Recall that on a closed interval, the absolute) min and max of a continuous function occur at either a critical point or an endpoint. Find the absolute min and max of the function f(x) = 3x2 + 12x + 5
on the interval [-6, 1].

Answer:

15(2) + 15 (-5) . #45 drop

Step-by-step explanation:

Answer:

(x^2+3) ( 2x+5)

Step-by-step explanation:

2x^3 + 5x^2  + 6x+15

We can use factoring by grouping.

Factor an x^2 from the first two terms  and a 3 from the last two terms.

2x^3 + 5x^2  + 6x+15

x^2 ( 2x+5)  + 3( 2x+5)

Now factor out (2x+5).

(2x+5) ( x^2 +3)

The factored form is

(x^2+3) ( 2x+5)

The radius on the plan is 6 feet, hence the diameter will be

diameter on plan  = 6*2 = 12 feet

Given Data

First pool

Radius of pool on Plan/Blue Print = 5 inches

actual Radius = 20 feet

Second pool

Radius of pool on Plan/Blue Print = ???

actual Radius = 24 feet

From the first pool, we can see that the Proposed Radius is 4 time the Planned radius

Hence, for the second pool let us apply similar logic

Actual radius = 4*x

24 = 4x

divide both sides by 4

x = 24/4

x = 6 feet

Diameter = 6*2 = 12 feet

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Answer:

1) Area = 12cm²

2) x = 5cm

Surface area : 69cm²

Step-by-step explanation:

Opposites sides in a rectangle would equal the same.

so Top/bottom = 20+20=40

Front/back = 15+15=30

40+30=70cm²

94-70=24cm² for left and right side 24÷2=12cm²

2) Those lines represents what side it is equal too which also means the same.

3cm, you know that base x height = surface area so surface area ÷ height = base

15/3=5cm

x=5cm

Formula : Base x Height = One surface area

Front/Back= 15+15=30

Top/bottom = 5x3 = 15+15=30

side/side = 3x3=9

30+30+9=69cm²

The probability that x > 502,000 when a fair coin is tossed a million times is approximately 0.045. This is because the probability of getting heads on a fair coin is 0.5, so the probability of getting more than 502,000 heads in a million tosses is very low.

The probability that x > 502,000 can be calculated using the following formula: P(x > 502,000) = 1 - P(x <= 502,000)

The probability that x <= 502,000 can be calculated using the binomial distribution. The binomial distribution is a probability distribution that describes the number of successes in a sequence of independent trials. In this case, the trials are the coin tosses and the successes are the heads.

The probability that a coin toss results in a head is 0.5, so the probability that a million coin tosses result in 502,000 heads is:

P(x <= 502,000) = (0.5)⁽⁵⁰²⁰⁰⁰⁾ × (0.5)⁽⁵⁰⁰⁰⁰⁰⁾

Substituting this value into the first formula, we get:

P(x > 502,000) = 1 - (0.5)⁽⁵⁰²⁰⁰⁰⁾ × (0.5)⁽⁵⁰⁰⁰⁰⁰⁾

This value is approximately equal to 0.045.

Therefore, the probability that x > 502,000 when a fair coin is tossed a million times is approximately 0.045.

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Step-by-step explanation:

expand the bracket with 6

6ax+12-5ax=15+2a

group like terms

6ax-5ax-2a=15-12

ax-2a=3

cont with it

if the value of the stock investment decreased 20% over the last year, we can think that now we have the 80% of the initial value. So

To find the value of the stock investment a year ago, you can solve this equation:

So the answer is 16250

Answer:

2

--

5

Step-by-step explanation:

Start by multiplying 2 and -4/5 as fractions

2 -4 -8

------ x ------ = -------

1 5 5

Then multiply 6 and 1/3 as fractions

6 1 6 2

------ x ------ = ------- = -----

1 3 3 1

Lastly,add the two results after converting 2/1 to 10/5 to use the Greatest Common Factor so you can add.

-8 10 2

------- + ------ = -------

5 5 5

Answer:

(2,-2)

Step-by-step explanation:

Adding 3 to the graph shifts everything towards the positive y direction by 3 unites. The new minimum will mantain the same x coordinate, and has its y raised by 3, thus is \((2; -5+3) = (2;-2)\)

Answer:

The graph is below.

The area of the pre-images is 8 and the area of the image is 2.  The difference is 6 \(units^{2}\)

Step-by-step explanation:

Area of the large triangle

a = \(\frac{bxh}{2}\)  I am going to choose the vertical line to be the base because I can count the base to be 4 and the height straight up from the base to be 4.

a = \(\frac{4x4}{2}\) = 8

I found the base for the image in the same way

a = \(\frac{2x2}{2}\) 2

Helping in the name of Jesus.

Answer:

First option. \((53\times100)\)

Step-by-step explanation:

Five thousand, three hundred = 5300

\(53\times100=5300\) (Correct)

\(510\times59=30090\) (Incorrect)

\(100\times500=50000\) (Incorrect)

Answer:

You only have to solve each one until you get the right answer, in this case this is what you can do:

Step-by-step explanation:

53 times 100 = 5,300

510 times 59 =  30,090

100 times 500 = 50,000

The right answer is the first one!

Hope this is right, and helps!!!

Answer:

450$

Step-by-step explanation:

Answer:

5. B x=4

6. C x=18

7. B x=78

8.

9. 6 cups

10. B 7 in

Step-by-step explanation:

5. X /12= 48/144

You can simplify the fraction 48/144 by diving both numerator and denominator by 12.

(48/12)/(144/12)=4/12

So, x/12=48/144 is same as

x/12=4/12

So, x=4

6)

15/5=x/6

Cross multiply

5x=15*6

5x=90

x=90/5

x=18

7) 26/ x = 17/51

17x=26*51=1,326

x=1326/17

x=78

8)

x/14=9/3

Cross multiply

3x=14*9=126

x=126/3=42

9)

1 1/2 cups is 3/2 cups

5/(3/2)=20/x

Cross multiply

5x=20*(3/2)=10*3=30

x=30/5=6 cups

10)

52/28=13/x

x=(28*13)/52=7 inches

Answer:

So draw a straight line. This measures as 180 degrees on your protractor. Align your protractor to the straight line, with the circle point in the middle of the line and notice the labels on the side. One of them, between 90 and 180 on the outer scale will measure as 135. Mark this on top of the paper, and remove the protractor. When you remove it, extend your mark to the middle of your line, and this gives you an obtuse angle of 135 degrees. Be sure to recheck!

Step-by-step explanation:

Answer:

see the pic

Step-by-step explanation:

Hope it will help :)

Given that the probability of B given A is 0.5. Also, the probability of A and B are 0.4 and 0.4 respectively. We are supposed to determine the following in this given scenario:

a) P(A∩B)

b) P(A'∩B)

c) P(A∩B')

d) P(A'∩B2)Calculation:Let's use the formula of conditional probability to determine the probability of A given B.P(A∣B)=P(A∩B)/P(B)Here we can replace P(A∩B) by the formula P(B∣A)P(A)P(A∣B)=P(B∣A)P(A)/P(B)P(A∣B)=0.5*0.4/0.4P(A∣B)=0.5P(A∣B) refers to the probability of A and B together divided by the probability of B.

It means P(A∩B)/P(B)=0.5Again by the formula of probability, we know that:P(A∩B)=P(B) * P(A∣B)P(A∩B)=0.4*0.5P(A∩B)

=0.2Now we can calculate the other probabilities based on the following formulas:P(A'∩B)

=P(B)-P(A∩B)P(A∩B')

=P(A)-P(A∩B)P(A'∩B2)

=1-P(A)-P(B)+P(A∩B)By substituting the values, we get:P(A'∩B)

=0.4-0.2

=0.2P(A∩B')

=0.4-0.2

=0.2P(A'∩B2)

=1-0.4-0.4+0.2P(A'∩B2)

=0.2Therefore, the probabilities are:

P(A∩B)

=0.2P(A'∩B)

=0.2P(A∩B')

=0.2P(A'∩B2)

=0.2The above results show that the intersection of A and B is independent.

Also, the intersection of A' and B2 is independent.

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To verify if the given differential equation is exact, we need to check if the partial derivative of the expression with respect to y, denoted as (∂M/∂y).

Given differential equation: 2ydx + (2x+1)dy = 0

Since ∂M/∂y is equal to ∂N/∂x, the given differential equation is exact.

To solve the exact differential equation, we need to find a function f(x, y) such that its partial derivatives (∂f/∂x) and (∂f/∂y) match the coefficients of dx and dy, respectively. We can integrate the coefficient of dx, which is M = 2y, with respect to x, treating y as a constant:

∫M dx = ∫2y dx = 2xy + C(y)

2x + C'(y) = 2x + 1. So, the solution to the exact differential equation 2ydx + (2x+1)dy = 0 is given by the equation:

2xy + y + c = 0, where c is the constant of integration.

