50 POINTS! Plot function h on the graph.

NO LINKS

Answer:

15√3

Step-by-step explanation:

after grouping and adding them to get 15√9

then you apply Surds

Answer:

No.

Step-by-step explanation:

Negative decimal numbers are rational numbers since rational numbers include all the integers both positive and negative integers, decimal as well as a fraction because decimals can be written as fractions.

Answer:

e

Step-by-step explanation:

[tex]volume~of~cone=\frac{1}{3}volume ~of~cylinder\\volume~of~cylinder=3 \times volume ~of~cone=3 \times15=45 \\volume ~of~two~cylinders=2 \times45=90[/tex]

Answer:

86.9 km/h

Step-by-step explanation:

54 mph = 86.9046

Full number: 86.9046 km/h

The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

The given parameters are:

Wall =Square

Length = s

When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).

This means that

Area= 1.75s(2s + 3)

Expand the expression

Area= 1.75s * 2s + 1.75s * 3

Evaluate the products

Area= 3.5s^2 + 5.25s

This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s

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Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

It states that, for a normally distributed random variable:

Considering the mean of 110 and the standard deviation of 15, we have that:

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

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Answer:

-14

Step-by-step explanation:

[tex]\sqrt{16} = 4\\\\(\sqrt{16} - 1) = (4 -1) =3\\\\(3-9) = (-6)\\\\(3-9) ^2 = (-6)^2 = 36\\\\25 - 3 - 36 = 25 - 39 = -14\\[/tex]

[tex] \frac{3a}{4} > - 16 \\ 3a > - 64 \\ a > \frac{ - 64}{3} \\ a > 21 \frac{1}{3} [/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]

[tex]\mathsf{\dfrac{3}{4}a > - \dfrac{16}{1}}[/tex]

[tex]\huge\textbf{Divide \boxed{\dfrac{4}{3}} to both sides:}[/tex]

[tex]\mathsf{\dfrac{4}{3}\times\dfrac{3}{4}a > -16\times\dfrac{4}{3}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{a > \dfrac{4}{3}\times -16}[/tex]

[tex]\mathsf{a > - \dfrac{16}{1} \times\dfrac{4}{3}}[/tex]

[tex]\mathsf{a > \dfrac{-16\times4}{1\times3}}[/tex]

[tex]\mathsf{a > \dfrac{-64}{3}}[/tex]

[tex]\mathsf{a > -\dfrac{64}{3}}[/tex]

[tex]\mathsf{a > -21 \dfrac{1}{3}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{- \frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The regression equation based on the information given about the sugar contents will be 0.18x - 20.84.

It should be noted that from the information, the accompanying data are the caloric contents and the sugar contents of 11 high-fiber breakfast cereals.

The sugar content will be:

a. 160 calories

= 0.18x - 20.84.

= 0.18(160) - 20.84

= 7.96

b. 90 calories

= 0.18x - 20.84.

= 0.18(90) - 20.84

= -4.64

c. 175 calories

= 0.18x - 20.84.

= 0.18(175) - 20.84

= 10.66

d. 208 calories

= 0.18x - 20.84.

= 0.18(208) - 20.84

= 16.6

Therefore, the sugar contents is illustrated above.

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Answer:

The missing length of the right triangle is 13.41 inches.

A right angle triangle has one of its angles as 90 degrees.

The side length of a right triangle can be found using Pythagoras theorem.

Therefore,

c² = a² + b²

where

Therefore,

x² = 18² - 12²

x² = 324 - 144

x² = 180

x = √180

x = 13.416407865

x = 13.41 inches

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Answer:

The volume of the solid is  [tex]1,021m^3[/tex]

Step-by-step explanation:

1. Cylinder

For find the volume of a cylinder we use the next formula:

[tex]V_{cylinder} = \pi h r^2 = \pi \cdot 9m\cdot (5m)^2 \approx 706.86m^3[/tex]

Then the volume of the cylinder is equal to [tex]706.86m^3[/tex]

2. Cones

For find the volume of a cone we use the next formula:

[tex]V_{cone} = \pi \frac{h}{3} r^2 = \pi \cdot \frac{6m}{3} \cdot (5m)^2 \approx 157.08m^3[/tex]

However there are two cones so we have to multiply the volume of one cone for two and we get the total volume for the cones which is [tex]314.16m^3[/tex]

3. Sum of the volumes

Finally we sum the volumes of the cylinder and the cones for get the final result

[tex]V_{cylinder} + V_{cones} = 706.86m^3 + 314.16m^3 \approx 1021m^3[/tex]

So approximating the result is [tex]1021m^3[/tex]

The value of x in (1/6)/2 = x/3 is 1

The equation is given as

(1/6)/2 = x/3

Cross multiply in the above equation

x * 2 = (1/6) * 3

This gives

x * 2 = 1/2

Cross multiply

x = 2 * 1/2

This gives

x = 1

Hence, the value of x in (1/6)/2 = x/3 is 1

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The true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges

The series is given as:

[tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex]

Take the limit of the function to infinity

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)}[/tex]

This gives

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * (\infty +3)}[/tex]

Evaluate the sum

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * \infty}[/tex]

Evaluate the product

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty}[/tex]

Evaluate the quotient

[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = 0[/tex]

Since the limit is 0, then it means that the series diverges

Hence, the true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges

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Answer:

B. The series converges to [tex]\displaystyle{\frac{11}{2}}[/tex].

Step-by-step explanation:

Before evaluating the infinite series, the expression can be decomposed as the sum of two fractions (partial fraction decomposition) as follows.

Let [tex]\textit{A}[/tex] and [tex]\textit{B}[/tex] be constants such that

                                       [tex]{\displaystyle{\frac{9}{n\left(n+3\right)}}}} \ \ = \ \ \displaystyle{\frac{A}{n} \ \ \ + \ \ \frac{B}{n+3}}[/tex]

Multiply both sides of the equation by the denominator of the left fraction,

[tex]n\left(n+3\right)[/tex], yielding

                                              [tex]9 \ \ = \ \ A\left(n+3\right) \ \ + \ \ B \-\hspace{0.045cm} n[/tex]

Now, let [tex]n \ = \ 0[/tex], thus

                                             [tex]\-\hspace{0.2cm} 9 \ \ = \ \ A\left(0 + 3\right) \ + \ B\left(0\right) \\ \\ 3 \-\hspace{0.035cm} A \ = \ \ 9 \\ \\ \-\hspace{0.11cm} A \ \ = \ \ 3[/tex].

Likewise, let [tex]n \ = \ -3[/tex], then

                                            [tex]\-\hspace{0.5cm} 9 \ \ = \ \ A\left(-3 + 3\right) \ + \ B\left(-3\right) \\ \\ -3 \-\hspace{0.035cm} B \ = \ \ 9 \\ \\ \-\hspace{0.44cm} B \ \ = \ \ -3[/tex]

Hence,

                                       [tex]\displaystyle{\sum_{n=1}^{\infty} {\frac{9}{n\left(n+3\right)}}} \ = \ \displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right)[/tex].

First and foremost, write the nth partial sum (first nth terms) of the series,

          [tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ - \frac{3}{4} + \ \frac{3}{2} \ - \frac{3}{5} \ + \frac{3}{3} \ - \frac{3}{6} \ + \frac{3}{4} \ - \frac{3}{7}} \\ \\ \\ \-\hspace{3.58cm} + \ \displaystyle{\frac{3}{5} \ - \ \frac{3}{8} \ + \ \frac{3}{6} \ - \ \frac{3}{9} \ + \ \frac{3}{7} \ - \ \frac{3}{10}} \\ \\ \\ \-\hspace{3.58cm} + \ \ \dots[/tex]

                                                [tex]+ \ \ \displaystyle{\frac{3}{n-3} \ - \ \frac{3}{n} \ + \ \frac{3}{n-2} \ - \ \frac{3}{n+1}} \\ \\ \\ \ + \ \frac{3}{n-1} \ - \ \frac{3}{n+2} \ + \ \frac{3}{n} - \ \frac{3}{n+3}}[/tex].

Notice that the expression forms a telescoping sum where subsequent terms cancel each other, leaving only

        [tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ + \ \frac{3}{2} \ + \frac{3}{3} \ - \ \frac{3}{n+1}} - \ \frac{3}{n+2} \ - \ \frac{3}{n+3}}}[/tex].

To determine if this infinite series converges or diverges, evaluate the limit of the nth partial sum as [tex]n \ \rightarrow \ \infty[/tex],

         [tex]\displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \lim_{n \to \infty} \left(\displaytstyle{\frac{11}{2} \ - \ \frac{3}{n+1} \ - \ \frac{3}{n+2} \ + \ - \ \frac{3}{n+3}\right) \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2} \ - \ 0 \ - \ 0 \ - \ 0} \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2}[/tex]

Answer: B: (1-5x²)³, all real numbers

Step-by-step explanation:

The notation [tex]f\circ g(x)[/tex] is called function composition, which is where you pass one function in as the value of another function. In other words, [tex]\( f\circ g(x)=f(g(x)) \)[/tex].

Since we have the values for f(x) and g(x), let's plug them in.

[tex]f(g(x))\\f(1-5x^2)\\(1-5x^2)^3[/tex]

Hence, the best answer choice is B, as all real numbers would work and it is the cube of 1 - 5x².

Hello and Good Morning/Afternoon!

Let's take this problem step by step:

Let's consider some facts:

 ⇒ angles are opposite each other

    ⇒ by the Vertical Angle Theorem

        ⇒ angles opposite each other are equal in measure

So:

 [tex]\hookrightarrow 4x + 12 = 64[/tex]

Let's solve

  [tex]4x + 12 = 64\\4x = 52\\x = 13[/tex]

x's value is 13

Answer: 13

Hope that helps!

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The sum of the set of x - values given to us is calculated as; ∑X = -1

We are given;

X1 = 2, X2 = -8, X3 = 4, X4 = -8 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6

1) ∑X = X1 + X2 + X3 + X4

∑X = 2 + (-8) + 4 + 1 = -1

2) ∑Y = Y1 + Y2 + Y3 + Y4

∑Y = 3 + (-8) + 10 + 6

∑Y = -11

3) ∑ X² = X₁² + X₂² + X₃² + X₄²

∑X² = (2)² + (-8)² + (4)² + (1)²

∑X² = 85

4) ∑Y² = Y₁² + Y₂² + Y₃² + Y₄²

∑X² = (-3)² + (-8)² + (10)² + (6)²

∑X² = 209

Complete question is;

Two variables, X and Y assume the values X1 = 2, X2 = -5, X3 = 4, X4 = 1 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6, respectively. Calculate (a) ∑X, (b) ∑ Y, (c) ∑ X² (d) ∑ Y²

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The graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of equations is shown in the graph.

As we know, if two equations of a function intersect on the coordinate plane that means they have a solution.

If there will be no intersection then the equations have no solution.

Thus, the graph first, and the graph fifth have no solution because there are no intersection options (A) and (E) are correct.

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The average force exerted by the block exists at -375 N.

Given:

Initial Velocity, u = 50m/s

Displacement, s = 10cm = 0.10m

Mass, m = 0.03Kg

Using the relation,

[tex]$v^{2}-u^{2}=2 a s[/tex]

Substitute the values in the above equation, we get:

[tex]$&0^{2}-50^{2}=2 \mathrm{a}(0.10) \\[/tex]

[tex]$ \mathrm{a}= -12500 \mathrm{~ms}^{-2}[/tex]

We know that, f = ma

Putting the values, we get:

f = (0.03)(-12500)

f = -375 N

The average force exerted by the block exists at -375 N.

