For each ordered pair, determine whether it is a solution to the system of equations.

The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%

P of 6%

= P (p > 0.06)

we would have to use the formula that is given below

[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]

where we have n = 465

p = 6%

P = 0.57

Q = 1 - 0.57 = 0.43

We would have to put the values into the equation that we have here as:

0.06 - 0.057 = -0.51

0.57 x 0.43 / 465 = 0.000527

√0.000527 = 0.022956

The probability =  -0.51 /  0.022956

= -22.22%

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Answer:

  3a.  $8493.42

  3b.  139.0 months

  4a.  10

  4b.  10.2 years

Step-by-step explanation:

Given exponential equations, you want values for specific times, and you want times for specific values.

In part (a), the value is found by substituting an appropriate value for t and doing the arithmetic.

In part (b), logarithms will be involved in solving for t.

(a) Use t=12, the number of months in one year. You want the value of ...

  S = 8000·1.005^12 ≈ 8493.42

The amount after 1 year is $8493.42.

(b) The time it takes to double the investment is the value of t such that ...

  16000 = 8000·1.005^t

  2 = 1.005^t . . . . . . divide by 8000

  log(2) = t·log(1.005) . . . . . take logarithms

  t = log(2)/log(1.005) ≈ 138.976

The investment will double in about 139.0 months.

(a) Use t=0 and evaluate.

  y = 2500 -2490e^(-0.1·0) = 2500 -2490 = 10

The population of otters was 10 when they were reintroduced.

(b) The time it takes for the population to reach 1600 is the value of t such that ...

  1600 = 2500 -2490e^(-0.1t) . . . . use 1600 for y

  -900 = -2490e^(-0.1t) . . . . . . . . . subtract 2500

  900/2490 = e^(-0.1t) . . . . . . . . . divide by -2490

  ln(900/2490) = -0.1t . . . . . . . . . take natural logs

  t = ln(900/2490)/-0.1 . . . . . . . . divide by the coefficient of t

  t ≈ 10.176 ≈ 10.2

It will be 10.2 years before the otter population reaches 1600.

By doing addition and subtraction of integers, the result obtained is

Mohammed had $5290 at the end of the month

What is addition and subtraction of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.

To find how big or small one integer is from the other, then the operation used is called subtraction of integers.

Here we will use addition and subtraction of integers

Bank balance of Mohammed = $8376

Amount of money taken out by Mohammed next month to buy a car = $4595

Amount of money needed to buy new tires for his car = $1200

Amount of salary received by Mohammed next day = $2709

Amount of money Mohammed had at the end of the month =

$(8376 - 4595 - 1200 + 2709)

= $5290

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It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.

a) Given equation

h(t) = v₀t - 16t^2

Substitute v₀ = 40, h(t) = 0 in the given equation

40t - 16t^2 = 0

Solve for t

⇒ 16t^2 = 40t

⇒ 16t = 40

⇒ t = 40/16

⇒ t = 2.5 seconds

Hence, water will take 2.5 seconds to hit the nozzle on the way down.

b) The function that represents the given condition

h(t) = -16t^2 + 40t + 5

The maximum value of the function is the y-coordinate of the vertex.

The x-coordinate of the vertex

= -40/2(-16) = 5/4

Find the y-coordinate of the vertex by substituting t = 5/4

⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5

⇒ h(5/4) = -25 + 50 + 5

⇒ h(5/4) = 30

Hence, the maximum height of the water is 30 ft.

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The radical expression [tex]\sqrt[5]{x^3}^8.x^4[/tex] simplifies to [tex]x^\frac{44}{5}[/tex].

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, [tex]\sqrt[5]{x^3}^8.x^4[/tex].

= [tex]x^3(^\frac{8}{5}).x^4[/tex].

= [tex]x^\frac{24}{5}.x^4[/tex].

= [tex]x^\frac{24}{5}^{+4}[/tex].

= [tex]x^\frac{24 + 20}{5}[/tex].

= [tex]x^\frac{44}{5}[/tex].

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The calculation of the following income statement figures are as follows:

The income statement is the first financial statement that summarizes the revenues and expenses for a business period to arrive at different profit points.

One of the profit points is the gross profit, which is the difference between the sales revenue and the cost of goods sold.

The other profit points include the operating income, income before tax, and net income.

Gross sales                            $170,000

Sales returns and allowances   9,000

Net Sales                               $161,000

Cost of goods sold:

Beginning inventory $8,000

Net purchases           18,000

Ending inventory       (5,000) $21,000

Gross profit                          $140,000

Operating expenses             (56,000)

Net Income                          $84,000

Thus, the calculation of the income statement figures shows a net income of $84,000.

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Answer:

7.8

Step-by-step explanation:

Switch 8 and 7, it round to 8 and end in tenths.

Answer:

7.8

Step-by-step explanation:

7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.

By using normal distribution of probability, it can be inferred that

For [tex]x_1 = 325[/tex], z = -1.5

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex], z = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]

where  [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

For [tex]x_1 = 325[/tex]

[tex]z = \frac{325 - 496}{114} = -1.5[/tex]

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex]

[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

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Step-by-step explanation:

81 3/8 ÷ 9 2/5

81*8+3 = 651

651/8

9 2/5 = 9*5+2=47

47/5

651/8 ÷ 47/5 =

651/8 * 5/47 = 3255/376 =

8.65691489362

The annual rate of interest have to be 3.87%.

Mathematically, compound interest can be calculated by using this formula:

A = P(1 + r/n)^{nt}

Where:

Making the interest rate (r) the subject of formula, we have:

r = n[(A/P)^{1/nt} - 1]

Note: A = SI + P = 600 + 30,000 = $36,000

Substituting the given parameters into the formula, we have;

Interest rate, r = 1[(36,000/30,000)^{1/1 × 4.8} - 1]

Interest rate, r = [(1.2)^{0.20833333333} - 1]

Interest rate, r = [1.0387 - 1]

Interest rate, r = 0.0387

Interest rate, r = 3.87%.

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Answer:

No entendí porfavor puedes ponerlo en Español

The answer will be A-3*13.75+30 using arithmetic operation.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Alisha used her bank card to buy a bus pass 3 times.

Each time she bought a pass it cost her $13.75,

She then deposited $30 into her bank account.

So the expression A-3*13.75+30

A is the initial value.

Hence this will be the expression A-3*13.75+30

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The area to the right of x in the normal distribution is 0.807

The normal distribution is the probability distribution that helps to find the probability for continuous variables.

For a probability x, for a normal distribution, we have that

P(X ≤ x) + P(X ≥ x) = 1

Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.

Since P(X ≤ x) + P(X ≥ x) = 1 where

Making P(X ≥ x) subject of the formula, we have that

P(X ≥ x) = 1 - P(X ≤ x)

Given that P(X ≤ x) = 0.193

Substituting this into the equation, we have  

P(X ≥ x) = 1 - P(X ≤ x)

P(X ≥ x) = 1 - 0.193

P(X ≥ x) = 0.807

So, the area to the right of x is 0.807

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The slope is 5 and the y-intercept is -2000.

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.

(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.

In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b).  y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.

(a) Consider two points

(x₁, y₁) = (400, 0)

(x₂, y₂) = (500, 500)

The slope is given as

m = (y₂ - y₁)/ (x₂ - x₁)

= (500-0)/(500-400)

= 500/100

= 5

To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)

0 = 5(400)+b

0 = 2000 + b

b= - 2000

(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.

(c) Let the number of customers per week = x

And the profit per week = y

Then, the situation can be modeled using slope-intercept form as

y = 5x -200

(d) Put x= 2500 in y = 5x -200

y = 5(2500)-2000

= 12,500-2000

= 10,500

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The values of x in the equations are as follows:

1. x = 8 or 4

2. x = 2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

log₄ x² - 12x + 48 = 2

using law of logarithm

4² = x² - 12x + 48

16 = x² - 12x + 48

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

x² - 4x - 8x + 32 = 0

x(x - 4) - 8(x - 4) = 0

(x - 8)(x - 4) = 0

Therefore,

x = 8 or x = 4

[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]

[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]

[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]

[tex]3^{12x-18} =3^{-4x+14}[/tex]

Cancel the base

Therefore,

12x - 18 = - 4x + 14

12x + 4x = 14 + 18

16x = 32

x = 32 / 16

x = 2

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The value of TV for the similar triangles is 25

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

Similar triangles are not the same as congruent triangles though.

triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.

Let UV = p, it means also that WV = P. which means WU = 2p

so since the two triangles are similar, the ratio of their corresponding lengths are equal

meaning,

UV/UW = TV/XW

substituting their values, we have

p/2p = TV/50

by cross multiplying,

2p x TV = 50p

2TV = 50

TV = 50/2 = 25

In conclusion,  the value of TV is half the value of WX = 25

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The money was spent on a pass and lunch for each student is $28.07

It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.

Therefore the amount spent on pass will be:

= Total amount / Number of people

= 654.84 / 34

= 19.26

The amount spent on each student will be:

= 281.92 / 32

= 8.81

The amount spent in pass and lunch will be:

= 19.26 + 8.81

= $28.07

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Answer:

30

Step-by-step explanation:

3/8 is less than 1.

30 is much greater than 1.

Answer: 30

Answer:30 is greater

Step-by-step explanation:

a) The test statistic is: t = -7.44.

b) The p-value is: < 0.0001.

c) The conclusion is that the null hypothesis is rejected.

d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.

From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:

The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.

Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.

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The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).

what is the slope-intercept?

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

The slope-intercept form: y = mx + b

m - a slope

b - y-intercept

Here, we have

A slope m = 1/4.

Substitute: y = 1/4 x + b

We know that

the line passes through the point (8, 3) → x = 8, y = 3.

Put the values of x and y into the slope of the line:

1/4 · 8 + b = 3

2 + b = 3 |-2

b = 1

Hence, the y-intercept is (0, 1)

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1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4.  The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.

2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.

Complete sentence:

1) The formula for the number of shaded squares in the Nth figure is n+n-1.

2) There would be 99 shaded squares in the 50th figure.

explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.

Answer: 231 thousand

Step-by-step explanation:

given,

total number of undergraduate students enrolled = 414000

let us take number of total number of male students as, X

then, total number of female students will be X + 48000

now we get,

total number of male students + total number of female students = total number of students enrolled.

X + (X + 48000) = 414000

X + X + 48000 = 414000

2X = 414000 - 48000

X = 366000/2

X = 183000

total number of male students is 183000

total number of female students is

X + 48000

183000 + 48000 = 231000

Answer:

??

Step-by-step explanation:

where are the equations ?

Answer:

Step-by-step explanation:

Answer:

8.25 % I got this answer right.

The function will be;

⇒ y = 3x - 1

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The domain and the range is shown in table.

Two points on the line are (2, 5) and (7, 20).

Now,

Since, The equation of line passes through the points (2, 5) and (7, 20).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (20 - 5) / (7 - 2)

m = 15 / 5

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - 5 = 3 (x - 2)

⇒ y - 5 = 3x - 6

⇒ y = 3x - 6 + 5

⇒ y = 3x - 1

Therefore, The function will be;

⇒ y = 3x - 1

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Answer:_______________________________

The equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following statement - "4 less than a number is given w".

Assume the number to be [x].

We can write the equation representing the statement -

"4 less than a number is given w" as a mathematical expression as -

[w] = x     where x ∈ (- ∞, 4)

Therefore, the equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

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1) y = 3x+2, where slope is 3 and point is(3, -5).

2) y+6 = 4(x-5) is the equation for the given slope and point.

                      y = mx + b

                       Slope = m = tan θ = (y2 - y1)/(x2 - x1)

1) y + 5 = 3(x-1)x-x

Compare this equation to y - y₁ = m(x - x₁)

y = 3x - 3 + 5

y = 3x + 2

2) Given:

Slope = 4; point (5, -6)

y - y₁ = m(x - x₁)

y + 6 = 4(x -5 )

Option A

Hence, i) y = 3x+2, where slope is 3 and point is(3, -5) and ii) y+6 = 4(x-5) is the equation for the given slope and point.

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Answer: B)

Step-by-step explanation: