please someone tell me why the answer is 7/8 I need working out

The Area of Trapezoid of figures given below.

The area of a trapezoid is found using the formula, A = ½ (a + b) h,

where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid.

Given:

1. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (22+ 11) x 12

= 33 x 6

= 198 m²

2. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (38+ 24) x 26

= 806 mm²

3. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (105 + 212) x 78

= 12363 Km²

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When a fraction is equivalent to a percentage greater than 100, it means that the numerator represents a value that is greater than the denominator.

A percentage is a way to express a number as a fraction of 100. For example, 50% is the same as 50/100, which simplifies to 1/2.

Suppose we have a fraction that is equivalent to a percentage greater than 100, such as 125%. This means that the fraction represents 125 parts out of 100, or 125/100.

To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor(GCF), which is 25 in this case. This gives us:

125/100 = (125 ÷ 25)/(100 ÷ 25) = 5/4

As we can see, the numerator (5) is greater than the denominator (4). This is because the original percentage value (125%) is greater than 100%, which means the fraction must have a numerator that is greater than the denominator to reflect this increase.

In general, if a fraction is equivalent to a percentage greater than 100, its numerator will be greater than its denominator because the percentage value represents a quantity that is greater than the whole (100%).

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a) Note that  the probability that the 10th transistor  produced is the first with a defect is: ≈ 0.0171

b) The probability that the machine produces no defective transistors in a batch of 100 is: ≈ 0.1338

c) The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:  = 50

d) The expected value and standard deviation for the number of transistors produced before the first with a defect is ≈ 18.71

e)  Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

(a) Since each transistor is independent, the probability that the 10th transistor produced is the first with a defect is the same as the probability that the first 9 transistors are not defective and the 10th one is defective. The probability that a transistor is not defective is 1 - 0.02 = 0.98. Therefore, the probability is:

P(1st defective on 10th) = (0.98)⁹ x 0.02 ≈ 0.0171

(b) The probability that the machine produces no defective transistors in a batch of 100 is:

P(no defects in 100) = (0.98)¹⁰⁰ ≈ 0.1338

(c) The number of transistors produced before the first with a defect follows a geometric distribution with parameter p = 0.02. The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:

E(X) = 1/p = 1/0.02 = 50

The variance of a geometric distribution is (1-p)/p², so the standard deviation is:

σ = √((1-p)/p²)

= √(0.98/0.0004)

≈ 22.36

(d) The expected value and standard deviation for the number of transistors produced before the first with a defect are calculated in the same way as in (c), but with a different value of p:

E(X) = 1/p = 1/0.05 = 20

σ = √((1-p)/p₂)

= √(0.95/0.0025)

≈ 18.71

(e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

As the probability of an event increases, the expected wait time until success decreases. In other words, the mean becomes smaller. However, as the probability of an event increases, the variability in the wait time until success also increases.

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Answer:

(a) 0.0167

(b) 0.1326

(c) The expected value, mean, μ = 50        SD, σ = 49.4975

(d) The expected value, mean, μ = 20        SD, σ = 19.4936

(e) Increasing the probability of an event decreases the mean and standard deviation of the wait time until success.

Step-by-step explanation:

The solution of the given compound inequality in the interval notation is (∅).

What is compound inequality?

Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols. Typically, we use the not equal symbol to indicate that two values are not equal.  But to compare the values, whether it is less than or greater than, different inequalities are used.

Given a compound inequality,

 1/4 x - 3  ≥ 1 and -3(x - 2) ≥ 2

To solve this we take the first inequality.

1/4 x - 3  ≥ 1

1/4 x ≥ 4

x ≥ 16

Now solve the second inequality.

-3(x - 2) ≥ 2

-3x +6 ≥ 2

-3x ≥ -4

x ≤ 4/3 (The inequality sign reverses because we are dividing by a negative number, -3)

Now from both solved inequalities, we can see that x should be greater than 16 as well as it should be less than 4/3.

There exists no such number.

Therefore the solution of the given compound inequality in the interval notation is (∅).

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The area of the square  is 196.1019 square inches

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

area of the circle = 3.14r² , r =radius

=> 153.94 = 3.14r²

=> r² = 153.94/3.14 = 49.0254

=> r= ± √ 49.0254 =± 7.0018

=> r= +  7.0018, r= - 7.0018

Consider positive value

r= +  7.0018

Diameter, d= 2r = 2*7.0018  = 14.0036 inches

Side (a) of square = Diameter = 14.0036 inches

The area of the square

= a²

= 14.0036²  square inches

= 196.1019 square inches

The area of the square  is 196.1019 square inches

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[tex]\textit{Partial Variation} \\\\ y = k_ox+k_1\hspace{5em}\textit{"y" varies partly with a constant and directly with "x"} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{"D" varies partly with a constant and directly with "V"}}{D=k_oV+k_1}\qquad \textit{we know that} \begin{cases} V=40\\ D=150\\[-0.5em] \hrulefill\\ V=54\\ D=192 \end{cases}[/tex]

[tex]\boxed{\begin{array}{llll} 150=40k_o+k_1\\\\ 192=54k_o+k_1 \end{array}}\qquad \stackrel{ \textit{using elimination method} }{\begin{array}{llll} -150=-40k_o-k_1\\\\ ~~ 192= ~~ 54k_o+k_1\\\cline{1-1} ~~ 42~= ~~ 14k_o+0 \end{array} }\qquad \implies 42=14k_o \\\\\\ \cfrac{42}{14}=k_o\implies \boxed{3=k_o}\hspace{5em}\stackrel{\textit{substituting on the 1st equation}}{150=40(3)+k_1}[/tex]

[tex]\cfrac{150}{40(3)}=k_1\implies \boxed{\cfrac{5}{4}=k_1}\hspace{5em} {\Large \begin{array}{llll} D=3V+\cfrac{5}{4} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{when V=73, what is "D"?}\qquad D=3(73)+\cfrac{5}{4}\implies D=\cfrac{881}{4}\implies D=220\frac{1}{4}[/tex]

Answer:

32 degrees

Step-by-step explanation:

We know that the two opposite angles are equivalent so we need to figure out what each one equals.

First we find what x equals so:

9x - 55 = 5x + 21

When we solve for x we get 19 so we can put this back into the expression to find out the first angle

5(19) + 21 = 116

Since we know both sides are 116 we can add them and get 232

We know now that since all sides all add to 360 we can do

360-232= 128

then split 128 in two for the left and right sides we get 64 degrees

Since the line VU bisects the left angle we know the angle WOV is half of 64 which is:

32 degrees

Answer:

The rule for a reflection over the y -axis is (x,y)→(−x,y) .

A'(-(x) ; y)

A'(-(-5) ; 3)

A'(5 ; 3)

The age of Julia is 13 years.

Integers are whole numbers, including both positive and negative numbers, that do not have any fractions or decimals. In mathematics, integers are often used to represent real-world quantities such as age, time, and money.

In this problem, Julia is the oldest of three siblings whose ages are consecutive integers. We can represent this using the equation x + (x+1) + (x+2) = 42, where x is Julia's age.

To solve this equation, we can use the distributive property to expand the left side of the equation to 3x + 3 = 42.

We can then subtract 3 from both sides of the equation to get 3x = 39. Finally, we can divide both sides by 3 to get x = 13.

Therefore, Julia's age is 13.

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Complete Question:

Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.

Answer:

4/6 and 2/6

Step-by-step explanation:

2/3 = 4/6

1/3 = 2/6

4/6 + 2/6 = 6/6 = 1

Answer:

No, 3,816+467 is not a good estimate! 3,816 is very far from 8,000. 467 is a very low number to be added to 3,816. most likely when you add the two you will get a low number. when you add the two you get 4,283 which is not even close to the number you are trying to reach!

Step-by-step explanation:

hope this helps!

Time  is 4.053 hours (to the nearest thousandth of an hour).

What is average rate?

This refers to  the change in speed over a selected period of time. It depends on when you take the measurements. •

Solving for average rate:

Average Rate = 123.362 mi per hr

Distance = 500 (mile)

Time =?

Average Rate = Distance

                            Time  

123.362 mi per hr =   500 (mile)

                                     Time    

Making time subject of the formular we have:

Time = 500 (mile)

            123.362 mi per hr

Time = 4.053 hrs

Time  is 4.053 hours  (to the nearest thousandth of an hour).

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The correct statements of the given ones are -

Two circles are said to be similar if the ratio of their corresponding radius, circumferance and areas are proportionally constant.

Given are the two circles such that circle P is similar to circle Q.

{ 1 } -

Circle Q is a dilation of circle P with a scale factor of 7.

Proof :

r{Q}/r{P} = 28/4 = 7

{ 2 } -

Circle Q is a translation of circle P, 6 units up.

