solve a+1= √b+1 for b

Answer:

Events A and B are independent but Event C is dependent on both Event A and Event B.

Step-by-step explanation:

Find whether events A, B and C are independent.

- Events A and B are independent of each other, because the appearance of an odd number on die X does not effect or influence the appearance of an even number on die Y.

- Event C, on the other hand, is dependent on both event A and event B. How?

For Event C to take place, one die will have to show an odd number while the other shows an even number.

NOTE: The odd number must not show up on die X and the even number show up on die Y. Both number types can appear on any die.

The key is just that one number must be odd and the other even; in order for their sum to be an odd number.

Answer:

t = log(2)/0.12  years (exact value)

= 5.776 years (to three decimal places)

Step-by-step explanation:

The future value of an amount P at continuous interest rate i% for t years can be calculated using the continuous interest formula:

FV = Pe^((i)t)

where e is the Euler's constant = 2.7182818284....

We're given

10000 = 5000 e^((0.12)t)

simplify

2 = e^(0.12t)   ........................ see below

[ please compare if this is the same as the one shown in the original question, the formula posted as  "2 = e 120" does not look right, probably because of typographical difficulties, then answer if the equation given in the question can be used to solve the problem]

take (natural) log using the power property of logarithms

log(2) = 0.12t log(e)

using natural log, log(e) = 1

log(2) = 0.12t

simplify

t = log(2)/0.12  years (exact value)

To obtain the time (in years)

t = log(2)/0.12 = 0.6931/0.12 = 5.7762 years

Check using the rule of 72 (approximate)

72/12(%) = 6,

Since continuous interest accumulates interest faster, so 5.8 years sound reasonable.

Answer:

(66.3-14.62)/0.6-0.22

(51.68)/0.6-0.22

(51.68/0.6)-0.22

(86.14667)-0.22

85.92667

Answer:

[tex]\boxed{y=|\frac{1}{2}x - \frac{3}{2}|+3}[/tex]

Step-by-step explanation:

The translation is a horizontal translation.

The graph is translated 1 unit to the left. So the value of x is added by 1.

[tex]f(x+1)[/tex]

[tex]y=|\frac{1}{2} (x+1)-2|+3[/tex]

[tex]y=|\frac{1}{2}x + \frac{1}{2} -2|+3[/tex]

[tex]y=|\frac{1}{2}x + - \frac{3}{2}|+3[/tex]

Answer:

We could rewrite 7/2 as 7a + 2

Step-by-step explanation:

Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.

Answer:

40 apples

Step-by-step explanation:

2 apples= [tex]\frac{1}{5}[/tex] grams

x apples= 4 grams

 8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40

Answer:

40

Step-by-step explanation:

edu instruction correct

Answer:

(3+2x)4  = 16x4+96x3+216x2+216x+81

Step-by-step explanation:

Answer:

(3+2x)^4

(3)^4+4(3)³(2x)¹+6(3)²(2x)²+4(3)¹(2x)³+(2x)⁴

81+216x¹+216x²+96x³+16x⁴

Answer:

[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

Part 1: Rewriting equation to match ax² + bx + c = 0 (quadratic function)

The given equation is not written in quadratic form. To rewrite the equation:

To overcome this difficulty, follow these mathematical steps:

[tex]2x^2=8x-7\\2x^2-8x=-7\\2x^2-8x+7=0[/tex]

Subtract 8x from both sides of the equation to rearrange it to the left side. Then, add 7 to rearrange it as well. Finally, set the three values on the left of the equation equal to zero.

Part 2: Using the quadratic formula

The quadratic formula is defined as [tex]\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }[/tex].

Using the parent quadratic function, the values are easy to find in the given equation. [tex]\boxed{a=2, b=-8, c=7}[/tex]

Substitute these values into the quadratic formula and solve for x.

[tex]x=\frac{8\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)} \\\\x=\frac{8\pm\sqrt{64-4(14)}}{4}\\\\x=\frac{8\pm\sqrt{64-56}}{4} \\\\x=\frac{8\pm\sqrt{8}}{4}\\\\x= 2\pm\frac{\sqrt{8}}{4}\\ \\x=2\pm\frac{\sqrt{2}}{2}[/tex]

Part 3: Solving for x with the values from the quadratic formula

Now that x is set equal to the simplified version of the equation, the operations have to be followed through with.

This equation will have two zeros/roots to solve for by setting x equal to zero.

Operation 1: Addition

[tex]x=2+\frac{\sqrt{2} }{2}\\\\x=\frac{4+\sqrt{2}}{2}[/tex]

Operation 2: Subtraction

[tex]x=2-\frac{\sqrt{2}}{2}\\ \\x=\frac{4-\sqrt{2}}{2}[/tex]

Because both values are the exact same (minus the operations), the roots can be simplified even further to one value:

[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]

Answer:

see explanation

Step-by-step explanation:

Under a rotation ( clockwise or anticlockwise ) about the origin of 180°

a point (x, y ) → (- y, - x ), thus

A(5, 3 ) → A'(- 3, - 5 )

B(8, 10 ) → B'(- 10, - 8 )

C(11, 3 ) → C'(- 3, - 11 )

Answer:

B: 3,0,-3,-6

Step-by-step explanation:

An arithmetic sequence has constant adding or subtracting. In this case, 3 is being subtracted as a constant.

Answer:

a) The sinusoidal equation is;

The function is h = -24·cos[π(t )] + 24

The sketch of one full revolution is attached

b) The height of the nail at 0.8 seconds is 43.42 cm

Step-by-step explanation:

The sinusoidal equation that models the nails height can be given as follows;

y = A·cos[B(x - C)]+D

A = The amplitude = Half maximum height =  48/2 = 24 cm

The period = 2·π/B = Time to complete one oscillation = 2 seconds

∴ B = 2·π/2 = π

x = t  = Time

C = The horizontal shift

D = the vertical shift = 24 cm

y = The height of the nail = h

We have;

h = -24·cos[π(t - C)] + 24

At t = 0, h = 0, therefore, we have;

0 = -24·cos[π(0 - C)] + 24

24·cos[π(0 - C)] = 24

∴ cos[π(0 - C)] = 24/24 = 1

π(0 - C) = 0

C = 0

The function is h = -24·cos[π(t )] + 24

b) The height of the nail at 0.8 seconds is given as follows;

h = -24×cos[π(0.8)] + 24 =

h = 19.42 + 24 = 43.42 cm.

Answer:

La última página que Sandra deberá leer es la página 380.

Step-by-step explanation:

Sandra y Roberto tienen un libro de 760 páginas y se lo dividen, la pregunta es ¿Cuál es la última página que debería leer Sandra de tal manera que ella y Roberto pasen la misma cantidad de tiempo leyendo la novela?

Para que ambos pasen la misma cantidad de tiempo leyendo la novela, tendrían que dividirse el libro a la mitad, por lo que cada uno debería leer 760 ÷ 2 = 380 páginas.

Por lo que Sandra deberá leer de la página 1 a la 380 y Roberto leerá de la 381 a la 760.

Por lo tanto, la última página que Sandra deberá leer es la página 380.

Answer:

yes you're right it is 14 + 28p = 315

Answer:

C

Step-by-step explanation:

I had this question edge 2021

Answer:

Current price $50eax135hats= $6750

Step-by-step explanation:

If he sells the hats at $52 he sells 3 less hats so $52x132=$6864

if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc

$56 x 126=$7056

Answer:

1/4

Step-by-step explanation:

Well see how far each points are from each other.

Start at the red triangle and go up 1, go to the right 4.

Thus,

the rise/run is 1/4.

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

To find the rise/run, you first need to pick two points from the line.  You can pick whichever points you want, and you will get the right answer.  I will pick (-8, -3) and (8, 1).

Divide the difference of the y's by the difference of the x's.

-3 - 1 = -4

-8 - 8 = -16

-4/-16 = 1/4

The rise/run is 1/4.

Answer:

The answer is

Step-by-step explanation:

Area of a circle is given by πr²

Where r is the radius

From the question

Area = 64 ft²

So the radius is

64 = πr²

Divide both sides by π

[tex] {r}^{2} = \frac{64}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{64}{\pi} } [/tex]

r = 4 ft

Hope this helps you

The answer is 8 not 4.5 or 4!!!!!!!!

