A berry farmer needs to separate
and enclose two adjacent rectangular fields, one for
blueberries and one for strawberries. If a lake forms
one side of the fields and 240 yd of fencing is avail-able, what is the largest total area that can be enclosed?

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

learn more about linear equations here :

https://brainly.com/question/29739212

#SPJ1

"The given statement is False." The wheels on an automobile are not classified as a variable cost with respect to the volume of cars produced in an automobile assembly plant.

The statement is incorrect. The wheels on an automobile are not typically classified as a variable cost with respect to the volume of cars produced in an automobile assembly plant.

Variable costs are costs that vary in direct proportion to the level of production or activity. They increase or decrease as the volume of production changes.

Examples of variable costs in automobile manufacturing would include items such as raw materials, direct labor, and electricity costs.

On the other hand, the cost of wheels for an automobile assembly plant would typically be considered a fixed cost. Fixed costs are costs that do not vary with the level of production. These costs remain constant regardless of the number of cars produced.

Fixed costs in automobile manufacturing may include expenses like the purchase or lease of manufacturing equipment, facility rental, and salaries of administrative staff.

For more such questions on Automobile:

https://brainly.com/question/30541305

#SPJ8

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

Learn more about integration :

https://brainly.com/question/18125359

#SPJ4

Answer: x= -3

Step-by-step explanation:

You would use the formulas b^x=y <----> log∨b(y)=x

b=4

x=?

y=1/64

Plug in:

log(∨4)(1/64)= x

then you use...

log(y)/log(b)=x

log(1/64)/log(4)

plug into calculator and you would get -3 for x

hope that helps :)

Answer:

d = dependant; t = independant

Step-by-step explanation:

The d value is dependant on the t value, therefore it is the dependant. The t is the only valuable that can be changed in the equation, therefore being the independant.

Answer:

\(D\) = dependent; \(t\) = independent

Step-by-step explanation:

\(D\) is the independent variable since its value relies/depends on the value of \(t\).

\(t\) is the independent variable since it is the input variable which can be changed.

Hope this helps :)

Sally deposits $1,600 into a savings account earning a simple interest rate of 7.00%., then the interest Sally will earn after 180 days is $55.09.

To calculate the amount of interest Sally will earn after 180 days on depositing $1600 in a savings account with a simple interest rate of 7%, the following formula applies;Interest = P × r × t

where;P is the principal (amount deposited),r is the annual interest rate (7%),t is the time in years or fraction of a year.

We can convert 180 days to fraction of a year by dividing it by the total number of days in a year as follows;

180 days ÷ 365 days = 0.49315068 years

Substitute the values of P, r and t to calculate the interest;

Interest = 1600 × 0.07 × 0.49315068

Interest = 55.09

To two decimal places, the interest Sally will earn after 180 days is $55.09.

Learn more about interest rates at

https://brainly.com/question/2437603

#SPJ11

Answer:

minute 600

Step-by-step explanation:

$1 = 100 pennies

60 = x pennies

x =6000/10

x = 600 minutes

The value of f(5) in the function below is 8. (option-a)

The function `f(x) = 1/2*x` means that the output `f(x)` is equal to half of the input `x`.

To find `f(5)`, we substitute `5` for `x` in the function:

`f(5) = 1/2*5 = 5/2`

Therefore, the value of `f(5)` is `5/2`, which is an irrational number, and the answer is not listed among the options provided.

However, if we assume that the answer choices contain errors and we are asked to find the closest listed approximation to `5/2`, we can use commonly known approximations such as 3.14 for π to evaluate:

`5/2 ≈ 2.5`

The closest listed answer choice is option A, which approximates `2.5` to `8`. While this is not the exact value of `f(5)`, it is the closest listed approximation to `5/2`. (option A)

For such more questions on function

https://brainly.com/question/11624077

#SPJ8

Answer:

Step-by-step explanation:

answer the prenthese first then multiply the numbers that are not in the prenthese. if u dont understand it let me know

Answer: I calculated the value after 5 years to be 5,734.40 or 5,734

Step-by-step explanation:

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer: 2π

Explanation

Given the radius (r = 4 ) and the arc length (s = 8π), we can use the following formula to find the angle:

where θ is the angle.

Thus, by replacing the values and simplifying we get:

From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

To learn more about equation from the given link

https://brainly.com/question/28871326

#SPJ1

Answer:

Given -

Now, we'll calculate the work done by both the taps -

\( \\ \sf \: \frac{1}{4} + \frac{1}{6} \\ \\ \\ \bf \: lcm \: \: of \: \: 4 \: \: \& \: \: 6 = 12 \\ \\ \\ \implies \sf \: \frac{3 + 2}{12} \\ \\ \\ \implies \sf \frac{5}{12} \\ \\ \)

Now, reciprocal it -

\( \\ \implies \sf \frac{12}{5} = 2 \frac{2}{5} \\ \)

Therefore, time taken by both the taps will be 2 2/5 hours.

Answer:

-6

Step-by-step explanation:

Pls leave “thanks“ heart if I helped

Answer: I believe its 36

Step-by-step explanation:......

x is rational, because it can be expressed as the ratio of two integers (d-b) and (a-c).

Let's multiply both sides of the given equation by cx+d to eliminate the denominator:

ax + b = cx + d

ax - cx = d - b

x(a-c) = d - b

x = (d - b)/(a - c)

Since a, b, c, and d are integers and a ≠ c, (a-c) is also an integer. Therefore, x is rational, because it can be expressed as the ratio of two integers (d-b) and (a-c).

Note that this is a special case of the more general result that if p(x) and q(x) are polynomials with integer coefficients and q(x) ≠ 0 for some real number x, and if p(x)/q(x) is an integer, then p(x) is divisible by q(x).

In this case, q(x) = cx + d, which is nonzero because a ≠ c, and p(x) = ax + b - (cx + d) = (a-c)x + (b-d). Since p(x) is an integer and q(x) is an integer except possibly at x = -d/c, it follows that p(x) must be divisible by q(x), and hence x = (d-b)/(a-c) is rational.

To know more about rational number refer to-

https://brainly.com/question/24540810

#SPJ11

Both the classical method and the p-value method lead to the conclusion that the average distance cars travel per year is less than 20,000 kilometers,

a) t =  -2.564

b)  t = -2.564

To test the claim that the average distance cars travel per year is less than 20,000 kilometers, we can conduct a hypothesis test using the classical method and the p-value method.

a) The steps we need to follow are:

Step 1: Formulate the null and alternative hypotheses:

Null hypothesis (H₀): The average distance cars travel per year is 20,000 kilometers.

Alternative hypothesis (H₁): The average distance cars travel per year is less than 20,000 kilometers.

Step 2: Determine the test statistic:

Since we know the sample size (n = 100), the sample mean (x = 19,000 kilometers), and the sample standard deviation (s = 3900 kilometers), we can use the t-test statistic.

t = (x - μ₀) / (s / √n)

where μ₀ is the assumed population mean under the null hypothesis.

Step 3: Set the significance level:

The significance level is given as 0.05, which means we want to be 95% confident in our conclusion.

Step 4: Calculate the critical value:

Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value corresponding to a 0.05 significance level and degrees of freedom (df) = n - 1 = 99. From the t-distribution table or calculator, the critical t-value is approximately -1.660.

Step 5: Calculate the test statistic:

t = (19,000 - 20,000) / (3900 / √100)

t = -10 / (3900 / 10)

t ≈ -2.564

Step 6: Compare the test statistic with the critical value:

Since -2.564 is less than -1.660, the test statistic falls in the rejection region. We reject the null hypothesis.

Step 7: Make a conclusion:

Based on the classical method, since the test statistic falls in the rejection region, we conclude that the average distance cars travel per year is significantly less than 20,000 kilometers.

b) The P-value method:

Using the same test statistic t = -2.564 and the degrees of freedom (df) = 99, we can calculate the p-value. The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

From a t-distribution table or calculator, the p-value corresponding to t = -2.564 and df = 99 is approximately 0.0075 (or 0.75% if multiplied by 100).

Since the p-value (0.0075) is less than the significance level (0.05), we reject the null hypothesis. This suggests strong evidence that the average distance cars travel per year is significantly less than 20,000 kilometers.

Learn more about standard deviation at:

https://brainly.com/question/475676

#SPJ4

Answer:

\( 0.8 \bar3\)

Step-by-step explanation:

\( \frac{5}{6} = 0.83333... \\ \\ = 0.8 \bar3\)

\(g(x)=a f(b(x-h))+c\)

We're given:

\(f(x)=x^3\)

\(f'(x)=x^3-3\)

f'(x) is equal to f(x) + 3.

This is the same as the "c" value mentioned above, which is a vertical translation.

If c is positive, the function translates up.

Therefore, it moves 3 units upward.

It moves 3 units upward.

Both +33 and -33 are units of zero because both start from 0.

This is because, -33 starts from the left side of zero, whereas, +33 starts after some numbers in zero. Either left or right, as they both have a common number 0, therefore, -33 and +33 are units of zero.

Hope it helps you...

( Answered by Benjemin)

Answer:

$267.7

Step-by-step explanation:

Answer: like he dark line represents all the numbers that satisfy x≤2 . If we pick any number on the dark line and plug it in for x, the inequality will be true. The following graph represents the inequality x < 2 . Note that the open circle on 2 shows that 2 is not a solution to x < 2 .

Step-by-step explanation: