someone help me ASAP

(i) Every entry not on the diagonal of \(P^2\) must be 0. For instance, the (1, 2)-th entry in \(P^2\) is

\(\begin{pmatrix}-\dfrac12&a&a\end{pmatrix}\begin{pmatrix}a\\-\dfrac12\\a\end{pmatrix} = -a+a^2\)

All other non-diagonal entries have the same value. Then

\(-a+a^2 = a(a-1) = 0 \implies \boxed{a=0 \text{ or }a=1}\)

Meanwhile, the diagonal entries are

\(\begin{pmatrix}-\dfrac12&a&a\end{pmatrix}\begin{pmatrix}-\dfrac12\\a\\a\end{pmatrix} = \dfrac14+2a^2\)

(ii) Since \(P^2\) is diagonal, the determinant is simply the product of the entries along the diagonal. If a = 0, these entries are each 1/4, so that

\(|P^2| = \left(\dfrac14\right)^3 = \boxed{\dfrac1{64}}\)

If a = 1, they are 9/4, so that

\(|P^2| = \left(\dfrac94\right)^3 = \boxed{\dfrac{729}{64}}\)

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C

The given diagram is a triangle with the following sides

Hypotenuse = AC = 18

m<A = 68 Degrees

We need to determine the measure of a, b and m<C

Using the trigonometry identity

sin 68 = a/18

a = 18sin68

a = 16.7

Similarly;

cos68 = c/18

c = 18cos68

c = 6.7

Since the sum of angles in a triangle is 180 degrees, hence:

m<C = 90 - m<A

m<C = 90 - 68

m<C = 22 degrees

Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.

Learn more on triangles here: https://brainly.com/question/1058720

#SPJ1

cosine = adjacent / hypotenuse

So that means the adjacent side = 15 and the hypotenuse = 17

By Pythagorean Theorem, we know that

opposite^2 = hypotenuse^2 - adjacent^2

opposite^2 = 17^2 - 15^2

opposite^2 = 289 - 225

opposite^2 = 64

opposite side = 8

sine = opposite / hypotenuse

So,

sine A = 8 / 17

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

For more such questions on equation.

https://brainly.com/question/16949303

#SPJ11

Answer:

see explanation

Step-by-step explanation:

The most likely error is adding the exponents instead of multiplying them, that is

\((a^{m}) ^{n}\) = \(a^{mn}\) , then \((3^{3}) ^{1}\) = \(3^{3(1)}\) = 3³ = 27

However

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\) ← the student may have used this definition to obtain 81

The simplified ratio of total marbles to red marbles is 27 to 8

In this question, we have the following parameters

Blue marbles = 24

Red marbles = 16

White marbles = 14

The above parameters mean that

Total marbles = sum of the individual marbles

Substitute the known values in the above equation, so, we have the following representation

Total marbles = 24 + 16 + 14

Evaluate

Total marbles = 54

The ratio is then represented as

Ratio = Total : Red

This gives

Ratio = 54 : 16

Simplify ratio

Ratio = 27 : 8

Hence, the simplified ratio is 27 : 8

Read more about ratio at

brainly.com/question/1781657

#SPJ1

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer: 71.57

Step-by-step explanation:

You are going to use SOH CAH TOA to find the angle

because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)

TanΘ=\(\frac{9}{3}\)

now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)

71.57

Answer:

1

Step-by-step explanation:

Answer:17

Step-by-step explanation:

its just the order of operations aka PEMDAS If you want to know more about the order of operations just look it up. :)

Answer:

He can get 5 whole pieces at 3/4 of a foot long because 3/4 times 5 equals 3 and 3/4.

Step-by-step explanation:

Hope this helps . . . <3

Answer:

185 ove r198

Step-by-step explanation:

Probability at least one will have a defect = 1 - probability (none will have a defect) = 1 - C(7,0) (0.03)^0 (0.97)^7 = 1 - 0.808 = 0.192.

The probability that at least one product will have a defect is 0.52.

A probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

Given is a manufacturing machine has a 10% defect rate.

The binomial probability can be calculated using the formula -

P(X = x) = C(n, x) pˣ (1 - p)ⁿ ⁻ ˣ

defect rate = 10% = 10/100 = 0.1 = p

Now, the probability that at least one will not have a defect can be calculated using -

P(X = 0) = C(7, 0)(0.1)⁰(0.9)⁷ = 1 x 1 x 0.48 = 0.48

Then, the probability that at least one will have a defect = 1 - P(X = 0)

1 - P(X = 0)

1 - 0.48

0.52

Therefore, the probability that at least one will have a defect is 0.52.

To solve more questions on Binomial Probability Distribution, visit the link below-

https://brainly.com/question/21883407

#SPJ2

Answer:

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

Step-by-step explanation:

Slope is calculated using the formula \(\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\).

To solve this problem, take two points and plug them into this equation.

For this example, I'll use (0,1) and (2,0).

This means \(x_{1} = 0, y_{1} = 1, x_{2} = 2,\) and \(y_{2} = 0\).

Plugging them into the equation, you'd get:

\(\frac{0-1}{2-0}\) which simplifies to \(-\frac{1}{2}\).

Therefore, the slope of the line represented by the table is m = \(-\frac{1}{2}\).

Answer:

82%

Step-by-step explanation:

0.82x100=82

=82%

Hope this helps

Answer:

B. 82%

Step-by-step explanation:

.82 can also be written as 82/100 and 82/100 can be turned into 82% because they are all based on 100

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

YU = 4.82.  angle STR = 23°

Step-by-step explanation:

7) Angle between U and V = 72°, since angles on a straight line add up to 180°. so angle UV = 180 - 108 = 72°.

similarly, angle YU = 180 - 85 - 72 = 23°.

length of circumference of full circle = π X diameter = π (2r)

= 2πr (radius = half of diameter).

circumference = 2π(12) = 24π.

there are 360° in full circle.

remember that angle YU = 23°.

length YU = (23/360) X 24π

= (23π)/15

= 4.817

= 4.82 to nearest one hundredth.

8) triangle RST sits inside of half the circle, ie in the semicircle.

angle RST = 90° because the angle in a semicircle =  90°.

there are 180° in a full triangle.

since angle RST = 90°, angle STR must be less than 180 - 90.

angle STR < 90°. so STR must be 23°.

The probability of those that favors building the health center is 0.196

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.

According to the scenario, 70% of the community favoured in building a health centre.

Hence , p=0.7.

In order to find the probability, binomial theorem will be used as follows :

= 0.196

Hence, The probability is 0.196

Learn more about the probability at:https://brainly.com/question/13604758

#SPJ1

The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To know more about Confidence interval visit: https://brainly.com/question/29680703

Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

For more such questions on quadrilaterals

https://brainly.com/question/27991573

#SPJ8

Answer:

The answer is in the picture above

9514 1404 393

Explanation:

1: fill the 3-gallon jug, empty it into the 5-gallon jug. Fill the 3-gallon jug again, and finish filling the 5-gallon jug from the 3-gallon jug. The 3-gallon jug will hold 1 gallon. (3×2-5=1)

2: fill the 5-gallon jug, fill the 3-gallon jug from it. The 5-gallon jug will hold 2 gallons. (5-3=2)

3: fill the 3-gallon jug. It will hold 3 gallons.

4: fill the 5-gallon jug, fill the 3-gallon jug from it. Dump the 3-gallon jug and empty the remaining 2 gallons from the 5-gallon jug into it. Fill the 5-gallon jug and finish filling the 3-gallon jug from it. The 5-gallon jug will hold 4 gallons. (5×2-3×2=4)

5: fill the 5-gallon jug. It will hold 5 gallons.

6: fill the 3-gallon jug, empty it into the 5-gallon jug. Fill the 3-gallon jug again. The jugs hold a total of 6 gallons. (3×2=6)

7: Do the procedure for 4 gallons. The jugs together hold 7 gallons. (5×2-3=7)

8: fill both jugs. Together, they hold 8 gallons. (5+3=8)

Answer:

X = 9

Step-By-Step Explanation:

Log3 x=2

Log(a) b=c

A(c) = b

So we can Take The original Question:

Log3 x=2

And rewrite it to:

3(2) = X = 9

x=2/3................................

a. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. The tennis ball is initially at a height of 126 feet above the ground.

a. The x-coordinate of the vertex is 2. To find the y-coordinate, we substitute this value back into the equation:

h(2) = -14(2)² + 56(2) + 126

h(2) = -14(4) + 112 + 126

h(2) = -56 + 112 + 126

h(2) = 182

Therefore, the vertex of the equation is (2, 182). In this context, the vertex represents the highest point reached by the tennis ball during its trajectory. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. In order to find the y-intercept, we set t equal to zero and evaluate h(t):

h(0) = -14(0)² + 56(0) + 126

h(0) = 126

The y-intercept is 126. In this context, the y-intercept represents the initial height of the ball when it is thrown. Therefore, the tennis ball is initially at a height of 126 feet above the ground.

Learn more about equations

https://brainly.com/question/2972832

#SPJ1

Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

To solve more questions on equation modelling, visit the link below-

brainly.com/question/6593383

#SPJ1

The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.

Take a look at the quadratic function:

f(x) = 2x^2 + 8x + 7

In this situation, a = 2 and b = 8, yielding:

f(x) = 2(x^2 + 4x) + 7

It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:

f(x) = 2(x^2 + 4x + 16 - 16) + 7

The expression inside the parenthesis can now be written as a perfect square:

f(x) = 2((x + 2)^2 - 16) + 7

Finally, the phrase is simplified by spreading the 2:

f(x) = 2(x + 2)^2 - 32 + 7

f(x) = 2(x + 2)^2 - 25

Learn more about functions on

https://brainly.com/question/10439235

#SPJ1

What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7

Answer:

57.5$

Step-by-step explanation:

5$ a pound, 11.5 pounds, multiply them and you get 57.5$

Answer:

45

Step-by-step explanation: