Nathan needs some paint for his bedroom. He finds two cans of white paint, four cans of green paint and three cans of pink paint in his garage. If he chooses a can of paint without looking at the color, what is the chance that he will paint his bedroom pink

Answer:

-5x - 3x = 16

-8x = 16

x = -2

y = x

Step-by-step explanation:

Answer:

(-2, -2)

Step-by-step explanation:

Make use of the 2nd equation to eliminate x or y in the 1st equation:

-5x - 3(x) = 16

Then -8x = 16, and x = -2.  Since we are told that y = x, y = -2.

The solution is (-2, -2).

Final answer:

To find the probability that the sample mean is between two hours and three hours, calculate the z-scores and use the z-table to find the probability.

Explanation:

To find the probability that the sample mean is between two hours and three hours, we need to calculate the z-scores corresponding to these values and use the z-table to find the probability.

First, we calculate the z-score for two hours:

z = (2 - 2.5) / (0.25 / sqrt(60)) = -3.16

Next, we calculate the z-score for three hours:

z = (3 - 2.5) / (0.25 / sqrt(60)) = 3.16

Using the z-table, we find that the probability of getting a z-score between -3.16 and 3.16 is approximately 0.9986. Therefore, the probability that the sample mean is between two hours and three hours is approximately 0.9986.

]

Answer:

6x-76

Step-by-step explanation:

If you graph it out, you'll realize it makes a line that cuts the y-intercept at -76, thus the last value. The slope also has a gradient of 6, thus the coeffecient of x.

Final answer:

The slope of the line through the points given is 6, calculated using the slope formula with the rise over run between the two points.

Explanation:

The slope of a line is calculated by finding the ratio of the vertical change (the rise) to the horizontal change (the run) between two points on the line. Using the coordinates provided (12, -4) and (15, 14), we can apply the slope formula slope (m) = (y_2 - y_1) / (x_2 - x_1). Plugging in the values gives us (14 - (-4)) / (15 - 12) = 18 / 3 = 6. Therefore, the slope of the line that contains these points is 6.

The  volume of the cylinder is 452.16 cubic centimeter

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We have to find the volume of cylinder

Radius of cylinder is 4cm and height is 9cm

The formula for volume of cylinder = πr²h

Plug in the values of r and h

Volume = π(4)²(9)

= π×16×9

=3.14×16×9

=452.16 cubic centimeter

Hence, the  volume of the cylinder is 452.16 cubic centimeter

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The approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm is 452.16 cm³, using the formula V = πr²h with π approximated as 3.14.

Calculating the Volume of a Cylinder

To find the approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm using 3.14 for π, you can use the formula for the volume of a cylinder, which is V = πr²h. In this case, V = 3.14 × (4 cm)² × 9 cm.

First, calculate the area of the base (which is a circle) by squaring the radius and multiplying by π: Area = π × r² = 3.14 × 4² = 3.14 × 16 = 50.24 cm². Next, multiply the area of the base by the height of the cylinder to get the volume: Volume = Area × Height = 50.24 cm² × 9 cm = 452.16 cm³.

Therefore, the approximate volume of the cylinder is 452.16 cm³.

Answer:

Compound Interest Formula Solved For Rate:

log (1 + rate) = {log(total) -log(Principal)} ÷ Years

log (1 + rate) = {log(5,800) -log(5,000)} ÷ 5

log (1 + rate) = [3.7634279936 -3.6989700043] / 5

log (1 + rate) = 0.0644579893  / 5

log (1 + rate) = 0.0128915979

Then we raise 10 to the power of 0.0128915979  which equals

1.0301289629  = 1 + rate

Therefore, rate = .0301289629  and we multiply by 100 to make a percentage:

3.01289629 %

Source: https://1728.org/compint2.htm

https://1728.org/compint.htm

Step-by-step explanation:

Using the compound interest formula and the provided values, the interest rate for Mr Tan's investment is calculated to be approximately 3.02%.

The subject problem belongs to the topic of Compound Interest in mathematics. The formula used for compound interest is A = P (1 + r/n)^(nt), where A represents the total amount received, P represents the principal (initial investment amount), r represents the rate of interest, n represents the number of times interest is compounded per time period, and t represents the time period.

In this problem, Mr Tan's initial investment, P, is $5000. The total amount, A, he received after 5 years is $5800. The interest is compounded annually meaning that n is 1. We rearrange the compound interest formula to solve for the interest rate: r = [(A/P)^(1/nt) - 1]n .

Using Mr Tan's values, the calculation becomes: r = [(5800/5000)^(1/5) - 1]*1. Thus, the interest rate is approximately 0.0302 or 3.02%.

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1200 ml  of water needs to be added to lower it to a 2% solution.

Step-by-step explanation:

Given that,

A scientist has 400ml of a 8% solution.

you need to find how water is required to lower the 400 ml to 2% solution.

Let 'x' be the amount of water added to lower it 2% solution.

The formula is given by,

volume of the liquid × % of solution = volume of the new liquid × new %

This can be denoted in chemical relationship ⇒ c₁v₁=c₂v₂ where c is concentration and v is volume .

Now, to find the total volume of new liquid in ml :

400 ml = v₁

0.08= c₁  

0.02=c₂

v₂=?

400 × 0.08 =v₂ × 0.02

v₂=1600 ml

To find the x value :

Amount to be added = volume of new liquid - volume of liquid before.

⇒ x =1600-400

⇒ x =1200 ml

∴ 1200 ml of water needs to be added to lower it to a 2% solution.

Step-by-step explanation:

It is a right angled triangle so with reference angle 37°

hypotenuse (b) = 10

perpendicular (p) = x

So

tan 37° = p/ b

0.75 = x / 10

x= 0.75/10

Therefore x = 0.075

Hope it will help you :))

Answer:

0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.

Step-by-step explanation:

We are given the following information:

We treat adult using smartphones in meetings or classes as a success.

P(Adult using smartphone) = 46% = 0.46

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 = 9

We have to evaluate:

[tex]P(x = 3)\\\\= \binom{9}{3}(0.46)^3(1-0.46)^6\\\\= 0.2027[/tex]

0.2027 is the probability that exactly 3 out of 9 adults use their smartphones in meetings or classes.

Final answer:

To find the probability that exactly 3 of the 9 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

Explanation:

To find the probability that exactly 3 of the 9 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula. The binomial probability formula is given by:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

where:

P(X=k) is the probability of getting exactly k successes

C(n,k) is the combination formula

p is the probability of success (46% in this case)

n is the total number of trials (9 in this case)

Plugging in the values, we get:

P(X=3) = C(9,3) * (0.46)^3 * (1-0.46)^(9-3)

P(X=3) = 84 * (0.46)^3 * (0.54)^6

P(X=3) = 0.299 (rounded to three decimal places)

Answer:

(4+x)(5+x)(5+x) = 700

x^3 + 14x^2 + 65x + 100 = 700

x^3 + 14x^2 + 65x - 600 = 0

x = 4.225

rounding = 4.23

Step-by-step explanation:

Answer:

D. [0,pi/2]

Step-by-step explanation:

when Ф = 0 in radian

r²=  4cos (2(0))

r² = 4 * 1

r² = 4

∴ r = √4 = 2

r = 2.

when Ф = π/2 in radian

r²=  4cos (2(π/2))

r² = 4 * -1

r² = -4

∴ r = 0

The value of n in given proportion is 16

Solution:

We have to find the value of "n" in the proportion

Given proportion is:

[tex]\frac{n}{28} = \frac{4}{7}[/tex]

We can solve the above proportion by cross-multiplying

Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction

Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction

Set the two products equal to each other

Solve for the variable

[tex]->\frac{n}{28} = \frac{4}{7}[/tex]

[tex]-> 7 * n = 4 * 28[/tex]

[tex]-> n = \frac{4 * 28}{7}[/tex]

[tex]-> n = 4 * 4 = 16[/tex]

Thus the value of n in given proportion is 16

Answer:

the value of n in given proportion is 16

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

1 + 4x = -5 + 7x

Subtract 4x from each side

1 + 4x-4x = -5 + 7x-4x

1 = -5+3x

Add 5 to each side

1+5 = -5+5+3x

6 = 3x

Divide each side by 3

6/3 = 3x/3

2 =x

Answer:

About 11.31

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + b^2 = 12^2

16    + b^2 = 144

-16                  -16

b^2 = 128

Take the square root of both sides

b= approximately 11.31

Answer:

1:2

 2:1

2:3

Step-by-step explanation:

3:6

Divide each side by 3

3/3: 6/3       1:2

10:5

Divide each side by 5

10/5 : 5/5      2:1

16:24

Divide each side by 8

16/8: 24/8     2:3

Answer:

Step-by-step explanation:

Let the number of allowable guess be x.

The difference between allowable guess and 645 must not exceed 20.

So, either,

|645 - x| ≤ 20

Or

|x - 645| ≤ 20

where that sign represents the absolute sign.

Hope this Helps!!!

Answer:

| x - 645 | = 20

665

Step-by-step explanation:

We have to guess the amount of beans in a jar to be within 20 of the actual number.

Therefore, the total has to be equal to 20.

We know that the equation required to calculate the minimum and maximum quantity of beans that will win the contest will be:

| x - 645 | = 20

But as we want is the maximum, we break the absolute value and assume "+"

Thus:

x - 645 = 20

fixed for x:

x = 20 + 645

x = 665

The maximum guess you could win is 665

Answer: 7/25 or 0.28

Step-by-step explanation:

Given that 7/15 play a sport and 3/5 play a musical instrument.

The probability that a NCVPS student play a sport AND a musical instrument means multiplication of the two probabilities

7/15 × 3/5 = 21/75 = 7/25

Answer:

Correct option: (d) 7.

Step-by-step explanation:

Let the number be denoted by x.

