In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Answer:

[tex]54[/tex]

Step-by-step explanation:

Formula for average A of two numbers m and n is:

[tex]A=\frac{m+n}{2}[/tex]

Substitute the value m=36 and n=72

[tex]A=\frac{36+72}{2}[/tex]

This is equivalent to:

[tex]A=\frac{108}{2}[/tex]

The average is:

[tex]A=54[/tex]

The equation for resistor 2, R₂ is (d) R₂ = R₁Rt/(R₁ - Rt)

From the question, we have the following parameters that can be used in our computation:

Rt = R₁R₂/(R₁ + R₂)

The question implies that we make R₂ the subject of the formula

So, we have

Rt = R₁R₂/(R₁ + R₂)

Cross multiply the equations

(R₁ + R₂)Rt = R₁R₂

Open the brackets

So, the equation becomes

R₁Rt + R₂Rt = R₁R₂

Collect the like terms

R₁R₂ - R₂Rt = R₁Rt

Factor out R₂

R₂(R₁ - Rt) = R₁Rt

Make R₂ the subject

R₂ = R₁Rt/(R₁ - Rt)

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Answer:

2, R₂ is (d) R₂ = R₁Rt/(R₁ - Rt)

Step-by-step explanation:

Maximum of 16 months, will take Jim to save $947.

Total Cost of Computer = $947

Amount that Jim can save monthly = $60

Let time taken by Jim to save amount which is equal to cost of computer = x months

So, the equation for the above statement can be written as: 60x = 947

Dividing both sides by, 60

[tex]\frac{60x}{60} =\frac{947}{60}[/tex]

[tex]x=\frac{947}{60} =15.78[/tex]

⇒Number of months=16

Maximum of 16 months, will take Jim to save $ 957.

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Answer:

D

Step-by-step explanation:

4 - 8 × 2 ← perform multiplication before doing subtraction

= 4 - 16

= - 12

Answer:

undefined

Step-by-step explanation:

division by zero is undefined

Division Property of zero

For any nonzero real number a

The quotient of "a" and 0 is undefined. That is a/0 is undefined

The number of units manufactured at a cost of $8450 is x = 101.

A function is a relation where every input is connected to only one possible output from a set of available inputs.

The given function is C(x) = x² - 18x + 67.

To find the number of units manufactured at a cost of $8450, substitute C(x) = 8450 into the given equation and solve for x:

8450 = x² - 18x + 67

x² - 18x + 67 - 8450 = 0

x² - 18x - 8383 = 0

x² - 101x + 83x - 8383 = 0

x(x - 101) + 83(x - 101) =0

(x + 83)(x - 101) = 0

(x + 83) = 0 or (x -101) = 0

x = -83 or x = 101

Since the number of manufactured units cannot be negative, it follows

x = 101.

Hence, the number of units manufactured at a cost of $8450 is x = 101.

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Correct statement for whose batch of cookies was more chocolaty is option (c) Neither, The batches were equally chocolaty

Consider Tanvi's cookies
Number of cups of chocolate chips = 1 cups

Number of cups of plain sugar = 3 cups

Total number of cups = 1 + 3 = 4  cups

Then the fraction of chocolate = 1 / 4

= 0.25

Consider Beth's cookies

Number of cups of chocolate chips = 2 cups

Number of cups of plain sugar = 6 cups

Total number of cups = 2 + 6 = 8  cups

Then the fraction of chocolate = 2 / 8

= 1 / 4

= 0.25

Hence, correct statement for whose batch of cookies was more chocolaty is option (c) Neither, The batches were equally chocolaty

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The slope of the vertical line in the given graph is undefined.

The equation of the line is x = 2.

The slope of a vertical line is usually undefined because the horizontal change (change in x) is equal to 0. Thus, we cannot divide a number by 0. Therefore, the slope of a vertical line is undefined.

The line given is a vertical line that intersects the x-axis at 2. Its slope is undefined. Since its slope is undefined, it is impossible to write the equation of the vertical line in the traditional version of the point-slope form. Hence, it is written as x = b, where b is the point where the x-axis is intersected by the line.

Slope of the line is undefined. The equation is x = 2.

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Using the dimensions of the figure, Thomas will have enough money to paint the surface area.

The dimensions of a two-dimensional figure are its lengths and widths.

The product of the length and width results in the surface area, which is stated in square units.

Since Thomas has $1,300, and the squared surface of the figure is equal to 260 square units, when $5 is multiplied into 260, the product is $1,300.

This amount is equal to the money available to Thomas for the painting.

If the dimensions produced a surface area of more or less than 260 square units, we can calculate Thomas' ability to complete the painting based on the information.

The length of the figure is given as 20 units.

The width of the figure is given as 13 units.

The surface area of the figure = 260 square units

The cost of paint per square unit = $5

The total cost for painting the figure = $1,300 ($5 x 260)

The amount available to Thomas for the painting = $1,300

Difference between the total cost and the available amount = $0.

Thus, we can assert that, given the dimensions of the figure, Thomas can complete the painting with the available funds.

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Length of the figure = 20 units

Width of the figure = 13 units

Answer:

$100

Step-by-step explanation:

Round each price to the nearest 10 and add.

$10 + $30 + $60 = $100

Answer: $100

first off, let's convert all those mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{11\frac{4}{5}}\implies \cfrac{11\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{59}{5}} ~\hfill \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\\\ \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{Sarah}{\cfrac{59}{5}}\hspace{5em}\stackrel{Greg}{Sarah - \cfrac{7}{6}} \hspace{5em}\stackrel{Jane}{Greg - \cfrac{4}{3}} \\\\\\ \stackrel{\textit{\LARGE Jane} }{\cfrac{59}{5}~ - ~\cfrac{7}{6}~ - ~\cfrac{4}{3}}\implies \cfrac{(6)59~~ - ~~(5)7~~ - ~~(10)4}{\underset{\textit{using this LCD}}{30}}\implies \cfrac{279}{30}\implies \cfrac{93}{10}\implies {\Large \begin{array}{llll} 9\frac{3}{10} \end{array}}[/tex]

Answer:

D

Step-by-step explanation:

y-7 = -1/2 (x-(-2)

y-7 = -1/2 (x+2)

y -7 = -1/2 x - 1

y = -1/2 x -1 +7

y = -1/2 x + 6

Answer:

52 problems

Explanation:

8.13 hours

8.13 hours × 60 minutes = x minutes

487.8 minutes

487.8 minutes ÷ 9.3 minutes = 52.4516129 problems

Answer: the estimated mean score is 78

Step-by-step explanation: I took the quick check

well, the height of the building is 119 feet, as we can see right there on the picture.  Now, there are 7 floors from the ground up, so the ratio is simply

[tex]\cfrac{\stackrel{overall~height}{119}}{\underset{floors}{7}}\implies \cfrac{17}{1}\implies \stackrel{unit~rate}{17}\hspace{5em}\cfrac{17~feet}{1~floor}\qquad \begin{array}{llll} \textit{each floor is}\\ \textit{17 feet high} \end{array}[/tex]

Using partial quotient, the place value while subtracting is determined by the dividend.

divisor    dividend    quotient  multiplication  subtraction  new dividend

5             1175            200         200 * 5 = 1000        1175 - 1000 = 175

5             175             30            30 * 5 = 150             175 - 150    =  25    

5             25              5              5 * 5 = 25                 25 - 25      = 0

The quotient is then added as

= 200 + 30 + 5

= 235

Assuming the quotient was written 2. While subtracting, the dividend for the first value (1175) is in thousands. placing the the 2 in thousands makes it more than the dividend hence the 2 should be in hundreds

1175 - 2000 incorrect

1175 - 200 correct

for the second stage

175 - 150 correct (since 150 < 175)

last stage

25 - 25

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The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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By using the formula for slope of a line, it can be calculated that

For 12'' candle

Two points are (1, 10) and (4, 2)

Slope = [tex]-\frac{8}{3}[/tex]

For 8'' candle

Two points are  (3, 4) and (6, 0)

Slope = [tex]-\frac{4}{3}[/tex]

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta\\[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

Here,

For 12'' candle

Two points are (1, 10) and (4, 2)

Slope =

[tex]\frac{2-10}{4-1}\\-\frac{8}{3}[/tex]

For 8'' candle

Two points are  (3, 4) and (6, 0)

Slope =

[tex]\frac{0-4}{6 - 3}\\-\frac{4}{3}[/tex]

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The fraction of magazines that were delivered to families who were at home is 0.4 if total number of families are 25 out of which 10 were at home and rest are away.

Total number of families = 25

Families at home = 10

So the ratio of the required families

= Families at home/total number of families

= 10/25

= 2/5

To convert the fraction into decimal form, we have to divide and we get

= 0.4

Hence, the number of families in decimal to which magazines got delivered are 0.4

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The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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1/2048 is  the probability of getting 11 heads in 11 tosses.

Probability of getting heads in one toss = 1/2

Probability of getting heads in 11 tosses = [tex](1/2)^{11[/tex]= 1/2048 (a one in 2048 chance of occurrence)

It should, therefore, NOT be surprising in a sample space of 950 (which is more than double 2048), that 11 heads can be obtained in a row.

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1/2048 is  the probability of getting 11 heads in 11 tosses.

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The solution of the differentiated equation is dy/dx = -6x⁵

From the question, we have the following equations that can be used in our computation:

x = ⁶√t

y = 8 - t

To start with:

We need to make the variable t the subject of the formula in the equation x = ⁶√t

Make t the subject

So, we have

t = x⁶

Substitute t = x⁶ in the equation y = 8 - t

y = 8 - x⁶

The rule of first principle of differentiation is represented as

If y = axⁿ, then dy/dx = naxⁿ⁻¹

Using the above as a guide, we have

y = 8 - x⁶

dy/dx = 0 * 8x⁰⁻¹ - 6 * x⁶⁻¹

Evaluate the difference

So, we have

dy/dx = 0 * 8x⁻¹ - 6 * x⁵

Evaluate the products

So, we have

dy/dx = 0 - 6x⁵

Evaluate the sum

So, we have

dy/dx = -6x⁵

Hence, the equation result is dy/dx = -6x⁵

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Answer:

Step-by-step explanation:

The square of 7 is:

[tex](7)^2=49[/tex]

The difference x and square of 7 is:

[tex]x-49[/tex]

Two times the difference of x and square of 7 is:

[tex]2(x-49)[/tex]

Answer: 10.7142857kg in each bag

Step-by-step explanation: If you divide 75 by 7 you would get 10.7142857. There fore there is about 10.7142857kg of chocolate in each bag.

Answer:

x8659-3358468854---6666x

Answer:

[tex]\frac{\sqrt{3} }{2}[/tex] sinx - [tex]\frac{1}{2}[/tex] cosx

Step-by-step explanation:

using the sum identity for cosine

cos(a + b) = cosacosb - sinasinb

then

cos(x + [tex]\frac{4\pi }{3}[/tex] )

= cosxcos([tex]\frac{4\pi }{3}[/tex]) - sinxsin([tex]\frac{4\pi }{3}[/tex] )

[ [tex]\frac{4\pi }{3}[/tex] is an angle in the third quadrant where sin and cosine < 0 ]

[ the related acute angle to [tex]\frac{4\pi }{3}[/tex] = [tex]\frac{4\pi }{3}[/tex] - π = [tex]\frac{\pi }{3}[/tex] ]

= cosx × - cos([tex]\frac{\pi }{3}[/tex] ) - sinx × - sin([tex]\frac{\pi }{3}[/tex] )

= cosx × - [tex]\frac{1}{2}[/tex] - sinx × - [tex]\frac{\sqrt{3} }{2}[/tex]

= - [tex]\frac{1}{2}[/tex] cosx + [tex]\frac{\sqrt{3} }{2}[/tex] sinx

= [tex]\frac{\sqrt{3} }{2}[/tex] sinx - [tex]\frac{1}{2}[/tex] cosx

Answer:

Step-by-step explanation:

The digit in the ones place is 7, The digit in the tenths place is 6, and The digit in the tens place is 4.

What do you mean by place value?

In mathematics, each digit in an integer has a place value. Place value refers to the value that a digit in a number represents dependent on where it sits within the number.

For instance, 700 or 7 hundreds is the place value of the number 7. But 7,432 has a place value of 7,000, or 7,000. The place value of the digits changes despite the fact that they are the same in both numbers due to their position.

The chart is attached in the answer by which we can conclude that The digit in the ones place is 7, The digit in the tenths place is 6, and The digit in the tens place is 4.

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The expression equivalent to  cd[tex]\sqrt{22}[/tex] is b)[tex]\sqrt{22}[/tex]cd.

What is expression?

 Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it. a collection of symbols, numbers, and operators (like and) that represent the value of something. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

Here the given expression is ,

=> cd[tex]\sqrt{22}[/tex] which is ,

=> c×d×[tex]\sqrt{22}[/tex]

=>[tex]\sqrt{22}[/tex]cd.

Therefore the expression equivalent to  cd[tex]\sqrt{22}[/tex] is b)[tex]\sqrt{22}[/tex]cd.

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