Step-by-step explanation: It's not just "64" its 64pi. when you posted the question your device could not put the pi symbol so people were thinking that it was just 64.

The correct answer to this question is A. 9.4 x [tex]10^{-8}[/tex], 9.25 x [tex]10^{-6}[/tex], 2.5 x [tex]10^{3}[/tex], 7 x

Explanation:

These numbers are written in scientific notation. In this system, the exponent shows the number of spaces the period has been moved to make the number shorter. Additionally, a positive exponent shows the number has a certain number of digits to the right, while a negative exponent shows the number has digits to the left. In this way, the numbers presented can be converted as:

9.4 x [tex]10^{-8}[/tex] = 0.000000094 (Exponent indicates eight spaces to the left)

9.25 x [tex]10^{-6}[/tex] = 0.00000925 (Exponent indicates six spaces to the left)

2.5 x [tex]10^{3}[/tex] = 2500 (Exponent indicates three spaces to the right)

7 x [tex]10^{3}[/tex] =  7000 (Exponent indicates three spaces to the right)

Answer:

apply the BODMAS concept

brackets, off, division, multiplication, addition, subtraction

Step-by-step explanation:

(6²+10)÷(-5×3)-5

in this case the answer is D

Answer:

The answer is

negative 12 s squared + 11 s t minus 2 t squared

Step-by-step explanation:

( - 3s + 2t)( 4s - t)

Expand the terms

We have

- 12s² + 3st + 8st - 2t²

Simplify

We have the final answer as

Hope this helps you

Answer:

D. -12s^2+11st-2t^2

Answer:

(-2,4)

Step-by-step explanation:

First, put x+y=2 into slope-intercept form: y=-x+2

Second, set the to equations equal to each other: -x+2=1/2x+5

Then, add x to both sides: -x+x+2=1/2x+x+5 to get: 2=3/2x+5

Next, subtract 5 from both sides: 2-5=3/2x+5-5, to get -3=3/2x

Finally, to get the x-value, divide both sides by 3/2: -3(2/3)=3/2x(2/3), to get x=-2

Lastly, substitute -2 for x into one of the equations to find y:

x+y=2

-2+y=2

add 2 to both sides: -2+2+y=2+2, to get y=4

The solution is (-2,4)

Answer:

(- 2, 4 )

Step-by-step explanation:

Given the 2 equations

x + y = 2 → (1)

y = [tex]\frac{1}{2}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)

x + [tex]\frac{1}{2}[/tex] x + 5 = 2 ( multiply through by 2 to clear the fraction )

2x + x + 10 = 4

3x + 10 = 4 ( subtract 10 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

Substitute x = - 2 into (1) and evaluate for y

- 2 + y = 2 ( add 2 to both sides )

y = 4

Solution is (- 2, 4 )

Answer:  Exponential function

Step-by-step explanation:

A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.

An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.

If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .

Hence it is an exponential equation.

Answer:

D.

Step-by-step explanation:

if you remove the low value outlier, the variation from the mean will decrease therefore decreasing the varianc.

Answer:

D. Removing the outlier will decrease the spread of the graph of the data set.

Step-by-step explanation:

Outliers increase the spread of the data set.

So removing an outlier will generally decrease the spread or variance or standard deviation of a data set.

The answer is

D. Removing the outlier will decrease the spread of the graph of the data set.

Answer:

Step-by-step explanation:

First, we can find the measures of center for each group.

Group A

Mode: 1

Median: (1 + 2) / 2 = 3 / 2 = 1.5

Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6

Group B

Mode: 3

Median: 92 + 3) / 2 = 5 / 2 = 2.5

Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4

From here, we can see that...

Hope this helps!

Answer:

ABC

Step-by-step explanation:

[tex]f(x)=-x^2+1[/tex]

Plug in the value [tex]x=-3[/tex] into this function

[tex]f(-3)=-(-3)^2+1[/tex]

[tex]=-(9)+1[/tex]

[tex]=-8[/tex]

Thus, your answer will be D) -8. Let me know if you need any clarifications, thanks!

Answer:

D. -8

Step-by-step explanation:

We are given

f(x)= -x^2+1

and asked to evaluate f(x) for x= -3. Therefore, we must substitute -3 for x in the function.

f(x)= -x^2+1 for x= -3

f(-3)= -(-3^2)+1

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

First, evaluate the exponent: -3^2

-3^2= -3*-3= 9

f(-3)= -(9)+1

f(-3)=-9+1

Next, add -9 and 1

f(-3)= -8

When f(x)= -x^2+1 is evaluated for x= -3, the result is -8. Therefore, the correct answer is D. -8

Answer:

315/1200 = 63/240 = 21/80 = 0.2625 = 26.25%

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x^2+y^2=250\\\\x^2-2xy+y^2+2xy=250\\\\(x-y)^2=250-2xy\\\\(x-y)^2=250-2\cdot117\\\\ (x-y)^2=16\\\\x-y=4\qquad\qquad\vee\qquad \qquad x-y=-4\\\\x=4+y \qquad\qquad \vee\qquad\qquad x=-4+y\\\\(y+4)y=117\qquad\vee\qquad\quad (y-4)y=117\\\\y^2+4y-117=0\qquad\vee\qquad y^2-4y-117=0\\\\y=\dfrac{-4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\qquad\vee\qquad y=\dfrac{4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\\\\y=\dfrac{-4\pm\sqrt{16+468}}{2}\qquad\ \ \vee\qquad y=\dfrac{4\pm\sqrt{16+468}}{2}[/tex]

[tex]y_1=\dfrac{-4-22}{2}\ ,\quad y_2=\dfrac{-4+22}{2}\ ,\quad y_3=\dfrac{4-22}{2}\ ,\quad y_4=\dfrac{4+22}{2}\\\\y_1=-13\ ,\qquad y_2=9\ ,\qquad\quad\qquad\ y_3=-9\ ,\qquad y_4=13\\\\x_{1,2}=4+y_{1,2}\qquad\qquad\qquad\qquad\qquad x_{3,4}=-4+y_{3,4}\\\\x_1=-9\ ,\qquad x_2=13\ ,\qquad\quad\qquad x_3=-13\ ,\qquad x_4=9[/tex]

Answer:

G = 66.0

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan theta = opp/ adj

tan G = 9/4

take the inverse tan of each side

tan ^ -1 ( tan G) = tan^-1( 9/4)

G = 66.03751103

To the nearest tenth

G = 66.0

Answer:

52.7

Step-by-step explanation:

Of means multiply

85% * 62

.85 * 62

52.7

Turn the percentage into a decimal.

85% = 0.85

Multiply.

62 * 0.85 = 52.7

So, 52.7 is 85% of 62.

Best of Luck!

Answer:

[tex]\sqrt[3]{88c^{2} }[/tex]

Step-by-step explanation:

If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.

So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.

[tex]\sqrt[3]{88c^{2} }[/tex].

Hope this helped! (By the way, this was my 100th answer!)

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

Explanation:

G = amount of money George starts with

T = amount of money Tia starts with

Initially the ratio of their money is 9:4 so G/T = 9/4. Solve for G to get G = (9/4)T.

--------

After George spends 24 dollars he's left with (G-24) dollars. Tia gains 11 dollars so she has (T+11) dollars. They have the same amount of money after these two events occur, so G-24 = T+11.

Plug in G = (9/4)T and solve for T

G-24 = T+11

(9/4)T-24 = T+11 ... replace G with (9/4)T

4*[  (9/4)T-24 ] = 4*[ T+11 ] ... multiply both sides by 4 to clear out fraction

9T - 96 = 4T + 44 ... distribute

9T - 4T = 44 + 96

5T = 140

T = 140/5

T = 28

Tia started off with 28 dollars. We could stop here because your teacher is only asking about Tia's initial amount.

----------

If you want to find how much George started with, then plug T = 28 into G = (9/4)T to get...

G = (9/4)T

G = (9/4)*28

G = 2.25*28

G = 63

George started off with 63 dollars

The ratio of 63:28 reduces to 9:4 after dividing both parts by the GCF 7. This confirms the first fact we're given.

Notice how 63 drops to 63-24 = 39 after George spends $24. At the same time, Tia's amount increases to 28+11 = 39, which is the same as George's updated amount. Both facts match the description, so we have confirmed the answer.

Answer:

$28

Step-by-step explanation: