the volume of the cone, we would need to find out how many times we'd need to use the cone to fill up the cylinder's volume.

To find the volume of the cone, we would do the same as last time. Since the cone's radius is 5 centimeters, and its height is 10 centimeters, we would first multiply the radius times itself twice, which would be 5 times 5, which is 25, then multiply that by the height, which would be 25 times 10, which is 250. The fraction part of the formula means this- the numerator "1" means you would multiply what you have so far times 1, and the denominator "3" means you will divide what you have so far NOW by 3. So 250 times 1 = 250, and 250 divided by 3 = 83.3333333333, though we'd say that answer up to the hundredths place, which would be 83.33. If you need the exact answer, we'd put the pi sign next to it as 83.33 \pi , and you're done.Tho we didn't find the approximate volume of the cone.So we'd trace back to what answer we had before moving on to the step with the fraction  \frac{1}{3} . Since we were on 250, we'd multiply that by 3.14, which is 785, and continue with what we did with the fraction. 785 times 1 = 785, and 785 divided by 3 = 261.666666667, and saying the answer up to the hundredths place, the approximate volume of the cone would be 261.66

Now since we know the volume of the cylinder, exact = 2,000 \pi  and approximate volume = 6280, this means this is how much of the cylinder should be filled when we use the cone to pour in the water.

We could easily determine this by division.

Finding with the exact volume, you would do 2,000 (from cylinder's volume) divided by 83.33 (from cone's volume), which is 24.0009600384, and since it's not a whole answer, you would move it up a whole number. Why you may ask? Well you can't pour 0.0009600384 of a cone's volume into the cylinder now can you? :P  So it would take 25 times of pouring the cone filled with water into the cylinder in order for the cylinder to be full using the exact volumes of both objects.

Now finding with the approximate volumes of both objects, we'd do the same we did last time. The cylinder's volume divided by the cone's volume, which is 6280 divided by 261.66, would be 24.0006114805, and saying the answer up to the hundredths place, 24.00, but for the same reason as the last one when we were using the exact volumes, we'd round 24 up a whole number, so it would approximately take 25 times to fill the cylinder with the cone.

Either way, using exact or approximate volumes, your final answer would be 25 times. =DI hope I helped! ^-^

By calculating the volume of cone and cylinder, we find that one need to 24 times use the completely filled cone to completely fill the cylinder with water.

What is volume of cone and cylinder?

The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.

The volume of cone will be equal to one-third of the product of the area of the base and its height.

For a cylinder, the formula is πr²h. For a cone it is 1⁄3πr²h.

Volume of cylinder = π\(r^{2}\)h =  π * 10* 10 * 20 = 2000π

Volume of cone =  \(\frac{1}{3}\)*π\(r^{2}\)h = 1/3 *  π * 5 * 5 * 10 = 250 π/3

Number of times one needs to use the completely filled cone to completely fill the cylinder with water =

= Volume of cylinder/Volume of cone

= 2000π / (250π/3) = 24

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what's the highest common factor of 5y and y^2?

Answers

Answer:  y

This is because y is a factor of 5y and it's also a factor of y^2 = y*y

It's the largest common factor between the two given expressions.

Hello.

The highest common factor of

\(\mathrm{5y} \:and\:y^{2}\)

is

\(y\)

y is the greatest common factor (G.C.F.) also called the Highest Common Factor (HCF)

Therefore, y is the highest common factor of 5y and y².

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

I’ll give brainliest

Ill give brainliest

Answers

Answer:

B

Step-by-step explanation:

We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.

We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.

Thus, the answer is B.

~ an aesthetics lover

Write the linear equation that gives the rule for this table.
x y
1 10
2 5
3 0
4 –5
Write your answer as an equation with y first, followed by an equal's sign.

Answers

The linear equation that gives the rule for this table is y = -5x + 15

How to determine the linear equation?

The table of values is given as:

x y

1 10

2 5

3 0

4 –5

On the above table, we can see that:

As x increases by 1, the value of y decreases by 5

This means that the slope is

Slope = -5

Also, the above table can be modified as follows (using the slope of -5)

x y

0 15

1 10

2 5

3 0

4 –5

This means that the y-intercept is

y-intercept = 15

A linear equation is represented as

y = slope * x + y-intercept

So, we have

y = -5x + 15

So, the equarion is y = -5x + 15

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the slope of the line tangent to the graph of y=xe^x at x=ln 2 is

Answers

Answer:

2 + 2 ㏑2

Step-by-step explanation:

y = x (e^x)

to dy/dx (slope), we need to perform the product rule:

if y = f(x) g(x), where both f(x) and g(x) are functions in x, then dy/dx = f(x) g'(x) + f'(x) g(x).

let u = x (dy/dx = 1) and v = e^x ( dv/dx = e^x).

then dy/dx = u (dv/dx) + v (du/dx)

= x (e^x) + e^x. this is the slope.

at x = ㏑2:

dy/dx = ㏑2 (e^㏑2) + e^㏑2

= ㏑2 (2) + 2

= 2 + 2 ㏑2

If I got a 43 out of 49 on my test what is the score

Answers

You would have a grade of an 88%

\((3x^{2} -14x-5)/(x-5)\)

Answers

What method are you required to use to solve this given expression? Are you simply dividing, or it is a specific method of division? If you could lmk, I'd be more than happy to assist you asap. Thanks!

What is the value of the product (3-2i)(3 + 2i)?
O 5
O 9 + 4i
O 9–4i
o 13

Answers

Answer:

9 + 4i

Step-by-step explanation:

Multiply using the FOIL method, then combine the real and imaginary parts of the expression.

The value of the products is given by the equation A = 13

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p = ( 3 - 2i )

Let the second number be q = ( 3 + 2i )

And , A = pq

Substituting the values in the equation , we get

A = ( 3 - 2i ) ( 3 + 2i )

On simplifying , we get

A = 3 ( 3 + 2i ) - 2i ( 3 + 2i )

A = 9 + 6i - 6i - 4i²

On further simplification , we get

A = 9 - 4i²

where the value of i² = -1

So , A = 9 - 4 ( -1 )

A = 9 + 4

A = 13

Therefore , the value of A is 13

Hence , the product of equation is A = 13

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Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)

Find the length of the third side. If necessary, round to the nearest tenthPythagorean Theorem (Rounding)

Answers

To use the Pythagorean theorem:
  ⇒ define Pythagorean theorem

Definition of Pythagorean Theorem: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides

     (look at the diagram attached for a better understanding)

Information Given:

length of the two legs: 5, 9

Information Wanted:

length of hypotenuse

Solve:

   \(5^2+9^2=hypotenuse^2\\hypotenuse^2 = 5^2 +9^2 = 25 + 81 = 106\\hypotenuse = 10.29\)

Rounded to nearest tenth:

 Answer: Length of hypotenuse is 10.3

Hope that helps!

Find the length of the third side. If necessary, round to the nearest tenthPythagorean Theorem (Rounding)

PERFOMANCE TASK: Solve the word problem below. You may draw the figure to solve the problem The legs of a right triangle are congruent, and the hypotenuse is 5v2 units long. Find the length of each leg. (Use the Pythagorean Theorem, c2 al + b2D​

Answers

Answer:

x =5

Step-by-step explanation:

c = 5√2

a = x

b = x

Formula

x^2 + x^2 = c^2                    Combine the x^2

Solution

2x^2 = (5√2)^2                    Expand the right side

2x^2 = 2*25                         Divide both sides by 2

x^2 = 25                               Take the square root of both sides.

x = 5

Gary bought a bond with a face value of $12,000 and a coupon rate of 6.5%. The bond will mature in 10 years.

How much interest will he receive semiannually?

A) $780
B) $650
C) $468
D) $390​

Answers

Answer:d

Step-by-step explanation:

12,000 x 6.5% = 780 divided by 2 =390

D. $390​

May I get brainliest please? :)

A car consumes fuel at a rate of 8L/100km. 2.4.1. How many litres are needed to travel 400km?
2.4.2. How far can you travel with 50L?​

Answers

Answer:

2.4.1. To calculate how many litres of fuel are needed to travel 400km, we need to use the given fuel consumption rate of 8L/100km:

Fuel consumed for 400km = (8/100) x 400 = 32 litres

Therefore, 32 litres of fuel are needed to travel 400km.

2.4.2. To calculate how far you can travel with 50L of fuel, we can rearrange the formula from part 2.4.1 to solve for distance:

distance = (fuel consumed / fuel consumption rate) x 100

Plugging in the values we have:

distance = (50 / 8) x 100 = 625 km

Therefore, with 50 litres of fuel, you can travel 625 km.


Which of the following best describes ethics?






it is a set of thoughts that are made about kinds of individuals
or their manners of conducting activities






it is a set of values that define r

Answers

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

commission expense is budgeted to be $16,000 at a planned sales level of 4,000 units. if only 2,900 units are sold, how much commission expense will appear on the flexible budget, and is the activity variance favorable or unfavorable?

Answers

The amount of commission expense that will appear on the flexible budget if 2900 units were sold is; $11600

The activity variance is favourable.

According to the question;

The budgeted commission expenses is to be $16,000 at a planned sales level of 4,000 units.However, only 2900 units are sold.

To solve this;

We must be aware that the commission expense is directly proportional to the number of units sold.

In essence;

$16,000 is expected at 4,000 units of sale.Therefore, $x is expected at 2,900 units of sale.

By cross product;

x = (2900 × 16000)/4000

x = $11,600

Ultimately, the activity variance is favourable bas less commission expense is recorded for less sale.

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A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ( ♥ and , called " hearts" and " diamonds") are red, and the other two ( spades and ♧ ) are black. The cards in the deck are placed in random order ( usually by a process called " shuffling"). What is the probability that the top two cards are both red?

Answers

The probability that the top two cards are both red will be 0.2451.

What is probability?

The percentage of favorable events to the total number of occurrences.

A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards.

Two of the suits (hearts and diamonds) are red, and the other two (spades and club) are black.

The cards in the deck are placed in random order ( usually by a process called " shuffling").

Then the probability that the top two cards are both red will be

Total event = ⁵²C₂

Total event = 1326

Favorable event = ²⁶C₂

Favorable event = 325

Then the probability will be

P = 325 / 1326

P = 0.2451

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Find a sinusoidal function with the following four attributes: (1) amplitude is 10, (2) period is 5, (3) midline is y = 31, and (4) ƒ(3) = 41. f(x) = =

Answers

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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