help with 19 and 20!!!

Answer:

A.1

Step-by-step explanation:

looking at the function, you can see that you should use the second equation, x^3-9x^2+27x-25, x>=2

step 1: insert 2 into the equation. (2)^3-9(2)^2+27(2)-25

step 2: simplify equation 8-36+54-25=1

The value of function g(2) is 1. Therefore, option A is the correct answer.

The given function is g(x)=\(\left \{ {{(\frac{1}{2} )^{x-3} \hspace{6em} x < 2} \atop {{x^{3}-9x^{2} +27x-25} } \hspace{6em}x \geq2}} \right.\).

We need to find the value of g(2).

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Now, g(2)= \((\frac{1}{2} )^{x-3} =2\)

g(2)=2³-9(2)²+27×2-25

=8-36+54-25=1

The value of function g(2) is 1. Therefore, option A is the correct answer.

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Answer:

The equation of the exponential function will be:

Step-by-step explanation:

The general exponential function is defined as

y = abˣ

Here,

From the table, it is clear that the y-intercept is (0, 10). Note that the y-intercept can be determined by setting x=0 and solving for y.

here

at x=0, y=10

so a = 10

If we check the y-values, it is clear that every next value of y can be obtained by multiplying the previous y-value by 1/5.

In other words, the common multiplier = b = 1/5

Thus, the equation becomes

\(y\:=\:10\cdot \left(\frac{1}{5}\right)^x\)

Thus, the equation of the exponential function will be:

Answer:

3231360

Step-by-step explanation:

5280 x 612 equals 3231360

Answer:

K = 42

Step-by-step explanation:

K/2 = 21

2* k/2 =2*21

k=42

Answer:

1. -13 degrees

2. $12

3. 6 yards

4. 15 points

Step-by-step explanation:

1. -5 - 8 = -13

2. $100 - $88 = $12

3. 13 - 7 = 6

4. 10 x 2 = 20 - 5 = 15

Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.

initial height = 5

final height =20

height to travel =20-5 =15

\(15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0\)

solving we get, t = 0.255 or -2.44

since, -2.44 is not possible,

t = 0.255 seconds.

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a) P(x) = 1/600 probability/m .b) The probability is P(x) * 100 m = (1/600) * 100 m = 1/6. c) The constant probability densities are \(P_1\) = 3/1000 probability/m and \(P_2\) = 1/1000 probability/m. d) The probability that Mrs. Reeve's car is in the first 400 m of the lot is 0.8 or 80%.

(a) If the probability density is constant, it means that the probability is equally distributed over the entire length of the lot. Since the lot is 600 m long, the probability density, P(x), would be the reciprocal of the length of the lot. Therefore, P(x) = 1/600 probability/m.

(b) To find the probability that Mr. Vanderbilt's car is in the first 100 m of the lot, we need to calculate the area under the probability density curve over that range. Since the probability density is constant, the probability can be obtained by multiplying the probability density by the length of the range. Thus, the probability is P(x) * 100 m = (1/600) * 100 m = 1/6.

(c) For Mrs. Reeve's car, the probability density is constant in two intervals: \(P_1\) for 0 < x < 200 m and \(P_2\) for 200 m < x < 600 m. We are given that \(P_2 = P_1/3.\) To find the values of \(P_1\) and \(P_2\), we need to ensure that the total probability over the entire range sums to 1.

The total probability can be calculated by integrating the probability density function over the respective ranges and setting it equal to 1:

\(\int\ P(x) dx = \int\limits^{200}_{0}P_1 dx + \int\limits^{600}_{200}P_2 dx = 1\)

Since P(x) is constant within each interval, the integrals simplify to:

\(P_1 * 200 + P_2 * 400 = 1\\Substituting P_2 = P_1/3, we can solve for P_1:\\P_1 * 200 + (P_1/3) * 400 = 1\\200P_1 + 400P_1/3 = 1\\600P_1 + 400P_1 = 3\\1000P_1 = 3\\P_1 = 3/1000\)

\(Since P_2 = P_1/3, we can find P_2:\\P_2 = (3/1000)/3\\P_2 = 1/1000\)

Therefore, the constant probability densities are \(P_1\) = 3/1000 probability/m and \(P_2\) = 1/1000 probability/m.

(d) To find the probability that Mrs. Reeve's car is in the first 400 m of the lot, we need to calculate the area under the probability density curve over that range. Since the probability densities are constant within their respective intervals, the probability is given by the product of the probability density and the length of the range:

\(Probability = (P_1 * 200 m) + (P_2 * 200 m)\\= (3/1000) * 200 m + (1/1000) * 200 m\\= (3/1000 + 1/1000) * 200 m\\= (4/1000) * 200 m\\= 800/1000= 0.8\)

Therefore, the probability that Mrs. Reeve's car is in the first 400 m of the lot is 0.8 or 80%.

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Answer:

(-4,0)

Step-by-step explanation:

1. First, let's graph f(x) = |x + 4|.

(The image is below the explanation).

2. As you can see, the line at first starts going down, but then the turning point occurs at (-4,0). The graph then continues to go upwards.

Therefore, the answer is (-4, 0).

Answer:

(0,20) (16,8) (8,4) so A

Step-by-step explanation:

By default it is dilating centered at the origin because not specified. Therefore you just multiply every coordinate by the scale factor, in this case 2. Hope this helped!

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Answer:

x < -7/2

Step-by-step explanation:

First, perform the indicated multiplication:

4(1-2x)>32 becomes 4 - 8x > 32.  

Next, isolate the -8x term by subtracting 4 from both sides of this inequality:

-8x > 28

Finally, solve for x by dividing both sides by -8.  This requires that we reverse the direction of the inequality sign:

x < -28/8, or, after reduction, x < -7/2

The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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Answer:

When solving a rational equation, start by grouping or canceling out like terms. So cancel out x on the numerator and denominator of 2+7x/x. While the equation itself results in a contradictory statement - 5=9, the first step to figuring this out would be canceling out x.

The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

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Answer:

x = 10

6x - 6 = 54

Step-by-step explanation:

The hypotenuse of both triangles are 63 and 6x - 6; the second longest sides are 49 (greater than 35) and 42 (greater than 30).

So our proportion:

63/(6x-6) = 49/42

Cross multiply

63*42 = 49*(6x-6)

2646 = 294x-294

2940 = 294x

x = 10

Double-check:

63/(6*10 - 6) = 49/42

63/(60 - 6) = 49/42

63/54 = 49/42

7/6 = 7/6

6x - 6 = 6(10) - 6 = 60 - 6 = 54

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions. Option c is correct.

An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance . (You can test this with any value of x and find that they all work!)

So to find the equations that have infinite solutions, we need to see which have the same exact sides.

(Choice A)

-6x+35 = -6x-35 have the different thing on each side: , so this has no solution.

(Choice B)

6x+35  = -6x-35 does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1).

(Choice C)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

(Choice D)

6x+35=-6x+35 And finally,  has the different thing on each side: , so it has one solution.

Hence , -6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

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The height of the quarter is given by the polynomial -16t^2 + 250 feet and the height of the dime is given by the polynomial -16t^2 - 10t + 100 feet.

To compare the height of the quarter and dime at any time t, we need to find the difference between their heights.

Let's first find the height of the dime when the quarter is released, which is at t=0:

Height of the quarter at t=0: 16(0)^2 + 250 = 250 feet

Height of the dime at t=0: -16(0)^2 - 10(0) + 100 = 100 feet

So, the initial height difference between the quarter and dime is 250 - 100 = 150 feet.

Now, let's find the height difference between the quarter and dime at any time t:

Height of the quarter at time t: 16t^2 + 250

Height of the dime at time t: -16t^2 - 10t + 100

So, the height difference at time t is:

(16t^2 + 250) - (-16t^2 - 10t + 100) = 32t^2 + 10t + 150

Therefore, the height difference between the quarter and dime at any time t is given by the polynomial 32t^2 + 10t + 150.

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The values in the missing observation are:

X1    X2

76 22  

82 25

91 32

101    41

88 28

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x1 x2

76 22  

82 __

91 32

__    41

88 28

The difference between each row are:

76 - 22 = 54

82 - 25 = 57

91 - 32 = 59

101 - 41 = 60

88 - 28 = 60

We see that,

57 - 54 = 3

59 - 57 = 2

60 - 59 = 1

60 - 60 = 0

So,

The difference between the numbers is consecutive as 3, 2, 1, 0.

Thus,

The missing values of X1 and X2 are 101 and 25.

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Answer:

5100

Step-by-step explanation:

Answer:

b. 75

Step-by-step explanation:

Calculation for how many people must attend the festival

Using this formula

Numbers of people to attend the festival=Expenses/Charges

Let plug in the formula

Numbers of people to attend the festival=($115+$110)/$3

Numbers of people to attend the festival=$225/$3

Numbers of people to attend the festival= 75 people

Therefore the numbers of people that must attend the festival is 75

Answer:

12r -9

Step-by-step explanation:

(8r2−7r−9)+(−r2+r)

= 16r -7r -9 +2r +r

= 12r -9

Answer:

w= -44

Step-by-step explanation:

Answer:

∠BAC=70°

Step-by-step explanation:

If AB || CD and BC II DE that means the two triangles are congruent or the same, this means ∠BAC°=∠DCE°, ∠ABC°=∠EDC°, and ∠BCA°=∠DEC°. The three angles of a triagle add up to 180°. If ∠DEC=45° and ∠EDC=65°

Total°-(∠DEZ°+∠EDC°)=∠DCE° or ∠ECD°

180°-(65°+45°)=70°

∠BAC°=∠DCE°

Therefore ∠BAC=70°

Answer:

Distance traveled is equal to the length of wheel circumference as it “unrolls” along the ground as the wheel turns. One full turn of the wheel will move the robot one circumference's distance. Therefore, students will find the distance traveled by multiplying circumference by the number of rotations.

The graph of the line represents the total cost for a month as a function of the number of visits made.

To graph the function y = 20 + 2x, we can plot several points and then connect them with a straight line. Here are a few points we can use:

When x = 0 (no visits), y = 20

When x = 1 (one visit), y = 22

When x = 2 (two visits), y = 24

When x = 3 (three visits), y = 26

We can plot these points on a coordinate plane with x on the horizontal axis and y on the vertical axis. After this, we can then connect the dots with a straight line. This line represents the total cost for a month as a function of the number of visits made.

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Answer:

x= 2 and x= -(2/3)

Step-by-step explanation:

Step 1 :Multiply all terms by the same value to eliminate fraction denominators

x^2/ x+6 = 1/2

2(x+6)*(x^2/x+6) = 2(x+6) * 1/2

Step 2: Cancel multiplied terms that are in the denominator

2x^2= x+6

Step 3: Move terms to the left side

2x^2 - (x+ 6) = 0

Step 4: Distribute

2x^2 - x - 6 = 0

Step 5: Use the quadratic formula

x= ( - (-1) +- Squar((-1)^2-4*2(-6)) ) / 2*2

Step 6: Simplify

x= (1+- 7)/ 4

Step7: Separate the equations

x= (1+7)/ 4 and x= (1- 7)/ 4

Step 8: Solve that 2 small equation

x= 2 and x= -(3/2)

Answer:

x = - \(\frac{3}{2}\) , x = 2

Step-by-step explanation:

x² : x + 6 = 1 : 2

express the ratio in fractional form

\(\frac{x^2}{x+6}\) = \(\frac{1}{2}\) ( cross- multiply )

2x² = x + 6 ( subtract x + 6 from both sides )

2x² - x - 6 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

2x² - 4x + 3x - 6 = 0 ( factor the first/second and third/fourth terms )

2x(x - 2) + 3(x - 2) = 0 ← factor out (x - 2) from each term

(x - 2)(2x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - \(\frac{3}{2}\)

Answer:

19, 18, 15.5

Step-by-step explanation:

To solve this problem, you need to substitute the given values into the function.

b(x = -2) = 18 - 0.5(-2) = 18 + 1 = 19

b(x = 0) = 18 - 0.5(0) = 18 - 0 = 18

b(x = 5 ) = 18 - 0.5(5) = 18 - 2.5 = 15.5

Answer:

AC = 70

BG = 38

GC = 28

AE = 63

Step-by-step explanation:

The given parameters are;

The centroid of ΔABC = G

The length of FC = 35

The length of AG = 42

The length of BF = 57

The length of DG = 14

Given that the centroid is the intersection of the medians, we have;

FA = FC = 35 Definition of median line FB, (point F is the midpoint of AC)

AC = FA + FC = 35 + 35 = 70 by segment addition postulate

AC = 70

BG = 2/3 × BF = 2/3 × 57 = 38 Definition of median line BF

BG = 38

DG = 14 = 1/3 × DC Definition of median line

∴ DC = 3 × DG = 3 × 14 = 42

GC = 2/3 × DC = 2/3 × 42 = 28 Definition of median line DC

GC = 28

AG = 42 = 2/3 × AE Definition of median line AE

∴ AE = 3/2 × 42 = 63

AE = 63.

On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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Answer:

Step-by-step explanation:

Answer:

x=c-g or x=-g+c

Step-by-step explanation: