Please explain part i

A histogram is a graph that shows the frequency of numerical data using rectangles.

A set of quantitative data with varying values may be shown as a list or a data display.

Center and spread are ways to describe data sets like this.

Center describes a typical value of a data point. Two measures of center are mean and median.

Spread describes the variation of the data. Two measures of spread are range and standard deviation.

The mean is useful for describing the center of data with similar values.

The mean is the average value.

mean = sum of values / number of values

A histogram is a graph that shows the frequency of numerical data using rectangles.

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The given pair of events are independent when your first coin flip results in heads. and your second coin flip results in heads.

Events that occur independently of any other events are referred to as independent events. if we flip a coin in the air and get the head, we will then flip the coin again, but this time we will get the tail. The occurrence of both events is unrelated in either instance. Tossing the coin the first time does not affect the outcome of the second toss.

Note that the events are not mutually exclusive as it is possible that both the first and the second toss are headed.

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At one time, the British advanced corporation tax system taxed British companies' foreign earnings at a higher rate than their domestic earnings.

This was put in place to discourage multinational corporations from artificially shifting profits earned in the UK to low-tax jurisdictions. The policy was aimed at preventing companies from avoiding tax by moving profits out of the UK and into tax havens. By imposing a higher tax rate on foreign earnings, the UK government hoped to make it less attractive for companies to engage in profit-shifting practices.

The policy was controversial and faced criticism from some business groups, who argued that it placed an unfair burden on companies operating overseas. However, the government defended the policy as necessary to ensure that companies paid their fair share of tax in the countries where they operated. Eventually, the policy was replaced by a territorial tax system, which only taxes companies on their profits earned in the UK. This change was made to simplify the tax system and make it more attractive for companies to invest in the UK.

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Answer: its d

Step-by-step explanation:

Given expression:

By taking L.C.M, we get

→ \(\frac{15(x+6)+7(x-6)}{(x-6)(x+6)}\)

→ \(\frac{15x+90+7x-42}{x^2-36}\)

→ \(\frac{22x+48}{x^2-36}\)

Thus the response above i.e., "option D" is correct.

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Answer:

x=28/3

Step-by-step explanation:

combine multiplied terms into a single fraction

7 = 3x/4

multiply all terms by the same value to eliminate fraction denominators

4 · 7 =  4 · 3x/4

cancel multiplied terms that are in the denominator

4 · 7 = 3x

multiply the numbers

28 = 3x

divide both sides of the equation by the same term

28/3 = 3x/3

simplify

a. cancel that are in numerator and denominator

28/3 = x

b. move the variable to the left

x = 28/3

The linear function f is y = f(x) = (-3/2)x+b, with f(-9) = 10 and f(-1)=-2.

The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.

The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,

m = (y₂ - y₁)/(x₂ - x₁)

The given values are,

f(-9) = 10 and f(-1) = -2.

The given  coordinates are (-9, 10)  and (-1, -2)

Let the linear function is,

y= mx+b    (1)    

To find the linear function,

Find the slope

m = -2 - 10 / -1 - (-9)

m = -12 / 8

m = -3 / 2.

Substitute the value of m in equation (1),

y=(-3/2)x+b

To find the value of b, substitute y = -2,

-2=(-3/2)(-1)+b

b=-7/2

The required linear function is,

y=(-3/2)x -7/2

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Answer:

x=-7

Step-by-step explanation:

After rewriting the given function sin^4(2x) using the power-reducing formulas, we obtain (3/8) - (1/2)cos(4x) + (1/8)cos(8x).

The double-angle and half-angle identities as well as the Pythagorean identities can be used to generate the power-reduction formulas.

sin2 θ = (1 – cos 2θ)/2

cos2 θ = (1 + cos 2θ)/2

tan2 θ = (1 – cos 2θ)/(1 + cos 2θ)

cosec2 θ = 2/(1 – cos 2θ)

sec2 θ = 2/(1 + cos 2θ)

cot2 θ = (1 + cos 2θ)/(1 – cos 2θ)

So, the function we have is:

sin^4(2x)

Rewriting the expression using power-reducing formulas as follows:

The half-angle formula has an alternative form that:

sin²x = (1/2) [1 - cos(2x)]  or  sin2(2x) = (1/2) [ 1 - cos(4x) ]

Therefore, we substitute the half-angle version for both sin²(2x):

sin²(2x) * sin²(2x) = (1/2) [1-cos(4x)] (1/2) [1 - cos(4x)]

This reduces to

(1/4)[1-cos(4x)]²  
Next, the squared expression is "FOIL" ed:

(1/4) [ 1 - 2cos(4x) + cos2(4x)]

Distribute:

(1/4) - (1/2) cos(4x) + (1/4) cos²(4x)

