(Score for Question 1: of 3 points)
1. Represent each situation with an inequality.
(a) The sum of a number and 12 is at most -8.
(b) A number increased by -8 is greater than 12.
(c) -8 less than a number is no more than 12.
Answer:

Answer:

Yes, there are many people who can help you with a finance question. Some of the people who can help you include: financial advisors, accountants, financial planners, and financial analysts. Additionally, there are many online resources available such as personal finance forums, websites, and blogs.

Step-by-step explanation:

The linear constraint form of the variables is X1 =< 0.75(X1 + X2 + X3)

The term linear refers the algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Here we have given that x1 must be at most 75% of the blend of x1 , x2 , and x3 ,

Abd here we must have to find the linear constraint of the form of the variables.

While we looking into the given question we have identified the three are three variables are given they are x1, x2 and x3.

And we have also given that x1 must be greater than 75% when we convert this into decimal then we get the value 0.75.

Here the term of blend refers the sum of the terms,

Then the linear constraint form of the variables is written as,

=> X1 =< 0.75 (X1 + X2 + X3)

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As per the binomial distribution, the value of the normal approximation is 0.6573

The term binomial distribution refers the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

Here we have given that n = 95 P = 0.96 and q = 0.04

Now, here we have to check  the binomial distribution to see whether it can be approximated by the normal distribution.

While we looking into the given question we know that the value of n = 95 P = 0.96.

Then as per the binomial distribution formula, the normal distribution is calculated as,

=> P(X=1) = 95C4 * (0.96)⁴ * (1-0.96)⁹⁵⁻⁴

When we simplify this one then we get the value as 0.6573

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Standard deviation will be √3.3516 .

To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².

After that , we have to calculate the Xbar by using

Xbar = ∑fiXi / N

for which we need the value of fi , Xi and N

N = 100

fiXi = 6478

we have calculated the values from the given data ,

Therefore ,

Xbar = 6478 / 100

= 64.78

Var(X) = αx² - ∑fiXi² / N - (Xbar²)

= 419980 / 100 - (64.78)²

= 4199.80 -4196.4484

=3.3516

Thus,

standard deviation ax = √var(X)

= √3.3516

Therefore , the standard deviation will be  √3.3516

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Answer:

  x = 15

Step-by-step explanation:

You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.

The angle sum theorem tells you the sum of angles in a triangle is 180°.

  U +V +W = 180°

  (3x -10)° +(6x +5)° +(4x -10)° = 180°

  13x -15 = 180 . . . . . . . divide by °, collect terms

  13x = 195 . . . . . . . add 15

  x = 15 . . . . . . . divide by 13

The value of x is 15.

The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.

As per the given data,

we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

We know that,

Probability(Event) =Number of Favorable Outcomes/Total number of

                                Outcomes = x/n.    

Total number of Outcomes is 52 (given)

So,  we will calculate Number of Favorable Outcomes as follows:

The total no. of King in deck of card is 4

The total no. of queen in deck of card is 4.

The total no. of ace in  deck of card is 4.

The total no. of jack in deck of card is 4.

Therefore, the number of favorable outcomes is 4+4+4+4= 16

Now, putting values in the above stated formula of probability, we get:

Probability= 16/52=4/13

Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.

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Answer:

1000

Step-by-step explanation:

If any of the digits 0-9 can be used then there are 10^3 possible codes.

10^3 = 1000

When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

let length be l and width be w.

l=3w+8

l*w=256

(3w+8)*w=256

3w²+8w=256

3w²+32w-24w-256=0

3w(w-8)+32(w-8)=0

(3w+32)(w-8)=0

w=-32/3, 8

w=8 inch

l=3*8+8

l=32 inch

The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.

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The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

Now, According to the question:

The given sphere is of radius R.

Let h be the height and r be the radius of the cylinder inscribed in the sphere.

We know that:

Volume of cylinder

V = [tex]\pi R^2h[/tex]    .....(1)

In right Triangle OBA

[tex]AB^2 + OB^2 = OA^2[/tex]

[tex]R^2 + \frac{h^2}{4} = r^2[/tex]

So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]

Putting the value of [tex]R^2[/tex] in equation (1), We get

V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]

V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex]   ....(2)

dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)

For, Stationary point, dV/dh = 0

[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0

[tex](r^2 - \frac{3h}{4} )[/tex]   => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]

Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]

[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex]   = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0

Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]

Maximum volume is :

[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]

[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]

[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit

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The angle A is an obtuse angle of the regular polygon.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The interior angle of a polygon is [(n-2)180°]/n.

Where n is the number of sides of the polygon.

The number of sides of the polygon is 8.

The measure of the interior of the polygon is [(8-2)180°]/8

= 135°

The obtuse angle is an angle that more than 90°.

Therefore angle is an obtuse angle.

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Answer: i think 15/8 but, im not sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.

The graph of the equation y = (1/3)x + 2 is passing through points  

(3, 3) and ( -3, 1).

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A linear equation y = (1/3)x + 2.

Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.

When x = 3, y = 3 ⇒ (3, 3).

When x = - 3, y = 1 ⇒( -3, 1).

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A. The top cycle in this case is a -> b -> c -> a.

B. The agenda that wins the candidate is:

First vote:

a vs b -> a wins

Second voice:

versus. c -> a wins

The agenda that Candidate B wins is:

First vote:

b vs c -> b wins

Second Voice:

b vs a -> b wins

The agenda that Candidate C wins is:

First vote:

c vs a -> c wins

Second Voice:

c vs b -> c wins

C. Using the Borda count system, the candidates' scores are as follows:

a:

18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)

b:

18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)

c:

18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)

d:

12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)

e:

12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)

f:

12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)

g:

6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)

Therefore, candidates a, b, and c tie for first place with 18 points each.

D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.

E. The candidate with the worst score in the Borda count is  g of 6 points.

F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:

a:

15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)

b:

15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)

c:

15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)

Day:

10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)

e:

10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)

f:

10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)

In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.

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Answer:

final answer would be $6,550

Step-by-step explanation:

To calculate the state income tax owed on a $50,000 per year salary, we can use the progressive tax rate provided in the question. We can divide the salary into three ranges, corresponding to the three tax rates:

Income Range: $0 - $10,000

Progressive Tax Rate: 3%

Tax Owed: $0 - $10,000 * 3% = $0 - $300

Income Range: $10,001 - $50,000

Progressive Tax Rate: 5%

Tax Owed: $10,001 - $50,000 * 5% = $500 - $2,500

Income Range: $50,001 - $100,000

Progressive Tax Rate: 5.5%

Tax Owed: $50,001 - $100,000 * 5.5% = $2,750 - $5,500

Thus, the total state income tax owed on a $50,000 per year salary would be $300 + $2,500 + $2,750 = $6,550. This amount should be rounded to the nearest whole dollar amount, so the final answer would be $6,550.

Answer: x = 9/10 - 7/10

Step-by-step explanation:

The required probability is P(X≥3) =0.3234

The average number of winning tickets that the woman buys each month is 2.

The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.

The probability mass function of the binomial distribution is defined as:

[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]

Given that,

n = 20

p = 0.10

The required probability is P(X≥3)

P(X≥3) = 1-P(X<3)

P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)

P(X≥3)= 1- 0.1216- 0.270- 0.285

P(X≥3) = 0.3234

The mean of the distribution is defined as μ=n*p= 20*0.10= 2

The average number of winning tickets that the woman buys each month is 2.

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Answer:

1) -10x + 5

2) 5p - 26

3) -5y + 6

Answer:

42

Step-by-step explanation:

If 2/7 left that means that 5/7 are still there.

5/7x = 30  Multiple both sides by 7/5

x = [tex]\frac{30}{1}[/tex] x [tex]\frac{7}{5}[/tex]

x = 42

The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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The equation of the line would be y = x/3 + 1/2.

Option (B) is correct.

What is the slope-intercept form of the line?

The slope-intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the y-axis. The slope intercept form equation is given as, y = mx + b.

As we can see in the graph the line cuts the y-axis at y = 1/2

so the y-intercept of the line would be c = 1/2.

And when x=4, y = 2

So we can prepare the equation as y = x/3 + 1/2.

Hence, the equation of the line would be y = x/3 + 1/2.

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Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.

To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.

A = $6,250.00

I = A - P = $1,250.00

Formula: A = P(1 + rt)

First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.

Fixing our equation

A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00

Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.

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Answer: C

Step-by-step explanation: Because

The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

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The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius

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

Area of a circle

The formula for the area of a circle is represented as

A = πr²

Express the formula as a product

So, we have the following representation

A = π * r²

In the above formula, we can see that the square of r is multiplied by pi

Hence, the required quantity is the square of the radius of the circle

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Answer:

0.25

Step-by-step explanation:

Step 1: Convert all fractions to decimals

Two-thirds = 0.6666

Three-quarters = 0.75

One-half = 0.5

Step 2: Multiply all fractions

0.6666 * 0.75 * 0.5 = 0.25

Step 3: The answer is 0.25

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Three-quarters of one half:

[tex]\implies \dfrac{3}{4} \times \dfrac{1}{2}=\dfrac{3 \times 1}{4 \times 2}=\dfrac{3}{8}[/tex]

Two-thirds of "Three-quarters of one half":

[tex]\implies \dfrac{2}{3} \times \dfrac{3}{8}=\dfrac{2 \times 3}{3 \times 8}=\dfrac{6}{24}=\dfrac{6 \div 6}{24 \div 6}=\dfrac{1}{4}[/tex]

Answer:

70

Step-by-step explanation:

0.3% is the percentage rate of increase  in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                   The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 50( 1.3)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

   1 + r = 1.3

     r = 0.3 ⇒  0.3%

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If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.

What is arithmetic series?

A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Here, we have

Given:  1+3+5+7+…+49 =625

We have to find the value of 2+4+6+8+…+50.

Here, we calculate the sum of all even numbers and we get

2+4+6+8+…+50 = 650

Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.

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The equation of the function described as;  y = 7 sin ( 4x + π/2 ) + 3

The general equation of the sine curve can be written as;

y = a sin ( nx + α ) + b

where : a is the amplitude, n = 2π/period, b = shift in the direction of y

            α°= shift in the direction of x

We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.

 Thus,

a = (maximum - minimum)/2 = (10 - -4)/2

a = 7

 n = 2π/period = 2π/(π/2)

n = 4

 b = maximum - a = 10 - 7

b= 3

To find α as y-intercept = 10

y = 10 at x = 0

Substitute in the general function;

y = a sin ( nx + α ) + b

10 = 7 sin ( 4*0 + α ) + 3

Thus, we have;

sin α = 1

α = π/2

So, the equation of the function described is;

 y = 7 sin ( 4x + π/2 ) + 3

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