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Answer:

1/6

Step-by-step explanation:

Given the function

f(x)=x^3+x^2+x

Get the inverse. Let y = f(x)

y = x^3+x^2+x

Replace y with x

x = y³+y²+y

Differentiate with respect to x

1 =3y²dy/dx + 2ydy/dx + dy/dx

1 = (3y²+2y+1)dy/dx

dy/dx = 1/3y²+2y+1

g'(x) = 1/3(g(x))²+2g(x)+1

If x = 3

g'(3) = 1/3(g(3))²+2g(3)+1

g'(3) =1/3(1)²+2(1)+1

g'(3) = 1/3+2+1

g'(3) = 1/6

Hence g'(3) = 1/6

The correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.

In the proof of the given question, it is given that the ∠AOP and ∠POB are complementary angles by linear pair of theorem but the linear pair of the theorem is applied to the angles with the sum of 180.

Therefore the correct answer is option C the error is that the linear pair of the theorem can not be used to say that ∠AOP is complementary to ∠POB

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Answer: Both:

The linear pair theorem cannot be used to state ∠XMN is complementary to ∠NMY.

The linear pair theorem cannot be used to state ∠AOP is complementary to ∠POB.

Step-by-step explanation:

Edmentum/Plato

To sketch the graph of the function f(x, y) = sin(x), we can visualize it as a surface in a three-dimensional coordinate system. The graph of the function f(x, y) = sin(x) represents a surface in three-dimensional space. The graph depicts a series of sinusoidal waves as x varies.

To sketch the graph of the function f(x, y) = sin(x), we can visualize it as a surface in a three-dimensional coordinate system. In this case, the function depends only on the variable x, while y remains constant. As x changes, the value of sin(x) varies, resulting in a series of wave-like patterns along the x-axis.

When sketching the graph, we can plot various points on the surface by selecting different values for x and y, and evaluating sin(x) at those points. As x increases or decreases, the graph will display the familiar oscillating pattern of the sine function. The amplitude and frequency of the waves will depend on the range and step size chosen for x.

It is important to note that the graph of f(x, y) = sin(x) is a surface and not a curve in the traditional sense. It represents a continuous variation of the sine function along the x-axis, with the y-coordinate remaining constant.

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Answer: 64 minutes

Step-by-step explanation:

Start by finding the rate how many minutes does it take to ride a km by dividing 48 by 15

48/15= 3.2

Now multiply 3.2 by 20 to find how many minutes it will take to ride 20 km

3.2x20=64

∠ XYQ is 122 degrees.

Angles are an important concept in mathematics and geometry. They are formed when two rays or line segments intersect at a common endpoint, known as the vertex. Angles can be measured in degrees, which is a unit of angular measure. A full circle is 360 degrees, and angles can be classified based on their measure relative to this standard. For example, an angle measuring less than 90 degrees is called an acute angle, while an angle measuring exactly 90 degrees is a right angle. An angle measuring between 90 and 180 degrees is an obtuse angle, and an angle measuring exactly 180 degrees is a straight angle. Angles are used in many applications, such as trigonometry, physics, and engineering. They are also important in everyday life, such as determining the direction of travel or the position of objects.

We can start by using the fact that angles XYQ and ZYQ are co-interior angles (also known as consecutive interior angles) and that they lie on a straight line, which means they add up to 180 degrees. So we have:

∠XYQ + ∠ZYQ = 180

Substituting the given values for ∠ZYQ and ∠XYQ, we get:

(10a + 2) + (5a - 2) = 180

Simplifying and solving for a, we get:

15a = 180

a = 12

Now we can substitute this value back into the expression for angle ∠XYQ to find its value:

∠XYQ = 10a + 2 = 10(12) + 2 = 122

Therefore, angle ∠XYQ is 122 degrees.

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Answer:

Lyle and Kyle each shot 18 baskets.

Step-by-step explanation:

Let's represent the number of baskets that Cliff shot with the variable C. Since Lyle shot three times as many baskets as Cliff, we can represent the number of baskets that Lyle shot with 3C. Similarly, since Kyle shot 12 more baskets than Cliff, we can represent the number of baskets that Kyle shot with C + 12.

Since Lyle and Kyle shot the same number of baskets, we can set the expressions 3C and C + 12 equal to each other:

3C = C + 12

Subtracting C from both sides of the equation gives us:

2C = 12

Dividing both sides of the equation by 2 gives us:

C = 6

Since Cliff shot 6 baskets, Lyle and Kyle each shot 3 times as many baskets as Cliff, or 3 * 6 = 18 baskets.

the answer is Lyle and Kyle each shot 18 baskets.

Answer:

15/3=45/x

We move all terms to the left:

15/3-(45/x)=0

Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R

We add all the numbers together, and all the variables

-(+45/x)+15/3=0

We add all the numbers together, and all the variables

-(+45/x)+5=0

We get rid of parentheses

-45/x+5=0

We multiply all the terms by the denominator

5*x-45=0

We add all the numbers together, and all the variables

5x-45=0

We move all terms containing x to the left, all other terms to the right

5x=45

x=45/5

x=9

Step-by-step explanation:

The gallons of gas required by Ryan to travel 286 miles is 13.2 gallons.

As the stated question;

Total gallon of gas used to drive the 260 miles = 12 gallons

Let 'x' be the gallon of gas used to drive the 286 miles.

Then, bu using the proportion

12 / 260 = x / 286

Thus,

x = 286 x 12 / 260

x = 13.2 gallons

Thus, the amount of gas required by Ryan to travel 286 miles is 13.2 gallons.

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Answer:

2. x=16

4. x=18.75, y=11.2

Step-by-step explanation:

2. x/8=30/15 ⇒x=2x8=16

4. x/15=8/6.4 ⇒x=1.25x15=18.75

  y/14=6.4/8 ⇒y=0.8x14=11.2

The missing side lengths x = 16; y = 11.2 and x = 18.75

Similar figures (2)

Given that the triangles are similar, we make use of the following equivalent ratio

8 : 15 = x : 30

Multiply the first ratio by 2

So, we have

16 : 30 = x : 30

By comparison, we have

x = 16

Similar figures (4)

Given that the triangles are similar, we make use of the following equivalent fraction equation

y/6.4 = 14/8

So, we have

y = 6.4 * 14/8

Evaluate

y = 11.2

For x, we have

x/8 = 15/6.4

This gives

x = 8 * 15/6.4

So, we have

x = 18.75

Hence, the value of x is 18.75

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Answer:

No 6 1/2 is 6.5, which is not 73

Step-by-step explanation:

Answer:

no, 6+1/2 equals 6'5

if you mean 6*1/2, it still doesn't equal 73 but 3

Step-by-step explanation:

Answer:

To generate a simple random sample (SRS) X1,⋯,Xn for the population X∼N(2,32), we can use the R function "rnorm(N,2,3)" to collect observed samples.

In statistical analysis, a simple random sample (SRS) is a subset of individuals selected from a larger population in such a way that each individual has an equal probability of being chosen. In this case, we are aiming to generate an SRS for a population X that follows a normal distribution with a mean of 2 and a standard deviation of 3.

To generate the SRS, we can utilize the "rnorm(N,2,3)" function in the R programming language. The function "rnorm" generates random numbers from a normal distribution, and it takes three arguments: N (the number of samples), 2 (the mean of the distribution), and 3 (the standard deviation of the distribution). By specifying the desired number of samples, we can collect observed samples that approximate the population distribution.

For example, if we want to collect 100 samples, we can use the following code in R: "sample <- rnorm(100, 2, 3)". This will generate a sample of 100 values that follow a normal distribution with a mean of 2 and a standard deviation of 3.

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Answer:

a:77

Step-by-step explanation:

260 miles in 4 hours means 65 mph because 260 divided by 4 is 65. 12 mph more than 65 (12+65) is 77, so your answer is 77mph.

Answer:

Step-by-step explanation:

Given: Kite WXYZ

Prove: That at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.

A diagonal is a straight line from one vertex to another of a given shape or figure.

Considering diagonal WY of the kite,

<WYZ ≅ <WYX (diagonal WY is the bisector of <Y)

<ZWY ≅ <XWY (diagonal YW is the bisector of <W)

WZ ≅ WX (congruent property)

YZ ≅ YX (congruent property)

Thus,

ΔWYZ ≅ ΔWYX (Angle-side-Angle congruent property)

Therefore, the given kite can be decompose into 2 congruent triangles (ΔWYZ and ΔWYX).