A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces (in ounces). When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find an equation that gives the yield y when n stalks are planted.

The equation of the exponential graph shown over the x-y coordinate is y=100.(1/2)x.

The equation of the exponential graph represent the exponential function with the initial value and common ratio.The equation of the exponential graph is given as,

\(y=ab^x\)

Here, (a) is the initial value and (b) is the common ratio.

In the graph given in the problem, the initial value is 100 where the value of x is zero, such as,

\(x=0; y=100\)

Put these values in the above equation.

\(100=ab^0\\100=a\times1\\100=a\)

Now, when the value of x is 2 in the graph, the value of y is 25. Put these values again in the equation.

\(25=(100)b^2\\b=\sqrt{\dfrac{25}{100}}\\b=\sqrt{\dfrac{1}{4}}\\b=\dfrac{1}{2}\)

The value of b is 2 and a is 100. Thus, the equation of the exponential graph shown over the x-y coordinate is y=100.(1/2)x.

\(y=100\times(\dfrac{1}{2})^x\)

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Answer:

13) 57.6 units²

14) 285.6 units²

15) 114.2 units²

(All answers rounded off to the nearest tenth)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

a)2

B)2

Step-by-step explanation:

To solve this problem, we have to figure out the time spent travelling and then use the speed-distance-time equation to find the distance between the two places. The distance between Seattle and St. Louis is 2295 miles.

To calculate the miles or distance between Seattle and St. Louis, we have to take into consideration that out of the 42 hours she spent in her journey, she stayed 15 hours over at St. Louis.

\(42 - 15 = 27\)

She spent 27 hours travelling.

Her speed in the first journey was 50mi/h and her speed in the second journey was 35mi/h.

This implies she was faster in her first journey compared to her second journey.

Data;

\(speed = \frac{distance}{time} \\distance = speed * time\)

Let's substitute the values

\(distance = (50 + 35) * 27 = 2295mi\)

The distance between Seattle and St. Louis is 2295 miles

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Answer:

m = -0.204

Step-by-step explanation:

Start by creating points (72, 133) and (24, 235.2+133)

You are relating the charge (as a whole number) to the total distance traveled at a respective percentage. At 72% you traveled 133 miles and at 24% you traveled a total of 368.2 miles.

Thus, you can use the slope formula \((y2-y1)/(x2-x1)\)

Thus, (72-24)/(133-368.2) = -0.204 (approx.)

Hope this helps!

Answer:

$12

Step-by-step explanation:

If we stuck with the price of $8, then we end with an income of $2400

Increasing it by $1 will decrease attendance by 20

8 x 300 = 2400

9 x 280 = 2520

10 x 260 = 2600

11 x 240 = 2640

12 x 220 = 2640

13 x 200 = 2600

We're starting to go down, so let's stop there

The ticket price of $11 or $12 appears to give the most income

I would stick with $12 since your still getting more money from one ticket

The price of a ticket stick at $12 since you still get more money from one ticket.

Last year 300 people attended a play with a ticket price of $8.

The school estimates that 20 fewer people attend for each $1 increase in price.

If we keep the price at $8, we'll end up with a $2400 profit.

Increasing it by $1 will result in a 20 percent drop in attendance.

8 × 300 = 2400

9 × 280 = 2520

10 × 260 = 2600

11 × 240 = 2640

12 × 220 = 2640

13 x 200 = 2600

Let's come to a halt here since we're starting to descend.

The $11 or $12 ticket price looks to generate the most revenue.

I'd continue with $12 because you'll still make more money with one ticket.

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The formula for calculate the volume of a rectangular prism is shown below:

Where "l" is the length, "w" is the width and "h" is the height.

In this case you can identify that:

Then, you can substitute these values into the formula:

Finally you must evaluate, in order to find the volume of this rectangular prism:

The answer is:

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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Answer:

Below

Step-by-step explanation:

Angle 4 + 60 + 61 = straight line = 180 °

angle 4 = 180 - 60 - 61 = 59°

The completed statement with regards to the area of the square and the rectangle are;

The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.

The area of a square is the product of the side lengths which are congruent, therefore;

Area of a square = Side length, s × Side length, s = s²

The possible figure in the question includes;

A shaded square that is 125 square inches

An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches

Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.

Therefore;

The side length of the square = √(125) inches =  5·√5 inches

The estimated value of the side length of the square is; 5·√5 inches

The area of a rectangle = Length × Width

The length of the rectangle = 7·√5 inches

The width of the rectangle = 5·√5 inches

Therefore;

The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175

The estimated area of the unshaded rectangle is 175 square inches

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Answer:

122 Degrees

Step-by-step explanation:

Since we are given that angle 1 and 2 make a linear pair:

angle 1 + angle 2 = 180 degrees ----------------------------(1)

We have also been told that angle 2 is 6 more than twice the measure of angle 1

Which means: angle 2 = (2*angle1)  + 6 -------------------(2)

From putting the value of angle 2 in (1) from (2)

angle 1 + 2*angle 1 + 6 = 180

3*angle 1 = 174

angle 1 = 58 degrees -----------------------(3)

From (1) and (3):

angle 2 + 58 = 180

angle 2  = 122 degrees

Therefore, the measure of angle 2 is 122 degrees

the p-value is between 0.05 and 0.1, which means we can conclude that there is weak evidence against the null hypothesis at the 5% level of significance.the answer is 0.05 < p < 0.1.

To find the p-value for a chi-square test for homogeneity, we need to use the chi-square distribution table with the appropriate degrees of freedom and compare the computed chi-square statistic to the critical value at the desired level of significance.

The degrees of freedom for a chi-square test for homogeneity is given by the formula df = (r - 1) * (c - 1), where r is the number of rows and c is the number of columns in the contingency table. In this case, we have three populations and one categorical variable with three values, so the contingency table has 3 rows and 3 columns. Therefore, the degrees of freedom is df = (3 - 1) * (3 - 1) = 4.

Using the chi-square distribution table with 4 degrees of freedom and looking up the value of chi-square at 2.05, we can see that the corresponding p-value is between 0.1 and 0.05. Specifically, the p-value is between 0.05 and 0.1, which means we can conclude that there is weak evidence against the null hypothesis at the 5% level of significance.

Therefore, the answer is 0.05 < p < 0.1.

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(3+4)h÷2=10.5

7h÷2=10.5

×2=×2

7h=21

÷7=÷7

h=3

The coordinates of point E is (-37/7, 23/7)

The formula for calculating a coordinate points using the points (-1, -1) and point A is located at (-7, 5) in the ratio 2:5 is expressed as:

E (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}

Substitute the coordinates and ratios to have;

E (x, y) = {(2(-1)+5(-7))/2+5, (2(-1)+5(5))/2+5}

E(x, y) = {-35-2/7, -2+25/7}

E(x, y) = (-37/7, 23/7)

Hence the coordinates of point E is (-37/7, 23/7)

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The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

Question 4: 70 degrees

Question 5: 150 degrees

Step-by-step explanation:

Question 4:

The shape is a polygon therefore we need to first find the sum of the angle. The formula is: (number of sides - 2) * 180

Rewrite: (5 - 2) * 180 = 540

To get the answer we add all angles together which is:

135 + 120 + 80 + 135 = 470

Minus to get the last angle:

540 - 470 = 70 degrees

So the answer is 70 degrees:

x = 70 degrees

Question 5:

Again the type of shape is an polygon so first we need to find the sum of the angle.

(6 - 2) * 180 = 720

Next add up all the angles together. The square boxes mean the angle is a right angle. So we can just add 90 degrees for every box you see.

90 + 90 + 120 + 120 = 420

Minus the answer with the sum of the total angle to get the missing value:

720 - 420 = 300 degrees

Next since there are two x, and they are at the same position they are the same value so we can just divide and get the answer.

300 / 2 = 150 degrees

Therefore the answer for both x are 150 degrees:

x = 150 degrees.

Answer:

B

Step-by-step explanation:

Answer:

B)...  A and C

Step-by-step explanation:

A is a square with a length of 6 so the area is 36

but the perimiter is 24

C is a rectangle with a width of 4 and a length of 12 so the area is 36 also

but the perimiter of C is  32

A and C have the same area but a diffrent perimiter

Answer:

C and D

Step-by-step explanation:

\(\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}\)

Answer:

320

Step-by-step explanation:

4,800 ÷ 15 = 320

Checking this

15 × 320 = 4,800

Answer:

12

Step-by-step explanation:

Pythogorean Theorem:

a squared + b squared = c squared

9 squared or 81 + ? squared = 15 squared or 225

Inverse Pythagorean Theorem:

c squared - a squared = b squared

225 - 81 = 144

sqrt (144) = 12

12 = b

Hope this helps! Good luck!

The value of a and b are 6 and -13.

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = ax² + bx + 2 / 2x² - 8

f(x) horizontal asymptote:

y = 3

f(x) has a removable discontinuity:

x = 2

Now,

f(x) has a horizontal asymptote if:

Degree of the denominator = Degree of the numerator

It is given by:

y = coefficient of higher x of the numerator ÷ coefficient of higher x in the denominator

We have,

y = a / 2

3 = a / 2

a = 6

Removable discontinuity at x = 2 means:

Numerator of f(x) = 0

We have,

ax² + bx + 2 = 0

6 x (2)² + b x 2 + 2 = 0

24 + 2b + 2 = 0

2b = -26

b = -13

Thus the value of a and b are 6 and -13.

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

30%

Step-by-step explanation:

Convert fraction to 21 / 70 and then change to percent Answer: 30%

I hope this helps u

The sampling method used in this problem is classified as:

Simple Random Sampling

Samples may be classified as:

In this problem, all the options are assigned a number and then taken, hence a Simple Random Sample is used.

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Answer:

0.78 x 30 = 23.4. I think 23.4 is 78 % of 30.

Step-by-step explanation:

Answer:

.50r + 2p

Step-by-step explanation:

cost of ruler * number of rules  + cost of pens * number of pens

.50 *r + 2 *p

.50r + 2p

Answer:

350 milliliters

Step-by-step explanation:

70% of 500 is 350

Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:

C and D

Step-by-step explanation:

A and B are wrong because 6.3 is smaller than those numbers