Solve kx + 9 = 7 for x.
O A. X=-
--
k
O B. x=
x=
O C. X=
x=1
O D. X=-
---

Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

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We are asked to determine whether the set of all n by n skew symmetric matrices is a subspace of M₁(R), the vector space of all n by n matrices with real entries. Since the set of all n by n skew symmetric matrices satisfies all three conditions, it is a subspace of M₁(R).

To prove that the set of all n by n skew symmetric matrices is a subspace of M₁(R), we need to show that it satisfies three conditions: closure under addition, closure under scalar multiplication, and contains the zero matrix.

1. Closure under addition: Let A and B be two skew symmetric matrices. We need to show that A + B is also skew symmetric. Taking the transpose of A + B, we have (A + B)ᵀ = Aᵀ + Bᵀ. Since A and B are skew symmetric, we have Aᵀ = -A and Bᵀ = -B. Therefore, (A + B)ᵀ = -A - B = -(A + B), which shows that A + B is skew symmetric.

2. Closure under scalar multiplication: Let A be a skew symmetric matrix and c be a scalar. We need to show that cA is also skew symmetric. Taking the transpose of cA, we have (cA)ᵀ = cAᵀ. Since A is skew symmetric, we have Aᵀ = -A. Therefore, (cA)ᵀ = c(-A) = -cA, which shows that cA is skew symmetric.

3. Contains the zero matrix: The zero matrix is skew symmetric since its transpose is equal to itself.

Since the set of all n by n skew symmetric matrices satisfies all three conditions, it is a subspace of M₁(R).

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Answer:

5/22

Step-by-step explanation:

A bag has 6 blue marbles, 4 red marbles, and 2 green marbles. Wo marbles are randomly chosen without replacement.

Total number of marbles =

6 blue marbles + 4 red marbles + 2 green marbles

= 12 marbles

The probability of picking a blue marble = P(B) = 6/12

Therefore, the probablilty that both marbles picked are blue without replacement is

= 6/12 × 5/11

= 30/132

= 5/22

Answer:

3

Step-by-step explanation:

\(3+11t-9u\\\\\rightarrow\boxed{t = 9; u = 11}\\\\3+11(9)-9(11)\\\\3+99-99\\\\102-99\\\\\boxed{3}\)

Hope this helps.

Answer:

4

Step-by-step explanation:

I saw karma so i came as fast as I could- welp anyways

Lets test the first equation and coordinate #1 first, 3x-2y=12, and (10,9).

Here we can substitute x as 10 and y as 9, and solve the equation to see if 3(10)-2(9) equals 12 or not.

30-18=12, yep

now lets test the second coordinate, (0, -6). Substitute x as 0 and y as -6, and solve the equation.

3(0)-2(-6)=12

0+12=12, yep

So I definitely works

For II, lets do the same thing

(10, 9) -- 9=3/2*10-6

9=15-6, works

(0, -6) — -6= 3/2*0-6

-6=0-6, also works

So uh therefore I and II both work you see what I mean-

i apologize in advance if i made you more confused than you already are-

Answer:

There cannot be a triangle with sides a = 3, b = 4, and c = 100 because it would violate the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side.

Step-by-step explanation:

In this case, we have a + b = 3 + 4 = 7, which is less than c = 100. This violates the triangle inequality and therefore, a triangle cannot be formed with sides of length 3, 4, and 100.

To understand why the triangle inequality holds, consider drawing a triangle with sides a, b, and c. Then, we can use the Pythagorean theorem to relate the lengths of the sides:

a^2 + b^2 = c^2

We can rearrange this equation to get:

c^2 - a^2 = b^2

Now, since b is a side of the triangle, it must be positive. Therefore, we can take the square root of both sides of the equation to get:

sqrt(c^2 - a^2) = b

But we also know that b + a > c, so we can substitute b = c - a into this inequality to get:

c - a + a > c

which simplifies to:

a > 0

Therefore, we can conclude that c^2 - a^2 > 0, or equivalently, c > a. By a similar argument, we can also show that c > b. This proves the triangle inequality: c > a and c > b, which implies that a + b > c.

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Answer:?9

Step-by-step explanation:

i dont know

4

5

y6

wa

Answer:

20 minutes

Step-by-step explanation:

Find the speed per km. 2km/8min. This is 4 minutes per km.

Next, multiply the minutes per km by km. 4 min x 5 km.

This equals 20 :)

Therefore, the probability of selecting a red marble first, followed by another red marble, and then a green marble is 7/55.

The probability of selecting a red marble on the first draw is 7/11 since there are 7 red marbles out of 11 total marbles in the box.

After the first red marble is drawn and not replaced, there are 10 marbles left in the box, including 6 red marbles, 3 green marbles, and 1 grey marble. Therefore, the probability of selecting a second red marble on the next draw is 6/10 or 3/5.

Finally, after the second red marble is drawn and not replaced, there are 9 marbles left in the box, including 5 red marbles, 3 green marbles, and 1 grey marble. Therefore, the probability of selecting a green marble on the third draw is 3/9 or 1/3.

To calculate the probability of these three events occurring in succession, we multiply the individual probabilities together:

\((7/11) * (3/5) * (1/3) = 7/55\)

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The denominator of the next term in the given Geometric Sequence is 162.

We have been given the following Geometric Sequence whose first four terms are as follows: 1/2, 1/6, 1/18, 1/54

To find the denominator of the next term in the given Geometric Sequence, we need to find the common ratio between consecutive terms of the sequence.

This can be done by dividing any term in the sequence by its previous term or any term after it by its previous term. Therefore, let's divide the second term by the first term:

{1/6}/{1/2} = 1/6. 2/1 = 3

Thus, the common ratio between consecutive terms of the sequence is 1/3.

Now we can use the formula for the nth term of a geometric sequence, where a1 is the first term and r is the common ratio between consecutive terms. This formula is given by:

aⁿ = a₁ rⁿ⁻¹

We need to find the denominator of the next term in the sequence, i.e. the term with index n=5.

We can see that the first term is 1/2 and the common ratio is $1/3. Therefore, the fifth term can be calculated as follows:

a₅ = 1/2 1/3⁴ = 1/2 1/81

= 1/162

Therefore, the denominator of the next term in the given Geometric Sequence is 162.

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A hyperbola is the locus of focus in a plane with the end goal that the distinction of the distances to two fixed focuses called the foci is steady.

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

The equation of the hyperbola is given as,

x²/a² - y²/b² = 1

A hyperbola is homogeneous along its conjugate axis and resembles the ellipse in many ways. A hyperbola is subject to concepts like foci, directrix, latus rectus, and eccentricity. Examples of graphs of the function that are frequently seen include the path taken by the tip of a sundial's light, the dispersion route of elementary particles, etc.

A hyperbola is the locus of focus in a plane with the end goal that the distinction of the distances to two fixed focuses called the foci is steady.

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Answer:

0.3149608 in. wide

Step-by-step explanation:

1 milimeter=0.0393701 inches

8x0.0393701=0.3149608in. wide

Answer:

0.315 inches

Step-by-step explanation:

1 millimeter = 0.1 cm

2.54 cm = 1 in

Now convert 8 millimeters to inches

8mm x \(\frac{0.1 cm}{1 mm}\) x \(\frac{1 inch}{2.54 cm}\)  ; multiply across and divide and cancel units

\(\frac{0.8 inch}{2.54}\) = 0.315 inches

Waiter is given $10.52 and total bill including tax and tip = $67.33

Tip is the amount of money given by the customer himself so as to express the gratitude towards the hospitality from a particular service sector.

before tax paying cost for food = $52.60

sales tax rate is 8%

so, the amount of tax = $52.60 × 8/100 = $ 4.21

If 20% tip is given by customer, then the amount of tip =$52.60 × 20/100

amount of tip = $10.52

Waiter is given $ 10.52.

total bill including tax and tip = $52.60 + $4.21 + $10.52

                                               = $67.33

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Answer:

Step-by-step explanation:

v(x) - W(x) = x² + 2x  - 4 - [x³ + 2x² + x + 5]

                = x² + 2x - 4 - x³ - 2x² -x - 5

                = x² - 2x² - x³ + 2x - x -4 - 5

               =  -x² - x³ + x - 9

Answer:

x³ - 3x² + x - 9

Step-by-step explanation:

