A gas pump fills 2^-3 gallon of gasoline per second. How many gallons does the pump fill in one minute?

Answer:

a) 0.0156

b) 0.4219

c) 0.1406

Step-by-step explanation:

We are given the following information:

We treat adult having type O+ blood as a success.

P(Adult have type O+ blood) = 0.25

Then the number of adults follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 3

a) All three are type O+

[tex]P(x =3)\\= \binom{3}{3}(0.25)^3(1-0.25)^0\\= 0.0156[/tex]

b) None of them is type O+

[tex]P(x =0)\\= \binom{3}{0}(0.25)^0(1-0.25)^3\\= 0.4219[/tex]

c) Two out of the three are type O

[tex]P(x =2)\\= \binom{3}{2}(0.25)^2(1-0.25)^1\\= 0.1406[/tex]

Using the principle of binomial probability, the probability o the required events are :

Recall :

A.) Probability that all 3 are O+ :

x = 3

P(x = 3) = 3C3 × 0.25³ × 1 = 0.0156

B.) Probability that none 3 are O+

x = 0

P(x = 3) = 3C0 × 1 × 0.75³= 0.4219

C.) Probability that 2 out of the three are O+

x = 2

P(x = 2) = 3C2 × 0.25² × 0.75¹ = 0.1406

Therefore, the required probabilities are : 0.0156, 0.4219 and 0.1406 respectively.

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Answer:

option A is the correct one

Step-by-step explanation:

The product of the expression negative 9 x (5 minus 2x) is 18x² - 45x.

The correct option is c) negative 18 x minus 45 x.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given expression:

Negative 9 x (5 minus 2x).

To find the product:

First, we simplify the expression,

-9x (5 - 2x)

Solving the parenthesis,

-9 (5 - 2x)

= -45x + 18x².

= 18x² - 45x.

= 18 x squared minus 45 x

Therefore, 18x² - 45x is the required expression.

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FOLLOW ME FOR CLEARING YOUR NEXT DOUBT

Hey there!

The Distributive Property states that

a(b+c)=ab+ac

Now simplify this expression:

6.3(m+7)+m+2

Distribute 6.3:

6.3m+44.1+m+2

Combine Like terms:

6.4m+m+44.1+2

7.4m+46.1

With this we're done!

Hope everything is clear.

Let me know if you have any questions!

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[tex]\boxed{An~Emotional~Helper}[/tex]

Answer:

7

Step-by-step explanation:

To find the slop, use (rise/run)

The y goes from 0 to 7/3

The x goes from 0 to 1/3

This means it would be (7/3)/(1/3)

This equals 7 as when you divide fractions, the second fraction goes to its reciprocal and you multiply

7/3 * 3/1

You can eliminate both 3 leaving you with 7/1 which is 7

Given:

AB is the diameter of a circle.

m∠CAB = 26°

To find:

The measure of m∠CBA.

Solution:

Angle formed in the diameter of a circle is always 90°.

⇒ m∠ACB = 90°

In triangle ACB,

Sum of the angles in the triangle = 180°

m∠CAB + m∠ACB + m∠CBA = 180°

26° + 90° + m∠CBA = 180°

116° + m∠CBA = 180°

Subtract 116° from both sides.

116° + m∠CBA - 116° = 180° - 116°

m∠CBA = 64°

The measure of m∠CBA is 64°.

The size of angle CBA is 128 degrees.

To find the size of CBA, we can use the fact that angles in a triangle add up to 180 degrees. Since AB is a diameter, it divides the circle into two semicircles, and angle CAB is an inscribed angle that is half the measure of the central angle.

Therefore, m(CAB) = 26 degrees, and m(CBO) = 2 * 26 = 52 degrees. Since angle CBA is an exterior angle of triangle CBO, it is equal to the sum of the remote interior angles, which is 180 - 52 = 128 degrees.

So, the size of CBA is 128 degrees. The answer is option D. 74.

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Answer: 2m+5=15

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2x+5=15 can represent this situation. 15-5=10... 10/2= 5

Answer:

Step-by-step explanation:

$

1050

Explanation:

To calculate interest the formula is :  

P

r

t

=

i

where P= Principle, r=rate as a decimal, t+ time in years.

(assuming simple interest)

P

r

t

=

i

5000

⋅

0.07

⋅

3

=

i

i

=

$

1050

Answer:

1050

Step-by-step explanation:

Based on the circle shown above, the name of segment AC include the following: C. diameter.

In Mathematics and Euclidean Geometry, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point.

Generally speaking, the diameter of a circle simply refers to a straight line that passes through the middle (center) to the other end of the circle, thereby, measuring the distance from one end point to another.

