a random number is selected from a random set 2,3,4,10

Answer:

The hypotenuse is [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

Taking the square root of each side

[tex]\sqrt{58} = \sqrt{c^2}[/tex]

[tex]\sqrt{58} =c[/tex]

The area of the shaded part is 8.1447cm²

The formula to calculate the area of the shaded region is expressed as:
Area of the shaded region = Area of sector - Area of triangle

Determine the area of the sector

Area of sector = r²β/2

Area of sector = 14²(46π/180)/2

Area of sector = 78.64 cm²

Determine the area of triangle

Area of triangle = 1/2r²sinβ

Area of triangle = 1/2(14²sin46)

Area of triangle = 140.99/2

Area of triangle = 70.49 cm²

Area of shaded part = 78.64 cm² -  70.49 cm²

Area of shaded part = 8.1447cm²

Hence the area of the shaded part is 8.1447cm²

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Answer:

4 inches

Step-by-step explanation:

Given information:

Let y = height of snow on the lawn

Let t = time in hours

⇒ y = 2 + 0.5t

To find how much snow is on the lawn after 4 hours of snowing, substitute t = 4 into the found equation and solve for y:

⇒ y = 2 + 0.5(4)

⇒ y = 2 + 2

⇒ y = 4 inches

Therefore, Amadou will have 4 inches of snow on his lawn after 4 hours of snow falling.

After 4 hours of continuous snowfall at a rate of 0.5 inches per hour, Amadou would have 4 inches of snow on his lawn. After t hours of snow falling at the same rate, he would have 2 + 0.5t inches of snow on his lawn.

After 4 hours of snow falling at a constant rate of 0.5 inches per hour, Amadou would have:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × 4 hours)

Snow accumulation = 2 inches + 2 inches

Snow accumulation = 4 inches of snow.

After t hours of snow falling, the amount of snow on Amadou's lawn would be:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × t hours)

Snow accumulation = 2 + 0.5t inches of snow.

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Answer:

Well, it depends if you are asking the rate per gallon it would be 12 miles per gallon.

Answer:

○ Length = 20 centimeters and Width = 5 centimeters

Step-by-step explanation:

Let the length = L

Then the width is L - 15

A = lw

100 = L(L - 15)

L² - 15L - 100 = 0

(L - 20)(L + 5) = 0

L - 20 = 0  or  L + 5 = 0

L = 20  or  L = -5

Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.

L = 20

width = L - 15 = 20 - 15 = 5

Answer:  ○ Length = 20 centimeters and Width = 5 centimeters

Answer: 8x+70

Step-by-step explanation:

[tex]\sum^{5}_{n=2} (2x+5n)=(2x+10)+(2x+15)+(2x+20)+(2x+25)=\boxed{8x+70}[/tex]

Answer:

Graph C

Step-by-step explanation:

Graph A (-3, -2) (0, 7)

3(7) + 9(0) = 21

21 = 21 ✓

3(-2) + 9(-3) = 21

-6 - 27 = 21

-33 = 21  ✖

Graph B (0, -7) (3,2)

We know from above that (0, 7) is a point on the line 3y + 9x = 21, therefore point (0, -7) cannot be on that line.

3(2) + 9(3) = 21

6 + 27 = 21

33 = 21  ✖

Graph C (0, 7) (3, -2)

We know from above that (0, 7) is a solution.

3(-2) + 9(3) = 21

-6 + 27 = 21

21 = 21 ✓

Since both points on graph C is a solution to the equation of the line given, it is the answer (looking at graph D is not necessary unless you want to double check your answer).

The equivalent expression to ∑n(n+1) is ∑n²+∑n.

Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.

Here, given expression;

       ∑(n(n+1))

     = ∑ (n² + n)

     = ∑n²+∑n

Thus, the equivalent expression to ∑n(n+1) is ∑n²+∑n.

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Using the Poisson distribution, it is found that:

a) The mean is of 15.63.

b) The probability is of 0.0911 = 9.11%.

c) The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The mean is given by:

[tex]\mu = \frac{5705}{365} = 15.63[/tex]

Item b:

The probability is P(X = 17), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 17) = \frac{e^{-15.63}(15.63)^{17}}{(17)!} = 0.0911[/tex]

The probability is of 0.0911 = 9.11%.

