Evaluate −x^2−5 y^3 when x = 4 and y = 1

Answer:

B

Step-by-step explanation:

P(AUB)=P(A)+P(B)-P(A∩B)

191/400=7/20+P(B)-49/400

P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4

The value of P(B) is 1/4.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = p/q

Given data as :

P(A) = 7/20,

P(A∪B) = 191/400,

P(A∩B) = 49/400 ,

P(AUB) = P(A) + P(B) - P(A∩B)

Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,

191/400 = 7/20 + P(B) - 49/400

Rearrange the terms in the equation,

P(B) = 191/400 + 49/400 - 7/20

P(B) = 240/400 - 7/20

P(B) = 12/20 - 7/20

P(B) = 5/20

P(B) = 1/4

Hence, the value of P(B) is 1/4.

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Answer:

The numbers:

-43    and     58

Step-by-step explanation:

a + b = 15

a = b - 101

then:

(b-101) + b = 15

2b = 15+101

2b = 116

b = 116/2

b = 58

a = b - 101

a = 58 - 101

a = -43

Check:

a + b = 15

-43 + 58 = 15

Answer:

3

Step-by-step explanation:

f(x)=3x-3

g(x)=-x^2+4,

f(2) = 3(2) -3 = 6-3 =3

g(-2) = -(-2)^2+4 = -4+4 = 0

f(2)-g(-2)= = 3-0 = 3

Answer:

The answer is 90+0+0.1+0.02+0.005.

Step-by-step explanation:

The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.

Answer:

The equation is y= -4x -8

Step-by-step explanation:

The -4 is the slope and the -8 is the y intercept

Answer:

Slope: -4

Line type: Straight and diagonal from left to right going down.

Rate of change: a decrease by 4 for every x vaule

y-intercept is: (0,-8)

x-intercept is: (-2,0)

Step-by-step explanation:

Slope calculations:

y2 - y1 over x2 - x1

0 - 4

-2 - ( -3) or -2 + 3

=

-4/1 =

-4

More slope info on my answer here: https://brainly.com/question/17148844

Hope this helps, and have a good day.

Answer:

20 %

Step-by-step explanation:

The experimental probability is 4/20 = 1/5 = .2 = 20 %

Answer:

the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.

Step-by-step explanation:

From the given information:

Sample size n = 200

The standard deviation for a sampling distribution for two brands are equally likely because the individual has no ability to discriminate between the two soft drinks.

∴

The population proportion [tex]p_o[/tex] = 1/2 = 0.5

NOW;

[tex]\sigma _p = \sqrt{\dfrac{p_o(1-p_o)}{n}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.5(1-0.5)}{200}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.5(0.5)}{200}}[/tex]

[tex]\sigma _p = \sqrt{\dfrac{0.25}{200}}[/tex]

[tex]\sigma _p = \sqrt{0.00125}[/tex]

[tex]\sigma _p = 0.035355[/tex]

However, in order to determine the symmetrical limits of the population percentage given that the z probability is 90%.

we use the Excel function as computed as follows in order to determine the z probability  = NORMSINV (0.9)

z value = 1.281552

Now the symmetrical limits of the population percentage can be determined as: ( 1.28, -1.28)

[tex]1.28 = \dfrac{X - 0.5}{0.035355}[/tex]

1.28 × 0.035355 = X - 0.5

0.0452544= X - 0.5

0.0452544 + 0.5 = X

0.5452544 = X

X [tex]\approx[/tex] 0.545

X = 54.5%

[tex]-1.28 = \dfrac{X - 0.5}{0.035355}[/tex]

- 1.28 × 0.035355 = X - 0.5

- 0.0452544= X - 0.5

- 0.0452544 + 0.5 = X

0.4547456 = X

X [tex]\approx[/tex] 0.455

X = 45.5%

Therefore , we can conclude that the probability is 90% that the sample percentage is contained within 45.5% and 54.5% symmetric limits of the population percentage.

Answer:

C. 42 square units

Step-by-step explanation:

This is a rectangle and to calculate the area of a rectangle we multiply length and width

The length of this rectangle is 7 units and the width is 6 units

6 × 7 = 42 square units

Answer:

[tex]\boxed{x=15}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} =\frac{x}{20}[/tex]

[tex]\sf Cross \ multiply.[/tex]

[tex]4 \cdot x = 20 \cdot 3[/tex]

[tex]4x=60[/tex]

[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]

[tex]\frac{4x}{4} =\frac{60}{4}[/tex]

[tex]x=15[/tex]

Answer:

Approximately 13.1521 units.

Step-by-step explanation:

To find the diagonal, we can use the Pythagorean Theorem.

Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:

[tex]a^2+b^2=c^2[/tex]

Substitute 9.3 for a and b, and let c equal d:

[tex](9.3)^2+(9.3)^2=d^2[/tex]

Instead of squaring, add the like-terms:

[tex]2(9.3)^2=d^2[/tex]

Take the square root of both sides:

[tex]d=\sqrt{2(9.3)^2}[/tex]

Expand:

[tex]d=\sqrt{2}\cdot\sqrt{(9.3)^2}[/tex]

The right cancels:

[tex]d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}[/tex]

Answer:

see explanation

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) , that is

f(x) - g(x)

= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1

= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms

= - 5x³ + 8x - 8

Substitute x = - 2 into this expression, thus

(f - g)(- 2)

= - 5(- 2)³ + 8(- 2) - 8

= - 5(- 8) - 16 - 8

= 40 - 16 - 8

= 16

Answer:

a) AD is Median

b) AM is Perpendicular Bisector

Step-by-step explanation:

c) Yes because the Median divides the line into two equal parts

Answer:

87; 2%

Step-by-step explanation:

An exponential growth model is defined as :

F(x) = A( 1 + r)^x

Where;

A = Initial amount,

r = rate of increase

x = time

Comparing the exponential growth function with the exponential growth model given;

f(x)=87(1.02)^x

A = 87 = Initial amount

The growth rate of the model expressed as a percentage :

Taking :

(1 + r) = 1.02

1 + r = 1.02

r = 1.02 - 1

r = 0.02

Expressing r as a percentage :

0.02 * 100% = 2%

Answer:

800×200= 8 × 200 hundreds= 1600 Hundreds = 160000

Answer: x < 28

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]h = 12 cm\\d = 8cm\\r =d/2 = 8/2 =4\\V = ?\\V =\pi r^2h\\\\V= 3 \times 4^2\times12\\V = 576 cm^3[/tex]

Answer:

His earnings for the period= $123

Step-by-step explanation:

Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.

If 30% of his earnings = $369

His earnings = x

30/100 * x= 369

X= 369*100/30

X= 123*10

X=$ 1230

His earnings for the period= $123

Answer:

C(x)=1.2x+8,000.

Step-by-step explanation:

C(x)=cost per unit⋅x+fixed costs.

The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by

In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.

Suppose that you have to sell [x] number of bars to make profits. So, we can write -

{2x} - {1.20x} > {8000}

0.8x > 8000

8x > 80000

x > 10000

Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

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Answer:

A. (1, 4), (-4, 2), (8, 1), (-8, 2)

Step-by-step explanation:

Each x goes to only 1 y to be a function

A. (1, 4), (-4, 2), (8, 1), (-8, 2)

function

B. (1, 4), (-4, 6), (1, 3), (-8, 2)

1 goes to 4 and 3 so not a function

C. (1, 0), (-4, 3), (8, 1), (-4, 5)

-4 goes to 3 and 5 so not a function

D. (8, 1), (-4, 4), (1, 1), (8, 2)

8 goes to 1 and 2 so not a function

Answer:

[tex]\Large \boxed{\mathrm{A. \ (1, 4), (-4, 2), (8, 1), (-8, 2)}}[/tex]

Step-by-step explanation:

[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]

[tex](1, 4), (-4, 2), (8, 1), (-8, 2) \ \sf represents \ a \ function.[/tex]

[tex](1, 4), (-4, 6), (1, 3), (-8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]

[tex](1, 0), (-4, 3), (8, 1), (-4, 5) \ \sf does \ not \ represent \ a \ function.[/tex]

[tex](8, 1), (-4, 4), (1, 1), (8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]

Answer:

18

Step-by-step explanation:

Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:

10x + 33 = 0 or 11x + 60 = 0

10x = -33 or 11x = -60

x = -33/10 or x = -60/11

Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.

Answer:

The function is  continuous at  x = 36

Step-by-step explanation:

From the question we are told that

      The  function is [tex]f(x) = x * \sqrt{ \frac{x}{ (x-6) ^2 } }[/tex]  

       The  point at which continuity is tested is  x =  1

Now from the definition  of continuity ,

   At function is continuous at  k if  only  

       [tex]\lim_{x \to k}f(x) = f(k)[/tex]

So

      [tex]\lim_{x \to 36}f(x) = \lim_{n \to 36}[x * \sqrt{ \frac{x}{ (x-6) ^2 } }][/tex]

                            [tex]= 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

                             [tex]= 7.2[/tex]

Now  

     [tex]f(36) = 36 * \sqrt{ \frac{36}{ (36-6) ^2 } }[/tex]

     [tex]f(36) = 7.2[/tex]

So  the given function is continuous at  x =  36

because

          [tex]\lim_{x \to 36}f(x) = f(36)[/tex]

Answer:

[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]

Step-by-step explanation:

number of counties = 159

n number of people are mutually independent and equally likely home locations

considering the details given in the question

n ≤ 159

The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]

since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in

therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]

Answer:

Hey there!

The area of a rectangle is the length times width.

Thus, we can write the equation, 600=30w.

Solving for the width, we get that the width is equal to 20 ft.

Let me know if this helps :)

Answer:

20 feet across.

Step-by-step explanation:

You will have to do a simple equation solve.

x is how many feet across the court is.

* could be our multiplying sign

600 = 30*x

Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.

That leaves 20 = x.

So it is 20 feet across.

Complete question is;

Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?

Test the relevant hypotheses using α = 0.01

Answer:

The Test result doesn't support the claim that proportion of the time the coin would land heads is not 0.5. Rather it supports the the probability to be 0.5. So the students shouldn't interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5

Step-by-step explanation:

The hypotheses would be;

Null hypothesis; H0: p = 0.5

Alternative hypothesis; Ha: p ≠ 0.5

We are given, X = 163 and n = 350

Thus; p^ = X/n = 163/350 = 0.4657

Since we are not given standard deviation, we will use test statistic formula;

Z = (p^ - p)/(√(p(1 - p)/n)

Z = (0.4657 - 0.5)/(√(0.5(1 - 0.5)/350)

Z = -1.28

From online P-value from T-score calculator as attached, we have;

p-value = 0.201395.

Since the p-value is > 0.01, it's not significant and so we will fail to reject the null hypothesis H0.

We will conclude that the Test result supports the conclusion that p = 0.5

Answer:

91 animals

Step-by-step explanation:

Because every elephant saw 3 monkeys, there were 9 * 3 = 27 monkeys and because every monkey had 1 tortoise in each hand and we know that monkeys have 2 hands, there were 27 * 2 = 54 tortoises. To find the total number of animals that were going to the river, we can calculate 1 + 9 + 27 + 54 = 91 animals.

Answer:

  10

Step-by-step explanation:

Only the rabbit and the 3 monkeys are described as going to the river. The tortoises seem to be going to the river by virtue of being taken there by the monkeys. Those on the path to the river were ...

  1 rabbit

  3 monkeys

  6 tortoises

A total of 10 animals.

Answer:

$179.80

Step-by-step explanation:

799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.

Answer:

8

Step-by-step explanation:

Ham with or without cheese-2 choices

Bologna with or without cheese-2 choices

Bologna with cheese with water or juice-2 choices

Bologna without cheese with juice or water-2 choices

Ham with cheese with juice or water -2 choices

Ham without cheese with juice or water -2 choices

2+2+2+2=8

Kile has 8 choices for lunch

Answer:

1) The dependent variable is : time to complete the maze

2) The analysis used should be : One -way within-subjects ANOVA ( B )

3) Null hypothesis is ; There will be no difference between any group means

4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

5) degree of freedom for the denominator = 11

6) critical F value = 3.49

Step-by-step explanation:

The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .

The analysis used should be : One -way within-subjects ANOVA ( B )

Null hypothesis is ; There will be no difference between any group means

Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11

The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F -  table the critical value would be 3.49

Answer:

(a) 658,008 different samples can be chosen.

(b) 222,111 samples will contain at least one defective board.

(c) The probability that a randomly chosen sample of five contains at least one defective board is 0.34.

Step-by-step explanation:

We are given that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.

(a) To find how many different samples can be chosen, we will use a combination formula here because the order of selecting a sample of 5 from the production run of 40 doesn't matter.

Here, n = total sample = 40 and r = selected sample = 5

So, the combination formula is; [tex]^{n}C_r= \frac{n!}{r! \times (n-r)!}[/tex]

             [tex]^{40}C_5= \frac{40!}{5! \times (40-5)!}[/tex]

              [tex]^{40}C_5= \frac{40!}{5! \times 35!}[/tex]

              [tex]^{40}C_5[/tex] = 658,008 ways

So, 658,008 different samples can be chosen.

(b) To find how many samples will contain at least one defective board, we will first find how many samples will contain no or 0 defective board.

For this also, we will use a combination where n = 40 - 3 = 37 non-defective computer board and a sample of r = 5 computer boards.

So,          [tex]^{n}C_r= \frac{n!}{r! \times (n-r)!}[/tex]

             [tex]^{37}C_5= \frac{37!}{5! \times (37-5)!}[/tex]

              [tex]^{37}C_5= \frac{37!}{5! \times 32!}[/tex]

              [tex]^{37}C_5[/tex] = 435,897 ways

This means that 435,897 of the 658,008 samples will contain no defective board.

Now, the samples that will contain at least one defective board = Total samples - Samples that contain no defective board

           = 658,008- 435, 897

           = 222,111

(c) The probability that a randomly chosen sample of five contains at least one defective board is given by;

      Required Probability =  [tex]\frac{222,111}{658,008}[/tex]

                                         =  0.34 or 34%