V(x) - W(x) =

- x² + 2x - 4 - (- x³ + 2x² + x + 5) ← distribute parenthesis by - 1

= - x² + 2x - 4 + x³ - 2x² - x - 5 ← collect like terms

= x³ - 3x² + x - 9

Answer:

SEE BELOW FOR ANSWER

Step-by-step explanation:

THE PROBLEM TELLS US JAMES AND THEN ELAINE

SO THE RATIO IS JAMES 2 AND ELAINE 3

JAMES RECEIVED 2 AND ELAINE 3

PLS MARK BRANLIEST IT WOULD HELP ME OUT ALOT TYSM GOD BLESS

The value of the product expression -3w⁸(-9w) is 27w⁹

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

-3w^8(-9w)

Rewrite the expression properly

This is represented as

-3w⁸(-9w)

Remove the bracket

So, we have the following representation

-3w⁸(-9w) = -3w⁸ * -9w

Evaluate the product of the constants

-3w⁸(-9w) = 27w⁸ * w

Evaluate the product of the variables

-3w⁸(-9w) = 27w⁹

Hence, the product is 27w⁹

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Answer:

870

Step-by-step explanation:

6190-5320=870

Answer:

870 (or 900)

Step-by-step explanation:

If you estimate you round:

6190- 6200

5320- 5300

6200- 5300= 900

Or you could do simple subtraction...

6190- 5320= 870

Answer:

Integer, Natural, Whole

Step-by-step explanation:

your to nice (:

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years.

a) The hypotheses that can be used to challenge the validity of the claim made by the shareholders' group.

H₀ : u ≤ 9

Hₐ : u > 9

So, the correct option is option (A).

b) T- statistic value is -2.571 for a sample of 90 companies.

c) The critical value for t i.e P-value is 0.0059

d) P-value < α = 0.01, implies reject the null hypothesis. We can conclude that the mean tenure of a CEO is significantly lower than 9 years. The claim of the shareholders group is not valid. So, the correct option is option(D).

We have given that,

x-bar= 7.27 , σ = 6.38, n = 90

a) Test that the mean tenure for a chief executive officer (CEO) was atleast nine years .

Null and alternative hypothesis is

H₀ : u <= 9

Hₐ : u > 9

b) test statistic:

t =( x-bar - μ ) /σ/√n

=> t = (7.27 - 9 )/6.38/90

=> t = - 1.73/0.67251

=> t = -2.571

c) P-value :

P-value = P( tₙ₋₁ < t) = P(t₉₀₋₁ < t )

=> P-value = P( t₈₉< - 2.571)

=>P-value = P( t₈₉ >2.571)

=> P-value = 1 - P( t₈₉< 2.571)

P-value = 1 - 0.9941 = 0.0059

d) Significance level, = 0.01

we see that p-value= 0.0059 < 0.01

Decision : Reject the null hypothesis H₀

We have no evidence to support the claim.

Hence, we calculate all the required result.

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Complete Question :

A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x = 7.27 yearsfor CEOs with a standard deviation of

s = 6.38 years.

(a)Formulate hypotheses that can be used to challenge the validity of the claim made by the shareholders' group. multiple choice:

i)H0: μ ≤ 9

Ha: μ > 9

ii)H0: μ ≥ 9

Ha: μ < 9

iii) H0: μ > 9

Ha: μ ≤ 9

iv)H0: μ < 9

Ha: μ ≥ 9

v) H0: μ = 9

Ha: μ ≠ 9

(b)Assume 90 companies were included in the sample. What is the test statistic? (Round your answer to three decimal places.)

c)What is the p-value for your hypothesis test? (Round your answer to four decimal places.)

p-value =

(d) At = 0.01,what is your conclusion? MULTIPLE CHOICE:

Answer:

Step-by-step explanation:

it is 2x

The scale factor from triangle V to triangle W is 48/7, implying that the related side lengths in triangle W are 48/7 times the comparing side lengths in triangle V.

We can compare the side lengths of the two triangles to determine the scale factor from triangle V to triangle W.

In triangle V, the side lengths are:

The side lengths of the triangle W are as follows:

VW = 7 cm

VX = 4 cm

VY = 6 cm

WX = 12 cm;

WY =?

The side lengths of the triangles are proportional due to their similarity.

We can set up an extent utilizing the side lengths:

Adding the values: VX/VW = WY/WX

4/7 = WY/12

Cross-increasing:

4 x 12 x 48 x 7WY divided by 7 on both sides:

48/7 = WY

From triangle V to triangle W, the scale factor is 48/7.

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The test score is 91.5.

z-score:

A z-score is the number of standard deviations from the mean value of the reference population.

Here we have to find the test score.

Mean(μ) = 90

Standard deviation(б) = 15

z-score = 0.1

Formula for z-score:

z = X - μ / б

Now putting the values in the equation:

0.1 = X - 90 / 15

1.5 = X - 90

X = 91.5

Therefore the test score is 91.5.

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The correlation coefficients and security returns provided suggest a relationship between security 1 and security 2.

The given information includes security returns and correlation coefficients between different securities. Based on the data, it is evident that there is a relationship between security 1 and security 2. The correlation coefficient P12 is -1, indicating a perfect negative correlation between the two securities. This means that when security 1's returns increase, security 2's returns decrease, and vice versa.

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The new functions are:

(f + g)(x) = 3x - 4

(g - h)(x) = 6x - 4

(f o g)(x) = 2x - 4

(g o h)(x) = -8x - 1

And the value of (f-g)(3) = -2.

To find new functions, we can combine the given functions using arithmetic operations.

(f + g)(x) = f(x) + g(x) = (x - 1) + (2x - 3) = 3x - 4

(g - h)(x) = g(x) - h(x) = (2x - 3) - (1 - 4x) = 6x - 4

(f o g)(x) = f(g(x)) = f(2x - 3) = (2x - 3) - 1 = 2x - 4

(g o h)(x) = g(h(x)) = g(1 - 4x) = 2(1 - 4x) - 3 = -8x - 1

To find (f-g)(3), we need to evaluate the function (f - g) at x = 3:

(f - g)(3) = f(3) - g(3) = (3 - 1) - (2(3) - 3) = 1 - 3 = -2

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The given question is incomplete, the complete question is

If  f(x) = x -1, g(x) = 2x - 3, and h(x) = 1 - 4x, find the following new functions, as well as any values (f-g)(3)

(f + g)(x)

(g - h)(x)

(f o g)(x)

(g o h)(x)

Answer:

D

........................

Answer:

Step-by-step explanation:

\((6 \times 183 )= 1098\)

A) Their graphs will be different from the graph of the linear parent function. B) In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends.

The y-intercept is the point where the graph of a function intersects with the y-axis. It is the point at which the value of x is 0.

Part A:

The linear parent function is represented by y = mx + b, where m is the slope and b is the y-intercept. The slope of the linear parent function is constant, while the y-intercept can vary.

In Jack's function, d = 0.05t, the slope is 0.05, which means that for every minute he runs, he travels 0.05 miles. The y-intercept is 0, which means that he starts at 0 miles.

In Jill's function, d = 0.04t + 0.5, the slope is 0.04, which means that for every minute she runs, she travels 0.04 miles. The y-intercept is 0.5, which means that she starts at 0.5 miles.

Both functions are linear, but they have different slopes and y-intercepts. Therefore, their graphs will be different from the graph of the linear parent function.

Part B:

Comparing Jack and Jill's functions to the linear parent function can give us insights into their race. The fact that their functions are linear means that they are running at a constant rate. However, the different slopes and y-intercepts mean that they are running at different rates and starting at different distances.

For example, we can see from their functions that Jack is running faster than Jill since his slope is larger. We can also see that Jill has a head start since her y-intercept is larger. By comparing their functions, we can make predictions about who will win the race or how far ahead one person will be at a certain time.

In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends. By understanding the relationship between variables, we can make informed decisions and predictions.

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Answer:

x = 31

So 2x-7 = 55

x + 4 = 35

Step-by-step explanation:

\(2x-7+x+4=90\\3x-3=90\\3x=93\\x=31\)