About how many hours

The answer of the given question based on the function is ,  the turning point of the function f(x+4)+5 is at the point (-4, -5).

In mathematics, a function is a rule that assigns each input value (or argument) in a set to a unique output value in another set. In other words, it is a relationship between two sets of numbers, where each input value produces exactly one output value. Functions are usually represented using function notation, where the name of the function is followed by the input value in parentheses.

To find the turning point of the function f(x+4)+5, we need to first rewrite the function in vertex form, which is given by:

f(x) = a(x-h)² + k

where (h, k) is vertex of parabola.

To do this, we can start by completing the square:

f(x+4) + 5 = a(x+4-h)² + k

f(x+4) = a(x+4-h)² + k - 5

To complete the square, we need to add and subtract (4-h)²/4a inside the parentheses:

f(x+4) = a(x+4-h)² + k - 5 + (4-h)²/4a - (4-h)²/4a

f(x+4) = a(x+4-h)² + (4-h)²/4a + (4a*k-20a)/4a

Now the function is in vertex form:

f(x+4) = a(x+4-h)² + (4-h)²/4a + (4a*k-20a)/4a

The vertex of the parabola is at (h, k), so in this case, the vertex is at (-4, -5).

Therefore, the turning point of the function f(x+4)+5 is at the point (-4, -5).

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As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.

A function in mathematics is a rule or association that gives each input value a distinct output value. A function, then, is a collection of ordered pairs, each pair consisting of an input value (also known as an argument or predictor variable) and the control signal value (also known as the value or dependent variable). The output value for each given input value can be found using the formula or graph of a function.

Option B provides the justification for why a graph that fails the vertical line test cannot be used to represent a function: One x-value is coupled with numerous y-values on a vertical line.

A vertical line is not a function since a function cannot have one x-value associated with multiple separate y-values.

To ascertain whether a graph accurately depicts a function, use the vertical line test.

Each vertical line that crosses the graph more than once has an x value and several y values, which is against the definition of a function.

As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.

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Using the height formula of the trapezoid, we know that the height is 5000m respectively.

In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English or a trapezium in British and other forms of English.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The bases of the trapezoid are the parallel sides.

There are four sides to a trapezoid.

A trapezium is another name for a trapezoid.

It features two parallel sides that are not equal and two nonparallel sides.

So, find the height of the trapezoid as follows:

Formula: h = 2A/a+b

a = 8mm, b = 6 mm

A = 35 mm²

Unit conversion:

a = 8*10⁻³mm

b = 6*10⁻³mm

Using the formula:

h = 2A/a+b

h = 2*35/8*10⁻³+6*10⁻³

h = 5000m

Therefore, using the height formula of the trapezoid, we know that the height is 5000m respectively.

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If Corey buys 27 inches of trim for a craft project, Corey bought 3/4 of a yard of trim for the craft project.

To determine what fraction of a yard Regina buys, we need to know how many inches are in a yard. There are 36 inches in a yard.

To convert 27 inches to yards, we need to divide by 36:

27 ÷ 36 = 0.75 yards

So Corey bought 0.75 yards of trim for the craft project.

To find the fraction of a yard, we need to express 0.75 as a fraction with a denominator of 1:

0.75 = 75/100 = 3/4

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Complete question is:

Corey buys 27 inches of trim for a craft project. What fraction of a yard does Regina buy?

Answer:

y=x+5;1

Step-by-step explanation:

Hope this helps! =D

Answer:

x=4

Step-by-step explanation:

If the equation is:

[tex]x^{2} =16[/tex]

then the answer is 4, because to solve this, you would have to take the square root of both sides to cancel out the square on the left side of the equation:

[tex]\sqrt{x^{2} } =\sqrt{16}\\ x=4[/tex]

Hope this helps :)

Gary's average speed is approximately 44.4 mph. This is found by dividing the total distance traveled (800 miles) by the total time taken (18 hours) and rounding to the nearest tenth.

To calculate Gary's average speed, we need to use the formula

Average speed = Total distance ÷ Total time

In this case, the total distance is 800 miles, and the total time is 18 hours. So we can plug these values into the formula and simplify

Average speed = 800 miles ÷ 18 hours

Average speed = 44.444444... miles per hour

Rounding to the nearest tenth, we get

Average speed ≈ 44.4 miles per hour

Therefore, Gary's average speed during his 800-mile trip was approximately 44.4 miles per hour.

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Determining the absolute age of a rock sample requires knowledge of the isotopic or fossil content of the rock, or its position in a sequence of rocks with known ages.

In order to determine the absolute age of a rock sample, you would need the following information:

The amount of a radioactive isotope present in the rock sample: Some isotopes are unstable and decay over time into stable isotopes.

The ratio of different isotopes of the same element present in the rock sample: Some isotopes of an element are not stable and can decay into other isotopes of the same element.

The sequence of rock layers in which the sample was found: If the rock sample is found in a layered sequence of rocks, the relative age of the rock can be determined based on its position in the sequence.

The presence of index fossils: Certain fossils are known to have existed during specific time periods in Earth's history.

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The value of the product is 6.9  × 10⁵ m

It is important to note that to determine the product of two different measurements, we need to make sure they have the same units.

Now, we have that;

6.9cm *10000000m​

First, let's convert the centimeters to meters , we have;

1m = 100cm

then, xm = 6.9cm

cross multiply the values

x = 6.9/100

Divide the values

x = 6. 9 × 10⁻²m

Then, we have;

6. 9 × 10⁻² × 10⁷m

Multiply the values and add the exponents

6. 9  × 10⁻²⁺⁷

Add the values

6.9  × 10⁵ m

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Step-by-step explanation:

okay as we know a circle is a quarter 360° in total therefore all you have to do is say 360° multiplied by 165

Answer:

[tex]S = \dfrac{v^2 - u^2}{2a}[/tex]

Step-by-step explanation:

We can solve for S using algebraic manipulation.

[tex]v^2 = u^2 + 2aS[/tex]

↓ subtract [tex]u^2[/tex] from both sides

[tex]v^2 - u^2 = 2aS[/tex]

↓ divide both sides by [tex]2a[/tex]

[tex]\dfrac{v^2 - u^2}{2a} = S[/tex]

[tex]\boxed{S = \dfrac{v^2 - u^2}{2a}}[/tex]

[tex]\sf \boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}[/tex]

[tex]\sf v^{2} =u^{2} +2aS[/tex]

[tex]\sf v^{2}-u^{2} =u^{2} +2aS-u^{2}\\ \\v^{2}-u^{2} =2aS[/tex]

[tex]\sf \dfrac{v^{2}-u^{2} }{2a} =\dfrac{2aS}{2a} \\ \\ \\\dfrac{v^{2}-u^{2} }{2a} =S\\ \\ \\\boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}.[/tex]

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Here is the complete equation using the provided values

6x+8=2x+24

6x-2x+8=2x-2x+24

4x+8=24

4x+8-8=24-8

4x=16

x=4

Factorization is the process of finding the factors of a given number or expression. A factor is a number or expression that divides the original number or expression without leaving a remainder. In other words, factorization is the process of expressing a number or expression as a product of its factors.

For example, the number 12 can be factored into 2 and 6, or into 3 and 4, because 2 and 3 are factors of 12 and their product gives 12. Similarly, the expression x^2 - 4 can be factored into (x+2)(x-2), because if we multiply (x+2) and (x-2), we get x^2 - 4.

Factoring is an important tool in algebra, as it allows us to simplify expressions, solve equations, and work with polynomials in a more efficient way.

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Answer:

4. The smaller angle is 35°.

5. AngleCAB = 40°

AngleDAC = 50°

Step-by-step explanation:

4) The 3 angles shown all together add up to 180°.

3x+10 + 90° + 2x+5 = 180°

combine like terms.

5x + 105 = 180

subtract 105

5x = 75

divide by 5

x = 15

One of the angles is 3x+10 and the other is 2x+5.

2x+5 is the smaller angle. If x=15, then 2x+5

= 2(15) + 5

= 30 + 5

= 35

The smaller angle is 35°.

5) The two angles in this question add up to 90°.

7x-16 + 6x+2 = 90°

combine like terms

13x - 14 = 90

add 14

13x = 104

divide by 13

x = 8

Angle CAB = 7x - 16

= 7(8) - 16

= 56 - 16

= 40

AngleCAB = 40°

AngleDAC = 6x + 2

= 6(8) + 2

= 48 + 2

= 50

We also could have just subtracted to find angleDAC 90 - 40 = 50.

AngleDAC = 50°

Answer:

8/27.

Step-by-step explanation:

To find out which class had the greatest fraction of students who preferred vanilla ice cream, we need to compare the ratios of students who preferred vanilla to the total number of students in each class.

For second period class:

Number of students who preferred vanilla = 725

Total number of students = unknown

Ratio of students who preferred vanilla to total number of students = unknown/unknown = undefined

For fourth period class:

Number of students who preferred vanilla = 8

Total number of students = 27

Ratio of students who preferred vanilla to total number of students = 8/27

For sixth period class:

Number of students who preferred vanilla = 30% of total number of students

Total number of students = unknown

Ratio of students who preferred vanilla to total number of students = 0.3*unknown/unknown = 0.3

Therefore, the fourth period class had the greatest fraction of students who preferred vanilla ice cream, with a ratio of 8/27.

Since 1 gallon = 4 quarts → (1/2) gallons = 2 quarts

1 gallon = 8 pints → (1/2) gallons = 4 pints

1 gallon = 16 cups → (1/2) gallons = 8 cups

Therefore from the given relation with gallons we can describe the relation between the cups, quarts and pints.

(1/2) Gallon > quarts > pints > cups

If we need 1 cup of milk then a pint container will be the best choice at a grocery store.

Answer: 1  pint would because a quart has 4 cups and 1/2 a gallon would be way to much. and a pint would be 2.

Step-by-step explanation:

1 pint  would be because a quart has 4 cups and 1/2 a gallon would be way to much. and a pint would 1 cup more than you need so 1 pint is right

The claim that makes the most accurate statement regarding how many cookies the institution will require There will be 480 pupils who favour cookies at the college.

Decimals or fractions can also be used to represent percentages. Divide a percentage by 100 to turn it into a fraction.

If the sample of 225 students was truly random and not just selected from a certain group, we may calculate percentages depending on it.

As a result, "There will be roughly 640 pie-loving pupils at the college."

Thus, the claim that makes the most accurate forecast regarding how many cookies the institution will require There will be 480 pupils who favour cookies at the college.

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The Central Limit Theorem describes the relationship between the distribution of sample means and the population distribution that the samples are taken from.

The Central Limit Theorem (CLT) states that if you take random samples of a population and calculate the mean of each sample, the distribution of those sample means will be approximately normally distributed, regardless of the underlying population distribution.

This means that as the sample size increases, the distribution of sample means becomes more and more normal. The CLT is a fundamental concept in statistics because it allows us to make inferences about population parameters based on sample statistics. It is widely used in hypothesis testing, confidence intervals, and other statistical applications.

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The calculated Social Security tax is $ 6621.60 on the maximum taxable earning, that is $106800 on the rate of 6.2% and Medicare tax is  $1812.50 on the annual salary, that is $125,000 on the rate of 1.45%.

Hence option d is the correct option.

The annual salary of an individual is given as  $125,000.

Medicare tax is levied on the annual salary of an individual, that is on $125,000. It is given as 1.45 % on $125,000.

The maximum taxable earnings is $106,800 and Social Security tax is levied on this $106,800. It is given as 6.2% on $106,800.

Thus, applying basic rule of percentage calculation we get,

Earnings from Social Security tax  = $(6.2% of 106800)

= ${(62/100*10)(106800)

= $ 6621.60

Earnings from Medicare tax = $(1.45% of 125000)

=  $(145/100*100)(125000)}

= $1812.50

Hence option d Social Security tax: $6,621.60, Medicare tax: $1,812.50 is the correct option.

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The number of infants born to 45-year-old mothers who have Down syndrome on average is approximately 1 in 30 or 3.33%. The Down disorder may be a hereditary clutter that happens when there's an additional duplicate of chromosome 21.

The chance of having a child with Down disorder increments with maternal age. Agreeing to the American College of Obstetricians and Gynecologists, at age 35, the hazard of having an infant with Down disorder is around 1 in 350, or 0.29%. By age 40, the hazard increments to around 1 in 100, or 1%. And by age 45, the chance is around 1 in 30 or 3.33%.

In any case, pre-birth testing can offer assistance distinguish the chance of Down disorder and other hereditary anomalies amid pregnancy. This will offer assistance to hopeful guardians to make educated choices approximately their pregnancy and their baby's wellbeing. 

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Answer:

A

Step-by-step explanation:

It is not a function because both x-values -4 and 2 have multiple y-values. Try the vertical line test if you don't understand.

We cannot have a fraction of a person in the sample, we need to round up to the next whole number, which is 1022.

So, you will need to sample at least 1022 individuals to achieve a 95% confidence level with a margin of error no more than 3%.

This means that the correct answer among the given options is "at least 1068".

To estimate the sample size needed for survey, you can use the formula for sample size calculation in a proportion estimation problem.

The formula is:
[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]
where:
n = required sample size
Z = Z-score, which corresponds to the desired confidence level (1.96 for a 95% confidence level)
p = estimated proportion (0.35 in this case)
E = desired margin of error (0.03 in this case)
Now, let's plug the values into the formula:
[tex]n = (1.96^2 * 0.35 * (1-0.35)) / 0.03^2[/tex]
n = (3.8416 * 0.35 * 0.65) / 0.0009
n = 0.919326 / 0.0009
n ≈ 1021.473.

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Answer:

No

Step-by-step explanation:

If you divide 6 by 7, it is not equal to the number you get when you divide 1 by 2, therfore making them not equavalent.

~~~Harsha~~~

Answer:

No, the are not equivalent

Step-by-step explanation:

The ratios 6:7 & 1:2 are already in their simplest form, meaning we can't simple them anymore.

6:7 ≠ 1:2

Answer:

53b - 7b - 6b + 1 with b = 25 simplifies to 1001.

Step-by-step explanation:

To simplify 53b - 7b - 6b + 1 with b = 25, we substitute 25 for b and simplify the expression as follows:

53b - 7b - 6b + 1 = 53(25) - 7(25) - 6(25) + 1

= 1325 - 175 - 150 + 1

= 1001

Therefore, 53b - 7b - 6b + 1 with b = 25 simplifies to 1001.

For the heights, areas and perimeters of the shapes:

5. The trapezoid can be divided into a rectangle and a right triangle. Let the height of the trapezoid be h.

The area of the trapezoid is A = (1/2)(13.9 + 9.3)h = 11.6h.

We are given that A = 120.8cm², so solve for h:

11.6h = 120.8

h = 10.4 cm

Therefore, the height of the trapezoid is 10.4 cm.

6. Let s be the side length of the equilateral triangle. Then, we have:

s + s + s = 45

3s = 45

s = 15

The perimeter of the equilateral triangle is 45 inches.

The area of an equilateral triangle can be found using the formula:

Area = (√(3)/4)s²

Plugging in s = 15:

Area = (√(3)/4)(15²) = 97.31 in²

Therefore, the area of the equilateral triangle is 97.31 square inches.

7. Let a be the side length of the inscribed square and let A be the area of the inscribed square. Let b be the side length of the circumscribed square.

The area of the outer square is 169in², so b² = 169. Therefore, b = 13.

The diagonal of the inscribed square is equal to the diameter of the circle, which is equal to the side length of the outer square. Therefore, a×√(2) = 13.

Solving for a:

a = 13/√(2) = 9.19

The area of the inscribed square is A = a² = (13/√(2))² = 84.5 in².

The ratio of the area of the inscribed square to the area of the circumscribed square is:

A/(b²) = 84.5/169 = 0.5

Therefore, the area of the inscribed square is half the area of the circumscribed square.

8. Let d₁ and d₂ be the diagonals of the rhombus. Let s be the side length of the rhombus.

We know that d₁ = 6 inches and d₂ = 8 inches. We also know that the diagonals of a rhombus intersect at a right angle and bisect each other. Therefore, we can form a right triangle with legs of length s/2 and s/2 and hypotenuse of length d₁/2.

Using the Pythagorean theorem:

(s/2)² + (s/2)² = (d1/2)²

s²/4 = 9

s = 6

Therefore, the side length of the rhombus is 6 inches.

The perimeter of the rhombus is 4s = 24 inches.

The area of the rhombus can be found using the formula:

Area = (1/2)d₁d₂

Plugging in d₁ = 6 and d₂ = 8:

Area = (1/2)(6)(8) = 24 square inches

Therefore, the perimeter of the rhombus is 24 inches and the area of the rhombus is 24 square inches.

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Answer: 0.8982

Step-by-step explanation:

math

Answer:

x ≈ 0.898

Step-by-step explanation:

using the rule of logarithms

log [tex]x^{n}[/tex] = n log x

given

[tex]6^{x}[/tex] = 5 ( take natural logarithm ln of both sides )

ln [tex]6^{x}[/tex] = ln 5

x ln 6 = ln 5 ( divide both sides by ln 6 )

x = [tex]\frac{ln5}{ln6}[/tex] ≈ 0.898 ( to the nearest thousandth )

Answer:

Zeroes of f(x):

x + 1 = 0, so x = -1

Vertical asymptotes of f(x):

x^2 - 4 = 0, so x = -2 and x = 2

End behavior of f(x):

As x --> negative infinity, f(x) --> 0

As x --> infinity, f(x) --> 0

No holes in f(x).

Answer:

Step-by-step explanation:

1) Pythagorean Theorem: a² + b² = c²

4²+b²=5²

b²=5²-4²

b²=25-16

b=√9

b = 3

2) Good Job! Second Question is correct with accurate work shown.

In normal distribution the area above 66 for a n(60, 10) is 0.726

What is normal distribution?

In probability theory and statistics, the Normal Distribution, which is also called the Gaussian Distribution, is the most significant continuous probability distribution.  It is also called a bell curve. In this distribution a large number of random variables are either nearly or exactly represented. Moreover, it can be used to approximate other probability distributions,

From the given data n(60, 10) so mean = 60 and standard deviation= 10

Now x≥ 66

so the z-score will be (66-60)/10

                                   = 6/10

                                   = 0.6

Now P(z>0.6)= 1- P(z< 0.6)

                     = 0.726

So, in normal distribution the area above 66 for a n(60, 10) is 0.726.

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