In the diagram below, circle O has a radius of 10. If the measure of arc AB is 72°, find the area of shaded sector AOB, in terms of π. Show all your work that leads to the final answer.

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

Interval of function f(x) is sometimes negative and sometimes positive.

The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.

Given function,

f(x) = (2x – 1)(3x + 5)(x + 1),

Zeros of function,

x = 1/2 = 0.5

x = -5/3 = - 1.6667

x = -1

From the graph

Interval of function is negative between -∞ < x < -1.6667

Interval of graph is positive between -5/3 < x < -1

Interval of function is negative between -1 < x < 0.5

Interval of graph is positive 0.5 < x < ∞

Hence, f(x) has sometimes positive interval and sometimes negative interval.

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Solution :

a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.

P (correct in the 4th attempt)

= [tex]$(1-0.75)^3 \times 0.75$[/tex]

= 0.01171875

b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.

P( X = 3) for X = B in (n = 10, p = 0.75)

= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]

= 0.0031

c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :

There are = 6 success, p = 0.75.

Therefore, this is a case of a negative binomial distribution.

[tex]$E(X)=\frac{k}{p}$[/tex]

         [tex]$=\frac{6}{0.75}$[/tex]

         = 8

So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]

     [tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]

        = 1.6330

Answer:

3/5

Step-by-step explanation:

here,

0.6

in fraction = 6/10

in simplest form 6/ 10 both term can be divided by 2 so,

6/10 ÷2

= 3/5

Answer:

170.7

Step-by-step explanation:

We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7

what you're trying to do is form an equation for y

6x + 5y = 10    

5y = -6x + 10         we need y to be singular so divide by numeral before y

y = - 6x/5 + 10/5

y = - 6x/5 + 2

The three main log rules you'll encounter are

The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.

Here are examples of each rule being used (in the exact order they were given earlier).

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

Here's a slightly more complicated example where the log rules are used.

log(x^2y/z)

log(x^2y) - log(z)

log(x^2) + log(y) - log(z)

2*log(x) + log(y) - log(z)

Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.

Answer:

Option C is correct

Step-by-step explanation:

[tex]log( {10}^{3} )[/tex]

[tex]3 \: log \: (10)[/tex]

[tex]3×1[/tex]

[tex]3[/tex]

Answer:

± 5

Step-by-step explanation:

2x/-5 = -10/x

2x^2 = 50

x^2 = 25

x = ± 5

Answer:

x=5

Step-by-step explanation:

Start with writing it like 2x/-5= -10/x

Then cross multiply: 2[tex]x^{2}[/tex]= 50

Divide by 2: [tex]x^{2}[/tex]=25

Square root of 25: 5

x=5

Answer:

C) sixty five units

Step-by-step explanation:

have a great day

Answer:

the Si unit of temprature in Kelvin (K)

Step-by-step explanation:

Answer:

The answer is Kelvin (k).

Step-by-step explanation:

The kelvin (K) is defined by taking the fixed numerical value of the Boltzmann constant k to be [tex]1.380649*10^{-23}[/tex] when expressed in the unit of joule per kelvin. The temperature 0 K is commonly referred to as "absolute zero." On the widely used Celsius temperature scale, water freezes at 0 °C and boils at about 100 °C. One Celsius degree is an interval of 1 K, and zero degrees Celsius is 273.15 K. An interval of one Celsius degree corresponds to an interval of 1.8 Fahrenheit degrees on the Fahrenheit temperature scale.

The kelvin is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson (known as Lord Kelvin). An absolute temperature scale has as its zero point absolute zero (−273.15° on the Celsius temperature scale and −459.67° on the Fahrenheit temperature scale), the theoretical temperature at which the molecules of a substance have the lowest energy; hence, all values on such a scale are nonnegative.  

Answer:

General Educational Development (GED) tests

What do subject do you need help?

Step-by-step explanation:

The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.

The cost of the cereal if the grocery store buys 250 boxes is $475

We know that:

The cost function is:

c(n) = 2*n              if n < 100

c(n) = 1.9*n            if  100 ≤ n ≤ 500

c(n) = 1.8*n            if   n > 500.

(we can assume that the cost function is in dollars)

This is a piecewise function, this means that we need to see in which interval we have the number n, and then select the correct function to use.

Now, we want to find the cost of the cereal if the store buys 250 boxes.

Then we have n = 250.

We can see that n = 250 is in the second interval,  100 ≤ n ≤ 500, then we will use the second function to find the cost.

We will get:

c(250) = 1.9*(250) = $475

We can conclude that the cost if the store buys 250 boxes is 475

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Answer:

Step-by-step explanation:

[tex]p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\dfrac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \dfrac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}[/tex]

Answer:

✔️6 × 5²

✔️6 × 5 × 5

✔️150

Step-by-step explanation:

6 times 5 squared is written as 6 × 5²

Thus:

6 × 25 = 150

Evaluate each of the expressions given to determine whether they are equivalent to 150 or not

✔️5 × 6² = 5 × 36 = 180 (NOT EQUIVALENT)

✔️6 × 5² = 6 × 25 = 150 (EQUIVALENT)

✔️192 ≠ 150 (NOT EQUIVALENT)

✔️6 × 5 × 5 = 6 × 25 = 150 (EQUIVALENT)

✔️6 × 5 × 2 = 6 × 10 = 60 (NOT EQUIVALENT)

✔️150 = 150 (EQUIVALENT)

✔️6 + 5 × 5 = 6 + 25 = 31 (NOT EQUIVALENT)

9514 1404 393

Answer:

  all real numbers

Step-by-step explanation:

The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.

The domain of g(x) = f(-x) is all real numbers.

