mJWL=87 degrees. Find the value of x.

Answer:

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours is

= 89 cells

Step-by-step explanation:

A cell divides into two cells every 20 minutes

In one hour, the cell will divide into 60/20 * 2 = 6 cells

Each cell growth 6 cells per hour

Initial population of a culture = 50 cells

t = time in hours

a. Relative Growth rate = 10% (6/60 * 100)

b. Number of cells after t hours = 50 * 1.1^t

c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)

d. The number of cells after 6 hours = initial population * growth factor

= 50 * 1.772

= 88.6

= 89 cells

We need to find the percent, let's start but making the equation.

The price is 2.69

The tax cost is 0.13

So what percent of 2.69 is = 0.13.

Equation: X/100 x 2.69 = 0.13

Multiply each side by 100 so we can get x alone with the price: 2.69x = 13

Now to get x alone, we must divide both sides by 2.69: x = 4.8

Finally, we just round 4.8 to the nearest whole number, which is 5 (5 or above give it a shove, 4 or below let it go, we have 8 so we give it a shove). This means that the answer will be 5%.

I hope this helps! :)

Answer:

Each ice cream seller wants the maximum number of customers:

True

The two ice cream stands will most likely be 1/3 mile away from each other.

True

Step-by-step explanation:

This distance enables the two ice cream stands to give access to the maximum number of customers at the beach, which will be almost equal at their right-hand and left-hand sides.  Therefore, the two ice cream stands will most likely be 1/3 mile away from each other.  Such positioning exposes the ice cream stands to almost equal number of customers since the people standing along the beach are uniformly located.  Taking the extreme locations along the 1-mile-long beach will shrink location opportunities for both stands.

Answer:

The answer is "Principal of marginal analysis".

Step-by-step explanation:

To determine unless the benefits of even an aggressive resource would outweigh its costs, and therefore increase utility, individuals and businesses can use a valuation model to compare the risks versus the benefits of more activities, like whether to create or consuming more. It's the amount during which net value is greater than or equal to marginal cost that's the optimal quantity in this situation. The amount where the marginal social cost curve and consumer surplus line connect.

Answer:

B. [tex]\left[\begin{array}{ccc}-1&2\\0&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}0\\-2\\\end{array}\right][/tex]

Step-by-step explanation:

Given the systems of equations

-x + 2y = 0

y = -2

This can also be written as:

-x + 2y = 0

0x + y = -2

We are to write in this form AX = b

A is a 2by2 matrix with coefficients of x nd y

X is a column matrix containing the unknown

b is a column matrix with the values at the right hand sides (0 and -2)

Writing in matrix form;

[tex]\left[\begin{array}{ccc}-1&2\\0&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}0\\-2\\\end{array}\right][/tex]

Answer:

6.5sin(.04x+.4pi)-8

The function intersects its midline at (-pi,-8) and has a maximum point at (pi/4, "-1.5). The  final equation is h(x) = 4 sin(2x +  π /2) + 3.

A function is defined as a relation between the set of inputs having exactly one output each.

The function intersects its midline at (3π/4, 3) then the midline is d= 3.

The amplitude is just the positive distance between the maximum/minimum and the midline,

so the amplitude a = 7 - 3 = 4

Also, given that period is 2π/b and the fact that the period is π from our given maximum,

we have the equation 2π/b= π where b = 2

we know that the phase shift, -c/b is - π/4 (or  to the left)

since -π /4. Therefore, c = π /2.

our final equation is

h(x) = 4 sin(2x +  π /2) + 3.

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Answer:

[tex]p =2.15n - 875[/tex]

Step-by-step explanation:

Given

[tex]CD_s= n[/tex]

[tex]Charges = 2.50[/tex] per CD

Expenses

[tex]E_1 = 875[/tex]

[tex]E_2 = 0.35[/tex] per CD

Required

The profit (p)

First, calculate the total income on n CDs

[tex]Total = Charges * n[/tex]

[tex]Total = 2.50 * n[/tex]

[tex]Total = 2.50n[/tex]

Next, the expenses on n CDs

[tex]Expenses = E_1 + E_2 * n[/tex]

[tex]Expenses = 875 + 0.35 * n[/tex]

[tex]Expenses = 875 + 0.35n[/tex]

The profit (p) is:

[tex]p = Total - Expenses[/tex]

[tex]p =2.50n - (875 + 0.35n)[/tex]

Open bracket

[tex]p =2.50n - 875 - 0.35n[/tex]

Collect like terms

[tex]p =2.50n - 0.35n - 875[/tex]

[tex]p =2.15n - 875[/tex]

Answer:

