Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.

A system of equations. x plus 5 y equals 21. x plus y equals 9.

The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.

A coordinate grid showing Garden Produce with Batches of Salsa on the x axis and Batches of Tomato Sauce on the y axis and two lines. The first line passes through (0, 9) and (6, 3). The second line passes through (1, 4) and (6, 3).

Which statement is true about the graph?

Mike can make 3 batches of salsa and 6 batches of tomato sauce using all of his garden produce.
Mike can make 3 batches of salsa and 3 batches of tomato sauce using all of his garden produce.
Mike can make 6 batches of salsa and 3 batches of tomato sauce using all of his garden produce.
Mike can make 6 batches of salsa and 9 batches of tomato sauce using all of his garden produce.

Answer:

Combining these results, it follows that there are 676 x 1000 = 676,000 different license plates possible.

Answer:

Step-by-step explanation:

   2.3, rounded

The equation of line slope intercept form:

1. y = -4x+6.

2. y = 3x -1

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

4. Inappropriate coordinates.

A straight line is an infinite length line that does not have any curves on it. A straight line can be formed between two points also but both the ends extend to infinity.

1. Given;  Slope (m) =  -4 ; y-intercept (c) = 6

  Slope intercept form of straight line:

    y = mx + c

     y = -4x + 6

2. Slope 3 ; passes through (2,5)

   Equation of line;

      (y - y₁) = m(x - x₁)

      y - 5 = 3(x - 2)

      y -5 = 3x - 6

      y = 3x - 6 + 5

      y = 3x -1

3.  passing point (1,-1) , (-2,0)

     (y - y₁) = (y₂-y₁)/(x₂-x₁) (x - x₁)

     (y - (-1)) = (0-(-1))/(-2-1) (x - 1)

      y + 1 = 1/(-3) (x-1)

     -3(y+1) = x -1

     -3y - 3 = x - 1

      -3y = x - 1 + 3

      -3y = x + 2

        y = (-x-2)/3

4. Coordinates are inappropriate.

Learn more about Straight line from:

https://brainly.com/question/27560536

#SPJ1

Answer:

Step-by-step explanation:

17

The large-sample z statistic is 1.923. Based on this result, we reject the null hypothesis and conclude that there is evidence to suggest that a majority of people prefer the taste of fresh-brewed coffee over instant coffee.

To test the claim that a majority of people prefer fresh-brewed coffee, we need to set up the null and alternative hypotheses:

Null hypothesis: p ≤ 0.5 (i.e., the proportion of people who prefer fresh-brewed coffee is less than or equal to 0.5)

Alternative hypothesis: p > 0.5 (i.e., the proportion of people who prefer fresh-brewed coffee is greater than 0.5)

We will use a one-tailed test with a significance level of α = 0.05.

To calculate the large-sample z statistic, we first need to calculate the sample proportion of people who prefer fresh-brewed coffee

P = (60 - 21) / 60 = 0.65

where 60 is the total number of subjects and 21 is the number who prefer instant coffee.

Next, we need to calculate the standard error of the sample proportion:

SE = sqrt(P(1-P)/n) = sqrt(0.65(1-0.65)/60) = 0.078

where n is the sample size.

Finally, we can calculate the z statistic:

z = (P - p) / SE = (0.65 - 0.5) / 0.078 = 1.923

Learn more about z statistic here

brainly.com/question/22443207

#SPJ4

The given question is incomplete, the complete question is:

A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 60 subjects who participate in the study, 21 prefer the instant coffee. Let p be the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee. (In practical terms, p is the proportion of the population who prefer fresh-brewed coffee.)

Test the claim that a majority of people prefer the taste of fresh-brewed coffee. Report the large-sample z statistic

Question 1-

To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.

Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:

A. (1,9) and (9,5)

B. (1,9) and (5,7)

C. (2,7) and (4,3)

D. (2,7) and (6,5)

Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.

Question 2-

To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:

Slope = (change in y) / (change in x)

However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:

A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.

