5. In a recent year, the population of Springfield, Illinois was one hundred
sixteen thousand, four hundred eighty-two. Write this number in standard
form. Show your work in the space below. Remember to check your solution

The constant in the expression represents that the company earned  85 billion dollars in 2008.

The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward

An example of a quadratic function is ax² + bx + c

Where: a,b, c are real numbers not equal to zero

c = constant.

The constant in this question is 85. It is the amount earned in 2008

Here are the options:

The company earned  85 billion dollars from 2008 to 2018

The company earned  85 billion dollars in 2008

The company earned 14  billion dollars from 2008 to 2018.

The company earned  14 billion dollars in 2008.

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The producer surplus at the equilibrium point is 1.0146

An equilibrium (or equilibrium point) of a dynamical machine-generated via an autonomous machine of everyday differential equations (ODEs) is a solution that doesn't change with time.

Equilibrium is the country in which the marketplace delivers and calls for stability each different, and as a result, expenses turn out to be solid. usually, an over-deliver of products or services reasons charges to head down, which leads to higher demand—at the same time as a below-supply or scarcity reasons costs to head up resulting in fewer calls.

The equilibrium equations (balance of linear momentum) are given in index form as(1.4)σji,j+bi=ρu¨i, I,j=1,2,3where σij are additives of (Cauchy) stress, ρ is mass density, and bi is body force additives.

Producer Surplus = area of shadestportion

Area of shaded portion = free of rect minus area of OneD

Aves of OABO=Now serving from

"[3√74-3/5]

= √(x+3)" de

=2 (2√6-√5)

(Jon= √46 = Fure=456-255

(x+3)+1

Area of rectangle OA BC =316

= 3√6

producer surplus = 3√6 - (ure -2√5)

= 2√3-66

= 1.0146

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Answer:

6 2 point shots 2 3 points

Step-by-step explanation:

3 two point shot 1 3 point shot = 9

6 two point shot 2 3 point shot =18

The test That holds true for this inequality is given as 1/4 and 1

3/2 y - 2x > 1

The goal is to make y the subject

then

3/2 y > 2x + 1

We have to divide through the equation by 3/2

Such that  y  > 4/3 x + 2/3

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Answer: 180 meters

Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.

Answer:  18

Step-by-step explanation:  the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.

Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]

Step-by-step explanation:

[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]

[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]

Considering the situation described, the classification of the elections is given as follows, according to their order of finish:

David, Greg, Victor, Mac, Bill.

We take the situation that is described, and build the classification from it. The classification has the following format:

P1 - P2 - P3 - P4 - P5

With P1 being the first placed candidate, P2 being the second placed candidate, and so on until P5 which is the fifth placed candidate.

From the text given in this problem, we have that:

Hence the classification of the election is given by:

David, Greg, Victor, Mac, Bill.

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Answer:

Infinite solutions

Step-by-step explanation:

You can put in any number for x and the 2 sides of the equation will equal each other.

Answer:

The equation has not solution, both parts of the equation correspond to the same line.

Step-by-step explanation:

-6 -(2x+7) = -2(x+6) - 1

-6 -2x - 7 = (-2*x + (-2*6)) - 1

-6 - 2x - 7 = -2x - 12 - 1

-2x - 13 = -2x - 13

-2x = - 2x

The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.

Given that,

a = <−9, 12> , b = <6, 4>

These vectors can be rewritten as,

a = <−9, 12> = −9i + 12j

b = <6, 4> = 6i + 4j

a + b = −9i + 12j + 6i + 4j

a + b = −9i + 6i + 12j + 4j

a + b = (−9 + 6)i + (12 + 4)j

a + b = −3i + 16j

6a = 6 (−9i + 12j )

6a = −54i + 72j

9b = 9(6i + 4j)

9b = 54i + 36j

Now add 6a and 9b together,

6a + 9b = −54i + 72j  + 54i + 36j

6a + 9b = −54i + 54i + 72j + 36j

6a + 9b = 0i + 108j

If a = a₁i + a₂j, |a| = √a₁² + a₂²

Here, a = −9i + 12j

|a| = √(−9)² + (12)²

|a| = √81 + 144 = √225

|a| = 15

a - b = −9i + 12j - (6i + 4j)

a - b = −9i - 6i + 12j - 4j

a - b = −15i + 8j

Now use the formula to find the magnitude of a vector,

|a − b| = √(-15)² + (8)²

|a − b| = √225 + 64 = √289

|a − b| = 17

Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.

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Answer:

B

Step-by-step explanation:

First create the equation that has slope of -1 in the form of y=mx+b. Because the slope is -1, m=-1, so the equation is y=-x+b. Now we see that we are given the point (-3, 8) as an intersection point. Substitute x and y for -3 and 8 in our equation. With this information, our equation becomes 8=3+b. Solving, b=5. Our equation is now y=-x+5.

