1
Select the correct answer.
Over which interval of the domain is function h decreasing?
x < 1
(22,
√x + 3,
z ≥ 1
h(x) =
O A.
O B.
O C.
O D. (-∞0, ∞0)
(1, 00)
(-∞0, 1)
The function is increasing only.

The quadratic function on the graph is:

y = (-4/9)*(x - 3)^2 + 6

Here we can see that we have a quadratic equation, remember that if the vertex is (h, k) and the leading coefficient is a, then we can write this as:

f(x) = a*(x - h)^2 + k

Here we can see that the vertex is at (3, 6), then we can write:

f(x) = a*(x - 3)^2 + 6

And we can see that the y-intercept is (0, 2), then we can write:

2  =a*(0 - 3)^2 + 6

2 = a*9 + 6

2 - 6 = a*9

-4/9 = a

Then the function is:

y = (-4/9)*(x - 3)^2 + 6

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Therefore , the solution of the given problem of probability comes out to be rotating blue has two positive results.

Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

A. The number of potential outcomes for each spin can be multiplied to determine the number of outcomes in the sample space. Since there are two potential outcomes for each spin in this scenario, there are a total of:

=> 2 x 2 = 4

There are four potential outcomes in the sample space as a result.

B. There are two of these branches: blue-blue and red-red. Therefore, spinning the same hue twice in a row has two positive results.

C. Counting the number of branches that lead to blue on either spin will allow us to determine how many good outcomes there are for spinning blue. These stems come in two varieties: blue-red and blue-blue. Therefore, rotating blue has two positive results.

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Answer:

Bailey earned approximately $499.99 on Thursday, including his commission

Step-by-step explanation:

Bailey's earnings on Thursday consist of his base pay plus his commission. His base pay is $90, and his commission is 11% of his sales.

Let's call Bailey's sales on Thursday "S". Then his commission is 0.11S.

We know that Bailey's total earnings on Thursday were $500. So we can write an equation:

$90 + 0.11S = 500$

To solve for S, we can subtract $90$ from both sides of the equation:

$0.11S = 410$

Then we can divide both sides by $0.11$:

$S = 3,727.27$

So Bailey's sales on Thursday were $3,727.27.

To find Bailey's total earnings, we can add his base pay and commission:

$90 + 0.11(3,727.27) \approx 499.99$

So Bailey earned approximately $499.99 on Thursday, including his commission.

Pythagorean theorem: This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

12² + 12² = x²

288= x²

x =16.98 = 17

Answer:

4x4x4 and the value of 4^3=64

Step-by-step explanation:

4x4x4 is equivalent to 4^3. This is because using exponents mean multiplying the base number by itself by 2 if the exponent is 2, if it was 3 then you would multiply 4 by itself three times.

Answer:

Step-by-step explanation:

To find the number of newborn babies weighing between 4 and 7 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.

For 4 pounds: z = (4 - 5.8) / 2.1 = -0.857

For 7 pounds: z = (7 - 5.8) / 2.1 = 0.571

Using the normal distribution table, the area between z = -0.857 and z = 0.571 is 0.5418.

So, the expected number of newborn babies weighing between 4 and 7 pounds is:

0.5418 x 1100 = 596 (rounded to the nearest whole number)

To find the number of newborn babies weighing less than 6 pounds, we need to calculate the z-score for 6 pounds and use the normal distribution table.

z = (6 - 5.8) / 2.1 = 0.095

Using the normal distribution table, the area to the left of z = 0.095 is 0.5375.

So, the expected number of newborn babies weighing less than 6 pounds is:

0.5375 x 1100 = 591 (rounded to the nearest whole number)

To find the number of newborn babies weighing more than 5 pounds, we need to calculate the z-score for 5 pounds and use the normal distribution table.

z = (5 - 5.8) / 2.1 = -0.381

Using the normal distribution table, the area to the right of z = -0.381 is 0.6499.

So, the expected number of newborn babies weighing more than 5 pounds is:

0.6499 x 1100 = 715 (rounded to the nearest whole number)

To find the number of newborn babies weighing between 5.8 and 10 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.

For 5.8 pounds: z = (5.8 - 5.8) / 2.1 = 0

For 10 pounds: z = (10 - 5.8) / 2.1 = 1.905

Using the normal distribution table, the area between z = 0 and z = 1.905 is 0.4713.

So, the expected number of newborn babies weighing between 5.8 and 10 pounds is:

0.4713 x 1100 = 518 (rounded to the nearest whole number)

If Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.

What is multiplication ?

Multiplication is a mathematical operation that involves combining groups of equal sizes to find a total quantity. It is represented by the symbol "×" or "⋅" and involves two or more factors. The result of a multiplication operation is called the product.

1 gallon is equal to 128 fluid ounces, so 3 gallons is equal to 3 x 128 = 384 fluid ounces.

To find out how many times Colin's mom would have filled her 12-fluid-ounce mug, we divide the total amount of coffee by the size of the mug:

384 fluid ounces ÷ 12 fluid ounces/mug = 32 mugs

Therefore, if Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.

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Answer:

2008 and 2010 is 52 units per year.

Step-by-step explanation:

To find the average rate of change of sales between 2008 and 2010, we need to calculate the change in sales over that period, and divide by the time interval.

The sales in 2008 is f(2008) = 520, and the sales in 2010 is f(2010) = 624. The time interval is 2 years.

Therefore, the change in sales over that period is:

f(2010) - f(2008) = 624 - 520 = 104

The average rate of change of sales between 2008 and 2010 is:

(104) / (2) = 52

So the average rate of change of sales between 2008 and 2010 is 52 units per year.

In the given problem, using central limit theorem,  the sample average score that corresponds to the 33rd percentile of all such sample averages is 100.66.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample averages is approximately normal, regardless of the distribution of the population, as long as the sample size is sufficiently large.

The mean of the sample means is equal to the population mean, which is 101. The standard deviation of the sample means, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error of the mean is:

SE = 17 / sqrt(416) = 0.831

To find the sample average score that corresponds to the 33rd percentile of all such sample averages, we need to find the z-score that corresponds to the 33rd percentile and then use it to calculate the sample average score.

The z-score corresponding to the 33rd percentile is given by:

z = invNorm(0.33) = -0.439

where "invNorm" is the inverse normal distribution function.

We can use the formula for the z-score of a sample mean:

z = (x - μ) / SE

Rearranging this formula, we get:

x = z * SE + μ

Substituting the values we have, we get:

x = -0.439 * 0.831 + 101 = 100.66

Therefore, the sample average score that corresponds to the 33rd percentile of all such sample averages is 100.66.

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If she makes her goal pace 80% of the time and plans to run for the next 10 days, the probability or likelihood that she will make her goal pace every day is 80%.

Probability describes the chance, odds, or likelihood of an expected outcome, event, or success occurring when there are many possible outcomes.

Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.

Thus, it is 80% likely that she will make her goal pace every day if she runs for the next 10 days.

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The value οf p that satisfies the prοpοrtiοn is 16.

Prοpοrtiοn is explained majοrly based οn ratiο and fractiοns. A fractiοn, represented in the fοrm οf a/b, while ratiο a:b, then a prοpοrtiοn states that twο ratiοs are equal. Here, a and b are any twο integers. The ratiο and prοpοrtiοn are key fοundatiοns tο understand the variοus cοncepts in mathematics as well as in science.

Prοpοrtiοn finds applicatiοn in sοlving many daily life prοblems such as in business while dealing with transactiοns οr while cοοking, etc. It establishes a relatiοn between twο οr mοre quantities and thus helps in their cοmparisοn.

Tο sοlve fοr p in the prοpοrtiοn:

10/p = 5/8

We can crοss-multiply tο οbtain:

5p = 80

Dividing bοth sides by 5, we get:

p = 16

Therefοre, the value οf p that satisfies the prοpοrtiοn is 16.

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Therefore, we need 7.4 ounces of rye flour and 29.6 ounces of whole-wheat flour to make a loaf of bread weighing 37 ounces, according to the recipe.

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

Let's first assign variables to represent the amounts of rye and whole-wheat flour we need to use:

Let x be the number of ounces of rye flour.

Let y be the number of ounces of whole-wheat flour.

We know from the recipe that we need to use 1 oz of rye flour for every 4 oz of whole-wheat flour. This can be expressed as:

x = y/4 (equation 1)

We also know that the total weight of the loaf of bread should be 37 oz. This means that:

x + y = 37 (equation 2)

Now we can use equation 1 to substitute for x in equation 2:

y/4 + y = 37

Multiplying both sides by 4 to eliminate the fraction, we get:

y + 4y = 148

5y = 148

y = 29.6

So we need 29.6 ounces of whole-wheat flour. Using equation 1 to find x:

x = y/4 = 29.6/4 = 7.4

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The stem and leaf plot for the data given is obtained as -

Stem  Leaf

0         3 3 3 5 6

1          2 2 3 3 3 4 5 9

2         2 2 2 3 3

3         7 7 9  

4         3

What is stem and leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

The data is given that represents the number of grams of fat in breakfast meals offered at a local fast food restaurant.

According to the data, the stem and leaf plot is -

Stem  Leaf

0         3 3 3 5 6

1          2 2 3 3 3 4 5 9

2         2 2 2 3 3

3         7 7 9  

4         3

The stem contains the first digits of the number, and the leaf plot contains the second digits of the number.

Therefore, the stem and leaf plot is obtained.

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The parametric equations for the curve are X = 4 sin(5t), Y = -48 sin²(5t) + 8 sin(5t) + 45

A parametric equation is a set of equations that express the coordinates of a point as functions of one or more parameters. These equations define a curve or a surface in a space and are commonly used in mathematics, physics, engineering, and computer graphics to model and analyze various phenomena.

Parametric equations can be useful in many applications, such as modeling the motion of particles, designing curves and surfaces, and creating computer animations. They also allow for the visualization of complex shapes and curves that may be difficult to describe using traditional equations.

To find the parametric equation of the given curve, we need to express the coordinates x and y in terms of a parameter t. We can use the trigonometric identities to simplify the given equations and get:

X = 4 sin(5t)

Y = -48 sin²(5t) + 8 sin(5t) - 3

Let's start with Y. We can use the identity sin²(θ) + cos²(θ) = 1 to rewrite -48 sin²(5t) as -48 (1 - cos²(5t)) = -48 cos²(5t) + 48. Substituting this into the equation for Y, we get:

Y = -48 cos²(5t) + 8 sin(5t) - 3

Now, we can use another trigonometric identity, sin²(θ) + cos²(θ) = 1, to rewrite cos²(5t) as 1 - sin²(5t). Substituting this into the equation for Y, we get:

Y = -48 (1 - sin²(5t)) + 8 sin(5t) - 3

Y = -48 sin²(5t) + 8 sin(5t) + 45

So, the parametric equations for the curve are:

X = 4 sin(5t)

Y = -48 sin²(5t) + 8 sin(5t) + 45

This is the final answer.

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Answer:

We can find the value of f(-2) by substituting -2 for x in the given function:

f(-2) = 2(-2)^(2) - 3(-2) + 6

= 2(4) + 6 + 6

= 8 + 12

= 20

Therefore, f(-2) = 20.

Step-by-step explanation:

Answer:

F(-2)=20

Step-by-step explanation:

You have to Substitute The X’s in your question with -2

This gives you: 2(-2)^2-3(-2)+6

2(-2)^2=2(4)=8 (Remember, A negative times a negative is a positive!)

-3(-2)=6

This leaves us with 8+6+6 which is equivalent to 20.

Answer:

I had 4 dollars, but I spent 2.27 on my new pencil.

Step-by-step explanation:

You need to create a situation where you have 4 of 'blank' and you take away 2.27 of 'blank' to answer this question.

Answer:

The correct answer is B) rhombus, rectangle, and square.

A parallelogram is defined as a quadrilateral with two pairs of parallel sides. A rhombus, a rectangle, and a square are all special cases of parallelograms with additional properties.

A rhombus is a parallelogram with all sides equal in length.

A rectangle is a parallelogram with four right angles.

A square is a parallelogram with four equal sides and four right angles.

A kite and a trapezoid are not parallelograms since they do not have two pairs of parallel sides. While a trapezoid has one pair of parallel sides, a kite has no parallel sides.

By using the chain rule, we will see that the derivative is:

h'(2) = 5/12

Remember the chain rule, for the derivative of a composition of two functions f(x) and g(x), if we define:

k(x) = g(f(x))

Then:

k'(x) =g'(f(x))*f'(x)

In this case we know that:

h(x) = √(6 + 5*f(x))

We can define then:

g(x) = √(6 + 5x)

and write h(x) = g(f(x))

Now the differentiation will give:

h'(x) = (1/2)*(√(6 + 5f(x))⁻¹*f'(x)

Evaluating this in x = 2 we will get:

h'(2) = (1/2)*(√(6 + 5f(2))⁻¹*f'(2)

And we know that f(2) = 6 and f'(2) = 5

Then:

h'(2) = (1/2)*(√(6 + 5*6))⁻¹*5

h'(2) = (1/2)*(6)⁻¹*5 = 5/12

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The net present value οf the prοject is  $516.

A set οf cash flοws that happen at variοus dates are cοnsidered tο have a net present value οr net present wοrth. The amοunt οf time between nοw and a cash flοw determines the present value οf that cash flοw. The discοunt rate is anοther factοr. NPV takes the time value οf mοney intο the accοunt.

Here, we have

Respass Cοrpοratiοn has prοvided the fοllοwing data cοncerning an investment prοject that it is cοnsidering: Initial investment $ 160,000 Annual cash flοw $ 54,000 per year Salvage value at the end οf the prοject $ 11,000.

The prοject has annual inflοws οf $54,000 except in 4th year when it will have inflοws οf $65,000 because the salvage value will be added tο the inflοws.

Present value οf inflοws = 54,000/1.12 + 54,000/1.12² + 54,000/1.12³ + 65,000/1.12⁴

= $160,516

Net Present Value = 160,516 - 160,000

= $516

Hence, the net present value is $516.

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The two pairs of congruent segments are PS = QR and PQ = SR

The two pairs of supplementary angles are P and Q; and S and R.

Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:

A + B = 180 degrees

For example, if angle A is 60 degrees, then its supplementary angle would be angle B, which is 120 degrees, because:

A + B = 60 + 120 = 180 degrees

Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and lines. For instance, if two lines intersect, the opposite angles formed are always supplementary.

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Answer:

The area of the rhombus CDEF is 32 units squared.

Step-by-step explanation:

The area of the rhombus CDEF is 24 square units. This can be determined by using the formula for finding the area of a rhombus which is A = 1/2 × d1 × d2 where d1 and d2 are the lengths of the diagonals of the rhombus. In this case, d1 is the distance from C to E and d2 is the distance from D to F. Calculating the lengths of the diagonals gives d1 = 8.9 and d2 = 8. Therefore, the area of the rhombus is 24 square units.

Answer:

(-2,-4)

Step-by-step explanation:

The solution to a system of equations is the point at which the lines (that are defined by the equations) intersect, or touch each other.

In the graph, we can see that the lines intersect when x = -2 and y = -4.

In the format (x,y), this is expressed as: (-2,-4)

Answer: $2.55

Step-by-step explanation:

Unit price = Total cost ÷ Length of fabric

$15.29 ÷ 6 = 2.54833333

Rounded to the nearest tenth is 2.55

The total surface area of the triangular prism is 556 unit²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

The total surface area is the sum of each face area of the triangular prism. Hence:

Total surface area = [(1/2) * 8 * 17] + [(1/2) * 8 * 17] + (10 * 17) + (10 * 14) + (10 * 11) = 556 unit²

The total surface area is 556 unit²

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Comparing the three in their simplest form we have the smallest ratio as 3 to 4.

A mathematical phrase that compares two values is called a ratio. It is written as the product of the division of two different quantities. As in 2:1 or 2/1, ratios are frequently expressed as a fraction or with a colon.

Mathematicians employ ratios in many different contexts, such as arithmetic, algebra, and geometry. They are used to compare amounts, identify equivalent values, and resolve proportional and rate-of-change issues.

Convert the ratios in their simplest form:

3 to 4 can be simplified by dividing both terms by their greatest common factor, which is 1. Therefore, 3 to 4 is already in its simplest form.

10 to 12 can be simplified by dividing both terms by their greatest common factor, which is 2. So, 10 to 12 simplifies to 5 to 6.

2 to 1 is already in its simplest form.

Thus, comparing the three we have the smallest ratio as 3 to 4.

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762 base 10 to base 7 is 2136 base 7

Base Numbers are the number of units, or numbers, we use in our counting system. The most common base number is ten because the digits 0-9 are used in the number system.

And  it is a base-7 number system we would only use seven different digits, like 0-6.

How to determine this

By dividing the number 762 base 10 in base 7 until it can no more be divided in base 7.

First divide 762 /7 = 108 remainder 6

108/7 = 15 remainder 3

15/7 = 2 remainder 1

2/7 = 0 remainder 2

Where the remainders arranged in descending is the base system.

So, by arranging from the bottom

= 2136 base 7

Therefore, 762 base 10 is 2136 base 7

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Step 1: Convert zeros to factors of the polynomial.

If "k" is a zero, then (x-k) is a factor of the polynomial.

The allows us to convert zeros of -3, -1, and 2 into the factors (x+3)(x+1)(x-2).

So right now we have y= (x+3)(x+1)(x-2), but there's a missing piece, the leading coefficient of "a", so really we currently have

   y = a · (x+3)(x+1)(x-2)

This is where the point (3,5) comes in.  We need to substitute x=3 and y=5 into the equation above to find a.

        5 = a · (3+3)(3+1)(3-2)

        5 = a · (6)(4)(1)

        5 = a · 24

   5/24 = a

That's the full function:

    f(x) = 5/24 (x+3)(x+1)(x-2)

Answer:

[tex]f(x)=\dfrac{5}{24}x^3+\dfrac{5}{12}x^2-\dfrac{25}{24}x-\dfrac{5}{4}[/tex]

Step-by-step explanation:

The zeros of a polynomial f(x) are the values of x which satisfy f(x) = 0.

If the polynomial function is degree 3 with 3 zeros, in factored form it can be written as f(x) = k(x - r₁)(x - r₂)(x - r₃) where r are the zeros and k ≠ 0.

Substitute the given zeros -3, -1 and 2 into the formula:

[tex]\implies f(x)=k(x-(-3))(x-(-1))(x-2)[/tex]

[tex]\implies f(x)=k(x+3)(x+1)(x-2)[/tex]

To find the value of k, substitute the given point (3, 5) into the function:

[tex]\begin{aligned}\implies f(3)&=5\\k(3+3)(3+1)(3-2)&=5\\k(6)(4)(1)&=5\\24k&=5\\k&=\dfrac{5}{24}\end{aligned}[/tex]

Therefore, the factored form of the polynomial function is:

[tex]\implies f(x)=\dfrac{5}{24}(x+3)(x+1)(x-2)[/tex]

To write in standard form, expand and distribute:

[tex]\implies f(x)=\dfrac{5}{24}(x^2+4x+3)(x-2)[/tex]

[tex]\implies f(x)=\dfrac{5}{24}(x^3+2x^2-5x-6)[/tex]

[tex]\implies f(x)=\dfrac{5}{24}x^3+\dfrac{10}{24}x^2-\dfrac{25}{24}x-\dfrac{30}{24}[/tex]

[tex]\implies f(x)=\dfrac{5}{24}x^3+\dfrac{5}{12}x^2-\dfrac{25}{24}x-\dfrac{5}{4}[/tex]