The half-angle formula also has an alternative form, which is:

cos²x = (1/2)[ 1 + cos(2x)]   or  cos²(4x) = (1/2)[ 1 + cos(8x) ]

Substituting the equivalent half-angle term for the remaining squared term:

(1/4) - (1/2)cos(4x) + (1/4)[(1/2)(1+cos(8x))]

Simplify:

(1/4) - (1/2)cos(4x) + (1/8)[ 1 + cos(8x) ]

Distribute:

(1/4) - (1/2)cos(4x) + (1/8) + (1/8)cos(8x)

Lastly, combine the two constants to obtain:

(3/8) - (1/2)cos(4x) + (1/8)cos(8x)

Therefore, after rewriting the given function sin^4(2x) using the power-reducing formulas, we obtain (3/8) - (1/2)cos(4x) + (1/8)cos(8x).

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Answer:

13

Step-by-step explanation:

13x75000=975000

Check for reasonableness...

975000/75000=13

So the answer is 13 gallons.

P.S. There will still be 25,000 drops left, which is 1/3 of a gallon.

The total area of the composite figure is 258 squared centimeters.

The figure in the diagram is composed of two triangle and a rectangle?

The area of a triangle = 1/2 × base × height

Area of a rectangle = length × width

From the diagram;

Triangle 1

Triangle 2

Rectangle

To find the area of the composite figure, we find the area of the two triangle and rectangle and add.

Area = area of triangle 1 + area of triangle 2 + area of rectangle.

Area = ( 1/2 × base × height ) + ( 1/2 × base × height ) + ( length × width )

Area = ( 1/2 × 4 × 12 ) + ( 1/2 × 12 × 3 ) + ( 18 × 12 )

Area = ( 2 × 12 ) + ( 6 × 3 ) + ( 18 × 12 )

Area = 24 + 18 + 216

Area = 258cm²

Therefore, the area is 258 squared centimeters.

Option C) 258cm² is the correct answer.

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Answer:

258cm^2

Step-by-step explanation:

Answer:

c = 13

Step-by-step explanation:

1. Pythagorean theorem states that c^2 = a^2 + b^2

2. In this case, a = 5, b = 12. Therefore, the equation is:

c^2 = 5^2 + 12^2

3. c^2 = 25+144 = 169

4. square root both sides

5. c = 13, c = -13

6. c = 13 since a length cannot be negative.

7. Final answer: C = 13

Answer:

A

Step-by-step explanation:

81 - 1 1/5x \(\leq\) 55

Subtract 81 from  both sides

- 1 1/5x \(\leq\) -26

Turn - 1 1/5 into the improper fraction -6/5

-6/5x \(\leq\) -26

Divide by sides by -6/5 by multiplying by the reciprocal. This also changes the direction of the sign.

x \(\geq\) 65/3

x \(\geq\) 21 2/3

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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The present value of this investment project is $72,500. This can be solved by the concept of Compound interest.

The perpetual cash flow of $4,350 per year can be considered as an annuity perpetuity, where the cash flow is constant forever. To calculate the present value of this perpetuity, we can use the formula:

Present Value = Annual Cash Flow / Discount Rate

Here, the annual cash flow is $4,350, and the discount rate is the interest rate of 6%. Thus, we can calculate the present value as:

Present Value = $4,350 / 0.06

Present Value = $72,500

Therefore, to participate in this investment project, you would need to pay $72,500 today to receive $4,350 per year forever, starting from one year from now

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Check the picture below.

now, if you look at the picture of the piece-wise, is barely ever continuous, it has a vertical asymptote at x = 2, notice the dashed rational subfunction.

now, where the red cubic subfunction meets the rational subfunction at the origin and then the rational goes off to the vertical asymptote, we can say that little piece is continuous since both of them meet, that'll be between -1 excluding -1, and 2 excluding 2 because is an asymptote, (-1 , 2).

Answer

A m2=m23

Step-by-step explanation:

cause you have to look at a way so you can find the anser to it

These partitions represent all the unique combinations of odd numbers that add up to 6.

To answer this question, we need to consider the different ways that we can partition the number 6 using only odd numbers.
First, let's list out all the possible odd numbers that we can use: 1, 3, and 5.
To partition 6, we can start with using just one odd number:
- 1 + 5
- 3 + 3
If we use two odd numbers, we can have:
- 1 + 1 + 1 + 3
- 1 + 1 + 5
- 1 + 3 + 1
- 1 + 5 + 1
- 3 + 1 + 1
- 3 + 3
If we use three odd numbers, we can have:
- 1 + 1 + 1 + 1 + 1 + 1
- 1 + 1 + 1 + 3
- 1 + 1 + 3 + 1
- 1 + 1 + 5
- 1 + 3 + 1 + 1
- 1 + 3 + 3
- 1 + 5 + 1
- 3 + 1 + 1 + 1
- 3 + 1 + 3
- 3 + 3 + 1
- 5 + 1 + 1
- 5 + 1
In total, there are 11 different ways to partition 6 using only odd numbers.
There are three different ways to partition the number 6 using only odd numbers (1, 3, 5, ...). These partitions are:
1. 1 + 1 + 1 + 1 + 1 + 1 (six ones)
2. 1 + 1 + 1 + 3 (three ones and one three)
3. 3 + 3 (two threes)
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Answer: D. She is above 11.5% of test takers

Step-by-step explanation:

So logically we can eliminate like 3 answers and let me explain why

So first we can eliminate both A and B because the question asks "Does this score place Sheila in the bottom 10% of test takers?" If the answer were yes she wouldn't be "above 8.5%" or "above 11.5%" because she would be below.

So that would leave both C and D right. Lets look at C first. It says "No, she is above 8.5% of test takers" But if she is above 8.5% she could hypothetically be in the 9% or the 9.5% of test takers. Since this answer doesn't gurantee she would be above 10% we can't choose it. Now D it says "No, she is above 11.5% of test takers" This is correct because She is not in the bottom 10% because according to the empirical rule she is I would say around or just under 16% of test takers. Also the 11.5% part gurantees that anything above the number 11.5 is greater than 10%. Unlike in C which only says the number is greater than 8.5 which means the number could be 8.6 which is NOT greater than 10.

The sample size required for the true proportion of students who have parents who have remarried is 607.

The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.

We may also need to consult the table to determine the Z value.

For the given question,

α = 0.1

Consider the Z-table,

Zα/2 = Z (0.1/2)

Z (0.05) = 1.645

Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.

For calculating the margin error 'E' that is given 3%.

n = Z² (α/2) / E² × (P°(1 - P°))

Put the given values.

n = (1.645)² / (0.03)²  × (0.28(1 - 0.28))

On solving,

n = 3006.669(0.2016)

n = 606.144

n ≈ 607

Thus, the sample size required for the true proportion of students who have parents who have remarried is 607.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

x + 0.15x = OP

Step-by-step explanation:

OP= Original Price

a) Approximate Doubling Time Dappx = 70/r, where r is the annual interest rate in percentage terms.Assuming that r = 5%, 10%, 20%, 40%, and 60%Doubling time for 5% = 70/5 = 14 yearsDoubling time for 10% = 70/10 = 7 yearsDoubling time for 20% = 70/20 = 3.5 yearsDoubling time for 40% = 70/40 = 1.75 yearsDoubling time for 60% = 70/60 = 1.1667 yearsb) Exact Doubling Time Dexact = ln2/r where r is the annual interest rate in decimal terms.

Assuming that r = 5%, 10%, 20%, 40%, and 60%For 5%: ln2/0.05 ≈ 13.86 yearsFor 10%: ln2/0.1 ≈ 6.93 yearsFor 20%: ln2/0.2 ≈ 3.47 yearsFor 40%: ln2/0.4 ≈ 1.73 yearsFor 60%: ln2/0.6 ≈ 1.16 yearsc)

The percentage error is given by:(Dexact − Dappx)/Dexact × 100%For 5%: (13.86 - 14)/13.86 x 100% ≈ 1.18%For 10%: (6.93 - 7)/6.93 x 100%

≈ 1.15%For 20%: (3.47 - 3.5)/3.47 x 100%

≈ -0.86%For 40%: (1.73 - 1.75)/1.73 x 100%

≈ -1.15%For 60%: (1.16 - 1.1667)/1.16 x 100%

≈ -0.60%Note that the percentage error is small for lower values of interest rates but increases as the interest rate increases.

Also, the percentage error is negative for 20%, 40%, and 60%, which means that the approximate doubling time is actually larger than the exact doubling time.

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Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

\(t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}\)

The sum of these times must be equal to the total time of the trip, therefore:

\(t_{stage1} + t_{stage2} = 5\)

\(\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10\)

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Answer: x = 3 and y = 4

Step-by-step explanation:

Step: Solve x + y= 7 for x:

x + y = 7

x + y + −y= 7+−y

x = −y + 7

Step: Substitute −y + 7forxinx+2y=11:

x + 2y = 11

−y + 7 + 2y = 11

y + 7 = 11

y + 7 + −7 = 11 + −7

y=4

Step: Substitute 4 for y in x = −y + 7:

x = −y + 7

x = −4 + 7

x = 3

Answer:

x = 3 and y = 4

Hope I did it right

Answer:

3.5cm

Step-by-step explanation:

10mm = 1 cm

35mm = ?cm

35/10 = 3.5cm