Let k be a real number and A = |k 1 - 2 10. 7 1 Then A is a singular matrix if Ok=15/2 k=5 O k=10 None of the mentioned

Answer:

-61 degrees F

Step-by-step explanation:

In each of the following situations, I will describe a sample space S for the random phenomenon involving a basketball player:

Situation 1: A basketball player shoots four free throws, and you record the sequence of hits and misses.

Step 1: The sample space S represents all possible outcomes for the number of baskets the basketball player makes out of the four free throws. The sample space consists of the numbers 0, 1, 2, 3, and 4, where each number represents the number of successful baskets made by the player. There are five possible outcomes in the sample space S.

Sample space S: {HHHH, HHMH, HHHM, HHMM, HMHH, HMMH, HMHM, HMMM, MHHH, MHMH, MHHM, MHMM, MMHH, MMMH, MMHM, MMMM}

Situation 2: A basketball player shoots four free throws, and you record the number of baskets she makes.

Step 2: The sample space S represents all possible outcomes for the number of baskets the basketball player makes out of the four free throws. The sample space consists of the numbers 0, 1, 2, 3, and 4, where each number represents the number of successful baskets made by the player. There are five possible outcomes in the sample space S.

Sample space S: {0, 1, 2, 3, 4}

In both situations, the sample space S is important for calculating probabilities and determining the likelihood of certain outcomes. By defining the sample space S, we can determine the probability of a specific outcome occurring and make informed decisions based on this probability.

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Answer:

150m^2

Step-by-step explanation:

Given data

a=8m

b=17m

h=12m

We know that the expression for the area of a trapezoid is given as

Area= (a+b/2)*h

substitute

Area= (8+17/2)*12

Area= 25/2 *12

Area= 12.5*12

Area= 150 m^2

Hence the area is 150m^2

Step-by-step explanation:

Assuming there are no other parts,

the Whole = A + B is the denominator:

Whole = 2 + 1 = 3

Part A = 2 and Part B = 1 are numerators for each fraction.

The fractions are then:

2/3 and 1/3

Meaning:

Part A is 2/3 of the whole

Part B is 1/3 of the whole

a.  4 is an extraneous root. , b. 0 is an extraneous root. , c. -3 is an extraneous root. , d. -13.21 is an extraneous root. , e. 9.22 is an extraneous root.

To solve the equation, we can begin by finding a common denominator for the fractions on the left-hand side. The common denominator is (x + 3)(x - 4). We can then rewrite the equation as follows:

[4x(x - 4) + 3(x + 3)] / [(x + 3)(x - 4)] = 5

Expanding and simplifying the numerator, we have:

[4x^2 - 16x + 3x + 9] / [(x + 3)(x - 4)] = 5

Combining like terms, we obtain:

(4x^2 - 13x + 9) / [(x + 3)(x - 4)] = 5

To eliminate the fraction, we can cross-multiply:

4x^2 - 13x + 9 = 5[(x + 3)(x - 4)]

Expanding the right-hand side, we get:

4x^2 - 13x + 9 = 5(x^2 - x - 12)

Simplifying further:

4x^2 - 13x + 9 = 5x^2 - 5x - 60

Rearranging the equation and setting it equal to zero, we have:

x^2 - 8x - 69 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation may not yield rational roots, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 8x - 69 = 0, we have a = 1, b = -8, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(-69))) / (2(1))

= (8 ± √(64 + 276)) / 2

= (8 ± √340) / 2

= (8 ± 2√85) / 2

= 4 ± √85

So, the possible solutions for x are x = 4 + √85 and x = 4 - √85.

Now, let's check which of the given options (a, b, c, d, e) are extraneous roots by substituting them into the original equation:

a. 4: Substitute x = 4 into the equation: 4(4)/(4 + 3) + 3/(4 - 4) = 5. This results in a division by zero, which is undefined. Therefore, 4 is an extraneous root.

b. 0: Substitute x = 0 into the equation: 4(0)/(0 + 3) + 3/(0 - 4) = 5. This also results in a division by zero, which is undefined. Therefore, 0 is an extraneous root.

c. -3: Substitute x = -3 into the equation: 4(-3)/(-3 + 3) + 3/(-3 - 4) = 5. Again, we have a division by zero, which is undefined. Therefore, -3 is an extraneous root.

d. -13.21: Substitute x = -13.21 into the equation and evaluate both sides. If the equation does not hold true, -13.21 is an extraneous root.

e. 9.22: Substitute x = 9.22 into the equation and evaluate both sides. If the equation does not hold true, 9.22 is an extraneous root.

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Answer:

no

Step-by-step explanation:

A: 360 -150 = 210 * (1+7%) = 224.7

B: 360 * 1.07  -150 =385.2 -150 =235.2

Answer:

(4x4) + (6x11) = 82 for area

4+4+10+11+7+6= 42

Step-by-step explanation:

You can calculate this by calculating the two squares separately, and on the bottom line, it is 10, so just subtract 4 to make the rectangle on the right, separate from the square on the left. (for area)

Answer:

Step-by-step explanation:

17 + 4 = 21

Answer:

B + 4 = 17+4

21 is the answer

Answer:

The slopes of three sides of triangle are as follows:

AB = -3

BC = 2/3

AC = -1/4

Step-by-step explanation:

The slope is denoted by m and is calculated using the formula

\(m = \frac{y_2-y_1}{x_2-x_1}\)

The given vertices are:

A(-2,4) B(-1,1) C(2,3)

The sides will be:

AB, BC, AC

Let m1 be the slope of AB

Let m2 be the slope of BC

Let m3 be the slope of AC

Now

\(Slope\ of\ AB = m_1 = \frac{1-4}{-1+2} = \frac{-3}{1} = -3\\Slope\ of\ BC = m_2 = \frac{3-1}{2+1} = \frac{2}{3}\\Slope\ of\ AC = m_2 = \frac{3-4}{2+2} = \frac{-1}{4} = -\frac{1}{4}\)

Hence,

The slopes of three sides of triangle are as follows:

AB = -3

BC = 2/3

AC = -1/4

Our confidence interval is (66, 102).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Now, here:

Mean, μ = 84

Standard deviation, σ = 9

It is a 95% confidence interval. We know that, within 2 standard deviations of the mean lies 95% of the population. Hence, z = 2.

Now, calculating μ - z.σ and μ + z.σ to find the intervals.

μ - z.σ  = 84 - 2x9 = 66

μ + z.σ = 84 + 2x9 = 102

Thus, our confidence interval is (66, 102).

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Answer:

455455

Step-by-step explanation:

do diddfdcv

Answer:

y2 - y1 / x2 - x1

Step-by-step explanation:

The SAS standard for similarity of triangles states that triangles are similar if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent.

Statement : The statement can be expressed as follows:

If two triangles ABC and DEF are such that

∠A=∠D and AC /DF =AB/DE

then △ABC∼△DEF

Proof :

Given: △ABC and △DEF are such that

AC /DF =AB/DE and ∠A=∠D

To Prove : △ABC∼△DEF

Construction : Draw a line PQ such that DP= AB , DQ= AC

In △ABC and △DPQ

AB = DP ( by construction)

DQ= AC ( by construction)

∠A=∠D (given)

=> △ABC ≅△DPQ (by SSA congruence property)

AB/DE = AC/DF (given )

=> DP/DE = DQ/DF ( using AB = DP ; DQ= AC)

=> PQ||EF (by converse of B.P.T)

Now , ∠P =∠E and ∠Q =∠F ( by corresponding angles)

△DEF ≅ △DPQ (Using AAS congruence )

=> △ABC ∼△DEF ( because two congrunt triangles are always similar )

Hence proved .

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Answer:

109m/s

Step-by-step explanation:

You idiot sandwich

Step-by-step explanation:

You have to find the decimals of them

So the 3rd on is correct

Correct order:-

A. 3/2 is not a proper fraction because it is greater than 1.

A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). In the fraction 3/2, the numerator (3) is greater than the denominator (2), which means it is not a proper fraction. This can be expressed as a formula using inequality symbols:

Numerator < Denominator

3 < 2

Since 3 is not less than 2, 3/2 is not a proper fraction.

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The rate of change of angle of elevation between the radar station and airplane is

                       \(\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)\)

The airplane is flying at the speed of 200 mph

The airplane is at an altitude of 3 miles over the radar station

The distance travelled by the airplane after 3 mins

      distance = speed x time

                     = 200 mi/hr x 3 min

Since the speed is hour let us convert it to mins

                     = 200 x 3 x 1/60

                     = 600 / 60

                    = 10 miles

So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles

Then the elevation angle of the between radar station and airplane can be find by

                              tan θ = O / A
where O is the opposite side to the angle of elevation

          A is the adjacent side to the angle of elevation.

But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time

                                \(\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}\)

                                        \(\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}\)

                                       \(\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}\)

The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.

                                   \(\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}\)

We had found the value of sec²θ = (hyp/adj)²

                                    \(\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}\)

Now , let us convert in terms of rad/min

                                   \(\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)\)

                                  \(\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)\)    

Therefore , the rate of change of angle of elevation is -10/109 (rad/min)    

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Answer:

\(\frac{7^2}{7^6}\)

If you have a negative exponent you must place it in the opposite part of the fraction.

Step-by-step explanation:

1/(7^6)*1/1/(7^2)

1/(7^6)*(7^2)/1

(7^2)/(7^6)

7^(2-6)

7^(-4)

1/7^4

The solution for the given inequality is 1 < m ≤ 4. The graph for the obtained solution set is shown below.

Two expressions are related by comparative operations like 'less than or 'greater than or 'less than or equal or 'greater than or equal. Then that equation is said to be an "inequality equation".

For example, a < k ≥ b, etc.

The given inequality equation is

-2 < 3m - 5 ≤ 7

On adding 5 to the inequality, we get

-2 + 5 < 3m - 5 + 5 ≤ 7 + 5

⇒ 3 < 3m ≤ 12

On dividing by 3, we get

⇒ 3/3 < 3m/3 ≤ 12/3

⇒ 1 < m ≤ 4

Therefore, the solution set for the given inequality is (1, 4].

The obtained solution set is shown on the number line here.

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The height of the shorter flagpole is 22.5 feet, given that the taller 30-foot flagpole casts a shadow of 20 feet and the shorter flagpole casts a shadow of 15 feet.

We have two flagpoles, a taller one and a shorter one. We are given the following information:

The taller flagpole is 30 feet tall, the taller flagpole casts a shadow of 20 feet, the shorter flagpole casts a shadow of 15 feet.

We want to find the height of the shorter flagpole, denoted as "h."

We can use the concept of similar triangles to solve this problem. Similar triangles have the same shape but can be different in size. In this case, the two flagpoles and their shadows form similar triangles.

Let's set up a proportion using the heights and shadows of the flagpoles: h / 15 = 30 / 20.

We know that the ratio of corresponding sides in similar triangles is equal. In this case, the ratio of the heights of the flagpoles is equal to the ratio of their shadows.

Now, we can solve the proportion to find the height of the shorter flagpole (h): h = (15 * 30) / 20

Simplifying the equation: h = 450 / 20

h = 22.5 feet. Therefore, the height of the shorter flagpole is 22.5 feet.

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Answer:

The coordinates of the point P  in the directed line segment from (-2,-8) to (5,-1) that partitions the segment into the ratio of 1 to 6 will be:

Step-by-step explanation:

Let P be the point.

As the point P is in the directed line segment from (-2,-8) to (5,-1) into the ratio of 1 to 6

i.e.

(x₁, y₁) = (-2,-8)

(x₂, y₂) = (5,-1)

Rise = y₂ - y₁ = -1 - (-8) = -1 + 8 = 7

Run = x₂ - x₁ = 5 - (-2) = 5 + 2 = 7

1 : 6 ratio means the point P lies at

\(\frac{1}{6+1}=\frac{1}{7}=14\%\)

Thus,

rise for P = 7 × 14% = 1

run for P =  7 × 14% = 1

Thus, coordinates of P will be:

x = -2 + 1 = -1

y = -8 + 1 = -7

Thus,

The coordinates of the point P  in the directed line segment from (-2,-8) to (5,-1) that partitions the segment into the ratio of 1 to 6 will be:

\(2 - 3csc(x) > 8 \\ 2 - \frac{3}{sin(x)} > 8 \\ - 6 > \frac{3}{sin(x)} \\ - 2 > \frac{1}{sin(x)} \\ \frac{ - 1}{2} < sin(x) \: \: or \: \: \: sin(x) > \frac{ - 1}{2} \\ \\ \)

\(sin( \frac{ - \pi}{6} ) = \frac{ - 1}{2} \)

\(x \: in \: \: [0, \frac{7\pi}{6}[U] \frac{11 \pi }{6} ,2\pi] + 2k\pi\)

Answer:

D. pi<x<7pi/6 and 11pi/6<x<2

Step-by-step explanation:

Took the test and this is the correct answer

The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.

Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.

This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.

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See attachment for math work and answer.

Answer:

Decrease of 4% ($4).

Step-by-step explanation:

Suppose the initial price was $100. An increase of 20% will make the price $120.

Now we decrease it 20% which brings it to 120 - 0.20 * 120

= 120 - 24

= $96.

So that's an overall decrease of $4 or 4%.

Answer:

8.   7x exponent 3 + x exponent 2 - x + 64

9.  x exponent 3 + 5x exponent 2 - x + 28

12.  -7x exponent 2 y exponent 2 - x exponent 3 + 5y exponent 3 + 13

** I hope this helps

Step-by-step explanation:

Answer:

Connor will earn more interest because he is getting compound interest.

Step-by-step explanation:

I have to assume in this case that the interest is 3.5% Per year:

Simple Interest = P(r + t)

{P = Principle, r = interest rate, t = time)

Wendy = $8,300 x (3.5% x 25)

Wendy = $7,262.50 (2 d.p)

Wendy = $8,300 + $7,262.50

Wendy = $15,562.50

Compound Interest = \(P (1 +r )^{t}\)

{P = Principle, r = interest rate, t = time)

Connor = $8,300 x \((1 + 0.035)^{25}\)

Connor = $19,614.93

Wendy's Interest = $15,562.50 - $8,300 = $7,262.50

Connor's interest = $ 19,614.93 - $8,300 = $11,314.93

Connor earned more interest by $4,052.43

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The shortest distance ladder that will reach from the ground, over the fence (4 ft tall) to the wall of the building (2 ft away) is 8.04 ft long.

The first step is to calculate the total height that needs to be reached by the ladder. The height of the fence (4 ft) is added to the distance between the fence and the wall of the building (2 ft). This gives a total height of 6 ft.Next, the length of the ladder is calculated using the Pythagorean theorem, which states that a2 + b2 = c2. The equation is rearranged to solve for c, the length of the ladder. In this case, a is equal to the height (6 ft) and b is equal to half the height (3 ft). This gives a result of c = 8.24 ft. This result is rounded to the nearest hundredth, giving a final result of 8.04 ft.

a2 + b2 = c2

62 + 32 = c2

36 + 9 = c2

45 = c2

√45 = c

c = 6.708 ft (rounded to 8.04 ft)

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