Use the figure to find measures of the numbered angles.

Answer: (8,

-4) and (3,8)

Step-by-step explanation:

The vertex of the equation is (-3, 2). And the range will be the set of all real numbers equal to or larger than 2, written as:

y ≥ 2.

For an absolute value function of the form:

y = |x - a| + b

The vertex is a the point (a, b).

And the range (the set of the possible values of y that we can get with the function) will be the set of all real values equal or larger than b.

In this case, the absolute value function is:

y = |x + 3| + 2

Comparing it with the general one, we can see that the vertex is (-3, 2)

And then the range is y ≥ 2.

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Answer:100 cm

Step-by-step explanation: first, you would find the area of the whole rectangle.

L x W = A

10x14=140

Next, find the area of the unshaded part. To do this, you would subtract 6 from 14

14-6=8

After that, times 8 by 10, then divide by 2

10x8=80

80÷2=40

Take 40 and subtract it from the area of the whole rectangle

140-40=100

Given the function f(x), we can write it like this:

Using the formula for polynomial derivatives, we get:

Therefore, the derivative f'(x) is 12/x^5

Account balance after 2 years $441.

Based on the given condition, here the details:

P = $400

r = 5 % = 0.05

n = 1

t = 2

Formulate and substitute all above:

F = P · (1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]

F = 400. 1 + [tex]\frac{0.05}{1}[/tex])²

F = $441

From this as general, account balance is:

A checkbook, a savings account, or an investment account, for example, has a balance that shows how much money is available in the account. This is also called the current account value. The current value of account balances is shown by financial institutions on both paper statements and online tools.

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Answer:

Step-by-step explanation:

-1>-4>-6

-1 is the greatest number.

The initial velocity = vi = 6m/s

The final velocity = vf = 16 m/s

The total time = t = 20 seconds

The rate of change in velocity is called acceleration (a) that can be written as:

or

Put the values in the equation to get the value of 'a'.

or

hence, the value of a is 1/2.

Answer:

2.5

Step-by-step explanation:

Plug is -3 for y and solve for x

2x -3 = 2  Add 3 to both sides

2x = 5  Divide both sides by 2

x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5

Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769

Proportion means a share from total set being discussed.

Data from the given case:

- The assembly has 769 team members.

- The assembly has 353 stations

- At each station, there are 2 shifts operations.

Assuming that 1 person is assigned to 1 shift operation, then there will:

353 x 2 = 706 person assigned.

The remaining team members that not assigned is:

769 - 706 = 63 person.

Therefore, the share or the proportion of unassigned team members is:

63/769

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Answer:

The actual area of the warehouse would be:

[tex]72000~\text{feet}^{2}[/tex]

Step-by-step explanation:

Step 1:  Convert all the blueprint lengths into real lengths:

Each inch in the blueprint represents 20 feet in the real world.

So, the real-life length (18 inches in blueprint) would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times18~\text{inch}= 20\times18~\text{feet}\\18~\text{inch}= 360~\text{feet}\\[/tex]

Similarly, the real-life width would be:

[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times10~\text{inch}= 20\times10~\text{feet}\\10~\text{inch}= 200~\text{feet}\\[/tex]

Step 2: Calculate the area

The area of the warehouse would be given by:

[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

The length is 360 feet, and the width is 200 feet, so the total area would be:

[tex]\text{Area}=\text{Length}\times \text{Width}\\\\\text{Substitute the values for the length and width}\\\text{Area}= 360\times 200\\\text{Area}=72000[/tex]

Given a rectangular peice of paper

Length = 34 cm

Width = 16 cm

So, the area of the rectangle = 34 x 16 = 544 cm²

Two semicircles cut out of it

The diameter of the circle = d = 16 cm

So, the radius of the circle = r = d/2 = 8 cm

The area of the two semicircles = area of the complete circle

so, the area of the circle = πr² = 3.14 x 8² = 200.96 cm²

So, the area of the remaining paper = area of the rectangle - area of the circle

= 544 - 200.96 = 343.04 cm²

So, the answer will be Area = 343.04 cm²

The mean value of expected value for a binomial distribution is given by the next formula:

Where n is the number of trials and p is the probability of success. So, using the given data:

So the expected value or mean is 48

Answer:

Explanation:

Here, we want to deduce the median change

The median is a measure of central tendency that represents the middle number is a set of numerical observations

Firstly, let us get the previous median

We start by sorting the numbers from bottom to top

We have that as:

121,129,132,145,160,175

Since the count of observations is even, we have the median as the average of the two mid-values

We have that as:

Adding the last value, the set becomes

121,129,132,145,160,173,175

In this case, the median value would be 145 which shows an increase in the value of the median

Answer:

A. Increase

Step-by-step explanation:

I took the

Answer:

for the first one: d ≥ 1

for the second one: d > 5

Answer:

2 1/2 (D)

Step-by-step explanation:

1 8/12 + 5/6

you have to make the denominator on the right equal to the denominator on the left. in order to do that, multiple the numerator and denominator on the left my two.

5/6 become 10/12.

1 8/12 + 10/12

1 18/12

Simplify,

2 6/12 (1/2)

Answer:

[tex]1\frac{8}{12}+\frac{5}{6}=2\frac{1}{2}[/tex]

Answer:

a₉₀ = 168

Step-by-step explanation:

there is a common difference between consecutive terms, that is

- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 10 and d = 2 , then

a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168

The student that has the greatest percent error is Ebony.

The percentage error will be calculated as:

= Change in value / Initial values × 100

From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:

= (Measured length - Actual length) / Actual length × 100

= (2.1 - 1.6)/1.6 × 100

= 0.5 / 1.6 × 100

= 31.25%

Ebony had the higher percentage error.

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Hello,

Two parallel lines have the same slope, which means that our line's slope, will also be 1.2.

So now we have a point and a slope, so we can use the following formula to find the equation of the line:

y-y1 = m (x-x1)

Where:

y1 - y coordinate of a point on the line

x1 - x coordinate of the same point on the line

m - slope

Plugging in we get:

y+3 = 1.2 (x-0)

y = 1.2x - 3 (slope intercept form)

or

5y-6x = -15 (standard form)

Cheers

The given polynomials are as ,

We have to subtracrt these given polynomials,

Option D is correct.

The probability that joe and jane end up in the same class is 0.3258 .

In the question ,

it is given that

90 students is to be split into 3 equal size classes , so ,

the three classes  will have 30 students each .

let these classes be Class A , Class B and Class C .

Let Joe and Jane be in Class A .

the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .

Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students  in C(88,28) ways ,

So , the probability that Joe and Jane end up in the same class is

= C(88,28)/C(90,30) .

Since there are three  classes ,

the required probability is 3*C(88,28)/C(90,30) .

= 3×[tex]\frac{88!}{28!*60!}[/tex]×[tex]\frac{60!*30!}{90!}[/tex]

= 29/89

= 0.3258

Therefore , the probability that joe and jane end up in the same class is 0.3258   .

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The factors of the given monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. There are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variable x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer. If many variables, say x,y,z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a,b,c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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The factors of the monomial are given below

What is a monomial?

A monomial is, broadly speaking, a polynomial with just one term in mathematics. there are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variables x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer, if many variables, say x, y, z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a, b, c non-negative integers.

The factors of the monomial 16x²y are 2.2.2.2.x.x.y

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Option C, 59° is correct answer, The angle JIL is equal to 59 degree.

What is angle?

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.

Given information in the question,

∠HIL = (6x-7)°

∠JIL = (5x+4)°

The ray IL bisects the ∠HIJ

Since, IL bisects angle HIJ then, angle HIL = angle JIL

So,

6x - 7 =  5x + 4

x = 11

Putting the value of x in given value of JIL to get the angle JIL

∠JIL = (6x-7)°

∠JIL = (6(11)-7)°

∠JIL = 59°

Therefore angle JIL is equal to 59 degrees.

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The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.

The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.

The sides of an equilateral triangle are 9.4 cm

The perimeter of an equilateral triangle = 3 × length of the side

The perimeter of an equilateral triangle = 3 × 9.4

The perimeter of an equilateral triangle = 28.2 cm

Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.

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Answer:

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

Explanation:

To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.

Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so

r² = 537/1986

r² = 0.2704

r = √0.2704

r = 0.52

Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so

For 1 hour

Amount left = 1986(0.52) = 1032.7 grams

In the same way, the amount left after 3 and 4 hours is

For 3 hours

Amount left = 537(0.52) = 279.2 grams

For 4 hours

Amount left = 279.2(0.52) = 145.2 grams

Therefore, the complete table is

Hour elapsed 0 1 2 3 4

Grams 1986 1032.7 537 279.2 145.2

After simplification of 4√(384.5)³ using logarithm​, the resulting answer is 30158.13684.

So,  4√(384.5)³ using logarithm​:

Therefore, after simplification of 4√(384.5)³ using logarithm​, the resulting answer is 30158.13684.

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For the right triangle shown in the picture, recall the trigonometric identity of the cosine function:

Isolate a from the equation:

Substitute for c=6.3 and B=43.8°:

Use a calculator to evaluate the expression:

Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.

There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.

There are 2 rows of 3 seats each.

We will try to find the number of ways each seat can be filled.

So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.

Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.

For the third seat remaining in the first row, one out of the remaining  pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.

Now after filling the first row in this manner, the second row can be filled in only 2 ways.

So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways

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2.6

Given the expression;

Simplify the expression in the bracket to have:

Simplify the result to have;

Hence the result of the given function on simplification is 2.6