What value of n makes the equation true? Show your work.

Answer:

35.09 units

Step-by-step explanation:

This is a right-angled triangle where:

Hypotenuse = x units

With respect to angle 20°:

Opposite = 12 units

Use trigonometric function sinФ to solve for x:

sinФ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

∴sin20° = [tex]\frac{12}{x}[/tex]

Cross-multiplication is applied:

[tex](x)(sin20) = 12[/tex]

x has to be isolated and made the subject of the equation:

∴[tex]x = \frac{12}{sin20}[/tex]

x = 35.09 units (Rounded to 2 decimal places)

Answer:

The length of x is 35.09 units to two decimal places.

Step-by-step explanation:

In the given right triangle, we have been given the length of the side opposite the angle and need to find the length of the hypotenuse.

To find the value of x, use the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Substitute θ = 20°, O = 12 and H = x into the ratio and solve for x:

[tex]\implies \sin 20^{\circ}=\dfrac{12}{x}[/tex]

[tex]\implies x=\dfrac{12}{\sin 20^{\circ}}[/tex]

[tex]\implies x=35.085652...[/tex]

[tex]\implies x=35.09\; \sf (2\;d.p.)[/tex]

Therefore, the length of x is 35.09 units to two decimal places.

Answer: According to the histogram, a sum of 28 is not unusually low. The bar representing a sum of 28 has a height of 9, which is relatively high compared to some of the other bars. Additionally, the histogram is roughly symmetric, so a sum of 28 is not far from the mean of the distribution.

To find the probability that a person would roll a sum less than 28, we can standardize the value using the formula z = (x - mu) / sigma, where x is the sum of 28, mu is the mean of 35, and sigma is the standard deviation of 5.72.

z = (28 - 35) / 5.72 = -1.22

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.22 is approximately 0.1112, or 11.12%. Therefore, there is about an 11.12% chance that a person would roll a sum less than 28.

Step-by-step explanation:

Answer:

We can use the concept of proportions to solve this problem. We know that the ratio of the height of the tree to the length of its shadow is the same as the ratio of the height of the mailbox to the length of its shadow.

Let's call the height of the mailbox "x". Then, we can set up the proportion:

height of tree / length of tree's shadow = height of mailbox / length of mailbox's shadow

Plugging in the values we know, we get:

36 / 18 = x / 4

Simplifying the left side of the equation, we get:

2 = x / 4

To solve for x, we can multiply both sides of the equation by 4:

8 = x

Therefore, the mailbox is 8 feet tall.

Step-by-step explanation:

Answer:

Height of mail box = 8 ft

Step-by-step explanation:

Given information,

→ 18 ft shadow is formed by a 36 ft tree.

→ A mail box casts 4 foot shadow.

Now we have to,

→ Find the height of the mail box.

Let us assume that,

→ Height of mail box = h

Forming the equation,

→ 36/18 = h/4

Then the value of h will be,

→ 36/18 = h/4

→ h/4 = 36/18

→ h/4 = 2

→ h = 2 × 4

→ [ h = 8 ft ]

Hence, the value of h is 8.

Therefore, the total cost price of the goods is #5400.

Cost price refers to the amount of money that is spent by a business or individual to acquire or produce a product or service. It includes all the costs involved in the production or acquisition of the product or service, such as raw materials, labor costs, transportation costs, and other expenses. The cost price is usually used as a starting point for calculating the selling price of a product or service and is an important factor in determining the profitability of a business.

by the question.

Let's assume the cost price of the goods to be "x".

According to the problem, the trader sold the goods at a price of #5184 and incurred a loss of 4%.

we know that,

selling price = cost price - loss

Substituting the given values in the above formula, we get:

#5184 = x - 0.04x

Simplifying the equation, we get:

#5184 = 0.96x

Dividing both sides by 0.96, we get:

x = #5400

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Answer:

From the given figure, we can write the following equations:

n(A) = 2x + 4

n(B) = x + 5

n(A∪B) = n(A) + n(B) - n(A∩B)

Since we are given that n(A) = n(B), we can substitute the expressions for n(A) and n(B) to get:

2x + 4 = x + 5

x = 1

(a) x = 1

(b) n(A) = 2x + 4 = 2(1) + 4 = 6

(c) n(B) = x + 5 = 1 + 5 = 6

(d) n(A∪B) = n(A) + n(B) - n(A∩B)

We still need to find n(A∩B) to calculate n(A∪B). Looking at the figure, we can see that there are 2 elements that are common to both A and B. Therefore,

n(A∩B) = 2

Substituting this value, we get:

n(A∪B) = n(A) + n(B) - n(A∩B) = 6 + 6 - 2 = 10

Therefore, (d) n(A∪B) = 10.

Step-by-step explanation:

The expression that does not have the same value as -2 + 3×65 is 3×(65-2) which evaluates to 183, the correct option is D.

The expression -2 + 3×65 represents a mathematical calculation that involves the operations of addition and multiplication. The order of operations dictates that multiplication should be done before addition, so we start by multiplying 3 and 65 and then adding the result to -2.

The value of -2 + 3×65 is 193.

we need to evaluate each expression and compare it to 193.

Option A: 3×65 - 2 = 193

Option B: (3-2)×65 = 65

Option C: 65×3 - 2 = 193

Option D: 3×(65-2) = 183

expression that does not have the same value as -2 + 3×65 is option D: 3×(65-2) which evaluates to 183.

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The complete question is :

Which expression does not have the same value as −2+3×65?

Option A: 3×65 - 2 = 193

Option B: (3-2)×65 = 65

Option C: 65×3 - 2 = 193

Option D: 3×(65-2) = 183

Answer: She

bought a total of 5 notebooks and 13 pencils.

Step-by-step explanation:

Answer:

  C

Step-by-step explanation:

You want to identify the set of ordered pairs corresponding to the given pattern definitions.

The x-pattern starts at 2.

The y-pattern starts at 0.

The first (x, y) ordered pair is (2, 0). This matches answer choice C.

__

Additional comment

The x-rule tells you the sequence is ...

  2, 2+6 = 8, 8+6 = 14, 14+6 = 20 . . . . . {2, 8, 14, 20}

The y-rule tells you the sequence is ...

  0, 0+5 = 5, 5+5 = 10, 10+5 = 15 . . . . . {0, 5, 10, 15}

Then the (x, y) pairs are ...

  (2, 0), (8, 5), (14, 10), (20, 15)

Note that when X and Y are the variables involved, we conventionally use the ordered pair (x, y). When other variables are involved, the ordered pair may be different, not always alphabetic order.

Generally, the independent variable is listed first. Here, neither depends on the other, so that criterion does not apply. Listing X first here is also suggested by the fact that the X pattern rule is defined first.

Answer:

1,610,000

Step-by-step explanation:

To round to the nearest hundred, we need to go to the hundreds place. In 683, we can round this to the nearest hundred by using this rule:

5 or more, let it sore

4 or less, let it rest

683 rounded to the nearest hundred is 700

2329 rounded to the nearest hundred is 2300

Now we just need to multiply both of them to get the product

[tex]2300\times 700=1,610,000[/tex]

The equations that can be used to solve for y, the length of the room are: y² - 5y - 750 = 0 , (y - 30)(y + 25) = 0 , y(y - 5) + 750 = 0

An equation is a mathematical statement that asserts the equality of two expressions, often with variables and constants.

To solve for y, we can use the same equation we used for x, since y represents the length of the room. Therefore, the equation we can use to solve for y is:

y² - 5y - 750 = 0

This equation can be factored as (y - 30)(y + 25) = 0, which gives us two solutions: y = 30 or y = -25. However, since the length of a room cannot be negative, the only valid solution is y = 30.

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Answer:

the formula for density is:

density = mass/volume

We know that the density of the object is 8 grams per liter, and its volume is 16 liters. We can use this information to solve for the mass:

density = mass/volume

8 g/L = mass/16 L

To solve for the mass, we can cross-multiply and simplify:

8 g/L * 16 L = mass

128 g = mass

Therefore, the mass of the object is 128 grams.

Answer:

5. To find the time in which the loan of N3,900 at the rate of 5% yields N585, we can use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate (as a decimal), and t is the time (in years).

Plugging in the given values, we get:

585 = 3900 * 0.05 * t

Solving for t, we get:

t = 3 years

Therefore, it will take 3 years for the loan to yield N585 in interest.

6. To find the time it will take for the simple interest on N70,000 at the rate of 7% to be N20,000, we can again use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

20000 = 70000 * 0.07 * t

Solving for t, we get:

t = 4 years

Therefore, it will take 4 years for the simple interest on N70,000 at the rate of 7% to be N20,000.

7. To find the time it takes for N300 to amount to N390 at the rate of 3%, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

where A is the final amount, P is the principal (the initial amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

Plugging in the given values, we get:

390 = 300 * (1 + 0.03/1)^(1*t)

Simplifying, we get:

1.3^t = 1.3

Taking the logarithm of both sides, we get:

t = log(1.3) / log(1.3)

t ≈ 1.82

Therefore, it takes approximately 1.82 years for N300 to amount to N390 at the rate of 3%.

8. To find the rate percent per annum for a simple interest of N80 on N5600 in 1 year, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

80 = 5600 * r * 1

Solving for r, we get:

r = 0.0143 or 1.43%

Therefore, the rate percent per annum is 1.43%.

9. To find the year in which N5100 will yield an interest of N170 at the rate of 2 1/2 per annum, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

170 = 5100 * 0.025 * t

Solving for t, we get:

t = 2/3 years

Since the question asks for the year, we need to add 2/3 years to the current year. Assuming the current year is 2021, we get:

2021 + 2/3 ≈ 2022.67

Therefore, N5100 will yield an interest of N170 at the rate of 2 1/2 per annum in the year 2022.

10. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can again use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

230 = 4600 * r * 2

Solving for r, we get:

r = 0.025 or 2.5%

Therefore, the rate per annum is 2.5%.

11. To find the time it takes for N8100 to yield an interest of N729 at the rate of 9% per annum, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

729 = 8100 * 0.09 * t

Solving for t, we get:

t = 1 year

Therefore, it takes 1 year for N8100 to yield an interest of N729 at the rate of 9% per annum.

12. To find the rate of interest per annum for an interest of N23 on N2300 for 2 years, we can use the formula for simple interest:

I = P * r * t

Plugging in the given values, we get:

23 = 2300 * r * 2

Solving for r, we get:

r = 0.005 or 0.5%

Therefore, the rate of interest per annum is 0.5%.

Answer:

[tex]\mathrm{D.\:\:\:f(x) = 2x^2 - 2x - 4; A = 8}[/tex]

Step-by-step explanation:

The formula for the area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width. In this case, the length is 2x - 4 units and the width is x + 1 units. Therefore, the function that models the area of the rectangle is:

f(x) = (2x - 4)(x + 1)

f(x) = 2x^2 - 2x - 4

Therefore, option D is the correct answer.

To find the area when x = 3, we substitute x = 3 into the function:

f(3) = 2(3)^2 - 2(3) - 4

f(3) = 18 - 6 - 4

f(3) = 8

Therefore, when x = 3, the area of the rectangle is 8 square units.

Answer: 11 and more

Step-by-step explanation:

Answer: 345.6149

Step-by-step explanation:

Answer:

345.6149

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be $240 which will cover the cost of the new motorbike.

The task can be completed by multiplying the data gathered using this type of nanosection along with two individuals variable  who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.

Here,

The quantity supplied and the quantity requested are equal when there is equilibrium. As a result, we can equalise the two formulae and find the equilibrium quantity:

=> -57P + 364 = 25P + 26

=> 82P = 338

=> P = 4.12

We can use either equation to determine the equilibrium amount now that we know the equilibrium price. Use the supply calculation as an example:

=> Q = 25P + 26

=> Q = 25(4.12) + 26

=> Q = 129.5

So, rounded to two decimal places, the equilibrium amount of beer is roughly 129.5.

=> $60 + $180 = $240

which will cover the cost of the new motorbike.

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Answer:

The answer to your problem is, A. 900

Step-by-step explanation:

How we would need to find it:

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

27/150 = 0.18

Next, estimate the number of people who prefer mustard in the entire population of 5,000 attendees we can multiply/x this proportion by the total number of attendees:

0.18 x 5,000 = 900

Thus the answer to your problem is, A. 900

The expression for the area of the shaded region in its simplest form is x² + 23x + 49.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

The shaded area is the difference of the areas of the rectangle and the square.

Rectangle:

A₁ = (x + 10)(2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

Square:

A₂ = (x + 1)² = x² + 2x + 1

Shaded region:

A₁ - A₂ = 2x² + 25x + 50 - (x² + 2x + 1)

= 2x² + 25x + 50 - x² - 2x - 1

= x² + 23x + 49

Hence, the expression for the area of the shaded region in its simplest form is x² + 23x + 49.

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Complete question:

Enter your answer and show all the steps that you use to solve this problem in the space provided.

A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

The way the principal can use a random - number table to pick 30 students from the school is explained below.

To use a random-number table to select 30 students at random from a school of 500 students, the principal should :

This method ensures that every student has an equal chance of being selected.

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For the first finding on job-search satisfaction scale, the estimated Cohen’s d is not provided in the question. However, assuming that it is provided in the actual data, the psychologist can use Cohen’s guidelines for interpreting the effect size based on the estimated Cohen’s d. According to Cohen’s guidelines, an effect size of 0.2 is considered small, 0.5 is considered medium, and 0.8 or higher is considered large. Therefore, the psychologist needs to compare the estimated Cohen’s d with these values to evaluate the effect size.

For the second finding on the number of months worked in the last year, the estimated Cohen’s d is also not provided in the question. The psychologist can use the same approach to evaluate the effect size using Cohen’s guidelines based on the estimated Cohen’s d.

Alternatively, the psychologist can also use r² as a measure of effect size. R² represents the proportion of variance in the outcome variable that is explained by the treatment or intervention. According to Cohen’s guidelines for r², an effect size of 0.01 is considered small, 0.09 is considered medium, and 0.25 or higher is considered large. Therefore, the psychologist can compare the estimated r² with these values to evaluate the effect size.

Based on the information provided, both findings show statistically significant results with treatment effects. However, the actual effect sizes cannot be evaluated without the estimated Cohen’s d or r² values.

Effect size for job-search satisfaction is Cohen's d = 0.7, t statistic = 4.12 and r² = 0.49.

According to Cohen's guidelines, a Cohen's d of 0.7 is considered a large effect size. This means that the workshop had a significant impact on the job-search satisfaction of the participants. The t statistic of 4.12 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.49 indicates that the workshop accounted for 49% of the variance in job-search satisfaction.

Effect size for months worked

Cohen's d = 0.36

t statistic = 2.38

r² = 0.13

According to Cohen's guidelines, a Cohen's d of 0.36 is considered a medium effect size. This means that the workshop had a significant impact on the number of months worked by the participants. The t statistic of 2.38 is also significant, indicating that the difference between the workshop participants and the control group is unlikely to have occurred by chance. The r² of 0.13 indicates that the workshop accounted for 13% of the variance in months worked.

Interpretation

Both of the effect sizes found by the psychologist are significant, indicating that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect size for job-search satisfaction is larger than the effect size for months worked, suggesting that the workshop had a greater impact on job-search satisfaction than on the number of months worked.

Conclusion

The psychologist's findings suggest that the workshops had a positive impact on the job-search satisfaction and the number of months worked by the participants. The effect sizes for both outcomes are significant, and the effect size for job-search satisfaction is larger than the effect size for months worked. These findings suggest that the workshops may be an effective way to help unemployed people find jobs.

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The true statement are:

A. 15m3-6m=3m(5m2-6m),

B. 40m6-4=4(10m6-1),

C. 6m2+18m=6m2(1+3m),

Therefore the correct option is A, B, C.

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The correct question is:

Which statements are true

15m3-6m=3m(5m2-6m),

40m6-4=4(10m6-1),

6m2+18m=6m2(1+3m),

32m4+12m3(8m+3)

Therefore , Highest Common Factor (HCF) of two or more numbers by prime factorisation method can be done by following below given steps

This generally recognized ease, preexisting variables, and any necessary elements from the initial Diocesan customizable query may all be used to complete the job. Consequently, you might be given another chance to use the item. Otherwise, important impacts on algorithmic statistics will vanish.  

Here,

To find the Highest Common Factor (HCF) of two or more numbers by prime factorisation method, follow these steps:

Express each number as a product of prime factors.

Identify the common prime factors among the numbers.

Take the product of the common prime factors. This product will be the HCF of the given numbers.

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The two cars will draw level at a distance of 12 kilometers from the starting point, taking their speed and into consideration, as further explained below.

Since both cars are traveling towards the same destination, the distance between them will decrease over time until they draw level. Let's call the distance between the starting point and the meeting point "d" kilometers. We can use the formula:

distance = rate × time

Since car A has a three-minute head start, car B will have to travel for three minutes less than car A. Let's call the time it takes for car B to catch up to car A "t" hours. Then:

time for car A = t + 3/60 hours

time for car B = t hours

We want to find the distance between the starting point and the meeting point, which is the same for both cars. So we can set up an equation based on their distances:

distance traveled by car A = distance traveled by car B

(rate for car A) × (time for car A) = (rate for car B) × (time for car B)

60 × (t + 3/60) = 70 × t

3 = 10t

t = 3/10 hours

Now that we know the time it takes for car B to catch up to car A, we can use either car's rate and time to find the distance between the starting point and the meeting point. Let's use car A's rate and time:

distance = rate × time

distance = 60 × (t + 3/60)

distance = 60 × (3/10 + 1/20)

distance = 60 × (4/20)

distance = 12 kilometers

Therefore, the two cars will meet 12 kilometers from the starting point.

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With 4.5% compounded semi-annually, Sarah will need to make installments for roughly 20.82 years in order to save $10,000. Hence, 20.82 is the answer.

Is every two years or semiannually?

Simply said, semiannual refers to events that occur twice a year. A couple might commemorate their nuptials each two years, a corporation might hold workplace celebrations each two years, as well as a family might go on vacation each two years. Every two years, something that happens twice a year does.

We can utilize the calculation again for future value of an annuity to resolve this issue:

FV = P × ((1 + r/n) - 1) / (r/n)

Where:

FV = Future value

P = Periodic payment

r = Annual interest rate

n = Compounding cycles per year, number

t = Number of years

In this instance, Sarah plans to deposit $300 each six months in order to save $10,000. She will so be required to make two payments each year. P thus equals $300, n equals 2, r equals 0.045 (decimalized 4.5%), and FV equals $10,000. The number of years, t, needs to be solved for.

$10,000 = $300 × ((1 + 0.045/2) - 1) / (0.045/2)

When we simplify this equation, we obtain:

20 = (1 + 0.0225) - 1

21 = (1 + 0.0225)

Using both sides' natural logarithms:

ln(21) = ln((1 + 0.0225))

ln(21) = 2×t × ln(1 + 0.0225)

t = ln(21) / (2 × ln(1 + 0.0225))

t = 20.82

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let's keep in mind that in the IV Quadrant, the cosine is positive whilst the sine is negative, so hmm

[tex]\cos(\theta )=\cfrac{\stackrel{adjacent}{8}}{\underset{hypotenuse}{9}} \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{8}\\ o=opposite \end{cases}[/tex]