This ultimately implies that, the diameter of a circle is double the length of the radius of a circle;

Diameter = 2 × radius

Answer:

13 Millilitres.

Step-by-step explanation:

Yoku uses 2ml to cover [tex]50cm^2[/tex] of his skin.

He wants to know how many millilitres of sunscreen he will need to cover [tex]325cm^2[/tex] of his body.

If Yoku covers [tex]50cm^2[/tex] of his skin will 2ml

He will cover [tex]1cm^2[/tex] of his skin with [tex]\frac{2}{50}ml[/tex] of sunscreen.

Therefore:

To cover [tex]325cm^2[/tex] of his body, he will use:

[tex]\frac{2}{50} X 325 ml\\=13ml[/tex]

he would require 13 Millilitres.

Answer:

13 is the answer!!!

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Formula for finding a circumference = [tex]2\pi r[/tex]

You are given the circumference which is [tex]22\pi[/tex]

[tex]22\pi =2\pi r[/tex]

So you divide both sides by [tex]2\pi[/tex] and [tex]\pi[/tex] cancels out

[tex]\frac{22\pi }{2\pi } =\frac{2\pi }{2\pi } *r[/tex]

r=11

Answer:

11

Step-by-step explanation:

Answer:

1st one and the third one

Step-by-step explanation:

25(0)=25

25+0=25

Answer:

25(1) = 25

25 + 0 = 25

those are the correct answers

Answer:

27Pi cm2

Step-by-step explanation:

took the test

27π square centimeters(Volume) of metal was used to make the holder.

The amount of space within a cylinder is its volume. You can find it by dividing the base area by the height.

Given that, a candle holder of metal whose radius is 3 cm and height is also 3 cm. Since the given object is a cylinder. Hence,

volume of candle holder = Area of base * height

the volume of candle holder = π 3² * 3 = 27π

Therefore, the metal used in the candle holder is 27π square centimeters (Volume).

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Answer:

11m.

Step-by-step explanation:

500cm=5m

6+5=11m

Answer:

0

Step-by-step explanation:

1/3(21)-1-1/2(12)

7-1-6=6-6=0

Answer:

This is true because negative and positive is positive that why there is a addition sign in the middle and positive 40 becomes negative

Step-by-step explanation:

Answer:

1. 26.6

2. 12.3

3. 23.3

4. 10.9

Step-by-step explanation:

1. tan(31) = 16/x

x = 16/tan(31)

x = 26.62847172

2. sin(43) = x/18

x = 18sin(43)

x = 12.27597048

3. cos(53) = 14/x

x = 14/cos(53)

x = 23.26296198

4. cos(33) = x/13

x = 13cos(33)

x = 10.90271738

Answer:

1. 26.6 units

2. 12.3 units

3. 23.3 units

4. 10.9 units

Step-by-step explanation:

1. We have the opposite and adjacent sides here for angle 31 degrees. So we need to use tangent, which is opposite / adjacent:

[tex]tan(31)=16/x[/tex]

[tex]x=16/(tan(31))[/tex] ≈ 26.6 units

2. We have the opposite and hypotenuse sides here for angle 43 degrees. So we need to use sine, which is opposite / hypotenuse:

[tex]sin(43)=x/18[/tex]

[tex]x=18*sin(43)[/tex] ≈ 12.3 units

3. We have the adjacent and hypotenuse sides here for angle 53 degrees. So we need to use cosine, which is adjacent / hypotenuse:

[tex]cos(53)=14/x[/tex]

[tex]x=14/(cos(53))[/tex] ≈ 23.3 units

4. We have the adjacent and hypotenuse sides here for angle 33 degrees. So we need to use cosine, which is adjacent / hypotenuse:

[tex]cos(33)=x/13[/tex]

[tex]x=13*cos(33)[/tex] ≈ 10.9 units

Hope this helps!

Answer:

Sue's percentage profit = 9% on each tin of green paint she sells.

Step-by-step explanation:

Litres of green paints mixed = 50 litres

Ratio of litres of yellow paint and litres of blue paint = 1:4.

To determine the litres of yellow paint, we say:

[tex]yellow \: paint = \frac{1}{4} \times 50 = 10 \: litres[/tex]

To determine the litres of blue paint, we say:

[tex]blue \: paint = \frac{4}{5} \times 50 = 40 \: litres[/tex]

Since yellow paint is sold in 5 litres per tin and each tin cost £38; she has 10 litres of yellow paint in all. That implies that she has 10/5 = 2 tin of yellow paint. If one tin cost £38; 2 tin cost 2 × £38 = £76

Similarly,

Since blue paint is sold in 10 litres per tin and each tin cost £58; she has 40 litres of blue paint in all. That implies that she has 40/10 = 4 tin of blue paint. If one tin cost £58; 4 tin cost 4 × £58 = £232

Total cost of yellow and blue paints = £232 + £76

= £308

Since Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin and she has 50 litres in all; we say: 50/10 litres = 5 tins = 5 × £89.32 = £446.60.

Thus, selling price of the green paint = £446.60

[tex]profit \: \% = \frac{selling \: price - cost \: price}{cost \: price} \times \frac{100}{1} [/tex]

[tex]profit \: \% = \frac{446.60 - 308}{308} \times \frac{100}{1} [/tex]

[tex]profit \: \% = \frac{138.60}{308} \times \frac{100}{1} [/tex]

[tex]profit \: \% = 0.45 \times 100[/tex]

[tex]profit \: \% = 45\%[/tex]

Sue's percentage profit for selling all the tins of green paint is 45%, having sold 5 tins. Therefore, Sue's percentage profit for selling each of the paint will be:

[tex]profit \: \% \: on \: each \: green \: tin = \frac{45}{5} = 9\%[/tex]

Hence, Sue's percentage profit for selling each tin of green paint is 9%.

Proof

9% × 5 tins of green paint = 45%

Final answer:

Sue's percentage profit on each tin of green paint she sells is approximately 44.94%. This is calculated by finding the total cost of inputs, subtracting from the total sales revenue, and then finding the profit ratio to the cost.

Explanation:

To calculate Sue's percentage profit on each tin of green paint she sells, we need to first determine the cost of producing the green paint and then subtract that cost from the selling price. The green paint is produced in a ratio of 1:4 yellow to blue paint, making 50 litres total. Therefore, Sue uses 10 litres of yellow paint and 40 litres of blue paint to make 50 litres of green paint.

Yellow paint costs £38 for a 5-litre tin, so two tins are needed (costing £76 total) to get the required 10 litres. Blue paint costs £58 for a 10-litre tin, so four tins are needed (costing £232 total) to get 40 litres. This brings the total cost to £308 for 50 litres of green paint.

Sue sells her green paint at £89.32 per 10-litre tin. Therefore, for 50 litres, she gets 5 tins x £89.32 = £446.60.

The profit Sue makes is the selling price minus the cost price, which is £446.60 - £308 = £138.60. To find the percentage profit per tin, divide the profit by the cost and multiply by 100:

(£138.60 / £308) x 100 = 44.94%

Therefore, Sue's percentage profit on each tin of green paint she sells is approximately 44.94%.

Answer: The height of the tank is 9.02 feet

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cylinder = π radius² x height

Replacing with values given:

7252 = 3.14 ( 16 )² h

Solving for h (height)

7252 / 3.14(16)² =h

7252 /3.14 (256) =h

7252 / 803.84 = h

9.02 =h

The height of the tank is 9.02 feet

Feel free to ask for more if needed or if you did not understand something.

Answer:

9.02

Step-by-step explanation:

Answer:

2/7

Step-by-step explanation:

Each time you play, you get 1 number. Since 8/28 numbers win, you have a 8/28 chance to win if you buy one ticket. 8/28 = 2/7

I mean, you can divide the counters by the range 2 - 38.

I only managed to find out that 38 ÷ 2 = 19.

And 38 ÷ 19 = 2.

It says that there are more than 10 counters in each bag.

So 2 bags is the most liable option.

There are 2 bags and 19 counters in each bag.

Answer:

2 bags, 19 counters.

Step-by-step explanation:

This question is looking for factors of 38 with counters being a factor greater ten and the number of bags being the factor that multiplies the counters to get 38. First, find the factors of 38.

1 x 38 = 38

2 x 19 = 38

Since the problem says bags with an s, we can know that there has to be more than one bag. That leaves us with 2 x 19.

An expression for the profit of the company is 26x - 0.0002x^2 - 120,000.

To find the expression for the profit of a company, we need to subtract the cost from the revenue.

The cost of the company is given by the expression 14x + 120,000, where x represents the quantity of the product being produced or sold.

The revenue of the company is given by the expression 40x - 0.0002x^2, where x represents the quantity of the product being produced or sold.

To find the profit, we subtract the cost from the revenue:

Profit = Revenue - Cost

Profit = (40x - 0.0002x^2) - (14x + 120,000)

To simplify the expression, we distribute the negative sign:

Profit = 40x - 0.0002x^2 - 14x - 120,000

Combining like terms:

Profit = (40x - 14x) - 0.0002x^2 - 120,000

Simplifying further:

Profit = 26x - 0.0002x^2 - 120,000

Therefore, an expression for the profit of the company is 26x - 0.0002x^2 - 120,000.

Final answer:

The profit of a company is the difference between its total revenue and costs, and can be calculated using the formula P = R - (14x - 0.0002x²), where P is profit, R is revenue, and x is the number of units.

Explanation:

To calculate the expression for the profit of the company, we need to find the difference between the total revenue and the total cost.

Given the cost can be modeled by 14x - 0.0002x2, and assuming the revenue is R, the profit P can be represented as:

P = R - (14x - 0.0002x²)

If we are given a specific value for the revenue, we would substitute it in place of R to find an explicit expression for P. For instance, if the revenue is $200,000, the profit formula would be:

P = $200,000 - (14x - 0.0002x²)

It's important to note that the profit decreases as the cost increases, and when costs exceed revenue, the company experiences a loss.

The volume of the cone, calculated using the given slant length and diameter, is approximately 18.84 cubic units, therefore the correct answer is B. 18.84 cubic units.

The subject of this question is the volume of a cone. In order to calculate the volume of a cone, you need to use the formula: V = 1/3πr²h. However, in this case, you are given the slant length and the diameter. First, we need to find the radius (r) and the height (h) of the cone. The radius would be half the diameter, so r = 4/2 = 2. Then, from the given slant length (s) and radius (r), we can find the height by using Pythagoras' theorem: h = sqrt(s² - r²) = sqrt(5² - 2²) = sqrt(21). Now we can substitute r and h into the volume formula: V = 1/3*3.14*2²*sqrt(21) which is approximately 18.84 cubic units. So the answer is option B.18.84 cubic units.

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Answer: 205 buttons

Step-by-step explanation:

Garcia has 2 button collections. One has 321 buttons in it. The other has 704 buttons. The total button collection will be:

= 321 + 704 = 1025

Since she wants to divide it equally among 5 friends, we divide 1025 by 5. This will be:

= 1025 ÷ 5

= 205

Each friend will get 205 buttons.

Answer:

Each friend will receive 205 buttons

Step-by-step explanation:

In this question, we are tasked with calculating the number of buttons each of 5 Garcia's friend will receive

Firstly, we will need to find the total number of buttons available

That would be 321 + 704 = 1025 buttons

Now to find the distribution per friend, we simply divider the total by 5

That would be 1025 buttons ÷ 5 = 205 buttons

This means that each of the five friends will receive 205 buttons each

Answer:

Shapes 1 and 3 are congruent

Step-by-step explanation:

The only thing different between them is that the first one is tilted to look different.

Answer:

the 1st and 3rd one.

Step-by-step explanation:

the first 3 are similar in shape but, the 1st and 3rd one are congruent because they have the same size and shape.

Answer:

the answer is 1,555.2

Step-by-step explanation:

Answer:1.5552x10 cubed

Step-by-step explanation:

Answer:

108 ft2 is the area of the other rectangle

Step-by-step explanation:

If the first length is 3 and the second one is 6 if you find the width of the first rectangle, it has to be double like the length and 18*6 = 108

Answer:

108

Step-by-step explanation:

the scale is 2x

27/3 = 9

9 x 2 is 18

18 x 6 is 108

Answer:

it is many triangles

Step-by-step explanation:

Answer:

0-9 = 4

10-19 = 3

20-29 = 9

30-39 = 5

Step-by-step explanation:

I just did it right now!

The correct number into the boxes to complete the frequency table are,

Interval    Frequency

0-9                4

10-19              3

20-29            9

30-39             5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Wendy kept track of the number of text messages she sent each day for three weeks.

Now, We can formulate;

Interval    Frequency

0-9                4

10-19              3

20-29            9

30-39             5

Thus, The correct number into the boxes to complete the frequency table are,

Interval    Frequency

0-9                4

10-19              3

20-29            9

30-39             5

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Answer:

168miles

Corrected question;

12. Raymond is reading a road map. On the map, 1/4- inch represents 12 miles. Approximately

how many miles apart are two cities that are 3 1/2 - inches apart on Raymond's map?

F. 12

G. 48

H. 96

J. 132

K .168

Step-by-step explanation:

Given;

1/4 inch = 12 miles

3 1/2 = 7/2 = 14/4 inch

number of 1/4 inch in 14/4 inch is;

14/4 ÷ 1/4 = 14

14/4 inch = 12×14 miles = 168miles

Answer:

the base length of the triangle is 4 units, u can count that. and the height of triangle is 2 units, thats the dotted line one. and the equation of triangle area is (length x height) divided by 2so in this case it'll be (4x2) /2=4 square units.

Step-by-step explanation:

Answer:

The base is 7 and the height is 9

Step-by-step explanation:

vertices Q(-1,1), R(6, 1), S(6-8), and T(-1,-8)

If you look at the coordinates, you will notice that Q and R lie on line y = 1

and S and T lie on the line y = -8

so  line QR || line ST

that means the height of this rectangle is  |1 - -8| = 9

the  length must be  from point Q to R

length = |-1 - 6| = 7

dimension is  7 by 9