Written as a simplified polynomial in standard form, what is the result when
(x-7)^2 is subtracted from 1?

Maybe the side of the mountain or a cave where rain won't be able to get to the campsite.

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

If salary average of 4 players is making $200,000/yr, what's the total payroll?  It should be $200K x 4 or $800,000.

Now if you add in that 5th player at $400,000 what is the total payroll of all 5 players?  It should be $800,000 + $400,000 = 1,200,000.  From there you can find the average of the 5 players by dividing!

Answer:

Its B

Step-by-step explanation:

Got it right on the test

Answer:

The answer is B

Step-by-step explanation:

Edge 2021

Answer: D

Step-by-step explanation: it’s equivalent if u find the first system and then work it out to find the same system (2,-1)

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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Answer:

y = -2x + 1

Step-by-step explanation:

The linear equation is generally written in y = mx + b form. Since m (the value of the slope) is already given, only the value of b must be determined. To do this, plug in x, y, and m for their values in the equation to get:

13 = -2 (-7) + b

Then, simplify.

13 = 14 + b

b = -1

Once you find the b value, plug everything back in and get y = -2x + 1.

Answer:

Width = 4 m, Length = 16 m

Step-by-step explanation:

Perimeter = 40

Width = x

Length = 3x + 4

x + x + 3x + 3x + 4 + 4 = 8x + 8

40 - 8 = 32

32/8 = x

x = 4

Width = 4

Length = 16

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No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

Answer:

7pi/9

Step-by-step explanation:

subtract 360 from 500 as many times as you can

number left should be converted to radians

500 - 360 = 140

140 * (pi/180) =

140Pi/180 =

simplify by dividing by 20 top & bottom

7Pi/9

varsitytutors

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

Step-by-step explanation:

Answer: 0.07

Step-by-step explanation:

To find the relative frequency of people in the sample whose place of residence is suburban and whose highest degree is a two-year degree, we need to calculate the ratio of the number of people with those characteristics to the total sample size.

Looking at the contingency table, we can see that the number of people in the suburban category with a two-year degree is 21.

The total sample size is given as 311.

Therefore, the relative frequency can be calculated as:

Relative frequency = (Number of people in suburban category with two-year degree) / (Total sample size)

= 21 / 311

≈ 0.0676

Rounded to two decimal places, the relative frequency is approximately 0.07.

Answer:

there must me a second equation too. as an equation with two variables can not be solved by just one equation

There are 164 feet of string left on the spool.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

First, we need to convert all the measurements to the same unit. Since the question asks for the amount of string left in feet, let's convert the initial string length and the additional string used to feet as well:

80 yards of string = 240 feet (since 1 yard = 3 feet)

12 yards of string = 36 feet (again, 1 yard = 3 feet)

La let out 40 feet of string initially, so the total amount of string used so far is

40 feet + 36 feet = 76 feet

To find out how much string is left on the spool, we can subtract this amount from the initial string length:

240 feet - 76 feet = 164 feet

Therefore, There are 164 feet of string left on the spool.

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Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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The solution of the given equation are,

\(x=\frac{\pi }{2}+2n\pi , x = -0.33983 + 2n\pi , x = \pi +0.33983+2n\pi\)

What is solution of the equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other terms, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transform the equation into an equality.

Consider, the given equation

\(2-3cos^2(x)=2sin(x)\)

⇒ \(2-3cos^2(x) - 2sin(x)=0\)

Since, \(cos^2(x) = 1-sin^2(x)\)

Plug this value in the above equation.

\(2-3(1-sin^2(x))-2sin(x)=0\\2-3+3sin^2(x)-2sin(x)=0\\-1+3sin^2(x)-2sin(x)=0\\3sin^2(x)-2sin(x)-1=0\\\)

Substitute \(sin(x) = u\)

⇒

\(3u^2-2u-1=0\\3u^2-3u+u-1=0\\3u(u-1)+1(u-1)=0\\(u-1)(3u+1)=0\)

⇒

\((u-1)=0, (3u+1)=0\\u=1, u=-\frac{1}{3}\)

Back substitute: u = sin(x)

⇒

\(sin(x) = 1\\sin(x) = -\frac{1}{3}\)

For,

\(sin(x)=1 , x = \frac{\pi }{2}+2n\pi \\ sin(x)=-\frac{1}{3}, x = arcsin(-\frac{1}{3} )+2n\pi , x = \pi +arcsin(\frac{1}{3})+2n\pi\)

Combine all solutions, the we get

\(x=\frac{\pi }{2}+2n\pi , x = -0.33983 + 2n\pi , x = \pi +0.33983+2n\pi\)

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Complete question:

Solve the equation for x, 2 - 3 cos²(x) = 2 sin(x)

Answer:

500,000

Step-by-step explanation:

the value of 5 in the number 56242 is 500,000 or hundred thousand. to know the value of digit 5 in the number 564242 go to five the digit 5 and write zeroes after it.

have a wonderful  day

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

What do you mean by stwps? Please comment

Answer:

i can help u

Step-by-step explanation:

but i dont know what steps you need to memorize

V is a vector space with the operations of addition and scalar multiplication.

Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.

Let V denote the set of all differentiable real-valued functions defined on the real line.

You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.

On a different note, you cannot say that

f+g=f(t)+g(t)

but you can say that (f+g)(t)=f(t)+g(t)

So  V is a vector space with the operations of addition and scalar multiplication.

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Answer:

8 seconds after running 88 feet

Step-by-step explanation: this is what it told me the answer was

Answer:

The older sibling will catch the younger sibling after 8 second(s) and running 88 feet.

Step-by-step explanation:

Older Sibling:  11ft  22ft  33ft  44ft  55ft  66ft  77ft  88ft

Younger Sibling: 32ft  39ft  46ft  53ft  60ft  67ft  74ft  81ft

The younger sibling started at 32ft because of the headstart.  Each number was after 1 second. So this means it took 8 seconds for the older sibling to get to 88ft, and it took 8 seconds to get the younger sibling to 81ft.

I hope you can understand. :)

Answer:

$667.80

Step-by-step explanation:

30% of 900 is 270, so the price of the TV would be 630 without the tax. 6% of 630 is 37.8, so in total, the price would be $667.80

Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

$12

Step-by-step explanation:

50% is half off of something, which in this case would be the $24, so you would just take half off the 24. So you could divide it by 2 which would be 12.

Answer:

5

Step-by-step explanation:

0-4= -4

-4+9=5

Answer: The 5th Floor

Step-by-step explanation:

0 - 4 = - 4

- 4 + 9 = 5

Answer:

(0,-3)

Step-by-step explanation:

Answer: The second number goes on your X axis and the first number goes on your Y axis .

Step-by-step explanation:

(0,0)=Y,X

Answer:

which one substitution or elimination

Step-by-step explanation:

Substitution: (-1,-3 )

Elimination: (-1,-3)

i hope this helps you :)

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