The following shows a graph of y = x^2+ 5

Can we use this graph to find the solutions of 0 = c^2 + 5? Why or why not?

Answer:

3) p(2) = 22

4) k = 0

Step-by-step explanation:

Remainder theorem: If the polynomial p(x) is divided by the linear polynomial x -a then the remainder is p(a).

3)p(m) = m⁴ - 2m³ +  m² + 12m - 6

p(m) is divided by (m - 2).

m -2 = 0

m = 2. The remainder is p(2)

p(2) = 2⁴ - 2*2³ + 2² + 12*2 - 6

      = 16 - 16 + 4 + 24 - 6

      = 22

p(2) = 22

4) p(x) = 8x³ + 6x² + x + k

p(x) is divided by (2x + 3).

2x + 3 = 0

      2x = -3

         [tex]x = \dfrac{-3}{2}[/tex]

                               [tex]p(\dfrac{-3}{2})=-15[/tex]

 [tex]8*(\dfrac{-3}{2})^3+6*(\dfrac{-3}{2})^2-\dfrac{3}{2}+k=-15\\\\\\8*\dfrac{-27}{8}+6*\dfrac{9}{4}-\dfrac{3}{2} + k = -15\\\\\\-27 + \dfrac{27}{2}-\dfrac{3}{2}+k=-15\\\\\\-27 + \dfrac{24}{2}+k=-15\\\\[/tex]

        -27 + 12 + k = -15

                         k = -15 + 27 - 12

                        k = 0

The total volume of the pool is 156 yd³. Option D

First, to determine the volume, we need to note the properties of a rectangular prism.

The formula for volume of a rectangular prism is;

Volume = lwh

Given that;

Now, substitute the value

Volume = 8 × 3 × 13/2

Volume = 312/2

Volume = 156 yd³

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The largest three-digit number satisfying the given criteria is 964.

Given that all the digits of a three-digit integer are distinct and non-zero.

Further more, the three-digit integer is divisible by each of its digits.

We are to find the largest three-digit integer that has these properties.

What we know: We know that a number is divisible by its digit if and only if the number is divisible by the least common multiple of the digits of the number.

Since all the digits are distinct and non-zero, the least common multiple of the digits of the number is simply the product of the digits.

Let's assume the number to be a b c,

where a, b, and c represent digits of the three-digit integer.

We are required to find the largest such number satisfying the given criteria.

Since the number must be divisible by each of its digits, it follows that each digit must be a factor of the number.

Hence, we can write,

a b c = a x b x c

The number must be greater than 100.

Hence, a must be at least 1. b and c must be distinct from a and from each other.

Hence, the smallest possible value for b is 2, and for c is 3.

This gives us the following equations: 123 = 1 x 2 x 3124

= 1 x 2 x 4125

= 1 x 2 x 5126

= 1 x 2 x 6128

= 1 x 2 x 8129

= 1 x 2 x 9

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using 5.66 standard deviations provides a minimum guarantee of 99.85% of the data being covered.

When we use 5.66 standard deviations, we can guarantee at least 99.9% of the data falls within that range.

This is based on the empirical rule, which states that for a normal distribution, approximately 99.7% of the data falls within 3 standard deviations of the mean. Therefore, 5.66 standard deviations would cover a greater percentage of the data, which can be calculated as:

99.7% + [(100% - 99.7%) / 2] = 99.85% (rounded to one decimal place)

So, using 5.66 standard deviations provides a minimum guarantee of 99.85% of the data being covered.

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The best estimate for the weight of a cantaloupe is 2 kilograms (B).

A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.

Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.

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Complete Question:

Choose the best estimate for the weight of a cantaloupe. Responses

A 2 decigrams

B 2 kilograms

C 2 grams

D 2 milligrams

Step-by-step explanation:

The surface area of a rectangular prism can be found by adding the areas of all six of its faces.

In this case, the rectangular prism has side lengths of 3, 6, and 12 feet. So, its faces are:

Top and bottom faces: Each of these faces is a rectangle with side lengths of 3 feet and 6 feet. Therefore, the area of each of these faces is 3 ft * 6 ft = 18 ft². Since there are two of these faces, their combined area is 2 * 18 ft² = 36 ft².

Front and back faces: Each of these faces is a rectangle with side lengths of 3 feet and 12 feet. Therefore, the area of each of these faces is 3 ft * 12 ft = 36 ft². Since there are two of these faces, their combined area is 2 * 36 ft² = 72 ft².

Side faces: Each of these faces is a rectangle with side lengths of 6 feet and 12 feet. Therefore, the area of each of these faces is 6 ft * 12 ft = 72 ft². Since there are two of these faces, their combined area is 2 * 72 ft² = 144 ft².

To find the total surface area, we add the areas of all six faces:

Total surface area = 36 ft² + 72 ft² + 144 ft²

Total surface area = 252 ft²

Therefore, the surface area of the rectangular prism is 252 square feet.

Answer:

Step-by-step explanation:

12*3*2= 72 because there are two rectangles with the same length.

6*3*2= 36 because there are two widths with the same area.

6*12*2= 144 because there are a top and bottom with the same area.

72+36+144= 252

Surface area is 252 ft squared.

What is y'all's teacher teaching y'all!? I learned this two months ago!

Therefore, the inverse of f(x) is not a function, as it fails the vertical line test.

One output is produced for one input by a function, a form of rule. The formula y=x2 serves as an illustration of this. A single output for y results from any input for x. Given that x is the input value, it is appropriate to say that y is a function of x.

We can determine if the inverse of f(x) = 8x² + 27 is a function by finding the inverse and checking if it passes the vertical line test.

To find the inverse, we first replace f(x) with y:

y = 8x² + 27

Next, we swap the roles of x and y:

x = 8y² + 27

Solving for y gives:

8y² = x - 27

y² = (x - 27)/8

y = ±√((x - 27)/8)

Notice that we have a ± sign in front of the square root, which means that for each x value, we have two possible y values.

Therefore, the inverse of f(x) is not a function, as it fails the vertical line test.

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Answer: (-3,-2)

Step-by-step explanation:

y²+2y+11 = 5-3y

y^2+2y+11-5+3y =0

y^2+5y+6=0

y^2+3y+2y+6=0

y(y+3)+2(y+3)=0

(y+3)(y+2)=0

y= -3, -2

All you do is plug in the x value to the equation

Hope it helps:)

The sample consists of the 15 workers selected to participate in the survey.

The population consists of 200  workers.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers

SAMPLE: This is a representative part of a population on which a research is about the population is administered

POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken

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200 kids 50 adults?

answer may vary

Therefore, to calculate the design strength of the double-angle shape with the given parameters, the procedure of AISC Section E4 (a) is used to calculate the flexural and flexural-torsional design strength, which can then be compared to determine the highest design strength.

The design strength for the double-angle shape is calculated using the procedure of AISC Section E4 (a).

The given information is: 2L8 times 4 times 3/4, long legs 3/8-in. back-to-back, Fy = 36 ksi; KL is 20 feet for all axes, and there are two intermediate connectors.

To calculate the flexural design strength, the flexural buckling strength is first determined by calculating Euler's critical stress, Fcr, and then multiplying it by the design section modulus.

The Fcr can be calculated using the formula Fcr =[tex]0.658 x SQRT(Fy x KL)[/tex]and the design section modulus can be calculated using the formula [tex]Z = (b x d^2)/6[/tex].

To calculate the flexural-torsional design strength, the flexural-torsional buckling strength is first determined by calculating the effective length, Kx, and then multiplying it by the torsional constant, J. The Kx can be calculated using the formula Kx = 2.6 (L/r) and the torsional constant, J, can be calculated using the formula J = [tex](b d^3)/3.[/tex]

Finally, the flexural design strength and the flexural-torsional design strength can be compared to determine the highest design strength of the double-angle shape.

