If a point is randomly chosen on the square shown, what is the probability that it will be in the red sección of figure?

You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.

Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.

The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:

Cost of bananas = AED 7.35 * 1.4 = AED 10.29

The total cost of apples is given by the equation:

Cost of apples = $10.20 * x

The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:

Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15

Substituting the known values, we have:

(10.29 + 10.20 * x) / (1.4 + x) = 8.15

Cross-multiplying and simplifying, we get:

10.29 + 10.20 * x = 8.15 * (1.4 + x)

Expanding the equation, we have:

10.29 + 10.20 * x = 11.41 + 8.15 * x

Rearranging the equation, we get:

10.20 * x - 8.15 * x = 11.41 - 10.29

1.05 * x = 1.12

Dividing both sides by 1.05, we find:

x = 1.12 / 1.05

x ≈ 1.067

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The required it will take 2 hours for the friends to put 7 km between them.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the number of hours it takes the friends to be "x". During that time, Rae will have traveled 2x km. And Dana will have traveled 3(x-1) km (since she left an hour later).

We can now set up an equation:

2x + 3(x-1) = 7

Expanding the second term:

2x + 3x - 3 = 7

Combining like terms:

5x - 3 = 7

Adding 3 to both sides:

5x = 10

Finally, dividing both sides by 5:

x = 2

So it will take 2 hours for the friends to put 7 km between them.

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Answer:

x<29

Step-by-step explanation:

divide both sides by -1 since x cannot be negative

510,000,000 million km²

Let us represent the total surface area of the earth as = x

We are told in the question that:

Water covers 70.8%, or about 3.61 × 10⁸ km², of the Earth's surface.

70.8% = 0.708

Hence,

0.708 × x = 3.61 × 10⁸

x = 3.61 × 10⁸/0.708

x = 361000000/0.708

x = 509,887,005.65km²

Therefore, the total surface are the earth approximately to the nearest million = 510,000,000 million km²

This is the number "510 million"

=======================================================

Work Shown:

The times 10⁸ means "times 100 million"

3.61 x 10⁸ = 3.61 * 100 million = 361 million

S = surface area of the earth

70.8% of S = water coverage area

70.8% of S = 361 million square km

0.708S = 361 million square km

S = (361/0.708) million square km

S = 509.887 million square km

S = 510 million square km

S = 510,000,000 square km

The derivative is f'(x) = (4x - 1) / (2x² - x).

To find the derivative of the function f(x) = ln(2x² - x), we can use the chain rule.

Begin by identifying the function to be differentiated, which is f(x) = ln(2x² - x).

Apply the chain rule, which states that if we have a composition of functions, f(g(x)), the derivative is given by (f'(g(x))) g'(x).

Let's consider the inner function g(x) = 2x² - x.

To differentiate g(x), we need to apply the power rule and the constant rule. The derivative of 2x² is 4x, and the derivative of -x is -1.

Now, we differentiate the outer function f'(g(x)). The derivative of ln(x) is 1/x.

Finally, we multiply the derivatives obtained in steps 3 and 4. Thus, the derivative of f(x) = ln(2x² - x) is:

f'(x) = (1 / (2x² - x)) * (4x - 1)

Simplifying further, we have:

f'(x) = (4x - 1) / (2x² - x)

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Answer:

greater risk of a Type I error and a lower risk of a Type II error

Step-by-step explanation:

Remember, in statistics, alpha (or the significance level) α,  refers to the probability of rejecting the null hypothesis when it is true.

Hence, setting alpha at 0.05 (or 5%) instead of 0.01 (or 1%) implies that the researcher is increasing how far away the statistics data needs to be from the null hypothesis value before they can decide to reject the null hypothesis. In other words, a probability of 5% is greater than 1%, resulting in a greater risk of a Type I error and a lower risk of a Type II error.

Answer: D.

Step-by-step explanation:

Edge 2020

The time interval between which the ball will be 15 feet above the ground is from 0.4594 seconds to 2.04 seconds.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The solutions of a quadratic equation can be found using the formula,

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Given that the height of a tennis ball tossed into the air is modelled by h(x)=40x – 16x², where x is elapsed time in seconds.

Now, the time interval will the tennis ball be at least 15 feet above the ground is,

h(x) = 40x – 16x²

Substitute the height of the ball as 15 feet,

h(x) = 40x – 16x²

16x² - 40x + 15 = 0

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2 - 4(16)(15)}}{2(16)}\\\\\)

x = 2.04056, 0.4594

Therefore, the time interval between which the ball will be 15 feet above the ground is from 0.4594 seconds to 2.04 seconds.

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Let's suppose you have a population of 1000 people.

If the incidence rate of the disease is 0.9%, it means that 1000(0.009) = 9 people will have the disease

It means that 991 people will not have the disease.

Of the 9 people who have the disease, 4% of them will test negative, then 9(0.04) = 0.36 people will test negative, so the remaining 8.64 people will test positive.

Of the 991 people who don't have the disease, 991(0.02) = 19.82 people will test postive.

Then, the probability will be:

The probability is 0.30358 or 30.358%

To paint , 7 rooms in white or yellow, 128 possible outcomes are there.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

There are seven rooms in the house and each can be painted either yellow or white.

And probability of total number of different outcomes

= total number of options

So, total number of different outcomes = 2⁷

 Total number of different outcomes = 128

Therefore the total number of outcomes are 128.

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The complete question is;

A house has seven rooms. Each room can be painted white or yellow. How many possible outcomes are there?

The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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Answer:

x ≥ 6/5

Step-by-step explanation:

2/5 ≥ x - 4/5

Add 4/5 to both sides

2/4 + 4/5 ≥ x

6/5 ≥ x

Put the variable on the left

x ≤ 6/5

Answer:

-11/12

Step-by-step explanation:

The velocity of the two cars are 50km/hr and 60km/h

Velocity is the rate of change of distance with time. it is measured in meter per second and it is a vector quantity.

let the faster car be A and slower car be B

V(A) = V(B) +10

S( A) = v × t

S(B) = v(b) × t

S( A) = 5( v(b) +10)

S(A) +S(B) = 550

5v(b) +50+5vb = 550

10v(b) = 550-50

v(b) = 500/10

v(b) = 50km/h

v(a) = 50 +10

v(a) = 60km/h

Therefore the velocity of the two cars are 50km/h and 60 km/h

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Answer:

4,832

Step-by-step explanation:

im not sure if this is what you are looking for...

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Explanation:

This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.

Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16

The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

Answer:

The percentage of 18 people out of 50 is 36 %

Step-by-step explanation:

The percentage refers to the per hundred or hundredths and is ended with the symbol %.  By dividing two amounts, ratios and percentages are both used to compare the two amounts.

so,

Therefore the percentage of 18 people out of 50 people is 36 %.

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Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

9514 1404 393

Answer:

Step-by-step explanation:

The area is the product of length and width:

  A = LW

  144 = (w+10)(w)

  w^2 +10w -144 = 0 . . . . . . subtract 144 and put in standard form

  (w +18)(w -8) = 0 . . . . . . . . factor

  w = -18 or 8 . . . . . . . values that make the factors zero, -18 is extraneous

The width of the wall is 8 ft; the length is 18 ft.

_____

Additional comment

The equation is factored by looking for factors of -144 that have a sum of 10. We can choose from the different ways 144 can be factored:

  -144 = -1(144) = -2(72) = -3(48) = -4(36) = -6(24) = -8(18) = -9(16) = -12(12)

The respective sums are 143, 70, 45, 32, 18, 10, 7, 0.

So, the factors of -144 that have a sum of 10 are {-8, 18}. These are the constants that go into the binomial factors.

Answer:

-155

Step-by-step explanation:add them all up together

The new status of John's account at this point is -$155

Using this formula

 New status=(-Account status-Cheque amount)-Bank charges

Let plug in the formula

 New status= (-$112-$22)-$21-

 New status=-$134-$21

 New status=-$155

Inconclusion The new status of John's account at this point is -$155

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Her monthly payment would be $180.56, the total of all her monthly payments would be $13,000 and the total finance charge is $3000.

The expression for the final amount for simple interest is

A = p(1+rt)

Given data

Principal = $10,000

Rate= 5 %= 0.05

Time = 6years (Assume)

A = p(1+rt)

A = 10,000(1+0.05×6)

A = 10,000(1+0.30)

A = 10,000(1.30)

A = 13,000

So the final amount for simple interest is $13,000

To determine her monthly payment

Given that it is spread over 6 years

There are 12×6 months= 72months

So monthly pay = 10000/72 = $180.56

The total of all her monthly payments would be $13,000 which is equal to the final amount.

The finance charge is equal to the interest.

⇒ $13,000 - $10,000 = $3000

So the finance charge would be $3000.

Therefore, her monthly payment would be $180.56, the total of all her monthly payments would be $13,000 and the total finance charge is $3000.

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The expression consists of 4 terms, and each term contains 2 factors.

1) In this expression:

ab +cd + ef +gh

We can make the following definitions:

2) Factors are numbers or letters (in algebra) that we can use to multiply themselves and yields another number.

Terms can be defined as letters, numbers within an expression.

3) Hence, In this expression, we have then:

4 terms: ab, cd, ef, and gh

2 factors per term.

The expression consists of 4 terms, and each term contains 2 factors.

Answer:

4

\(3.5x - 11 = 3 \\ 3.5x = 3 + 11 \\ 3.5x = 14 \\ x = \frac{14}{3.5} \\ x = 4\)

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Let x be the temperature at 9 AM. It increased 12°F until noon and then decreased 9°F until 6 PM.

The temperature at 6 PM can be calculated by:

x + 12 - 9

That is the required 3-term expression.

It can be used to calculate the temperature at 6 PM if we know the temperature at 9 AM was x = 45°F. Substituting:

45 + 12 - 9 = 48

The temperature at 6 PM was 48°F

Now we are given the temperature at 6 PM as 30°F. It's required to find the initial temperature at 9 AM. We write the equation:

x + 12 - 9 = 30

Operating:

x + 3 = 30

Subtracting 3:

x = 27°F

The temperature was 27°F at 9 AM

We used the expression to solve an equation that gave us the value of x