You must present the procedure and the answer correct each question in a clear way. 1- Maximize the function Z = 2x + 3y subject to the conditions: x > 4 y5 (3x + 2y < 52 2- The number of cars traveling on PR-52 daily varies through the years.

Answer:

(-2,4)

Step-by-step explanation:

First, put x+y=2 into slope-intercept form: y=-x+2

Second, set the to equations equal to each other: -x+2=1/2x+5

Then, add x to both sides: -x+x+2=1/2x+x+5 to get: 2=3/2x+5

Next, subtract 5 from both sides: 2-5=3/2x+5-5, to get -3=3/2x

Finally, to get the x-value, divide both sides by 3/2: -3(2/3)=3/2x(2/3), to get x=-2

Lastly, substitute -2 for x into one of the equations to find y:

x+y=2

-2+y=2

add 2 to both sides: -2+2+y=2+2, to get y=4

The solution is (-2,4)

Answer:

(- 2, 4 )

Step-by-step explanation:

Given the 2 equations

x + y = 2 → (1)

y = \(\frac{1}{2}\) x + 5 → (2)

Substitute y = \(\frac{1}{2}\) x + 5 into (1)

x + \(\frac{1}{2}\) x + 5 = 2 ( multiply through by 2 to clear the fraction )

2x + x + 10 = 4

3x + 10 = 4 ( subtract 10 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

Substitute x = - 2 into (1) and evaluate for y

- 2 + y = 2 ( add 2 to both sides )

y = 4

Solution is (- 2, 4 )

Answer:

Greatest number is 65432

Lowest number is 23456

Step-by-step explanation:

\(65432+23456=88888\)

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

The equations to solve are x + y = 100 and 15x + 20y = 1650. Solving these equations gives x = 70 and y = 30. Therefore, 70 type A masks and 30 type B masks were sold in April 2020.

To find the number of masks of each type sold in the month of April, we can set up a system of equations based on the given information.

Let's assume that 'x' represents the number of type A masks sold and 'y' represents the number of type B masks sold.

From the given information, we know that the cost of a type A mask is Rs. 15 and the cost of a type B mask is Rs. 20. The total sales for 100 masks is Rs. 1650.

So, we can write the following equations:

x + y = 100 (Equation 1: Total number of masks sold is 100)

15x + 20y = 1650 (Equation 2: Total sales amount is Rs. 1650)

To solve this system of equations, we can use the substitution method. Rearrange Equation 1 to solve for x:

x = 100 - y

Substitute this value of x into Equation 2:

15(100 - y) + 20y = 1650

Expanding the equation:

1500 - 15y + 20y = 1650

Combine like terms:

5y = 150

Simplifying:

y = 30

Substitute this value of y back into Equation 1 to find x:

x + 30 = 100

x = 100 - 30

x = 70

Therefore, 70 type A masks and 30 type B masks were sold in the month of April.

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Answer:  1) y = (-5/7)x + 11/7

               2) y = (-1/4)x - 3

               3) y = (1/2)x - 1

Step-by-step explanation:

Use the Point-Slope equation:    y - y₁ = m(x - x₁)    where

(x₁, y₁) = (-2, 3)     m = -5/7

y - 3 = -5/7(x + 2)

y - 3 = (-5/7)x - 10/7

y      = (-5/7)x + 11/7

(x₁, y₁) = (-4, -2)     m = -1/4

y + 2 = -1/4(x + 4)

y + 2 = (-1/4)x - 1

y      = (-1/4)x - 3

(x₁, y₁) = (2, 0)     m = 1/2

y - 0  = 1/2(x - 2)

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

y      = (1/2)x - 1

Answer:

the third answer

5+18 *dont know if that 8 or 5 sorry*

Step-by-step explanation:

Answer:

Step

Y-0=-3/4(x-8)

Y=-3/4x+6

Answer:

x12

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

slow eater lol.

in one fifth of a minute, they ate 3 pieces. so add the other four fifths, 3 + 3 + 3 + 3 + 3, and youll get 15. easier to just multiply tho, 1/5 is 3, so 5/5 would be 3(5) = 15. hope this helps

it can be concluded that the population standard deviation is within or less than 12.

To construct a hypothesis test to determine whether the population standard deviation of σ≦12 should be rejected for Costco, we can use a chi-square test for variance.

Step 1: State the null and alternative hypotheses:
- Null hypothesis (H₀): σ ≤ 12
- Alternative hypothesis (H₁): σ > 12

Step 2: Determine the level of significance (α = 0.05) and degrees of freedom (df = n - 1 = 11 - 1 = 10).

Step 3: Calculate the test statistic:
- χ² = (n - 1) * (s² / σ²) = 10 * (11.3² / 12²) = 10 * 0.94 = 9.4

Step 4: Determine the critical value:
- The critical value at α = 0.05 with df = 10 is χ²ₐ = 18.307

Step 5: Compare the test statistic with the critical value:
- Since χ² = 9.4 < χ²ₐ = 18.307, we fail to reject the null hypothesis.

Step 6: Conclusion:
- Based on the given sample data, there is not enough evidence to reject the hypothesis that the population standard deviation of σ≤12 for Costco.

Therefore, it can be concluded that the population standard deviation is within or less than 12.

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0.529 is the probability that a student does not have a college degree.

From the information given, we know that:

The formula for conditional probability:

P(A|B) = P(A and B) / P(B)

Let A be the event of not having a college degree, and B be the event of being married. We want to find P(A).

Using these values, we can calculate:

P(college degree and B) = (1/2) * (400/850) = 0.235

P(A and B) = 310/850 - 0.235 = 0.07

Finally, we can calculate P(A) using the formula for total probability:

P(A) = 1 - P(college degree)

= 1 - (400/850)

= 0.529

Therefore, the probability that a student does not have a college degree is 0.529.

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So, 15 and 1 is the pair of numbers whose difference is 14, with the smallest product as 15.

To find the pair of numbers with the smallest product whose difference is 14, we can start by taking the two numbers to be as close to each other as possible. This means we can take one number to be 14 less than the other. For example, we can take the numbers to be 15 and 1. The difference between these two numbers is 14, and their product is 15, which is the smallest product possible for a pair of numbers whose difference is 14.

So, 15 and 1 is the pair of numbers whose difference is 14, with the smallest product as 15.

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Answer:

2.5% of 15,530 is 388.25

Using a standard normal distribution table or a statistical software, we can determine that the probability is approximately 0.9091. To calculate the probability between -2.08 and 1.46 for the standard normal random variable, Z, we need to find the area under the standard normal curve between these two values.

This probability represents the proportion of observations that fall within this range. Using a standard normal distribution table or a statistical software, we can find the corresponding z-scores for -2.08 and 1.46. These z-scores indicate how many standard deviations away from the mean each value is in the standard normal distribution. Looking up the z-score of -2.08 in the table, we find that it corresponds to a cumulative probability of approximately 0.0192. Similarly, the z-score of 1.46 corresponds to a cumulative probability of approximately 0.9279. To find the probability between these two z-scores, we subtract the cumulative probability of -2.08 from the cumulative probability of 1.46. Hence, the probability that -2.08 < Z < 1.46 is approximately 0.9279 - 0.0192 = 0.9087. Therefore, the closest answer choice is 0.9091, indicating that the probability is approximately 0.9091.

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The range of the function f (x) = - 3x² + 5 is,

⇒ (- ∞, 5]

⇒ All real numbers less than or equal to 5

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ f (x) = - 3x² + 5

Now, We an draw the graph of function f (x) = - 3x² + 5.

In graph the range is the defined as cover by up and down.

Hence, The range of the function f (x) = - 3x² + 5 is,

⇒ (- ∞, 5]

⇒ All real numbers less than or equal to 5

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Answer:24

Step-by-step explanation:

i think its right just try

The coordinates of point b ( x, y) are ( - 5, 4 ).

The midpoint of the line ab is m( -1, -1 ).

The coordinates of the endpoints of the line are a( 3, -6) and b( x, y).

Now, the midpoint of the line with two endpoints A(x, y) and B( c, d) is given as:

m = [ ( x + c) / 2 , ( y + d) / 2 ]

Therefore,

m = [ ( 3 + x) / 2, ( - 6 + y ) / 2 ]

( -1 , - 1) = [ (3 + x / 2 ), ( -6 + y / 2 ) ]

Therefore,

(3 + x) / 2 = - 1

3 + x = - 2

x = - 2 - 3

x = - 5

And;

-6 + y / 2 = - 1

- 6 + y = - 2

y = - 2 + 6

y = 4

Therefore, ( x, y) = ( - 5, 4).

Therefore, the coordinates of point b are ( - 5, 4 ).

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Let A and B be two independent events. If P(B) = 0.5. We can say about P(B|A) that D. It is equal to 0.5.

Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Since A and B are independent events, the probability of event B occurring given that A has occurred (P(B|A)) is the same as the probability of event B occurring without knowledge of whether or not A has occurred (P(B)). Therefore, P(B|A) = P(B) = 0.5.

Hence Option D is correct.

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Answer:

c = 4,9

d = 4,6

Answer:

480ft.it does not matter how much east or west they are.it asks how much"they are apart"

so it should be 480.

