The length of o a rectangle is 12 cm and its width is 2 cm less than ¾ of its length

Draw an illustration pls

After factoring the given expression -2xy³ - 8xy² + xy, the resultant answer is -2xy²(xy-4).

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

A group of terms coupled with the operations +, -, x, or form an expression, such as 4 x 3 or 5 x 2 3 x y + 17.

A statement with an equal sign, such as 4 b 2 = 6, asserts that two expressions are equal in value and is known as an equation.

So, we have the expression:

-2xy³ - 8xy² + xy

Now, factor out as follows:

=  -2xy³ - 8xy² + xy

= xy(-2xy² - 8xy)

= -2xy²(xy-4)

Therefore, after factoring the given expression -2xy³ - 8xy² + xy, the resultant answer is -2xy²(xy-4).

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Answer:

24.8 gallons of water

Step-by-step explanation:

We Know

A showerhead claims to use 9 gallons of water in 4 minutes.

9 / 4 = 2.25 gallons of water per minute.

If a shower lasts 11 minutes, how many gallons of water were used?

We Take

2.25 x 11 = 24.75 gallons of water

So, the answer is 24.8 gallons of water

Answer:

Step-by-step explanation:

To find the volume of the solid formed by rotating the region about the x-axis, we can use the method of disks.

At a given value of x, the distance between the curve y = 9 + x^2 and the x-axis is 9 + x^2. Thus, the area of the disk at x is A(x) = π(9 + x^2)^2. The limits of integration are 0 and 1, since the region is bounded by the lines x = 0 and x = 1.

Therefore, the volume of the solid is given by:

V = ∫(0 to 1) π(9 + x^2)^2 dx

Using integration techniques (such as substitution), we can evaluate this integral to get:

V = (112π/5) cubic units (rounded to 3 decimal places)

Therefore, the volume of the solid formed by rotating the region about the x-axis is (112π/5) cubic units

The likelihood that at least one of the five individuals has received a vaccination is therefore roughly 0.9551, or nearly 95.51%.

Probability is a way to gauge how likely something is to happen. To quantify uncertainty, one uses a mathematical construct. A number between 0 and 1 represents the likelihood of an event, with 0 denoting impossibility and 1 denoting certainty. The ratio of outcomes that lead to an event A to all potential outcomes can be used to calculate the probability of that occurrence. This is stated as follows: Probability of A is equal to the proportion of conceivable possibilities that lead to A.

given

To solve this issue, we may calculate the likelihood that none of the five individuals have had a vaccination and then remove that from one to calculate the likelihood that at least one of them has.

1 - 0.56 = 0.44 is the likelihood that any one person has not had a vaccination. As a result, the likelihood that all five individuals are unvaccinated is:

0.44 x 0.44 x 0.44 x 0.44 x 0.44 = 0.0449 (rounded to four decimal places) (rounded to four decimal places)

By deducting the aforementioned result from 1, we can determine the likelihood that at least one person has had vaccinations:

1 - 0.0449 = 0.9551

The likelihood that at least one of the five individuals has received a vaccination is therefore roughly 0.9551, or nearly 95.51%.

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Step-by-step explanation:

so you can do it in this way

Step-by-step explanation:

it is not fully clear what you need.

the text says to find the (length of) arc TVU.

we don't know the size of the circle or anything that's related to this (like length of the line UT).

so, we cannot calculate the absolute length of any arc of the circle.

but then the answer field suddenly says "angle of arc TVU". and this we can do.

the arc angle of UT :

since the vertex (T) of the angle 56° is on the circle (as RS is a tangent), the enclosed arc angle is twice the size of the vertex angle.

arc angle UT = 2×56 = 112°.

therefore, we know that the

arc angle TVU = 360 - 112 = 248°

because it is the remainder to the arc UT of the whole circle.

Answer:

To solve the inequality 3x - 14 ≥ 11 - x, we need to isolate the variable x on one side of the inequality symbol. We can do this by adding x to both sides and adding 14 to both sides:

3x - 14 + x ≥ 11

Combining like terms, we get:

4x - 14 ≥ 11

Adding 14 to both sides, we get:

4x ≥ 25

Dividing both sides by 4, we get:

x ≥ 6.25

Therefore, the solution to the inequality is x ≥ 6.25, which can be represented as the interval [6.25, ∞) on the number line

The difference in weekly pay for these jobs is $176 (rounded to the nearest dollar).

To find the difference in the weekly pay for the two job offers, we first need to convert the annual salaries to weekly salaries.

For the first job offer with an annual salary of $48.3K, the weekly salary can be calculated as:

Weekly salary = Annual salary/number of weeks in a year

Assuming 52 weeks in a year, the weekly salary for this job offer is:

Weekly salary = $48.3K / 52 = $928.84 (rounded to two decimal places)

For the second job offer with an annual salary of $57.5K, the weekly salary can be calculated as:

Weekly salary = Annual salary/number of weeks in a year

Again assuming 52 weeks in a year, the weekly salary for this job offer is:

Weekly salary = $57.5K / 52 = $1,105.77 (rounded to two decimal places)

The difference in weekly pay between the two job offers is therefore:

$1,105.77 - $928.84 = $176 (rounded to the nearest dollar)

Therefore, the difference in weekly pay for these jobs is $176 (rounded to the nearest dollar).

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The probability that a randomly selected light bulb will last between 750 and 900 hours is given as follows:

P = 47.5%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

In the context of this problem, we have that:

The normal distribution is symmetric, hence the probability of an observation between the mean and two standard deviations above the mean is given as follows:

0.5 x 95 = 0.475 = 47.5%.

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[tex] \: [/tex]

((x/y)^(n+1)) > ((x/y)^n) for all n ≥ 1 and x > y > 0.

To prove this statement by induction, we will use the principle of mathematical induction.

Base case: When n = 1, we have:

((x/y)^(1+1)) = ((x/y)^2) = (x^2)/(y^2)

((x/y)^1) = (x/y)

Since x > y > 0, we have x/y > 1. Therefore, (x^2)/(y^2) > (x/y), which means that the base case is true.

Inductive step: Assume that ((x/y)^(k+1)) > ((x/y)^k) for some arbitrary positive integer k. We want to prove that this implies that ((x/y)^(k+2)) > ((x/y)^(k+1)).

Starting with ((x/y)^(k+2)), we can write:

((x/y)^(k+2)) = ((x/y)^(k+1)) * ((x/y)^1)

Using the induction hypothesis, we know that ((x/y)^(k+1)) > ((x/y)^k), and we also know that x/y > 1. Therefore, we have:

((x/y)^(k+2)) > ((x/y)^k) * (x/y)

Simplifying this expression, we get:

((x/y)^(k+2)) > ((x/y)^k) * (x/y)

((x/y)^(k+2)) > ((x^k)/(y^k)) * (x/y)

((x/y)^(k+2)) > ((x^(k+1))/(y^(k+1)))

Therefore, we have shown that ((x/y)^(k+2)) > ((x/y)^(k+1)) for all positive integers k, which completes the inductive step.

By the principle of mathematical induction, we have proven that ((x/y)^(n+1)) > ((x/y)^n) for all n ≥ 1 and x > y > 0.

Answer:

B

Step-by-step explanation:

Answer:

its either D or C but I think its D

Step-by-step explanation:

Answer:

1440

Step-by-step explanation:

explanation in the picture

option C is correct. The range of penguin heights is greater at Cityview Zoo than at Countryside Zoo.

How to calculate data?

Based on the given data, we can see that the penguin heights at Countryside Zoo are distributed more evenly across the range of heights, with heights ranging from 35cm to 45cm, and a fairly consistent distribution across this range. In contrast, the penguin heights at Cityview Zoo are more concentrated around the height of 38cm, with fewer penguins at the extremes of the range.

Therefore, option C is correct. The range of penguin heights is greater at Cityview Zoo than at Countryside Zoo.

Option A is incorrect because the range of penguin heights is greater at Countryside Zoo than at Cityview Zoo.

Option B is incorrect because the ranges of penguin heights are not the same.

Option D is also incorrect because there is no mode of penguin heights at either zoo. A mode is defined as the value that appears most frequently in a distribution. In this case, no height appears more frequently than any other.

In conclusion, we can say that the penguin heights are distributed differently at the two zoos, with Countryside Zoo having a more evenly distributed range of heights, while Cityview Zoo has a more concentrated distribution around a particular height.

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Answer: The solution to the system of equations by substitution is (x, y) = (10, 1).

Step-by-step explanation:

Answer: option B.

Step-by-step explanation:

We can use the formula for the margin of error of a confidence interval for a proportion:

Margin of error = zsqrt(p(1-p)/n)

where z is the critical value from the standard normal distribution for the desired confidence level (98% in this case), p is the estimated proportion (0.60), and n is the sample size.

We are given that the margin of error should be 0.07. Setting this equal to the above expression, we have:

0.07 = zsqrt(0.60(1-0.60)/n)

We need to solve for n. To do this, we first need to find the appropriate value of z for a 98% confidence level. Using a standard normal distribution table or calculator, we can find that z = 2.33.

Substituting this into the above equation and solving for n, we have:

0.07 = 2.33sqrt(0.60(1-0.60)/n)

Squaring both sides and solving for n, we get:

n = (2.33^2)(0.60(1-0.60))/(0.07^2) ≈ 265

Therefore, the sample size needed to construct a 98% confidence interval with a margin of error of 0.07 is approximately 265.

So the correct answer is option B.

Answer:

Step-by-step explanation:

Value of x :-

Therefore, the value of x is 23.

________________________

Hope this helps!

The f(x) of the linear function is:

f(x) = -4x - 7

Since f is a linear function. The general form of a linear function is:

y = mx + b

where y = f(x), m is the slope and b is the y-intercept

Since f (−3) = 5, we have:

x = -3 and y = 5

Substitute into y = mx + b:

y = mx + b

5 = -3m + b ---- (1)

Also, f(5) = −27, we have:

x = 5 and y = -27

Substitute into y = mx + b:

y = mx + b

-27 = 5m + b ---- (2)

Solving (1) and (2) simultaneously by elimination method:

-3m + b = 5

5m + b = -27

-8m = 32

m = 32/(-8)

m = -4

Put m = -4 in (1) and solve for b:

-3x + b = 5

-3(-4) + b = 5

12 + b = 5

b = 5 - 12

b = -7

Put m and b into f(x) = mx + b to get f(x). That is:

f(x) = mx + b

f(x) = -4x - 7

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Step-by-step explanation:

all triangles here are right-angled.

ABC, ADB, ADC, AED.

let's say CD = x, AD = height

just by using Pythagoras :

8² = height² + (10-x)² = height² + 100 -20x + x²

64 = height² + 100 -20x + x²

6² = height² + x²

36 = height² + x²

64-36 = 100 - 20x

28 = 100 - 20x

-72 = -20x

x = 72/20 = 3.6 ft

6² = height² + 3.6²

36 = height² + 12.96

height² = 23.04

height = 4.8 ft

height² = ED² + 3²

23.04 = ED² + 9

ED² = 14.04

ED = 3.746998799... ft ≈ 4 ft

Based on the given information, the answer is (d) no solutions.

What is a system of equations?

A system of equations is a set of two or more equations that need to be solved together to find the values of the variables that satisfy all of the equations.

To solve the system of equations y + 4 = x² and y - x = 2, we can substitute y - x = 2 into y + 4 = x² and get:

y - x + 4 = x²

y = x² + x + 4

Substituting y = x² + x + 4 into y - x = 2, we get:

x² + x + 4 - x = 2

x² + 3 = 2

x² = -1

This equation has no real solutions for x, which means there is no solution for the system of equations.

Therefore, the answer is (d) no solutions.

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Answer:

9%

Step-by-step explanation:

To find the increased amount, subtract this month sales from the last month sales.      

Increased amount = 196200 - 180000

                              = £ 16,200

Now, find the increased percentage using the formula,        

[tex]\boxed{\bf Increased \ percentage = \dfrac{Increased \ amount}{Original \ amount}*100}\\\\[/tex]

                                        [tex]= \dfrac{16200}{180000}*100\\\\= 9\%[/tex]

The calculated value of the exact value of v is <-4, 6>

To find the exact value of v, we need to determine the components of the vector v.

The horizontal component of v, denoted as v_x, is equal to the change in x-coordinates between the initial and terminal points, which is -4 - 0 = -4.

The vertical component of v, denoted as v_y, is equal to the change in y-coordinates between the initial and terminal points, which is 6 - 0 = 6.

Therefore, the exact value of v is:

v = <v_x, v_y> = <-4, 6>

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Using expression 4 x 300,  we can predict that the population of the town in 2016 will be 4,300.

What exactly are expressions?

In mathematics, an expression is a combination of symbols that represent a value or a mathematical relationship between values. An expression can contain numbers, variables, operators, and/or functions, and it can be used to perform operations such as addition, subtraction, multiplication, and division.

Now,

We can use the information given to find the rate of decrease in the population, and then use that rate to predict the population in 2016.

From 2010 to 2012, the population decreased by 6,100 - 5,500 = 600.

This corresponds to a decrease of 600 / 2 = 300 per year, since the decrease is assumed to be constant over time.

Therefore, we can predict the population in 2016 as follows:

From 2012 to 2016 is a time period of 4 years.

At a rate of 300 per year, the population would decrease by 4 x 300 = 1200 over this time period.

Starting from the population in 2012 of 5,500, the predicted population in 2016 is 5,500 - 1,200 = 4,300.

Therefore, based on the given information, we can predict that the population of the town in 2016 will be 4,300.

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Answer:

[tex]3x-3y=31[/tex]

Step-by-step explanation:

Adding the equations yields [tex]3x-3y=20+11=31[/tex].

Answer:

The travel bag that can hold exactly 3,150 cubic inches is the bag that is 21 inches long.

Step-by-step explanation:

The travel bags can be modelled as rectangular prisms.

The formula for the volume of a rectangular prism is:

[tex]\boxed{\textsf{Volume} = l \times w\times d}[/tex]

where:

Given that all three bags have a depth of 10 inches and a width of 15 inches, we can create an equation for the volume of any of the bags by substituting d = 10 and w = 15 into the formula:

[tex]\begin{aligned}\sf Volume &=l \times w \times d\\&= l \times 15\times10\\&=l \times 150\\&=150\;l\end{aligned}[/tex]

To determine which travel bag can hold exactly 3,150 cubic inches, substitute volume = 3150 into the formula and solve for length, l:

[tex]\begin{aligned}\sf Volume &=150\;l\\\\ \implies 3150&=150\;l\\\\\dfrac{3150}{150}&=\dfrac{150\;l}{150}\\\\21&=l\\\\l&=21\;\sf in\end{aligned}[/tex]

Therefore, the travel bag that can hold exactly 3,150 cubic inches is the bag that is 21 inches long.

Answer: Assuming a standard normal distribution, we know that the total area under the curve is equal to 1. Since 0.8904 of the area lies between -z and z, the remaining area (0.1096) lies outside of this range.

Since the normal distribution is symmetric around the mean, the area to the left of -z is the same as the area to the right of z. Therefore, we can find the area to the right of z by subtracting 0.1096 from 1 and dividing by 2:

(1 - 0.1096)/2 = 0.4452

We can use a standard normal distribution table or calculator to find the z-score that corresponds to an area of 0.4452 to the right of the mean. This z-score is approximately 1.70.

Therefore, the value of z such that 0.8904 of the area lies between -z and z is approximately 1.70. Rounded to two decimal places, this is 1.70.

Step-by-step explanation:

Answer:

[tex]V=(3.14)(2.25)^2(3)[/tex]

Step-by-step explanation:

In order to find the volume of a cylinder you have to use the formula [tex]V=\pi r^2h[/tex]

For [tex]\pi[/tex], we plug in 3.14 (because that is what the question asks for)

To find the radius (r), we take half of the diameter

[tex]4.5/2[/tex]

For h, we plug in the height of the mold

When we plug all of these in, we get

[tex]V=(3.14)(2.25)^2(3)[/tex]

Answer:

Let's call the number we're trying to find "x".

According to the problem, when this number is decreased by 40% of itself, we get 54.

In other words,

x - 0.4x = 54

Simplifying the left side, we get:

0.6x = 54

Dividing both sides by 0.6, we get:

x = 90

Therefore, the number we're looking for is 90.

Answer:

5/12

Step-by-step explanation:

We are only looking at people who have a dog, which is 12

Now we need to determine if they have a cat

P( cat given that they have a dog)

            = number of people with a cat/ they have a dog

           = 5/ (5+7)

          = 5/12

Jeriel's hourly wage was $24.80/hour.

Earnings refer to the total amount of money that someone has earned from work over a given period of time. Wage, on the other hand, specifically refers to the amount of money earned per hour or per unit of work completed.

To find Jeriel's hourly wage, we can divide his total earnings by the number of hours he worked:

hourly wage = total earnings / number of hours worked

In this case, Jeriel earned $520.80 and worked for 21 hours, so his hourly wage is:

hourly wage = $520.80 / 21 hours

hourly wage = $24.80/hour

Therefore, Jeriel's hourly wage was $24.80/hour.

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Jeriel worked 21 hours for $520.80, making his hourly pay:

Jeriel got paid $24.80 per hour.

No matter if it is paid based on working time, output, piecework, or regular payments, earnings and wages are defined as "the total payment, in cash or in kind, payable to all individuals determined on the payrol in return for work performed during the accounting period."

We may divide Jeriel's overall income by the number of hours he worked to determine his hourly rate:

hourly wage = total earnings / number of hours worked

In this instance, Jeriel worked 21 hours for a total of $520.80, making his hourly rate:

hourly wage = $520.80 / 21 hours

hourly wage = $24.80/hour

Jeriel was therefore paid $24.80 per hour.

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