A store has two types of animal feed available. Type A contains 9 pounds of oats and 3 pounds of corn per bag. Type B contains 2 pounds of oats and 10 pounds of corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 57 pounds of oats and at least 75 pounds of corn. The store only has 15 bags of type A feed and 15 bags of type B feed in stock. Type A costs $1 per bag, and type B costs $4 per bag. How many bags of each type should the farmer buy to minimize his cost?

The graph of the piece-wise function f(x) is given by the image shown at the end of the answer.

The value of a for lim x → a f(x) does not exist is given as follows:

a = 2.

A piece-wise function is a function that has different definitions, depending on the intervals of the input x of the function.

The function for this problem has three definitions, given as follows:

The value of a for which the limit does not exist is a = 2, as the function approaches x = 2 to the left and to the right at different values, 1 to the left and 4 to the right).

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The probability that exactly one 6 is rolled is 42.9%

Rolling a six-sided dice and an eight-sided die can yield a variety of results. The probability of rolling exactly one 6 out of the two dice is 6/14, or approximately 42.9%.

This is calculated by taking the total number of ways to roll one 6 (6) and dividing it by the total number of combinations possible (14). This means that there is a 42.9% chance of rolling one 6 when two dice are rolled.

The probability will be calculated by:

6/14

= 0.429

0.42× 100

=42.9

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The unit rate of the situation is 12/25 per hour

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

Size of the room painted = 1/5 of a room

Time spent painting the room = 5/12-hour

The unit rate of the scenario is then calculated using the following unit rate equation

Unit rate = Size of the room painted/Time spent painting the room

Substitute the known values in the above equation, so, we have the following representation

Unit rate = (1/5)/(5/12)

Evaluate the quotient

So, we have the following representation

Unit rate = 12/25

Hence, the unit rate is 12/25 per hour

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The number of zinc in grams present in the chemical that contains zinc and copper in the ratio of 3 to 9 is  247 grams.

A ratio can be defined as the smallest fraction between two quantities in terms of their physical properties.

To calculate the grams of zinc the chemical contains, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the mass of zinc is 247 grams.

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The system of equation is written to be $58 + $16x = $68 + $14x

the expenditure and the pay will both be $218

the number of hours of work is 5 hours

Let the number of hours of work be x

information from the problem

Ernest spent $58 on equipment and hired a server who makes $16 per hour

$58 + $16x

Ernest is hoping to make up these expense at the next job that is scheduled, which pays a base of $68 in addition to $14 per hour

$68 + $14x

In theory, this event could pay enough to cancel out Ernest's expenditures. hence it will be equated, the expenditure =  pay

$58 + $16x = $68 + $14x

16x - 14x = 68 - 58

2x = 10

x = 5

the expenditure =  pay,

$58 + $16x

= $58 + $16 * 10

= $58 + $160

= $218

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Answer:

1 [tex]\frac{19}{40}[/tex]

Step-by-step explanation:

Rewire with 40 as the common denominator

[tex]\frac{20}{40}[/tex] + [tex]\frac{24}{40}[/tex] + [tex]\frac{15}{40}[/tex] = [tex]\frac{59}{40}[/tex]

This can be rewritten

[tex]\frac{40}{40}[/tex] + [tex]\frac{19}{40}[/tex]  another name for [tex]\frac{40}{40}[/tex] = 1

1[tex]\frac{19}{40}[/tex]

The first step in constructing a segment congruent to a given segment is to draw a vertex and a ray.

Step 1: draw a vertex and a ray

Step 2: Draw a line segment that is longer than the specified line segment if we are not given the line segment on which we are to create the congruent section. The portion we just sketched will be known as the second line segment.

Step 3: Place the needle of the compass at an endpoint of the second line segment.

Step 4: Draw an arc of the circle so that it intersects the line segment.

Step 5: Label the point where we placed the needle and the point of intersection using two letters. The congruent line segment we want is the line segment formed by these two endpoints.

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The representation that is most appropriate to show the relationship between the number of chapters and the total pages of a book is given by:

Graph 1.

Before choosing the correct graph, we must classify the function as discrete or continuous, as follows:

Then the graph of each type of function is given as follows:

The input and output variables in this problem are given as follows:

The number of chapters assumes only integer values, hence the function has a discrete domain, meaning that the graph is composed by dots.

However, the first graph is correct, as the third graph has a range of input and output values that is not present on the table, while the range in the first graph is according to the table.

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Answer: the 3rd graph because it has no time data

Step-by-step explanation:

The coordinate of B, given the coordinates of A and C and the distance between A and B, is  - 2

To find the coordinate of B, you first need to find the distance between A and C which is :

= Coordinate of C - Coordinate of A

= 12 - ( - 9 )

= 12 + 9

= 21

The distance between A and B is 1 / 3 of this distance so it is:

= 21 x 1 / 3

= 7

The coordinate of B is therefore :

= Coordinate of A + distance between A and  B

= - 9 + 7

= - 2

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The expression x - 4 is a factor of the polynomial f(x) = 4x³ - 21x² + 26x - 24 as f(4) = 0. And (x - 4)(4x² - 5x + 6) is the product of two factors for f(x).

The factor theorem states that: if f(x) is divisible by x - a if and only if f(a)=0.

We shall evaluate f(4) to know if x - 4 is a factor of the polynomial f(x) as follows;

f(4) = 4(4)³ - 21(4)² +26(4) - 24

f(4) = 256 - 336 + 104 - 24

f(4) = 360 - 360

f(4) = 0

The first row of the synthetic division is derived as follows:

4x³ divided by x equals 4x²

x - 4 multiplied by 4x² equals 4x³ - 16x²

subtract 4x³ - 16x² from 4x³ - 21x² + 26x - 24 will result to -5x² + 26x - 24

Thus x - 4 is a factor and we will divide the polynomial expression 4x³ - 21x² + 26x - 24 exactly to get the quotient 4x² - 5x + 6.

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A set of triangles can be proven to be congruent using the angle-side-angle rule.

The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.

There is not enough detail provided. Triangles can be shown to be congruent by LA if the congruent acute angle and leg are corresponding. The triangles cannot be proven to be congruent if the pieces are not matching.

A set of triangles can be proven to be congruent using the angle-side-angle rule. According to the ASA rule, two triangles are congruent if their two included sides and two angles are the same as those of another triangle.

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The integral by reversing the order of integration is  (e⁴⁹ - 1)/ 14

The given integral is e ^ (x ^ 2) dx from 7y to 7 dy from 0 to 1

Frist Integral from 0 to 1 and second integral from 7y to 7 e power x power 3 dxdy

We will first change the integration order by dydx as follows

The integration limits are:

0≤y≤1 , 7y≤x≤7

Now we first put y=0 and we will get

0≤x≤7

Also from 7t≤x≤7 we get

0≤yx/y

So that the double integral after reversing integral order will be

Frist Integral from 0 to 7 and second integral from 0 to x/7  e power x power 3 dydx

Now we have have the integral wrt x dx as

Frist Integral from 0 to 1 and second integral from 7y to 7 e power x power 3 dxdy= (e⁴⁹ - 1)/ 14

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Jack's maximum and minimum time to fold his laundry is |x - 30| = 10: option is D.

Remember that the statement says Jack's time can vary from the average of 30 minutes by 10 minutes. By implication it means that the maximum and minimum time will be 30 minutes plus or minus 10 minutes, or 40 minutes and 20 minutes, respectively. We can represent these values using the variable x.

The maximum time will be represented by x + 10 and the minimum time will be represented by x - 10. We can use the absolute value function to represent the difference between these two values and the average time of 30 minutes.

The absolute value function is represented as |x|. The absolute value of x is the distance between x and 0 on a number line. For example, the absolute value of -5 is 5, because the distance between -5 and 0 on a number line is 5 units.

Using the absolute value function, we can represent the difference between the maximum and minimum times and the average time of 30 minutes as follows:

|x + 10 - 30| = |x - 30| = 10

|x - 20| = 10

|x - 30| = 10

Therefore, the correct equation is |x - 30| = 10.

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Answer:175ft cube is the volume of the figure.

Step-by-step explanation:The volume of lower part is,

V=L*B*H

V=5*7*2

V=70ft cube

Volume of upper grade part is,

V2=L*B*H

V2=3*5*7

V2=105ft cube

Therefore total volume=V+V2

=175 ft cube

The value of investment after 2 years is found to be $43.

Thus,

Two points taken from graph are-

(x1 , y1) = (0,25)

(x2, y2) = (1, 25.75)

slope m = (25.75 - 25) / (1 - 0)

m = 0.75

Equation of line,

y - y1 = m(x - x1)

y - 25 = 0.75(x - 0)

y - 25 = 0.75x

y = 0.75x + 25  ...eq 1

Thus, the price after 2 years or 24 months,

Put x = 24  in eq 1

y = 0.75*24  + 25

y = 43

Thus, the value of the investment after 2 years is found to be $43.

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The researchers can use the table of random digits to assign each item to one of the three groups. They can assign the first 400 items to group 1, the next 400 items to group 2, and the final 400 items to group 3.

By randomly assigning the items to the different groups, the researchers can eliminate any bias that could be caused by selecting the items in a particular order.

Once the items have been randomly assigned, the researchers can drop the items from the plane with the appropriate parachute and measure the time to deploy and reliability for each group. They can then compare the results across the three groups and draw conclusions about the effectiveness of each process.

Researchers can use a table of random digits to randomly assign 1,200 objects into three equally sized treatment groups suitable for comparison. They can then drop the items from the plane with the appropriate parachute and measure the time to deploy and reliability for each group to compare the results and draw conclusions about the effectiveness of each process.

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Aeronautical researchers place the objects in randomly designed table divided into three equally sized groups from left to right given by :

Assigned the 400 items in group 1 , next 400 items in group 2 then remaining 400 in group 3.

As given in the question,

Total number of objects need to drop from parachute is equal to 1200.

Therefore, the processes required to arranged the randomly selected objects drop from parachute are group 1 contain first 400, group 2 next 400 and group 3 should contain the remaining 400 objects.

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Drought is a natural disaster that occurs over an extended period of time. It is a condition in which there is a lack of sufficient water for a long period of time, usually due to a lack of rain or other natural sources of water. This can lead to a variety of problems, such as crop failure, dehydration, and other negative effects on the environment and economy. It is important to be prepared for droughts and to take steps to conserve water during these times.

Expanding the square terms and rearranging the expressions for simplification , we can solve for x. The answer is x = [tex]\frac {5}{2}[/tex] or [tex]\frac {3}{2}[/tex] .

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

[tex](2x-3)^2 = 4x-6\\4x^2 -12x+9 =4x-6\\4x^2 - 16x +15 =0\\4x^2-10x-6x+15 =0\\2x(2x-5)-3(2x-5)=0\\(2x-5)(2x-3)=0[/tex]

x = [tex]\frac {5}{2}[/tex] or [tex]\frac {3}{2}[/tex]

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Answer:

70.9%

Step-by-step explanation:

"56 out of 79" can be written as (56/79).  This is equal to a decimal value of 0.708861, or a percentage of 70.8861%.  Round to 1 decimal point to give 70.9%.

The enrollment of the school each year after 2000 is a linear function and the equation is f(x) = 1200 + 35x

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

Initial number of students = 1200

Rate of student per year = 35

The above parameters implies that there is a constant increment of 35 students each year since 2000

This means that the scenario is a linear equation

A linear equation is represented as

y = mx + c

In this case, we have

c = Initial number of students = 1200

m = Rate of student per year = 35

Substitute the known values in the above equation, so, we have the following representation

y = 35x + 1200

Hence, the equation is y = 35x + 1200

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The critical value for the test would be +/- 1.984

The critical value for a two-tailed t-test with a significance level of 0.05 and degrees of freedom of 99 is the value beyond which we can reject the null hypothesis. This means that if the test statistic (t-value) is greater than or less than this critical value, we can conclude that the null hypothesis is not true and the alternative hypothesis is more likely to be true.

To find the critical value, we can use a t-distribution table or a calculator with t-test functionality. We input the desired significance level (0.05), the degrees of freedom (99), and the type of test (two-tailed). The resulting value is the critical value for this test.

In this case, the critical value for the test would be +/- 1.984. This means that if the t-value calculated from the sample data is greater than 1.984 or less than -1.984, we can reject the null hypothesis and conclude that the mean foam height is not equal to 175 mm. If the t-value is between these two values, we cannot reject the null hypothesis and cannot conclude that the mean foam height is different from 175 mm.

Complete Question

A consumer products company is formulating a new shampoo and is interested in foam height (in mm). foam height is approximately normally distributed and has a standard deviation of 20 mm. the company wishes to test h0: μ = 175 mm versus h1: μ ≠ 175 mm. the company plans to use a sample of 100 shampoo bottles and conduct a two-tailed t-test with a significance level of 0.05. what is the critical value of this test?

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If the sample average is = 185, the p value would be 0.057

In this question we have been given a company is formulating a new shampoo and is interested in foam height (in mm).

Foam height is approximately normally distributed and has a standard deviation of 20 mm.

The company wishes to test H0: μ = 175 mm

versus H1: μ > 175 mm, using a random sample of n = 10 samples

We need to find the p-value if the sample average is = 185.

we first compute the z-score.

We know that the formula for the z-score is:

z = (x{bar} - μ)/(σ/√N)

Here, x{bar} = 185

μ = 175

σ = 20

N = 10

so, z = (185 - 175)/(20/√10)

z = 1.5811

From the standard noram table, a p-value associated to z = 1.5811 is:

p = 0.0569

p = 0.057

So the p-value is  0.057

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The complete question is:

A consumer products company is formulating a new shampoo and is interested in foam height (in mm). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test H0: μ = 175 mm versus H1: μ > 175 mm, using a random sample of n = 10 samples.(a) Find P-value if the sample average is = 185? Round your final answer to 3 decimal places.

The correlation Illustrates that B. The graph shows a positive correlation, and it is a non-linear model.

In this scenario, the width would be plotted on the x-axis of the scatter plot while the length in centimeters would be plotted on the y-axis of the scatter plot.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select the format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the width and length, a linear equation for the line of best fit is given by y = 1.31x + 0.02.

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Answer: The graph shows no correlation, and it is neither linear nor exponential.

Step-by-step explanation:

try doing a line of fit you're ALWAYS. gonna be ignoring other dots/points/coorids.

Why it's not a correlation is because nothing is together. You could consider a lot of dots on the edge.

If that doesn't make sense to you lets go through each answer

The graph shows a negative correlation, and it is a linear model.

The coordinates don't form any specific line

None of the coordinates are together

there's no slope since there's no line of fit.

it's THE SAME FOR THE OTHER ANSWER CHOICES BESIDES:

'The graph shows no correlation, and it is neither linear nor exponential.'

Step-by-step explanation:

Add up 1,2,4 which is 7. Then do 14,000/7 which gives you 2,000kg. Then multiply the 2,000kg with each number in the ratio. It can be tricky to grasp this method at first, but believe me when I say that after practice it becomes almost second nature.

Answer:

2,000kg X 1 = 2,000kg

2,000kg X 2 = 4,000kg

2,000kg X 4 = 8,000kg

2,000kg X 1 = 2,000kg

2,000kg X 2 = 4,000kg

2,000kg X 4 = 8,000kg

Answer:

I don't really understand this question. But i hope it helps.

Step-by-step explanation:

214,000,000
+ 907,000

Answer:

Answer Below

Step-by-step explanation:

Let us take the variables as x,x+1

x+x+1 = 214907000

2x+1 = 214907000

2x = 214906999

x = [tex]\frac{214906999}{2}[/tex]

x = 107453499.5

1st number = x = 107453499.5

2nd number = x + 1 = 107453499.5 + 1 =107453500.5

Hence , the number that need to be added to get 214,907,000 are 107453499.5 and 107453500.5

Answer:

1) y = 3x + 0

54 houses = 3 houses/week * x weeks

x = 18 weeks

2) y = -450x + 18000

6000 gallons = -450 gallons/day * x days + 18000

x = 10 days

The packaging that will use more material would be the 6 rows in 2.

Packaging is a method used by companies to present a finished product to the population in such a way that their products can be easily accessed.

The first choice of packaging= 3 rows in 4 which means that it's only three packages that would be used.

The second choice of packaging = 6 rows in 2 which means that it's up to six packages that would be used.

Therefore, it would be better for the company to chose the 3 rows in 4 which is the first choice as it will save up materials for them.

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The gradient vector field ∇f of f(x,y) = x^2 -5y is <2x, -5>

The gradient vector field is a vector-valued function that is used to describe the direction of the steepest ascent of a scalar field. The gradient vector field of a scalar field f is given by ∇f = <∂f/∂x, ∂f/∂y>

In this case, the gradient vector field of f(x, y) = x^2 − 5y is <2x, -5>.

To sketch the gradient vector field, we can start by plotting a few points on the x-y plane and then drawing the gradient vector at each point.

For example, the gradient vector at the point (1,0) is <2, -5>; at the point (0,1) is <0, -5>; at the point (-1, 0) is <-2, -5>; at the point (0, -1) is <0, -5>.

The vector field will be pointing towards the direction where the function increase the most, in this case, the vector field will be pointing upwards and to the right in the x-y plane.

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The inequality 1.10 < 1+ (55/60) can be used to find how much longer Emma can run and still beat her previous time. This inequality is formed by taking her previous 10-kilometer time of 1 hour and 10 minutes and adding the number of minutes she has already run (55 minutes) divided by 60. If the result is greater than 1.10, she will beat her previous time.

1.10 < 1 + (55/60)

1.10 < 1.9166667

0.79166667 < 0.9166667

Therefore, Emma can run for up to 0.79166667 more hours and still beat her previous time.

The inequality 1.10 < 1+ (55/60) can be used to find how much longer Emma can run and still beat her previous time. This inequality is formed by taking her previous 10-kilometer time of 1 hour and 10 minutes and adding the number of minutes she has already run (55 minutes) divided by 60. The equation can be written as

1.10 < 1+(55/60).

If the result is greater than 1.10, she will beat her previous time. To calculate, we first divide 55 minutes by 60 to get 0.91666667 and then add 1 to get 1.91666667. We then compare this value to 1.10 and see that 1.10 is less than 1.91666667, so Emma can run for up to 0.79166667 more hours and still beat her previous time. This is equivalent to 47 minutes. Therefore, if Emma runs for a total of 1 hour and 42 minutes, she should beat her previous time.

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To reflect a point over the x-axis, we need to negate the y-coordinate. So the reflections of points J, K, and L over the x-axis are:

J'(2,4)

K'(3,-7)

L'(6,1)

Note that the x-coordinates are unchanged because the x-axis is the line of reflection.