B  at -1 minus we go to - ∞

at -1 plus  we to + ∞

Step-by-step explanation:

         x^2 -x

g(x) = ---------

         x+1

Factor out x

         x(x-1)

g(x) = ---------

         x+1

As x is to the left of -1

   x is negative (x-1) is negative

        x+1  will be slightly negative

g(-1 minus) = -*-/ -  = -  and we know that the denominator is very close to zero  we are close to infinity  so we go to - ∞

As x is to the right of -1

   x is negative (x-1) is negative

        x+1  will be slightly positive

g(-1 plus) = -*-/ +  = +  and we know that the denominator is very close to zero  we are close to infinity  so we go to  ∞

Answer:

The critical value used is [tex]T_c = 2.132[/tex]

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

[tex]\overline{x} = \frac{16+21+22+12+22}{5} = 18.6[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(16-18.6)^2+(21-18.6)^2+(22-18.6)^2+(12-18.6)^2+(22-18.6)^2}{4}} = 4.45[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 5 - 1 = 4

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.132. The critical value used is [tex]T_c = 2.132[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.132\frac{4.45}{\sqrt{5}} = 4.243[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 18.6 - 4.243 = 14.357

The upper end of the interval is the sample mean added to M. So it is 18.6 + 4.243 = 22.843.

The 90% confidence interval for the average net change in a student's score after completing the course is (14.357, 22.843).

Answer:

Graph (1)

Step-by-step explanation:

Given rule for the rotation of a figure is,

A(x, y) → A'(-y, x)

This rule defines the rotation of point A by 90° counterclockwise about the origin.

Coordinates of point A → (-2, 0)

Coordinates of point C → (-1, 0)

Following the rule of rotation,

A(x, y) → A'(-y, x)

A(-2, 0) → A'(0, -2)

C(-1, 4) → C'(-4, -1)

Now search the image points from the graphs attached,

Graph (1) will be the answer.

Answer:

See below.

Step-by-step explanation:

Sleeping:

8/24 * 365 = 121.76 days

Eating:

3/24 * 365 = 45.63 days

Total sleeping and eating: 167 days

Summer Vacation & Holidays:

90 + 21 = 111 days

Saturdays and Sundays: 52 + 52 = 104 days

Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days

It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.

Distance = √[ ( 7 - 3 )^2 + ( 2p - 0 )^2 ]

Distance = √(4)^2 + ( 2p)^2

Distance = √16 + 4p^2

As the question said : Distance = √80

√80 = √16 + 4p^2

Thus :

16 + 4p^2 = 80

Subtract both sides 16

16 - 16 + 4p^2 = 80 - 16

4p^2 = 64

Divide both sides by 4

4p^2 ÷ 4 = 64 ÷ 4

p^2 = 16

Thus :

p = 4 or p = - 4

Answer:

384 kmph

Step-by-step explanation:

Answer:

See the expressions and the answers below

Step-by-step explanation:

Given data

The first expression is given as

x^2+169 .-> we can not factorize the expression anymore

The second expression

5x^2-50x+125

5(x^2-10x+25)

The third expression

100x^2-25y2

25(4x^2-y^2)

9514 1404 393

Answer:

Step-by-step explanation:

Part A: All of the coefficients have a common factor of 3. All of the variable products have a common factor of y, so the greatest common factor of all terms is 3y. The expression can be written as ...

  (3y)(2x^2 -1x -8xy +4y)

__

Part B: The remaining factor can be factored pairwise:

  3y(x(2x -1) -4y(2x -1)) = 3y(x -4y)(2x -1)

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

(a) The surface area  consists of the sum of the area of 3 sets of 2 congruent rectangles. The 2 rectangles are on opposite sides of the solid.

= 2(15*15) + 2(5*15) + 2(5&15)

= 450 + 150 + 150

= 750 unit^2.

(b). Similarly to the above:

Surface area = 2(12*6) + 2(4*12) + 2(4*6)

= 144 + 96 + 48

= 288 unit^2.

(c)  Again:

Surface area =  2(25*16) + 2(25*16) + 2(16*16)

= 400 + 400 + 256

= 1056 unit^2.

Answer:

(-∞,∞)

Step-by-step explanation:

Answer:

The domain of the function is  (-∞, ∞)

hope this helps!

Answer:

The 95% confidence interval for the population mean is ($6510, $7138).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{340}{\sqrt{7}} = 314[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 6824 - 314 = $6510.

The upper end of the interval is the sample mean added to M. So it is 6824 + 314 = $7138.

The 95% confidence interval for the population mean is ($6510, $7138).

Answer:

The Next fiver tems are - 2, -2,-8,-12,-16

Step-by-step explanation:

Answer:

2,-6,2,-6,2

Step-by-step explanation:

a1 = 2

an = -an-1 -4

Let n =2

a2 = -a1 -4 = -2-4 = -6

Let n=3

a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2

Let n = 4

a4 = -a3 -4 = -2 -4 = -6

Let n=5

a5 = -a4 -4 = -(-6) -4 = +6-4 = 2

Answer:

a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.

b.in

[tex] \sqrt{2 x} [/tex]

the power if x will be

[tex]x {}^{ \frac{1}{2} } [/tex]

which is not a whole number so it is not a polynomial.

but in

[tex] \sqrt{2} x[/tex]

the power if x is a positive whole number.so it is a polynomial.

c.the greatest power of variable of the term is called degree of polynomial

87 is the mean.

To find the mean, you must

- add all of the numbers

- divide by the amount of numbers given

In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.

let number of green balls= x

let number of orange balls=x+4

x+x+4=38

2x=38-4

2x=34

x=17

number of green balls=17

number of orange balls=21

Answer:

7 x 4

Step-by-step explanation:

Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7

The probability of the event. par or above is 0.74

Using the table in the question as reference, we are to calculate the probability of an event par or above.

This probability is represented as: P(par or above)

The par value from the question is:

[tex]par = 70[/tex]

So, the required probability is:

[tex]P(par\ or\ above) = P(x \ge 70)[/tex]

This mean that we consider scores that are 70 and above

So, the formula to use is:

[tex]P(par\ or\ above) = P(70-74) + P(75 -79) +..... + P(100\ or\ above)[/tex]

Using the data from the question, the equation becomes

[tex]P(par\ or\ above) = 0.28+ 0.20 +0.12+ 0.07+ 0.03+ 0.03+ 0.01​[/tex]

[tex]P(par\ or\ above) = 0.74[/tex]

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Answer:

The probability of Josh scoring par or above is 0.75.

Step-by-step explanation:

Find where par is on the table (70-74). Since it is par or above, you would take the probabilities of par and all numbers higher than par. Add them together, and you have your answer.

(.29) + (.21) + (.11) + (.08) + (.02) + (.03) + (.01) = 0.75

**I attached a screenshot of the table and the correct answer

good luck! <3

Answer:

0.0698

Step-by-step explanation:

Given :

Population mean, μ = 20

Sample mean, xbar = 21.1

Sample standard deviation, s = 4.3

Sample size, n = 35

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (21.1 - 20) ÷ (4.3/√(35))

T = 1.1 ÷ 0.7268326

Test statistic = 1.513

Using the Pvalue calculator :

df = n - 1 = 35 - 1 = 34

Pvalue(1.513, 34) = 0.06976

Pvalue = 0.0698 (4 decimal places)

The p-value is 0.0698 if rounded to 4-decimal places.

It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.

The average number of hours that the 35 students was 21.1 hours.

The sample standard deviation is 4.3 hours.

It is required to find the p-value.

It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.

We can test the hypothesis using the Z test, the formula for the Z-test is given below:

[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]

Where x is the sample mean

            u is the population mean

            s is the standard deviation

            n is the sample size.

The hypothesis are: H0 : μ = 20  V/s  H1 : μ > 20

We have x = 21.1

               u = 20

               s = 4.3

               n = 35

Putting these values in the above formula, we get:

[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]

Z = 1.513

difference or df = n -1 ⇒ 35-1 ⇒ 34

P-value at (1.513, 34) =  0.06976  (From the p-value calculator)

P-value = 0.0698 (Rounded to 4-decimal places)

Thus, the p-value is 0.0698 if rounded to 4-decimal places.

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5+5x>8(x-1)

5+5x>8x-8

5x-8x>-8+5

-3x>-3

5 + 5x > 8(x-1) is equivalent to -3x > -13.

Let, the expression be 5 + 5x > 8(x-1)

By applying Multiplicative Distribution Law, we get

5 + 5x > 8x - 8

Rearrange unknown terms to the left side of the equation, then

5x - 8x > -8 - 5

Combine like terms, we get

-3x > -8 - 5

Calculate the sum or difference

-3x > -13

Divide both sides of the inequality by the coefficient of the variable, then we get

[tex]$x < \frac{-13}{-3}$[/tex]

Determine the sign for multiplication or division:

[tex]$x < \frac{13}{3}$[/tex]

Therefore, the correct answer is -3x > -13.

Complete question:

Which of the following is equivalent to 5 + 5x > 8(x - 1)?

-3x > -12

3x < 13

3x < 6

-4x > -12

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Answer:

Step-by-step explanation:

1-399

2  C

 3-A 99999

4a  

5b

7 b

8 C

9D

10c

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05

Since the p-value is smaller than alpha, this means we reject the null hypothesis.

The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".

Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.

In short, the p-value being smaller than alpha = 0.05 means we reject the null.

In order to accept the null, the p-value must be 0.05 or larger.

Answer:

28 blue marbles

Step-by-step explanation:

yellow: blue

8               4

To get to 56 yellow marbles multiply by 7  

yellow: blue

8*7           4*7

56             28

There will be 28 blue marbles