What is the volume of the rectangular prism?

Answer:

22cm

Step-by-step explanation:

Start by writing down what you know:

Area of rectangle = length x width = L · W = 20

Since decreasing the length by 2.5 and increasing the width by 3 results in a square, we also know: L - 2.5 = W + 3

Solve the above for L: L = W+5.5

Substitute W+5.5 in for L in A = (W+5.5)·W = 20

Distribute on the left, subtract 20 from both sides, and solve the resulting quadratic. NOTE: Remember that we're dealing in length, so only the positive solution counts!

One side of the square = either W+3 or L-2.5, and perimeter of a square is 4s.

Answer:

Step-by-step explanation:

A range

Answer:

θ=41.3∘,138.7∘,221.3∘,318.7∘ Explanation: 3sin2θ−10(1−2sin2θ)=0 23sin2θ−10=0 s

Step-by-step explanation:

Answer:

A point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated is of 0.553.

Step-by-step explanation:

Point estimate:

The point estimate of a proportion is the sample proportion(number of desired outcomes divided by the number of total outcomes).

Find a point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated.

167 out of 302. So

\(p = \frac{167}{302} = 0.553\)

A point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated is of 0.553.

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Answer:

9.3

Step-by-step explanation:

148.8 divided by 16=9.3

The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045

We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:

P(A | B) = P(B | A) * P(A) / P(B)

where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.

To find P(B), we can use the law of total probability, which states that:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.

Substituting the values, we get:

P(B) = 0.85 * 1/300 + 0.05 * 299/300

= 0.059

Now we can plug in the values into Bayes' theorem:

P(A | B) = 0.85 * 1/300 / 0.059

= 0.0045 or 0.45%

Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).

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Answer:

The gain percent is 33.3 %

Step-by-step explanation:

Let the selling price of 1 m cloth is p.

Cost of 33 m = 33 p

gain = cost of 11 m = 11 p  

The gain percentage is given by

\(\frac{11 p}{33 p}\times 100\\\\= 33.3 %\)

The gain percent is 33.3 %.

Answer:

Right square pyramid

Solve for surface area

A=a2+2aa2

4+h2

a Base edge

Enter value

h Height

The two combinations that shows that the landscapers work hours and total work fee are proportional are: 3 hours for $105 and 7.5 hours for $262.50(option A and F)

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol.

Direct proportion is given by y= kx, where k is the constant and y and x are the variables.

If x represents the landscapers work hours and y represents the total work fee.

y= kx

when y = $140 and x= 4hours

k= 140/4= 35

therefore when x= 3 then y= 3×35=105

similarly when x= 7.5, y= 35×7.5=262.50

Only option A and F obeys the proportional relationship.

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Answer:

A.

Step-by-step explanation:

The sum of an irrational number and an irrational number are always irrational.

All the given options give an irrational number.

Given,

A. the sum of two irrational numbers

B. the product of two irrational numbers

C. the sum of a rational number and an irrational number

D. the product of a rational number and an irrational number

We need to find which of the following is an irrational number.

A rational number is a number that is terminating and recurring.

Example: 3, 12.34 and 31.3333333

An irrational number is a number that is non-terminating and non-recurring.

Example: pi and 1.456839532...

We have,

- the sum of two irrational numbers.

pi + pi = 2pi

It will always be an irrational number.

- the product of two irrational numbers

It is always an irrational number.

pi x pi = pi²

- the sum of a rational number and an irrational number

It is always an irrational number.

12 + pi is an irrational number.

- the product of a rational number and an irrational number

It is always an irrational number.

32 x pi = 32pi is an irrational number.

Thus all the given options give an irrational number.

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Answer:

1/4

Step-by-step explanation:

The square root of 16 is 4, so its the same with fractions.

Answer:

1/3 (A)

Step-by-step explanation:

We take \(\frac{3}{8} *\frac{8}{9}\) and we combine them together. It leaves us with:

\(\frac{(3)(8)}{(8)(9)}\) Now, we must solve for what we have by multiplying both the top and bottom of our fraction and that leaves us with:

\(\frac{24}{72}\)

And now, we simplify that into our answer: \(\frac{1}{3}\)

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

3/11

Step-by-step explanation:

First find the slope of the line

m = (y2-y1)/(x2-x1)

    = ( 7 - -4)/(2 - 5)

    = (7+4)/(2-5)

   =11/ -3

We want a line that is perpendicular, so it is the negative reciprocal

-1 / ( -11/3)

+3/11

A line that is perpendicular will have a slope that is 3/11

Answer:

A

Step-by-step explanation:

All triangles have angle measures that must add up to 180

We want to evaluate:

This is the same thing as:

Simplifying this, we have:

That is the answer

Answer:

Step-by-step explanation:

2x*2x=4x^2

2x*3=6x

Keep in mind 4x^2-6x

then next part:

3*2x=6x

3*3=9

6x-9

So totally

(4x^2-6x)-(6x-9)

Minus and minus is equal to +

(4x^2-12x+9)+2=45

4x^2-12x+11=45

-11 on both sides

4x^2-12x=34

X= -17/-2

Step-by-step explanation:

2x-3(2x-3)+2=45

2x-6x+9+2=45

-4x=45-11

x=34/-4=-17/2

Answer:

\(m = \frac{1}{18}\)

Step-by-step explanation:

The slope formula:  \(\frac{y2-y1}{x2-x1}\)

The two coordinates: (9,8) and (−9,7)

-

Now let's substitute:

1) \(m =\frac{7-8}{-9-9}\)

2) \(m = \frac{1}{18}\)

As per the given function, the value of x is lies between the closed interval [0, 4].

The term function in statistics is defined as a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Here we have given that the function f is continuous and differentiable on the closed interval [0,4].

And we need to find correct statement about this interval.

As per the concept of function, we know that if there is a number c in the closed interval [a , b] such that f(c) ≥ f(x) for all x in [a , b].

Here let us consider that a be the number that has been selected.

So, based on the rule of function can be written as,

=> f(a) ≥ f(x)

where a lies between [0, 4].

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Answer:

a1 = 4

a2= -2

a3 = -8

a4= -14

a5= -20

Step-by-step explanation:

a12= a1 + 11d

-62 = 4 + 11d

-62-4 = 11d

-66= 11d

d = \(\frac{-66}{11}\\\)

  = -6

a1 = 4

a2 = 4 - 6 = -2

a3 = 4 - (6×2) = -8

a4 = 4 - (6×3) = -14

a5 = 4 - (6×4) = -20

The simplified expression of 2√35 −3√5 x 6√7 is −16√35

From the question, the expression is given as

235−−√×35√−67√

Rewrite properly as

2√35 −3√5 x 6√7

Start by evaluating the products

So, we have the following representation

2√35 −3√5 x 6√7 = 2√35 − 18√35

The above expression is a radical expression

The radicals in the expression is √35

This means that we can add or subtract the like terms

Solving further, we have

2√35 −3√5 x 6√7 = −16√35

Hence, the solution is −16√35

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Answer:

$21.00

Step-by-step explanation:

1(x+3)+x=45

x+3+x=45

x+x=42

2x=42

x=21

We will use the probability formula to solve this question

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

In the first sentence, we were told that 7 out of the first 10 students who entered the gym carried backpacks.

In this case, to find the probability of those who carried bags

The total outcome=10

The number of outcomes= 7

Therefore, the probability is

Then to find the expected number of students who will carry backpacks in a sample of 700 students.

we will use the formula

Expected=0.7 x 700

Expected = 490

Hence, if 700 students were at the assembly, 490 students will be expected to carry backpacks

Answer:

Step-by-step explanation:

$100x0.5x1=$5

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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A) (3, -5)

B) Reflection over x-axis and y-axis

C) (1, -1)

D) Translate 2 units left, 4 units up

Answer:

2x +6

Step-by-step explanation:

Multiply using the distributive property.

Answer:

2x+6

Step-by-step explanation:

2 x x= 2x

2 x 3= 6

2x+6