Gary has 9 quarts of paint. If He Uses Half How Much gallons will he have.

A. The gauge is showing 3/8 fraction of the fuel tank and B. 30 Liters must be added o the fuel tank to fill it.

A) Each division in the Fuel gauge represent the fraction ,

So,

To find what fraction the gauge shows multiply 6 by 1/16.

= 6 x 1/16

= 6/16

= 3/8

B) We know that,

The tank has 3/8 of its total capacity.

So,

to fill the tank must be added 1-3/8 Liters.

= 5/8 L

Therefore,

Multiplying 5/8 by 48

= 5/8 x 48

= 30 Liters.

So, 30 Liters of fuel must be added to the tank to completely fill it.

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Complete question - (a) What fraction does the Gauge show?

(b) The fuel tank holds 48 litres when it is full. How many Litres must be added to fill the tank?

The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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List of conditions for creating confidence interval when there are two means with standard deviation known independent samples, normal distribution, known standard deviation, random sampling and adequate sample size,

When creating a confidence interval for the difference between two means with known standard deviations, the following conditions should be met:
1. Independent samples: The two samples should be independent of each other and not paired in any way.
2. Normal distribution: The populations from which the samples are drawn should be approximately normally distributed. This condition can be relaxed if the sample sizes are large, as the Central Limit Theorem will apply.
3. Known standard deviations: The population standard deviations should be known for both samples. This is important because it allows for accurate calculation of the standard error and confidence interval.
4. Random sampling: The samples should be collected through a random sampling process to ensure that they are representative of the populations.
5. Adequate sample size: The sample sizes should be large enough to provide meaningful results. As a general guideline, each sample should have at least 30 observations.
By meeting these conditions, you can calculate the confidence interval for the difference between the two means using a formula involving the standard deviations and sample sizes. This confidence interval will provide an estimate of the true difference between the population means, along with a measure of the uncertainty surrounding that estimate.

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Answer:

48

Step-by-step explanation:

1 to 4 = 12 to ?

multiply the small one by 4 to get the bigger one

Step-by-step explanation:

1:4

12:x

1=4

12=x

cross multiply

x=4×12

x=48

Answer:

6715

Step-by-step explanation:

I hope this helps, :)

The ascending order of the given numbers is  2×\(10^{-4}\) <0.004< 4×\(10^{-2}\) < 0.042 < 0.24

The first number = 0.24

The second number = 4×\(10^{-2}\)

The second number is the form of scientific notation. To compare the numbers, all the numbers should be in same form. So we have to convert the scientific notation to the decimal form

4×\(10^{-2}\) = 0.04

The third number = 0.042

Third number is decimal form

The fourth number = 2×\(10^{-4}\)

Convert the scientific notation to the decimal form

2×\(10^{-4}\) = 0.0002

The fifth number = 0.004

The order of the numbers from least to greatest

= 2×\(10^{-4}\) <0.004< 4×\(10^{-2}\) < 0.042 < 0.24

Hence, the order of the given numbers from least to greatest is 2×\(10^{-4}\) <0.004< 4×\(10^{-2}\) < 0.042 < 0.24

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∑ Hey,  shanellmccullough ⊃

Answer:

(a) Width of the garden : 64 m

(b) Length of the window: 95 cm

Step-by-step explanation:

Given:

(a) The perimeter of a rectangular garden is 306 m. If the length of the garden is 89 m, what is its width?

(b) The area of a rectangular window is 5130 cm². If the width of the window is 54 cm, what is its length?

Solve:

(a) The perimeter of a rectangular garden is 306 m. If the length of the garden is 89 m, what is its width?

Formula for perimeter: P = (L + W) × 2

Which;

P = Perimeter

L = Length

W = Width

Which also could be written as:

L + L + W + W = P

Hence, since it given that;

306 = P and L = 89

Then

We know that ;

89L + 89L + W + W = 306

So we can add 89 + 89 or 89 × 2

which is 178

Now we know that;

178 + 2w = 306

Solving for 2w:

178 + 2w = 306

178-178 + 2w = 306 - 178

2w = 128

W = 64

Hence, width is 64.

