Which represents the solution(s) of the system of equations, y + 4 = x² and y - x = 2? Determine the solution set by graphing.

O (-2, 0)
O (-2, 0) and (2, 0)
O (-2, 0) and (3, 5)
Ono solutions

Answer:

The sum of the sequence is 40.

Step-by-step explanation:

The given sequence is an arithmetic sequence with a common difference of 3. To find the value of n for the number 14 in the sequence, we can use the explicit formula for an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_n is the nth term of the sequence, a_1 is the first term, d is the common difference, and n is the term number.

Substituting the given values, we get:

14 = 2 + (n-1)3

Simplifying the equation, we get:

12 = 3n - 3

15 = 3n

n = 5

Therefore, the number 14 appears as the 5th term in the sequence.

To find the sum of the sequence, we can use the arithmetic sum formula:

S_n = (n/2)(a_1 + a_n)

where S_n is the sum of the first n terms of the sequence.

Substituting the given values, we get:

S_5 = (5/2)(2 + 14)

S_5 = 40

Therefore, the sum of the sequence is 40.

Step-by-step explanation:

the difference is 3 a is is first term which is 2

the formula is sn= a+(n-1)d

2+(n-1)3

2+(3n-3)

Step-by-step explanation:

so you can do it in this way

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

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.

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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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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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:

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]

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:

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 x-coordinate (or t-coordinate) of the vertex is 1.5 seconds and represents the time at which the rocket reaches its maximum height. The y-coordinate (or h-coordinate) of the vertex is 334 feet and represents the maximum height reached by the rocket.

A function is a mathematical relationship that describes how one quantity (the output or dependent variable) depends on one or more other quantities (the inputs or independent variables).

A function can be thought of as a machine that takes in input values, applies a set of rules or operations to them, and produces an output value. The input values can be any set of numbers or other objects that the function is defined for, and the output values can be any set of numbers or objects that the function can produce.

To find the x-coordinate (or t-coordinate) of the vertex, we can use the formula:

x = -b / (2a)

where a is the coefficient of the squared term, b is the coefficient of the linear term, and x represents the time at which the rocket reaches its maximum height. The equation of the parabolic function that models the height of the rocket is:

h = at² + bt + c

where h is the height of the rocket at time t.

We can use the coordinates of the points on the parabola to find the values of a, b, and c:

(0, 260): 260 = a(0)² + b(0) + c, so c = 260

(2, 324): 324 = a(2)² + b(2) + 260, so 4a + 2b = 64

(6.5, 0): 0 = a(6.5)² + b(6.5) + 260, so 42.25a + 6.5b = -260

We can solve this system of equations to find the values of a and b:

4a + 2b = 64

42.25a + 6.5b = -260

Multiplying the first equation by 3.25 and subtracting from the second equation, we get:

42.25a + 6.5b - 13a - 6.5b = -260 - 208

29.25a = -468

a = -16

Substituting a = -16 into the first equation, we get:

4(-16) + 2b = 64

b = 48

Therefore, the equation of the parabolic function is:

h = -16t² + 48t + 260

The x-coordinate (or t-coordinate) of the vertex is:

t = -b / (2a) = -48 / (2(-16)) = 1.5

The x-coordinate (or t-coordinate) of the vertex is 1.5 seconds and represents the time at which the rocket reaches its maximum height.

To find the y-coordinate (or h-coordinate) of the vertex, we can substitute t = 1.5 into the equation of the parabolic function:

h = -16(1.5)² + 48(1.5) + 260 = 334

Therefore, the y-coordinate (or h-coordinate) of the vertex is 334 feet and represents the maximum height reached by the rocket.

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The complete question is:

Answer:

1440

Step-by-step explanation:

explanation in the picture

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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The two numbers that multiply to 2 but add to -5 are -1 and -2.

The two numbers that multiply to 2 and add to -5 are -1 and -2.

To see why, you can use the factoring method:

Find two numbers whose product is 2 (possible pairs are 1 and 2, or -1 and -2).

Check if their sum is -5.

If you use 1 and 2, the sum is 3, so they don't work.

If you use -1 and -2, the sum is -3-2 = -5, so they work.

Therefore, -1 and -2 are the two numbers that multiply to 2 and add to -5.

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If the federal reserve sets the reserve rate to %4, the resulting money multiplier is 25.

The link between the quantity of reserves kept by banks and the amount of money that may be generated through the practise of fractional reserve banking is known as the "money multiplier" in economics and finance. Under a system known as fractional reserve banking, banks are only obligated to maintain a portion of their deposits as reserves and are free to lend the remainder to borrowers.

The reserve ratio, or the percentage of deposits that banks must retain in reserves, is used to compute the money multiplier.

The money multiplier is determined using the formula:

Money multiplier = 1 / reserve ratio

Given the reserve ratio is 4% = 0.04.

Thus,

Money multiplier = 1 / 0.04 = 25

Hence, if the federal reserve sets the reserve rate to %4, the resulting money multiplier is 25.

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Answer:

Step-by-step explanation:

Value of x :-

Therefore, the value of x is 23.

________________________

Hope this helps!

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

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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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:

Zoe started with 7.917 meters of cloth.

Step-by-step explanation:

If each pillowcase uses 5/8m of cloth and Zoe made 12 pillowcases, then the total amount of cloth used is:

(5/8) x 12 = 15/2 or 7.5 meters

If Zoe has 5/12m of cloth left, then the total amount of cloth she started with is:

7.5 + 5/12 = 90/12 + 5/12 = 95/12 or 7.917 meters

Therefore, Zoe started with 7.917 meters of cloth.

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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Answer: 9.84*10^6

Step-by-step explanation: Multiply 2.46 by 4

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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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

Answer:

B

Step-by-step explanation:

Answer:

its either D or C but I think its D

Step-by-step explanation:

The correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.

What is an inequality?

Let's start by defining a variable for the number we are trying to find. Let's call it "x".

"One half of a number" can be represented as (1/2)x.

"Decreased by 3" means we need to subtract 3 from (1/2)x. So, "one half of a number decreased by 3" can be represented as:

(1/2)x - 3

Now, the problem says that this expression is "at most -5". "At most" means that the expression can be equal to -5 or any number less than -5. We can represent this as:

(1/2)x - 3 ≤ -5

To simplify this inequality, let's add 3 to both sides:

(1/2)x ≤ -2

Multiplying both sides by 2 (to eliminate the fraction) gives:

x ≤ -4

Therefore, the correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.

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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: 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: