A store has two types of animal feed available. Type A contains 3 pounds of oats and 3 pounds of corn per bag. Type B contains 1 pound of oats and 7 pounds of
corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 18 pounds of oats and at least 54 pounds of corn. The store
only has 11 bags of type A feed and 12 bags of type B feed in stock. Type A costs $4 per bag, and type B costs $1 per bag. How many bags of each type should
the farmer buy to minimize her cost?
Note that the ALEKS graphing calculator can be used to make computations easier.
Type A feed:
Type B feed:
bag(s)
bag(s)

I=PRT

$60= 400 ×.05 × t

$60= 20× t

t= 60/20

3=t

Answer:

$20.70

Step-by-step explanation:

5 × $3.70 = $18.50 + $2.20 =

$20.70

Rounding to the nearest tenth, the area of the triangular windowpane is approximately 8.2 square feet.

To find the area of a triangular windowpane, we need to use the formula for the area of a triangle, which is:

Area = (1/2) x Base x Height

In this case, the base is 4 feet 8 inches and the height is 3 feet 6 inches. However, we need to convert these measurements to the same units before we can calculate the area. Since there are 12 inches in 1 foot, we can convert the measurements as follows:

Base = 4 feet + 8 inches/12 = 4.67 feet

Height = 3 feet + 6 inches/12 = 3.5 feet

Now we can plug in these values into the formula and calculate the area:

Area = (1/2) x 4.67 feet x 3.5 feet

Area = 8.1675 square feet

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Answer:

We have 3 variables to solve for.  We will start by writing two equations in three variables but, with the given information, will eventually have those equations written in 2 variables.  The strategy is to set up equations from the given information and solve the equations simultaneously.  Let's assign variables...

c= #children total

s= #students total

a= #adults total

c+s+a=900.............Eq1, total attendance, given

4c+6s+8a=5600....Eq2, total receipts, given

a=(1/2)(c+s)

 =(1/2)c+(1/2)s.....Eq3, #adults total, given

Let's substitute Eq3 into each Eqs1,2 to get two equations in two variables...

c+s+(½c+½s)=900.........Eq1, substitute for"s"

      1.5c+1.5s=900.......combine like terms

            3c+3s=1800.....Eq4, multiple equation

                                      by 2 to eliminate fraction

4c+6s+8(½c+½s)=5600...Eq2, substitute for "s"

   4c+6s+(4c+4s)=5600...distribute 8

               8c+10s=5600...Eq5, combine like terms

Let's solve newly arrived at Eq4,5 simultaneuously...

    3c+3s=1800......Eq4

  8c+10s=5600......Eq5

-24c-24s=-14400...Eq4 multiplied by (-8)

24c+30s=16800...Eq5 multiplied by 3

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

          6s=2400.....add all terms vertically

        ∴ s=400.......divide both sides by 6

Substitute value back into Eq4, solve for "c"...

      3c+3s=1800...Eq4

3c+3(400)=1800...substitute for"s"

  3c+1200=1800

            3c=600.....subtract 1200, both sides

          ∴ c=200....divide both sides by 3

Substitute values back into Eq3, solve for "a"...

  a=(1/2)(c+s).............Eq3

    =(1/2)(200+400)...substitute for "c,s"

    =(1/2)(600)

∴ a=300.....................simplify

We now have our three variables solved.  Let's substitute those values back into original Eqs1,2 to check against the problem requirements...

          c+s+a=900.......Eq1

200+400+300=900....substitute for "c,s,a"

               900=900......true, √check

                  4c+6s+8a=5600.....Eq2

4(200)+6(400)+8(300)=5600...substitute for

                                                  "c,s,a"

        800+2400+2400=5600...simplify

                         5600=5600......true, √check

So our calculated values are correct. Always check your solutions and work!

In summary, we have...

200 children, 400 students, and 300 adults in attendance at the theater for the screening.

Step-by-step explanation:

There were total 150 childrens, 450 students and 300 adults.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a theater that has a seating capacity of 900 and charges $2.50 for children, $4 for students, and $5.50 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The total money brought in was $3825.

Assume that there were [x] childrens, [y] students and [z] adults. Then, we can write the equations as -

x + y + (1/2)(x + y) = 900

2.5x + 4y + (5.5)(1/2)(x + y) = 3825

Plot the graph. We will get x = 150 and y = 450.

Then -

z = (1/2)(150 + 450) = (1/2)(600) = 300

Therefore, there were total 150 childrens, 450 students and 300 adults.

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Answer:

\(\boxed{\boxed{\pink{\sf \leadsto Hence \ the \ slope \ of \ line \ is \ 1.}}} \)

Here a graph of line is given and we need to find the slope. So here we can see that the line intersects y - axis at (0,2) and x - axis at (2,0 ). And we know that the slope of the line is tan∅.

\(\green{\bf \implies Slope = tan\theta }\\\\\bf\implies Slope = \dfrac{perpendicular}{base} \\\\\bf \implies Slope = \dfrac{y_2-y_1}{x_2-x_1} \\\\\bf\implies Slope = \dfrac{2-0}{2-0} \\\\\bf\implies Slope =\dfrac{2}{2}\\\\\bf\implies \boxed{\red{\bf Slope = 1 }}\)

Answer:

Para encontrar la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6, primero debemos encontrar la pendiente de la línea 3x - 2y = 6.

La forma estándar de la ecuación de una línea es y = mx + b, donde m es la pendiente y b es la intersección en y. Podemos reescribir la ecuación 3x - 2y = 6 en esta forma:

3x - 2y = 6

-2 años

Por lo tanto, la pendiente de la línea 3x - 2y = 6 es 3/2.

Dado que la línea L es paralela a esta línea, también tiene una pendiente de 3/2. Ente

y - y1 = m(x - x1)

donde m es la pendiente y (x1, y1) es un punto en la línea. Nos

y - 4 = (3/2)(x - (-2))

Simplificando esta ecuación, obtenemos:

y - 4 = (3/2)x + 3

y = (3/2)x + 7

Por lo tanto, la ecuación de la línea L que pasa por el punto (-2, 4) y es paralela a la línea 3x - 2y = 6 es y = (3/2)x + 7.

Step-by-step explanation:

espero te sirva, traducelo si no puedes español.

Answer:

f(1) = 15

f(-9) = -65

f(0) = 7

Step-by-step explanation:

f(1) = 8(1) + 7

f(1) = 8 + 7

f(1) = 15

f(-9) = 8(-9) + 7

f(-9)  = -72 + 7

f(-9) = -65

f(0) = 8(0) + 7

f(0) = 7

Answer:1250

Step-by-step explanation:

Answer:

4/1x plus 2

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Length * width

4 * 3 = 12 ft\(^2\)

Answer:

24 square feet

Step-by-step explanation:

Area = area of triangle - area of rectangle

\(Area \ of \ triangle = \frac{1}{2} \times base \times height =\frac{1}{2} \times(4 +5) \times (5+3) = 9 \times 4 = 36 \ ft^2\\\\Area \ of \ rectangle = Length \times Breadth = 3 \times 4 = 12 \ ft^2\\\\\\Area \ of \ the\ shaded \ region = 36 - 12 = 24 \ ft^2\)

Answer:

a. 90

b. 40

c. 55

d. 6

e. 72

Step-by-step explanation:

a: This is a rectangle so all the full corners are 90 degrees. ABC is a corner angle.

b: 1 and 3 are the congruent angles so 3 has the same measure as 1.

C: 1 is a part of the corner, which adds up to 90 degrees. That means angle 2 and angle 1 should add up to 90. They say m<1= 35, so 90-35=55.

d. In a rectangle, the interesecting lines have the same length. AC is 12, so then DB is 12. However, DE is halfway. Half of 12=6.

e. This one has a few steps. Angle 1 is 36, and angle 2 is the other part to the 90 degree corner. 90-36= 54. That gives us angle 2. We know all angles in a triangle add up to 180 degrees. The angle across from angle 2 in the same triangle is the same value, so that is also 54. To find angle 5, it must add up to 180 degrees. 54+54+x=180, in other words. 54+54=108. 180-108=72.

Answer:

increase = 59-50

increase = $9.00

Percent = (increase/whole value) x 100

Percent = (9/50) x 100

Percent  = 18%

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\(Answer: \large\boxed{Cos(\theta_{1} )=\frac{84}{85}}\)

Step-by-step explanation:

Thinking about a triangle in Quadrant IV, we can imagine sin as opposite/hypotenuse. Therefore, the hypotenuse is 85 and the opposite angle is -13. To find the adjacent angle, we use the pythagorean theorum,

\(a^2+b^2=c^2\)

\(-13^2+b^2=85^2\)

\(169+b^2=7225\)

\(b^2=7056\)

\(b=\sqrt{7056}\)

\(b=\pm84\)

Taking only the positive number, the adjacent angle is 84

Now that we have all 3 sides, we can find the cosine.

Cosine is adjacent/hypotenuse

Therefore,

\(Cos(\theta_{1} )=\frac{84}{85}\)

See the attached picture:

In summary, given a simple dataset with 30 points, the following steps were performed: (a) OLS estimation was used to calculate the coefficients β^0 and β^1 for the regression of Y on X.

(b) the predicted value of Y was calculated for each observation; (c) the residuals were calculated for each observation; (d) the Explained Sum of Squares (ESS), Total Sum of Squares (TSS), and Residual Sum of Squares (RSS) were calculated separately; (e) the coefficient of determination R^2 was calculated; (f) the predicted value of Y was determined when X equals the last digit of the CUNY ID plus one; and (g) the interpretation of β^0 and β^1 was provided.

In detail, to calculate the OLS estimates of coefficients β^0 and β^1, a regression model of Y on X was fitted using the given dataset. β^0 represents the intercept term, which indicates the value of Y when X is zero. β^1 represents the slope of the regression line, indicating the change in Y corresponding to a unit change in X.

The predicted value of Y for each observation was obtained by plugging the corresponding X value into the regression equation. The residuals were then calculated as the difference between the observed Y values and the predicted Y values. ESS represents the sum of squared differences between the predicted Y values and the mean of Y, indicating the variation explained by the regression model.

TSS represents the total sum of squared differences between the observed Y values and the mean of Y, representing the total variation in Y. RSS represents the sum of squared residuals, indicating the unexplained variation in Y by the regression model. R^2, also known as the coefficient of determination, was calculated as ESS divided by TSS, indicating the proportion of total variation in Y explained by the regression model. Finally, the predicted value of Y was determined when X equals the last digit of the CUNY ID plus one, allowing for an estimation of Y based on the given information.

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Answer:

=3x to the power of 12+20x to the power of 6+6

Step-by-step explanation:

simplify step-by-step-

\(3x1x^{2} 2+2x^{2} 0x6+6x^{2} x12\)

There are no like terms so that means that the answer is

=3x to the power of 12+20x to the power of 6+6

For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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The domain is 0 ≤ x ≤ 52. The maximum number of laws that she can mow with 13 gallons is of 52, and the minimum number is of 0.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 13, hence the intercept b is given as follows:

b = 13.

When x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is:

y = -0.25x + 13.

From the intercept, the minimum amount can be mowed is given as follows:

0.

The maximum amount is given as follows:

-0.25x + 13 = 0

0.25x = 13

x = 13/0.25

x = 52.

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Answer: The answer is (-8, 4)

Step-by-step explanation:

(a) Without more information, we cannot determine the initial number of insects. (b) The differential equation satisfied by P(t) is: dP/dt = kP, where k is the growth rate of the insect population.

(c) To find the time it takes for the population to double, we can use the formula:

2P(0) = P(0)e^(kt)

where P(0) is the initial population size. Solving for t, we get:

t = ln(2)/k

(d) Without more information, we cannot determine the time at which the population will equal a certain value.
Hi! To answer your question, I need the specific function P(t). However, I can provide you with a general framework to answer each part of your question once you have the function.

(a) To find the initial number of insects, evaluate P(t) at t=0:
P(0) = [Insert the function with t=0]

(b) To find the differential equation satisfied by P(t), differentiate P(t) with respect to t:
dP(t)/dt = [Insert the derivative of the function]

(c) To find the time at which the population doubles, first determine the initial population, P(0), then solve for t when P(t) is twice that value:
2*P(0) = P(t)
Solve for t: [Insert the solution for t]

(d) To find the time at which the population equals a specific value (let's call it N), set P(t) equal to N and solve for t:
N = P(t)
Solve for t: [Insert the solution for t]

Once you have the specific function P(t), you can follow these steps to find the answers to each part of your question.

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Answer:

830.53 in²

Step-by-step explanation:

To find the area of one semicircle, find the area of the full circle and divide it by 2:

Use the circle area formula, A = \(\pi\)r²

Plug in 3.14 as pi, and plug in the radius:

A = \(\pi\)r²

A = 3.14(23²)

A = 1661.06

Divide this by 2:

1661.06 / 2

= 830.53

So, the area of one semicircle is 830.53 in²

Answer:

850.53 in² is the answer

Answer: 89 cm^2/minute

Step-by-step explanation:

Initial Area:                11 x 5 = 55 cm^2

Area after 1 minute:  18 x 8 = 144 cm^2

The area of the triangle is increasing by

Answer:

p/gh=m

Step-by-step explanation:

divide both sides by gh to isolate m

Answer:

I do!

Step-by-step explanation:

10: It appears to be (6, 4.75)

11: It looks like (-4, -4)

You can desmos graphing calculator to check yourself, if you'd like!

I hope this helps!

Point (-3,5) is  a solution to the system of inequalities

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

For this case, what we must do is find a point that meets both inequalities.

y> -2

x + y <4

We have then:

For (0,4):

First inequation:

4> -2 (correct)

Second inequality:

0 + 4 <4 (incorrect)

For (1,4):

First inequation:

4> -2 (correct)

Second inequality:

1 + 4 <4 (incorrect)

For (-3,5):

First inequation:

5> -2 (correct)

Second inequality:

-3 + 5 <4 (correct)

Point (-3,5) is system solution

For (-2,-3):

First inequation:

-3> -2 (incorrect)

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Answer:

-15

Step-by-step explanation:

if its just asking for what number would represent a loss of 15 it would be negative 15

i dont know if there's more to the problem or not

Answer:

-15

Step-by-step explanation:

This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,

hope this helps!

Answer:

The scale factor relationship between the radio coverages is 1:1.33 (or approximately 1:4/3).

Step-by-step explanation:

Part A:

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

For two-way radio A, the radius is 6 miles. Therefore, the area covered by two-way radio A is:

A = π(6)^2

A = 113 square miles (rounded to the nearest whole number)

Therefore, two-way radio A covers 113 square miles.

Part B:

For two-way radio B, the radius is 12.88 kilometers. To find the area covered by two-way radio B, we need to convert the radius to miles and then use the formula A = πr^2.

1 mile = 1.61 kilometers, so:

12.88 kilometers = 12.88/1.61 miles

12.88 kilometers = 7.998 miles (rounded to three decimal places)

Now we can calculate the area covered by two-way radio B:

A = π(7.998)^2

A = 201 square miles (rounded to the nearest whole number)

Therefore, two-way radio B covers 201 square kilometers.

Part C:

To compare the areas covered by two-way radios A and B, we need to convert the area covered by two-way radio A to kilometers:

1 mile = 1.61 kilometers, so:

113 square miles = 113 x (1.61)^2 square kilometers

113 square miles = 292.05 square kilometers (rounded to two decimal places)

Therefore, two-way radio B covers a larger area than two-way radio A.

Part D:

The scale factor relationship between the radio coverages can be determined by dividing the radius of two-way radio B by the radius of two-way radio A:

12.88 kilometers/6 miles = 12.88/9.66 = 1.33 (rounded to two decimal places)

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Answer:

x=29°

Step-by-step explanation:

as lines are parallel.

external alternate angles are equal.

7x-86=4x+1

7x-4x=1+86

3x=87

x=87/3=29

Option C

Answer:

7) (f+g) (x) = 4^x + 5x -5

8) (f-g) (x) = 4^x + x - 5

Step-by-step explanation:

7)  Find (f +g)(x)

(4^x + 3x + 2x - 5)

(4^x + 5x -5)

(f+g) (x) = 4^x + 5x -5

8) Find (f-g)(x)

(4^x + 3x - 2x - 5)

(4^x + x - 5)

(f-g) (x) = 4^x + x - 5