Check Answer:

64 × 2 + 89 × 2 =  306

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

(b) The area of a rectangular window is 5130 cm². If the width of the window is 54 cm, what is its length?

Formula for area: A = Lw

Which;

A = Area

L = Length

W = Width

So, since we know the width we can just do 5130/54 to find Length

5130/54 = 95

Hence, the length of the window is 95 cm.

Check Answer :

A = Lw

A = 95 × 54

A = 5130 cm²

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

xcookiex12

8/18/2022

We need to roll the die at least 5 times to ensure that the probability is at least 2/3 that at least one 2 will appear.

To calculate the probability of rolling a 2 on a fair six-sided die, we first need to know the probability of rolling any number on a single roll, which is 1/6.

Since each roll of the die is independent of the previous roll, we can use the formula for the probability of independent events occurring together to find the probability of rolling a 2 at least once in a certain number of rolls.

Let's call the probability of rolling a 2 at least once in n rolls "P(n)". We can find P(n) using the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. So, the probability of not rolling a 2 in n rolls is (5/6)^n, since there are 5 possible outcomes (1, 3, 4, 5, or 6) on each roll that is not 2. Therefore, we can write:

P(n) = 1 - (5/6)^n

We want to find the minimum number of rolls needed to ensure that P(n) is at least 2/3, or 0.667. In other words, we want to find the smallest value of n that satisfies the inequality:

P(n) ≥ 2/3

Substituting the formula for P(n), we get:

1 - (5/6)^n ≥ 2/3

By multiplying both sides by -1 and rearranging, we get:

(5/6)^n ≤ 1/3

Taking the natural logarithm of both sides, we get:

n ln(5/6) ≤ ln(1/3)

Dividing both sides by ln(5/6), we get:

n ≥ ln(1/3) / ln(5/6)

Using a calculator, we find that:

n ≥ 4.81

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To convert percent to a number divide it by 100

Then to convert 838% to a number divide it by 100

To simplify divide up and down by 2

The improper fraction is 419/50 in the simplest form

The value of x in the given polygon is 71°

A closed, flat polygon is a geometry comprised of just straight lines.

The exterior angle of a polygon is the angle created when a polygonal side is extended.

A polygon's outside angles add up to 360°.

The sum of external angles in a polygon is 360°

In the given questions all the angles, whose values are given, are external angle.

2x-46° + 2x-50° + 2x-33° + 32° + 31° = 360°

6x - 129° + 63° = 360°

6x - 66° = 360°

6x = 360° + 66°

6x = 426°

x = 426°/6

x = 71°

The value of x in the given polygon is 71°

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Answer:

-3 < x <= 3

Step-by-step explanation:

draw it on a number line to check

Answer:

-3>x\(\leq \\\)3

Step-by-step explanation:

> is the greater than

< is the less than

hope this helped have a great day

Answer:

Graph (0,4), graph (6,7) then connect in a straight line.

Step-by-step explanation:

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

6j + 6r :)))))))))))))))))

Answer:

6j + 6r

Step-by-step explanation:

Answer:

\(4^{6}\) = 4096

Step-by-step explanation:

The rule is \((a^{b})^c\) = \(a^{bc}\).

So you can just multiply the exponents together.

-3* -2 = 6

So the answer is \(4^{6}\) which is 4096. I don't know how your professor wants you to write the answer.

Answer:

(6/5) mph

Step-by-step explanation:

Answer:

8 ≤ x

Step-by-step explanation:

6(2 − 6x) ≤ 4 − 35x

Expand bracket;

12 - 36x ≤ 4 − 35x

Add 36x to both sides to get;

12 ≤ 4 + x

Subtract 4 from both sides to get;

8 ≤ x

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to solve the inequality 6(2-6x)≤4-35x.

\(\triangle~\fbox{\bf{KEY:}}\star\)

First, we can use the distributive property and distribute 6:

\(\star\large\pmb{12-36x\leq4-35x}\)

Now, add 35x to both sides:

\(\star\large\pmb{12-x\leq 4}\)

And now, subtract 12 from both sides:

\(\star\large\pmb{-x\leq-8}\)

Divide both sides by -1 and watch what happens:

\(\star\large\pmb{x\geq 8}\)

Have you noticed that the inequality sign changed from "less than" to "greater than"?

Well, that happened because we divided both sides by a negative number, -1.

Thus, \(\star~\large\pmb{x\geq 8}\)

Hope this helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

\(\pmb{M^ar_ib^el\:P^eri}\)

The component form of the vector that translates A to A' is (11, -17)

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

In translation, the shape of the figure does not change but its size may change.

Other transformation processes are reflection and rotation.

The component form of the vector is governed by the rule; A' - A

so we subtract corresponding x- coordinates and corresponding y- coordinates

A' - A = (7, -9) - (-4, 8)

       = ( 7 - - 4, -9 - 8)

       -= ( 11, -17)

In conclusion, the vector that translates A to A' is ( 11, -17 )

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Answer:

i say d

Step-by-step explanation:

The probability of event d is 0.58.

d, e, and f are mutually exclusive and exhaustive events.Moreover, P(e) = 0.17 and P(f) = 0.25.

The probability of event d, we need to use the law of probability as follows:

P(d) = 1 - P(e) - P(f)

Since events d, e, and f are mutually exclusive and exhaustive, the sum of their probabilities is 1.

So, P(d) + P(e) + P(f) = 1P(e) = 0.17 and P(f) = 0.25

Hence, P(d) = 1 - P(e) - P(f) = 1 - 0.17 - 0.25= 0.58

Therefore, the probability of event d is 0.58.

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Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.

The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square

The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.

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Answer:

the tip would be $11.83

Step-by-step explanation:

hope that helps

On solving the provided question we can say that  the least to greatest : \(14/9 , sqrt 7, sqrt 13, sqrt 40, 4^3\)

A number can be multiplied by its square root in order to obtain that number. The final square root of "sqrt" stands in for the square root as a symbol. An alternative to squaring an integer is to take its square root. A number's square root is the number that, when multiplied by itself, yields the original number. The square root of 4, for instance, is 2, denoted by the formula 4 = 2. That is to say, multiplying by two results in the number four, which is proven by the formula 2 + 2 = 4.

By square root -

\(4^3 = 64\\sqrt 40 = 6.32\\sqrt 13 = 3.61\\14/9 = 1.56\\sqrt 7 = 2.66\\\)

least to greatest : \(14/9 , sqrt 7, sqrt 13, sqrt 40, 4^3\)

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Answer:

Total = m + j

= 3 + m + 21

Step-by-step explanation:

Mails = 3 miles

Jared = 3 miles + 21 miles

j = m + 21

m = 3

Total = m + j

= 3 + m + 21

Where,

m = 3

Total = 3 + m + 21

= 3 + 3 + 21

= 27

Answer:

D

Step-by-step explanation:

there are 9 digits.

and round it off to the nearest hundred million which is 3.

There are 8 digits before the 3... so 10 gets to the power of 8.___ 10⁸

3,0×10⁸ m.s^-1

Answer:

O The numerical value of the circumference is less than the numerical value of the area.

Step-by-step explanation:

as pi>2, therefore, only 'the numerical value of the circumference is greater than the numerical value of the area. The numerical value of the circumference is less than the numerical value of the area' is correct.

The most plausible sequence for the percent of yellow candies obtained in the five samples is 35%, 35%, 35%, 35%, 5%, 60%.

Since the manufacturer produces 35% yellow candies, it is reasonable to expect that the majority of the samples will have a percentage close to 35%.

The first four samples are all 35%, which is the most likely outcome considering the manufacturer's production rate. The fifth sample of 5% is also plausible since it is possible to randomly select a sample with a lower percentage of yellow candies.

The last sample of 60% is less likely but still within the realm of possibility, as some random samples may have a higher concentration of yellow candies.

Therefore, the sequence of percentages 35%, 35%, 35%, 35%, 5%, 60% is the most realistic among the given options.

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Answer:

Step-by-step explanation:

(9a⁴b⁷) x (6a³b⁸)

(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)

54 x a⁷ x b¹⁵ = 54a⁷b¹⁵

Answer:

(9a⁴b⁷).(6a³b⁸)

=54a⁷b¹⁵