In a class of 60 students, 20 can speak English, 35 can speak French, 20 can't speak neither English, nor French. What number of students speak both English and French?​

Answer: y=-4x-27

Step-by-step explanation:

\(y=mx+b\)

Lines are parallel if their slopes are equal

\(y=-4x+2\)

⇒ m=-4

⇒ y=-4x+b

A line passes through (-8.5)

⇒ x=-8    y=5

\(5=-4(-8)+b\\5=32+b\\5-32=32+b-32\\-27=b\)

So, y=-4x-27

Answer:

40 minutes

Step-by-step explanation:

rate = distance/time = miles/hr

rate = 240 mi/2 hr = 120 mi/hr

time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes

(0.67 hr)(60 min/hr) = 40 minutes

To prove that a cycle graph Cn has exactly n labeled spanning trees, we can use the principle of inclusion-exclusion. First, consider a tree T that is composed of the n edges of Cn. This tree has n edges and is therefore an n-edge tree. In order for it to be a labeled spanning tree, every vertex must be labeled with a distinct label. Since Cn has n vertices, there are n! ways to label the vertices, giving us n! labeled spanning trees.

Now, we can use inclusion-exclusion to determine the number of labeled spanning trees that are a subset of T. For each vertex vi in T, we can choose any label from the set of n labels. For each of these labels, we can choose any edge from the n edges in T. The total number of labeled spanning trees that are a subset of T is therefore: n2 × n!

Now, we can subtract the number of labeled spanning trees that are a subset of T from the total number of labeled spanning trees to get the number of labeled spanning trees that are not a subset of T. The number of labeled spanning trees that are not a subset of T is: n! - n2 × n! = n! - n2! Therefore, the total number of labeled spanning trees of Cn is n!.

This proves that a cycle graph Cn has exactly n labeled spanning trees.

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Answer:

[D] \(\displaystyle \lim_{h \to 0} \frac{[5(x + h)^2 - 2(x + h)] - (5x^2 - 2x)}{h}\)

General Formulas and Concepts:

Calculus

Limits

Derivatives

Definition of a Derivative: \(\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f(x) = 5x^2 - 2x\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer: 675

Step-by-step explanation:

6/10 = 0.6

0.6 * 1125 = 675

The amount of paint needed to apply a coat of paint is 1.00 m³.

Given:

a coat of paint 0.06 cm thick to a hemispherical dome with diameter 40 m.

we are asked to  estimate the amount of paint needed to apply a coat of paint.

The amounts

Volume of a hemisphere, V = (2/3)πr³

r = 40/2

= 20 m

dr = 0.04 cm = 0.0004 m

dV≈2πr²dr

= 2π(20)²(0.0004) m³

=  1.0048 m³

rounding it of to two decimal places.

= 1.00 m³

Hence the amount of paint needed is 1.00 m³

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Answer:

140°

Step-by-step explanation:

a° = 180°-(75°-35°) = 180°-40° = 140°

The little red dashes on the segments means they are congruent. EM = MG

Let's plug the expressions from the picture into our equation above.

7x = 8x - 6

Subtract 8x from both sides.

-x = -6

Divide both sides by -1

x = 6

EM = 7x = 7(6) = 42

Answer:

sinB=p/h

sin45=8/y

1/√2=8/y

y=8√2in

The Number of Associates and Number of Partners assigned to the case by the law firm is 5 and 9 respectively. We can solve this by using the concept of Linear Equation.

Given that,

Daily rate charged to the client for each Associate = $ 800

Daily rate charged to the client for each Partner = $ 1700

Let number of Associates assigned to case = X

And number of Partners assigned to case = Y

So, According to Question

X + Y = 14    ----(1)

800X + 1700Y = 19300        ---(2)

From the equation (1) , Y = 14 – X

Substituting the value of Y into equation (2) we get,

800X + 1700(14-X) = 19300

800X + 23800 – 1700X = 19300

23800 – 900X = 19300

23800 – 19300 = 900X

4500=900X

4500/900 = X

X = 5

Put the value of X into equation (1),

5 + Y = 14

Y = 14 -5

Y = 9

So we let the number of Associates assigned to case X and number of partners assigned to case Y and the value of X is 5 and Y is 9 .

Hence the number of Associates assigned to the case is 5 and the number of Partners assigned to the case is 9.

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Answer:

100

Step-by-step explanation:

100

The total area of the four squares is the sum of each individual area of each square. Hence, the total area of the square is 100 ft²

Given that :

The area of each square can be calculated thus :

The area of the entire square :

(5² + 5² + 5² + 5²)

(25 + 25 + 25 + 25) = 100 ft²

The total area of the square is 100 ft²

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To create a side view, you can use a straightedge to outline the object from a side perspective. If the object has congruent segments, you can measure the length of one segment and use the compass to mark off the same length on the straightedge to create the other segments.

For congruent angles, you can use the compass to mark off the same angle on the straightedge. If the object has parallel or perpendicular lines, you can use the straightedge to draw those lines accurately. If the object has special shapes such as equilateral triangles, squares, or regular hexagons, you can use the compass to draw those shapes.

To create a top view, you can use a straightedge to outline the object from a top perspective. If the object has congruent segments, you can measure the length of one segment and use the compass to mark off the same length on the straightedge to create the other segments.

For congruent angles, you can use the compass to mark off the same angle on the straightedge. If the object has parallel or perpendicular lines, you can use the straightedge to draw those lines accurately. If the object has special shapes such as equilateral triangles, squares, or regular hexagons, you can use the compass to draw those shapes.

To create a front view, you can use a straightedge to outline the object from a front perspective. If the object has congruent segments, you can measure the length of one segment and use the compass to mark off the same length on the straightedge to create the other segments.

For congruent angles, you can use the compass to mark off the same angle on the straightedge. If the object has parallel or perpendicular lines, you can use the straightedge to draw those lines accurately. If the object has special shapes such as equilateral triangles, squares, or regular hexagons, you can use the compass to draw those shapes.

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tesfa = x

dad = 4x

mom= 4x-1

x+4x+4x-1=101

9x+1=101

9x=100

100/9= 11.1

Answer:

1 1/9 miles

Step-by-step explanation:

If john swims 5/12 of a mile in 3/8 of an hour, then;

5/12 miles = 3/8 hours

TO get the number of miles he swims in an hour, we will say;

x miles = 1 hour

Equating both expressions

5/12 miles = 3/8 hours

x miles = 1 hour

Cross multiply

3/8 x = 5/12

3x/8 = 5/12

3x * 12 = 5 * 8

36x = 40

x = 40/36

x = 10/9

x = 1 1/9

The amount he swims in an hour is 1 1/9 miles

Answer:

Step-by-step explanation:

The exponential decay function is

\(v(t)=a(b)^t\) where b, the rate of decay, for us is (1 - .115) and a is the original value of the car which, for us, is 18000. t is the time in years. Using this information to write the equation we need to solve for the value when the car is 10 years old:

\(v(t)=18000(.885)^t\) and we sub in 10 for t:

\(v(t)=18000(.885)^{10\) which simplifies to

v(t) = 18000(.2947356754) so

v(t) = 5305.24

Each function represents a different mapping of elements from the domain set to the range set.

To find all functions from the set (a, b, c) to the set (1, 2), we can use the concept of Cartesian product. Since there are 3 elements in the domain set (a, b, c) and 2 elements in the range set (1, 2), we have a total of 2^3 = 8 possible functions. Each function will map each element from the domain set to an element in the range set.
Here are the 8 functions:
1. (a -> 1, b -> 1, c -> 1)
2. (a -> 1, b -> 1, c -> 2)
3. (a -> 1, b -> 2, c -> 1)
4. (a -> 1, b -> 2, c -> 2)
5. (a -> 2, b -> 1, c -> 1)
6. (a -> 2, b -> 1, c -> 2)
7. (a -> 2, b -> 2, c -> 1)
8. (a -> 2, b -> 2, c -> 2)
Each function represents a different mapping of elements from the domain set to the range set.

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Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test

Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.

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In Darcy's law, the average linear velocity of water is directly proportional to (B) specific discharge.

This is because Darcy’s law defines the relationship between the rate of flow of a fluid through a porous material, the viscosity of the fluid, the effective porosity of the material and the pressure gradient. Specific discharge refers to the volume of water that flows through a given cross-sectional area of the aquifer per unit of time per unit width.

Darcy's law is used to determine the flow of fluids through permeable materials such as porous rocks. This law assumes that the flow of fluids is proportional to the pressure gradient and the properties of the permeable material. The specific discharge is the volume of fluid that passes through a unit width of the aquifer per unit time. Effective porosity is the ratio of the volume of void space to the total volume of the porous material.

