Find the absolute extrema, if they exist, as well as values of x where they occur.
F(x) = -x^4 – 4x^2 + 8x62 + 20
o absolute maximum: 20 at x=0, absolute minimum: 7 at x=1 o absolute maximum: 148 at x=-4, no absolute minimum o absolute maximum: 148 at x=-4, absolute minimum: 0 at x=0 o absolute minimum: 148 at x=-4, no absolute maximum

Answer:

\(y=\frac{3}{2} x+5\)

Step-by-step explanation:

subtract 6x

-4y = -6x + 20

divide by -4

\(y=\frac{3}{2} x+5\)

Answer:

y= 3/2x-5

Step-by-step explanation:

Slope intercept form means to solve for y. So,

6x-4y=20 (Subtract 6x)

-4y=-6x+20 (Divide by -4)

y= 3/2x-5

Justine can charge $56 or $14 per hat to earn exactly $800 in profit.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Selling price of hat = x

Number of hats which will be sold in the first month = -2x + 128

Cost to create each hat = $6

Profit per hat = x - 6

Profit of hats sold in the first month = (-2x + 128) (x - 6)

If the profit is $800,

(-2x + 128) (x - 6) = 800

-2x² + 128x + 12x - 768 = 800

-2x² + 140x - 1568 = 0

x² - 70x + 784 = 0

This is a quadratic equation.

Discriminant = \(\sqrt{(-70)^2-(4*1*784)}\) = 42

x = (70 ± 42) / 2

x = 56 and x = 14

Hence the price of hat can be $56 or $14 per hat to earn exactly $800.

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Answer:

Perpendicular

Step-by-step explanation:

Th length of pregnancies of humans has a mean of 265 days and a standard deviation of 10 days percentage of pregnancies between 237.5 and 292.5 days is 99.4%.

The properties of a normal distribution.

(a) To find the value for k for the length of pregnancies in the interval between 250 and 280 days, to calculate the z-scores for both values and then find the percentage of the area under the curve between those z-scores.

The z-score formula is given by:

z = (x - μ) / σ

Where:

x is the given value,

μ is the mean, and

σ is the standard deviation.

For 250 days:

z1 = (250 - 265) / 10

= -1.5

For 280 days:

z2 = (280 - 265) / 10

= 1.5

To find the percentage of pregnancies between these z-scores. Use a standard normal distribution table or a calculator to find the corresponding probabilities.

Looking up the z-scores in the table or using a calculator, the area to the left of z = -1.5 is approximately 0.0668, and the area to the left of z = 1.5 is approximately 0.9332.

To find the area between z1 and z2, we subtract the area to the left of z1 from the area to the left of z2:

P(250 ≤ x ≤ 280) = P(z1 ≤ z ≤ z2) = 0.9332 - 0.0668 = 0.8664

So, the percentage of pregnancies between 250 and 280 days is 86.6%.

(b) Similarly, to find the percentage of pregnancies between 237.5 and 292.5 days,  to calculate the z-scores for those values.

For 237.5 days:

z1 = (237.5 - 265) / 10

= -2.75

For 292.5 days:

z2 = (292.5 - 265) / 10

= 2.75

Using the standard normal distribution table or a calculator,  the area to the left of z = -2.75 is approximately 0.0028, and the area to the left of z = 2.75 is approximately 0.9972.

To find the area between z1 and z2:

P(237.5 ≤ x ≤ 292.5) = P(z1 ≤ z ≤ z2) = 0.9972 - 0.0028 = 0.9944

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In summary the equivalence relation on the set of real numbers is:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

To show that the relation {(x, y) | x − y ∈ Q} is an equivalence relation on the set of real numbers, we need to verify three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any real number x, we have x - x = 0, which is a rational number (0 ∈ Q). Therefore, (x, x) ∈ {(x, y) | x − y ∈ Q} for all x, and the relation is reflexive.

2. Symmetry: If (x, y) ∈ {(x, y) | x − y ∈ Q}, then x - y is a rational number. Since the negation of a rational number is still a rational number, -(x - y) = y - x is also a rational number. Therefore, (y, x) ∈ {(x, y) | x − y ∈ Q}, and the relation is symmetric.

3. Transitivity: If (x, y) ∈ {(x, y) | x − y ∈ Q} and (y, z) ∈ {(x, y) | x − y ∈ Q}, then x - y and y - z are both rational numbers. The sum of two rational numbers is also a rational number, so (x - y) + (y - z) = x - z is a rational number. Therefore, (x, z) ∈ {(x, y) | x − y ∈ Q}, and the relation is transitive.

Since the relation satisfies all three properties (reflexivity, symmetry, and transitivity), it is an equivalence relation on the set of real numbers.

Now, let's determine the equivalence classes [1], [1/2], and [π].

The equivalence class [1] consists of all real numbers x such that x - 1 ∈ Q. In other words, [1] = {x ∈ R | x - 1 ∈ Q}. This means that any real number x in the form x = 1 + q, where q is a rational number, belongs to [1].

Similarly, the equivalence class [1/2] consists of all real numbers x such that x - 1/2 ∈ Q. Therefore, [1/2] = {x ∈ R | x - 1/2 ∈ Q}, which means that any real number x in the form x = 1/2 + q, where q is a rational number, belongs to [1/2].

Finally, the equivalence class [π] consists of all real numbers x such that x - π ∈ Q. Thus, [π] = {x ∈ R | x - π ∈ Q}. This means that any real number x in the form x = π + q, where q is a rational number, belongs to [π].

In summary:

- [1] = {x ∈ R | x = 1 + q, q ∈ Q}

- [1/2] = {x ∈ R | x = 1/2 + q, q ∈ Q}

- [π] = {x ∈ R | x = π + q, q ∈ Q}

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Answer:

5%

Step-by-step explanation:

220/11 = 20

100% / 20% = 5%

hope this helps you ;)

Answer:

5%.

Step-by-step explanation:

220 is the starting value.

209 is the decreased value.

To calculate a percentage decrease, you must first subtract the starting value from the decreased value.

220 - 209 = 11.

Then, divide the difference by the absolute value of the starting value.

**ABSOLUTE VALUE - A NUMBER'S DISTANCE FROM 0.**

The absolute value of 220 is 220.

11 / 220 = 0.05.

Lastly, multiply the quotient by 100

0.05 × 100 = 5.

Therefore, the price was reduced by 5%.

The product is positive; this means there was a decrease in price, and not an increase. Ex. 5

If the product is negative, this means there was an increase in price, and not a decrease. Ex. -5

From the given equation, we are to solve for b.

Hence the answer of b is -108.

The correct answer is option (a) 50 tan(27°).

Let's consider the right triangle formed by the horizontal distance from the observer to the base of the plateau (adjacent), the height of the plateau (opposite), and the straight line from the observer to the top of the plateau (hypotenuse). The angle of elevation is the angle between the horizontal and the hypotenuse.

Using trigonometry, we can relate the opposite and adjacent sides of the triangle to the hypotenuse as:

tan(27°) = opposite / adjacent

We are given that the height of the plateau is 50 meters, so:

opposite = 50 meters

Solving for adjacent, we get:

adjacent = opposite / tan(27°)

= 50 meters / tan(27°)

≈ 91.8 meters

Therefore, the observer is about 91.8 meters away from the base of the plateau.

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Given:

a,) The half-life of iodine-131 is 8 days.

b.) A hospital receives a shipment of 200 grams.

c.) Determine how much would remain after 32 days.

We will be using the following formula:

Where,

We get,

Therefore, in 32 days, only 12.5 grams of Iodine-131 will remain.

Answer:

y= 2.1

Step-by-step explanation:

I use a Graphing Calculator called Desmos. I suggest you try it.

Answer:

#565 is the best answer I can give you

Answer: I'm sorry, but the information provided is not enough to determine the value of x. The statement "mA = 3x°" does not provide enough context to understand what "mA" and "x" represent, and what the relationship between them is. Additionally, the statement "m" does not provide any information that can help determine the value of x. Can you please provide more information or context?

Step-by-step explanation:

First frame is for b and second frame is for c

Answer:

-10

Step-by-step explanation:

I am most positively sure that -10 is the answer based on what I did and that is what I got

Answer:

y = 3x + 19

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

     y = 3x + 4

m = 3

Parallel lines have same slope.

   m = 3

y = 3x + b

Substitute (-5,4) in the above equation.

        4 = 3*(-5) + b

        4 = -15 + b

  4 + 15 = b

           b = 19

Equation of the line: y = 3x + 19

Answer: y = 3x +19

Step-by-step explanation:

-Parallel lines have the same gradient

y = 3x + c

rearrange to give c= y - 3x

substitute x = -5 and y = 4

c = 3 - (3x-5)

c= 19

so the equation is y = 3x + 19

Answer:

429.34

Step-by-step explanation:

I know trust me

This density in kilograms per pint is 0.946.

Important conversions:

1 gram = 0.001 kilogram

1 ml = 0.001 litres

1 pint = 0.473 litres

1 litre = 2.113 pints

Step 1 : Convert 2 grams per millilitre of volume (2 g/ml) into kilograms per litre (kg/l)

=> (2  x 1000)/ (0.001) = 2 kg / l

Therefore, we get the density in kilograms per litre (kg/l) as 2 kg/l.

Step 2 : Convert the density in kilogram per litre (kg/l) into kilograms per pint (kg/pint)

=> 2 x 0.473 = 0.946 kg/l

Therefore, by converting 2 grams per millilitre of volume into kilograms per pint, we get the density as 0.946 kg/pint.

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Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)

Answer:

Step-by-step explanation:

You want the points of intersection of the line y=2 with the parabola y=1/2x², the lengths of segments between those points and the vertex, and the area of the triangle formed.

The points of intersection will satisfy the two equations ...

Setting the y-expressions equal, we have ...

  2 = 1/2x²

  4 = x² . . . . . . multiply by 2

  ±2 = x . . . . . . . take the square root

The y-values of each point are 2, so the two points of intersection are ...

  B = (-2, 2)

  A = (2, 2)

We recognize that segments OA and OB are each the hypotenuse of a right triangle that is 2 units on each side. The Pythagorean theorem tells you that hypotenuse has length ...

  OA = OB = √(2² +2²) = √(2²·2)

  OA = OB = 2√2

Of course AB is 4 units, the difference between the x-values of its ends.

The area of the triangle is ...

  A = 1/2bh

where the base b is AB = 4 units, and the height is y=2.

  A = 1/2·4·2 = 4 . . . . square units

The area of the triangle is 4 square units.

Answer:

This is gebber gabber but yes

Step-by-step explanation:

Following execution, the flags will be ZF=0, SF=0, and CF=0, and register R12 will be A0 (in Hex).

Given,

The following instruction is executed. assume that before execution, register r12 contains 0xa0, r15 initially contains 0x61, and the flags are ZF.

After execution, register R12 contains A0 (in Hex) and the flags will be ZF = 0, SF = 0, and CF = 0.

CMP instruction does not change values so R12 remains the same.

CMP instruction internally subtracts R12 - R15. Since R12 is not equal to R15, ZF = 0. Since R12 > R15, SF = 0 and CF = 0.

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Answer: 10 marbles are still in the bag.

Step-by-step explanation:

(8+9)-7

17-7

10

The value of data that might affect the statistical measures of spread and center is B. There is a high data value that causes the data set to be asymmetrical for the males.

Outliers stretch out the data further, resulting in a wider range and a higher standard deviation. On the other hand, eliminating outliers reduces data spread, resulting in a lower range and standard deviation.

When an outlier is present, it might change the way the graph looks since it raises the mean. From the chart, there is a high data value in the males which will therefore make the data to be asymmetrical for the males as the larger spread for the males means the data set tilts towards them.

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Answer:

b

Step-by-step explanation:

because the 1 is negative

By using a sampling technique  we ensure that we choose a sample of students that is representative of all 8:00 am classes.

There are  varieties of sampling strategies: chance sampling includes random selection, permitting you to make sturdy statistical inferences approximately the complete organization. Non-opportunity sampling entails non-random selection primarily based on convenience or different standards, permitting you to without problems gather records.

Random sampling is part of the sampling technique wherein every sample has an same possibility of being chosen. A sample chosen randomly is meant to be an unbiased representation of the overall population.

explanation;

we conclude the

Since the students' lecture hallsare on different building the samples are

Dividing the students into groups, the students will be grouped by the buildings of their lecture halls.

The number of students in each building is:

There are 100 students in each building

Then select at random an equal proportion of student from each building let 20 students in each building.

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Answer:

\(\boxed {y = \frac{2}{3}x - \frac{5}{6}}\)

Step-by-step explanation:

First you need to solve the expression in order to get the expression in Slop-Intercept Form:

\(y = mx + b\)

-The following equation:

\(-6y + 4x = 5\)

Solve:

\(-6y + 4x = 5\)

\(-6y + 4x - 4x = 5 - 4x\)

\(-6y = 5 - 4x\)

\(\frac{-6y}{-6} = \frac{5 - 4x}{-6}\)

\(y = \frac{5 - 4x}{-6}\)

\(\boxed {y = \frac{2}{3}x - \frac{5}{6}}\)

Therefore, the expression in Slope-Intercept Form is \(y = \frac{2}{3}x - \frac{5}{6}\).

Answer:

None of these choices are correct.

Step-by-step explanation:

75 = perimeter

The limit of the series Sₙ = ∑ₓ=₁ⁿ[k².42/n³ + k12/n² + 30/n],

lim n →∞ Sₙ = 22.

A limit of a series is the value the series tends to as the independent variable tends to a given value

Given the series Sₙ = ∑ₓ=₁ⁿ[k².42/n³ + k12/n² + 30/n], we need to find the limit \(\lim_{n \to \infty} S_n\). So, we proceed as follows.

Since the series Sₙ = ∑ₓ=₁ⁿ[k².42/n³ + k12/n² + 30/n], we have that

Sₙ = ∑ₓ=₁ⁿ[k².42/n³ + k12/n² + 30/n]

Sₙ = ∑ₓ=₁ⁿ[k².42/n³ +  ∑ₓ=₁ⁿk12/n² +  ∑ₓ=₁ⁿ30/n]

Sₙ = 42/n³(∑ₓ=₁ⁿk²) +  12/n²(∑ₓ=₁ⁿk) +  30/n(∑ₓ=₁ⁿ 1)

Now, we know that

So, substituting the values of the variables into the equation, we have that

Sₙ = 42/n³(∑ₓ=₁ⁿk²) +  12/n²(∑ₓ=₁ⁿk) +  30/n(∑ₓ=₁ⁿ 1)

Sₙ = 42/n³[n(n + 1)(2n + 1)/6] +  12/n²[n(n + 1)/2) +  30/n[n]

Factorizing out the n's , we have that

Sₙ = 42/n³[n × n × n(1 + 1/n)(2 + 1/n)/6] +  12/n²[n × n(1 + 1/n)/2) +  30/n[n]

Sₙ = 42/n³[n³(1 + 1/n)(2 + 1/n)/6] +  12/n²[n²(1 + 1/n)/2) +  30/n[n]

Sₙ = 42[(1 + 1/n)(2 + 1/n)/6] +  12[(1 + 1/n)/2) +  30

So, the limit of the series \(\lim_{n \to \infty} S_n\) = \(\lim_{n \to \infty}\)42[(1 + 1/n)(2 + 1/n)/6] +   \(\lim_{n \to \infty}\)12[(1 + 1/n)/2) +  \(\lim_{n \to \infty}\)30

= 42[(1 + 1/∞)(2 + 1/∞)/6] +  12[(1 + 1/∞)/2) + 30(0)

= 42[(1 + 0)(2 + 0)/6] +  12[(1 + 0)/2) + 0

= 42[(1)(2)/6] +  12(1)/2 + 0

= 42[2/6] +  12/2 + 0

= 42/3 +  6

= 16 + 6

= 22

So, the limit \(\lim_{n \to \infty} S_n\) = 22

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Answer:

DGE and BGA

Step-by-step explanation:

Supplementary angles are two angles whose measures add up to 180°

so BGD + DGE = 180 or BGD + BGA = 180

so both DGE and BGA are supplementary to BGD

The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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