The original fraction is: [tex]\frac{29}{62}[/tex]

Add x to the numerator, i.e. 29 and subtract 2x from the denominator, i.e. 62.

The new fraction is: [tex]\frac{29+x}{62-2x}[/tex]

Now equate the new fraction to [tex]\frac{3}{4}[/tex] and solve for x as follows:

     [tex]\frac{29+x}{62-2x}=\frac{3}{4}[/tex]

[tex]4(29+x)=3(62-2x)\\116+4x=186-6x\\4x+6x=186-116\\10x=70\\x=7[/tex]

The value of x is 7.

Thus, the correct option is (d).

The total number of possible New York license plates is 17,576,000.

The number of different license plates possible for a standard configuration in New York, where a license plate is composed of 3 digits followed by 3 letters, can be determined through combinatorial math.

Step-by-Step Solution:

Answer:

14 m

Step-by-step explanation:

We are given that

Height of tree=AB=12 m

[tex]\theta=40^{\circ}[/tex]

We have to find the distance from the spotlight to the base of the tree.

We know that

[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]

[tex]\frac{AB}{BC}=tan40[/tex]

[tex]\frac{12}{BC}=tan40[/tex]

[tex]BC=\frac{12}{tan40}=14.3\approx 14[/tex]

Hence, the distance from the spotlight to the base of the tree=14 m

Answer:

B

Step-by-step explanation:

-The balanced chemical reaction of oxygen and water is written as:

[tex]2H_2_{(g)}+O_2_{(g)}->2H_2O_{(l)}[/tex]

-You notice that 2 moles of hydrogen gas reacts with one mole of oxygen gas to form 2 moles of water

-Hence, the correct choice is B

Final answer:

The area of a 3in by 3in square is calculated by squaring the side length. The area is 9 square inches.

Explanation:

The area of a 3in by 3in square can be calculated by multiplying the length of one side by the length of another side since the sides are equal in a square. In this case, both sides measure 3 inches.

The formula for the area of a square is:

Area = side × side

Applying the formula for our 3in by 3in square:

Area = 3in × 3in = 9 square inches

This straightforward calculation represents how the surface area of a square object changes when the sides of the square are altered. When the sides of a square are scaled down by a fraction, the area changes by the square of that fraction (e.g., scaling down by 3/4 leads to an area that is 9/16 of the original).

Answer:21y^4= B*7y^3

B=(21y^4)/(7y^3)

B=3y

i think this is correct

Answer:

millimeter

Step-by-step explanation:

1/1000

Answer:

fraction which has a terminating decimal as its decimal expansion is:

1/5

Step-by-step explanation:

We are given 4 fractions:

1/3 , 1/5 , 1/7 and 1/9

We have to find which fraction has terminating decimal.

1/3 = 0.33333...

1/5 = 0.2

1/7 = 0.142857142857...

1/9 =0.11111.....

Hence, fraction which has a terminating decimal as its decimal expansion is:

1/5

Final answer:

A fraction will have a terminating decimal if its denominator is a power of 2, a power of 5, or a combination of both since the base of our number system is 10. Examples like 1/8 and 5/16 have terminating decimals because their denominators are powers of 2.

Explanation:

A fraction will have a terminating decimal expansion if its denominator can be written in the form 2n5m, where n and m are nonnegative integers. This is because the base of our number system is 10, which is 2×5. So any fraction with a denominator that is a factor of a power of 10 will have a terminating decimal expansion.

Example:

In contrast, a fraction like 1/3 does not have a prime factorization that matches the form 2n5m and therefore has a non-terminating decimal expansion (0.333...).

Answer:

P(Q or C) = 0.25

Step-by-step explanation:

We are given the following in the question:

Letters:

A, C, Q, U, A, I, N, T, A, N, C, E

Total number of observations, n  = 12

We have to find the probability that a randomly selected letter is Q or C.

Formula:

[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]

P(Q or C) =

[tex]=\dfrac{\text{n(Q or C)}}{n} = \dfrac{3}{12} =0.25 = 25\%[/tex]

Thus,

P(Q or C) = 0.25

Answer:

x2-x1/y2-y1

-2--2/3-9=-2+2/3-9

=0/-3

Ok i'm so sorry but if you could answer this for me? nobody else will! >0<

Enter the equation of the circle described below.

Center (-3, 0), radius /5

Answer:(X+3)^2 +y^2 =25

This is the correct answer, i just found it out

Answer:

= 1700 :)

Step-by-step explanation:

-multiply all the sides,

-add them,

- then double the answer (or times it  by 2):

1) 30 times 20 = 600

30 times 5= 150

20 times 5 =100

2) Add them:

600+150+100 = 850

then times 850 by 2

850 times 2 = 1700

Hope that helped :)

Answer:

Guys for this one the 30, 20, 5 is 1700

Step-by-step explanation:

Answer:

2x

Step-by-step explanation:

Cost of x articles at 2 dollars each = 2x