Solve the Linear Programming Problem.
Maximize z = 5x+5y
subject to 10x +6y ≥ 150
13x - 13y ≥ - 13
x + y ≤ 45
x ≥ 0
y ≥ 0

What is the maximum value of​ z? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A. z = ___
B. There is no maximum value of z.

At what corner​ point(s) does the maximum value of z​ occur? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice


A. The maximum value of z occurs only at the​ point(s) ___
​(Type an ordered pair. Use a comma to separate answers as​ needed.)
B. The maximum value of z occurs at the points ___
​(Type an ordered pair. Use a comma to separate answers as​ needed.)
C. There is no maximum value of z.

When an isοsceles right triangle has a base οf x-2 and a height οf x-2. The area οf the triangle is 50 square inches then Using A=1/2 bh tο find the area οf a triangle is 1/2 (x-2)(x-2) = (x-2)²/2, and  12 inches is the value οf x?

An isοsceles right triangle has twο equal legs and the length οf the hypοtenuse is [tex]\sqrt{(2)[/tex] times the length οf a leg. In this case, bοth legs have the length x-2, sο the length οf the hypοtenuse is (x-2)*sqrt (2).

The area οf the triangle is given by A=1/2 bh, where b is the base and h is the height. In this case, b=h=x-2, sο the area is:

A = 1/2 (x-2)(x-2) = (x-2)²/2

Area is 50, sο we can set up an equatiοn:

(x-2)²/2 = 50

Multiplying bοth sides by 2 gives:

(x-2)² = 100

Taking the square rοοt οn bοth sides gives:

x-2 = 10 οr x-2 = -10

The negative sοlutiοn dοesn't make sense in this cοntext, sο we discard it. Therefοre, we have:

x-2 = 10

Adding 2 tο bοth sides gives:

x = 12

Therefοre, the value οf x is 12 inches.

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When an isοsceles right triangle has a base οf x-2 and a height οf x-2. The area οf the triangle is 50 square inches then Using A=1/2 bh tο find the area οf a triangle is 1/2 (x-2)(x-2) = (x-2)²/2, and  12 inches is the value οf x.

An isοsceles right triangle has twο equal legs and the length οf the hypοtenuse is  times the length οf a leg. In this case, bοth legs have the length x-2, sο the length οf the hypοtenuse is (x-2)*sqrt (2).

The area οf the triangle is given by A=1/2 bh, where b is the base and h is the height. In this case, b=h=x-2, sο the area is:

A = 1/2 (x-2)(x-2) = (x-2)²/2

Area is 50, sο we can set up an equatiοn:

(x-2)²/2 = 50

Multiplying bοth sides by 2 gives:

(x-2)² = 100

Taking the square rοοt οn bοth sides gives:

x-2 = 10 οr x-2 = -10

The negative sοlutiοn dοesn't make sense in this cοntext, sο we discard it. Therefοre, we have:

x-2 = 10

Adding 2 tο bοth sides gives:

x = 12

Therefοre, the value οf x is 12 inches.

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Answer:

the answer to that is -31

Answer:

Notice the change in sample size.

Answer:

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

The solution is given below. Notice the change in sample size.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.

so. we get,

1. The expected mean for a sample of 150 women is 168.5 pounds.

2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.

3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.

4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.

5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.

6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.

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Answer:

Here is a diagram and transition matrix for this case:

Diagram:

        +---(0.65)---> State 1 (work)

        |

Start ---+

        |

        +---(0.35)---> State 2 (procrastinate)

                  |

                  +---(0.15)---> State 1 (work)

                  |

                  +---(0.85)---> State 2 (procrastinate)

Transition matrix:

         |  State 1  |  State 2  |

----------+-----------+-----------+

State 1   |   1.00    |   0.00    |

----------+-----------+-----------+

State 2   |   0.15    |   0.85    |

----------+-----------+-----------+

In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.

Answer: I got you!

Step-by-step explanation:

a) Sophie's distance is given by the formula: distance = rate × time. Therefore, her distance yesterday is s × t miles.

b) Rana's time is given by the formula: time = distance ÷ rate. Therefore, her time yesterday is m ÷ r hours.

c) Sophie's time is given by the formula: time = distance ÷ rate. Let's call the time Sophie waits for Rana "w". Then we have two equations:

Sophie's distance: s × (w + t) = 20

Rana's distance: r × (w + t) = 20 - m

We can solve for "w" by substituting the second equation into the first equation:

s × (w + t) = 20 - r × (w + t) + m

(s + r) × (w + t) = 20 + m

w + t = (20 + m) ÷ (s + r)

w = (20 + m) ÷ (s + r) - t

Therefore, Sophie waits for Rana for (20 + m) ÷ (s + r) - t hours.

d) Sophie's distance tomorrow is s × 3 miles, and Rana's distance tomorrow is r × 3 miles. Therefore, the difference in distance is (s - r) × 3 miles.

The correct standard form of the equation of the parabola is:

[tex]y = -x^2 - 1[/tex].

To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:

[tex]y = ax^2 + bx + c[/tex] ___________(1)

Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):

[tex]3 = 9a - 3b + c[/tex]

[tex]-1 = a + b + c[/tex]

To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:

[tex]4 = 8a - 4b[/tex]

Simplifying this equation, we get:

[tex]2 = 4a - 2b[/tex]

Dividing both sides by 2, we get:

[tex]1 = 2a - b[/tex]___________(2)

Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:

[tex]3 = 9a - 3(2a - 1) + c[/tex]

Simplifying this equation, we get:

[tex]3 = 6a + c + 3[/tex]

Subtracting 3 from both sides, we get:

[tex]0 = 6a + c[/tex]

Solving for c, we get:

c = -6a __________(3)

Substituting this expression for c into the second equation, we get:

[tex]-1 = a + (2a - 1) - 6a[/tex]

Simplifying this equation, we get:

[tex]-1 = -3a - 1[/tex]

Adding 1 to both sides, we get:

[tex]-3a =0[/tex]

Solving for a, we get:

[tex]a = 0[/tex]

Substituting this value of a into the equation(3) for c, we get:

c = 0

Substituting a = 0 into the equation(2) for b that we found earlier, we get:

[tex]1 = 0 - b[/tex]

Solving for b, we get:

[tex]b = -1[/tex]

Putting the values of a, b and c in (1), we get

[tex]y = -x^2 - 1[/tex]

Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:

[tex]y = -x^2 - 1[/tex]

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Complete question:

A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).

What is the correct standard form of the equation of the parabola?

The figure is in the image attached below

The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).

The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.

The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:

(i) Worked at least one hour as paid employees

(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise

(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.

⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.

⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.

⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.

Therefore, all the options are correct , which is Option(d).

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The given question is incomplete, the complete question is

Who of the following are included in the Bureau of Labor Statistics "employed" category?

(a) certain unpaid workers

(b) part-time workers

(c) workers on vacation

(d) All of the above are correct.

The number of lionfish after 6 years will be 85,609. The recursive equation for [tex]f(n)[/tex] will be [tex]f(n) = 4242.42(1.65)^n - 1300n[/tex].

Consider the function:

[tex]y = a (1 \pm r)^x[/tex]

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

lionfish are considered an invasive species, with an annual growth rate of 65%.

Then the equation will be

[tex]f(n) = P(1.65)^n[/tex]

[tex]\text{P = initial population}[/tex]

A scientist estimates there are 7,000 lionfish in a certain bay after the first year.

[tex]7000 = P(1.65)[/tex]

    [tex]P = 4242.42[/tex]

Then the equation will be

[tex]f(n) = 4242.42(1.65)^n[/tex]

The number of lionfish after 6 years will be

[tex]f(n) = 4242.42(1.65)^6[/tex]

[tex]f(n) = 85608.58[/tex]

[tex]f(n) \cong 85,609[/tex]

If scientists remove 1,300 fish per year from the bay after the first year.

Then the recursive equation for f(n) will be

[tex]f(n) = 4242.42(1.65)^n - 1300n[/tex]

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The new estimated value of the trust funds in 2038 would be $2.5 trillion.

Funds are resources of monetary value that can be used to acquire goods, services, or to meet financial obligations. They are usually obtained through the sale of goods and services or by borrowing. Funds can come from a variety of sources, including individuals, businesses, governments, and other organizations. Funds can be used to purchase assets such as stocks, bonds, real estate, or other forms of investments.

This is because a 10% relative increase over the original estimated 7.6% rate of decline means that the actual rate of decline is 8.36% (7.6% x 1.10 = 8.36%). Applying this rate to the original starting value of $4 trillion, the value of the trust funds in 2038 would be $4 trillion x 0.9164 (which is the equivalent of 1 - 0.0836) = $2.5 trillion.

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The new estimated value of the trust funds in 2038 would be $2.4 trillion.

A trust fund is a legal arrangement in which a person or organization (the trustor) transfers assets to another person or organization (the trustee) to be managed and distributed for the benefit of a third party (the beneficiary). The trustor sets out a set of instructions (the trust deed) on how the trust funds should be handled, managed, and distributed. The trustee is legally bound to abide by these instructions, and is responsible for the management and distribution of the trust funds according to the trust deed. Trust funds can be used for a variety of purposes, such as providing for a beneficiary's education, medical care, or retirement.

This is because a 10% increase in the rate of decline would result in a rate of decline of 8.36% (7.6% plus 10% of 7.6%).
Using this new rate of decline, the value of the trust funds in 2038 would be $4 trillion multiplied by (1 - 0.0836)⁵,
which is equal to $2.4 trillion.

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Answer: 84

Step-by-step explanation:

Area of whole rectangle = lb = 11x9 = 99

Area of Inner rectangle = lb = 5x3 = 15

Area of Shaded region = Area of whole rectangle - Area of Inner rectangle
                                      = 99 - 15

                                      = 84

Answer:

Area of shaded region = 84 units²

Step-by-step explanation:

Area = Area of bigger - Area of smaller

[tex] { \tt{area = (11 \times 9) - (5 \times 3)}} \\ \\ { \tt{area = 99 - 15}} \\ \\ { \tt{area = 84 \: units {}^{2} }}[/tex]

Answer:

[tex]xy^8[/tex]

Step-by-step explanation:

Notice if you have the same base you can ADD the exponent, for example:

[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]

[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]

so the answer is

[tex]xy^8[/tex]

Answer:

The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:

2, 4, 6, 8, 10

The average of these five integers is:

(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.

By answering the presented questiοn, we may cοnclude that 0.4 οf an expressiοns hοur is 0.4 x 60 = 24 minutes in this situatiοn. As a result, 3.4 hοurs equals 3 hοurs and 24 minutes.

An expressive in mathematics is a collection of numbers, variables, and complicated mathematical operations (such as addition, subtraction, multiplication, division, multiplicands, and others) that convey a quantity's value. Expressions can be as straightforward as "3 + 4" or as complex as "(3x2 - 2) / (x + 1)". They could also include functions like "sin(x)" or "lg(y)".

The real way to evaluate an expression is to insert the variables with their values and carry out the arithmetic operations in the order specified. For instance, the phrase "3x + 5" means 3(2) + 5 = 11 if x = 2. In mathematics, expressions are typically used to describe actual situations, build equations, and decompose challenging mathematical diagrams.

3 hοurs and 24 minutes is cοmparable tο 3.4 hοurs.

Yοu may separate the full number (which represents the hοurs) frοm the decimal tο cοnvert decimal hοurs tο hοurs and minutes (which represents the fractiοn οf an hοur in minutes).

0.4 οf an hοur is 0.4 x 60 = 24 minutes in th

is situation. As a result, 3.4 hours equals 3 hours and 24 minutes.

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The 1,262 students who received a merit scholarship, the amount they received varied per student and totaled an average of $3,458 ($454). That amount is 78.2% of the full tuition cost of $4,400.

Merit is a term used to describe the quality of something or someone that makes them worthy of recognition or respect. It is an indicator of worthiness and is usually based on a person's ability, effort, or accomplishments. Merit is often used when evaluating an individual or a group for a promotion, hiring, or award. Merit is subjective, as different people have different standards for what merits recognition.

Therefore, 21.8% of the students who received a merit scholarship did not receive enough to cover full tuition. Therefore, the percentage of students who received a merit scholarship and did not receive enough to cover full tuition is 21%.

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Answer:

Example of a function that satisfies the following conditions:

a. Domain and range are both all real numbers except 5:

f(x) =

{

x if x ≠ 5

0 if x = 5

}

b. Domain is all positive numbers greater than 1, including 1:

f(x) =

{

(x-1)^2 / (x-1) if x > 1

0 if x = 1 or x = 5

}

c. Domain is all positive numbers greater than 1, but not including 1:

f(x) =

{

(x-1)^2 / (x-1) if x > 1 and x ≠ 1

0 if x = 1 or x = 5

}

Answer:

We are given the cost equations for Emma's and Madison's text message plans as:

Emma's Plan: y = 0.10x + 10

Madison's Plan: y = 0.15x

where y is the cost in dollars and x is the number of texts sent. We are also told that Emma and Madison paid the same amount in one month. Let's set the two equations equal to each other and solve for x:

0.10x + 10 = 0.15x

Subtracting 0.10x from both sides, we get:

10 = 0.05x

Dividing both sides by 0.05, we get:

x = 200

Therefore, Emma and Madison sent 200 text messages in one month to pay the same amount

The area of the living room is 24.7 m², and the area of the game room is 37.05 m².

Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.

The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².

To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².

The area of the living room is 24.7 m², and the area of the game room is 37.05 m².

The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.

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The equation of the estimated population regression line is typically written in the form:

y = a + bx

where:

y is the dependent variable (or response variable)

x is the independent variable (or predictor variable)

a is the intercept (the value of y when x = 0)

b is the slope (the change in y for a unit change in x)

To create the correct equation of the estimated population regression line, Sonny should select the following options:

The variable y should be the dependent variable (or response variable).

The variable x should be the independent variable (or predictor variable).

The estimated intercept value should be plugged into the equation for a.

The estimated slope value should be plugged into the equation for b.

So, the correct equation of the estimated population regression line would be:

y = a + bx

where a and b are the estimated intercept and slope values, respectively.

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To construct a confidence interval for sigma the population from which the sample was drawn must be normally distributed. -

It is not necessary to make the normalcy assumption in order to build a confidence interval for sigma. To employ the central limit theorem, however, the sample size must be adequate which ideally enables the use of the normal distribution to approximate the sampling distribution of the sample variance. Alternative techniques, like t-distribution, can be employed if total sample size is limited.

It's also important to remember that, regardless of sample size, the distribution of sample variance will be normal if population is known and recognizable to have a normally distributed population. As long as the sample size is appropriate, the sample variance may still be utilized to create a confidence range for sigma even if the population is not normally distributed.

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Answer:

Step-by-step explanation:

B because after having the star and the circle comes the square.

Answer: C

Step-by-step explanation:

The correct answer is C.

The slope of the line represents the hourly wage, so Hunter's wage is $35 an hour, as given in option A and B. However, the y-intercept of the line represents the starting pay or the pay for zero hours worked. In this case, the y-intercept is 25, which means Hunter received $25 even if he did not work any hours. Hence, option C is correct as it states that Hunter's wage is $25 an hour, but it appears that he received no signing bonus.

Answer:

arc length = 2.2π inches

Step-by-step explanation:

arc length is calculated as

length = circumference of circle × fraction of circle

           = 2πr × [tex]\frac{22}{360}[/tex] ( r is the radius )

           = 2π × 18 × [tex]\frac{22}{360}[/tex] ( cancel 18 and 360 by 18 )

          = 2π × [tex]\frac{22}{20}[/tex]

        = [tex]\frac{44}{20}[/tex] π

       = 2.2π inches

As per the axial force, the support reaction at A is equal in magnitude to the axial force that is applied at the other end of the bar.

To determine the support reaction at A, we will draw a free-body diagram of the bar.

Since the bar is fixed at A, the support reaction at that end will be a vertical force, and we will label it as RA.

Using Newton's second law of motion, we can write the equation of equilibrium for the bar in the vertical direction:

ΣFy = 0

where ΣFy is the sum of all the forces in the vertical direction. Since there are only two forces acting on the bar, the axial force and the support reaction, we can write:

-FA + RA = 0

where FA is the axial force that is applied at one end, and RA is the support reaction at the other end.

From this equation, we can solve for RA:

RA = FA

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Complete Question:

Determine the support reaction at A

The axially loaded bar is fixed at A and loaded as shown. Draw a free-body diagram and determine the support reaction at A.

Using matrices, we can find that the products of EH and FG are defined, the rest does not satisfy.

A matrix is a rectangular array of values that are defined for mathematical operations including addition, subtraction, and multiplication.

The quantity of rows and columns in a matrix—also referred to as the order of the matrix—determines its size. A 6 4 symbol and 6 by 4 reading are used to symbolise and denote the order of a matrix having 6 rows and 4 columns.

Here in the question,

When the matrices, E and H are multiplied, the resulting matrix is a defined matrix.

Similarly, we can see when F and G are multiplied, the resulting matrix is a defined matrix.

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The constraint w1 w2 w3 < 1, where w1, w2, and w3 are 0-1 integer variables, is often called a packing constraint. The packing constraint w1 w2 w3 < 1 limits the number of variables that can be set to 1 and is used to control the number of items that can be selected in integer programming problems.

A packing constraint is a type of constraint used in integer programming that limits the number of items that can be selected from a set of items. In this case, the constraint limits the number of variables that can take the value 1 to be less than 1.

The term "packing" comes from the idea of packing items into a container. In the context of integer programming, packing constraints are used to limit the number of items that can be "packed" into a container (i.e., set to 1), while ensuring that the total value of the packed items meets certain requirements or constraints.

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The given argument is Valid because the conclusion follows the argument logically.

The argument is that "Every nonzero real number has a reciprocal. Zero(0) does not have a reciprocal. Therefore, zero is not a non-zero real number."

The argument can be expressed in logical form as:

⇒ Premise 1: For every nonzero real number x, there exists a reciprocal 1/x.

⇒ Premise 2: Zero does not have a reciprocal.

⇒ Conclusion: Therefore, zero is not a nonzero real number.

This argument is valid because the conclusion logically follows from the premises.

The premises establish that every nonzero real number has a reciprocal, and that zero does not have a reciprocal.

The conclusion then follows logically, as zero is explicitly excluded from the set of nonzero real numbers based on the definition of a reciprocal.

Therefore, the argument is valid.

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The given question is incomplete, the complete question is

Is The Following Argument Valid Or Invalid?

Every nonzero real number has a reciprocal. Zero does not have a reciprocal. Therefore, zero is not a nonzero real number.

Answer:

6)-56+567)-/(05(-)9

Step-by-step explanation:

Question

Katherine bought 312

pounds of oranges for $1.45

per pound, as well as 434

pounds of potatoes that cost $1.69

for 2

pounds. She gives the cashier a $10.00

bill.

Which equation represents the situation if x

is the amount of change in dollars Katherine should receive?

A 312(1.45)+434(1.69)+x=10

3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10

B 312(1.45)+434(1.692)+x=10

3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10

C 312(1.45)+434(1.692)−x=10

3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10

D (312+434)⋅(1.45+1.69)+x=10

HELP ME I WILL GIVE BRAINLIEST

Answer:

Step-by-step explanation:

To find the temperature corresponding to the 67th percentile, we need to find the z-score that has an area of 0.67 to the left of it in the standard normal distribution. We can use a table or a calculator to find this z-score.

Using a standard normal distribution table, we can look up the value that corresponds to an area of 0.67 to the left of the mean, which is 0.44. This means that P(Z ≤ 0.44) = 0.67, where Z is the standard normal random variable.

Next, we can use the formula for standardizing a normal random variable to convert this z-score to the corresponding temperature on the thermometer scale:

z = (x - μ) / σ

where μ is the mean, σ is the standard deviation, and x is the temperature we want to find.

Rearranging this formula, we get:

x = μ + z * σ

Plugging in the values, we get:

x = 0 + 0.44 * 1.00

x = 0.44

Therefore, the temperature corresponding to the 67th percentile is 0.44°C.

The answer of  the given question based on finding each measure of a circle the answer is , (a)  m(MNP) = 12.5° degrees , (b) m(KL) = 102.5° degrees , (c)  m(KJ) = 52.5° degrees , (d)  m(JN) = 102.5° degrees , (e)  m(JLM) =  12.5° degrees.

In geometry,  arc is a portion of  curved line that can be thought of as  segment of  circle. It is defined by two endpoints on  circle and the arc itself is the part of  circle between those two points. An arc can be measured in degrees, and its measure is equal to  central angle subtended by  arc. The length of  arc can also be calculated using the formula L = rθ, where L is  length of  arc, r is radius of  circle, and θ is  angle (in radians) subtended by  arc at center of circle.

Using the properties of angles and arcs in circles:

a. Angle MNP is inscribed in arc MP, so m(MNP) = 1/2m(MP) = 1/2(25) = 12.5° degrees.

Since angles NPM and MPK are vertical angles, we have m(MPK) = m(NPM) = m(MNP) = 12.5° degrees. Then, m(MN) = m(MPK) + m(KPM) = 12.5 + 40 = 52.5° degrees.

b. Angle LKP is inscribed in arc LP, so m(LKP) = 1/2m(LP) = 1/2(25) = 12.5° degrees.

Since angles PKL and LKN are vertical angles, we have m(PKL) = m(LKN) = m(LKP) = 12.5° degrees. Then, m(KL) = m(PKL) + m(PKC) = 12.5 + 90 = 102.5° degrees.

c. Angle PKJ is inscribed in arc PJ, so m(PKJ) = 1/2m(PJ) = 1/2(25) = 12.5° degrees.

Since angles LPK and LPJ are vertical angles, we have m(LPK) = m(LPJ) = m(PKJ) = 12.5° degrees. Then, m(KJ) = m(LPK) + m(LPJ) = 12.5 + 40 = 52.5° degrees.

d. Angle JNM is inscribed in arc JM, so m(JNM) = 1/2m(JM) = 1/2(25) = 12.5° degrees.

Since angles KJM and KJN are vertical angles, we have m(KJM) = m(KJN) = m(JNM) = 12.5° degrees. Then, m(JN) = m(KJM) + m(MJN) = 12.5 + 90 = 102.5° degrees.

e. Angle JLM is an inscribed angle that intercepts arc JM, so m(JLM) = 1/2m(JM) = 1/2(25) = 12.5° degrees.

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The temperature decreased by 41°F during the overnight hours.

Physical quantities with merely magnitude and no direction are called scalar quantities. Scalar values encompass things like mass, volume, temperature, and time. Real numbers, such as positive or negative integers or decimals, are frequently used to represent scalar quantities in mathematics.

In contrast, a vector quantity is a physical quantity that possesses both magnitude and direction. The terms displacement, velocity, force, and acceleration are all examples of vector quantities. Typically, vector values are represented by a number or symbol for the magnitude and an arrow or boldface letter for the direction.

Given that, the temperature went from 28 to -13.

The expression that represent this change are:

Expression 1: -13°F - 28°F

Expression 2: | -13°F - 28°F |

The temperature change can be calculated as:

| -13°F - 28°F | = |-41°F| = 41°F

Hence, the temperature decreased by 41°F during the overnight hours.

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