Quadrilateral HIJK is similar to quadrilateral LMNO. Find the measure of side OL.
Round your answer to the nearest tenth if necessary.
K
19
J
с
58
N
42
M M
H Н
L

Answer:

If the same cup of 190∘F soup is instead placed into a freezer set at 30∘F, what is the time required for the soup to cool from 190∘Fto135∘F in this situation?

Because x is greater than -8, the arrow is pointing to the left,

Because it is greater than, not greater than/equal to, the dot is empty.

Sorry if its a bit messy, I don't have amazing drawing skills on the computer. It should give a general idea though.

Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

Answer:

1.5gallons

Step-by-step explanation:

Here,

no. of bottles(a) : 12

no. of cups (b) :a*2

=12*2

=24

Now,

No. of gallons. :24/16

:1.5gallons

.·.A cartoon contains 1.5 gallons of lemon tea.

The postfix expression "3 8 7 7 + - 9 3 +" to an equivalent infix expression and show the evolution of the stack.

Postfix expression: 3 8 7 7 + - 9 3 +

1. Push the first two operands (3 and 8) onto the stack:

Stack: [3, 8]

2. Next, push operands 7 and 7 onto the stack:

Stack: [3, 8, 7, 7]

3. Now, encounter the first operator '+'. Pop the top two operands (7 and 7), perform the addition, and push the result (14) back onto the stack:

Stack: [3, 8, 14]

Infix: (7+7)

4. Next, encounter the operator '-'. Pop the top two operands (14 and 8), perform the subtraction, and push the result (-6) back onto the stack:

Stack: [3, -6]

Infix: (8-(7+7))

5. Push operand 9 onto the stack:

Stack: [3, -6, 9]

6. Push operand 3 onto the stack:

Stack: [3, -6, 9, 3]

7. Encounter the operator '+'. Pop the top two operands (3 and 9), perform the addition, and push the result (12) back onto the stack:

Stack: [3, -6, 12]

Infix: (9+3)

8. Finally, encounter the last operator '-'. Pop the top two operands (12 and -6), perform the subtraction, and push the result (18) back onto the stack:

Stack: [3, 18]

Infix: ((8-(7+7))-(9+3))

The equivalent infix expression is: 3 - ((8 - (7 + 7)) - (9 + 3))

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Probability of that all five households will have pets is 0.05.

The probability of that all five households will have pets is calculated as follows:

Probability that a household owns a pet, p = 0.55

Probability that a household does not own a pet, q = 1 - 0.55 = 0.45

Probability of that all five households will have pets = ₅C₅ * 0.55⁵ * 0.45⁽⁵⁻⁵⁾

Probability of that all five households will have pets = 0.05

In conclusion, the probability that all five households have pets is determined by combination probability.

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Answer:

21

Step-by-step explanation:

(3) Add: Under applied overhead 34,000

(4) Adjusted cost of goods sold 364,000

1 and 2 RAW MATERIAL INVENTORY

Beginning balance 75,000

a 225,000 150,000 b, Ending Balance 150,000

WORK IN PROGRESS INVENTORY

Beginning balance 140,000

b 125,000 352,000 g

c 60,000

f 105,000

j Ending Balance 78,000

FINISHED GOODS INVENTORY

Beginning balance -

g 352,000 330,000 h

Ending Balance 22,000

FACTORY OVERHEAD

b 25,000

c 40,000 105,000 f

d 74,000

Ending Balance 34,000

COST OF GOODS SOLD

h 330,000

Ending Balance 330,000

Factory overhead applied on the basis of direct labor cost .

Hence applied overhead = 60,000 x 175% = $105,000Step: 2

3)

Computation of under /(over) applied OH

Actual OH($) Applied OH ($) Under /(over) applied OH ($)

139,000 105,000 34,000

Actual manufacturing overhead:

$

Indirect material 25,000

Indirect Labour 40,000

Other manufacturing overhead 74,000

139,000

4)

Cost of goods sold (Unadjusted) 330,000

Add: Under applied overhead 34,000

Adjusted cost of goods sold 364,000

Actal manufacturing overhead is more than applied overhead,it means factory overhead under applied and it will be added in unadjusted cost of goods sold to ascertain adjused cost of goods sold.

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Answer:

Slope = m = 4

Step-by-step explanation:

y = 4x-6

Comparing this with the standard slope-intercept equation:

\(y = mx+b\)

Where m is the slope and b is the y-intercept.

So, we get:

Slope = m = 4

Answer:

4

Step-by-step explanation:

The equation of a line has a formula.

y = mx + b

Where m is the slope, and b is the y-intercept.

The equation for this line is given:

y = 4x + - 6

m = 4

b = -6

4 is the slope, and -6 is the y-intercept.

Answer:

9 = m

Step-by-step explanation:

-5 = 4 - m

-9 = -m

m=9

The equation of the tangent line to the serpentine curve at the point (3, 0.30) is y = -0.08x + 0.54.

To find the equation of the tangent line to the serpentine curve at the point (3, 0.30), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of the function y = x/(1 + x²) and evaluating it at x = 3.

Taking the derivative of y = x/(1 + x²) with respect to x, we get:

dy/dx = (1 + x²)(1) - x(2x)/(1 + x²)²

= (1 + x² - 2x²)/(1 + x²)²

= (1 - x²)/(1 + x²)²

Now, let's evaluate the derivative at x = 3:

dy/dx = (1 - (3)²)/(1 + (3)²)²

= (1 - 9)/(1 + 9)²

= (-8)/(10)²

= -8/100

= -0.08

So, the slope of the tangent line at the point (3, 0.30) is -0.08.

Next, we can use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form is:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the given point on the line and m is the slope.

Using the point (3, 0.30) and the slope -0.08, we have:

y - 0.30 = -0.08(x - 3).

Simplifying, we get:

y - 0.30 = -0.08x + 0.24.

Now, rearranging the equation to the slope-intercept form, we have:

y = -0.08x + 0.54.

So, the equation of the tangent line to the serpentine curve at the point (3, 0.30) is y = -0.08x + 0.54.

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By using the concept of function, it can be verified that

g(f(x)) = 5log(5(x)) + 4

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, the given functions are

f(x) = log(5x)

g(x) = 5x + 4

g(f(x)) = g(log(5x)) = 5log(5(x)) + 4

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Lizzie could have made 1 rectangle using 43 congruent paper squares, as the factors of 43 are prime and cannot form a rectangle. Combining pairs of factors yields 43, allowing for rotation.

To determine the number of different rectangles that Lizzie could have made, we need to consider the factors of the total number of squares she has, which is 43. The factors of 43 are 1 and 43, since it is a prime number. However, these factors cannot form a rectangle, as they are both prime numbers.

Since we cannot form a rectangle using the prime factors, we need to consider the factors of the next smallest number, which is 42. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

Now, we need to find pairs of factors that multiply to give us 43. The pairs of factors are (1, 43) and (43, 1). However, since the problem states that two rectangles are considered the same if one can be rotated to look like the other, these pairs of factors will be counted as one rectangle.

Therefore, Lizzie could have made 1 rectangle using the 43 congruent paper squares.

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the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.To find the values of m and b for the straight line that provides the best least-squares fit to the data, we need to complete the table and use the formulas for calculating the slope (m) and y-intercept (b).

First, let's complete the table by calculating the xy column:

X    y    xy

1    8    8

2    10   20

3    12   36

4    3    12

  Σχ=10   Σy=20   Σxy=76

Now, we can use the formulas:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

b = (Σy - m(Σx))/n

Plugging in the values from the table:

m = (76 - (10)(20)/4) / (30 - (10)²/4)

  = (76 - 200/4) / (30 - 100/4)

  = (76 - 50) / (30 - 25)

  = 26 / 5

  = 5.2

b = (20 - 5.2(10))/4

  = (20 - 52)/4

  = -32/4

  = -8

Therefore, the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.

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The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.

What is Pythagorean theorem?

The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.

The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.

The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.

The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.

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Answer:

1/16 of the pizza each.

Step-by-step explanation:

1/8 divided by 2 (because you are splitting the slice into two) equals 1/16.

Answer:

\(5\)

Step-by-step explanation:

Segments are named by their endpoints. Therefore, segment PQ will have endpoints P and Q. The length of the segment is equal to the distance between these points.

To find the distance between P and Q given their coordinates, use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let:

\(P(-2, 7)\implies (x_1, y_1),\\Q(1, 3)\implies (x_2, y_2)\)

The distance between these points is equal to:

\(d=\sqrt{(1-(-2))^2+(3-7)^2},\\d=\sqrt{3^2+(-4)^2},\\d=\sqrt{9+16},\\d=\sqrt{25},\\d=\boxed{5}\)

Answer:

\(5\)

Step-by-step explanation:

This problem gives one the following points on a line: (\(P(-2,7)\)), and (\(Q(1,3)\)). The problem asks one to find the distance between the two points. The formula to find the distance between two points on a coordinate point is the following,

\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Substitute the given values in and solve for the distance;

\(D=\sqrt{(-2)-(1))^2+((7)-(3))^2}\)

Simplify,

\(D=\sqrt{(-2)-(1))^2+((7)-(3))^2}\\\\D=\sqrt{(-3)^2+(4)^2}\\\\D=\sqrt{9+16}\\\\D=\sqrt{25}\\\\D = 5\)

The probability of waiting between 10 and 15 minutes at the Maryland Department of Motor Vehicles (DMV), given an exponential distribution with an expectation of 10 minutes.

The median waiting time, which represents the 50th percentile of the waiting time distribution, can be found by solving the equation involving the CDF of the exponential distribution. In this case, the median waiting time is approximately 6.9315 minutes.

The exponential distribution is often used to model the time between events that occur at a constant rate independently of past occurrences.

The parameter of the exponential distribution is the expectation or mean, which is given as 10 minutes in this case.

The probability of waiting between 10 and 15 minutes can be calculated by subtracting the probability of waiting less than 10 minutes from the probability of waiting less than 15 minutes.

This can be done using the CDF of the exponential distribution. Plugging in the appropriate values, the probability is approximately 0.0916, or 9.16%.

The median waiting time represents the time at which 50% of the waiting times are less than or equal to the median. In the exponential distribution.

The median can be calculated by solving the equation 1 - e^(-λt) = 0.5, where λ is the rate parameter of the distribution and t is the median waiting time.

In this case, the rate parameter is 1/10, as the expectation is 10 minutes. Solving the equation gives us t ≈ 6.9315 minutes, which is the median waiting time at the Maryland DMV.

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Answer:

$11,000

Step-by-step explanation:

Given that :

Time, t = 140 days = 140/365 = 0.3835years

Interest paid = 253.15

Interest % = 6%

Principal, p =?

Using the relation :

Interest = principal * rate * time

253.15 = p * 0.06 * (140/365)

253.15 = 0.0230136p

P = 253.15 / 0.0230136

P = 11000.017

Hence, the principal amount = $11,000

The future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

To find the future value of this loan, we can use the formula FV = PV(1 + r)^t, where FV is the future value, PV is the present value, r is the interest rate, and t is the time period in years.

In this case, we have PV = $17,592, r = 6.6%, and t = 8 months or 0.667 years (8/12).

Plugging these values into the formula, we get:
FV = $17,592(1 + 0.066)^0.667
FV = $17,592(1.066)^0.667
FV = $18,358.16

Therefore, the future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.

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Lagrange interpolation basis polynomials: Ln(x) = Σ[i=1 to k+1]\(F(x_i)Li(x)\)where, Li(x) = Π[j=1 to k+1, j ≠ i] \((x-x_j) / (x_i - x_j).\)

The formula for the Lagrange Interpolational Polynomial Ln(x) associated with the data (xi, F(x_i)), 1 ≤ i ≤ k + 1 is given by:

Ln(x) = Σ[i=1 to k+1] \(F(x_i)Li(x)\)

where,

Li(x) = Π[j=1 to k+1, j ≠ i] \((x-x_j) / (x_i - x_j)\)

are the Lagrange interpolation basis polynomials.

Lagrange Interpolation is a method of finding a polynomial that passes through a given set of data points. It makes use of the basis polynomials or Lagrange basis functions to construct the polynomial.

The Lagrange basis polynomials are defined as,

Li(x) = Π[j=1 to k+1, j ≠ i] \((x-x_j) / (x_i - x_j)\)

where, 1 ≤ i ≤ k+1 are the indices of the data points.

The Lagrange Interpolational Polynomial Ln(x) associated with the data

(xi, F(x_i)), 1 ≤ i ≤ k + 1 is given by,

Ln(x) = Σ[i=1 to k+1] \(F(x_i)Li(x)\)

Hence, the formula for the Lagrange Interpolational Polynomial Ln(x) associated with the data (xi, F(x_i)), 1 ≤ i ≤ k + 1 is given by:

Ln(x) = Σ[i=1 to k+1] \(F(x_i)Li(x)\)

where

Li(x) = Π[j=1 to k+1, j ≠ i] \((x-x_j) / (x_i - x_j)\) are the Lagrange interpolation basis polynomials.

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To model the decrease in the value of the car over time, we can use an exponential function of the form:

V(t) = V(0) * e^(-rt)

where:

V(0) is the initial value of the car (in this case, $20,000).

r is the annual rate of depreciation, expressed as a decimal (in this case, 0.103).

t is the number of years since the car was purchased.

Plugging in the given values, we get:

V(t) = $20,000 * e^(-0.103t)

This is the exponential function that models the value of the car in t years.

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Answer:

y = 4

Step-by-step explanation:

\(\frac{sin(90)}{4\sqrt{2} } = \frac{sin(45)}{y}\)

Answer:

y = 4

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = \(\frac{1}{\sqrt{2} }\) , then

cos45° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{y}{4\sqrt{2} }\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

y × \(\sqrt{2}\) = 4\(\sqrt{2}\) ( divide both sides by \(\sqrt{2}\) )

y = 4

adding two negative integers always yields a negative sum

Answer:

30%

Step-by-step explanation:

yellow = 20%

red = 20%

orange = 10%

blue = 10%

green = 10%

Brown = 100% - (20% + 20% + 10% + 10% + 10%) = 100% - 70% = 30%

So, the probability of getting the brown m&m is 30%

Answer:

The length of the long side is 147 ft

The length of the short side is 30 ft

Step-by-step explanation:

L=5s-3

s= 324-2L

324=2(5s-3)+s

distribute

324=10s-6+s

simplify

324=11s-6

add 6 to both sides

330=11s

divide by 11

30=s

Plug in the s value to determine the length of the long side

It is well known that utilizing a zip file is an effective method for reducing the size of the document in order to boost storage and sharing possibilities. A zipped folder may be smoothly moved from one place (the transmitter) to another without any issues (the receiver).

One or more files can be compressed and stored together in one location using the ubiquitous ZIP file format. As a result, the file size is less and is simpler to transport and store. After transmission, the receiver can use the files in their original form by unzipping (or extracting) her ZIP file.

In order to increase storage and sharing capabilities by lowering the size of the document, it is known that using a zip file is an efficient technique. A zipped folder may be effortlessly transferred without any hiccups from one location (the transmitter) to another (the receiver). Using Zip files has the primary benefit of reducing the time required to send large files over email. The document's quality is unaffected and is identical to the original file when it is compressed using a zip file.

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Answer:

ok

Step-by-step explanation: