Find the value of x that makes Triangle DEF~ triangle XYZ.

The bars in a histogram are not separated because the data being represented is continuous.

A histogram is a graphical representation of the distribution of data. Histograms are used to illustrate the frequency of data values in a set of information. They provide an estimation of the probability distribution of a continuous variable, which is critical for data analysis in numerous fields.

A histogram can be a bar chart with a frequency count, percentage frequency, or density. Histograms are used to visualize continuous data because they represent an estimation of the underlying probability density function of the random variable that produces the data.

Continuous data is quantitative data that can be measured and manipulated in fractions or decimal points. This data is often represented as a line on a graph. Discrete data, on the other hand, can only take on specific values that are distinct from one another.

Examples of discrete data are the number of pets you have or the number of cars in your garage. They can also be represented graphically as a bar graph because the information falls into discrete bins.

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The length and the width of the rectangle are 86m and 86m respectively

The maximum area of a rectangle with a given perimeter, we need to use the fact that the perimeter of a rectangle is the sum of all four sides, or twice the length plus twice the width.

Let L be the length and W be the width of the rectangle, then we have:

Perimeter = 2L + 2W = 344 meters

We want to find the length and width that maximize the area of the rectangle, given this perimeter.

The area of a rectangle is given by the formula:

Area = Length x Width = L x W

To maximize the area, we can use the fact that the area is a quadratic function of one of the variables (either L or W) and that it has a maximum at the vertex of the parabola.

To find the vertex of the parabola, we can use the formula:

Vertex = (-b/2a, f(-b/2a))

where a, b, and c are the coefficients of the quadratic function f(x) = ax^2 + bx + c.

In this case, the area function is:

f(L) = L(172 - L)

where 172 is half the perimeter (since 2L + 2W = 344, we have L + W = 172, so W = 172 - L).

To find the vertex of this parabola, we need to find the value of L that maximizes the area. We can do this by taking the derivative of f(L) with respect to L, setting it equal to zero, and solving for L:

f'(L) = 172 - 2L = 0

L = 86 meters

This gives us the length of the rectangle that maximizes the area. To find the width, we can substitute L = 86 into the equation for the perimeter:

2L + 2W = 344

2(86) + 2W = 344

W = 86 meters

Therefore, the length and width of the rectangle that has the given perimeter and a maximum area are 86 meters and 86 meters, respectively.

The Perimeter of Rectangle could be considered as one of the important formulae of the rectangle. It is the total distance covered by the rectangle around its outside. you will come across many geometric shapes and sizes, which have an area, perimeter and even volume. You will also learn the formulas for all those parameters. Some of the examples of different shapes are circle, square, polygon, quadrilateral, etc. In this article, you will study the key feature of the rectangle

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Answer:

Mr. Jones would have 21 total pencils.

Answer:

42

Step-by-step explanation:

multiply 14 times 3

Answer:

395= 156+c

Hope this helps :))

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Determine the corresponding sides by the same opposite angles.

Opposite sides to 24° angle are FG and KL.

Correct expression is A:

Answer:

A. Zero

Step-by-step explanation:

The upside down parabolic graph has no roots because it not linear

Answer: 4/9 or 0.4 with a reapeating 4.

Step-by-step explanation:

Answer:

he last ratio is written incorrectly.

Mandy reversed the input and output in the numerator and denominator.

The correct ratio is 50/10.

The relationship is proportional.

Answer:

Rounded to 73

Step-by-step explanation:

The exact number does not end so rounded to the closest whole number is 73

Answer:

72.78 if you want to round to the nearest hundrendths place or if you want the remainder, it would be 72 R51

We have shown that \(sin a \times cos a\) is equal to (√2 - 1) given that tan a = √2 - 1.

To prove that sin a cos a is equal to (√2 - 1), given that tan a = √2 - 1, we'll use the basic trigonometric identities and properties.