Proof :

Apply the rule (x, y + 6) to the coordinate (2, -3), we get (2, 3).

Therefore, the correct statements of the given ones are -

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The area of the sector is 16.1 ft².

The formula for the area of a sector of a circle is given as;

A =  θ/360⁰  x ( r² )

where;

The angle of the sector is calculated as follows;

sin (θ/2) = 3 / 5

sin (θ/2) = 0.6

θ/2 = sin⁻¹ ( 0.6 )

θ/2 = 36.87⁰

θ = 2 x 36.87⁰

θ = 73.74⁰

The area of the sector is calculated as;

A = (73.74 / 360 ) x π (5²)

A = 16.1 ft²

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The correct answer about experiment, trial, and outcome is

a. The experiment identifies whether a head or tail

b. The experiment is flipping the coin  

d. A trial is one flip of the coin  

An experiment in probability is a process or activity that involves observing or measuring an outcome or event, in order to determine the likelihood or probability of certain outcomes.

In probability, an outcome refers to a possible result that can occur from an experiment or event. It is one of the possible outcomes that can happen, and it may be a single result or a set of results.

In probability, a trial is a single repetition of an experiment or event. It is the process of observing or measuring the outcome of an event or experiment once.

Here we have

At a sports event, a fair coin is flipped to determine which team has possession of the ball.

The coin has two sides, heads, (H), and tails, (T).  

From the given options correct answers are

a. The experiment identifying whether a head or tail is flipped is correct because the experiment is to determine which side of the coin will be facing up after the coin is flipped, either heads (H) or tails (T).

b. The experiment is flipping the coin is correct because the experiment involves physically flipping the coin.

d. A trial is one flip of the coin is correct as a trial is defined as a single performance of an experiment, in this case, flipping the coin once.  

Therefore,

The correct answer about experiment, trial, and outcome is

a. The experiment identifies whether a head or tail

b. The experiment is flipping the coin  

d. A trial is one flip of the coin  

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Answer:

(3/5) (30x - 15) = 72 ⇔ 18x - 9 = 72

(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72

(3/5) (30x - 15) = 72 ⇒ x = 4.5

Equation 1 and 2 have the same value.

Equations C and D have the same value.

A formula is given to us: 3/5 (30x -15) = 72. The equations with the same value of x are the ones we are to choose.

Let's tackle the issue at hand.

3/5 . 30x - 3/5 . 15=72

3.6x - 3.3= 72

18x - 9 = 72

As a result, option C is the best one.

As we factor 3 out of the equation above, we get:

3 . 6x - 3 . 3 = 72

3(6x-3)=72

As a result, option D is also a good decision.

Let's figure out what x is: 3(6x-3) / 3 = 72/3

6x-3=24

x = 4.5

As a result, the final choice is also right.

(3/5) (30x - 15) = 72⇔ 18x - 9 = 72

(3/5) (30x - 15) = 72 ⇔ 3(6x - 3) = 72

(3/5) (30x - 15) = 72 ⇒ x = 4.5

Equations C and D have the same value.

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The amount that will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% closed on April 12th is $9,457.19.

The APR represents the annual percentage rate.

The annual percentage rate is the interest rate for the year, including other finance charges.

To compute the interest, the annual percentage rate is multiplied by the loan amount and the period divided by 365 days.

Loan amount = $250,000

Annual percentage rate (APR) = 5.25%

Loan closing date = April 12th

April 12th to December 31st = 263 days

Interest for the year = $9,457.19 ($250,000 x 5.25% x 263/365)

Thus, for the year, the interest is $9,457.19.

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If a circular garden with a radius of 3 ft. Is bordered by a circular sidewalk that is 2 ft. Wide, then The area of the sidewalk is 28.26 ft².

To calculate this, first calculate the area of the garden, which is 28.27 ft² (A=πr²). After that subtract this from the area of the sidewalk, which is 56.54 ft² (A=π(r+2)²). The area of the sidewalk is the difference between these two values, which is 28.26 ft².

To calculate the area of the garden, we use the formula A=πr², where r is the radius of the garden. In this case, the radius is 3 ft., so the area is 28.27 ft². To calculate the area of the sidewalk, we use the formula

where r is the radius of the garden and 2 is the width of the sidewalk. In this case, the radius is 3 ft. and the width is 2 ft., so the area is 56.54 ft². The area of the sidewalk is then the difference between these two values, which is 28.26 ft².

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Answer:

[tex]5x^{7} -x+2[/tex]

Step-by-step explanation:

[tex]6x^{7} -x+8[/tex] minus [tex]x^{7} +2[/tex] equals to [tex]5x^{7} -x+2[/tex].

We can solve this by subtracting [tex]x^{7}[/tex] from [tex]6x^7[/tex]. This will make it [tex]5x^7[/tex].

x cannot be subtracted, so it becomes [tex]5x^7 -x[/tex].
8-6 is 2, so it becomes [tex]5x^7-x+2[/tex]

Therefore , the solution of the given problem of fraction comes out to be the restaurant could make 48 cups of pudding from the 8 quarts they have.

An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction. A measurement that reflects a portion of the whole is a percentage.

Here,

There are different ways to approach this problem, but one possible method is to use unit conversions to find how many cups are in 8 quarts, and then divide by 1/6 of a quart per cup.

1 quart = 4 cups (by definition of quart)

Therefore, 8 quarts = 8 x 4 cups = 32 cups

1/6 of a quart = 1/6 x 4 cups = 2/3 cups

Therefore, the number of cups of pudding that could be made is:

32 cups / (2/3 cups) = 48 cups

Therefore, the restaurant could make 48 cups of pudding from the 8 quarts they have.

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The slope of the line tangent to the quadratic equation f(x) = x² + x + 8 is approximately equal to 27.996.

In this case we need to estimate the slope of a line tangent to a quadratic equation based on behavior exhibited by a set of secant lines. A secant line is a line that passes through only two points of the curve and a tangent line is a line that passes through only one point of the curve. The slope of the secant line can be determined by the following expression:

m = Δf(x) / Δx

Now we proceed to determine the slopes associated with each secant line:

x = 4

f(4) = 4² + 4 + 8

f(4) = 28

x = 4.1

f(4.1) = 4.1² + 4.1 + 8

f(4.1) = 28.91

x = 4.01

f(4.01) = 4.01² + 4.01 + 8

f(4.01) = 28.091

x = 3.9

f(3.9) = 3.9² + 3.9 + 8

f(3.9) = 27.110

x = 3.99

f(3.99) = 3.99² + 3.99 + 8

f(3.99) = 27.910

And the slope of the tangent line can be estimated by average:

m = 0.5 · [f(3.99) + f(4.01)]

m = 0.5 · (27.910 + 28.091)

m = 27.996

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Answer:

Step-by-step explanation:

a. The average rate of change in the number of worldwide cell phones can be calculated as:

Average rate of change = (change in number of cell phones) / (change in time)

The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,

Average rate of change = 1.94 billion / 2 years = 0.97 billion/year

So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.

b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:

C(t) - 14.02 = 0.97t

Simplifying, we get:

C(t) = 0.97t + 14.02

So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.

c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).

C(7) = 0.97(7) + 14.02 = 20.83 billion

Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.

The solution is, the average speed of the boat relative to the water is 9 mph

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time

here, we have,

Let x represent the speed of the boat.

The rate of the current was 7 mph,

Assuming the boat travelled against the current while going upstream, the total speed would be x - 7

Assuming the boat in the direction of the current while going downstream, the total speed would be x + 7

Time = speed × time

Since she travelled 32 miles upstream and 32 miles downstream, then,

Time taken to go upstream = 32/(x -7)

Time taken to go downstream = 32/(x + 7)

Since the total time of the trip was 18 hours, then

32/(x -7) + 32/(x + 7) = 18

Cross multiplying by (x - 7)(x + 7), it becomes

32(x + 7) + 32(x - 7) = 18[(x - 7)(x + 7)

32x + 224 + 32x - 224 = 18(x² + 7x - 7x - 49

32x + 32x = 18x² - 882

18x² - 64x - 882 = 0

Dividing through by 2, it becomes

9x² - 32x - 441 = 0

9x² + 49x - 81x - 441 = 0

x(9x + 49) - 9(9x + 49) = 0

x - 9 = 0 or 9x + 49 = 0

x = 9 or x = - 49/9

Since the speed of the boat cannot be negative, then x = 9

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The statement that the Property damage liability pays for injuries to a driver or their passengers caused by an uninsured or underinsured driver is false.

Auto insurance policy is a contract between the insurance company and the person being insured which protects the person under any financial loss caused by accident or theft.

There are mainly six types of auto insurance coverage that the company basically provide.

They are Property damage liability, Bodily injury liability, PIP, Uninsured and underinsured motorist coverage, collision and comprehensive.

Property damage liability pays for the damage that the person insured causes to someone else's property, which include someone else's car, buildings or so.

The given coverage in the statement is the Uninsured and underinsured motorist coverage.

Hence the given statement is false.

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let the total population be x

Step-by-step explanation:

38.8%of x=12,900,000

x=12,900,000*100/38.8

x=12,900,000*100*10/388

The description corresponds to an experiment.

Mathematics is the sciences and study of quality, structure, space, and change. Mathematician's are seek out patterns, formulate new conjectured, and establish truth by the  rigorous seduction from appropriately choden axioms and definitions.

An experiment is a type of scientific research method in which a researcher manipulates one or more variables and measures the effects of the manipulation on other variables. In this example, the researcher divided the thirty university students into two groups and manipulated one variable (free tutoring in mathematics) to measure the effects on another variable (final mathematical examination scores). Therefore, this is an experiment.

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If Precision Engineering Factory consumes 12,500 units of a component in every three- month period.  the total cost of material is TZS 6,060 per year.

The annual demand for the material can be calculated as follows:

Annual demand = (12,500 units/3 months) x (4 quarters/year) = 50,000 units/year

Ordering cost = TZS 3 per order

Number of orders = (50,000 units/year) / (12,500 units/order) = 4 orders/year

Ordering cost per year = (4 orders/year) x (TZS 3/order) = TZS 12/year

Trucking cost = TZS 12 per order

Trucking cost per year = (4 orders/year) x (TZS 12/order) = TZS 48/year

Deterioration and obsolescence cost = TZS 0.04 per unit per year

Deterioration and obsolescence cost per year = (50,000 units/year) x (TZS 0.04/unit/year) = TZS 2,000/year

Interest cost = TZS 0.06 per unit per year

Interest cost per year = (50,000 units/year) x (TZS 0.06/unit/year) = TZS 3,000/year

Storage cost = TZS 1,000 per year for 50,000 units

Storage cost per unit per year = (TZS 1,000/year) / (50,000 units) = TZS 0.02/unit/year

Storage cost per year = (50,000 units/year) x (TZS 0.02/unit/year) = TZS 1,000/year

Total cost of material = Ordering cost + Trucking cost + Deterioration and obsolescence cost + Interest cost + Storage cost

Total cost of material = TZS 12/year + TZS 48/year + TZS 2,000/year + TZS 3,000/year + TZS 1,000/year

Total cost of material = TZS 6,060/year

Therefore, the total cost of material is TZS 6,060 per year.

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So, in response to the above question, we can state that The projected sum is $800, or around $780. Hence, equation  of Mr. Foreman's estimation is accurate.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Nine touchdowns by the Tigers, each earning six points, for a total of nine times six or 54 points.

The Leopards scored 5 touchdowns for a total of 5 x 6 = 30 points, each of which was worth 6.

We may deduct the total points scored by the Leopards from the total points scored by the Tigers to see how many more points the Tigers scored than the Leopards:

Leopards' points minus Tigers' points equals 54 - 30 = 24.

As a result, the formula is p, where p = 24, where Tigers' points Equal Leopards' points.

Hence, the Tigers outscored the Leopards by 24 points.

$105 + $448 + $115 + $143 - $21 = $790

We have the following by rounding the numbers to the closest tens:

$110 + $450 + $120 + $140 - $20 = $800

The projected sum is $800, or around $780. Hence, Mr. Foreman's estimation is accurate.

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Based on given question, average rate of change or slope is-0.004 and

the predicted price for 7500 shirts is $47.

The ordered pairs for the historical data are:

(12000, 29) and (18000, 5)

To find the slope (average rate of change) between these two data points, we can use the formula:

slope = (change in y) / (change in x)

slope = (5 - 29) / (18000 - 12000)

slope = -24 / 6000

slope = -0.004

Rounding to three decimal places, the slope is -0.004.

To find the linear equation, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Using the point (12000, 29) and the slope we just calculated, we get:

p - 29 = -0.004(x - 12000)

Simplifying and solving for p, we get:

p(x) = -0.004x + 77

Therefore, the equation for the price p they can charge for x shirts is p(x) = -0.004x + 77.

To predict the price they can charge for 7500 shirts, we can substitute x = 7500 into the equation:

p(7500) = -0.004(7500) + 77

p(7500) = 47

Therefore, the predicted price for 7500 shirts is $47.

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Answer:

40x + 17(468-x) = 11912

       23x = 11912 - 17*468     |Solve for x and then find (468-x) as well