The equation 8h = 200 can be used to find how many hours h a person needs to work to earn $200 at $8 per hour. How many hours does a person need to work to earn $200?

Answer:

The integer is 1

Step-by-step explanation:

Required

Translate and solve

Let the positive integer be x.

So, we have;

The square of the integer is: x^2

Plus 5 times its consecutive integer is: x^2 + 5(x + 1)

Equals 11 is: x^2 + 5(x + 1) = 11

So, we have:

\(x^2 + 5(x + 1) = 11\)

Open bracket

\(x^2 + 5x + 5= 11\)

Subtract 11 from both sides

\(x^2 + 5x -6= 0\)

Expand

\(x^2 + 6x - x-6= 0\)

Factorize:

\(x(x + 6) - 1(x+6)= 0\)

Factor out x + 6

\((x - 1) (x+6)= 0\)

Split

\(x - 1 = 0\ or\ x + 6 = 0\)

Solve for x in both cases

\(x = 1\ or\ x = -6\)

Since the number is positive, then \(x = 1\)

The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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P(A and B) is equal to 6.

To find P(A and B), we can use the formula:

P(A and B) = P(A) + P(B) - P(A U B)

Given the information:

P(A U B) = 32 (the probability of either event A or event B occurring)

Universal set contains 52 elements (total number of possible outcomes)

P(A intersection B) = 6 (the probability of both event A and event B occurring)

P(A) = 12 (the probability of event A occurring)

P(B) = 26 (the probability of event B occurring)

We can substitute the known values into the formula:

P(A and B) = P(A) + P(B) - P(A U B)

P(A and B) = 12 + 26 - 32

Simplifying the expression:

P(A and B) = 38 - 32

P(A and B) = 6

Therefore, P(A and B) is equal to 6.

The result indicates that the probability of both event A and event B occurring simultaneously is 6 out of the total number of possible outcomes in the universal set. It means that out of the 52 elements in the universal set, 6 of them satisfy the conditions of both A and B.

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

YlThe higher the grader the more hours they can work.

Step-by-step explanation:

We can see that the higher the grader the more hours they can work ; which could mean less academic work if the work defined is that with which to earn money but if the work defined is academic it means more hours of academic work

Answer:

86

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

1. The other angle marked with one arc must also be 43 deg.

2. The two angles put together make an angle of 86 deg.

3. In a parallelogram, the angle at lower right and the angle at upper right are supplementary (they add up to 180 deg.). The upper right angle is 180 - 86 = 94 deg.

4. The angle at lower left is the same, 94 deg.

5. The angles marked with two arcs are half of 94 deg. = 47 deg.

6. Now you have two out of three angles in the triangle. All three angles add up to 180 deg. so the measure of angle 1 is 180 - 47 - 43 = 90 degrees.

Answer:

Answer: 52.4 percent

Step-by-step explanation: So you'd want to subtract 7.80 from 16.40 to get 8.60. Then you'd multiply that by 100 which would give you 860. After you've done that you want to divide 860 by 16.40.

Answer:

Step-by-step explanation:

3/40 is the correct answer

Answer:

207.345

Step-by-step explanation:

SA of cylinder = 2π(r^2) + 2πr(h)

so plugging in the numbers:

SA = 2π(3^2) + 2π(3)(8)

SA = 18π + 48π = 66π

66π ≈ 207.345

Answer:

A = 0

cot A = 1/tanA = 1/tan0 = 1/0 = Undefined.

Answer: He will pay this amount, with interest, over a 4-year period payment that he must make After paying 20% as a down payment, they finance the Determine the monthly payments needed to amortize the loan and months, that payments can be made under each of the following options before the money runs out.

Step-by-step explanation:

Answer:

D. f(x) = √(1 + x).

Step-by-step explanation:

I'm assuming the () stands for f(x) and the root of 1 - and the root of 1+ has "x" at the end of them.

To determine which function is increasing, we need to check whether the function values increase as the input variable increases.

