You start at (-4, 0). You move left 1 unit and down 5 units. Where do you end?

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

To find the probability that at least 1 ball was​ red, given that the first ball was replaced before the second draw. Not replaced before the second draw:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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The complete question is given below:

Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was​ red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.

I'll focus on part (b) only.

======================================================

Explanation:

Replace the variable b with the commonly used variable x and c with some other constant, let's say the letter m. These replacements will become apparent when we use the quadratic formula shortly later on.

After the replacements are made, we have -3c²-4cb+4b²​ turn into -3m²-4mx+4x²​

This is the same as 4x²​-4mx-3m²

Compare this to the format of ax²​+bx+c

We can see that

Once again, m is constant.

Let's compute the discriminant.

[tex]d = b^2 - 4ac\\\\d = (-4m)^2-4(4)(-3m^2)\\\\d = 16m^2+48m^2\\\\d = 64m^2\\\\[/tex]

This discriminant is under the square root as part of the quadratic formula.

So 4x²​-4mx-3m² would have roots of...

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-b\pm\sqrt{d}}{2a}\\\\x = \frac{-(-4m)\pm\sqrt{64m^2}}{2(4)}\\\\x = \frac{4m\pm\sqrt{(8m)^2}}{8}\\\\x = \frac{4m\pm 8m}{8}\\\\x = \frac{4(m\pm 2m)}{4*2}\\\\x = \frac{m\pm 2m}{2}\\\\x = \frac{m+ 2m}{2} \ \text{ or } \ x = \frac{m-2m}{2}\\\\x = \frac{3m}{2} \ \text{ or } \ x = \frac{-m}{2}\\\\[/tex]

The whole time, the term "m" is treated as a constant. It is fixed to some unchanging number.

So why did we go through all that trouble to use the quadratic formula in the first place? It turns out that this formula is helpful to factoring quadratics. Recall that the roots of a polynomial tie very closely to its factorization.

For example, x²-4 factors to (x-2)(x+2) to have roots of x = 2 or x = -2. You could use the quadratic formula to solve x²-4 = 0 or x²+0x-4 = 0 and you should get x = 2 or x = -2 as the two solutions.

Anyways, back to the problem at hand.

Let's use the first root we found to form one of the factors needed.

The idea is to do a bit of algebra to get everything to one side. If fractions are present, then multiply both sides by the LCD to clear them out. We need to have 0 isolated on its own side.

[tex]x = \frac{3m}{2} \\\\ 2x = 3m\\\\ 2x-3m = 0[/tex]

So (2x-3m) is one factor

Through similar steps, you would find that the root [tex]x = \frac{-m}{2}[/tex] yields the factor of (2x+m)

Therefore, the factors are (2x-3m) and (2x+m)

------------------------------------

In summary so far, 4x²​-4mx-3m² factors to (2x-3m)(2x+m)

From here we replace x with b and replace m with c, so that we return back to the original variables used.

(2x-3m)(2x+m) becomes (2b-3c)(2b+c)

This can be confirmed using WolframAlpha. You could use the FOIL rule to expand out (2b-3c)(2b+c) and you should get 4b²​-4bc-3c²​ aka -3c²-4cb+4b²​

-------------------------------------

Those previous sections talked about part (i)

Part (ii) is where we plug in b = 4 and c = 3. In other words, we replace every copy of b with 4, and every copy of c with 3.

If you use the original expression, then,

-3c²-4cb+4b²​ = -3(3)²-4(3)(4)+4(4)²​ = -3(9)-4(12)+4(16) = -11

Or you could use the factored expression.

(2b-3c)(2b+c) = (2*4-3*3)(2*4+3) = (8-9)(8+3) = (-1)*(11) = -11

This very partially confirms that -3c²-4cb+4b² = (2b-3c)(2b+c) is indeed the case. Unfortunately you'd have to use infinitely many numeric examples to confirm the answer to part (i); however, something like the FOIL rule is far more efficient.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {z}^{2} - 14z + 48 }{ {z}^{2} + 6x - 27} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {z}^{2} - 8z - 6z+ 48 }{ {z}^{2} + 9z- 3z- 27} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {z(}^{} z- 8) - 6(z - 8) }{ {z}^{} (z+ 9)- 3(z + 9)} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {(}^{} z- 8) (z - 6) }{ {}^{} (z+ 9)(z - 3)} ÷ \cfrac{z -8}{z-3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ (z - 6) }{ {}^{} (z+ 9)}[/tex]

Break into two parts and simplify

[tex]\\ \rm\dashrightarrow \dfrac{z^2-14z+48}{z^2+6z-27}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{z^2-8z-6z+48}{z^2+9z-3z-27}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)}{(z+9)(z-3)}[/tex]

Now divide by the denominator

[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)(z-3)}{(z+9)(z-3)(z-8)}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{z-6}{z+9}[/tex]

The series is a convergent p-series with p = 3

We would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.

The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.

The value of [tex]\sqrt{9}= 3[/tex]

The formular for this is

∑[tex]\frac{1}{n^p} \\[/tex]

where n = 1

we know it is convergent because p is greater than 1. 3>1

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Answer: 4096.

Step-by-step explanation:

[tex](8^3)^8\div(8^4)^5=\\8^{3*8}\div8^{4*5}=\\8^{24}\div8^{20}=\\8^{24-20}=\\8^4=\\4096.[/tex]

By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of functions and these include the following;

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.  

Therefore, if log₁₀x < 1, then, x < 10.  Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

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The percentage of respondents who play only hockey is 27.24%.

According to the given question.

Total number of respondents = 2302

And, the number of reposdents who play only hockey = 627

Therefore,

The percentage of respondents said that they play only hockey

= (number of respondents who play only hockey/ total number of respondents)  × 100

[tex]= \frac{627}{2302} \times 100[/tex]

= 27.237 %

≈ 27.24%

Hence, the percentage of respondents who play only hockey is 27.24%.

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we can simply take the whole amount of 30 and divide it by (4 + 1), then distribute to each side accordingly, since they're in a 4 to 1 ratio.

[tex]\underset{\hspace{5em}4~\hfill to~\hfill 1\qquad }{\stackrel{\text{\LARGE 30}}{C\rule[0.35em]{18em}{0.25pt}E\rule[0.35em]{10em}{0.25pt}D}} \\\\\\ \stackrel{CE}{4\left( \frac{30}{4+1} \right)} ~~ : ~~ \stackrel{ED}{1\left( \frac{30}{4+1} \right)}\implies \stackrel{CE}{4\left( 6 \right)} ~~ : ~~ \stackrel{ED}{1\left( 6 \right)}\implies \stackrel{CE}{\text{\LARGE 24}} ~~ : ~~ \stackrel{ED}{\text{\LARGE 6}}[/tex]

Answer:

2, x - 2, x + 4

Step-by-step explanation:

The factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

From the question, we are to determine the each of the factors of the given quadratic expression

The given quadratic expression is

2x² - 4x - 16

Factoring

2x² - 4x - 16

First, factor out 2

That is,

2(x² - 2x - 8)

Now, we will factor x² - 2x - 8
x² - 2x - 8

x² - 4x + 2x - 8

x(x - 4) +2(x -4)

(x +2)(x -4)

Thus,

2x² - 4x - 16  = 2(x +2)(x -4)

Hence, the factors of the given quadratic expression, 2x² - 4x - 16, are 2, (x +2), and (x -4)

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Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.

From the question it is given that,

Carries family broke a package of graham crackers into 32 pieces.

Therefore total number of pieces will be 32 pieces.

carries two brothers each ate 1/8 of the pieces

This means that out of 32, 1/8 of the pieces were ate by the two brothers.

1/8 of 32 = 1/8 × 32 = 4 pieces

⇒ Carries two brothers each ate 4 pieces

the rest of the family ate 7/16 of the pieces

This means that out of 32, 7/16 of the pieces were ate by the rest of the family

7/16 of 32 = 7/16 × 32 = 14 pieces

⇒ the rest of carries family ate 14 pieces

remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces

⇒ there were 14 pieces remaining

Hence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.

carries two brothers each ate ____ pieces

the rest of carries family ate ____ pieces

there were ____ pieces remaining

Answer:

1  i(sqrt5)

2  7i

3  -9i

4  -64i

5  -5i(sqrt2)

6  -4i(sqrt3)

7  10i(sqrt3)

8  2i(sqrt2)

9  3i(sqrt7)

10  -30i(sqrt2)

Step-by-step explanation:

i is the square root of (-1). We can simplify each one as such.

The amount saved in 10 years is = $1,04,461.13

The correct option is B.

An annuity is a series of payments that are distributed evenly over time.

One way to express the future value of an annuity of payment P for n years is,

Total salary is $65000

The interest rate is 5.32%

Trent save 8%  of his salary every year.

Company puts  4.6% of salary every year.

[tex]\text { Future Value }=\mathrm{P} \times \frac{\left(1+\frac{i}{n}\right)^{n t}}{\frac{i}{n}}[/tex]

Given:

Total salary is $65000

The interest rate is 5.32%

Trent save 8% of his salary every year.

Company puts  4.6%of salary every year.

The 8% of salary is calculated as:

[tex]\text { Amount } &=\frac{8}{100} \times 65000\\[/tex]

               [tex]&=\$ 5200[/tex]

The following information is available on the company's put:

[tex]\text { Amount } &=\frac{4.6}{100} \times 65000\\[/tex]

                [tex]&=\$ 2990[/tex]

Total amount as follows:

[tex]\begin{aligned}\text { Amount } &=5200+2990 \\&=\$ 8190\end{aligned}[/tex]

The future value can be obtained as follows

[tex]\begin{aligned}\mathrm{FV} &=8190 \times \frac{(1+0.053)^{10}-1}{0.053} \\&=8190 \times 12.75 \\&=1,04,461.13\ \\\end{aligned}[/tex]

Hence, the amount saved in 10 years is = $1,04,461.13

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Formula for the circumference of a circle is

[tex]c = \pi \: d[/tex]

where c is the circumference, and d is the diameter.

When diameter is 27-in, then

[tex]c1 = \pi \times 27[/tex]

When diameter is 25-in, then

[tex]c2 = \pi \times 25[/tex]

.: 27π-in – 25π-in is the farther distance.

Finding the difference, we have:

2π ≈ 6.28

.: 6.28-in is our final answer.

Answer:

  50 miles/1 hour = 50 miles/hour

Step-by-step explanation:

The fraction is reduced by dividing numerator and denominator by their common factor of 2.

  100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour

Answer:

false

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The net of a cylinder has a rectangle for the lateral area and 2 circles for the bases, so it has 3 parts.

Answer: False

(a) The radius of the small sphere is 2 centimeters.

(b) The measure of the angle XAB is approximately 36.870°.

(c) The area of the shaded region is approximately 3.107 square centimeters.

Herein we have a geometric system formed by three big semicircles and a small circle, whose geometric diagram is attached below. (a) The relationship between the semicircles and the circle is represented by two formulae:

8² + h² = (8 + r)²     (1)

h + r = 8                  (2)

Where r is the radius of the small circle.

Then, we solve the system:

8² + (8 - r)² = (8 + r)²

64 + 64 - 16 · r + r² = 64 + 16 · r + r²

32 · r = 64

r = 2

The radius of the small sphere is 2 centimeters.

(b) The measure of the angle XAB is found by trigonometric relations:

cos m ∠ XAB = OA / AX

cos m ∠ XAB = 8 / 10

m ∠ XAB ≈ 36.870°

The measure of the angle XAB is approximately 36.870°.

(c) The area of the shaded region is the area of the triangle minus the area of the three circular sections:

A = 0.5 · (16 cm) · (10 cm) · sin 36.870° - (36.870° /180) · π · (8 cm)² - 0.5 · (106.260° / 180) · π · (2 cm)²

A ≈ 3.107 cm²

The area of the shaded region is approximately 3.107 square centimeters.

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Answer:

Graph b

Step-by-step explanation:

y = |x| is a "v"at x = 0

y = |x-1| is a "v" shifted to the right by 1 unit

The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).

Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:

f(x) = a · x² + b · x + c

f(x) = a · [x² + (b / a) · x + (c / a)]

f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]

f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²

If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.

The y-intercept is found by evaluating the quadratic equation at x = 0:

f(0) = a · 0² + b · 0 + c

f(0) = c

And the zeros are determined by the quadratic formula:

x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)

The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).

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Answer:

5/52

Step-by-step explanation:

There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.

The hypotenuse is [tex]c = a\sqrt{2}[/tex]  times the length of each leg 'a'. Triangle XYZ is a isosceles right triangle, therefore the Pythagoras theorem becomes  and this can be evaluated by using properties of isosceles triangle.

According to the statement

we have given that a theorem and we have to prove it.

So, For this purpose,

The given information is :

Isosceles triangle XYZ where [tex]Angle X = 45^{0}[/tex] [tex]Angle Y = 45^{0}[/tex] [tex]Angle Z = 90^{0}[/tex]

Let the sides of triangle XYZ be a, b, and c. Then side XY = c, YZ = b and ZX = a.

Now, it is given that triangle XYZ is isosceles triangle therefore, the shorter sides must be equal that is, a = b.

Now use Pythagoras theorem

[tex]a^{2} + b^{2} = c^{2}[/tex]

But here a= b then the equation become

[tex]a^{2} + a^{2} = c^{2}[/tex]

Then after solving it become

[tex]2a^{2} = c^{2}[/tex]

And here we have to find the value of the hypotenuse,

so we solve it for c.

Then

[tex]c = a\sqrt{2}[/tex]

From this it is clear that the

it can be concluded that the hypotenuse is  times the length of each leg 'a'.

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D box plot correctly represents the data

A box plot or boxplot is a technique for illustratively displaying the localization, dispersion, and skewness groups of numerical data through their quartiles.

Using a five-number summary (the minimum, first quartile (Q1), median, third quartile (Q3), and "maximum"), a boxplot is a common method of visualizing data distribution.

The median value for the provided data will be the sixth data point's value, or 3.

The median of the data's lower half is now the first quartile. The third data point's value of 1 will therefore be in the lower quartile.

The median of the data's upper half is now referred to as the upper or third quartile. This means that the value of the ninth data point, which is 6, will represent the upper quartile.

Thus, box-plot D effectively displays the data from above.

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Answer:

The answer is D.

Edg 2023.

The windmill's blade measures 7 feet in length.

To find the measure of the windmill's blade:

Therefore, the windmill's blade measures 7 feet in length.

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The correct question is given below:

The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

Answer: 18

Step-by-step explanation: 18=1+8=9

its complicated but when you check something like

23= 2+3 =5

 10 = 1+0=1

the individual digits of 18 are 1 and 8

Sum = 1+8=9

multiply 9 by 2 we get 18

18 is also a multiple of 9.

I hope this helps

The total surface area of the square pyramid (SA) = 144 yd².

A square pyramid is a solid shape that has a square base and four rectangular lateral faces.

The total surface area of a square pyramid is the sum of the area of its square base and four rectangular lateral faces. To find the total surface area, the following formula is used:

Total surface area of a square pyramid (SA) = A + 1/2(Pl), where:

Given the following:

Area of base (A) = 8² = 64 yd²

Perimeter of base (P) = 4(8) = 32 yds

Slant height of pyramid (l) = 5 yds

Plug in the values

Total surface area of a square pyramid (SA) = 64 + 1/2(32)(5)

Total surface area of a square pyramid (SA) = 64 + 80

Total surface area of a square pyramid (SA) = 144 yd².

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Answer:

Step-by-step explanation:

Use the distributive property.

Distributive property is a serving to distribute or allot or disperse.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

-10(1-9x)+6(x-10)

Expand.

-10(1-9x)

-10*1=-10

-10*9x=90x

[tex]\longrightarrow \sf{=-10+90x+6\left(x-10\right)}}[/tex]

6(x-10)

6*x=6x

6*10=60

6x-60

Rewrite the problem down.

= -10+90x+6x-60

Combine like terms.

90x+6x-10-60

Add the numbers from left to right.

90x+6x=96x

96x-10-60

Finally, subtract the numbers from left to right.

-10-60=-70

[tex]\Longrightarrow \boxed{\sf{96x-70}}[/tex]

Therefore, the final answer is 96x-70.

I hope this helps, let me know if you have any questions.

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Distributive Property :

[tex]-10(1-9x)+6(x - 10)[/tex]

[tex]-10(-9x+1)+6(x - 10)[/tex]

[tex]90x-10+6x-60[/tex]

[tex]90x-70+6x[/tex]

[tex]96x-70[/tex]

[tex]answer : \boxed{\pink\star\tt{96x-70}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━

Common factor :

[tex]- 10(1 - 9x) + 6(x - 10)[/tex]

[tex]96x - 70[/tex]

[tex]2(48x - 35)[/tex]

[tex] answer : \boxed{ \pink \star\tt{2(48x - 35)}}[/tex]

Answer:

First number = 33, Second number = -19

Step-by-step explanation:

We can use F to represent the first number and S to represent the second number.

Our two equations then are F + S = 14 and 2F + 3S = 9

We can use substitution:

[tex]F+S = 14\\2F+3S=9\\F=14-S\\2(14-S)+3S=9\\28-2S+3S=9\\28+S=9\\S=-19\\\\F-19=14\\F=33[/tex]

The computation shows that the time before

they can no longer communicate will be 10 minutes

From the information, it was stated that two hikerd are wandering through heavy woods with walkie talkies and that the walkie talkies have a range c of 100 yards.

It should be noted that after t hours, the distance between the hikers will be:

d² = (0.24t)² + (0.17t)² - 2(0.24t)(0.17t) cos 109.10°

d = 0.0568

Therefore, we will find the time when d = 0.0568. This will give a time of 10 minutes.

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The solution to 0.5^(x + 2) > 9 is x  > -5.170

The inequality expression is given as:

0.5^(x + 2) > 9

Take the logarithm of both sides of the inequality expression

log(0.5^(x + 2)) > log(9)

Rewrite the inequality expression as

(x + 2)log(0.5) > log(9)

Divide both sides by log(0.5)

x + 2 > -3.170

Subtract 2 from both sides

x  > -5.170

Hence, the solution to 0.5^(x + 2) > 9 is x  > -5.170

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Answer:

A     [tex] \dfrac{2x^3}{3yw} [/tex]

Step-by-step explanation:

[tex] \dfrac{xy(24x^2y^3w)}{36y^5w^2} = [/tex]

[tex] = \dfrac{2 \times 12 x^3y^4w}{3 \times 12y^5w^2} [/tex]

[tex] = \dfrac{2x^3}{3yw} [/tex]