[tex]o=\pm\sqrt{ 9^2 - 8^2}\implies o=\pm\sqrt{ 81 - 64 } \implies o=\pm\sqrt{ 17 }\implies \stackrel{ IV~Quadrant }{o=-\sqrt{17}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \tan(\theta )=\cfrac{\stackrel{opposite}{-\sqrt{17}}}{\underset{adjacent}{8}}~\hfill[/tex]

To find the value of tan(θ) when cos(θ) = 8/9 and θ is in the fourth quadrant, use the relation sin^2(θ) = 1 - cos^2(θ) to determine sin(θ). Then compute tan(θ) = sin(θ) / cos(θ). The result will be negative

Given the equation cos(θ) = 8/9 in the fourth quadrant of the Cartesian plane, you are required to determine the value of tan(θ). In the fourth quadrant, cosine values are positive, and sine values are negative. You can use the relation sin^2(θ) = 1 - cos^2(θ). So, sin(θ) would be -sqrt(1 - (8/9)^2). The tangent of an angle in any quadrant can be found by taking the ratio of the sine to the cosine, i.e., tan(θ) = sin(θ) / cos(θ). Substitute the values of sine and cosine to find the value of tan(θ). It turns out that tan(θ) will be negative in the fourth quadrant.

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Answer:

To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to get the percentage.

The difference between the original price and the new price is:

80 - 44 = 36

To find the percentage decrease, we divide this difference by the original price:

36 / 80 = 0.45

Finally, we multiply by 100 to get the percentage:

0.45 * 100 = 45%

Therefore, the percentage decrease from $80 to $44 is 45%.

Answer:  The percentage decrease is 45%.

Step-by-step explanation:

Percentage decrease = [tex](\frac{Oringinal Value-NewValue}{Oringinal Value} )*100[/tex]

                                    = [tex](\frac{80-44}{80} )*100[/tex]

                                    = 45%

The three coordinates that satisfy the system of inequalities include the following:

(0, -2)

(-7, - 5)

(-2, -8).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

By critically observing the graph of the given system of inequalities y < -2x + 4 and 2x - 4y ≥ 3, the three required solutions that satisfies it include following;

Ordered pair = (0, -2).

Ordered pair = (-7, - 5).

Ordered pair = (-2, -8).

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Answer:

Let's use the formula:

distance = rate × time

Let's assume Latasha's rate of travel as "r". Then, Nathan's rate of travel would be "r + 8".

For Latasha:

distance = r × 9

For Nathan:

distance = (r + 8) × 9

According to the problem, the combined distance they traveled is 288 miles. So:

r × 9 + (r + 8) × 9 = 288

Simplifying the equation:

18r + 72 = 288

18r = 216

r = 12

So, Latasha's rate of travel is 12 mph, and Nathan's rate of travel is 20 mph (12 + 8).

Therefore, Latasha is traveling at 12 mph and Nathan is traveling at 20 mph.

The prοbability οf  that the number οf lοst-time accidents οccurring οver a periοd οf 9 days will be at least 4  is 0.3975.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

We can use here Pοisson distribution with λ=0.4 * 8=3.2

[tex]P[X\geq 4]=1-P[X < 4][/tex]

[tex]=1-{P[X=0] + P[X=1] + P[X=2] +P[X=3] =1-{0.0408+ 0.1304+ 0.2087 + 0.2226} =0.3975[/tex]

Where,

[tex]P[X=0]=\frac{e^{-3.2}(3.2)^0}{0!} = 0.0408[/tex]

[tex]P[X=1]=\frac{e^{-3.2}(3.2)^1}{1!} = 0.1304[/tex]

[tex]P[X=2]=\frac{e^{-3.2}(3.2)^2}{2!} = 0.2087[/tex]

[tex]P[X=3]=\frac{e^{-3.2}(3.2)^3}{3!} = 0.2226[/tex]

Hence the prοbability of  that the number of lost-time accidents οccurring over a period of 9 days will be at least 4  is 0.3975.

To learn more abοut probability refer the below link

https://brainly.com/question/13604758

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