A. f(x) = √x^2 is equal to |x|, which is increasing for x ≥ 0 and decreasing for x < 0. So, f(x) is increasing for x ≥ 0.

B. f(x) = √1 is a constant function, which is neither increasing nor decreasing.

C. f(x) = √(1 - x) is decreasing for x in the domain [0,1], since as x increases in this domain, the square root of 1-x gets smaller. Therefore, f(x) is not an increasing function.

D. f(x) = √(1 + x) is an increasing function, since as x increases, the square root of 1+x also increases.

Therefore, the function that is increasing is D. f(x) = √(1 + x).

The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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I dont think I can be answered with just the given info... is some of the q missing still?

Closest we can do with above is dress cost = 120+ c

Answer:

A

Step-by-step explanation:

Answer:

A) I hope I helped you ◉‿◉

Answer:

175 /2

Step-by-step explanation:

First, let's find the area of the rectangle.We know that the area of a rectangle is the length times width, or  20⋅32in this example:20⋅32=640So the area of the rectangle is  640ft2.You may not know the area of a semicircle, but that's fine  −we know the area of a circle, or  πr2.Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by  2:So the area of a semicircle is  πr22.The question asks for  πto just be  3.14, so instead the equation is  A=3.14r22The picture gives the diameter of the circle.To find the radius, or  r, we divide the diameter by  2:202=10Now we can solve for the area of the semicircle:3.14(10)223.14(100)23142157ft2Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:640+157=797ft2

Answer:

Answer: $3.5 per pound

Step-by-step explanation:

Solution: Convert 1 and 1/2 into a decimal which is 1.5 Then divide 5.25 by 1.5 to see how much it is per pound. $3.5 per pound is the answer!

Answer:

$3.5 per pound

Step-by-step explanation:

Convert 1 and 1/2 into a decimal which is 1.5 Then divide 5.25 by 1.5 to see how much it is per pound. $3.5 per pound is the answer

Answer:

We use thales theorem

Therfore the answer is 34

Answer:

Perimeter = 8π cm

Area = (32π - 64) cm²

Step-by-step explanation:

ABCD is a square.

Therefore:

The perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.

The arcs AC are quarter circles of a circle with radius 8 cm.

Therefore the perimeter of the shaded area is:

\(\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm\)

To find the area of the shaded area, subtract the two unshaded areas from the area of the square.

As the two unshaded areas are congruent we only need to find the area of one unshaded area.

The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).

\(\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}\)

Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:

\(\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}\)

An equation of the line that passes the through point (0, 9) and has slope m = \(\frac{2}{3}\) is 3y-2x-27=0

What is point-slop equation of a line?

The point-slope equation of a line is

                      y - \(y_{1}\) = m ( x  -\(x_{1}\) )

The equation is useful when we know:

and want to find other points on the line.

Given that,

slope , m =  \(\frac{2}{3}\)  and passing through the point is (0,9)

An equation of a line given the slope and a point is

             y - \(y_{1}\) = m ( x  -\(x_{1}\) )

or          y - 9 =  \(\frac{2}{3}\) (x - 0)

or          y - 9 =  \(\frac{2}{3}\) x

or          y =  \(\frac{2}{3}\) x + 9

or          y = \(\frac{2x + 27}{3}\)

or          3y = 2x + 27

or         3y - 2x - 27 = 0

Hence, an equation of the line that passes the through point (0, 9) and has slope m = \(\frac{2}{3}\) is 3y-2x-27=0

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The rule that relates the total distance is d =20g

From the question, we have the following parameters that can be used in our computation:

Most cars can travel around 20 miles per gallon of gas that is in their tank

This means that

Rate = 20 miles per gallon

Given that

Distance = d

Gas = g

We have

d = 20 * g

Evaluate

d =20g

Hence, the rule is d =20g

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Answer:

(x1,y1)   is  (2,7)

    (x2,y2)   is  (0,1)

Step-by-step explanation:

Point-slope form is:

  (y-y1) = ( (y2-y1) / (x2-x1) )(x - x1)

   y - 7 =( (-6)/(0-2) )(x-2)

   y - 7 = 3x - 6

    y = 3x + 1    [slope-intercept form]

Check:

  Is  (2,7) on the line:

       7 = 3(2) + 1   ?

       y = 7   ?yes

  Is (0,1) on the line:

       1 = 3(0) + 1   ?

       1 = 1   ? yes

Answer:

y=3x+1

to find the slope, find the change in y/change in x

7-1=6

2-0=2

6/2=3

3 is your slope

your y intercept occurs when x=0, and that was given to you in the problem

(0,1)

your y int is 1

y=3x+1

Based on the definition of  parallelogram, the conclusion about the quadrilateral is that: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

If a quadrilateral is a parallelogram, the two pairs of opposite sides will be parallel to each other.

If two sides of a shape have the same slopes, it then means the shape is a parallelogram.

The quadrilateral that is given is said to have the following:

Two equal slopes of 5/4 and 5/4; and 2/5 and 2/5, this means the sides that have the same slope values are opposite to each other.

Since they are opposite to each other and they have the same slope, therefore, the conclusion about the described shape is: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

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Rita bought 338 yards of ribbon for $3.38 or 338 cents.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The price of the ribbon was cents per yard and after that purchase, there was $16.62 left on Rita's $20 debit card.

Therefore she bought ribbons worth $(20 - 16.62).

= $3.38.

Or, (3.38×100) cents.

= 338 cents.

Given, One yard of ribbon costs one cent, therefore for 338 cents she bought 338 yards of ribbon.

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Answer:

90

Step-by-step explanation:

10 x 9

=> 90

10 times 9 is 90.

The area of the square is given by the  quadratic expression:

\(A = 9x^2 - 6xy + y^2\)

If we have a square whose side measures S, the area of said square is given by the equation:

\(A = S^2\)

In this case, we know that the side length of our square is given by:

\(S = 3x - y\)

Replacing that in the area equation we get:

\(A = (3x - y)^2\)

Now we just need to expand that product, we will get:

\(A = (3x - y)^2 = (3x)*(3x) + (3x)*(-y) + (-y)*(3x) + (-y)*(-y) \\\\A = 9x^2 - 6xy + y^2\)

Then we can see that the correct option is the last one.

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From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC

The two column proof to show that ∠BAC ≅ ∠DAC is as follows:

Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD

Reason 1: Given

Statement 2: AB ≅ AD

Reason 2:  Definition of isosceles Triangles

Statement 3: ∠1 and ∠2 are right angles

Reason 3: Definition of perpendicular

Statement 4: AC ≅ AC

Reason 4: Reflexive Property

Statement 5: ΔABC and ΔADC are right triangles

Reason 5: Definition of right triangle

Statement 6: ΔABC ≅ ΔADC

Reason 6: HL Congruency

Statement 7: ∠BAC ≅ ∠DAC

Reason 7: CPCTC

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The probability of forming this committee with equal representation is approximately 0.570 or 57.0%.

The total number of individuals in the ATU COVID-19 team of Marshalls is 50 (13+15+10+12). To form an executive committee of 16 with equal representation, we need to choose 4 individuals from each group (4 lecturers, 4 students, 4 administrative staff, and 4 medical personnel).
Using the combination formula, we can calculate the number of ways to choose 4 individuals from each group:
C(13,4) × C(15,4) × C(10,4) × C(12,4) = 715 × 1,455 × 2,385 × 4,095 = 7,976,476,875
Therefore, there are 7,976,476,875 possible ways to form the executive committee with equal representation.
To calculate the probability of forming this committee, we need to divide the number of possible ways by the total number of ways to choose any 16 individuals from the ATU COVID-19 team of Marshalls:
C(50,16) = 13,983,816
The probability of forming the executive committee with equal representation is:
7,976,476,875 / 13,983,816 = 0.570

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