B. The slope is 4, which means that the amount the student raised increases by $4 each hour.

C. The slope is 12, which means that the student will finish raising money after 12 hours.

D. The slope is 20, which means that the student started with $20.

From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

To know more about cuboid visit:

brainly.com/question/27662032

#SPJ1

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

Read more about Equivalent fractions at: https://brainly.com/question/17220365

#SPJ1

In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

Learn more about a linear equation

brainly.com/question/29739212

#SPJ1

Answer:

What are you options

Step-by-step explanation:

I think this is right

Answer:

8 forks

Step-by-step explanation:

12:2

This ratio means there are 12 spoons and 2 forks,

12x4=48 and 2x4=8

48+8=56

Therefore there are 8 forks.

There is a 3.51% probability that a group of 10 persons will exceed the load limit of the elevator.

To find the probability that a group of 10 persons will exceed the load limit of the elevator, we need to calculate the probability that the total weight of the group exceeds 2000 lb.

Since the weights of the people are normally distributed with a mean of 185 lb and a standard deviation of 22 lb, we can use the properties of the normal distribution to solve this problem.

First, we need to calculate the mean and standard deviation of the total weight of the group. The mean of the total weight is simply the mean weight of a person multiplied by the number of persons, which is 185 lb * 10 = 1850 lb.

The standard deviation of the total weight is calculated by taking the square root of the sum of the variances of each person's weight. Since the weights are independent, the variance of the total weight is equal to the sum of the variances of each person's weight. So, the standard deviation of the total weight is sqrt(10) * 22 lb ≈ 69.296 lb.

Next, we can use the normal distribution to calculate the probability that the total weight exceeds 2000 lb. We standardize the value using the formula z = (x - mean) / standard deviation, where x is the threshold value of 2000 lb.

Calculating the z-score: z = (2000 - 1850) / 69.296 ≈ 1.81

Finally, we look up the probability corresponding to this z-score in the standard normal distribution table or use a calculator to find the area under the curve to the right of the z-score. The probability that the group of 10 persons will exceed the load limit of the elevator is approximately 0.0351, or 3.51%.

Therefore, there is a 3.51% probability that a group of 10 persons will exceed the load limit of the elevator.

To know more about probability, visit:

https://brainly.com/question/23743305

#SPJ11

Answer:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Step-by-step explanation:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Answer:

b)612÷6

Step-by-step explanation:

6)612(102

-6

01

- 0

12

-12

0

=102

In linear programming, the feasible region is the set of all feasible solutions that satisfy the constraints of the problem. The feasible corner points are the extreme points of the feasible region, which represent the optimal solutions to the problem. In this case, we have four feasible corner points: (48,84), (0,120), (0,0), and (90,0).

To find the maximum possible value for the objective function, we need to evaluate the objective function at each of the feasible corner points and select the one that gives the highest value. The objective function is a linear combination of the decision variables and represents the quantity that we are trying to maximize or minimize.

Assuming that the objective function is in the form of z = ax + by, where x and y are the decision variables and a and b are constants, we can evaluate the objective function at each of the feasible corner points:

At (48,84): z = a(48) + b(84)

At (0,120): z = a(0) + b(120)

At (0,0): z = a(0) + b(0)

At (90,0): z = a(90) + b(0)

Since we don't have the values of a and b, we cannot calculate the maximum possible value of the objective function. However, we can compare the values of the objective function at each of the feasible corner points and select the one that gives the highest value.

Therefore, we can conclude that the maximum possible value for the objective function will be obtained at one of the feasible corner points: (48,84), (0,120), (0,0), or (90,0).

For more details about linear click here:

https://brainly.com/question/15830007#

#SPJ11

Answer:

2.4 cups, 584 grams, 19.2 fl oz, 0.6 quarts, 115.2 tsp, 1 pint, 32 tbsp, 0.57 liters.

Domain: [-2, 2]

Range: [-4, 3]

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

It’s A.

Step-by-step explanation:

Answer:

a. length and width

Step-by-step explanation:

option a is correct answer

The line represented by the table is:

y = 2x + 40

A general linear relationship is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two pairs:

(6, 52) and (9, 58)

Then we will get:

a = (58 - 52)/(9 - 6)

a = 6/3 = 2

y = 2x + b

To find the value of b, we replace the values of one of the points, if we use the first one (6, 52), then we will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b

40 = b

The line is:

y = 2x + 40

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

30

Step-by-step explanation:

because it is tringle

Probability that customer buy parsley given buy any of two herb  

                =   0.5714

What is probability in math?

Parsley ( 0.4 , 0.6 )

buy  = B ∩ P = 0.08

Don't buy = DB ∩ P = 0.12

Cilantro = ( 0.15 , 0.85 )

buy  = B ∩ C = 0.06

Don't buy = DB ∩ C = 0.34

Don't buy anything = DB = 0.4

P( Buy anything ) = P(B∩P) + P( B ∩ C )

                          = 0.08 + 0.06 = 0.14

Now, P( P/B) = P( P ∩ B)/P(B)

                    = 0.08/0.14  = 4/7  = 0.5714

Hence, probability that customer buy parsley given buy any of two herb

                                          =   0.5714

Learn more about probability

brainly.com/question/11234923

#SPJ4

Answer:

(x + -6)(x + -6) = -36

Step-by-step explanation:

Simplifying

x2 + -12x + 72 = 0

Reorder the terms:

72 + -12x + x2 = 0

Solving

72 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.

72 + -12x + -72 + x2 = 0 + -72

Reorder the terms:

72 + -72 + -12x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0

0 + -12x + x2 = 0 + -72

-12x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72

-12x + x2 = -72

The x term is -12x.  Take half its coefficient (-6).

Square it (36) and add it to both sides.

Add '36' to each side of the equation.

-12x + 36 + x2 = -72 + 36

Reorder the terms:

36 + -12x + x2 = -72 + 36

Combine like terms: -72 + 36 = -36

36 + -12x + x2 = -36

Factor a perfect square on the left side:

(x + -6)(x + -6) = -36

Can't calculate square root of the right side.

The solution to this equation could not be determined.

MARK BRAINLIEST PLSSS

a. when x = 10, dy/dx = -1 and dy/dt = -20.

b. when x = 25, dy/dx = -4/25 and dy/dt = -125/4.

c. when x = 50, dy/dx = -1/25 and dy/dt = -500.

What is implicit differentiation?

The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately by expressing the derivative of the dependent variable as a symbol and by solving the resulting expression for the symbol.

To find dy/dx, we can use implicit differentiation:

Now we can substitute the given values of x and y to find the corresponding values of dy/dt and dy/dx.

(a) If x = 10 and xy = 100, then y = 10:

dy/dx = -y/x = -10/10 = -1

Using the chain rule:

dy/dt = dy/dx * dx/dt

20 = -1 * dx/dt

dx/dt = -20

Therefore, when x = 10, dy/dx = -1 and dy/dt = -20.

(b) If x = 25 and xy = 100, then y = 4:

dy/dx = -y/x = -4/25

Using the chain rule:

dy/dt = dy/dx * dx/dt

20 = (-4/25) * dx/dt

dx/dt = -125

Therefore, when x = 25, dy/dx = -4/25 and dy/dt = -125/4.

(c) If x = 50 and xy = 100, then y = 2:

dy/dx = -y/x = -2/50 = -1/25

Using the chain rule:

dy/dt = dy/dx * dx/dt

20 = (-1/25) * dx/dt

dx/dt = -500

Therefore, when x = 50, dy/dx = -1/25 and dy/dt = -500.

To know more about implicit differentiation visit,

https://brainly.com/question/30073882

#SPJ1

Answer:

\(\boxed {\frac{2}{1}}\)

Step-by-step explanation:

Use the rise over run to help you find the rate of change of the following graph:

\(\frac{rise}{run}\)

Since every point shows that it is going up, then it means that the numbers you going to have are going to be positive:

Rise = \(2\)

Run = \(1\)

\(\frac{rise}{run} = \boxed {\frac{2}{1}}\)

So, the rate of change is \(\frac{2}{1}\).

After solving 4sin²(x) - 8sin²(x/2), we get 4(cos(x) - cos²(x)) as an answer i.e, option (A) is the answer.

Trigonometry expression : 4sin²(x) - 8sin²(x/2)

What is Trigonometry expression?

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosec , cosine , cotangent , secant , sine , and tan.

Given expression, 4sin²(x) - 8sin²(x/2)

=> 4(sin²(x) - 2sin²(x/2))

=> 4(sin²x - 2(√(1 - cos x) / 2)²)

=> 4(sin²x - 2(1 - cos x) / 2)

=> 4(1 - cos²x - 1 + cos x)

=> 4(cos(x) - cos²(x))

Therefore, the answer is option(a) i.e,4(cos(x) - cos²(x)).

To read more about the Trigonometry.

https://brainly.com/question/25870256

#SPJ13