5 x 10^2 as a standard notation

For every hour that passes, the container loses 1.5 liters of oil.

To write a linear equation to estimate the remaining amount of oil based on the elapsed time, we can use the slope-intercept form of a linear equation, y = mx + b, where y represents the remaining amount of oil, x represents the elapsed time, m represents the slope of the line, and b represents the y-intercept.

Since the container is leaking at a constant rate, we can assume that the slope of the line is constant. We can find the slope by using the formula:

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

where (x1, y1) represents the first data point (hours, liters of oil), and (x2, y2) represents the second data point.

Using the given data, we have:

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

m = (4.5 - 6) / (2 - 1)

m = -1.5

This means that for every hour that passes, the container loses 1.5 liters of oil.

To find the y-intercept, we can use one of the data points and solve for b:

y = mx + b

6 = (-1.5)(1) + b

b = 7.5

This means that at time zero (when no time has elapsed), there are 7.5 liters of oil remaining in the container.

Therefore, the linear equation to estimate the remaining amount of oil based on the elapsed time is:

y = -1.5x + 7.5

This equation tells us that as time passes, the amount of oil in the container decreases at a constant rate of 1.5 liters per hour. The y-intercept of 7.5 represents the initial amount of oil in the container before any time has elapsed.

Learn more about equation brainly.com/question/10413253

#SPJ11

The ordered pair (1, 2) is not included in the solution set to the system of inequalities y < x^2 + 3 and y > x^2 - 2x + 8.

To determine which ordered pair is included in the solution set to the given system of inequalities, we need to evaluate each ordered pair by substituting the values into the inequalities and checking if they satisfy the conditions.

Let's consider the ordered pair (1, 2) as a candidate solution:

Substituting x = 1 and y = 2 into the first inequality:

2 < 1^2 + 3

2 < 4 (True)

Substituting x = 1 and y = 2 into the second inequality:

2 > 1^2 - 2(1) + 8

2 > 1 - 2 + 8

2 > 7 (False)

Since the second inequality is not satisfied, the ordered pair (1, 2) is not included in the solution set to the given system.

Therefore, the ordered pair (1, 2) is not included in the solution set.

Learn more about ordered pair here:

https://brainly.com/question/28737707

#SPJ11

The statement is false. the box of T-shirts contains 4 red T-shirts, 11 blue T-shirts, and the rest are either green or yellow.

Since the number of green and yellow T-shirts is not specified, we cannot conclude that it is more likely to select a green T-shirt than a yellow T-shirt. To determine the probability of selecting a green T-shirt versus a yellow T-shirt, we would need to know the specific quantities of each color. Without that information, we cannot make a definitive statement about the likelihood of selecting a green or yellow T-shirt from the box.

Learn more about probability

https://brainly.com/question/31828911

#SPJ4

The value of Erica's investment after 6 years is approximately $4,939.05.

To find the value of Erica's investment after 6 years, we can use the compound interest formula. The formula for compound interest is given as:

A = P\((1 + r/n)^(nt)\)

Where:

A is the final amount or value of the investment.

P is the initial principal or investment amount.

r is the annual interest rate (as a decimal).

n is the number of times the interest is compounded per year.

t is the number of years.

In this case, Erica's initial investment is $4000, the annual interest rate is 4% (or 0.04 as a decimal), and the investment is growing annually. Therefore, we have:

P = $4000

r = 0.04

n = 1 (since the interest is compounded annually)

t = 6 years

Plugging these values into the compound interest formula, we can calculate the final value of the investment:

A = $4000(1 + \(0.04/1)^(1*6)\)

A = $4000(1 + 0.04)^6

A = $4000(1.04)^6

Evaluating this expression, we find:

A ≈ $4,939.05

Therefore, the value of Erica's investment after 6 years is approximately $4,939.05.

This calculation assumes that no additional investments or withdrawals were made during the 6-year period and that the interest rate remains constant at 4% per year.

for more such question on investment  visit

https://brainly.com/question/29227456

#SPJ8

Answer:

Step-by-step explanation:

Using the given data, we can calculate the regression equation as follows:

First, calculate the means of x and y:

mean(x) = (7.3 + 23.6 + 4.3 + 22.1 + 7.1 + 3.9 + 21.2) / 7 = 13.1143

mean(y) = (22.9 + 74.1 + 13.5 + 69.4 + 22.3 + 12.3 + 66.6) / 7 = 42.3286

Then, calculate the sample standard deviations of x and y:

s_x = sqrt(((7.3 - 13.1143)^2 + (23.6 - 13.1143)^2 + ... + (21.2 - 13.1143)^2) / 6) = 7.8836

s_y = sqrt(((22.9 - 42.3286)^2 + (74.1 - 42.3286)^2 + ... + (66.6 - 42.3286)^2) / 6) = 25.3612

Calculate the sample covariance:

cov(x,y) = ((7.3 - 13.1143)(22.9 - 42.3286) + (23.6 - 13.1143)(74.1 - 42.3286) + ... + (21.2 - 13.1143)*(66.6 - 42.3286)) / 6 = 194.4714

Calculate the slope of the regression line:

b = cov(x,y) / s_x^2 = 194.4714 / (7.8836^2) = 3.1343

Calculate the intercept of the regression line:

a = mean(y) - b * mean(x) = 42.3286 - 3.1343 * 13.1143 = 1.1639

Therefore, the regression equation is:

y = 1.1639 + 3.1343x

To find the best predicted circumference for a diameter of 42.5 cm, we substitute x = 42.5 into the regression equation:

y = 1.1639 + 3.1343(42.5) = 133.262

The predicted circumference is 133.262 cm.

To determine whether the predicted value is significantly different from the actual circumference of 133.5 cm, we can calculate the standard error of the estimate:

s_e = sqrt(((22.9 - 133.262)^2 + (74.1 - 133.262)^2 + ... + (66.6 - 133.262)^2) / 5) = 17.2538

Using a significance level of 0.05 and a t-distribution with 5 degrees of freedom (n - 2), the critical t-value is 2.571. The margin of error is then:

ME = t_critic * s_e = 2.571 * 17.2538 = 44.3726

Since the actual circumference of 133.5 cm falls within the margin of error (133.262 - 44.3726 to 133.262 + 44.3726), we can conclude that the predicted value is not significantly different from the actual circumference. Therefore, the answer is:

b) Even though 42.5 cm is beyond the scope of the sample​ diameters, the predicted value yields the actual circumference.

Answer:

Hey there!

The reciprocal of a number, n, is 1/n.

Thus, the answer is n+7(1/n)

Let me know if this helps :)

Answer:

\(b = 3\)

The value of y triples

Step-by-step explanation:

Given:

\(\begin{array}{cccccc}x & {-2} & {-1} & {0} & {1} & {2} \ \\ y & {\frac{2}{9}} & {\frac{2}{3}} & {2} & {6} & {18} \ \end{array}\)

Required

Determine b value

An exponential equation is:

\(y = ab^x\)

When \(x = 0; y =2\)

So:

\(y = ab^x\)

\(2 = a * b^0\)

\(2 = a\)

\(a = 2\)

When \(x = 2; y = 18\)

So:

\(18 = a * b^2\)

Substitute 2 for a

\(18 = 2 * b^2\)

Divide by 2

\(9 = b^2\)

Take positive square roots of both sides

\(3 = b\)

\(b = 3\)

Answer:

x = 50

y= 40

Step-by-step explanation:

Step-by-step explanation:

\(\sf\green{x = 45° (diagonals \: \: of \: \: rectangle \: \: bisect \: \: eachother)}

\sf\green{y = 45° (diagonals \: \: of \: \: rectangle \: \: bisect \: \: eachother)}\)

Answer:

147

Step-by-step explanation:

braniest pls

Answer:

0.083333333

is the answer

Answer:

12

Step-by-step explanation:

The value of the expression is 1/(9x)^2

From the question, we have the following parameters that can be used in our computation:

(-9x)^-2

We can write the expression without negative exponents by using a fraction with a positive exponent:

(-9x)^-2 = 1/(-9x)^2

And without parentheses, this expression becomes:

1/(9x)^2

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

Answer:

x = -9/2

Step-by-step explanation:

-4x - 11 = 7

-4x = 7 + 11

-4x = 18

x = -18/4

x = -9/2

The correct answer is B. The graph of h is the graph of g vertically shifted up 1 unit.

The correct answer is:

B. The graph of h is the graph of g vertically shifted up 1 unit.

Explanation:

The original function g(x) = x² represents a basic quadratic function, which is a parabola that opens upward and has its vertex at the origin (0, 0).

When we consider the function h(x) = g(x) + 1, we are adding a constant value of 1 to the output (y) values of the function g(x). This results in a vertical shift of the graph of g(x) by 1 unit upward.

In other words, for every x-value, the corresponding y-value of the function h(x) will be 1 unit higher than the corresponding y-value of the function g(x).

Visually, this means that the graph of h(x) will be the same shape as the graph of g(x), but it will be shifted upward by 1 unit. The vertex of the parabola, which was originally at the origin, will now be at (0, 1).

The statement "The graph of h is the graph of g horizontally shifted left 1 unit" (Option A) is incorrect because there is no horizontal shift in this transformation.

The statement "The graph of h is the graph of g vertically shifted down 1 unit" (Option B) is incorrect because the transformation results in a vertical shift upward, not downward.

The statement "The graph of h is the graph of g horizontally shifted right 1 unit" (Option D) is incorrect because there is no horizontal shift in this transformation.

Therefore, the correct answer is B. The graph of h is the graph of g vertically shifted up 1 unit.

for more such question on graph visit

https://brainly.com/question/19040584

#SPJ8

Answer:

Я не вижу достаточно, чтобы прочитать весь вопрос, но я надеюсь, что это поможет.

и как человек с английским в качестве основного языка и изучающий русский, я с удовольствием использую эти навыки.

Answer:

calculating beats per minute

y=5x 7.5w+7.5d Answer:

Step-by-step explanation:

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week is , w + d ≤ 15 .

The relationship between two expressions or values that are not equal to each other is called 'inequality.

here, we have,

Given that w is the number of hours for washing a car and d is the number of hours to walking dogs.

The work hours  at most 15 hours altogether between both jobs in a given  in a week.

Hence, w + d ≤ 15 is the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week.

To learn more about inequality, use the link given below:

brainly.com/question/20383699

#SPJ2

Answer:

15.25 cups per batch

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

AD is a straight line and AC is 90 so DC = 180-90 =90

The arc is the same as the angle, since they go through the center

We want EDC = ED +DC

                      = 55+90

                        =145

Answer:

B. 145 degrees

Step-by-step explanation:

Angle EDC = 55 + 90

= 145°

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

Learn more about Parametric curves

brainly.com/question/15585522

#SPJ11

Answer:

In Crista’s class, 8 students have blonde hair, 14 have brown hair, 3 have black hair, and 2 have red hair. If one student is chosen at random, it is  

that the student has blonde hair, it is  

that the student has brown hair, it is  

that the student has black hair, and it is  

that the student has red hair.

Answer:

In Crista’s class, 8 students have blonde hair, 14 have brown hair, 3 have black hair, and 2 have red hair. If one student is chosen at random, it is

unlikely

that the student has blonde hair, it is

neither likely nor unlikely

that the student has brown hair, it is

unlikely

that the student has black hair, and it is

unlikely

that the student has red hair.

Step-by-step explanation:

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

Answer:

-x² + x -1

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

10-4=6

Determine the difference of 34.7 - (-8.6).

Since there are two negative signs, it cancels out, and becomes an adding sign or a positive.

Thus, it is now, 34.7 + 8.6

Solve:

34.7 + 8.6 = 43.3

Therefore, the difference of 34.7 - (-8.6) is 43.3

Answer:

x = gym memberships, and y = bottles of water

30x + 7y = 1050.....when x = 28

30(28) + 7y = 1050

840 + 7y = 1050

7y = 1050 - 840

7y = 210

y = 210/7

y = 30....so he would have to sell 30 water bottles

Step-by-step explanation:

Answer:

1188=35m+9w

Step-by-step explanation:

Answer

1. Solve for "y=" if necessary.

2. Substitute the value for "y" in the other equation.

3. Solve the new equation to find "x".

4. Substitute the value for "x" in either original equation to find "y".

5. Check your work.​

Explanation

1. Solve for "y=" if necessary.

2. Substitute the value for "y" in the other equation.

3. Solve the new equation to find "x".

4. Substitute the value for "x" in either original equation to find "y".

5. Check your work.​

Hope this Helps!!!

Answer: This is a nonfunction because there are two different x values for the y value of 20 . In order for it to be functional every x value has to have a different y value.

Step-by-step explanation:

Answer:

answer is the last one 4.

:)