9514 1404 393

Answer:

  $11,680.58

Step-by-step explanation:

Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.

__

The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.

The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...

  0.205×21,465 = 4400.325 ≈ 4400.33

The the total tax due on $70,000 is ...

  $7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000

_____

Additional comments

The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.

__

Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.

  ≤ 48535 -- income × 0.15

  ≤ 97069 -- income × 0.205 -2669.425

  ≤ 150,473 -- income × 0.26 -8008.22

  ≤ 214,368 -- income × 0.29 -12,522.41

  > 214,368 -- income × 0.33 -21,097.13

In this case, the second row of this simpler table would give the tax on $70,000 as ...

  tax = 70,000 × 0.205 -2669.425

  tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above

Answer:

x = 19.2

Step-by-step explanation:

tan(58)=x/12

x=12×tan(58)

x=19.2

Answered by GAUTHMATH

Answer:

10 or -10,

Read the explanation

Step-by-step explanation:

Rewrite this problem as a numerical expression. As per the wording of this problem, there can be two expressions derived.

1.     [tex]((\frac{1}{6}(10*3)*4)-30[/tex]

2.     [tex]30-((\frac{1}{6}(10*3)*4)[/tex]

Simplify, remember the order of operations. The order of operations is the sequence by which one is supposed to perform operations in a numerical expression. This order is the following:

1. Parenthesis

2. Exponents

3. Multiplication or division

4. Addition or Subtraction

Use this sequence when simplifying and solving the expression:

Expression 1

[tex]((\frac{1}{6}(10*3)*4)-30\\\\=((\frac{1}{6}(30)*4)-30\\\\=(5*4)-30\\\\=20 - 30\\\\= -10[/tex]

Expression 2

[tex]30-((\frac{1}{6}(10*3)*4)\\\\=30-((\frac{1}{6}(30)*4)\\\\=30-(5*4)\\\\= 30-20\\\\= 10[/tex]

Answer:

17,576,000

Step-by-step explanation:

there are 26 english letters (A-Z) and 10 digits(0-9).

there are 3 spaces for letters. therefore Any of the 26 letters can be combined with any 26 other letters and any of those can be combined with any of another 26 letters.

26*26*26= 17576

similarly 10 digits can combined in 1000 ways

10*10*10=1000

17576 letter combination can combine with 1000 digits combination.

so  17,576 x 1000 = 17,576,000 different plates could issue.

Step-by-step explanation:

Right Triangles and the Pythagorean Theorem. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.

Answer: B

Step-by-step explanation:

Why did historians choose to study this topic?

Answer:              It would be the first equation because:

Step-by-step explanation:        

In order to be an exponential function, the X

variable has to be in the exponent, that eliminates

the second and fourth answers

       f(X) = 4(3)X

using the point (2,36)

  f(2) = 4 (3)2

         = 4 (9 )

         = 36

The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the point on the graph be P ( 2 , 36 )

So , when x = 2 , the value of y = 36

f ( x ) = 4 ( 3 )ˣ   be equation (1)

when x = 2

f ( 2 ) = 4 ( 3 )²

f ( 2 ) = 4 x 9

f ( 2 ) = 36

Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ

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Answer:

864

Step-by-step explanation:

do the square root of the total number

Answer:

y=12x+10

Step-by-step explanation:

Slope-intercept form is y=mx+b

1. Add -12x to both sides of the equation

87 is the mean.

To find the mean, you must

- add all of the numbers

- divide by the amount of numbers given

In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.

I hope that helped you

9514 1404 393

Answer:

Step-by-step explanation:

The first equation describes the total number of coins. It says the sum of the numbers of dimes and quarters is 44, the total number of coins.

__

The second equation describes the total value of the coins. It will say that 0.10 times the number of dimes plus 0.25 times the number of quarters is 8.30, the total dollar value of the coins.

The two equations are ...

  d + q = 44

  0.10d +0.25q = 8.30

__

Additional comment

The solution can be found by substituting for d:

  0.10(44 -q) +0.25q = 8.30

  0.15q = 3.90

  q = 26

  d = 44 -26 = 18

Vinnie has 18 dimes and 26 quarters in his bag.

Answer:

0.9332

Step-by-step explanation:

We are given that

Mean diameter, [tex]\mu=73[/tex]

Variance, [tex]\sigma^2=4[/tex]

We have to find the probability that the diameter of a selected bearing is less than 76.

Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]

[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]

[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]

Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]P(x<76)=P(Z<1.5)[/tex]

[tex]P(x<76)=0.9332[/tex]

Hence, the probability that the diameter of a selected bearing is less than 76=0.9332

Answer:

10/21 of the distance

Step-by-step explanation:

2/7 distance

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

3/8 tank

The rest of the tank is 8/8 - 3/8 = 5/8

2/7 distance         x

------------------ = ----------------------

3/8 tank              5/8 tank

Using cross products

2/7 * 5/8 = 3/8x

10/56 = 3/8x

Multiply each side by 8/3

10/56 * 8/3 = 3/8x * 8/3

10/3 * 8/56=x

10/3 * 1/7 =x

10/21 =x

10/21 of the distance

Answer:

A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).

Step-by-step explanation:

If Kristine spends $20 and saves the rest when she gets paid, the amount she saves should always be 20 less than the amount she earned.

The points (20, 0) and (25, 5) accurately represent this, where x is how much she earns and y is how much she saves.

(20, 0) represents her earning $20 and saving $0, because she spends $20 every time she gets paid.

(25, 5) represents her earning $25 and saving $5, because she spent $20.

So, the correct graph is A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).

Answer:

d

Step-by-step explanation: