If gallon of paint covers of a wall, then how much paint is needed to cover the entire wall?

Answer:

1/8 Pounds

Step-by-step explanation:

Since Tracy gives 3/4 pounds of rice to 6 of her friends, you will need to divide it among 6 people.

3/4 ÷ 6

= 3/4 * 1/6

= 1/4 * 1/2 (cross multiplication)

= 1/8.

Therefore, each of her 6 friends received 1/8 Pounds of rice

I hope this helped!

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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According to the perimeter of rectangle, the amount of area that the fencing does he need to go around the field is 11 3/5 miles

The general formula to calculate the perimeter of the rectangle is written as,

=> P = 2(l + b)

where l refers the length of the rectangle and b refers the width of the rectangle.

While we looking into the given question, we have identified that the following values are given in the question,

=> Length of field = 2 3/10 miles

=> Width of field = 3 1/2 miles

Now, we have to convert the mixed fraction into normal fraction, then we get,

=> Length of field = 23/10 miles

=> Width of field = 7/2 miles

Then the Perimeter is calculated as,

=> 2 (23/10 + 7/2)

=> 2 ([23 + 35)/10)

=> 2 x (58/10)

=> 2 x 5.8

=> 11.6 or 11 3/5 miles

Therefore, the length of fencing used to enclose the rectangular field is 11 3/5 miles

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Answer:

He rode his bicycle for 40minutes

Hope it helps:)

Answer:.

Step-by-step explanation:

Answer:

y=5

Step-by-step explanation:

2y+8=18

2y=10

y=5

The value y is 5.

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculations

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given equation as:

⇒ 2y + 8 = 18

Substract from 8 both the sides of equation,

⇒ 2y + 8 - 8 = 18 - 8

⇒ 2y = 10

Divided by 2 both the sides of equation,

⇒ y = 5

Hence, the value y is 5.

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Answer:

1.11111111

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

In order to get an equivalent fraction you have to divide/multiply both the numerator and the denominator by the same number. 6/9 you can divide both numbers by 3. 6/3=2 and 9/3=3 so your new fraction is 2/3.

Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

Using the chain rule, Therefore, f'(0) = 2.

Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) to obtain :

f'(x) = f'(g(x)) * g'(x)

substitute x = 0, we get:

f'(0) = f'(g(0)) * g'(0)

We are given that g(0) = -2 and g'(0) = 3. Therefore, we need to find g(0) and g'(0) in order to determine f'(0).

To do this, we can use the fact that f(x) = f(g(x)). Substituting x = 0 into this equation, we get:

f(0) = f(g(0))

Since f(-2) = 2, we have:

f(g(0)) = f(-2)

Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) with respect to x to obtain:

f'(x) = f'(g(x)) * g'(x)

substitute x = -2, we get:

f'(-2) = f'(g(-2)) * g'(-2)

We are given that f'(-2) = 2 and g'(-2) = 3. Therefore, we can solve for f'(g(-2)):

f'(g(-2)) = f'(-2) / g'(-2) = 2/3

Since f'(x) = f'(g(x)) * g'(x), we can substitute g(0) = -2 and f'(g(-2)) = 2/3 into the equation f'(0) = f'(g(0)) * g'(0) to obtain:

f'(0) = f'(g(0)) * g'(0) = f'(g(-2)) * g'(0) = (2/3) * 3 = 2

Therefore, f'(0) = 2.

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The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

1/4096

Step-by-step explanation:

\((4*2)^{{(2-2*2)}^2}\\\\=8^{-2^2}\\\\=[\frac{1}{64}]^2\\\\=\frac{1}{4096}\)

you work from bottom to top

Answer: 2 hours and 42 minutes < 0.1 days 8370 seconds < 3 hours 138 minutes

Step-by-step explanation: 1 hour = 60 minutes, 60 seconds = 1 minute, 1 day = 24 hours

2 hours and 42 minutes is 2×60 minutes + 42 minutes = 162 minutes

0.1 day 8370 seconds is 0.1×24 hours and 8370/60 minutes = 2.4 hours and 139.5 minutes = 2×60 minutes + 0.4×60minutes + 139.5 minutes=283.5 minutes

3 hours and 138 minutes is 3×60 minutes + 138 minutes = 328 minutes

Hence,

2 hours and 42 minutes < 0.1 days 8370 seconds < 3 hours 138 minutes

Answer:

120 sq ft.

Step-by-step explanation:

REMEMBER: Area is found by multiplying one side, by the other side that isn't the same length as it.

Multiply 12 by 10 to get 120

120 is the area of the bedroom

The value of $100 in euros is $87.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Worth of 1 United States dollar is $0.87 in euros.

To find the value of $100 in Euros, use ratio property,

1 United States dollar = $0.87 in euros

100 United States dollar = $87 in euros.

The value of $100 in euros is $87.

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The roots of a graph are also known as the x-intercepts. If you use a graphing tool to graph the given equation you will be able to see the x- intercepts. For the answer the question is asking what the x cordinates of the x intercepts are. I think the answer is (0,2,-2) but im not sure so you should check my work.

the given equations are,

15y = 10x - 20 ......(1)

6x - 9y = 12

9y = 6x - 12 ............(2)

3y = 2x - 4 ............. x 5

15y = 10x - 20

so, both the equations are the same, thus, the answer is x = all real values or , y = all real values,

i have solved your problem in the answer tab.

if you have any doubt with this solution then let me know.

It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

11.7

Step-by-step explanation:

(−7.8)(−1.5)

Hope ths helps

The volume of the cylinder is 126π cubic meters.

Volume is the measure of the space occupied by a three-dimensional object. It is typically expressed in cubic units.

The radius of the cylinder is half of the diameter, so the radius is 3 meters. The formula for the volume of a cylinder is

V = πr²h,

where r is the radius and h is the height. Substituting the given values, we get V = π(3)²(14) = 126π cubic meters.

Therefore, the volume of the cylinder is 126π cubic meters.

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Answer:

x = 14

Step-by-step explanation:

The triangles are similar, so the ratios of corresponding sides are equal, that is

\(\frac{DF}{AC}\) = \(\frac{EF}{BC}\) , substitute values

\(\frac{x}{21}\) = \(\frac{18}{27}\) ( cross- multiply )

27x = 378 ( divide both sides by 27 )

x = 14

Answer:

f(2) = 4

f(3) = 9

Step-by-step explanation:

a function means you are supposed to input the given number into the statement you have been given, I hope it makes sense.

Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

<95141404393>

Answer:

Suppose we have an equation like:

\(\frac{A}{C} = \frac{B}{D}\)

If we want to remove the denominators, we should multiply both sides by each denominator.

First, let's multiply both sides by C.

\(\frac{A}{C}*C = \frac{B}{D}*C\)

\(A = \frac{B}{D}*C\)

Now let's multiply both sides by D.

\(A*D = \frac{B}{D}*C*D\)

\(A*D = B*C\)

So now we removed the denominators.

Now let's do this to our expression.

\(2 - \frac{3}{4*x} = \frac{9}{10}\)

First, let's multiply both sides by 10

\((2 - \frac{3}{4*x})*10 = \frac{9}{10}*10\)

\(20 + \frac{30}{4*x} = 9\)

Now let's multiply both sides by 4*x

\((20 + \frac{30}{4*x})*4*x = 9*4*x\)

\(20*4*x - 30 = 9*4*x\)

\(80*x - 30 = 36*x\)

Now we can solve this for x:

\(80*x - 36*x = 30\)

\(44*x = 30\)

\(x = \frac{30}{44} = 0.68\)

The percentage of cars traveling east is 28% of the total number of cars.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The commission counted 486 cars traveling east and 189 cars traveling west.

We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.

From this concept, the percentage of the cars were traveling east would be

The cars traveling east divided by the total numbers of cars time s100%.

= (189/486 + 189)×100%.

= (189/675)×100%.

= 0.28×100%.

= 28%.

So, 28% of the total cars traveling east.

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Answer:

9.46% -> 0.0947

Step-by-step explanation:

To find the probablility of the *first time* would be 4/13, shown on the graph right?
The second time would that 4/13 multiplied by 4/13 since there is another equal change.
That would mean there is about a 9.46 % chance of gettting two 5s in a row THEORETICALLY.

The formula to calculate the upper value for a 95% confidence interval for the mean weight of newborn babies in that community is:

\text{Upper value} = \bar{x} + z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)

where

\bar{x} = 7.63$ is the sample mean, \sigma = 2.22

is the population standard deviation, n = 20

is the sample size, and

z_{\alpha/2}$ is the z-score such that the area to the right of

z_{\alpha/2}

is  \alpha/2 = 0.025

(since it's a two-tailed test at 95% confidence level).

Using a z-score table,

we can find that z_{\alpha/2} = 1.96.

Substituting the given values into the formula,

we get:

\text{Upper value} = 7.63 + 1.96\left(\frac{2.22}{\sqrt{20}}\right)

Simplifying the right-hand side,

we get:

\text{Upper value} \approx 9.27

Therefore, the upper value for a 95% confidence interval for mean weight of babies in that hospital (in that community) is 9.27 pounds (rounded to two decimal points).

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Answer:

91 in2

Step-by-step explanation:

11+15 over 2 , times by 7 equals 91 ??