how many four-digit numbers greater than 2999 can be formed such that the product of the middle two digits exceeds 5?

Step-by-step explanation:

vertex form :

y = a(x - h)² + k

(h, k) are the coordinates of the vertex.

"a" is the orientation (up-down) and widening factor.

we use the given h, k and x, y (the given point) to calculate "a".

-5 = a(2 - 3)² + 1 = a(-1)² + 1 = a + 1

a = -6

and the full vertex form is then

y = -6(x - 3)² + 1

just a quick addition to the superb reply by "reinhard10158" above

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=3\\ k=1 \end{cases}\implies y=a(x-3)^2 + 1\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-5 \end{cases} \\\\\\ -5=a(2-3)^2 + 1\implies -6=a(-1)^2\implies -6=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=-6(x-3)^2 + 1 \end{array}} ~\hfill[/tex]

The measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

The measure of the arc RMP = 360 - Arc RP

The measure of the arc RMP = 360 - 120 = 240 degrees

The measure of the angle RQP = 1/2[240 - 120]

The measure of the angle RQP = 60 degrees

In the second circle:

9(9 + x) = 15(15)

9 + x = 25

After solving we get:

x = 16

Thus, the measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.

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Based on the slopes of both lines, the relationship between both lines is: D. a and b are perpendicular.

The relationship between two lines that are parallel is that they have the same slope, while the relationship between perpendicular lines is that their slopes are negative reciprocals of each other.

Find the slope of the line that passes through (-5, -2) and (-5, -5):

Slope (m) = change in y / change in x = (-5 -(-2)) / (-5 -(-5))

m = (-5 + 2) / (-5 + 5)

m = -3/0 [cannot divide, therefore, the slope is undefined).

The line is therefore a vertical line.

Find the slope of the line that passes through (0, 4) and (5, 4):

Slope (m) = change in y / change in x = (4 - 4) / (5 - 0)

m = 0/5

m = 0

This line is an horizontal line.

In conclusion, the relationship between a vertical and a horizontal line is that they are perpendicular to each other, therefore, the answer is: D. a and b are perpendicular.

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The sum of their ages 5 years ago is x + y -10.

The process of subtracting one number from another is known as subtraction.

Given that, Jean is x years old and her younger brother is y years old.

Age of Jean 5 years ago is:

x - 5

The age of Johnathan 5 years ago is:

y - 5

The sum of their ages 5 years ago is:

x - 5 + y - 5

= x + y -10

Hence, the sum of their ages 5 years ago is x + y -10.

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Answer:

.5x + 10 > 20

Step-by-step explanation:

x represents each delivery he makes:

.5x + 10 > 20

This shows that for the inequality to be true, it must total over $20

Hope this helped!

5.56 fluid ounce of tea remain in the pitcher

In mathematics, a variable is an alphabet that represent an unknown number. We let required amount as variable and then try to calculate its value

According to the question,

Total ounces of iced tea a pitcher contains = 17.6 fluid ounces

Amount of tea Erin pours to drink = 12.06 fluid ounces

Let "x"  fluid ounce of tea remain in the pitcher

So , total was 17.6

=> x + 12.06 = 17.6

Solving for x

Subtracting by 12.06 both the sides

=> x + 12.06 - 12.06 = 17.6 -12.06

=> x = 5.56 fluid ounce

Hence , 5.56 fluid ounce of tea remain in the pitcher

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.

This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.

Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.

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Answer: Yes, it will overload the truck.

Step-by-step explanation:

To begin, form an algebraic equation.

200(r) + 425(f)

Second, substitute your numbers for the variables.

200(18) + 425(11) = ?

Third, multiply your numbers of fridges by the weight of each.

3600 + 4675 = 8275 is the total

Finally, determine whether or not if it is greater than the weight limit the truck has.

7200 < 8275

Therefore, the total weight is greater than the weight limit.

Answer:

C no solution.

Step-by-step explanation:

The lines are parallel, they will never intersect.

The measure of the radius of the sphere is given as follows:

r = 359 cm.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h

Which is the base area given by πr² multiplied by the height h.

In the context of this problem, the parameters are given as follows:

The volume of the circumscribed cylinder is 2154.04π cm^3, hence the equation to solve for r is given as follows:

πr²h = 2154.04π

2πr³ = 2154.04π

2r³ = 2154.04

r = cube root of (2154.04/2)

r = 359.

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Answer: 32 jackets

Step-by-step explanation:

add 1280 to 1176 then divide the sum by 75

Answer:

On the 4th day, the sum of penalties and charges will be the same in both the school library and the town library.

Step-by-step explanation:

School library

Penalty-25

Every day charge-5

City library

Penalty-5

Every day charge-10

Let the day when total fee at both libraries will be same be x

Total charge in school library-25+5x

Total charge in city library-5+10x
They both amount to be equal

Answer:

Y=12

Step-by-step explanation:

ya bae

These rules of five letters (a, b, c, d, and e) and five numbers allow for 28,800 different passwords. Additionally, she makes sure that no two letters or two numbers are ever placed back-to-back.

The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. According to this statement, there are n*m methods to carry out both of these acts if there are n ways to execute one activity and m ways to conduct another action after that.

Here,

Eloise has 10 alternatives since the password's initial character can be any letter or number. She has five alternatives, and her second selection must be from the set (letter or number) that has not previously been utilized. She has four choices remaining, and Choice 3 is from the same group as Choice 1. She gets four possibilities since Choice 4 is the second item in the same set as Choice 2. The choices 5 and 6 come from separate sets, each of which has three possibilities; the choices 7 and 8 come from separate sets, each of which has two options; and the choices 9 and 10 come from separate sets, each of which has only one option left.

10 5 4 4 3 3 2 2 1 1

10 ×5 ×4 ×4 ×3 ×3 ×2 ×2 ×1 ×1 = 28,800

28,800 different passwords conform to these rules of five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive.

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Answer:

64

Step-by-step explanation:

do multiplication :)

The value of f(2)-g(-7) is -34

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

Given are two functions, f(x) = -|3-8x| and g(x) = x²+4x

f(2) = -|3-8x2|

= -|3-16|

= -13

g(x) = (-7)²+4(-7)

= 49-28

= 21

f(2)-g(-7) = -13-21 = -34

Hence, The value of f(2)-g(-7) is -34

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Answer:

It should be 1/5

Since the fractional versions of the ratios are equal, the ratios are equivalent.

On solving the given question, by the Help of LaPlace Inverse form we got - [tex]y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]

In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.

Take Laplace for DE we get -

[tex]L(y)" + 8L(y)' =0\\s^2Y (s) - sy(0) - y'(0) 8(sY(s) - y(0))=0\\Y(s)(s^2 + 8s) + 3s 4 + 24 =0\\Y(s)(s^2 + 8s) = -3s - 28\\Y(s) = \frac{-3s - 28}{(s^2 + 8s) } \\Right Side = \\\frac{-7}{2s} + \frac{1}{2(s+8)} \\ Now taking inverse LaPlace - \\y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]

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The ratio of the area of a square inscribed in a semicircle to the area of a square inscribed in a circle is 2/5.

What is a semicircle?

A semicircle in mathematics is a one-dimensional locus of points that makes up one-half of a circle. A semicircle's entire arc always measures 180 degrees. There is only one symmetry line in it.

For instance, if the radius is known, we can use the formula, which states that the area of a semicircle is equal to half that of a circle. As a circle's area is r2, Therefore, a semicircle's area is equal to 1/2(r2), where r is its radius. 3.14, or 22/7, is the value of.

Solution Explained:

Let's assume and take

The dimensions of the little square ABCD = 2 x 2 =4

of the little triangle's hypotenuse Radius of the semi-circle for BCG

H=sqrt(5) = The semicircle's radius

IHJK = 2sqrt is the diagonal of the huge square (5)

One side of the large square is IHJK when sin(45) x 2sqrt(5) = sqrt(10).

Therefore, the area of ABCD/area of IHJK is equal to 4/sqrt(10)2 = 2/5.

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The work that has been done on player 2 by player 1 is a negative work. Option A.

We define the work done as a situation in which the force that is applied moves a distance in the direction of the force. In this case we ought to know that a negative work is said to be done when the object is found to slow down at te application of the force. The meaning of this is that the force acts in such a way as to slow down motion which makes it a negative force.

For the fact that football player one pushes against football player two, causing player two to slow down from moving any farther down the field, a negative work is done.

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a. The solution of the equation x + 2 = √3x + 10 is x = -3 or x =2.

b. Extraneous solution is x= -3.

c. Extraneous solution does not satisfy original equation.

As given in the question,

Given equation :

x + 2 = √3x + 10

a. Squaring both the sides

( x + 2 )² = ( √3x + 10 )²

⇒ x² + 4x + 4 = 3x + 10

⇒ x² + x - 6 =0

⇒ x² + 3x -2x -6 =0

⇒ ( x+ 3) ( x -2) =0

⇒ x= -3 or x = 2

b. Extraneous solution:

x = -3

-3 + 2 = √3(-3)+ 10

⇒ -1  ≠ 1 extraneous solution.

x= 2

2+ 2 =√3(2) +10

⇒4 = 4 not extraneous.

c. Extraneous solution does not satisfy original equation

Therefore, the solution of the equation is x = -3 or x=2and its extraneous solution is x =-3. Extraneous solution does not satisfy original equation.

The complete question is :

Use the equation below to answer these questions.

x + 2 = √3x + 10

a) What is the solution to the equation?

b) What is the extraneous solution? Why?

c) In general, what is an extraneous solution?

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Answer:

cos x = - 0.809, find the values of x. ( - 180≤ x ≥ 180 )

x = - 135° and x = 45°

The critical value for right tailed test is 2.998, the critical value for left tailed test is - 1.717.

First, we must know the following data,

df = degree of freedom = n - 1

α = significance level

Next, t test have three type of test which is

Then, to find critical value using the t distribution table search df value in left column of table and search the α in the top row of the table (depending on the type of test, use one tail row for this case). For example, see attached image.

Thus, the right tailed test critical value is 2.998, and the left tailed test critical value is - 1.717.

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The two methods are identical because by both using algebra tiles and factoring symbolically, one need to think of the factors.

Factoring simply has to do with the process of writing a number or another mathematical object as a product of different factors, and this is usually smaller or simpler objects that are of the same kind.

Factoring is a common mathematical process that's used for separating the factors, or numbers, which multiply to form another number. Some numbers are affected by multiple factors.

For example, in a situation when you multiply the factors 6 and 4, 8 and 3, 12 and 2, and 24 and 1, you get the number 24.

Algebra tiles are rectangular and square tiles that represent numbers and variables. Using algebra tiles allows us to solve our problems in a more visual manner. It allows us to see exactly what quantities we're dealing with. It's as if we're using building blocks to assist us.

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The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.

In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.

The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].

Firstly we check the convergence of the given series.

When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.

We can write the series as:

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]

As |0.3|<1 and |0.2|<1

Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.

So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]

Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28

Hence, the sum of the given series is 33/28.

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The right question is:

Determine whether the series is convergent or divergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]

If is is convergent, find the sum. (If the quantity diverges, enter diverges.)

Answer:

one solution

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is (1, 2 )

Since there is only 1 point of intersection then there is only one solution.

Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.

Given that,

Assume you are conducting a two-sample test of averages and that the variances in the population are identical. The information below is ours:

Sample 1: n₁=16, x₁=44, and s₁=5.

Sample 2:x₂ = 41, s₂ = 6, n₂ = 9.

We have to find the test statistic.

We know that,

n₁ = 16

x₁ = 44

s₁ = 5

n₂ = 9

x₂ = 41

s₂ = 6

We have

t= (x₂ - x₁)/√(n₁-1)s₁²+(n₂-1)s₂²/n₁+n₂-2(1/n₁+1.n₂)

t = 1.341.

Therefore, Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.

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The gain Renata Corporation got from the sale of equipment is $16420

The tax depreciation method used in the United States is called MACRS, or Modified Accelerated Cost Recovery System. In other words, the method used to determine your business's tax deductions based on the depreciation of your tangible (depreciable) assets is known as MACRS depreciation.

Equipment Book value =

Purchase price - MACRS depreciation

= $328, 400 - $147,780

=$1,80,620

Gain = sale price - Book value

= $197, 040 - $180620

=$ 16420

Gain up to total depreciation is to be treated as ordinary income, that is up to $147, 780. since the gain is $16,420 within depreciation, it is treated as ordinary income.

Renata Corporation has a gain of $16,420 of which $16, 420 is treated as ordinary income due to the section 1245 recapture

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The different ways in which 6 candles be chosen 84 ways.

What is a combination?

The combination is a method of choosing things from a collection where the order of the choices is irrelevant.

Given, When we have 'n' types of elements and choose 'r' elements from them, then we have C(n+r-1, r) combinations.

n=4(4 types of candles), r=6(no of candles to pick)

Choose 6 different candles, then

=C(4+6-1,6)

=C(9,6)

= 9! / (9-6)! (6!)

= 9!/ 6! 3!

=84

The different ways in which 6 candles can be chosen are 84 ways.

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The critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84

Given that,

Of the 62 swim teachers who participated in the survey, 37 claimed that teaching the butterfly stroke is the most challenging. Find the criticial value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% level of significance.

This is right tailed test

Z [tex]\alpha[/tex]  = Z 0.01 = 0.84   ( Using z table )  

Therefore, the critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84

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