The equation for Darcy’s law is expressed as:

Q = KA (h2 - h1) / L

Where:

Q = flow rate

K = hydraulic conductivity

A = cross-sectional area of the sampleh1 and h2 = the hydraulic heads at the ends of the sample

L = the length of the sample.

The specific discharge is a crucial parameter in groundwater hydrology because it determines the rate at which groundwater moves through the aquifer. The effective porosity is also an important parameter because it determines the amount of water that can be stored in the pore spaces of the material. In conclusion, the average linear velocity of water is directly proportional to the specific discharge in Darcy's law.

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Answer:

See answer below

Step-by-step explanation:

2b(2ab)² - a(2b²)² = XaY³(z - b)

\(2b(2ab)(2ab) - a(2b^2)(2b^2) = XaY^3(z-b)\)

\(8a^2b^3 - 4ab^4 = XaY^3(z - b)\)

\(4ab^3(2a-b) = XaY^3(z - b)\)

X = 4

y = b

z = 2a

⇒F(-5) just simply means that in the function F in the place of x you have to plug in -5 and simplify if possible.

\(f(-5)= -(-5)^{2} +9(-5)-17\\f(-5)=-(25)-45-17\\f(-5)=-25-45-17\\f(-5)=-70-17\\f(-5)=-87\)

the answer to f(-5) is -87

GOODLUCK!!

Answer:

n = 3

Step-by-step explanation:

Hope this helps you! :))

Answer:

n= 3

Step-by-step explanation:

when there is a multiplication with the same base, you can rewrite the base and make the sum of the exponents

3^(5+n) = 3^8

5 +3 = 8

so n=3

A bell-shaped histogram is a type of graph that displays a normal distribution, which is a probability distribution that is symmetrical and has a characteristic bell shape.

The bell-shaped histogram is created by plotting the data on a horizontal axis and the frequency or probability on a vertical axis. The data points are grouped into intervals called bins, and the number of data points that fall into each bin is plotted as a bar. The bars are typically drawn adjacent to one another and connected with lines to create a continuous curve that represents the normal distribution.

The resulting histogram will have a characteristic bell shape, with a high point at the mean, and decreasing frequency or probability as the values move away from the mean in either direction. The width of the curve is determined by the standard deviation of the data, with wider curves indicating greater variation in the data.

The bell-shaped histogram is commonly used in statistical analysis to represent normally distributed data, such as the heights or weights of a population, test scores, or other measurements that tend to cluster around a central value with a predictable range of variation.

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Answer:

13

Step-by-step explanation:

f(x)=2(3x)+1

f(2)=2(3X2)+1

f(2)=2(6)+1

f(2)=12+1

f(2)=13

The value of function f(2) is 13.

Function is a type of relation, or rule, that maps one input to specific single output.

Given function;  f(x) = 2 (3x) + 1

We need to find the value of f(2) .

f(x) = 2(3x)+1

f(2) = 2(3 * 2)+1

f(2) = 2(6)+1

f(2)=12+1

f(2)=13

Therefore, the value of function f(2) is 13.

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Answer:

yeah most likely

Step-by-step explanation:

Answer:

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In the form of x ± m e, the confidence interval 147.9 < μ < 307.1 can be expressed as x ± m e = 227.5 ± 79.6.

The first paragraph provides a summary of the answer. The confidence interval 147.9 < μ < 307.1 can be represented as ¯ x ± m e = 227.5 ± 79.6.

In statistics, a confidence interval is a range of values within which a population parameter, such as the population mean (μ), is estimated to lie. The confidence interval is typically expressed in the form of ¯ x ± m e, where  x represents the sample mean and m e represents the margin of error.

Given the confidence interval 147.9 < μ < 307.1, we can calculate the sample mean by taking the average of the lower and upper bounds: (147.9 + 307.1) / 2 = 227.5. This is represented as ¯ x = 227.5.

The margin of error (m e) can be calculated by finding the half-width of the confidence interval. It is determined by taking half the difference between the upper and lower bounds: (307.1 - 147.9) / 2 = 79.6. This is represented as m e = 79.6.

Therefore, the confidence interval 147.9 < μ < 307.1 can be expressed as x ± m e = 227.5 ± 79.6. This means that we estimate the population mean (μ) to be 227.5, with a margin of error of 79.6. The actual value of μ is expected to fall within the range of 147.9 to 307.1.

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