Simplifying all of the answer choices, we have

A. y=-x-5

B. y=-x+5

C. y=-x-5

D. and E. as what they already show

The only answer that matches is B.

Answer:

[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

Rearrange the given equation so that it is in slope-intercept form:

[tex]\implies -5x-7y=-17[/tex]

[tex]\implies -7y=5x-17[/tex]

[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]

Therefore, the slope of the given equation is -⁵/₇.

If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1.  Therefore, their slopes will be negative reciprocals of each other.

Therefore, the slope of the line perpendicular to the given equation is:

[tex]\sf m=\dfrac{7}{5}[/tex]

Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:

[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]

[tex]\implies -5=\dfrac{42}{5}+b[/tex]

[tex]\implies b=-\dfrac{67}{5}[/tex]

Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:

[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]

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The two numbers are 68 and 55.

Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.

We need to find the numbers,

Let's call the two numbers x and y. According to the given information, we have the following two equations:

x + y = 123 (The sum of the two numbers is 123)

x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)

Now, we can solve these two equations simultaneously to find the values of x and y.

Let's rearrange equation 1 to express x in terms of y:

x = 123 - y

Substitute this value of x into equation 2:

(123 - y) + 5y = 343

Now, solve for y:

123 + 4y = 343

4y = 343 - 123

4y = 220

y = 220 / 4

y = 55

Now that we have the value of y, we can find the value of x using equation 1:

x = 123 - y

x = 123 - 55

x = 68

So, the two numbers are 68 and 55.

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2.4kg.,

..

hope it helps

Answer:

• [tex](w \cdot u) (7)[/tex] =  [tex]\bf 8[/tex]

• [tex](u \cdot w) (7)[/tex]  =  [tex]\bf 22[/tex]

Step-by-step explanation:

We are given:

[tex]u(x) = x^2 + 6[/tex]

[tex]w(x) = \sqrt{x + 9}[/tex].

• [tex](w \cdot u) (7)[/tex]. read as "w of u of 7", means we have to input 7 into the function [tex]u(x)[/tex], and use the output we get as input for the function [tex]w(x)[/tex] :

[tex](w \cdot u) (7)[/tex]

⇒ [tex]w(u(7))[/tex]

⇒ [tex]w(7^2 + 6)[/tex]

⇒ [tex]w(55)[/tex]

⇒ [tex]\sqrt{55 + 9}[/tex]

⇒ [tex]\sqrt{64}[/tex]

⇒ [tex]\bf 8[/tex]

• Similarly, we can evaluate [tex](u \cdot w) (7)[/tex] :

[tex](u \cdot w) (7)[/tex]

⇒ [tex]u(w(7))[/tex]

⇒ [tex]u(\sqrt{7 + 9})[/tex]

⇒ [tex]u(\sqrt{16})[/tex]

⇒ [tex]u(4)[/tex]

⇒ [tex]4^2 + 6[/tex]

⇒ [tex]\bf 22[/tex]

The answers are :

(w o u)(7) = 8

(u o w)(7) = 22

To find the first answer, substitute u(x) in w(x), and set x = 7.

To find the second answer, substitute w(x) in u(x), and set x = 7.

The expected value or mean of binomial distribution is also increased by increasing the number of trials.

The standard deviation of binomial distribution is also increased by increasing the number of trials.

According to the question

There is binomial experiment.

The condition given in the question is 'if the number of trials is increased, what happens to the expected value and to the standard deviation'.

We all know,

In binomial distribution, The mean or expected value is given by np whereas the variance is given by np(1 - p) where (1 - p) taken as q is the probability of failure and p is the probability of success.

The standard deviation of binomial distribution is [tex]\sqrt{npq}[/tex].

From the expected value formula we can see that number number of trials is directly proportional to mean or expected value.

Thus we can say that

If the number of trials is increasing, then the expected value is also increasing.

From the standard deviation of binomial distribution we can see that if the number of trials increasing then the standard deviation also increasing because standard deviation is directly proportional to number of trials.

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Answer: 7/12

Step-by-step explanation: There is a total of 3+7+2 = 12 marbles in the bag. 7 are blue marbles so there is a 7/12 chance of getting a blue marble when one marble is drawn.

Answer:

7/12

or an 84%

Step-by-step explanation:

Answer:

==============================

Inequality:

1. Distribute:

2. Multiply:

3. Collect like terms:

4. Addition:

5. Divide both sides by 6:

Interval notation for this solution is:

Answer:

[tex]x < -3[/tex]

Interval notation:  (-∞, 3)

Step-by-step explanation:

Given inequality:

[tex]-4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right) > 8[/tex]

Divide both sides by -4 (remembering to change the direction of the inequality sign, since we are dividing by a negative):

[tex]\implies \dfrac{ -4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right)}{-4} > \dfrac{8}{-4}[/tex]

[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x < -2[/tex]

Subtract ⁵/₂ from both sides:

[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x-\dfrac{5}{2} < -2-\dfrac{5}{2}[/tex]

[tex]\implies \dfrac{3}{2}x < -\dfrac{9}{2}[/tex]

Multiply both sides by 2:

[tex]\implies \dfrac{2 \cdot 3}{2}x < -\dfrac{2 \cdot 9}{2}[/tex]

[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2}x < -\dfrac{\diagup\!\!\!\!2 \cdot 9}{\diagup\!\!\!\!2}[/tex]

[tex]\implies 3x < -9[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3} < \dfrac{-9}{3}[/tex]

[tex]\implies x < -3[/tex]

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See attached images for the graph.

Answer:

A=113 cm²

Step-by-step explanation:

If the length of the rope is 6 cm

then the radius of the circle we draw is 6 cm.

Area of the circle is A = π·r²

A = π·6² ≈ 3.14· 36 ≈ 113cm²

Answer:

Option 2

Step-by-step explanation:

There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.

177.8 centimeters.

The shortest distance between the tip of the cone and its rim:

cos θ= base/Hypotenuse

cos 77°=[tex]\frac{40}{H}[/tex]

[tex]0.22495=\frac{40}{H}[/tex]

[tex]H=177.8[/tex]

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The shortest distance between the tip of the cone and its rim exits 51.11cm.

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]

[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]

Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]

[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

simplifying the above equation, we get

[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

x = 51.11cm

The shortest distance between the tip of the cone and its rim exits 51.11cm.

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The rounding off a given number implies approximating the number to the required value. Thus the answer to the given question is 6 000 mm.

Rounding off a given number implies approximating the number to the required value. This can be done in two major ways: rounding up or rounding down.

Rounding up implies considering the required digit if it is up to or greater than 5, which turns to 1. Rounding down requires no consideration of digits less than 5 which turns to 0.

Thus considering the given question, Since the second digit is 4 which is lesser than 5, then it turns to a zero. So that;

rounding off 6 400 mm would give 6 000 mm.

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Step-by-step explanation:

This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:

[tex] \sin(60) = \frac{y}{32} [/tex]

[tex]y = \sin(60) \times 32[/tex]

[tex]y \approx28[/tex]

Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:

[tex] \cos(60) = \frac{x}{32} [/tex]

[tex]x = \cos(60) \times 32[/tex]

[tex]x = 16[/tex]

Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:

[tex] \tan(60) = \frac{12}{a} [/tex]

[tex]a = \frac{12}{ \tan(60) } [/tex]

[tex]a \approx7[/tex]

Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:

[tex] \sin(60) = \frac{12}{b} [/tex]

[tex]b = \frac{12}{ \sin(60) } [/tex]

[tex]b \approx14[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The first triangle is a 30-60-90 triangle,

so the sides are in the ratio 2 : 1 : √3,  where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.

So x = 1/2 * 32 = 16

and y = 16√3  or 27.71 to nearest hundredth.

The second one is the same special triangle, so

√3/2 = 12/b

b = 24/√3

 = 8√3  or 13.86  to nearest hundredth.

a = 1/2 b = 4√3 or 6.93 to nearest hundredth.

Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

At the null hypothesis, it is tested if the mean is of 7 ounces, that is:

[tex]H_0: \mu = 7[/tex]

At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:

[tex]H_1: \mu \neq 7[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters are given by:

[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]

Hence the value of the test statistic is found as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]

t = 1

Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]

Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

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Answer:

h = 5 cm

Step-by-step explanation:

Givens

d = 6cm

V = 45cubic cm

Formula

V = pi * r^2 h                                  substitute values into the formula

Solution

d = 2*r

6 = 2*r                                            Divide both sides by 2

6/2 = 2r / 2

3 = r

45 pi cm^3 = pi * (3)^2 * h            Divide both sides by pi

45 pi/pi = pi * 9 * h / pi

45 = 9h                                         Divide both sides by 4

45/4 = 9h/9                                    

5 cm

By direct evaluation, we will see that the limit is equal to 29.

Here we want to find the limit of the given expression when x tends to 5.

[tex]\lim_{x \to \ 5} x^2 + 4[/tex]

We can directly evaluate the expression in x = 5 and see if we get a real value different than zero.

By direct evaluation, we get:

[tex]\lim_{x \to \ 5} x^2 + 4 = 5^2+ 4 = 29[/tex]

Notice that the limit does give a whole number, then in this way, we conclude that the limit of the given expression when x tends to 5 is equal to 29.

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Answer:

square 29

Step-by-step explanation:

Answer:

10 is the right answer...

Step-by-step explanation:

thanks

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