Starting with the given equation, tan a = √2 - 1, we can rewrite it using the definition of tangent:

tan a = sin a / cos a

Multiplying both sides of the equation by cos a, we get:

\(tan a \times cos a = sin a\)

Now, using the Pythagorean identity sin² a + cos² a = 1, we can express sin a in terms of cos a:

sin a = √(1 - cos² a)

Substituting this expression into our previous equation, we have:

\(tan a \times cos a = \sqrt(1 - cos^2 a)\)

Squaring both sides of the equation, we get:

\((tan a \times cos a)^2 = 1 - cos^2 a\)

Expanding the left side of the equation, we have:

\(tan^2 a \times cos^2 a = 1 - cos^2 a\)

Rearranging the terms, we get:

\(cos^2 a \times (tan^2 a + 1) = 1\)

Now, recall the given value of tan a = √2 - 1. We can substitute this into our equation:

\(cos^2 a \times ((\sqrt2 - 1)^2 + 1) = 1\)

Expanding (√2 - 1)² + 1, we have:

\(cos^2 a \times (2 - 2\sqrt2 + 1 + 1) = 1\\cos^2 a \times (4 - 2\sqrt2) = 1\)

Dividing both sides of the equation by (4 - 2√2), we get:

cos² a = 1 / (4 - 2√2)

Taking the square root of both sides, we have:

cos a = √(1 / (4 - 2√2))

Now, we can substitute this value of cos a back into our original equation:

sin a * (√(1 / (4 - 2√2))) = √2 - 1

Multiplying both sides of the equation by (√(1 / (4 - 2√2))), we get:

sin a = (√2 - 1) * (√(1 / (4 - 2√2)))

Expanding the right side of the equation, we have:

sin a = (√2 - 1) * (√(1 / (4 - 2√2))) * (√(4 + 2√2) / (√(4 + 2√2)))

Simplifying the expression, we get:

sin a = (√2 - 1) * (√(4 + 2√2) / (√(4 + 2√2)))

Multiplying the numerators and denominators, we have:

sin a = (√2 - 1) * (√(4 + 2√2) / (√(4 + 2√2)))

sin a = (√2 - 1) * (√(4 + 2√2) / (2))

Simplifying further, we get:

sin a = (√2 - 1) * (√(2 + √2))

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If a typical somatic cell has 64 chromosomes, each gamete of that organism is expected to have 32 chromosomes.

In sexually reproducing organisms, somatic cells are the cells that make up the body and contain a full set of chromosomes, which includes both sets of homologous chromosomes. Gametes, on the other hand, are the reproductive cells (sperm and egg) that contain half the number of chromosomes as somatic cells.

During the process of gamete formation, called meiosis, the number of chromosomes is halved. This reduction occurs in two stages: meiosis I and meiosis II. In meiosis I, the homologous chromosomes pair up and undergo crossing over, resulting in the shuffling of genetic material. Then, the homologous chromosomes separate, reducing the chromosome number by half. In meiosis II, similar to mitosis, the sister chromatids of each chromosome separate, resulting in the formation of four haploid daughter cells, which are the gametes.

Since a typical somatic cell has 64 chromosomes, the gametes produced through meiosis will have half that number, which is 32 chromosomes. These gametes, with 32 chromosomes, will combine during fertilization to restore the full set of chromosomes in the offspring, creating a diploid zygote with 64 chromosomes.

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The equivalent expression of square root of -64 is 8i

We have:

square root of -64

Rewrite as:

√-64

Expand

√64 * √-1

Take the square root of 64

8√-1

In complex numbers

√-1  = i

So, we have:

8i

Hence, the equivalent expression of square root of -64 is 8i

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Assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is dependent on the voltage ratio of the primary and secondary coils. If the voltage ratio of the coils is the same as the turns ratio, then the current in the secondary coil will be identical to that in the primary coil. Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is determined by the voltage ratio of the primary and secondary coils. The voltage ratio is equal to the turns ratio, which is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. In an ideal transformer with 100% efficiency, the power output in the secondary coil will be equal to the power input in the primary coil. Since power is equal to voltage multiplied by current, and the voltage ratio is equal to the turns ratio, the current in the secondary coil will be the same as the current in the primary coil.

Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

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From the series, it can be deduced that the sum of the first two terms will be 18.

From the information given, it was stated that the transport charge starts with a minimum charge of R8 and thereafter it was increased by R2 for each kilometre.

The series is also given as S. = 8 + 10 + 12 + 14 +... Therefore, the sum of the first two terms will be:

= 8 + 10

= 18

Expressing T2 in terms of S, and S2 will be T2 = S + S2.

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The vector PQ, which connects the points P(0,0) and Q(-5,-3), can be visualized as an arrow pointing from P to Q in the xy-coordinate system. The magnitude of vector PQ is √34 (approximately 5.83) .

To sketch the vector PQ, we start at the origin (point P) and move 5 units to the left along the x-axis and 3 units downward along the y-axis to reach point Q. This creates an arrow that represents the direction and magnitude of the vector. The arrow starts at P(0,0) and ends at Q(-5,-3).

To compute the magnitude of vector PQ, we can use the distance formula derived from the Pythagorean theorem. The distance formula states that the distance between two points (x₁,y₁) and (x₂,y₂) in a Cartesian coordinate system is given by the square root of the sum of the squares of the differences in their x and y coordinates:

Magnitude = √(\((x₂ - x₁)² + (y₂ - y₁)²)\)

In this case, substituting the coordinates of P(0,0) and Q(-5,-3) into the formula, we get:

Magnitude = √((\(-5 - 0)² + (-3 - 0)²)\)\(-5 - 0)² + (-3 - 0)²)\)

= √\(sqrt{((-5)² + (-3)²)}\)

= √(25 + 9)

= √34

Therefore, the magnitude of vector PQ is √34 (approximately 5.83)

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Answer:

..................................

The probability that at least 80% of the alumni have a job in the field of their choosing is approximately 0.182.

The probability that between 60% and 76% of the alumni have a job in the field of their choosing is approximately 0.817.

The probability that fewer than 60% of the alumni have a job in the field of their choosing is approximately 0.001.

This problem can be solved using the binomial distribution formula, where:

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

where:

Probability that at least 80% of the alumni have a job in the field of their choosing:

Let X be the number of alumni who have a job in the field of their choosing. Then X follows a binomial distribution with n=25 and p=0.74. We want to find P(X >= 20), which can be calculated as follows:

P(X >= 20) = 1 - P(X < 20) = 1 - P(X <= 19)

= 1 - sum(C(25,k)0.74^k0.26^(25-k) for k=0 to 19)

≈ 0.182 (using a binomial calculator or software)

Therefore, the probability that at least 80% of the alumni have a job in the field of their choosing is approximately 0.182.

Probability that between 60% and 76% of the alumni have a job in the field of their choosing:

We want to find P(15 <= X <= 19), which can be calculated as follows:

P(15 <= X <= 19) = sum(C(25,k)0.74^k0.26^(25-k) for k=15 to 19)

≈ 0.817 (using a binomial calculator or software)

Therefore, the probability that between 60% and 76% of the alumni have a job in the field of their choosing is approximately 0.817.

Probability that fewer than 60% of the alumni have a job in the field of their choosing:

We want to find P(X < 15), which can be calculated as follows:

P(X < 15) = sum(C(25,k)0.74^k0.26^(25-k) for k=0 to 14)

≈ 0.001 (using a binomial calculator or software)

Therefore, the probability that fewer than 60% of the alumni have a job in the field of their choosing is approximately 0.001.

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At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

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an expression for the perimeter is: P = 6W +14

The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.

Given that,

Mr. Nowlings garden has a length that is 7 feet more than twice the width

Length: 2w + 7

Where w is the length

Applying the perimeter formula:

Perimeter: 2w + 2 L

Where L is the length,

Replacing with the values given:

P = 2w + 2(2w + 7)

Simplifying:

P =2w + 2 (2w) + 2 (7)

P = 2w + 4w + 14

P = 6W +14

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Answer:

Triangle MBT

Step-by-step explanation:

Congruent basically means an identical triangle in this situation, so the congruent triangle to VET would be MBT

Answer:

triangle mbt is congruent to triangle vet by sas

Step-by-step explanation:

sas stands for side angle side.

angle t is congruent for both triangles

the lines show that line mt and vt are congruent, and line et and bt are too.

since angle t is between both lines that are congruent, it would be through sas

Answer:

  0.4 m = 40 cm

Step-by-step explanation:

You want the height of a model water tower with a volume of 0.1 liters that models a city water tower 40 m high with a volume of 100,000 liters.

The scale factor for volume is the cube of the scale factor for linear dimensions, such as height. Conversely, the scale factor for height is the cube root of the scale factor for volume.

This lets us write a proportion for the height of the model tower:

  \(\dfrac{h}{40\text{ m}}=\sqrt[3]{\dfrac{0.1\text{ L}}{100000\text{ L}}}\\\\h=(40\text{ m})\sqrt[3]{10^{-6}}=\boxed{0.40\text{ m}}\)

Logan should make his tower 0.4 meters, or 40 cm high.

Answer:

the two triangles are congruent because they have the same sides and angles.

Answer:

Yes, they are congruent. Because the sides and the angles are the same.

Step-by-step explanation:

Answer:

The height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.

Step-by-step explanation:

Given:

To Find:

Formula used:

Let the height of each pole be H metres.

Also, let's assume that distance of the point from one pole (as shown in figure) be x m.

According to question, we have

tan60° = H/(80-x)

H = (80-x)√3.... (1)

Also, tan30° = H/x

H = x/√3... (2)

Putting value of eq(2) in eq(1), we get

x/√3 = (80-x)√3

x = 3(80-x)

x = 240 - 3x

4x = 240

x = 60 m

Putting value of x in eq(2), we get

H = 60/√3 = 20√3 m

So, the height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.

Answer:

Height of Pole: 20√3 m

Distance Of Point From Poles: 20m and 60m

Step-by-step explanation:

The attached graph may help you understand my explanation better

The two poles are Ab and CD and are 80m apart

O is the point between them

The angle of elevation from O to A is 60°

The angle of elevation from O to D is 30°

Since the two poles are given to be of equal height,

AB = CD

In ΔAOB using the law of tangents

tan 60° = AB/BO

tan 60° = √3 and AB = x

So we get

√3 = x/BO

Multiplying both sides by BO we get

√3 · BO = x

or BO = x/√3

Looking at ΔCOD

tan 30° = DC/OC

tan 30° = 1/√3

1/√3 = x/OC

OC · ( 1/√3) = x

OC = x ÷ 1/√3

= x · √3/1

OC = √3x

We also know that BO + OC = 80

Plugging this information with values computed gives us

x/√3 + √3x = 80

Multiply by √3 on both sides

(x/√3) · √3 +  (√3x) √3 = 80√3

(x/√3) · √3 = x since the √3 terms cancel out

(√3x) √3 = 3x

So we get

(x/√3) · √3 +  (√3x) √3 = 80√3

=>
x + 3x = 80√3

4x = 80√3

x = (80√3)/4

x =20√ 3

So the height of each pole = 20√ 3 m ≈ 34.64 m

The distance OC can be found from the previous equation
OC = √3x

=> OC = √3 x 20√3 = 20 x 3 =  60m

Since BO + OC = 80 m

BO = 80 - 60 = 20 m

Answer:
Height of each pole = 20√3 m

The point is located 20 m from one pole and 60 m from the other pole

Answer:

6(3h+5k)

Step-by-step explanation:

18h+30k

Factors of 18:

1, 2, 3, 6, 9, 18

Factors of 30:

1, 2, 3, 5, 6, 10, 15, 30

GCF of 18 and 30: 6

18h+30k = 6(3h+5k)

Check your answer:

6(3h+5k)

6(3h) + 6(5k)

18h + 30k

Hope this helps!

Answer:

Step-by-step explanation:

To factor this, we can factor both variables and then get a multiplier outside the parentheses and the new variables inside. (Sorry if it’s confusing)

18h = 2*3*3*h

30k = 2*3*5*k

Both have 2*3, which is 6. This will be the multiplier. To get the new variables, divide the old variables by 6.

18h/6 = 3h

30k/6 = 5k

The signs should not change.

6(3h+5k)

Hope this helps!

Answer:

806

Step-by-step explanation:

add 2,578-3,384 you have to subtract  that to get our final answer which is 806 that's how many they have left.

The value of the double integral ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3] is  0.677

In this question we need to calculate the double integral. 3x sin(x + y) dA, R = [0, π/6] × [0, π/3]

i.e., to find ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3]

First we integrate the function 3x sin(x+y) as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, π/6] (3x sin(x+y)) dy

G(x) = 0.402 xcos(x) + (3x sin(x) / 2)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, π/3] G(x) dx

= ∫_[0, π/3] [0.402 xcos(x) + (3x sin(x) / 2)] dx

= 0.677

Therefore, the solution to the double integral. 3x sin(x + y) da, r = [0, π/6] × [0, π/3] is  0.677

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Answer:

Lesson Summary

A milliliter is a metric unit used to measure capacity that's equal to one-thousandth of a liter. Capacity is the amount of liquid a container can hold. One liter contains 1,000 milliliters, so to convert liters to milliliters you multiply the number of liters times 1,000.

Look at the equivalent metric units of capacity. When converting from a larger unit to a smaller unit, multiply by 1,000. When converting from a smaller unit to a larger unit, divide by 1,000. Liters are larger than milliliters, so multiply by 1,000.

Step-by-step explanation:

Answer:

they are both simplified already, theres nothing else you can do with them

Step-by-step explanation:

im not sure exactly what they are looking for but there is nothing else you can do there except put it in different froms like slope intercept and standard form

The solution to the system of equations is x = -1 and y = -1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = -2x - 3   be equation (1)

5x = -4 + y

Adding 4 on both sides , we get

y = 5x + 4   be equation (2)

On simplifying the equations , we get

5x + 4 = -2x - 3

Adding 2x on both sides , we get

7x + 4 = -3

Subtracting 4 on both sides , we get

7x = -7

Divide by 7 on both sides , we get

x = -1

Substituting the value of x = 1 in equation (2) , we get

y = 5 ( -1 ) + 4

y = -5 + 4

y = -1

Therefore , the value of x and y are -1 respectively

Hence , the system of equations are solved

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Answer:

y=-3x+12

Step-by-step explanation:

basically parallel means same slope or m so in this equation you will keep the same slope in the given equation which is -3 (parallel=same slope, perpendicular=opposite slope) so now all u need to find is b so u then u plug ur coordinates (2,6) into y=mx+b, 6=-3(2)+b and then u do ur algebra 6=-6+b next u get b=12

The original assumption was incorrect, and 2√2 is irrational.

To prove that 2√2 is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0: 2√2 = a/b. Isolating the radical gives √2 = a/2b. The left side of the equation is irrational. Because the right side of the equation is rational, this is a contradiction. Therefore, the assumption is wrong, and the number 2√2 is irrational.

Step-by-step explanation:

1. Assume 2√2 is rational and set it equal to a/b, where b ≠ 0: 2√2 = a/b.

2. Isolate the radical by dividing both sides by 2: √2 = a/2b.

3. Identify the nature of the left side of the equation (√2): irrational.

4. Identify the nature of the right side of the equation (a/2b): rational.

5. Recognize that having an irrational number equal to a rational number is a contradiction.

6. Conclude that the original assumption was incorrect, and 2√2 is irrational.

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