Item c:

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-15.63}(15.63)^{0}}{(0)!} = e^{-15.63}[/tex]

The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

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Using the Poisson distribution, it is found that

a) The mean is 15.63.

b) The probability is[tex]e^{-15.63}[/tex] of 0.0911 = 9.11%.

c) The probability is, which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P\left(X=x\right)=\frac{e^{-\mu }\mu ^x}{x!}[/tex]

The parameters are

x is the number of successes.

e = 2.71828 is the Euler number.

[tex]\mu[/tex] is the mean in the given interval.

Item a:The mean is given by:

[tex]\:\mu =\frac{5705}{365}[/tex]

Item b: The probability is P(X = 17), hence:

[tex]P\left(X=17\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{17}}{17!}=0.0911[/tex]

The probability is of 0.0911 = 9.11%.

Item c:The probability is P(X = 0), hence:

[tex]P\left(X=0\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{0}}{0!}=e^{-15.63}[/tex]

The probability is,[tex]e^{-15.63}[/tex] which is less than 0.05,

hence 0 births in a single day would be a significantly low number of​ births.

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Step-by-step explanation:

[tex] = \frac{7}{8} + \frac{1}{4} \div \frac{6}{7} [/tex]

[tex] = \frac{7}{8} + \frac{1}{4} \times \frac{7}{6} [/tex]

[tex] = \frac{7}{8} + \frac{7}{24} [/tex]

[tex] = \frac{7 \times 3}{8 \times 3} + \frac{7}{24} [/tex]

[tex] = \frac{21}{24} + \frac{7}{24} [/tex]

[tex] = \frac{28}{24} [/tex]

[tex] = \frac{7}{6} [/tex]

7/8+(1/4÷6/7​)

1/4 ÷ 6/7 = 7/24

7/8 + 7/24 = 7/6 = 1 1/6

Using the cosine ratio, the value of cos(45) in the diagram is: B. 1/√2.

Cosine ratio is, cos ∅ = adjacent length/hypotenuse length of a right triangle.

The triangle is a 45-45-90 triangle, thus, the two legs will be the same length, which is: 9 units each.

Hypotenuse = √(9² + 9²) = √162 = 9√2 units

∅ = 45°

Adjacent = 9 units

cos 45 = 9/9√2 = 1/√2

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Answer:   for all values of x

Step-by-step explanation:

[tex](f+g)(x)=|x|+9-6=|x|+3[/tex]

Since the range of y = |x| is [tex]y \geq 0[/tex], adding 3 to this shifts the graph 3 units up, giving us that [tex](f+g)(x) \geq 3[/tex] for all values of x.

Answer: -2

Step-by-step explanation:

[tex]g(-3)=0\\\\g(-2)=-2\\\\\frac{g(-3)-g(-2)}{-3-(-2)}=\frac{0-(-2)}{-1}=\boxed{-2}[/tex]

Answer:

<3 and <5<4 and <6

Step-by-step explanation:

Now that we know how to identify consecutive interior angles, let’s talk about the theorem. The consecutive interior angles theorem states that when the two lines are parallel, then the consecutive interior angles are supplementary to each other. Supplementary means that the two angles add up to 180 degrees.

tell me your the greatest but once you turn they hate us

Answer:

370 + 80x ≤ 1090

Step-by-step explanation:

By using letter variables for the unknown numbers, we can break down the question into mathematical terms:

If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.

If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.

The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:

$370 (1 day) + $80 (x hours) ≤ $1090 per day

The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.

To simplify this, we can rewrite it as:

370 + 80x ≤ 1090

Answer:

three

Step-by-step explanation:

60 - 39 = 21

21/7 = 3

The solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

The graphed parabola is f(w), and we have the inequality:

f(w) ≤ 0.

So we need to identify the intervals such that the parabola is below the horizontal axis. By looking at the graph, we can see that the two intervals are:

Left side:

(-∞, -1]

Right side:

[3, ∞)

Where the brackets are used because points x = -1 and x = 3 are solutions.

Then the solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

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The expected number of employees working at Sprockets R Us in 2006 will be 8069.45.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006?

The number of the employees in 2006 will be calculated as:-

Number of employees decreased   = 0.5% x 8110

Number of employees decreased   = (0.5/100) x 8110

Number of employees decreased   = 40.55

The number of the employees in 2006 will be

N = 8110 - 40.55 = 8069.45

Therefore the expected number of employees working at Sprockets R Us in 2006 will be 8069.45.

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Answer:

Complemetry angle = 90° - 40°

= 50°

Hii!

___________________________________________________________

Answer:

[tex]\sf 48\textdegree[/tex]

Step-by-step explanation:

The sum of complementary angles is always 90 degrees.

We can find the complement of 90 by setting up an equation; (let x be the unknown angle).

[tex]\implies[/tex] 42+x=90

Subtract 42 from both sides

x=48

--

Hope that this helped! Best wishes.

--

Answer:

x²-16x+64

Answer:

  (x -8)² = x² -16x +64

Step-by-step explanation:

A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.

All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.

__

One of the patterns that is used with quadratics is the square of a binomial.

  (a - b)² = a² -2ab +b²

This is the result of applying the distributive property several times.

First of all, the exponent indicates repeated multiplication:

  (a -b)² = (a -b)×(a -b)

The distributive property tells you each term outside parentheses multiplies each term inside:

  = a×(a -b) -b×(a -b)

  = a·a -a·b -b·a +b·b . . . . . and again

Now, we collect terms, recognizing that ab=ba.

  = a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication

So, the pattern for the square of a binomial is ...

  (a -b)² = a² -2ab +b²

__

For your specific case, ...

  (x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern

  (x -8)² = x² -16x +64

_____

Additional comment

If you want to do this without using the pattern, just make use of the distributive property:

  [tex](x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}[/tex]

__

While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:

Then the product is ...

  (x -8)² = x² -8x -8x +64 = x² -16x +64

__

Of course, the distributive property is involved in what we call "collecting terms."

  -8x -8x = (-8-8)x = -16x

The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.

The average rate of change of the function will be 63.

The average rate of change of the function is used to find the slope of the graphed function which can be calculated by the change in y value divided by the change in x value.

The average rate of change of function f(x) in the interval [a,b] can be calculated as avearge rate of change= (f(b)- f(a))/(b-a)

Here given function is g(x) = 7x³-4

which is defined in the interval [-3,3].

So using the defination of the average rate of change, The average rate of change= (g(3)-g(-3))/(3-(-3))

= {(7(3³)-4)-(7*(-3)³-4)}/(3-(-3))

= {(189-4)-(-189-4)}/(3+3)

= (185-(-193))/6

= (185+193)/6

= 378/6

= 63

Therefore the average rate of change of the function will be 63.

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Answer:

m is not an element of real number

Answer:  The equation is   y = 4x+3

Slope = 4

y intercept = 3

========================================================

Explanation:

Let's start off by finding the slope.

[tex]A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\[/tex]

The slope is 4.

The y intercept is 3 because of the point (0,3)

We go from y = mx+b to y = 4x+3

m = slope

b = y intercept

---------------

Check:

Plug in x = 0 and we should get to y = 3

y = 4x+3

y = 4(0)+3

y = 0+3

y = 3

That works out. Now try x = 4. It should lead to y = 19

y = 4x+3

y = 4(4)+3

y = 16+3

y = 19

The answer is confirmed.

[tex]\angle P = \angle S \Rightarrow \angle S = 42 &^\circ\\\angle Q = \angle T \Rightarrow \angle S = 86 &^\circ\\\angle R = \angle U\\[/tex]

Sum of all angles in a triangle equals 180:

[tex]\angle R = 180 - (86 + 42) = 180 - 128 = 52[/tex]

Answer:

[tex]U = 52 &^ \circ[/tex]

The graph of the function is y = arcsec(x).