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Answer:

60.

100 (total) - 40 (amount in the library Saturday morning) = 60.

Type: Percentages / Fractions

Answer:

Step-by-step explanation:

graphing lines is just what it sounds like, you are taking the equation of the line and putting it on the graph. graphing inequalities shows the area of the coordinate plane that satisfies the inequality, it almost always splits the graph.

arithmetic: -6 , 1 , 8 , 15 , 22

geometric: 2 , 4 , 8 , 16, 32

The linear function whose points are given is f(x)=[tex]x/5 +1[/tex]

Given the points of the function f(-10)=-1,f(0)=1,f(10)=3.

We are required to find the function whose points are given.

Function is relationship between two or more variables that are expressed in equal to form. In function each value of x must have a corresponding y value.

x value is known as domain and y value if known as codomain of the function.

Take two points (-10,-1) and (0,1) and we can form one equation as under:

y+1=(1+1/0+10) * (x+10)

y+1=2/10 (x+10)

y+1=x/5 +10/5

y+1=x/5+2

y=x/5+2-1

y=x/5+1

Hence the linear function whose points are given is [tex]f(x) = x/5 +1[/tex]

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Answer:x>1

Step-by-step explanation:

Subract 11 from both sides

The total cost of the truck is $16,000

We know that first, we have a down payment of $4000.

And then we have a monthly payment of $250 for 4 years. In each year there are 12 months, then in 4 years there are:

4*12 = 48 months.

Then the student needs to pay $250 48 times, this is:

$250*48 = $12,000

Then the total cost is:

$12,000 + $4,000 = $16,000

The total cost of the truck is $16,000

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If ABC and DEF are complementary, then the value of x will be,

90 - ABC = x

90 - 53 = x

x = 37°

Answer:

x=37

Step-by-step explanation:

complementary means when added up they bring 90
so, 53+x=90

x=90-53

x=37

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Solving a system of equations we will see that Hari has 800 and Ram has 600.

Let's define the variables:

We know that:

(2/3)*R = (1/2)*H

We also know that in total they have 1400, then:

R + H = 1400.

So we have the system of equations:

(2/3)*R = (1/2)*H

R + H = 1400.

In the first equation we can isolate R.

R = (3/2)*(1/2)*H = (3/4)*H

Now we can replace that in the other equation:

(3/4)*H + H  =1400

H*(7/4) = 1400

H = (4/7)*1400 = 800

So Hari has 800, and:

R + H = 1400

R = 1400 - H = 1400 - 800 = 600

Hari has 800 and Ram has 600.

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Answer:

  3.9¢ per cup per week

Step-by-step explanation:

Revenue is the product of price and quantity sold. The rate of change in any of these quantities can be found by solving the derivative equation at using the given values.

Revenue (r) is the product of price (p) and quantity sold (q):

  r = pq

Differentiating with respect to time, we have ...

  r' = p'q +pq'

The values given for the problem are ...

Using the above derivative relation, we have ...

  0 = p'(50) +39(-5) . . . . . . fill in given values

  p' = 195/50 = 3.9 . . . . . . add 195, divide by 50

The price must be raised at the rate of 3.9 cents per week to maintain unchanging revenue.

Considering the definition of conditional probability, the probability that the team will win the second game given that they have already won the first game is 45.33%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Conditional probability is the probability that a given event will occur given that another event occurs. The conditional probability operator is the │ sign.

In other words, the conditional probability is the probability of some event A , given the occurrence of some other event B and is denoted by P(A|B) and is read “the probability of A , given B ”.

Then, when an event influences the outcome of a second event, the probability of the second event is said to be a conditional probability and is calculated using the expression:

P(A|B)= P(A∩B) ÷ P(B)

where:

In this case, you know that:

Replacing in the definition of conditional probability:

P(A|B)= 0.34 ÷ 0.75

P(A|B)= 0.4533= 45.33%

Finally, the probability that the team will win the second game given that they have already won the first game is 45.33%.

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