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Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

4/9 of an hour (26.666 minutes)

Step-by-step explanation:

4 * x * 40/60 = 1

x * 160/60 = 1

x=60/160 = 6/16 = 3/8 (this is the rate for one worker)

~~~~~~~~~~~~~~~~

6 * (3/8) * x = 1

x = 4/9

Answer:

21/13

Step-by-step explanation:

3 1/2 = 7/2

2 1/6 = 13/6

7/2 divided by 13/6

7/2 X 6/13 = 42/26 = 21/13

Answer:

Step-by-step explanation:

3 1/2 = 7/2 and 2 1/6 = 13/6

7/2 divided by 13/6 = 7/2 x 6/13

42/26

21/13 is your final answer.

Answer:

x² + 2² =(√15)²

x²+ 4. =15

x² =15-4

x² =11

x. =√11 mi

so the answer is 4th option

Answer:

1/2×d1×d2

=1/2× (4+4)(6+3)

=36

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

Answer:

(-1,-1)

Step-by-step explanation:

If you multiply the x and y points of A, (-3,-3), by 1/3 then you find: (-1,-1).

Answer:

C is the answer

Step-by-step explanation:

I'm sure it is

Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C

The scale factor will be equal to 1 / 5. the correct option is C.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,

Scale factor = Original size / dilated size

Scale factor = XY / AB

Scale factor = 9 / 45

Scale factor = 1 / 5

Therefore, the scale factor will be equal to 1 / 5. the correct option is C.

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Answer:

Moving 4 to the right on the x axis

The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

Peter sold a cup of lemon juice = $1.25

Peter sold a cup of apple juice =  $2.50

Total number of cups sold = 155 cups

Total amount = $256

Let number of cup of lemon juice be x and

let number of cup of apple juice be y

The equations for the above statements are

[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]

From equation 1,

⇒ [tex]x=155-y[/tex]

Now substitute x in equation 2,

⇒ [tex]1.25(155-y)+2.50y=256[/tex]

⇒ [tex]193.75-1.25y+2.50y=256[/tex]

⇒ [tex]1.25y=256-193.75[/tex]

⇒ [tex]1.25y=62.25\\[/tex]

⇒ [tex]y=\frac{62.25}{1.25}[/tex]

⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]

Now substitute y in equation 1,

⇒ [tex]x=155-50[/tex]

⇒ [tex]x=105[/tex]

Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

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Answer:

Third option:

Ax + By < 0

Step-by-step explanation:

The general form of an inequality is:

(something)  (symbol)  (another thing).

Where the symbols can be:

> = "larger than"

< = "smaller than"

≤ = "smaller than or equal to"

≥ = "larger than or equal to"

So, a given inequality can be:

K > M

This means that K is larger than M.

From the given options, the only one that has this general form is the third option:

Ax + By < 0

This can be read as:

"A times x, plus B times y, is smaller than zero"

Answer:

b. remains unchanged

Step-by-step explanation:

Formula for standard error of mean is;

SE = σ/√n

From the above, we can see that the standard error of mean is independent of the confidence coefficient as it doesn't affect the SE.

Now, we are given that;

random sample; n = 100

Standard deviation; σ = 1

Thus;

SE = 1/√100

SE = 1/10

Now, even if the confidence coefficient is reduced, we can see that it has no impact on the standard error of mean.

Thus, SE remains unchanged.

Answer:

54°

Step-by-step explanation:

Here :-

Measure of 6 :-

Answer:

m<6 = m<2 = 54º

Step-by-step explanation:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162 / 18

x = 9

13x + 9

13(9) + 9

126

180 - 126

54

m<6 = m<2 = 54º

Answer:

Step-by-step explanation:

The total distance = 1/6 + 3/8 miles Change the denominators to 24

D = 1/6 + 3/8 = 4*1/6*4 + 3*3 / 8 * 3

D = 4/24 + 9/24

D = 13/24 of mile.

Answer:

5:15 simplified as 1:3

Step-by-step explanation:

Answer: Choice D

The graph will be discrete because there is no such thing as a partial person to sign up, and the booth is set up once each day for sign ups.

=========================================================

Explanation:

Let's start with the independent variable d. This acts as the variable x. It's the input. The value of d only takes on positive whole numbers (eg: d = 1, d = 2, d = 3, etc). We cannot have something like d = 2.718

So this bit of evidence shows that our function is discrete. Discrete input values (d) plug into the function to produce corresponding discrete output values (m).

Furthermore, we know that m is discrete because the number of people cannot be a fractional or decimal number. We can't have half a person for instance.

---------------

A quick way to see if a set is discrete or continuous is to ask the question: "is it possible to apply the midpoint formula for ANY two values, and have the output make sense?"

So a set like {1,2,3,4,5,...} is discrete because the midpoint of 2 and 3 is 2.5, but that value is not in the set mentioned.

In other words, discrete sets have "gaps" so to speak, while continuous ones do not.

---------------

Another useful property is that let's say that a < x < b, and x is drawn from the domain set. This reduced set will be finite if we're dealing with discrete data. Eg: The set {1,2,3,4,5,...} has the subset {2,3,4} which is finite and discrete.

In contrast, the subset of real numbers x such that [tex]2 \le x \le 4[/tex] is continuous and this subset is infinitely large (has infinitely many members) because we could have things like 2.718 or 3.14 etc

Answer:

3x-2

---------

x-1

Step-by-step explanation:

simplify 18x/6x = 3x/1x

simplify 108/54 = 2/1

Answer:

a

Step-by-step explanation:

because is a ok yo12222122221112w

Answer:

Option C is correct

Step-by-step explanation:

[tex]3 + 11 + 13 = 27[/tex]

[tex]5 + 11 + 13 = 29[/tex]

[tex]2 + 7 + 19 = 28[/tex]

[tex] 2 + 5 + 13 = 20[/tex]

Answer:

The probability that they each will catch 3 fish is 0.000063956

Step-by-step explanation:

The hyper geometric distribution is used to solve this as it has a population, a sample , number of successes  for both the population and sample.

Here

Population size= N =200

Sample size= n =9= (3*3)

Number of successes in population = k = 3 hours

Number of successes in sample = x= 3

Applying the hyper geometric distribution

P (x=3) = kCx *(N-k) C (n-x)/ N Cn

   = 3 C 3 * 197 C 6/ 200 C 9

    =0.000063956

The probability that they each will catch 3 fish is 0.000063956

Answer:

p = 0

Step-by-step explanation:

1 - 4p - 2p = 1 - 5p

-6p + 1 = -5p + 1

-p + 1 = 1

-p = 0

p = 0

Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another,  that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:

Let's start with x = 1.

f(1) = [tex]17-(1)^2[/tex] so

f(1) = 16 and the coordinate is (1, 16).

f(5) = [tex]17-(5)^2[/tex] so

f(5) = -8 and the coordinate is (5, -8). Now we apply the slope formula:

[tex]m=\frac{-8-16}{5-1}=\frac{-24}{4}=-6[/tex] So the answer is -6.

Answer:

Probability of the chosen T-shirt not being black will be equal to 9/10

Step-by-step explanation:

In order to solve this we need to understand that probaility is equal to the number of those outcomes that we want divided by the total number of outcomes. In our case the total number of outcomes is 20 (2 + 7 + 11) which is the total number of T-shirts, and the number of outcomes that are favorable to us is equal to 18 (outcomes without a black T-shirt). Therefor probability of the chosen T-shirt not being black will be equal to...

18/20 = 9/10

Answer:

(1,-3) and (4,-6)

Step-by-step explanation:

The solutions are where the linear line intersects the graphed parabola.

Step-by-step explanation:

=> (3x-12) =(x+6)

or,3x - x = 6 + 12

or,2x = 18

or,x = 18/2

•: x=9#

Answer:

The answer is

[tex] \frac{3}{x} = \frac{11}{10} - \frac{4}{5} \\ \frac{3}{x} = \frac{55 - 40}{50} \\ \frac{3}{x} = \frac{15}{50} \\ \frac{3}{x} = \frac{3}{10} \\ x = 10[/tex]

Answer:

72

Step-by-step explanation:

6*6 = 36

3*12 = 36

36 + 36 = 72