There are three angles measured in degrees of a triangle where x is the largest angle, y is the middle angle, and z is the smallest angle.

The measure of the largest angle is 40 degrees less than twice the sum of the measure of the other two angles.

The measure of the largest angle is twice the smallest angle plus 10 degrees.

The sum of the angles of a triangle can be written as x + y + z = 180.

What are the other equations that represent this system of equations?

Select each correct answer.
a.) x=2y+10
b.) x=2z+10
c.) x=40-2(y+z)
d.) x=2z+y-40
e.) 2(y+z)-40

Using the binomial probability formula, we get a probability of approximately 1 or 100%.

This problem involves a binomial probability distribution, where we are interested in the number of successes (colleges with distance learning courses) in a fixed number of trials (picking 13 institutions), where each trial has a constant probability of success (the probability that a college offers distance learning courses).

We can use the binomial probability formula

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

where X is the number of successes, k is the number of successes we are interested in, n is the total number of trials, p is the probability of success, and C(n, k) is the binomial coefficient.

Substituting the given values, we get

P(X = k) = C(13, k) * 0.96^k * 0.04^(13-k)

To find the probability that at least one college offers distance learning courses, we can find the probability that none of the 13 colleges offer distance learning courses and subtract it from 1

P(X ≥ 1) = 1 - P(X = 0)

P(X = 0) = C(13, 0) * 0.96^0 * 0.04^13 = 0.000000005096

P(X ≥ 1) = 1 - 0.000000005096 ≈ 1

Therefore, the probability that at least one college out of 13 offers distance learning courses is approximately 1 or 100%.

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Answer:

Step-by-step explanation:

100000³ = 100000 × 100000 × 100000

100000 × 100000 × 100000 =

10000000000 × 100000 =

1e+15 or 1.000.000.000.000.000

The inverse of the graphs are added as an attachment

To plot the inverse of a graph, you can follow these steps:

See attachment for the graphs

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Answer:

  increasing: x > 0

Step-by-step explanation:

Given a table of function values, you want to know the interval on which the function is increasing.

A function is increasing if f(x)-values get larger when x-values get larger. As we go down the table, the x-values get larger.

In the first three lines of the table, the f(x)-values are getting smaller. The function is decreasing on that interval, x < 0.

In the last three lines of the table, the f(x) values are getting larger. The function is increasing on that interval, x > 0.

__

Additional comment

The point (0, 0) represents a minimum. The function is not increasing or decreasing at that point, so the interval of interest is x > 0, not x ≥ 0.

The length of the square garden is s = ( 3x - 4 ) feet

Given data ,

Let the length of the square garden be s

Now , The area of a square is given by the formula A = s², where s is the length of one side of the square.

We are given that the area of the garden is:

A = 9x² - 24x + 16

To find the length of the garden, we need to take the square root of the area:

s = √(A)

Substituting the given expression for A, we get:

s = √(9x² - 24x + 16)

We can simplify this expression by factoring the quadratic under the square root sign:

s = √[(3x - 4)(3x - 4)]

Using the property that the square root of a product is equal to the product of the square roots, we can simplify further:

s = (3x - 4)

Hence , the length of the garden is 3x - 4 feet

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The estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.

Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.

Out of the 31 students surveyed, 6 reported having no pets, 8 reported having one pet, 10 reported having two pets, 3 reported having three pets, and a total of 4 (1+2+1) reported having four or more pets.

Thus, the probability that a randomly selected student from this class has four or more pets at home is:

P(four or more pets) = 4/31 ≈ 0.13 (rounded to two decimal places)

Therefore, the estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.

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Using a system of equations, the number of bracelets made and the number of necklaces made are:

A system of equations is two or more equations that can be solved simultaneously or at the same time.

Simultaneous equations can be solved concurrently.

Quantity of gold in each bracelet = 6 grams

Quantity of gold in each necklace = 24 grams

The total number of bracelets and necklaces made = 16

The total quantity of gold used in making the 16 pieces = 258 grams

Let the number of bracelets made = x

Let the number of necklaces made = y

x + y = 16 ...Equation 1

6x + 24y = 258 ...Equation 2

Multiply Equation 1 by 6:

6x + 6y = 96 ...Equation 3

Subtract Equation 3 from Equation 2:

6x + 24y = 258

-

6x + 6y = 96

18y = 162

y = 9

x = 7 (16 - 9)

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The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.

The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.

Therefore, the height of the tank can be calculated as follows:

7.48 liquid gallons = 1 ft³

1100 liquid gallons = ?

cross multiply

volume of the tank = 1100 / 7.48 = 147.058823529 ft³

Therefore, let's find the volume of the cylindrical tank.

volume of the cylindrical tank = πr²h

where

Therefore,

r = 3.2 feet

h = ?

The volume of the cylindrical tank in feet cube is 147.058823529 ft³

Let's find the height, h

volume of the cylindrical tank = 3.14 × 3.2² × h

147.058823529 = 3.14 × 10.24 × h

32.1536h = 147.058823529

divide both sides by 32.1536

h = 147.058823529 / 32.1536

h = 4.57363405653

Therefore,

height of the water tank = 4.6 feet

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1. The equation of the line in graph 1 in slope-intercept form is

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

2. The equation of the line in graph 2 is

y = (1/3)x + 4/3.

a. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.

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

Substituting the given values, we get:

slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3

The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:

y - y1 = m(x - x1)

y - 4 = (2/3)(x - 3)

y = (2/3)x + 2/3

b. points obtained from the graph (-3, 1) and (-6, 0)

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

slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3

y - y1 = m(x - x1)

y - 1 = (1/3)(x - (-3))

y = (1/3)x + 4/3

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For given problem, The common denominator is 12 and Before adding the fractions the numerator of first fraction was 16 and numerator of second fraction was 15.

The representation of sections or portions of a whole using fractions is common. It consists of Numerator and the denominator reflects the total number of equally sized pieces that make up the whole, whereas the numerator represents the number of components we have.

For example, in the fraction 5/4, 4 is the denominator and 5 is the numerator.

Now for given problem,

Kiera had [tex]1\frac{1}{3}[/tex] cups of coffee in the morning, equivalent to [tex](4/3)[/tex] cups of coffee.

Kiera also had[tex]1 \frac{1}{4}[/tex] cups of coffee in the afternoon, equivalent to [tex](5/4)[/tex] cups of coffee.

Now we can add the two fractions together:

[tex](4/3) + (5/4)[/tex]

To find common Denominator;

(LCM) of 3 and 4 is 12

Making denominator of both fraction 12;

[tex](4/3) * (4/4) + (5/4) * (3/3)[/tex]

[tex](16/12) + (15/12)[/tex]

[tex]16/12 + 15/12 = (16 + 15)/12 = 31/12[/tex]

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Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.

Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.

Perimeter = 2 × (height + width)

Perimeter = 2 × (19 + 29)

Perimeter = 2 × 48

Perimeter = 96 centimeters

So the perimeter of the certificate is 96 centimeters.

To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:

Cost = perimeter × cost per centimeter

Cost = 96 × $0.03

Cost = $2.88

Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.

Answer: Vertical text sets are arranged in columns from top to bottom, while horizontal text sets are arranged in rows from left to right. The major differences between the two include:

Readability: Vertical text sets may be more difficult to read for individuals who are accustomed to reading horizontally, while horizontal text sets may be more natural for them to read.

Space utilization: Vertical text sets can utilize space more efficiently, especially in situations where vertical space is available, such as in tall and narrow posters or banners. Horizontal text sets, on the other hand, can utilize space more efficiently in situations where horizontal space is available, such as in wide-screen displays or landscape-oriented documents.

Cultural conventions: In some cultures, such as Japan and China, vertical text sets are traditionally used for writing, while in other cultures, such as the United States, horizontal text sets are the norm. Thus, the use of one or the other may depend on cultural context.

One situation where vertical text sets may be more beneficial is in designing a tall and narrow billboard. In this case, a horizontal text set may be difficult to read from afar, while a vertical text set can make use of the available space and be easily read from a distance. On the other hand, in designing a website, horizontal text sets may be more beneficial as they can utilize the full width of the screen and provide more space for additional content.

Step-by-step explanation:

Answer:

(x) = (-19/9)(x + 3)^2 + 5

Step-by-step explanation:f(x) = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola. Given that the vertex is (-3, 5), we can plug in these values into the vertex form equation:

f(x) = a(x - (-3))^2 + 5

which simplifies to:

f(x) = a(x + 3)^2 + 5

Now, we know that the function passes through the point (0, -14). We can plug in these values into the equation and solve for 'a':

-14 = a(0 + 3)^2 + 5

-14 = 9a + 5

Subtracting 5 from both sides:

-19 = 9a

Dividing both sides by 9:

a = -19/9

By the ratio of teaspoons of powdered lemonade mix and cup of water, jayden mix will be more lemony.

Ratio is a mathematical comparison between two or more quantities, typically expressed as a fraction or a colon (:). It represents the relationship or proportion between the quantities being compared. Ratios are used to describe the relative size or amount of one quantity in relation to another.

According to the given information:

Based on the given information, we can determine that option B, Jayden's mix will be more lemony.

This is because the ratio of powdered lemon mix to water is the same for both Khloe and Jayden, which is 2 teaspoons of powdered lemon mix per cup of water. However, Jayden uses only 1 cup of water, whereas Khloe uses 5 cups of water. Therefore, Jayden's mix will have a higher concentration of powdered lemon mix per cup of water compared to Khloe's mix, making Jayden's mix more lemony in flavor.

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The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.

To solve this problem, we need to use the formula for the area of a circle:

[tex]A = πr^2[/tex],

where A is the area and r is the radius.

We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.

First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:

dA/dt = 2πr(dr/dt)

where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.

Therefore, we can substitute these values into the formula to get:

dA/dt = 2π(3)(2)

dA/dt = 12π

So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the

radius is exactly 3 feet.

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Korey expect to make in profits in his fifth year of operation is $15,149.72. So, the correct answer is option A) $15,149.72.

To calculate Korey's expected profits in his fifth year of operation, we need to consider the expected growth rate of profits over the next four years.

Korey expects profits to increase by 6% each year for the next four years. To calculate his expected profits for each of the next four years, we can use the following formula:

Profit = Previous year's profit + (Previous year's profit x growth rate)

Using this formula, we can calculate Korey's expected profits for each of the next four years:

Year 1: $12,000 (average monthly profit of $1,000)

Year 2: $12,720 ($12,000 + ($12,000 x 0.06))

Year 3: $13,478.40 ($12,720 + ($12,720 x 0.06))

Year 4: $14,278.30 ($13,478.40 + ($13,478.40 x 0.06))

To calculate his expected profits in the fifth year, we can use the same formula:

Year 5: $15,149.72 ($14,278.30 + ($14,278.30 x 0.06))

Therefore, the correct answer is option A) $15,149.72.

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Answer:

A. ) 15,149.72

The graph shown in the equation y = - 2x - 4 is the graph that corresponds to that equation. The answer is option (B).

A data structure called a graph is used to show the mathematical connection between two or more objects. It is made up of nodes and edges, where nodes stand in for individual things and edges for the connections between them. In computer science, graphs are used to solve a variety of issues, including finding the shortest path between two points and figuring out whether a graph contains cycles. In addition, social networks, transportation networks, and many other kinds of networks can all be represented using graphs.

Option B's graph is the one that corresponds to the equation y = - 2x - 4.

The following is how the equation is written in slope-intercept form:

It is -2 degrees.

-4 is the intercept.

This shows that the slope of the graph is negative and that the trend line crosses the y axis at a negative four-degree angle.

The only graph with a negative slope and a -4 intercept is the one for option B.

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Complete question attached below,

The quarterly dividend payment per share based on the question above will be: $0.02.

The close price for the week will be: $5.45.

For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:

Close price = Total cost / Number of shares

                    = $2,790.40 / 512

                    = $5.45

To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:

Annual dividend per share = Total annual dividend / Number of shares

                                              = $40.96 / 512

                                                = $0.08

From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:

Quarterly dividend per share = Annual dividend per share / 4

                                                  = $0.08 / 4

                                                   = $0.02

Hence the quarterly dividend payment per share will be: $0.02.

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See text below

Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)

EARNINGS

52-WEEK

TICK

VOL.

WEEK'S

LATEST

THIS NEXT DIV

High Low

Name

Sym.

100s

Yld.

P/E Last Chg.

Year

Year

Year

Amt

8.50

3.20

Targa Resources

TRGP

412574 1.8

PO

dd

+0.41

0.25

0.18

0.12

Answer:

1) False--all whole numbers are integers.

2) False--no integers are irrational numbers.

3) False--no whole numbers are irrational numbers.

4) False--only zero and the positive integers are whole numbers.

The ratio of the area of the triangle to the area of the trapezoid is 3:8.

Area of the rectangle will be:

= 14 cm x 12 cm

= 168 cm²

Height of the triangle

= 14 cm - 8 cm

= 6 cm

Area of the triangle will be:

= 1/2 x 12 cm x 6 cm

= 36 cm²

Area of the trapezoid will be:

= 1/2 x (base1 + base2) x height

= 1/2 x (12 cm + 12 cm) x 8 cm

= 96 cm²

Ratio will be:

Area of the triangle / Area of the trapezoid

= 36 cm² / 96 cm²

= 3/8

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The probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0.0005.

Let X be the number of turns needed to sharpen a brand W pencil and Y be the number of turns needed to sharpen a brand H pencil. Then, we are interested in finding P(X > Y), the probability that the mean number of turns needed to sharpen a brand W pencil is higher than the mean number of turns needed to sharpen a brand H pencil.

The difference between the means of X and Y is 4.6 - 5.2 = -0.6. The standard error of the difference between the means can be calculated as:

SE = sqrt[(0.67^2/30) + (0.33^2/30)] = 0.178

The test statistic is:

Z = (-0.6 - 0) / 0.178 = -3.37

Using a standard normal distribution table, the probability of getting a Z-score less than -3.37 is approximately 0.0005.

Therefore, the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0.0005.

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Answer:

6.

solution:

8+5=13

8×5=40

Eric will need at least 6 cans of finish to cover the entire outside of the box with three coats.

To find the minimum number of cans of finish needed for the job, we first need to calculate the total surface area of the box that will be covered with the finish.

The box has a length of 42 inches, a depth of 24 inches, and a height of 20 inches. To find the total surface area, we can use the formula for the surface area of a rectangular prism:

Surface area = 2(length x width + width x height + height x length)

Surface area = 2(42 x 24 + 24 x 20 + 20 x 42)

Surface area = 2(1008 + 480 + 840)

Surface area = 6656 square inches

Since the finish will be applied in three coats, we need to multiply the total surface area by three to get the total area of finish needed:

Total area of finish = 3 x 6656 square inches

Total area of finish = 19968 square inches

Now we can convert the total area of finish from square inches to square feet by dividing by 144:

Total area of finish = 19968 square inches / 144 = 138.67 square feet

Since each can of finish covers about 27.5 square feet, we can calculate the minimum number of cans needed by dividing the total area of finish by the coverage of each can:

Minimum number of cans = 138.67 square feet / 27.5 square feet per can

Minimum number of cans = 5.04 cans

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A level 0.95 confidence interval is a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. So, the correct answer is C).

A level 0.95 confidence interval is a statistical measure used to estimate the true value of a population parameter based on a sample of data. It provides a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.

The level of confidence, in this case 0.95, means that if the same sampling method and data analysis were repeated multiple times, the resulting confidence intervals would contain the true population parameter in 95% of cases.

The width of the interval, or margin of error, is influenced by factors such as sample size, variability, and level of confidence. So, the correct option is C).

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Dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe.

To find out how much sugar Dominik used in total for both recipes, we need to add the amounts of sugar he used in each recipe.

7/8 cup + 3/4 cup

To add these two fractions, we need to find a common denominator. In this case, the smallest common denominator is 8, which is the same as the denominator of the first fraction.

7/8 cup + 3/4 cup = (7/8) cup + (6/8) cup

Now we can add the two numerators

(7/8) cup + (6/8) cup = 13/8 cup
Hence, Dominik used 13/8 cups of sugar for both recipes combined.

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Answer:

Step-by-step explanation:

Option A: 8,000(1+6(0.05))

is equal to 10,400

Option B is 10,479.72

Option C: 8,000(1+0.0475)^6

is equal to 10,568.52

making B about $80 more than A and $89 less than C

Answer:

20 tables

Step-by-step explanation:

12a is the small tables and 8b is the 8 large tables so they are adding it together and getting 20 tables.

Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.

Mrs. Brown should consider using a box plot (also called a box and whisker plot) and/or a modified box plot.

A box plot is a useful graphical representation because it shows the overall shape of the data and displays the 5-number summary, which includes the minimum value, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and the maximum value. A modified box plot also provides this information and additionally identifies any potential outliers in the data.

Therefore, Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.

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Correct question is "Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary then find which representations should Mrs. Brown consider? "

The correct representations of the inequality is

- 6x + 15 < 10 - 5x  and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

We have the inequality -3(2x - 5) < 5(2 - x)

Now, simplifying each side of inequality

-3(2x - 5) = -3(2x) + -3(-5)

-3(2x - 5) = - 6x + 15

and, 5(2 - x) = 5(2) + 5(-x)

5(2 - x) = 10 - 5x

So, - 6x + 15 < 10 - 5x

Now, Subtract 15 from both sides

- 6x < -5 - 5x

- x < - 5

x > 5

The correct statements are:

- 6x + 15 < 10 - 5x  and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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The line of reflection must be the line halfway between the x-coordinates of the corresponding vertices of each polygon. This line is x=4.

So, the line of reflection is x=4.

A line of reflection is a line used in mathematics that functions like a mirror, reflecting all points on one side of the line onto the other side so that each point is equally distant from the line as its reflected point on the other side. It is also known as the mirror line or the axis of reflection.

To determine the line of reflection that maps polygon ABCDE to polygon A' B' C' D' E', we need to look for a line that is equidistant from each corresponding pair of points.

Reflection across the x-axis or y-axis will not work because the corresponding vertices of the two polygons have different y-coordinates or x-coordinates, respectively.

Reflection across x=5 or y=6 will also not work because the line is not equidistant from each corresponding pair of points.

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