the starting salaries of individuals with a certain degree are normally distributed with a mean of $30,000 and a standard deviation of $2,500. what is the probability that a randomly selected individual with the degree will get a starting salary of at least $34,375?

Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.

Here,

(i) Let the length of the rectangle be y cm.

Then, the perimeter of the rectangle is given by:

2(x + y) = 112

x + y = 56

y = 56 - x

(ii) The area of the rectangle is given by:

Area = length x breadth

597 = yx

Substituting y = 56 - x, we get:

597 = x(56 - x)

597 = 56x - x²

x² - 56x + 597 = 0

(iii) Using the quadratic formula,

x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))

x = (56 ± √(3136 - 2388)) / 2

x = (56 ± √(748)) / 2

x = (56 ± 2√(187)) / 2

x = 28 ± √(187)

Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).

(iv) The length of the rectangle is y = 56 - x.

Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:

d² = y² + x²

d² = (56 - x)² + x²

d² = 3136 - 112x + 2x²

d = √(3136 - 112x + 2x²)

Substituting the value of x from part (iii) into the above equation, we get:

d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)

d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))

d = √(37400 ± 168√(187))

d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)

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You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.

The given expression is equivalent to

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

[tex]a(b+c)=a\times b+a\times c[/tex]

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])

The given expression is [tex]6g-18h[/tex]

We know that we can write

[tex]6=2\times3[/tex]

[tex]18=2\times9=3\times6[/tex]

Thus,

[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]

[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]

[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]

All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.

Thus,

The given expression is equivalent to

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Answer:C & D

Step-by-step explanation:

Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.

There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.

To calculate this, the total number of possibilities can be found by using the formula nPr,

where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]

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Answer:

3 pounds of coffee.

Step-by-step explanation:

Equation

y = -7.37x + 80  

substitute 57.89 for y

57.89 = -7.37 + 80   Subtract 80 from both sides

57.89 - 80 = -7.37 + 80 - 80

-22.11 = -7.37x  Divide both sides by -7.37

3 = x

3 pound of coffee

Helping in the name of Jesus.

Answer:

rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?​

Step-by-step explanation:

Let's first find out how much money Rita spent on coffee:

$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee

Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:

$7.37x = $22.11

Solving for x, we can divide both sides by $7.37:

x = 3

Therefore, Rita bought 3 pounds of coffee.

Answer: Associative property

Step-by-step explanation:

The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!

Answer:

[tex]\frac{11}{8}[/tex]

Step-by-step explanation:

3(2k+3)=6-(3k-5)

6k +9=6-3k+5

6k+3k=6+5

8k=11

k=[tex]\frac{11}{8}[/tex]

Answer: I think it is k=2/9

Step-by-step explanation:

The missing value to find the length of BC is 9x.

The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.

The distance formula is given as:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values of the coordinates of B and C we have:

distance = √((7x - (-2x))² + (-1y - (-4y))²)

distance = √((9x)² + (3y)²)

distance = √(81x² + 9y²)

distance = 3√(9x² + y²)

Hence, the missing value to find the length of BC is 9x.

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Answer:

2x=5 > -14

Step-by-step explanation:

6(x - 2) -3 ≥ -4 ( -3 + 9) +10​
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3    3        
2x=5 > -14

Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

We can write quadradic equation as [tex]y=1+x^2[/tex]

Where y is number οf dοts and x is step number.

Then if x=0 and y=1

If x = 1 and y = 2

If x = 2 and y = 5

If x = 3 and y = 10

Hence Patten B fοllοws the quadratic realatiοnship.

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The surface area of the rectangular prism is 170 square yards.

Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.

To calculate the surface area of the rectangular prism, add the areas of each of its faces.

The front and back faces are 5 yards by 6 yards in size, so each has an area of:

5 yards x 6 yards equals 30 square yards

The top and bottom faces are 5 yards by 5 yards, so each has an area of:

5 yards x 5 yards equals 25 square yards

The two side faces have dimensions of 6 yards by 5 yards, for a total area of:

30 square yards = 6 yards x 5 yards

As a result, the surface area of the rectangular prism is as follows:

Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area

= 30+30+25+25+30+30

= 170 square yards

As a result, the rectangular prism has a surface area of 170 square yards.

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Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.

A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).

The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.

A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:

The formula for the area of a trapezoid is as follows:

Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height

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2/7 + 1/4 = 15/28 ≅ 0.5357143

Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28 

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.

As per the given distance, the bus and the motorcycle will pass each other at 4:50 pm.

Now, let's find the distance the bus travels during that time. We know the speed of the bus is 60 mph, so we can use the formula distance = speed x time. Thus, the distance the bus travels is:

distance = speed x time

distance = 60 x t

Next, let's find the distance the motorcycle travels during the same time. The speed of the motorcycle is 72 mph, so we can use the same formula to find the distance the motorcycle travels:

distance = speed x time

distance = 72 x (t - 3/4)

Here, we subtract 3/4 from the time because the motorcycle leaves 45 minutes later than the bus. Remember, we need to convert 45 minutes to hours by dividing it by 60. Therefore, 45 minutes is equal to 3/4 of an hour.

Now that we have both distances, we can set them equal to each other since the bus and the motorcycle will meet at the same point in time:

60t = 72(t - 3/4)

Let's simplify and solve for "t":

60t = 72t - 54

12t = 54

t = 4.5

Therefore, it will take 4.5 hours for the bus and the motorcycle to meet each other. But, we need to find out what time that will be. We know the bus left at 12:20 pm, so we add 4.5 hours to that time:

12:20 pm + 4.5 hours = 4:50 pm

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The slope in the equation b = 0.29h + 1.35 is the measure of the rate at which the bike frame size changes with the height of the rider.

The slope in the equation b = 0.29h + 1.35 refers to the coefficient of the variable h, which represents the height of the rider. The slope is the measure of the rate at which the bike frame size changes with the height of the rider.

In this equation, the slope is 0.29, which means that for every inch increase in the rider's height, the bike frame size increases by 0.29 inches. The slope is a crucial component of the equation as it determines the proportionality of the two variables.

Moreover, the slope is essential in analyzing the relationship between the rider's height and the bike frame size.

It plays a vital role in determining the appropriate size of the BMX bike frame and analyzing the relationship between the two variables.

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Complete Question:

Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use the equation b 0.29h +1.35 where b is the size of the BMX bike frame in inches and h is the height of the rider in inches.

Which sentence explains the slope in the equation?

The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².

Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.

The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.

In this figure,

The 5cm flap will be adjacent to the side x. Therefore,

Length of the side x= 5cm

Area of the shaded region= l×b

because the shaded region is a rectangle.

area= 9*x

       =9*5= 45 cm²

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The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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Answer:

4m + 6

Step-by-step explanation:

Since the length is twice as long your equation should look like this

2(2m + 3) = L

which would be 4m + 6 as the length of the rectangle

a. Two levels of factor B were used in the experiment.

b. The degrees of freedom associated with interaction are 50.

c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.

Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.

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The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.

There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:

Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]

Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%

Therefore percent of teenagers who purchased something with their parents' money = 38.64%

Therefore, about 38.64% of the teenagers purchased something with their parents' money.

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Answer:

k

Step-by-step explanation:

2x+13<5x−20

Subtract 5x from both sides.

Combine 2x and −5x to get −3x.

Subtract 13 from both sides.

Subtract 13 from −20 to get −33.

Divide both sides by −3. Since −3 is negative, the inequality direction is changed.

​

x>11

Answer:

[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]

Answer:

A- 2

B- 4,100

C- 82

D- 4,182

The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].

Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.

If a marble is randomly selected from the box, we have to find the probability that it is not blue.

Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]

The probability that a marble is not blue:-

[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)

[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]

[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]

[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)

[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]

[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]

Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].

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Answer:

Step-by-step explanation:

5+3x/4 = 7/12

[(5*4)+3x]/4 = 7/12

(20+3x)/4 = 7/12

20+3x = 7/12*4

20+3x = 7/3

3x = 7/3 - 20

3x = [7-(20*3)]/3

3x = (7-60)/3

3x = -53/3

x = -53/3/3/1 ( reciprocal )

x = -53/3*1/3

x= -53/9

Answer:

To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:

r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5

Now we can substitute the center and radius into the standard form equation:

(x - 4)^2 + (y + 2)^2 = 5^2

Simplifying and expanding the right-hand side, we get:

Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.

To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.

Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.

For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.

The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.

Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.

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First of all, perfect squares do not end in 2.

The exponent has to be an even number when 2 is the base. For example 2^8 = 64. 8 is an even number. So 64 is a square number.

The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).

What are parallel lines?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.

If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (-5 - 7) / (8 - (-2))

slope = -12 / 10

slope = -6 / 5

So, the equations of the two parallel lines are:

y - 7 = (-6 / 5)(x + 2) --- equation 1

y + 5 = (-6 / 5)(x - 8) --- equation 2

To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).

So, after the rotation, the new coordinates of the two points will be:

(-(-2), -7) = (2, -7) --- for point (-2, 7)

(-(8), -(-5)) = (-8, 5) --- for point (8, -5)

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