How many solutions exist for the system of equations below?
[3x+y=18
3x+y=16

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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All the probabilities are provided for the three situations involving men and women: smoking, developing lung cancer, and developing lung cancer while simultaneously smoking. Then, these are even divided into gender categories.

However, the last query is limited to males who smoke who develop lung cancer. Therefore, I believe that all of the other information is merely a red herring. You just need to search through the other options to locate the answer, which is already there. You should first disregard any possibilities involving ladies because we are only interested in men. The likelihood that males with lung cancer smoke is the next statistic you discover. The solution is 90%.

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Using the percentages formula, we know that 80% of 350 is 280.

So, let the number be x:

Now, calculate as follows:

Therefore, using the percentages formula, we know that 80% of 350 is 280.

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Answer:

371

Step-by-step explanation:

hope it helped :)

Answer:

there are books on the right

371

Step-by-step explanation:

each shelves is 21

there are 32

books on the left 301

so the rest are on the right

21*32-301=371

so find how many are there and minus it by the books on the left side

[tex]21 \times 32 - 301[/tex]

Answer:

A-C are all true, What is option D?

Step-by-step explanation:

If D is 1.224 > 1.242 then that is the false statement

If D is 1.224 < 1.242 then there are no false statements.

Answer:

$400

Step-by-step explanation:

Suppose Ahmad and Daryl both started with the same x amount of dollars.

Ahmad gains another 180 from his father, so he now has x+180 dollars.

Daryl spends 255, so he now has x-255 dollars.

After these events, Ahmad has 4 times as much money as Daryl, so

x+180=4(x-255)

Now we can solve for x to get the original amount of money.

x+180=4(x-255)

x+180=4x-1020

1200=3x

x=400

Both Ahmad and Daryl started with $400.

The negative amortization at the end of year 1 is $2536.50

For the year 1 there will be still 12% rate of interest going on. There is a negative balance of $200 after payment of 1st month installment.

Thus negative amortization = FV(0.01x12 - 200)

Here 0.01 is the interest per month, 12 is the number of months in a year and -200 is the negative balance in first month

negative amortization = FV(0.01x12 - 200)

The negative amortization at the end of year 1 = $2536.50

The negative amortization at the end of year 5

The loan balance at the end of year 4 = FV(0.13x12x36x800 - 102536)

The loan balance at the end of year 4 = $16132.46

The negative amortization at the end of year 1 is $2536.50

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Answer: 9 hours

Step-by-step explanation:

       Assuming they keep earning money at the same rate, we will set up a proportion to help us solve.

[tex]\displaystyle \frac{\$9,000}{4\;\text{hours}} =\frac{\$20,250}{x\;\text{hours}}[/tex]

       Next, we will cross-multiply.

$9,000 * x = $20,250 * 4

$9,000x = $81,000

x = 9 hours

       It will take the same restaurant about 9 hours to earn $20,250.

Answer:

Step-by-step explanation: The equation for slope-intercept is y=mx+b

m= slope of the equation, b= y-intercept(what y is when x is zero)

there for the equation is y=5x-5

Answer: 2.01

Step-by-step explanation:

A percentage is equal to x/100.

For example, 5% would be equal to 5/100.

5/100 = 0.05

So 201% = 201/100.

201/100 = 2.01

Answer:

Assuming every single ball has an equal chance of being drawn, then if B is the probability of drawing a blue ball and R is the probability of drawing a red ball:

B + R = 1,

since either a red or blue ball will be drawn. Since each ball has an equal chance of being drawn:

16 p = 1, or

p = 1/16

where p is the chance to draw a single ball. Since there are 10 red balls, there are ten independent and different ways to draw a red ball, which means that

R = 10 p = 10/16 = 5/8.

You can either apply the first equation to find that

B = 1 - R = 3/8

or state directly that

B = 6 p = 6/16 = 3/8

since there are six independent and different ways to draw a blue ball from the bag.

Answer:

41.67%

Step-by-step explanation:

10+8+6= 24

10/24

First, you need to calculate your grade in percentages. The total answers count 24 - it's 100%, so we to get a 1% value, divide 24 by 100 to get 0.24. Next, calculate the percentage of 10: divide 10 by 1% value (0.24), and you get 41.67% - it's your percentage grade

Step-by-step explanation:

(x + 3) × -7 = -7x - 7×3 = -7x - 21

According to the central limit theorem, the standard deviation of the sample means is a) less than the population standard deviation.

According to the central limit theorem, as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or other distribution.

The sample means' standard deviation (also known as the standard error of the mean) will be less than the population standard deviation and equal to the population standard deviation divided by the square root of the sample size.

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If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

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Answer:

[tex]\text{GH} = 47[/tex]

Step-by-step explanation:

GH is one of the midsegments of triangle DEF. It divides both DE and EF to two equal segments (EH = HF, BG = GD).

A midsegment of a triangle has 3 characteristics:
- It splits the two sides it bisects into 2 equal segments.
- It is parallel to the side it doesn't bisect.
- It is equal to half the length of the side it doesn't bisect.

Applying the logic of the third characteristic, we can claim that GH = 1/2 * DF.

[tex]\text{GH} = \frac12\text{DF}\\\to 3x - 4 = \frac12 \times (9x - 59)\\\to 6x - 8 = 9x - 59\\\to 51 = 3x\\\to x = 17\\ \\\to \text{GH} = 3x - 4 = 3 \times 17 - 4 = 51 - 4 = 47[/tex]

Answer The sequence {an = (−a)n}

Step-by-step explanation:  The sequence {an = (−a)n} is bounded below by −1 and bounded above by 1, and so is bounded. This sequence does not converge, though; since |an − an+1| = 2 for all n, this sequence fails the Cauchy criterion, and hence diverges.

1 hour 30 minutes take her to do her homework if she has 30 pages to read and 45 math problems to complete.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Karen can read 10 pages and complete 15 math problems in 30 minutes.

So, if she reads 30 pages which is 3 times of 10.

Also, solve 45 maths problem which is 3 times of 15.

So, the time taken to complete 30 pages to read and 45 math problem

= 30 x 3

= 90 minutes

= 1 hour 30 minutes

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The value of (fоg)(3) = 134.

What is composition of functions?

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

Consider, the given functions

f(x) = 3x - 1, g(x) = 4x^2 + 9

First to find f(g(x)).

Let,

f(g(x)) = 3(4x^2 + 9) - 1

         = 12x^2 + 27 - 1

f(g(x)) = 12x^2 + 26

Now, to find f(g(3)).

Plug x = 3 in the above equation,

f(g(3)) = 12(3)^2 + 26

         = 12(9) + 26

f(g(3)) = 134

Hence, (fоg)(3) = 134.

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Answer:

Step-by-step explanation:

................ x2

Using equations, to raise the maximum amount of money, 160 adults and 80 students should attend the theater program on drinking and driving.

An equation is a mathematical statement of the equality of two or more mathematical expressions, using the equation symbol (=).

In this situation, we form a system of equations, to show the maximum number of adults and students allowed for the program.

We also form an objective constraint of inequality to show the limit of the allowed number of people for the program.

Admission fee for adults = $2.00

Admission fee for students = $1.00

The total number allowed in the theater = 240 persons

The ratio of adults to students = 2:1

The sum of ratios is 3

The number of adults = 2x, where, the number of students = x.

2x + x = 240 ... Equation 1

3x ≤ 240 ... Equation 2

If 3x = 240

x = 80

Check:

3x ≤ 240

3(80) ≤ 240

240 = 240

Adults = 160 (2 x 80)

Students = 80 (1 x 80), which meet the second requirement or constraint.

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The values are given below,

Left Hand Limit i.e. lim x -> 1- f(x) = 3 ,

Right Hand Limit i.e. lim x -> 1+ f(x) = 1 ,

Function value at x = 1 i.e. f(1) = 1 ,

Left Hand Derivative lim x -> 1- f'(x)= -6 and

Right Hand Derivative lim -> 1+ f'(x) = -6.

So, the function f(x) is neither continuous nor differentiable at x = 1.

Given, a piecewise function

              3㏑(3 - 2x) + 3                for x < 1

f(x) =

                   -3x² + 4                      for x ≥ 1

Now, for lim x -> 1- f(x) we will consider the function  3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.

lim x -> 1 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3

= 3 ㏑(1) + 3

= 0 + 3

= 3

Now, for lim x -> 1+ f(x) we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.

lim x -> 1 -3x² + 4 = -3(1)² + 4

= -3 + 4

= 1

Now, for f( 1 ) we will consider the function -3x² + 4,

f(1) = -3(1)² + 4

= -3 + 4

= 1

Now, for lim x -> 1- f'(x) we will consider the derivative of the function

3㏑(3 - 2x) + 3,

lim x -> 1 -6/(3 - 2x) = -6/(3 - 2(1))

= -6

Now, for lim -> 1+ f'(x) we will consider the derivative of the function

-3x² + 4,

lim x -> 1 -6x = -6(1)

= -6

So, the function f(x) is neither continuous nor differentiable at x = 1.

Hence, lim x -> 1- f(x) = 3 , lim x -> 1+ f(x) = 1 ,  f( 1 ) = 1 , lim x -> 1- f'(x) = -6 and lim -> 1+ f'(x) = -6.

The function is neither continuous nor differentiable at x = 1.

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Solutions for the given equalities:

m < - 2

y > 5

b > -4

What is inequality in mathematics?

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

The given inequalities are

1)              m - 1 < -3

     Adding 3 on both sides, we get

              m - 1 + 3 < -3 + 3

                m + 2 < 0

     Subtracting 2 from both the side, we get

                m + 2 - 2 < 0 - 2

                m < - 2

The graph of this inequality is shown below

2)             -4y < -20

      Dividing by -4, we get

              y > 5

The graph of this inequality is shown below

3)       5 + b > 1

     Subtracting 1 from both the side, we get

            b + 4 > 0

             b > -4

The graph of this inequality is shown below

4)      y = -18

This is a point on a number line, and it can be shown as

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2089.17 rounded off to nearest tenths(1 decimal place) is 2089.2

2089.17 rounded off to the nearest one is 2089

When you "round to the nearest _____" regardless of what is in the blank the steps are nearly always the same:

Identify which place value you are rounding off a number. The smaller the place value, the more accurate the final result shall be.

Find the next smallest place value, the digit to the right of the place value you're rounding off to. For example, if you want to round to the nearest ten you would have to find the number at the one's place.

If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round off. Any digits after that number become zeros, or drop-offs if they're located after the decimal point. This is called rounding down a number or a sequence of numbers.

If the smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding off to by one place (+1). Any remaining digits before the decimal point become zeroes, and any digits that are after the decimal point are dropped. This is called rounding up of numbers.

For example, for rounding off a number 838.274, depending on which place value you'll round to, the final rounded-off answer will vary. Rounding off 838.274:

Rounding off the nearest hundred is 800

Rounding off the nearest ten is 840

Rounding off the nearest one is 838

Rounding off the nearest tenth is 838.3

Rounding off the nearest hundredth is 838.27

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Answer:

FROM YOUR IXL I GOT IT FOR YOU

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

you can convert 1 half to 20/40 and 1/8 to 5/40 5,10,15,20 you can make 4 pizzas

The most important to determine before allowing employees to access the server remotely is B. security method of allowing connections.

Computer networking refers to the interconnection of computing devices that can exchange data and share resources. These networked devices use a set of rules known as communications protocols to transmit data over physical or wireless networks.

A computer network is a collection of computers that share resources that are located on or provided by network nodes. To communicate with one another, the computers use common communication protocols over digital interconnections.

Local-area networks (LANs) and wide-area networks (WANs) are the two basic network types (WANs). LANs connect computers and peripheral devices in a constrained physical area, such as a business office, laboratory, or college campus, using data-transmitting links (wires, Ethernet cables, fiber optics, Wi-Fi).

In this case, it should be noted that the security method that's used for allowing the connection is important. Based on the information illustrated, the correct option is B.

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[tex]{ \boxed{ \purple{ \sf{ \frac{dy}{dx} = \frac{3}{1 + {x}^{2}}}}}} [/tex]

Step-by-step explanation:

Given question is, [tex]{ \red{ \sf{y = {tan}^{ - 1}( \frac{3x - {x}^{3} }{1 - 3 {x}^{2} })}}}[/tex]

Put [tex]{ \tt{x = \tan \theta }}[/tex] then,

[tex]{ \tt{ \theta = { \tan}^{ - 1} x}}[/tex]

[tex]{ \red{ \sf{y = { \tan}^{ - 1}( \frac{3 \: tan \theta - { \tan}^{3} \theta}{1 - 3 { \tan}^{2} \theta})}}}[/tex]

But [tex]{ \green{ \sf{ \tan3 \theta = \frac{3 \: \tan \theta - { \tan}^{3} \theta }{1 - 3 \: { \tan}^{2} \theta}}}} [/tex]

[tex]{ \red{ \sf{y = { \tan}^{ - 1} ( \tan3 \theta)}}}[/tex]

[tex]{ \red{ \sf{y = 3 \theta}}}[/tex]

[tex]{ \red{ \sf{y = 3}}}{ \tt{ { \tan}^{ - 1} x}}[/tex]

[tex]{ \red{ \sf{ \frac{dy}{dx} = 3 \times }}}{ \tt{ \frac{1}{ {1 + x}^{2}}}} [/tex]

•°•[tex]{ \green{ \boxed{ \red{ \sf{ \frac{dy}{dx} = \frac{3}{1 + {x}^{2}}}}}}} [/tex]

Answer:

your answer is 25776

Step-by-step explanation:

Answer: 25776 is your answer

The commission when the salesman earns 40% commission on all the merchandise that he sells is $320.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the salesman earns 40% commission on all the merchandise that he sells and last month he sold $800 worth of merchandise.

The amount in commission will be:

= Commission percentage × Sales

= 40% × $800

= $320

The commission is $320.

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The polynomials in order of their degree from least to greatest are x, -3x² - 1, 4c² + c - 3, -8y³ + 5y - 2, y¹⁰

The list of options represents the given parameters

The degree of a polynomial is the highest power of the polynomial

Take for instance, a polynomial ax^n has a degree of n

This means that the degrees of the given polynomials are:

The above represents the order of the polynomials

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