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Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1.

To find \( A \), start by multiplying both sides by \( (4A) \). Then, you will have \( (4A)^{-1}(4A)=\left[\begin{array}{ll} 5 & 2 \\ 4 & 2 \end{array}\right] \). This simplifies to \( \left[\begin{array}{ll} 5A & 2A \\ 4A & 2A \end{array}\right] \). Since the right side of the equation is equal to the identity matrix, we can conclude that the diagonal elements are equal to 1. This means that \( 5A=1 \) and \( 2A=1 \). Solving these two equations yields \( A=\frac{1}{5} \).

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The cross product of the first two vectors is -60.

The given vectors are: \( \left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right),\left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right),\left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) \).

To find the cross product of the first two vectors, we use the formula:

\(\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right) \times \left(\begin{array}{l}b_1 \\ b_2 \\ b_3\end{array}\right) = \left(\begin{array}{l}a_2b_3-a_3b_2 \\ a_3b_1-a_1b_3 \\ a_1b_2-a_2b_1\end{array}\right) \)

Plugging in the values from the given vectors, we get:

\(\left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right) \times \left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right) = \left(\begin{array}{l}(3)(4)-(4)(0) \\ (4)(5)-(1)(4) \\ (1)(0)-(3)(5)\end{array}\right) = \left(\begin{array}{l}12 \\ 16 \\ -15\end{array}\right) \)

Now, to find the dot product of this vector with the third given vector, we use the formula:

\(\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right) \cdot \left(\begin{array}{l}b_1 \\ b_2 \\ b_3\end{array}\right) = a_1b_1 + a_2b_2 + a_3b_3 \)

Plugging in the values from the vectors, we get:

\(\left(\begin{array}{l}12 \\ 16 \\ -15\end{array}\right) \cdot \left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) = (12)(0) + (16)(0) + (-15)(4) = -60 \)

Therefore, the final answer is -60.

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There will be 40 cans that contain between 11.95 and 11.98 ounces of drink.

To calculate this, the total number of cans in the delivery truck must first be divided by the total range of ounces in the cans (12.00-11.95 = 0.05). 1500/0.05 = 30000.

This number is then multiplied by the range of ounces being searched for (11.98-11.95 = 0.03). 30000*0.03 = 900.

Finally, the total number of cans is divided by the total range of ounces again (12.00-11.95 = 0.05). 900/0.05 = 40 cans.

Therefore, 40 cans contain between 11.95 and 11.98 ounces of drink.

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The probability that the next kite Barbara sells will be a diamond is:

To find the probability that the next kite Barbara sells will be a diamond, we need to divide the number of diamond kites sold by the total number of kites sold.

The formula for probability is

= required outcome (number of diamond kites) / possible outcome (total number of kites)

required outcome

The number of diamond kites sold is:

11

possible outcome

The total number of kites sold so far is:

11 + 9 + 6 + 4 = 30

Therefore, the probability that the next kite Barbara sells will be a diamond is 11/30

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Answer:

36πmm^2

Step-by-step explanation:

6mm^2=36mm

36mm×π=36πmm^2

The given angle measures 120 degrees, which is indeed an interior angle of a regular hexagon

What is hexagon ?

A hexagon is a six-sided polygon, which is a two-dimensional geometric shape with straight sides. The word hexagon comes from the Greek words "hexa" meaning "six" and "gonia" meaning "angle."

To find the value of x in the regular hexagon, we can start by noting that the interior angles of a regular hexagon are all congruent and measure 120 degrees.

Next, we can see that the given angle (11x + 21)° is an interior angle of the hexagon. Therefore, we can set this angle equal to 120 degrees and solve for x:

11x + 21 = 120

11x = 99

x = 9

Therefore, the value of x is 9.

Note that we can check our answer by substituting x = 9 into the original equation:

11x + 21 = 11(9) + 21 = 120

Therefore, the given angle measures 120 degrees, which is indeed an interior angle of a regular hexagon

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Answer:

(7,4)

Step-by-step explanation:

Reflection across x-axis is making the y value the opposite of what it was prior. (x, y)→(x,-y)

That is the formula.

(Pls mark me brainiest if it's correct :)

The constant of proportionality, k, that relates the cost in dollars, y, to the number of tickets, x, is $62.30. The constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x, is 16. The circumference of the circle is approximately 23.876 feet.

1. To find the constant of proportionality, k, we need to divide the cost of the tickets by the number of tickets.
k = y/x = $498.40/8 = $62.30

Therefore, the constant of proportionality, k, is $62.30.

2. To find the constant of proportionality, k, we need to divide the number of cookies made by the number of cups of flour used.
k = y/x = 48/3 = 16

Therefore, the constant of proportionality is 16.

3. To find the circumference of a circle, we use the formula C = πd, where C is the circumference and d is the diameter.
C = π(7.6) = 23.876 feet

The measurement closest to the circumference of the circle in feet is 23.876 feet.

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Step-by-step explanation:

To fence a circular park with 3 rounds, we need to find the total length of wire required to go around the park 3 times.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, π is the constant pi, and d is the diameter.

Substituting the given diameter of the park (280 m) into the formula, we get:

C = π * 280 m

≈ 879.65 m

So the length of wire required to fence the park once is approximately 879.65 m.

To fence the park three times, we need to multiply this length by 3:

3 rounds of wire = 3 * 879.65 m

= 2638.95 m

Therefore, the length of wire required to fence a circular park of diameter 280 m with 3 rounds is approximately 2638.95 m.

Answer:

the meadian is 8

Step-by-step explanation:

The value of the middle-most observation is called the median of the data.

If the cost for using 21 HCF of water is $35.39.  the cost for using 56 HCF of water is  $82.64.

We can use the two given data points to find the slope and y-intercept of the linear function that represents the monthly cost of water use.

Let's use (21, 35.39) and (57, 83.99) as our two data points.

First, let's find the slope of the line:

slope = (y2 - y1) / (x2 - x1)

slope = (83.99 - 35.39) / (57 - 21)

slope = 48.6 / 36

slope = 1.35

Now that we have the slope, we can use either of the two data points to find the y-intercept. Let's use (21, 35.39):

y = mx + b

35.39 = 1.35 * 21 + b

35.39 = 28.35 + b

b = 35.39 - 28.35

b = 7.04

So the linear function that represents the monthly cost of water use is:

y = 1.35x + 7.04

where y is the cost (in dollars) and x is the amount of water used (in HCF).

Now we can use this function to find the cost for using 56 HCF of water:

y = 1.35x + 7.04

y = 1.35 * 56 + 7.04

y = 82.64

So the cost for using 56 HCF of water is  $82.64.

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The current thrοugh the 2.5 οhm resistοr is 2.4 A.

Electric current is defined as the rate οf flοw οf electric charge thrοugh any crοss-sectiοn οf a cοnductοr.

Tο calculate the current thrοugh a 2.5 οhm resistοr cοnnected acrοss a 6.0 V pοtential difference, we can use Ohm's law, which states that the current thrοugh a cοnductοr between twο pοints is directly prοpοrtiοnal tο the vοltage acrοss the twο pοints, and inversely prοpοrtiοnal tο the resistance between them. The mathematical expressiοn fοr Ohm's law is:

V = I x R

where V is the vοltage, I is the current, and R is the resistance.

We can rearrange this fοrmula tο sοlve fοr the current I:

I = V / R

Substituting the given values, we get:

I = 6.0 V / 2.5 οhm

I = 2.4 A

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The volume of the silo is approximately 9,685.73 cubic feet.

What is volume of a cylinder?

The volume of a cylinder can be calculated using the formula:

[tex]V = \pi r^2h[/tex]  where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

We are given that the diameter of the silo is 17 feet. The radius, which is half the diameter, is therefore:

r = 17/2 = 8.5 feet

We are also given that the height of the silo is 42 feet.

Using the formula for the volume of a cylinder, we can calculate the volume of the silo:

[tex]V = \pi r^2h[/tex]

[tex]= \pi(8.5)^2(42)[/tex]

≈ 9,685.73 cubic feet

Therefore, the volume of the silo is approximately 9,685.73 cubic feet.

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The polynomial for the number of miles between the two cars is d(t) = 5t + 150

Given that

Car A: 7t²+50t+150

Car B: 7t²+45t

The distance function is represented as

d(t) = 7t²+50t+150 - 7t² - 45t

So, we have

d(t) = 5t + 150

This means that t =3

So, we have

d(3) = 5 * 3 + 150

d(3) = 165

This means that d(t) = 200

So, we have

5t + 150 = 200

Evaluate the difference

5t = 50

So, we have

t = 10

Hence, the time is 10 hours

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Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41

What is purchase price?

The complete cost of purchasing an asset is known as the original cost. The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.

To determine which of Ann's investments has increased in value more, we need to compare the current value of the bonds and the stock to their original purchase value.

First, let's calculate the purchase price of the bonds:

7 bonds x $500 par value x 0.95626 market rate = $3,349.82

So, Ann initially invested $3,349.82 in the Cilla Shipping bonds.

Next, let's calculate the purchase price of the stock:

125 shares x $28.00 per share = $3,500.00

So, Ann initially invested $3,500.00 in the Cilla Shipping stock.

Now, let's calculate the current value of the bonds:

7 bonds x $500 par value x 1.06384 market rate = $37,286.48

So, the current value of the bonds is $37,286.48.

Let's also calculate the current value of the stock:

125 shares x $30.65 per share = $3,831.25

So, the current value of the stock is $3,831.25.

To determine which investment has increased in value more, we can calculate the percentage increase for each investment:

Percentage increase in bonds = [(current value - purchase price) / purchase price] x 100%

= [(37,286.48 - 3,349.82) / 3,349.82] x 100%

= 1010.46%

Percentage increase in stock = [(current value - purchase price) / purchase price] x 100%

= [(3,831.25 - 3,500.00) / 3,500.00] x 100%

= 9.48%

So, we can see that the bonds have increased in value more than the stock, by a significant amount.

The bonds have increased in value by 1,010.46%, while the stock has increased in value by only 9.48%. The bonds have increased in value by a total of $33,936.66 ($37,286.48 - $3,349.82), while the stock has increased in value by a total of $331.25 ($3,831.25 - $3,500.00).

Therefore, Ann's investment in Cilla Shipping bonds has increased in value more, by $33,605.41 ($33,936.66 - $331.25).

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The solution to the all given equations is that they have infinite many real solutions

Equation (a)

From the question, we have the following parameters that can be used in our computation:

√(x^2-14x+49)=x-7

When both sides of the equations are squared, we have:

x^2 - 14x + 49 = x^2 - 14x + 49

Evaluate the like terms

0 = 0

This represents infinite many solutions

Equation (b)

Here, we have:

√(4x^2-20x+25)=5-2x

When both sides of the equations are squared, we have:

4x^2-20x+25 = 25 - 20x + 4x^2

Evaluate the like terms

0 = 0

This represents infinite many solutions

For the remaining expressions, we have the following (using the above steps)

Equation (c)

√(y^4+2y^2+1) = y^2 + 1

y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1

0 = 0

Equation (d)

√(x^2+2x+1)=x+1

x^2 + 2x + 1 = x^2 + 2x + 1

0 = 0

Equation (e)

√(y^2-20y+100)=y-10

y^2 - 20y + 100 = y^2 - 20y + 100

0 = 0

Equation (f)

√(y^6-2y^3+1)=y^3-1

y^6-2y^3+1 = y^6-2y^3+1

0 = 0

Hence, the equations have infinite solutions

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The polynomial without fractions is 2x^4 + x^3 + 7x^2 + 4x - 4.

To make the polynomial contain only whole numbers, we need to find the least common denominator (LCD) of the fractions and multiply each term by the LCD.

The LCD of the fractions 1/2 and 7/2 is 2.

So, we multiply each term by 2 to get rid of the fractions:

2(x^4) + 2(1/2 x^3) + 2(7/2 x^2) + 2(2x) + 2(-2)

Simplifying the terms gives us:

2x^4 + x^3 + 7x^2 + 4x - 4

Therefore, the polynomial without fractions is 2x^4 + x^3 + 7x^2 + 4x - 4.

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0.2083335 is the Area of the triangle.

How do triangles work?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

                            180 degrees is the sum of the triangle's three angles. riangle derives from the Roman word triangulus, which means "three-cornered" or "having three angles," from the roots tri-, "three," and angulus, "angle or corner."

1 ft 1 in =  12 + 1 = 13 in

  the Area of the triangle = 1/2 * b * h

                                        = 1/2 *   1 * 0.416667

                                       = 0.416667/2

                                      = 0.2083335

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A/J≅B

The Fundamental Homomorphism Theorem states that for any homomorphism f from a ring A to a ring B, the kernel of f (the set of elements of A mapped to the identity of B) is an ideal of A. Applying this to the given problem, let A be a commutative ring and f:A→A be the homomorphism f(x)=x2. The kernel of f is J = {x∈A:x2=0}. Then J is an ideal of A.

To prove that (x+y)2=x2+y2 for all x,y∈A, consider (x+y)2 = (x+y)(x+y) = x2 + xy + yx + y2. Since A is commutative, xy=yx and so (x+y)2=x2+2xy+y2. Since 2xy=2yx, then (x+y)2=x2+y2, as desired.

Now, we can conclude that f is a homomorphism from A to A. In addition, B={x2;x∈A} is a subring of A, since for all x,y∈A, (x+y)2=x2+y2 and so x2+y2∈B. Moreover, since J is an ideal of A, A/J≅B.

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To find Pearson's correlation coefficient, we need to first calculate the means, standard deviations, and covariance of the given data. Let's first convert the heights in km to m for ease of calculation.

t (s) h (m)

0 25,000

5 28,000

10 30,000

15 31,000

25 33,000

30 34,000

(a) Pearson's correlation coefficient:

We can use the formula

r = (nΣxy - ΣxΣy) / sqrt[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]

where n is the number of data points, Σ is the sum, and x and y are the variables being compared (time and height, in this case).

Using the given data, we get:

n = 6

Σx = 85

Σy = 181000

Σx² = 1375

Σy² = 503,710,000

Σxy = 2,886,000

Substituting into the formula, we get:

r = (62,886,000 - 85181000) / sqrt[(61375 - 85²)(6503710000 - 181000²)]

r = 0.994

Therefore, Pearson's correlation coefficient is 0.994, indicating a strong positive correlation between time and height.

(b) Rocket's acceleration:

We can use the formula:

h = ut + (1/2)at²

where h is the height, u is the initial velocity (assumed to be 0), t is the time, and a is the acceleration.

Rearranging, we get:

a = 2h/t²

Using the final height of 34,000 m and the time of 30 seconds (when the rocket reaches this height), we get:

a = 2*34000/(30²)

a = 75.6 m/s²

Therefore, the rocket's acceleration is 75.6 m/s².

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well, the tax is cleary just 20.95 - 20 = 0.95, so 95 cents, now, if we take 20(origin amount) to be the 100%, what is 0.95 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 0.95& x \end{array} \implies \cfrac{20}{0.95}~~=~~\cfrac{100}{x} \\\\\\ 20x=95\implies x=\cfrac{95}{20}\implies x=4.75[/tex]

The fraction of the flowers in the bouquet are daffodils is   6/ 9f + 6

A fraction can be defined as the part of a whole number or variable.

The different types of fractions in mathematics are;

Ratio is defined as a comparison of two or more numbers indicating their sizes in relation to each other.

It shows the number of times one number contains another.

From the information given, we have that;

The ratio of lilies to daffodils to marigolds in a bouquet is 7f:6:2f.

Then, thte number of daffodils would be;

= 6/7f + f+ 2f

= 6/ 9f + 6

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Answer:
a. Y = X1 + X2 = 1(Heads) + 1(Heads) = 2
Z = X2 + X3 = 1(Heads) + 1(Heads) = 2
The joint probability mass function of (Y, Z) can be determined by multiplying the individual probabilities:
P(Y, Z) = P(Y) * P(Z)
P(Y, Z) = (2/8) * (2/8) = 1/16

b. Y and Z are not independent because they both include the result of the second coin toss (X2). If X2 is heads, both Y and Z will be affected, and if X2 is tails, both Y and Z will be affected. Therefore, the outcome of one variable affects the outcome of the other, meaning they are not independent.

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The lengths in the left side are proportional to the ones in the right side, with that we know that x = 10.

The lengths in the left side and the ones in the right side are proportional, such that the scale is k.

Then we can write:

21*k = 27

(x - 3)*k = (x - 1)

With the first equation, we can find the value of k, then we will get.

k = 27/21

Replacing that in the second equation we will get:

(x - 3)*27/21 = (x - 1)

Now we can solve this.

(x - 3)*27 = 21*(x - 1)

Now we can solve this for x.

27x - 81 = 21x - 21

27x - 21x = 81 - 21

6x = 60

x = 60/6 = 10

x = 10

That is the value of x.

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We can represent 1,250 raised to the power of three-fourths as the sum of its prime factors in order to write it in the simplest radical form:

1,250 = 2 × 5 × 5 × 5 × 5

Next, we can formulate the statement as follows by using the fact that (a b)c = ac bc:

[tex](2\times5^3)^3/4 = 2^{(3/4)} \times(5^3)^{(3/4)[/tex]

Now, by using the fourth root of 53, we can simplify the statement underneath the radical:

[tex](2\times5^3)^3/4 = 2^{(3/4)} \times5^{(9/4)[/tex]

As a result, the value under the radical is 5(9/4), or the fifth root of five multiplied by nine. 5 being a prime integer prevents any further simplification of this phrase.

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Answer:

5

Step-by-step explanation:

The answer above is correct.

a)1.597

b)0.1101

c)The population proportion is not equal to 0.14

The test statistic for this sample is 1.597. The corresponding p-value is 0.1101. The p-value is greater than alpha, so the decision is to fail to reject the null. As such, the final conclusion is that there is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.14. This conclusion is based on the Binomial Distribution and Statistic, which use the p-value to assess the evidence against the null hypothesis.

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Answer:

I think it is 0.68. Try that. If not sorry.

This is shorter than the path made up of the two shortest sides by 33%.

In the case where ABC is an equilateral triangle, the point S is the center of the triangle. The total length of the network in this case is the sum of the lengths of the three sides (AS, BS, and CS) of the triangle, which is 3 times the length of a single side.

This is shorter than the path made up of the two shortest sides by 33%,

since the total length of the path made up of the two shortest sides is the sum of the lengths of the two sides, which is 2 times the length of a single side.

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Answer: 80 meters wide and 100 meters long.

Step-by-step explanation:

Well, if the park has to have a larger area, but the same perimeter, all you need to do in this case is turn 70 to 80 and 110 to 100.

80 + 80 + 100 + 100 = 360 meters in perimeter

70 x 110 = 7700

80 x 100 = 8000   ← This has greater area than the park above