7/8 - 5/12 ayudaaa por favor es para mañana​

The absolute maximum value of f(x) is 4 and occurs at x = 0, while the absolute minimum value is -32 and occurs at x = -3.

To find the absolute maximum and minimum values of the function f(x) = 4 - 4x^2 on the interval [-3, 1], we'll first find the critical points and then evaluate the function at the endpoints and critical points.

Step 1: Find the derivative of f(x)
f'(x) = -8x

Step 2: Set the derivative equal to zero and solve for x to find critical points
-8x = 0
x = 0

Step 3: Evaluate f(x) at the critical point and the interval endpoints
f(-3) = 4 - 4(-3)^2 = -32
f(0) = 4 - 4(0)^2 = 4
f(1) = 4 - 4(1)^2 = 0

Step 4: Compare the function values and determine the maximum and minimum
Absolute maximum value: 4, occurs at x = 0
Absolute minimum value: -32, occurs at x = -3

So, the absolute maximum value of f(x) is 4 and occurs at x = 0, while the absolute minimum value is -32 and occurs at x = -3.

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The equation for line P such that the system has an infinite number of solutions is given as follows:

3) 2x + 2y = -2.

The first equation for the system of equations is given as follows:

x + y = -1.

A system of equations has an infinite number of solutions when the two equations are multiples.

Multiplying the equation by 2, we have that:

2x + 2y = -2.

Meaning that equation 3 is correct.

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Answer:

19,683

Step-by-step explanation:

Answer:

0.08

Step-by-step explanation:

5 ^-2 * cube root of 8

first of all, let us solve 5^-2

using the law of indices;

a^-2 = 1 / a ^2

following this law, we have;

5^-2 = 1 / 5^2

we know that 5^2 = 25

therefore,

5^-2 = 1 / 25

now, let is continue by solving the cube root of 8

now, there are three ways of solving this;

we could just simply think of any number that when multiplies itself three times times, it gives 8, or we could just simply use a calculator

regardless of what we use, we have to end up with the number 2 as the answer

leading is to our conclusion.

from all our solution, we have reduced our question to;

1 / 25 ( which is 5^-2) * 2 ( which is the cube root of 8 )

= 1 / 25 * 2 / 1

note that 2 is the same as 2 / 1. We put it like this when we want to carry out an operation on an integer ( e.g. 2) and and a fraction ( e.g. 1 / 25 )

so,

1 / 25 * 2 / 1 =

2 / 25 ( the two multiplies the 1 in 1 / 25 and the 25 multiplies the 1 in 2 / 1)

leaving our answer in decimal, we have;

0.08

hope this helps,

thanks!!!

The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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Answer:

nothing in the first blank -3 in the second blank and +2 in the last blank or just 2.

Step-by-step explanation:

The significance of the slope in regression can be determined by conducting a hypothesis test

The slope of the regression line in a regression analysis shows how  dependent variable changes as the independent variable increases by a unit. A hypothesis test on a slope coefficient, commonly referred to as the beta coefficient or the regression coefficient, can be used to ascertain the significance of the slope. The slope coefficient is compared to a null hypothesis value of zero in the hypothesis test.

The null hypothesis is rejected and it is determined that there is a significant association between the independent and dependent variables if the p-value for the slope coefficient is less than the significance threshold. Therefore, slope is not equal to zero and there is an association amongst changes in the independent variable and those in the dependent variable.

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Answer:

5

Step-by-step explanation:

17 dogs total all counted up.

17- 5 = 12

5 could have ran away

hope i could help! i tried my best, have a nice day!

Answer: x = 6

Step-by-step explanation:

Answer: the answer is x=6

Answer:

Cross Sectional

Step-by-step explanation:

A cross sectional is one in which an association is developed between a risk factor or an outcome.

In the given question the device is used to record the viewing habits of about 2500 ​households, and the data collected today will be used to determine  the proportion of households tuned to a particular news program. There will be risk factor in today's research with the future developed program which will the outcome.

For example there are 20 students in my class who cannot write. So I develop a program to help them write. But the next year there may not be any student who would require such help.So there's a risk factor associated with the outcome.

Cross sectional results are recorded in a two ways table showing do's and don'ts.

Answer:

5 buses

Step-by-step explanation:

Total number of 6th graders going for the field trip = 184

Step 1

Divide the total number of students by 4

184/4 = 46

We have 46 groups of six graders.

Step 2

There needs to be one chaperone for every four students.

We have 46 groups of six graders

This means there is need for 1 chaperone per group

Hence, we have 46 chaperones

Step 3

Find total number of people going for the field trip

184 students + 46 chaperones

= 230 people

Step 4

If a bus can hold 50 people, how many buses will they need for the trip?

50 people = 1 bus

230 people = ??y

50 × y = 230

y = 230/50

y = 4.6 buses

Hence, 4.6 buses would be needed but since we can't have 0.6(part) of a bus figuratively, as buses come in whole numbers, we approximate to the nearest whole number

= 4.6 ≈ 5

Therefore, they would be needing 5 buses for the trip.

5 buses

Step-by-step explanation:

i got 10 out of 10

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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Answer:

Step-by-step explanation:

\(Mass = 2.2kg\\Velocity = 10m/s \\K.E = \frac{1}{2} mv^2\\K.E = \frac{1}{2} \times 2.2 \times 10^2\\K.E = \frac{1}{2} \times 220\\K.E = \frac{220}{2} \\K.E = 110 joules\)

Answer:

Step-by-step explanation:

Kinetic energy ( KE) of an object is given by

\(KE = \frac{1}{2} m {v}^{2} \)

where

m is the mass

v is the velocity

From the question

m = 2.2 kg

v = 10 m/s

Substitute these values into the above formula

That's

\(KE = \frac{1}{2} \times 2.2 \times {10}^{2} \)

\(KE = 1.1 \times 10\)

We have the final answer as

Hope this helps you

Answer:

x=37

Step-by-step explanation:

a triangle is equal to 180°. so if you already have 50+56 then you have 74° left for 2x. and 74/2=37

Answer:

x=37 because 56+50=106 180-106=74 74÷2=37

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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The y-intercept of the line represented by the equation is; 60.

It follows from the task content that the y-intercept of the line represented by the equation is to be determined.

On this note, we must recall that the y-intercept of an equation is the value of y when x = 0.

Therefore, we have;

-60 (0) + 2y - 120 = 0

2y = 120

y = 60.

Hence, the y-intercept of the line represented by the equation is; 60.

Consequently, it can be inferred that the Ernesto is wrong in his evaluation of the y-intercept as 30.

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By applying the Schroder-Bernstein theorem, we can conclude that (0,1) and R have the same cardinality.

To show that (0,1) and R have the same cardinality, we can apply the Schroder-Bernstein theorem, which states that if there exist injective functions from set A to set B and from set B to set A, then A and B have the same cardinality.

First, we can define a function from (0,1) to R by using a bijection. For example, we can use the function f(x) = tan[(πx - π/2)].

This function maps each value in the interval (0,1) to a unique real number in R. Since the tangent function is injective in the interval (-π/2, π/2), the function f(x) is also injective.

Next, we can define a function from R to (0,1) by using the inverse of the tangent function. For example, we can use the function g(x) = (π/2 + arctan[x])/π.

This function maps each real number to a unique value in the interval (0,1). The function g(x) is also injective since the inverse of the tangent function is injective.

By applying the Schroder-Bernstein theorem, we can conclude that (0,1) and R have the same cardinality.

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(a)The probability that exactly 1 of the chosen Californians were born outside the US when 4 Californians are chosen randomly where 27% of California residents were born outside the united states is 0.42.

The possibility that a value would take one of two independent values given a certain combination of factors or assumptions is summarized by the statistical distribution known as the binomial distribution.

The basic presumptions of the binomial distribution are that each trial has a single possible outcome, that each trial has an equal chance of success, and that each trial is either independent of the others or mutually exclusive.

This is a case of Binomial distribution where there is 0.27 probability a resident of California were born outside US and 0.73 probability they were born inside the US.

In this case of Binomial distribution, the total number of successful trial(n) is the number of Californian residents chosen that is n = 4. Probability that exactly 1 of the chosen resident is

P = 4C1 × (0.27)¹ × (0.73)⁽⁴⁻¹⁾

= 4!/ ((4-1)! × 1!) × 0.27 × 0.73³

= 4 × 0.27 × 0.389017

= 0.42013836

≈ 0.42

(d)For Standard Deviation,

σX = √ (0-.81)2(.389) + (1-.81)2(.432) + (2-.81)2(.159) + (3-.81)2(.02) = 0.769

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The output when three workers are hired is 5 units..

To find the output when three workers are hired, we need to first determine the total cost and then use the marginal cost to calculate the output.

Find the total cost when three workers are hired.
Average total cost (ATC) = Total cost (TC) / Output (Q)
$50 = TC / Q
Since fixed cost (FC) is $130 and the marginal cost (MC) is $40 per worker, the total cost can be found by adding the fixed cost and the cost of the three workers.
TC = FC + 3(MC)
TC = $130 + 3($40)

Calculate the total cost.
TC = $130 + $120
TC = $250

Use the total cost and average total cost to find the output.
$50 = $250 / Q
Q = $250 / $50
Q = 5

Therefore, the output when three workers are hired is 5 units.

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Answer:

65 because the absolute value takes away the negative

The answer to the question is 65.

According to the information in the graph, it can be inferred that time has a tendency to decrease, however, there is no well-defined pattern of time that decreases in each Olympics.

To analyze the graph, we must take into account that each point represents the time relationship of the winner in the year of each Olympics. According to the above we can see that the winner of the year 1952 took 55 seconds, while the winner of the year 2008 took 47 seconds.

Therefore, we can show that there is a tendency to decrease the time to complete and win the 100-meter freestyle swim. However, there is no well-defined pattern on the decrease in time because in some years it has decreased more than in another and in some it has increased.

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Answer:

true

Step-by-step explanation:

<3

Answer:

20 yd^2.

Step-by-step explanation:

Area of base = 2^2 = 4 yd^2.

It has  4 side faces so:

Area of each triangular side = 1/2 * 2 * 4 = 4 yd^2

Total surface area = 4 + 4(4).

= 20 yd^2.

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

Step-by-step explanation:

1st step is to solve x from ΔWXY

∠W + ∠X + ∠Y = 180

where ∠W = 5x + 2

           ∠X = 7x + 4

           ∠Y = 180 - (15x - 18)

                 = 198 - 15x

now plugin values into the equation:

5x + 2   +   7x + 4  +  198 - 15x  = 180

combine similar terms:

5x + 7x - 15x = 180 - 2 - 4 - 198

simplify:

-3x = -24

x = -24 / -3

x = 8

2nd step is to substitute x = 8 into ∠XYZ

∠XYZ = 15x - 18

∠XYZ = 15(8)  - 18

∠XYZ = 102

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope / gradient

c is the y intercept

y = 3x + 7

Comparing this equation with the general form above

Gradient of the line = 3

2y - 6x = 8

Divide both sides by 2

We have

y - 3x = 8

To make y the subject move 3x to the right side of the equation

That's

y = 3x + 8

Comparing with the general form above that's y = mx + c

The gradient = 3

y = 3x + 7

A(2 , y ) , B( x , 4)

Since they lie on the line we can substitute their values into the equation to find the missing points

For A(2 ,y)

We have

y = 3(2) + 7

y = 6 + 7

For B( x , 4)

4 = 3x + 7

3x = 4 - 7

3x = - 3

Divide both sides by 3

Hope this helps you

Using the given information we found that the equation of the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

For a parabola with vertex (h, k), the equation is:

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

Here the vertex is (3, 5), so the equation is:

y = a*(x - 3)^2 + 5

And the y-intercept is y = 1, this means that:

1 = a*(0 - 3)^2 + 5

1 = a*9 + 5

1 - 5 = a*9

-4/9 = a

So the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

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Answer:

27°,63°

Step-by-step explanation:

Let the two angles be a and b.

They are complementary, meaning they add up to 90. Thus:

\(a+b=90\)

And we are told their difference is 36. Therefore:

\(a-b=36\)

Solve for the system of equations. Add b to both sides in the second equation:

\(a=b+36\)

Substitute this into the first:

\((b+36)+b=90\)

Combine like terms;

\(2b+36=90\)

Subtract 36:

\(2b=54\)

Divide by 2:

\(b=27\)

So, b is 27 degrees.

Use the second equation again:

\(a-b=36\)

Now that we know b is 27, substitute:

\(a-27=36\)

Add 27 to both sides:

\(a=63\)

So, a is 63 degrees.

And we're done :)

Answer:

27 and 63

Step-by-step explanation:

x - y = 36

x + y = 90

add the equations together

2x = 126

x = 63

substitute x for x in the first equation

63 - y = 36

y = 27