Describe a situation that can be represented by an equation and a situation that can be represented by an inequality. What features determine how the situation should be represented?

There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.

For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.

Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is

[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]

Answer:

sometimes

Step-by-step explanation:

a supplementary angle is "either of two angles whose sum is 180°".

So, x or y could be any degree, (less than 180 of course) and either one could be obtuse (>90) or acute (<90).

Answer:

take the dots and either put them together or rake them away

Step-by-step explanation:

Example: .....+..=....... five dots plus two dots equals seven dots.

......-...=... six dots minus three dots equals three since you are taking away three

i hope u found this helpful.

Circumference = diameter x PI

Circumference = 8 in x Pi

Circumference = 8PI in. (Exact)

Or as a decimal answer: 25.12 in.

Answer:

25.1 in (nearest tenth)

Step-by-step explanation:

Formula

Circumference = πd  (where d is the diameter)

From inspection of the diagram:

⇒ Circumference = 8π

                             = 25.1 in (nearest tenth)

The number of ways that Grant can arrange 3 of the 10 plants is 120 ways and the number of ways that 4 floats out of 8 can be arranged is 70 ways.

Grant can arrange 3 out of 10 plants in the following number of ways:

= 10!/ ((10! - 3!)3!)

= ( 10 x 9 x 8) / (3 x 2)

= 120 ways

The parade organizer can arrange 4 floats out of 8 as:

= 8!/((8! - 4!)4!)

= (8 x 7 x 6 x 5) / (4 x 3 x 2)

= 70 ways

When 4! is written in expanded form, it comes out as:

= (4 x 3 x 2)

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Answer:

The answer would be 5.

Step-by-step explanation:

To solve proportions, you multiply the denominator (6) by the numerator (15). 15 times 6 is equal to 90. You then divide 90 by the denominator (18) to get an answer of 5. I hope this helps you! Have a great day! :)

Using a t-distribution calculator, it is found that the critical value for the hypothesis test is of t = 1.3277.

The critical value is found considering three inputs:

Hence, for a two-tailed test, with a 0.2 significance level and 19 df, the critical value is of t = 1.3277.

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The banner attached to the archway will be at (1, 5) and (5.25, 3.938).

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The archway of the main entrance of a university is modeled by the quadratic equation

y = -x² + 6x ....1

The university is hanging a banner at the main entrance at an angle defined by the equation

4y = 21 − x ....2

Then the banner attached to the archway will be

From equations 1 and 2, we have

              4(-x² + 6x) = 21 - x

              -4x² + 24x = 21 - x

        4x² - 25x + 21 = 0

  4x² - 21x - 4x + 21 = 0

x(4x - 21) - 1(4x - 21) = 0

          (4x - 21)(x - 1) = 0

                             x = 5.25, 1

Then the value of y will be

When x = 5.25, then we have

y = -(5.25)² + 6(5.25)

y = 3.938

When x = 1, then we have

y = -(1)² + 6(1)

y = 5

The banner attached to the archway will be at (1, 5) and (5.25, 3.938).

The graph is given below.

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Answer:

5.656854249 cm

Step-by-step explanation:

Use the Pythagorean theorem to solve this (assuming that the bottom of the cup is a right angle). [tex]a^{2} +b^{2} =c^{2}[/tex]. a and b are sides, and c is the hypotenuse.

The length of the pencil would be the hypotenuse (c), and how tall the cup is (7 cm) would be one of the sides (a).     The diameter of the cup, would be the other side (b).

Plug this into the Pythagorean theorem to get the equation: [tex]7^{2} +b^{2} =9^{2}[/tex]. From here, we can find the diameter of the cup by isolating b - remove everything from the left side, but remember, what you do to one side you must do to the other.

First, solve all of the exponents: [tex]49+b^{2}=81[/tex]

Second, subtract 49 from both sides: [tex]b^{2}=32[/tex] This cancels out the 49 on the left.

Lastly, square root both sides: [tex]x=5.656854249[/tex] This cancels out the exponent on the left.

In conclusion, the diameter of the cup is 5.656854249 centimeters.

Answer:

B

Step-by-step explanation:

the hypotenuse........

Answer:

B

Step-by-step explanation:

The hypotenus is always opposite to the right and angle and always the longest side

There are 750 many outcome pairs you can have

The given parameters are:

Website 1 = 25

Website 2 = 30

The number of outcome pairs is calculated as:

Outcome = Website 1 * Website 2

So, we have:

Outcome = 25  * 30

Evaluate the product

Outcome = 750

Hence, there are 750 many outcome pairs you can have

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AND means multiply, so if probability is dependent on two things happening, then we will multiply the individual probabilities together.

1. P(A and 1) = 1/4 x 1/6 = 1/24

2. P(C and 2) = 1/4 x 2/6 = 2/24 = 1/12

3. P(B and 3) = 2/4 x 1/6 = 2/24 = 1/12

4. P(A and 4) = 1/4 x 2/6 = 2/24 = 1/12

5. P(C and 3) = 1/4 x 1/6 = 1/24

6. P(B and 2) = 2/4 x 2/6 = 4/24 = 1/6

7. P(a consonant and an odd #) = 3/4 x 2/6 = 6/24 = 1/4

8. P(a consonant and a prime #) = 3/4 x 3/6 = 9/24 = 3/8

9. P(a vowel and a 5) = 1/4 x 0/6 = 0

10. P(a vowel and a number less than 3) = 1/4 x 3/6 = 3/24 = 1/8

11. P(B and 1) = 2/4 x 1/6 = 2/24 = 1/12

Experimental probability is based on something that has already happened, or data that has already been collected.

12. P(1) = 3/30 = 1/10

13. P(2) = 8/30 = 4/15

14. P(3) = 7/30

15. P(4) = 5/30 = 1/6

16. P(5) = 3/30 = 1/10

17. P(6) = 4/30 = 2/15

Hope this helps!

The partial products of 5 * 1234 are 5 * 1000, 5 *200, 5 * 30 and 5 * 4

The product expression is given as:

5 * 1234

Express 1234 as the sum of numbers

5 * (1000 + 200 + 30 + 4)

Expand

5 * 1000 + 5 *200 + 5 * 30 + 5 * 4

Hence, the partial products of 5 * 1234 are 5 * 1000, 5 *200, 5 * 30 and 5 * 4

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It looks like the series could be

[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]

Recall that

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].

A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)

A) This is a parabolic graph and from the graph, we see that, the y-values remain the same from x-values of 0 to 15. Thereafter the x-values increases with a corresponding decrease in y-values until the vertex point before increase in x-values with corresponding increase in y-values.

A relationship could be: Battery percentage remains at the mark of 40 for the first 15 minutes of use. Thereafter, it begins to decrease parabolically until 45 minutes when it it is almost at 0 level and is charged before it starts to increase in a parabolic manner again for another 20 minutes when it increases linearly.

B) A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)

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The value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9

From the question, we are to determine the values of the missing sides

From the diagram,

Opposite = 9

Adjacent = y

Hypotenuse = x

Included angle = 45°

Using SOH CAH TOA, we can write that

[tex]tan 45^\circ= \frac{9}{y}[/tex]

[tex]1 = \frac{9}{y}[/tex]

∴ y = 9

Since the triangle is a right triangle, we can write that

x² = y² + 9² (Pythagorean theorem)

x² = 9² + 9²

x² = 81 + 81

x² = 162

x = √162

x = 12.7

Hence, the value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9

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Answer: 3ln4 + 3lna

Step-by-step explanation:

[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]

The height of the scale model 1.304 scale units.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Given:

The Bloomington Bank has a height of 163 meters.

Molly is making a scale model of this building using a scale of 125 meters.

125 meters = 1 scale unit

1 meter = 1/125 scale unit

So, for 163 meters = 1/125* 163

                              = 1.304 scale units.

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Answer:

below

Step-by-step explanation:

f. =. m²

------

3e

hope makes sense dive both sides by 3e to get f alone

The weighted average cost of capital for the firm will be 11.25%.

The weighted average cost of capital is the calculation of the cost of capital for a firm where each category of capital is weighted.

Here, the weighted average cost of capital will be:

= 0.5(10%)(1 - 15%) + 0.5(14%)

= 0.5(0.1)(0.85) + 0.5(0.14)

= 11.25%

The corporate value at 70% debt when WACC is 11.94% will be:

= (EBIT)(1 - T)/WACC

= (13.24)(1 - 0.15)/0.1194

= $94.26 million

The corporate value at 30% debt when WACC is 11.14% will be:

= (EBIT)(1 - T)/WACC

= (13.24)(1 - 0.15)/0.1114

= $101.02 million

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One possible interpretation of the results is that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts to achieve a total cost of $118.

To determine the amount of each type of nut the customer buys, we can set up a system of equations based on the given information.

Let's use the variables:

A = pounds of almonds

C = pounds of cashews

W = pounds of walnuts

From the given information, we can create the following equations:

A + C + W = 12 (since the customer buys a total of 12 pounds of mixed nuts)

7A + 10C + 12W = 118 (since the total cost of the nuts is $118)

W = C + 2 (since the customer buys 2 more pounds of walnuts than cashews)

We can now represent this system of equations as a matrix:

[1   1   1   12]

[7   10  12  118]

[0   -1  1   2]

To find the reduced row echelon form of this matrix, we can use Gaussian elimination or a similar method. Solving the system of equations represented by the matrix, we obtain the following reduced row echelon form:

[1   0   2   6]

[0   1   -3  4]

[0   0   0   0]

Now, let's interpret the results:

From the reduced row echelon form, we can deduce that there are infinitely many solutions to this system of equations. This means that there are multiple possible combinations of almond, cashew, and walnut quantities that satisfy the given conditions.

One possible interpretation of the results could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 0 pounds of walnuts. This satisfies the equation A + C + W = 12, and the total cost of nuts is $7 * 6 + $10 * 4 + $12 * 0 = $42 + $40 + $0 = $82. However, since the given total cost is $118, this interpretation is not valid.

Another possible interpretation could be that the customer buys 6 pounds of almonds, 4 pounds of cashews, and 2 pounds of walnuts. This satisfies all the given conditions. The equation A + C + W = 12 holds true, and the total cost is $7 * 6 + $10 * 4 + $12 * 2 = $42 + $40 + $24 = $106, which matches the given total cost of $118.

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Answer:

80 oz

Step-by-step explanation:

Answer:

yes it is

Step-by-step explanation:

It is a rational number, as it can be written as a fraction.

Step-by-step explanation:

|...| means absolute value of "...". that means always the "+" value of "...", even if it is negative.

in other words

|-x| = x

|x| = x

|-x - 2y| for x = -2 and y = 3

|- -2 - 2×3| = |2 - 6| = |-4| = 4

Answer:

40[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

V = L × W × H

V = 1.5 × 6 × 4.5

V = 40.5 or 40[tex]\frac{1}{2}[/tex]

Answer:

40 1/2ft

Step-by-step explanation:

H(4 1/2 )x W(1 1/2) = 6.75

HW(6.75)x L(6) = 40.5

Answer:

3 minutes per table

Step-by-step explanation:

15 minutes = 5 tables

to get how much it will be per table, divided both sides by 5

since 5 / x = 1 and x would be 5

15 / 5 minutes = 5 / 5 tables

3 minutes = 1 table

Answer:

step1:add 3y to both sides

step2:add 4 to both sides

step3:multiply both sides by(1/5)

14/15

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

A=12×11/2=66

Hope this helps:)

Answer:

g = 15

Step-by-step explanation:

Rearrange unknown terms to the left side of the equation: 3g - 2g = 15

Combine like terms: g = 15

Answer: g = 15