the perimeter of a triangle is 41x. if the length of two sides are 18x and 7x, find the length of the third side in terms of x.

For a rectangle model of park, the ratio of length of rectangle model to the sum of the length and width in inches is equals to the 8:21. So, option(A) is right one.

We have an architect builds a model of a park in the shape of a rectangle. The dimensions are defined as

The length of rectangle model of park

= 40.64 centimeters

Width of rectangle model = 66.04 cm

There is one inch equals to the 2.54 centimeters. We have to determine the ratio of the length to the sum of the length and width in inches. Using the unit conversion, one inch = 2.54 centimeters

=> 1 cm = 1/2.54 inches

So, length of model in inches = \( \frac{1}{2.54} × 40.64 \) = 16 inches

Width of rectangle model in inches = \( \frac{1}{2.54} ×66.04\) = 26 inches

Now, the sum of length and width inches = 16 + 26 = 42 inches

The ratio of length to the sum of length and width in inches = 16 : 42

=> \( \frac{16}{42}\)

= \( \frac{8}{21}\)

Hence, required value is 8:21.

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Answer:

m = \(\frac{2-p}{n}\)

Step-by-step explanation:

Given

mn + p = 2 ( subtract 2 from both sides )

mn = 2 - p ( isolate m by dividing both sides by n )

m = \(\frac{2-p}{n}\)

The formula for the function is f(x) = 0(x-9)(x-6) / (x-8) = 0. So the function is f(x) = 0.

The given function y = x² - 6x + 8 can be written as y = (x-2)(x-4)/(x-4). Simplifying the expression, we get y = x-2 for x ≠ 4 and y is undefined for x = 4. Hence, the graph has a hole at x = 4.

To find a possible formula for the rational function with the given properties, we can start by writing it in factored form as:

f(x) = A(x-9)(x-6) / (x-8)

where A is a constant that we need to determine. We know that the function has a horizontal asymptote of y = -5, which means that as x approaches positive or negative infinity, the function approaches -5. This means that the degree of the numerator and denominator must be the same, and the leading coefficient must be A. So we can set:

f(x) = A(x-9)(x-6) / (x-8) = (-5)x^n / x^n

where n is the degree of the polynomial. Multiplying both sides by x^n and simplifying, we get:

A(x-9)(x-6) = -5(x-8)^n

We know that the zeros are at x=9 and x=6, so we can substitute those values into the equation:

A(9-9)(6-6) = -5(8-8)^n

0 = 0

This doesn't give us any information about A, so we'll need to use the vertical asymptote. We know that the denominator of the function is zero at x=8, so we can substitute that value into the equation:

A(8-9)(8-6) = -5(8-8)^n

-A(1)(-2) = 0

2A = 0

A = 0

Now we can write the formula for the function:

f(x) = 0(x-9)(x-6) / (x-8) = 0

So the function is f(x) = 0.

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if the roots of the polynomial function are -9 and 7 - i, then the other factor of the polynomial function is x - (7  + i)

The roots of the polynomial function are given as:

-9 and 7 - i

The root is 7 - i is a complex number.

This means that its conjugate must also be a root of the factor.

The conjugate of 7 - i is 7 + i

So, we have:

x = 7 + i

Equate to 0

x - (7  + i) = 0

Hence, the other factor of the function is x - (7  + i)

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Answer:

A on edge 23

Step-by-step explanation:

trust me bro

1.The expected value of X & Y is = 1/2.

2.The variance of X & Y is = 3/8 & 13/36 respectively.

3.The standard deviation of X and Y is 0.866 and 0.605 respectively.

The probability of guessing the correct answer for a single question is 1/4. Let X be the number of questions answered correctly by guessing. Since there are two questions, X follows a binomial distribution with n = 2 and p = 1/4.

The expected value of X is given by E(X) = np = 2 x 1/4 = 1/2.

The variance of X is given by Var(X) = np(1-p) = 2 x 1/4 x 3/4 = 3/8.

The standard deviation of X is the square root of the variance, which is given by sqrt(3/8) ≈ 0.866.

If one of the two questions can be narrowed down to three answer choices, then the probability of guessing the correct answer for that question is 1/3. Let Y be the number of questions answered correctly by guessing in this scenario. Since there are two questions, Y follows a binomial distribution with n = 2 and p = 1/3 for the narrowed-down question and p = 1/4 for the other question.

To find the expected value of Y, we need to calculate the probabilities for each possible outcome and multiply by the number of questions answered correctly in that outcome. The probability distribution table for Y is shown below:

Y P(Y)

0 (2/3) x (3/4) = 1/2

1 (1/3) x (3/4) + (2/3) x (1/4) = 5/12

2 (1/3) x (1/4) = 1/12

Therefore, the expected value of Y is E(Y) = 0 x 1/2 + 1 x 5/12 + 2 x 1/12 = 1/2.

The variance of Y is given by Var(Y) = np(1-p) + np'(1-p') = 2 x 1/3 x 2/3 + 2 x 1/4 x 3/4 = 13/36.

The standard deviation of Y is the square root of the variance, which is given by sqrt(13/36) ≈ 0.605.

Overall, the expected value of X & Y is = 1/2, the variance of X & Y is = 3/8 & 13/36 respectively and The standard deviation of X and Y is 0.866 and 0.605 respectively.

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Part A

The two factors are 5 and 4x+6.

Part B

The first factor, 5, has 1 term.

The second factor, 4x+6, has 2 terms.

Part C

The coefficient of the variable term is 4.

It should be noted that the number of hours slept will have to be plotted on the x-axis.

Also, the number of mistakes that was made will be plotted on the y-axis.

Each point on the scatterplot will represent one participant in the study.

It should be noted that to illustrate the two variables given in Table 1, we can create a scatterplot using R code.

In this case the number of hours slept will have to be plotted on the x-axis, and the number of mistakes made will be plotted on the y-axis.

Looking at the scatter plot, we can see that there is a general trend that more hours of sleep are associated with fewer mistakes made.

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Answer:

0.04kg

Step-by-step explanation:

Kinetic energy Formula: eK=0.5×m×v²

to work out mass

we can rearrange the formula and make it:

~m=eK÷(0.5×v²)

now insert the missing digits into the formula:

m=200÷(0.5×100²)

work it out, and you get your answer

m=0.04kg

Hopefully this helped-have a good day)

Applying the angles of intersecting chords and secants theorems, we would have:

1. m∠YZW = 129°

3. m(QS) = 256°

5. m∠EFG = 41°

7. m(CF) = 147°

9. x = 16

11. x = 8

12. x = 12

The angles of intersecting chords theorem states that the measure of the vertical angle formed when two chords intersect equals half the sum of the measure of the intercepted arcs.

The angles of intersecting secants theorem states that if two lines intersect outside a circle, the measure of the angle formed equals half of the difference of the measure of the intercepted arcs.

1. m∠YZW = 1/2(144 + 114) [angles of intersecting chords theorem]

m∠YZW = 129°

3. m(QS) = 2(m∠PQS) [central anglle theorem]

Substitute

m(QS) = 2(128)

m(QS) = 256°

5. m∠EFG = 1/2(121 - 39) [angles of intersecting secants theorem]

m∠EFG = 41°

7. m∠DEF = 1/2[m(CF) - m(DF)] [angles of intersecting secants theorem]

Substitute

53 = 1/2[m(CF) - 41]

2(53) = m(CF) - 41

106 = m(CF) - 41

106 + 41 = m(CF)

m(CF) = 147°

9. 5x - 7 = 1/2(119 + 27) [angles of intersecting chords theorem]

2(5x - 7) = 146

10x - 14 = 146

10x = 146 + 14

10x = 160

x = 160/10

x = 16

11. 2x + 7 = 1/2(78 - 32) [angles of intersecting secants theorem]

2(2x + 7) = 46

4x + 14 = 46

4x = 46 - 14

4x = 32

x = 8

12. m∠BCF = 1/2[m(ED) + m(BF)] [angles of intersecting chords theorem]

Substitute

11x - 9 = 1/2(9x - 3 + 15x - 39)

2(11x - 9) = 24x - 42

22x - 18 = 24x - 42

22x - 24x = 18 - 42

-2x = -24

x = 12

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Answer:

I believe a pyramid has A. 5 faces

Answer:

A. 5

Step-by-step explanation:

A. 5 faces

Answer:

$0.59 more than the candy necklace

Step-by-step explanation:

you subtract .90 from .31

The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

7.) This triangle is obtuse.

To see this, we can use the Pythagorean theorem:

4*4 + 5*5 = 16 + 25 = 41

6*6 = 36 m

Since 41 > 36, we know that the triangle is obtuse.

8.) This triangle is right.

To see this, we can again use the Pythagorean theorem:

11*11 + 12*12 = 121 + 144 = 265

15*15 = 225 m

Since 265 = 225 + 40, we know that the triangle is right.

9.) This triangle is also right.

We can use the same method as before:

30*30 + 40*40 = 900 + 1600 = 2500

50*50 = 2500 m

Since 2500 = 2500, we know that the triangle is right.

Therefore, The given triangles are obtuse , right angled and right angled.

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It is  false that the value 5pi/4 is a solution for the given equation.

1. Collect the like terms

2. make the trigonometry ratio the subject of formula

3. Find the inverse of the trigonometry.

Given that a solution for the equation 3\(\sqrt{2}\) sinФ + 2 = -1.

Collect the like terms

3\(\sqrt{2}\)  Sin Ф = -1 - 2

3\(\sqrt{2}\)  SinФ = -3

Sin Ф = -3 / 3\(\sqrt{2}\)

SinФ = -1/\(\sqrt{2}\)

Rationalize the RHS

SinФ = -1/\(\sqrt{2}\)  x \(\sqrt{2}\) /\(\sqrt{2}\)

Sin Ф = -\(\sqrt{2}\) /2

Sin Ф = - 0.707

Ф = \(Sin^{-1}\)(-0.707)

Ф = 45°

Change the degree to radian

45 x \(\pi\)/180

\(\pi\)/4

Therefore, it is false that the value 5pi/4 is a solution for the given equation.

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Answer:

It's True

Step-by-step explanation:

I just took the quiz and the answer is true.

a) For chi-squared distribution with v=3 degrees of freedom, the statistic that can be constructed using Xi's is:

X2 = Σ i=1 3 (Xi − i)2 / 3.

X2 has chi-squared distribution with 3 degrees of freedom.

b) For t-distribution with v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

T = (X1 − 1) / [(X2/2)0.5].

T has t-distribution with 2 degrees of freedom.

c) For F-distribution with v1=1 and v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

F = [(X1 − 1)/1] / [(Σi=2 to 3 Xi2) / 2].

F has F-distribution with 1 and 2 degrees of freedom.

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the estimated height of the butte is approximately 4.09 miles or 21,611.2 feet.

How to solve the problem?

To solve this problem, we can use the concept of trigonometry and set up some equations based on the given information.

Let's assume that the height of the butte is "h" miles. We can also define the distance traveled towards the butte as "d" miles.

From the given information, we can set up the following equations:

tan(5°) = h/d --------(1)

tan(25°) = h/(d-6) --------(2)

We can solve these two equations for "h" and "d" as follows:

From equation (1), we get:

h = tan(5°) x d

From equation (2), we get:

h = tan(25°) x (d-6)

Equating both the expressions of "h", we get:

tan(5°) x d = tan(25°) x (d-6)

Simplifying this equation, we get:

d = 6 / (tan(25°) - tan(5°)) ≈ 46.24 miles

Using equation (1), we can find the height of the butte in miles:

h = tan(5°) x d ≈ 4.09 miles

To convert this into feet, we can multiply it by 5,280:

h = 4.09 x 5,280 ≈ 21,611.2 feet

Therefore, the estimated height of the butte is approximately 4.09 miles or 21,611.2 feet.

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Answer:

  8.5 minutes

Step-by-step explanation:

You want to know the time Fwam can use an internet cafe computer for $11.80 if the linear cost is $5.80 for 1 minute and $7.40 for 3 minutes.

The slope of the cost function is ...

  m = (C2 -C1)/(t2 -t1) = (7.40 -5.80)/(3 -1) = 1.60/2 = 0.80

Then the cost equation can be written in point-slope form as ...

  C -5.80 = 0.80(t -1)

We want to know the time (t) for a cost C = 11.80. Using that value in the cost function, we can solve for t:

  11.80 -5.80 = 0.80(t -1)

  6.00/0.80 = t -1

  7.5 +1 = t

  t = 8.5

Fwam can use the computer for 8.5 minutes if he can pay $11.80.

Answer:

D. (9,3)

Step-by-step explanation:

y-3=3*(x-9)

if x=9, y=3

3-3=3*(9-9)      True

so D (9,3)

The correct choice is: A. Reject H0 if Zstat < -Z*

To determine the decision made in a two-tailed hypothesis test with a significance level of 0.05, we need to compare the critical value (Z*) with the test statistic (Zstat).

In this case, Z* is given as -1.52.

The decision rule for a two-tailed test with a significance level of 0.05 is as follows:

Reject H0 (null hypothesis) if Zstat < -Z* or Zstat > Z*

Since the given Zstat is -1.52, we need to compare it with -Z* and Z*.

If -1.52 is less than -Z* (which is the negative value of the critical value from the standard normal distribution table), then we reject H0.

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Answer:

$15

Step-by-step explanation:

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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Answer:

V = 50.3 in ^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius is 2 and the height is 4

V = (3.14) * (2)^2 * 4

V =50.24

Rounding to the nearest tenth

V = 50.3 in ^2

The length of the protein molecule, in meters, is 208 × 10⁻⁹m.

To find the length of the protein molecule:

Diameter of hydrogen atom = 104 × 10⁻¹⁰m

We are given that A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom.

Therefore, the length of the protein molecule, in meters, is 208 × 10⁻⁹m.

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The correct question is given below:

The diameter of a hydrogen atom is about 1.04 cross times 10 to the power of negative 10 end exponent meters. A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation?

Answer:

The speed at which the Westbound train is traveling is 45 miles per hour

Step-by-step explanation:

Here, we want to know the speed at which the Westbound train is traveling.

Now, let the speed of the westbound train be x mi/hr, what this means is that the speed of the east bound train will be (x-10) mi/hr since it’s 10 mi/hr slower.

Now, we are told that they pass each other 6 hours later

Mathematically, we know that distance = speed * time

The distance covered by the westbound train in 6 hours will be 6 * x = 6x miles

The distance covered by the Eastbound train in 6 hours will be 6(x -10) = (6x-60) mi/hr

Since both trains pass by each other at the 6 hour mark, it means they have both covered the distance of 480 miles between them at this time.

So by adding the individual distances, then we have a total of 480 miles

Thus, mathematically;

6x + 6x -60 = 480

12x = 480 + 60

12x = 540

x = 540/12

x = 45 mi/hr

Kernel of L = {0, Aeˣ}, where A is a constant and Range of L is the set of all possible polynomial of the form ax² + bx + c, where a, b and c are constants.

Given the linear transformation L is defined as,

L(p(x)) = p(x) - p'(x)

We have to find the kernel and range of the transformation L.

Kernel of the transformation L is the set of all possible p(x) for which L(p(x)) = 0 happens.

So, L(p(x)) = 0 gives

p(x) - p'(x) = 0

Now let p(x) = A eᵐˣ, where A and m are arbitrary constants.

So, A eᵐˣ - Am eᵐˣ = 0

A - Am = 0 [Since eᵐˣ = 0 cannot be possible]

A (1 - m) = 0

Either A = 0

Or, 1 - m =0

m = 1

So the solutions are, p(x) = 0 and p = Aeˣ

So, the kernel of L = {0, Aeˣ}, where A is a constant.

p(x) is defined on P2 so the set of all basics 1, x, x².

So, L(1) = 1 and L(x) = x - 1 and L(x²) = x² - 2x

So, the Range of L is the set of all possible polynomial of the form ax² + bx + c, where a, b and c are constants.

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Answer:

x=√3

Step-by-step explanation:

Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."

In mathematics, a variable is a symbol or letter that represents a quantity that can vary or change. Variables are used to express mathematical relationships and to represent unknown values.

For example, in the equation "y = 2x + 3", "x" and "y" are variables. "x" represents an unknown value that can vary, while "y" represents the output value that is dependent on the input value of "x".

Variables can take on different values depending on the context of the problem being solved. In algebra, variables are commonly used to solve equations and to represent unknowns in formulas.

It's important to note that variables are not the same as constants, which are values that remain fixed throughout a mathematical expression or equation.

by the question.

The appropriate measure of variability for the data represented by the box plot is the interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data, and it is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). In this case, the box extends from 17 to 21, with a line at 19, which means that Q1 is 17 and Q3 is 21. Therefore, the IQR is:

IQR = Q3 - Q1 = 21 - 17 = 4

So, the appropriate measure of variability for the data is the IQR, and its value is 4.

Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."

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The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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Answer:

wut is this????

I didn't get a thing

The lithosphere's reservoir of carbon is approximately 10^5.25 or about 177,828 times greater than the biosphere's reservoir of carbon. Rounding this to the nearest order of magnitude gives an answer of (b) 10⁶.

Carbon is one of the most important elements on Earth as it forms the building blocks for life and plays a crucial role in regulating the planet's climate. The carbon cycle is a complex process that involves the exchange of carbon between different reservoirs such as the atmosphere, oceans, biosphere, and lithosphere.

To compare the size of the carbon reservoirs in the biosphere and lithosphere, we can take the ratio of the two reservoirs:

Lithosphere/Biosphere = 100,005,500/560

Simplifying the expression on the right-hand side gives:

Lithosphere/Biosphere = 178,933.93

To convert this ratio to orders of magnitude, we can take the logarithm base 10 of the ratio:

log10(Lithosphere/Biosphere) = log10(178,933.93)

log10(Lithosphere/Biosphere) ≈ 5.25

Therefore, the lithosphere's reservoir of carbon is approximately 10^5.25 or about 177,828 times greater than the biosphere's reservoir of carbon.

Rounding this to the nearest order of magnitude gives an answer of (b) 10⁶.

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