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A zero vertical asymptote removable discontinuity means that there is a zero of the function at the input value where the vertical asymptote would occur,

A zero of a function occurs when the value of the function is zero. A vertical asymptote of a function occurs when the value of the function becomes unbounded (either positive or negative) as the input approaches a certain value.

A removable discontinuity of a function occurs when there is a hole in the graph of the function at a certain input value, but the function can be made continuous at that point by defining its value at that input.

In the case of a zero vertical asymptote removable discontinuity, this means that there is a zero of the function at the input value where the vertical asymptote would occur, and the function can be made continuous at that input value by defining its value to be the value of the function at that input.

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Answer:

Solutions: (-5, 1), (-10, 1), (-10, 5)

Non-solutions: (0, 4), (5, 4), (10, 4)

Step-by-step explanation:

Solutions are in the shaded area. Non-solutions are in the non-shaded area and on the dashed line.

Solutions: (-5, 1), (-10, 1), (-10, 5)

Non-solutions: (0, 4), (5, 4), (10, 4)

The graph of g can be obtained using a horizontal stretch by a factor of 4 and a vertical translation 3 units up of the graph of f.

In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented by this mathematical expression g(x) = f(x) + N.

Where:

Based on the information provided about the parent function f, a function that represents g(x) is given by:

g(x) = 4f + N

g(x) = 4x + 3

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The factored form of this quadratic equation is equal to y = -2x² + 16x - 30.

In this exercise, you are required to determine the factored form of the given quadratic function that is written in vertex form (standard form).

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

y = a(x - h)² + k

Where:

Based on the information provided above, we have the following quadratic function:

y = -2(x - 4)² + 2

y = -2(x - 4)(x - 4) + 2

y = -2(x² - 4x - 4x + 16) + 2

y = -2(x² - 8x + 16) + 2

y = -2x² + 16x - 32 + 2

y = -2x² + 16x - 30

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Answer:

Step-by-step explanation:

Option 3

We can simplify the fraction by dividing both numbers by 4 (or by 2 two times), we will get the equivalent fraction 19/18

Here we have a quotient (or we can also call it a fraction) which is:

76/72

To simplify any fraction, what you need to do is divide both numerator and denominator by the same number.

For example, if we use 2, we will get:

76/2 = 38

72/2 = 36

then we have the equivalent fraction.

38/36

But we can keep simplifying this, divide by 2 again:

38/2 = 19

36/2 = 18

We get:

19/18

We can't simplify this anymore because 19 is prime.

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Answer:

1/12

Step-by-step explanation:

Out of the total number of candies, 1/2 of the pink candies are round.

To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:

pink candies = 5/6

round candies among the pink ones = 1/5

Therefore, the fraction of candies that are pink and round is:

(5/6) x (1/2) x 1/5 = 1/12

So, 1/12 of the candies are pink and round.

Answer: 40

Step-by-step explanation:

25/100 x ? = 10

multiply both sides by 100/25

x= 10 x 100/25

x=10

Confidence interval for the percentage of students at the college who do not check their email account on a regular basis is 49.6%< P < 65.8%.

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.

We must determine the proportion of achievements to which our problem pertains when calculating confidence intervals for proportions. This value should be used in the computations. Another thing to keep in mind is that the z-value is calculated by dividing the alpha value by two.

x = 82

n = 142

p = x/n = 82/142 = 0.577

Point estimate P = 0.577

1 - P = 1 - 0.577 = 0.423

At 95% confidence level the z is

[tex]\alpha[/tex] = 1 - 95%

= 1 - 0.95

= 0.05

[tex]\alpha[/tex]/2 = 0.025

[tex]z_\alpha _/_2 = 1.96[/tex]

Margin of error E = [tex]z_\alpha _/_2 *\sqrt{\frac{P(1-P)}{n} }[/tex]

= 1.96 x [tex]\sqrt{\frac{0.577(0.423)}{142} }[/tex]

= 0.081

At 95% confidence interval the P is

P - E < P < P + E

0.577 - 0.081 < P < 0.577 + 0.081

0.496 < 0.658.

confidence interval for the percentage of students at the college is 49.6% < P < 65.8%.

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Answer:Get a quadratic function from its roots. Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola.

Step-by-step explanation:Solve a quadratic equation using the quadratic formula.

Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c.

Write the Quadratic Formula. Then substitute in the values of a, b, and c.

Simplify.

Check the solutions.

Answer:

Area of the figure=126.5cm²

Step-by-step explanation:

As we can see based on the shape of the figure, we can divide it into a;

→ Triangle

→ Rectangle

Formulas that we need are;

⇒ Area of triangle =1/2×base×height

⇒ Area of rectangle =length × width

Let's solve the area of the triangle first;

Then the area of the rectangle;

Finally, we add the triangle and rectangle together-

Area of Triangle + Area of Rectangle = 38.5cm²+88cm²

Area of the figure=126.5cm²

RevyBreeze

Answer:$30

Step-by-step explanation:

45-14=31

31-1=30

so the answer is 30

hope this helps

Answer:

Step-by-step explanation:

[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]    

[tex]7 (x+\frac{9}{28} )=60[/tex]     (multiplied both sides by 3)

[tex]x+\frac{9}{28} =\frac{60}{7}[/tex]          (divided both sides by 7)

[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex]     (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)

Answer:

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing the score.

z = (x - mu) / sigma

Where:

x = 70 (score we are interested in)

mu = 60 (mean score)

sigma = 7 (standard deviation)

z = (70 - 60) / 7 = 1.43

Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.

Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).

When either the loan length or the interest rate is halved, the interest cost changes by the same amount, $6,000.

First, let's calculate the total interest cost for each option using the simple interest formula:

Interest = Principal × Rate × Time

Car dealer 10% interest, 4-year loan:

Interest = $15,000 × 0.10 × 4 = $6,000

Car dealer 10% interest, 8-year loan:

Interest = $15,000 × 0.10 × 8 = $12,000

Bank 5% interest, 8-year loan:

Interest = $15,000 × 0.05 × 8 = $6,000

Now, let's compare the differences in interest cost when changing either the loan length or the interest rate.

A. Halving the loan length (8-year loan to 4-year loan) with a 10% interest rate:

Difference = $12,000 - $6,000 = $6,000

B. Halving the interest rate (10% to 5%) with an 8-year loan:

Difference = $12,000 - $6,000 = $6,000

From the calculations above, we can see that both loan length and interest rate have an equal effect on the cost of interest for the loan.

When either the loan length or the interest rate is halved, the interest cost changes by the same amount, $6,000.

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The number of ways to arrange N people with A and B separated is given by expression   N! - 2*(N-1)! .

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:

Now,

Let the two particular people be A and B.

If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:

(N-1) * (N-2)!

Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.

To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.

Therefore, the number of ways to arrange N people with A and B separated is:

N! - 2*(N-1)!

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Gillian pocket money is x, then Gillian  has [tex]5/12x[/tex]left after spending on snacks and bus fare.

The term "spending" refers to the act of spending money to buy goods or services. It is the act of exchanging money for something, usually a product, service, or experience. Buying groceries, paying for transportation, or purchasing clothing are all examples of spending. To avoid debt and achieve your financial goals, it is critical to manage your spending wisely in personal finance.

If Gillian spends one-third of her pocket money on snacks and one-quarter on bus fare, she spends 7/12 of her pocket money on snacks and bus fare.

This means she only has [tex]1 - 7/12 = 5/12[/tex] of her pocket money remaining.

As a result, if her pocket money is x, she has 5/12x left after paying for snacks and bus fare.

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