The total amount spent buying ham and cheese is $187.20

What is the total cost of each item?

The total cost of each item can be determined as the price multiplied by the quantity bought

quantity of ham bought=x+4

quantity of cheese bought=x-3

price per pound of ham=$6.24

price per pound of cheese=$4.80

total amount spent on ham=(x+4)*6.24

total amount spent on ham=6.24x+24.96

total amount spent on cheese=(x-3)*4.80

total amount spent on cheese=4.80x-14.40

If the individual spent twice on as much on ham than cheese, it means that amount on ham is equals twice of the one spent on cheese

6.24x+24.96=2(4.80x-14.40)

6.24x+24.96=9.60x-28.80

24.96+28.80=9.60x-6.24x

53.76=3.36x

x=53.76/3.36

x=16

total amount spent=6.24x+24.96+4.80x-14.40

total amount spent=6.24(16)+24.96+4.80(16)-14.40

total amount spent=$187.20

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The initial equation is:

So if we use the distribution propertie, we have to multiply the 4 for all term in the parenthesis so:

and then we simplify:

So is option D)

Answer:

Step-by-step explanation:

The Answer is B.

2x - 31 = -2x - 31

x = 0

Answer:

1/3

Step-by-step explanation:

y is increasing by 1 and x is increasing by 3 so since y/x can't be simplified it's 1/3

Answer:

1/3

Step-by-step explanation:

to find the slope do rise/run and y -axis is increasing by 1 and x-axis is increasing by three just divide those two

We choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

a. To find the test statistic z, we use the formula:

z = (p - P) / sqrt [P(1-P) / n]

where p is the sample proportion, P is the hypothesized proportion under the null hypothesis, and n is the sample size.

Plugging in the values given, we get:

z = (0.43 - 0.5) / sqrt [0.5(1-0.5) / 100] = -1.96

b. To find the P-value for H_a: p < 0.50, we look up the probability of getting a z-score less than -1.96 in a standard normal distribution table. The P-value is the area under the standard normal curve to the left of -1.96.

The P-value is approximately 0.025.

c. Since the P-value is less than the significance level of 0.05, we can reject the null hypothesis at the 5% level of significance. The P-value gives strong evidence against H_0. Therefore, we choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

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Based on the decay of potassium-40 in the rock layers, the estimated age of the rock is approximately 1.4 billion years.

Potassium-40 has a half-life of 1.25 billion years, which means that after 1.25 billion years, half of the original amount of potassium-40 would have decayed. In this case, the scientist finds that the potassium-40 level has decayed to 93% of the original amount.

To estimate the age of the rock, we can use the concept of half-life. Since 93% of the original amount remains, we can deduce that two half-lives have occurred because each half-life reduces the amount by half.

If one half-life is 1.25 billion years, then two half-lives would be 2.5 billion years. However, since we are looking for the approximate age of the rock, we can divide this by 2 to get 1.25 billion years, which corresponds to one half-life.

Therefore, the estimated age of the rock is approximately 1.4 billion years (1.25 billion years + 0.25 billion years). It's important to note that this is an estimation and there may be some margin of error associated with it.

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The value of expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x is -18.82 Joules.

When there is a force action on an item, the thing travels some distance. The quantity of work done is given by the product of the magnitude of force applied to the object and the displacement of the object. Additionally, as the particle's speed changes, the difference in kinetic energy indicates the value of work done.

We have a body of mass = 4kg

It experiences a repulsive force of F = ax² + bx

Work done is given by the formula,

\(Work done = a(\frac{1}{x1}-\frac{1}{x2} ) + b*ln(\frac{x2}{x1} )\)

= 19(1/8.5 - 1/2.5) + 11 ln(2.5/8.5)

= -5.364 + -13.461

= -18.82 Joules.

Therefore, the value of the work done by the object is -18.82 Joules.

We have to find the velocity so we have

we have value of a = 19 and b= 11

velocity = 2ax + b

= 2 x 19 x (x4 - x3) + 11

= 2 x 19 x (12.5 - 1.3) + 11

= 2 x 19 x 11.2 + 11

= 436.6 m/s

So the velocity is given by 436.6 m/s.

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Answer:

Sophie in 9 days and Susan in 12 days

Step-by-step explanation:

This question is very vague and the answer in clearly in front of your eyes.

Answer:

The acceleration is 965 kg•ms^-2

Step-by-step explanation:

Mathematically;

Force = mass * acceleration

From the question;

Force = 1930 N (kg• ms^-2)

mass = 2kg

Acceleration = Force/mass = 1930/2 = 965 ms^-2