Prove the triangles are congruent. Make sure to include all the steps of a proof.

To find the length of the diagonal fence that stretches from one corner to the opposite corner of a rectangle, we can use the Pythagorean theorem, which states that the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the lengths of the two other sides (legs) of the rectangle.

In this case, the rectangle has dimensions 24 meters by 45 meters. Therefore, the length of the diagonal fence is:

Diagonal fence = √(24^2 + 45^2) meters

Simplifying the equation, we get:

Diagonal fence = √(576 + 2025) meters

Diagonal fence = √2601 meters

Diagonal fence = 51 meters

So Steve will need 51 meters of fencing to stretch diagonally from one corner to the opposite corner of his backyard.

The variable x, which represents the number of students who receive an offer, is a discrete variable.

The variable can take on one or more exact values, a countable number of values, or values that are finite, such as the number of students in a class, the number of cars in a parking lot, the number of seeds in a bag, and so on, if the variable is a discrete variable. A variable is referred to as continuous if it can take on an infinite number of values (although the values may be restricted to a certain range), and those values are not limited to specific points on a continuum.

For three students who are undergoing interviews at Brookwood Institute, the experimental results are defined in terms of the outcomes of the three interviews. Each interview would yield one of two possible results: either an offer for a job or no offer.

As a result, for each of the three interviews, there are two possible outcomes. If we multiply the possibilities for each of the three interviews, we get a total of eight possible outcomes, which can be listed as follows:

NNN, NNO, NON, NOO, ONN, ONO, OON, and OOO.

Let's assume that an 'O' represents an offer, while an 'N' represents no offer. The variable x represents the number of students who receive an offer. Since the variable can only take on one of four discrete values (0, 1, 2, or 3), it is a discrete variable.

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Answer:

Step-by-step explanation:

what number is 8% less than 200?

how do you solve this step by step?

200 : 100 x 8 =

16

200 - 16 =

184

Answer: There would 20-gon

Answer: 315.00 cm^3

Step-by-step explanation:

STEP 1: Plug the given numerical information into the equation for Volume (V = (l) (w) (h)); V = (9) (7) (5)

STEP 2: Determine the answer to above step [315]

Therefore, the answer to the question is 315 cm^3.

NOTE: Don't forget to add the Unit of Measurement to the answer. Answers to Volume related questions also get "cubed" (in this case at least).

***THE ANSWER IS 315 IN SIMPLEST FORM, HOWEVER, ROUNDED TO 2 DECIMAL PLACES IT IS 315.00.***

Answer:

77in^2

Step-by-step explanation:

L=15

W=5

The total is 75 but nearest is 77

Based on Kamila's description, the dot plot that matches her description is Dot plot 1.

The presence of an outlier and the right-skewed distribution can be inferred from the high frequency of data points on the left side of the plot and the single data point that is much larger than the others on the right side.

What is frequency of dot plot?

The frequency in a dot plot refers to the number of dots or data points that appear in a particular bin or category. In a dot plot, each dot typically represents one data point, and the frequency of the dot is the number of data points that have that value. For example, if a dot plot shows the heights of students in a class, with bins for each inch, then the frequency of a particular bin would be the number of students whose height falls within that bin. The frequency can be represented by the number of dots in that bin or by a numerical value.

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The expression that means the same as “a number plus 14” is “14 more than a number”.

In mathematical terms, when we say “a number plus 14”, we are essentially talking about adding 14 to an unknown number.

The word “plus” is used to indicate the operation of addition.
Similarly, when we say “14 more than a number”, we are also talking about the same operation of addition. Here, we are adding 14 to an unknown number.

However,

The words used to describe the operation are different.
Both expressions essentially convey the same mathematical idea, which is adding 14 to an unknown quantity. Depending on the context and the problem at hand, either expression can be used interchangeably.
It is important to note that in mathematics, expressions can be written in different forms while still conveying the same meaning.

This flexibility in writing expressions allows for more efficient and effective communication in problem-solving.

The expression that means the same as "a number plus 14" can be written in algebraic form as x + 14, where x represents any number.

In this expression, the variable x can be replaced by any number, and when we add 14 to that number, we get the result of "a number plus 14".

For example,

If we substitute x with 7, we get 7 + 14 = 21, which means "a number plus 14" is equal to 21.

The algebraic expression x + 14 means the same as "a number plus 14".

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x-coordinate of the other point on the line that has a y value of -12 is 0

The slope of a line in mathematics serves as a gauge for how steep it is. It is described as the proportion of the y-coordinate change to the x-coordinate change between any two locations on a line. A line's slope can be either positive, negative, zero, or undefinable.

Given

vertex=(8,6)

intercept=-12

To find:  x-coordinate of the other point that has a y value of -12

Equation of line

y=mx+c

Putting the values, we get

6=8m-12

m=18/8

m=9/4

Now, finding the x coordinate

y=mx+c

-12=9/4x-12

x=0

Hence,  x-coordinate of the other point that has a y value of -12 is 0.

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The area of the triangle is 62.35 square units. Option D

First, using the cosine identity, we have;

cos θ = adjacent/hypotenuse

cos 60 = x/12

find the value

x = 6

Using the sine identity,

sin 60 = x/12

x = 10. 49

Sum of the base = Line AD + Line DB = 6 + 6 = 12

Using the formula for area of a triangle;

Area = 1/2 base × height

Area = 1/2 × 12 × 10. 39

Multiply the values, we get;

Area = 62. 35 square units

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The given figure appears to be a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In the given figure, we can see that opposite sides are parallel, so it is a parallelogram.

We can also find that the measure of angle A is 120 degrees because the adjacent angles to angle A are 30 and 30 degrees, and the sum of adjacent angles in a parallelogram is 180 degrees. Similarly, the measure of angle C is 60 degrees.

The formula to find the area of a parallelogram is:

Area = base x height

We can choose any base and its corresponding height to find the area of the parallelogram. In the given figure, we can choose AB as the base and the perpendicular distance from AB to line DC as the height. Let's call this distance h.

From the figure, we can see that triangle ADE is a 30-60-90 triangle. The ratio of the sides in a 30-60-90 triangle is 1:sqrt(3):2. So, if AD is x, then DE is x*sqrt(3) and AE is 2x.

Since AE is parallel to DC, we can say that the height h is the same for triangles ADE and CFB. So, we can use triangle CFB to find the value of h.

Triangle CFB is a right triangle with angles 30, 60, and 90 degrees. The length of CB is 4 units and the length of CF is 2 units. So, the length of FB is 2*sqrt(3) units (using the ratio 1:sqrt(3):2). Therefore, the area of triangle CFB is:

Area = (1/2) x base x height

Area = (1/2) x 4 x 2

Area = 4

Since the area of triangle CFB is equal to the area of triangle ADE, we can say that:

Area of parallelogram ABCD = 2 x area of triangle CFB

Area of parallelogram ABCD = 2 x 4

Area of parallelogram ABCD = 8 square units

So, the area of the parallelogram is 8 square units.

The measure of the angles and arc length for the circle are:

a: m∠BAD = 40°; b. arc CE = 48°; c. m∠BCD = 40°; d. m∠ADC = 42°; e.  m∠ABE = 66°.

Hence, the distinction between chord length versus arc length is that the former provides the distance between two places, whilst the latter provides the entire area covered across two points.

The chord's length is equal to twice the angle's radius multiplied by its sine.

The arrow theorem and central angle theorem are other names for the inscribed angle arc  theorem. The measuring of the central angle equals equal to twice the value of the inscribed angle occupied by the same arc, according to this theorem.

arc BD = 80°

arc AC = 84°

∠CBE = 24°

Thus,

a: m∠BAD

m∠BAD = 1/2(arc BD)

m∠BAD = 1/2(80°)

m∠BAD = 40°

b: arc CE

m∠CBE = 1/2(arc CE)

24° = 1/2(arc CE)

24°*2 = arc CE

arc CE = 48°

c: m∠BCD

m∠BCD = 1/2(arc BD)

m∠BCD = 1/2(80°)

m∠BCD = 40°

d: m∠ADC

m∠ADC = 1/2(arc AC)

m∠ADC = 1/2*84°

m∠ADC = 42°

e: m∠ABE

m∠ABE = 1/2(arc AC + arc CE)

m∠ABE = 1/2(84° + 48°)

m∠ABE = 1/2(132°)

m∠ABE = 66°

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Answer: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

Step-by-step explanation: 8 a + 5 b - 9. Based on the given conditions, formulate: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

The surface area and volume of the two cuboids are 124 sq.ft, 72 cubic f

Surface area refers to the total area that the surface of a three-dimensional object covers. It is the sum of the areas of all the faces or surfaces of the object. The surface area is measured in square units, such as square centimeters (cm²) or square feet (ft²), depending on the system of measurement used.

It seems like you have provided two sets of dimensions. Let's calculate the surface area and volume for both the cuboids:

Given that,

Dimensions: 9 ft x 4 ft x 2 ft

Surface area of cuboid 1 = 2(lw + lh + wh)

= 2(94 + 92 + 4*2) sq.ft

= 2(36 + 18 + 8) sq.ft

= 2(62) sq.ft

= 124 sq.ft

Volume of cuboid 1 = l * w * h

= 9 * 4 * 2 cubic ft

= 72 cubic ft

Cuboid 2:

Dimensions: 3 ft x 1 ft x 2 ft

Surface area of cuboid 2 = 2(lw + lh + wh)

= 2(31 + 32 + 1*2) sq.ft

= 2(3 + 6 + 2) sq.ft

= 2(11) sq.ft

= 22 sq.ft

Volume of cuboid 2 = l * w * h

= 3 * 1 * 2 cubic ft

= 6 cubic ft

Therefore, the surface area and volume of the two cuboids are as follows: Surface area = 124 sq.ft, Volume = 72 cubic ft

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When gathering data, using two or more methods to confirm results is called option (c) triangulation

Triangulation involves using multiple methods or sources to collect data in order to validate or confirm results. By using different methods, researchers can obtain a more complete and accurate understanding of the phenomenon being studied, reducing the risk of bias or error. For example, a researcher might use both surveys and interviews to gather information about a particular group of people.

This approach can help to ensure that the data collected is reliable and can be used with confidence to draw conclusions. Triangulation is widely used in social science research, but can also be applied in other fields where multiple sources of information are available.

Therefore, the correct option is (c) triangulation

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From 1940 to 1970 the price of bread increased by 250%.

From 1970 to 1990 the price of bread increased by 300%.

From 1940 to 1990 the price of bread increased by 750%.

The monthly Net income paycheck is $1125

Gross income is the sum of all wages, salaries, profits, interest payments, rents, and other forms of earnings, before any deductions or taxes. The gross income is the addition of the taxes and the net income.

The gross income = net income + tax

The tax is 25% of the gross income

= 25/100 × 1500

= $375

The net income = 1500-375

= $1125

Therefore the monthly net income paycheck is $1125

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Answer:

£90

Step-by-step explanation:

1/5 =3

5/5=15

1/6=15

6/6=90

The total number of students in the college is expressed as: 5x

The parameters given are:

1/2 of the students who learn the flute also learn the violin.

3 times as many students learn the violin as learn the flute.

x students learn both the flute and the violin

Thus, the total who learn the flute = 2x

Number who learn only flute = x

Since 3 times as many students learn the violin as learn the flute. Then, 3x students only learn the violin.

Thus, total number of students at the college is:

x + x + 3x = 5x

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Complete question is:

Every student at a music college learns the flute, the violin, or both the flute and the violin. 1/2 of the students who learn the flute also learn the violin. 3 times as many students learn the violin as learn the flute. x students learn both the flute and the violin. Find an expression, in terms of x, for the total number of students at the college. Flute X Violin​

The regression line equation is given as y = -0.95X + 8.99

The chill factor when  the wind is 27 miles per hour is -16.66

Using a regression calculator, the regression line calculation is given as

Calculation Summary

Sum of X = 45

Sum of Y = 20

Mean X = 6.4286

Mean Y = 2.8571

Sum of squares (SSX) = 113.7143

Sum of products (SP) = -108.5714

Regression Equation = ŷ = bX + a

b = SP/SSX = -108.57/113.71 = -0.95477

a = MY - bMX = 2.86 - (-0.95*6.43) = 8.99497

y = -0.95477X + 8.99497

y = -0.95X + 8.99

b. The chill factor when the wind is 27 miles per hour

We would solve for this using the regression line output above

y = -0.95X + 8.99

here x = 27

y =  -0.95 * 27 + 8.99

y = -25.65 + 8.99

= -16.66

Final answer y =  -16.66

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Based on the above, the the midpoint of AB is M = (2, 1).

To find the midpoint of AB, we need to average the x-coordinates and the y-coordinates of A and B separately. That is:

Midpoint = ((x-coordinate of A + x-coordinate of B) / 2, (y-coordinate of A + y-coordinate of B) / 2) simply say:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

So, for A = (10, -1) and B = (-6, 3), we have:

Midpoint = ((10 + (-6)) / 2, (-1 + 3) / 2)

Midpoint = (2, 1)

Therefore, the midpoint of AB is M = (2, 1). This means that if we drew a line segment from A to B and marked the point exactly halfway between them, that point would be at the coordinates (2, 1).

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Answer:

To find the height of the water tank, we need to know the length of one side of the cube-shaped tank.

Let's assume that the length of one side of the tank is 'x' meters.

The volume of the cube-shaped tank is given as 512 cubic meters, so we have:

The volume of the tank = (length of one side)^3

512 = x^3

Taking the cube root on both sides, we get:

x = 8

Therefore, the length of one side of the tank is 8 meters.

Since the tank is a cube, the height of the tank is also 8 meters.

Step-by-step explanation:

Answer:

8 meter

Step-by-step explanation:

Volume of cubical tank = Area of base * height

Volume of cubical tank = a * a * a

[ all 3 sides of a cube are equal, assume the side as 'a' ]

Volume = a³

a³ = 512

a = ∛512

a = 8 meter

As all dimensions of a cubical tank are equal, height of this tank = 8 meter.

Answer:

1.) 18

2.) 162.5

3.) 4 hours

Step-by-step explanation:

Rule: speed= distance/time

Rule: distance= time x speed

Rule: time= distance/speed

1). 90/5= 18

2). 2.5 x 65= 162.5

3). 320/80= 4

In this scenario, the population would be all the chickens in the county, and it would be very difficult for Krista to survey every single chicken in the county.

A possible representative sample for Krista's claim could be to randomly select a certain number of chicken farms in the county and then record how many eggs their chickens laid on a given day.

The number of farms selected and the number of chickens counted would depend on the size of the county and the resources available to Krista.

However, it is important to note that even a random sample may not perfectly represent the entire population, and there could be other factors that affect egg production, such as the age and breed of the chickens or the quality of their feed.

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Answer:

nails weight 50 lbs by knowing the weight u can find the mss

The experimental probability that the next gumball dispensed will be pink is 5/46.

Experimental probabilities are probabilities determined from a series of experiments. Randomized experiments are performed and repeated several times to determine their probabilities, each repetition is called a trial. Experiments are performed to determine the probability of an event occurring or not occurring. It can be tossing a coin, rolling a dice or spinning a spinner.

The formula to calculate the probability of an experiment is:

P(E) = number of times the event occurs/total number of times the experiment runs

According to the Question:

Here the given is 10 pink gumballs and 82 other gumballs .

Then total outcome = 10+82 = 92

By using probability formula ,

Probability = No of favorable outcome / Total  no. of outcome

Now,

Probability of getting next gumball will be pink is then,

Or,  P( pink) = 10/92 = 5/46

Hence the probability of getting pink as a next gumball is 5/46.

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The logarithm base 7 of 49 i.e. [tex]log_749[/tex] is 2.

What is the natural logarithm?

The natural logarithm, denoted by ln(x), is a mathematical function that gives the logarithm of a number x with respect to the base e, where e is the mathematical constant approximately equal to 2.71828.

The logarithm base 7 of 49 can be evaluated by asking the question: "To what power must 7 be raised to obtain 49?"

We can see that 7 raised to the power of 2 equals 49, so:

[tex]log_749 = 2[/tex]

Therefore, the logarithm base 7 of 49 is 2.

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Answer:

$1.46

Step-by-step explanation:

a bottle of pineapple juice at store A is [tex]\frac{2.40}{5}=0.48[/tex]

a bottle of pineapple juice at store B is [tex]\frac{29.10}{15}=1.94[/tex]

the difference:

$1.94 - $0.48 = $1.46

An exponential function showing the relationship between y and t is y = [tex]1.024^t[/tex] x 380,000

Now let's consider the population after t years. We can use the formula we just derived to write:

y = [tex]1.024^t[/tex] x 380,000

This equation represents an exponential function where the initial population is 380,000 and the growth rate is 2.4%. The base of the exponential function is 1.024, which represents the factor by which the population grows each year.

This function relates the city's population to the number of years since the start of the study and can be written as:

y = [tex]1.024^t[/tex] x 380,000

This function can be used to make predictions about the city's population at any point in the future, given the number of years since the start of the study.

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