Simplify each expression.
1) 3(8Z² - 52 - 7)
2) 8d(2d-4)
6) 6(5x - 4)
7) 6q- 4

Answer:

0.0278 is the probability

Step-by-step explanation:

Okay, here we want to find the probability of 5 successes

The best way to go about this is by using the Bernoulli trial

So is p = probability of success = 0.51

Then q = probability of failure = 1-0.51 = 0.49

Mathematically, the Bernoulli approximation for k = 5 out of n = 18 is set up as follows;

P(k = 5) = nCk • p^k • q^(n-k)

P(k = 5) = 18C5 * 0.51^5 * 0.49^13

P(k = 5) = 0.027751047366 which is 0.0278 to 4 decimal places

Answer:

3 gallons of gas are still remaining in the tank

Step-by-step explanation:

Royston's car had 15 1/5 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and he refueled the car with 5 3/5 gallons. If the car consumed 17 4/5 gallons of gas during the trip, there are still ____________ gallons of gas remaining in the tank?

Given:

Initial gallons of gas=15 1/5

Refueled gallons of gas= 5 3/5

Used gallons of gas=17 4/5=89/5

Total gallons of gas available=

Initial + Refueled

=15 1/5 + 5 3/5

=76/5 + 28/5

=76+28/5

=104/5 gallons

Equivalent to

=20 4/5 gallons

Total remaining gallons of gas= Total gallons of gas available - Total gallons of gas used

=104/5 -89/5

= 104-89/5

=15/5

=3 gallons

Answer:

3 gallons

Step-by-step explanation:

Answer:

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

Answer:

C

Step-by-step explanation:

I had this question edge 2021

Answer:

300

Step-by-step explanation:

1/2 * 600 = 300

There are 300 times would you predict getting an even number.

We have to given that,

The probability of spinning an even number is 1/2.

And, you spin 600 times.

Hence, Number of times would you predict getting an even number is,

⇒ 1/2 of 600

⇒ 1/2 × 600

⇒ 600 / 2

⇒ 300

Therefore, There are 300 times would you predict getting an even number.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ6

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:

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!

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)

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

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:

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:

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:

B. Better measure of spread: the standard deviation

D. Better measure of center: the median

Step-by-step explanation:

The mean is the average of a data set.

The median value is best for measuring the center value because median measures the middle value of a set of data.

The IQR only measures the inner range of a data set.

The standard deviation is best for measuring the spread because standard deviation measures the spread of data distribution.

Answer:

not a right triangle

Step-by-step explanation:

We can use the Pythagorean theorem to see if it is a right triangle

a^2 + b^2 = c^2

15^2 + 12^2 = 21^2

225 + 144 = 441

369 = 441

This is not true so it is not a right triangle

Answer:

Step-by-step explanation:

A triangle is a right angled triangle if sum of squares of two sides is equal to the square of third side.

12²+15²=144+225=369

21²=441

so a²+b²≠c²

it is not a right angled triangle.

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:

[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:

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:

(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:

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:

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:  [tex]5x-5 \ge 0[/tex]

This is the same as [tex]x-1 \ge 0[/tex]

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

Explanation:

We have [tex]f(x) = \sqrt{5x-5}+1[/tex]

The stuff under the square root (this stuff is called the radicand) is what we'll focus on (the +1 at the end does not affect the domain at all). We want this to be 0 or larger. This is to avoid applying the square root to negative values, which leads to complications.

So 5x-5 must be 0 or larger meaning we write [tex]5x-5 \ge 0[/tex]

Optionally we can divide all three terms (5x, -5 and 0) by 5 to go from [tex]5x-5 \ge 0[/tex] to [tex]x-1 \ge 0[/tex]

If you wanted to solve for x, you would get [tex]x \ge 1[/tex] to set up the domain. Meaning that x = 1 is the smallest x value you can plug into the function. The x value can be anything larger than 1 as well.

Answer:

[tex]\boxed{\sf \ \ YES \ \ }[/tex]

Step-by-step explanation:

Hello

let's say that the price of the book was x

the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x

and this is $72 so we can write that

0.8*x=72

and then divide by 0.8 both parts

x = 72/0.8=90

So the list price value of the book is $90

and we can verify as 90 - 20%*90 = 90 - 18 = 72

Hope this helps

Answer:

where's the graph??? .......

Answer:

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

Step-by-step explanation:

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:

[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!)

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:

[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:

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:  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:

The quotient is 2x^2+4x+11

Step-by-step explanation: