What is the solution to x2 – 9x < –8?

x < 1 or x > 8
x < –8 or x > 1
1 < x < 8
–8 < x < 1

There are 60 professors and 168 lecturers according to the given information.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main BODY:

Let X be the number of professors and Y be the number of lecturers. As the total of both is 228:

X + Y = 228

Then, as there are 5 professors for every 14 lecturers:

5 X = 14 Y or X = (14/5) Y

Replacing this last value of X on the first equation:

(14/5) Y + Y = 228

(14/5) Y + (5/5) Y = 228

(19/5) Y = 228

Y = 228 * (5/19)

Y = (228*5)/19

Y = 1140 / 19

Y = 60

Then we can find X:

X = (14/5) Y = (14/5) * 60 = 168

X = 168

Hence thre are 60 professors and 168 lecturers.

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The following is an equation fo curve if it passes through the point (-2,3) is  y=2 x^2-x-7.

What is Slope?

A graph is a set of vertices—points—and edges—the lines connecting those vertices in discrete mathematics. Graphs come in a variety of forms, including connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.

Slope of the carne at (x, y) is 4 x-1

Let the curve is: y=2 x^2-x-7

[tex]$$\begin{gathered}\text { Slope: } \frac{d y}{d x}=\frac{d}{d x}\left[2 x^2-x-7\right] \\\frac{d y}{d x}=4 x-1\end{gathered}$$[/tex]

And passes Iowa's the point (-2,3).

[tex]$$\begin{aligned}& y=2 x^2-x-7 \\& 3=2(-2)^2-(-2)-7 \\& 3=8+2-7 \\& 3=10-7 \\& 3=3\end{aligned}$$[/tex]

Satisfied.

y=2 x^2-x-7

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[tex]x\div 32 > 1\implies \cfrac{x}{32} > 1\implies 32\left( \cfrac{x}{32} \right) > 32(1)\implies x > 32[/tex]

and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

Answer:  and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

Step-by-step explanation:and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

and that can be any value, so long is greater than that, 33 will do, but so does 1,000,000, and so on.

Since the formula for P only applies to positive z, the minus sign must be removed if z is negative.We change 1.96 to 1.65 for a CI of 90%, and we use 2.57 for a CI of 99%.

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Answer:

  m∠1 = m∠2 = 17°

Step-by-step explanation:

You want to know the measures of the base angles of an isosceles triangle with an a.pex angle of 146°.

The sum of angles in a triangle is 180°. We can use x to represent the measures of each of the two congruent base angles of the isosceles triangle:

  x + 146° +x = 180°

  2x = 34° . . . . . . subtract 146°

  x = 17° . . . . . . . divide by 2

The measures of the angles are ...

  m∠1 = m∠2 = 17°

Answer: x= -5

Step-by-step explanation:

2(7+2x) = 3x+9

14+4x=3x+9

isolate x

x=-5

Answer:

90

Step-by-step explanation:

To solve, you have to use the formula

I=Prt

I is the dollars of of simple interest earned

P is principal in dollars

R is the annual interest rate (decimal form)

T is the time in years

I=Prt

I =300*0.05*6

I = 90

Answer:

we use bodmas!

Step-by-step explanation:

The horizontal and vertical asymptotes of the hyperbola equation (x + 1)² / 25 - (y - 3)² / 16 = 1 are y = 4x / 5 + 19 / 5 and  y = -4x / 5 + 11/5 respectively

An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. This can be said to be a line that a curve approaches but never touches.

Basically, we have three types of asymptotes which are horizontal asymptotes, vertical asymptotes and oblique asymptotes.

In the hyperbola equation given

(x + 1)² / 25 - (y - 3)² / 16 = 1

The equation of asymptotes are;

Horizontal asymptotes : y = 4x / 5 + 19 / 5

Vertical asymptotes : y = -4x / 5 + 11/5

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Alfred gets pay as $2119.23 per week for a new part-time job as a butler.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, Alfred responds to an ad position that pays $110,200 a year.

We know that, there are 52 weeks in a year

Salary for one week =110,200/52

= $2119.23

Therefore, the weekly pay for Alfred is $2119.23.

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Cost function is fixed cost added with number of hours times the variable cost.

What is cost ?

The two primary categories of costs that organizations face are fixed and variable costs. While variable costs fluctuate with output, fixed costs do not.

                         Sometimes, fixed costs are referred to as overhead costs. They are incurred regardless of whether a company produces 100 or 1,000 widgets.

Given that  charge for a service call is $80.00 and $30.00 for each hour of work. So fixed cost is 80 and variable cost is 30.

Cost function is fixed cost added with number of hours times the variable cost.

Thus we have the cost function here,

where x is the hours of work.

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The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

Given that, parabola has its focus at (1,2) and its directrix is y= -2.

From graph, vertex is (h, k)=(1, 0) and p=2

Substitute (h, k)=(1,0) and p=2 in (x-h)²=4p(y-k), we get

(x-1)²=4(2)(y-0)

⇒ (x-1)²=8y

⇒ y=1/8 (x-1)²

The equation of a parabola is y=1/8 (x-1)². Therefore, option 4 is the correct answer.

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Hence, the equation for the question (7) is [tex]n + 19 = 84[/tex] and equation for (8) is [tex]3n = 12[/tex]. It can be solved by linear equation in one variable.

What is a linear equation in one variable?

A linear equation in one variable is written as [tex]ax+b = 0[/tex]. Here, [tex]a[/tex] and [tex]b[/tex] are constants and [tex]x[/tex] is a variable.

(7)

Consider n number of baseball cards does Mike have. Since this is 19 less then the cards Allan have hence, as you add 19 in n then it will give 84.

[tex]n + 19 = 84[/tex]

(8)

Consider the speed of Michelle is n. As, it is 3 times less than the speed of the Jamie hence, it you multiply 3 with n then it will give 12.

    [tex]3n = 12[/tex]

Hence, the equation for the question (7) is [tex]n + 19 = 84[/tex] and equation for (8) is [tex]3n = 12[/tex].

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Answer:

Step-by-step explanation:

The value of (i) AC is the right angled triangle is 20 cm, For (ii) AB is 12 cm.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

(i) To calculate the value of /AC/, we use the formula below.

From the question,

Given:

Substitute these values into equation 1

(ii) To calculate AB, use Pythagoras formula:

From the diagram,

Substitute these values into equation 2 and solve for AB

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Answer: Part 1: Dan, Part 2: 55%

Step-by-step explanation:

1. By noon, Jon has painted 1/5 (or 20%) of the hallway and Dan has painted 25% of the hallway. Therefore, Dan has painted more of the hallway than Jon.

2. In total, the two have painted 45% (20% + 25% = 45%) of the hallway by lunchtime. Therefore, 55% (100% - 45% = 55%) needs to be painted after lunch.

The annual cost for the 450 Plan is $645.03.

What is cost price?

The cost price represents the particular worth that represents unit worth purchased.

Main Body;

This consumer used less than 450 minutes a month every month except June and December. In June, they used 178 extra minutes and in December they used 189 extra minutes. In total, they used 367

extra minutes throughout the year. The basic fee for the 450 Plan is $39.99 per month so their annual cost is

annual cost = monthly fee* months + cost per minutes* extra minutes

=39.99 *12 +0.45* 367

=479.88+ 165.15

=645.03

Annual Cost Monthly fee months cost per minute extra minutes

The annual cost for the 450 Plan is $645.03.

The 900 Plan costs $59.99 per month for all 12 months for a total cost of $719.88. Even though the consumer had to pay extra during June and December, the 450 Plan was still less expensive than the 900 Plan.

Hence , The annual cost for the 450 Plan is $645.03.

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Step-by-step explanation:

Using squares of integers numbers, it is found that the solution of the equation is located between the integers x = 1 and x = 2.

The equation given is:

x^2=3

The solution of the equation given is:

X=√3

The squares of the integers numbers until the square root of 3 are:

1^2=1

2^2=4

Since , the square root of 3, which is the solution to the equation, is located between the integers x = 1 and x = 2.

n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.

The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level. The range of values within the 95% confidence interval represents the population's actual mean, with 95% confidence. The sample mean (the center of the CI) will differ between samples due to natural sampling variability. The process itself, not a certain CI, is what inspires confidence. According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, hence to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

At 99% confidence interval the critical value is [tex]z_{0.005}[/tex]=2.58

Margin of error=0.39

Or, [tex]z_{0.005}[/tex](σ/√n)=0.39

Or, 2.58(5.7/√n)=0.39

Or, n=(2.58×(5.7/0.39)²

Or, n=1422

n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.

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The value of s from the proportion s : t : u = 4 : 9 : 3 is s = 20

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the proportion be in the form s : t : u

where the value of the proportion is

s : t : u = 4 : 9 : 3

And , t - u = 30

Now , assume the value of s = 4x

where x is the unknown we have to calculate

So , the value of t = 9x

And , the value of u = 3x

From the equation , t - u = 30

Substitute the value of t and u in the equation , we get

9x - 3x = 30

6x = 30

Divide by 6 on both sides of the equation , we get

x = 5

Therefore , the value of x is 5

Now , substituting the value of x in the above equation , we get

s = 4x

s = 4 x 5

s = 20

Therefore , the value of s from the proportion is 20

Hence , The value of s from the proportion s : t : u = 4 : 9 : 3 is s = 20

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There are 407.83 square feet living room.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The carpet cost $4.15 per square foot and $97 to have it stalled.

And, Their total bill is $1, 789.50.

Now,

Let number of square feet living room = x

So, We can formulate;

⇒ 4.15x + 97 = 1,789.50

Solve for x as;

⇒ 4.15x = 1,789.50 - 97

⇒ 4.15x = 1,692.5

⇒ x = 1,692.5 / 4.15

⇒ x = 407.83 square feet

Thus, There are 407.83 square feet living room.

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The speed of the canoe in still water is 3 miles per hour and the speed of the water current is 2 miles per hour. The correct options are B and D.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given that the system of equations;

x + y = 5

x - y = 1

Solving the above equations by elimination we get

x = 3 and y = 2

Where, x represents the canoe's speed with no water current (in still water) and y represents the speed of the water current, in miles per hour.

Therefore, the speed of the canoe in still water is 3 miles per hour and

the speed of the water current is 2 miles per hour.

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Answer:

[tex]x < -5[/tex]

Step-by-step explanation:

-3x-3>12

Divide by -3, since you are dividing by a negative, flip the equality sign:

x+1<-4

Subtract 1 from both sides:

x<-5

Hello,

I hope you and your family are doing well!

To solve the inequality −3x−3>12, you can start by moving everything to one side of the inequality by adding 3 to both sides. This gives you −3x>15.

Next, you can divide both sides of the inequality by -3 to get x<-5.

Finally, you can simplify the inequality to its final form by flipping the direction of the inequality symbol, since you divided it by a negative number. This gives you the final solution: x>-5.

So, the solution to the inequality −3x−3>12 is x>-5. This means that any value of x that is greater than -5 will satisfy the inequality.

The answer is: x > -5

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To estimate the population proportion to within plus or minus 2% with 95% confidence, a sample size of at least 804 is needed.

This can be calculated using the formula for determining sample size for estimating a population proportion:

n = (Z^2 * p * (1-p)) / (E^2)

Where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population with the characteristic of interest (assumed to be 0.5 for this calculation), and E is the maximum margin of error desired (2% in this case). Plugging these values into the formula, we get:

n = (1.96^2 * 0.5 * (1-0.5)) / (0.02^2) = 803.84

Since this is a sample size estimate, we should round up to the next whole number, resulting in a sample size of 804.

Therefore, the correct answer is as given above

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Answer:

15

Step-by-step explanation:

Hello,

I hope you and your family are doing well!

To find the percent of decrease in the winning time, you can use the following formula:

percent decrease = (old value - new value) / old value * 100%

Plugging in the values from the problem, we get:

percent decrease = (11.0 seconds - 10.49 seconds) / 11.0 seconds * 100% = 0.51 seconds / 11.0 seconds * 100% = 4.636363636363636%

Rounding to the nearest tenth, the percent of the decrease in the winning time is:

4.6%

This means that the winning time decreased by 4.6% between the 1960 Olympics and the 1988 Olympics.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.

A function having the formula f(x) = ax' + b is said to be linear.

It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).

You would be given the value of f(x) and asked to locate x when solving a linear function.

F(x) is the barometric air pressure in inches of mercury.

x is the distance in miles from the eye of a severe hurricane.

It is given pressure 28inches of mercury

Put F(x) equal to 28

F(x) = 0.48ln(x+2) +27

28 = 0.48ln(x+2)+ 27

28-27= 0.48ln(x+2)

1= 0.48ln(x+2)

1/0.48= ㏑(x+2)

25/12= ㏑(x+2)

x+2= e^(25/12)

x+2=8.03119

x=8.03119-2

x= 6.03119

x = 6(round off)

Therefore, for 28 inches of mercury occurs about 6 miles from the eye of hurricane.

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The points that would be plotted are (2, 1.690), (3, 2.535), and (4, 3.380).

What are the coordinates?

Any one of a group of numbers used to describe where a point is on a line, a surface, or in space coordinates of latitude and longitude

Here, we have

If the following data were transformed and points with coordinates (x, log(y)) were plotted then we have to find what points would be plotted.

From the table:

At x = 2 and y = 49 ⇒ (x,log(y)) = ( 2 , log 49 ) =  (2, 1.690)

At x = 3 and y = 343 ⇒(x,log(y)) = ( 3 , log 343) =  (3, 2.535)

At x = 4 and y = 2401 ⇒(x,log(y)) = ( 4 , log 2401) =(4, 3.380)

Hence, The points that would be plotted are (2, 1.690), (3, 2.535), and (4, 3.380).

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1. In 60 weeks, both Zac and Jon will earn the same amount, equating to their different earnings.

2. The student's claim that the solution to the equation 200 + 20w = -100 + 25w is w = 50 is false as the solution shows that w = 60.

3. The two correct justifications for the given steps used in solving w are:

The fixed earnings of Zac = $200

Zac's earnings per week = $20

The total earnings of Zac in w weeks = 200 + 20w

Jon's fixed debt so far = $100

Jon's earnings per week = $25

The total earnings of Jon in w weeks = -100 + 25w

To determine the weeks when the total earnings of Zac and Jon will be equal, we can equate the two expressions above as follows and solve for w:

200 + 20w = -100 + 25w

20w - 25w = -300

-5w = - 300

w = -300/-5

w = 60

Thus, we can conclude that in 60 weeks, the earnings of Zac and Jon will become equal.

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Answer:

y = 2x + 3 and y = x + 4

Step-by-step explanation:

the first equation:

y = -3x - 6

(5) =-3(1) - 6

5 = 3-6

5≠-3

second equation:

y = 2x + 3

(5) = 2(1) + 3

5 = 2 + 3

5 = 5

third equation:

y = -7x + 1

(5) = -7(1) + 1

5 = -7 + 1

5 ≠ -6

fourth equation:

y = x + 4

(5) = 1 + 4

5 = 5

last equation:

y = -2x - 9

(5) = -2(1) - 9

5 = -2 - 9

5 ≠ -11