12. The length of one side of
a rectangle is
12cm.
The length of the diagnol of
the rectangle is 13cm
Calculate the area of the
rectangle

The probability P(5 ≤ x ≤ 9) is 0.6847

Assume that x has a normal distribution

We have been the mean and standard deviation μ = 6; σ = 2.

To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.

z = (5 - 6)/2

  = -0.5

and z = (9 - 6)/2

         = 1.5

Then the probability is calculated as:

P(x ≤ 5) = 0.3085

P(x ≤ 9) = 0.9932

P(5 ≤ x ≤ 9) = 0.9932 - 0.3085

P(5 ≤ x ≤ 9) = 0.6847

Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847

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Answer:

a. Yes

Step-by-step explanation:

If you plug in the ordered pairs, the -5 is x and 16 is y.

The equation would look like this:

16=30x-14

Add 14 on both sides

14+16=30

30=30x

divide by 30 on both sides

1=1

a. Yess

The probability that 3 of the people chosen would be women = 0.36.

Probability is basically a numerical description of how likely an event is supposed to happen. It is a number something between 0 and 1.

total number of people = 16

total number of women = 8

number of chosen employees randomly to receive tickets to a concert = 5

probability to find = that 3 of them will be women

Therefore, we can conclude that the probability of 3 of the chosen people will be women is 0.36.

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We have to replace the values in the equation

Since the square of a negative number is a positive number, (-4)^2 = +16

In a case whereby I baked a cake for my siblings ad  My brother ate large fraction 1/8 of the cake and my sister ate \large frac 3/4 ,  the amount of cake is left for me is 1/8.

In this question , we are dealing with fraction, which implies that the number of the cake that i am having is 1.

And we are told that 1/8 of the cake is been eaten by my brother, where 3/4 of the cake is been eaten by my sister, then to know the amount of cake that was left for me, we will need to perform some simplification as:

1-(1/8) - (3/4) =1/8.

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If a cake is baked, In which her brother ate 1/8 and sister ate 3/4. Then 1/8 of cake is left me.

A fraction represents a part of a whole

Given that a cake was baked for her  siblings.

Her big brother ate large part of the cake that is 1/8.

Her sister ate 3/4 of the cake.

We need to find the left out cake for her.

To do that we have to remove 1/8 and 3/4 from 1.

1-(1/8)-(3/4)

(8-1-6)/8

1/8

Hence she has 1/8 of cake which is left.

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The movies for the movie marathon can be chosen in 120  different ways .

In the question ,

it is given that

total number of movies = 10 movies

number of movies that need to be played in specific order = 7 movies .

we have to find how many different ways can the movies be selected for the movie marathon .

we can solve this with Combination ,

where n = 10  and r = 7

So C(n,r) =  C (10,7)

= 10! / (3! * 7! )

= (10*9*8*7!)/(3! * 7! )

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

= 10 * 3 * 4

= 120 ways .

Therefore , The movies for the movie marathon can be chosen in 120  different ways .

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we will solve as follows:

The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

sin 2x=2 tan x/(1+(tan x)²)

cos 2x=(1-(tan x)²)/(1+(tan x)²)

tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)

Here,

tan x=8/15

sin 2x=2 tan x/(1+(tan x)²)

= 2*8/15/(1+(8/15)²)

=(16/15)/(289/225)

=(16*15)/(289)

≈0.8304

cos 2x=(1-(tan x)²)/(1+(tan x)²)

=(1-(8/15)²)/(1+(8/15)²)

=(225-64)/(225+64)

≈0.557

tan 2x=sin 2x/cos 2x

tan 2x= 0.8304/0.557

=1.498

≈1.5

When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

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Option a is correct using algebric formulas.

(x + y)³ = x³ + y³ +3xy( x + y )

(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )

So breaking it into

(( x + y )³)² = (x³ + y³ +3xy( x + y ))²

(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

So after rearranging the terms

we get  (x + y)^6 as

x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6

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Answer:

A

Step-by-step explanation:

It is given that lines k and p are parallel. You also know that angles 2 and 3 are equal because of vertical angles. Due to the parallel lines, you can say that angles 1 and 2 are equal because they are corresponding angles (same-side).

These two angles are not alternate interior angles because angle 1 is exterior and on the same side as angle 2. The third option would not make sense because you are trying to prove two angles are equal, not that lines are parallel.

After 10 years, the car will be worth 0.54 of the price when Rob purchases it. The result is obtained using the exponential depreciation equation.

The depreciation can be calculated by the exponential depreciation equation.

y = P (1 - r)ˣ

Where

If given

How much will the car be worth after 10 years?

The depreciation rate would be

r = 6%

r = 6/100

r = 0.06

So, after 10 years, the car would be worth

y = P (1 - r)ˣ

y = P (1 - 0.06)¹⁰

y = P (0.94)¹⁰

y = P (0.54)

y = 0.54P

Hence, after 10 years, the car will be worth 0.54 of its original price.

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The probability that exactly 10 customers will use the atm during the next noon lunch hour is 0.0948

From the question, we have the following parameters:

Average number of customers = 12

Number of customers = 10

The above parameters means that:

x = 10

λ = 12

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

This gives

P(x = 12) = 10¹² * e⁻¹⁰/12!

Evaluate

P(x = 12) = 10¹² * e⁻¹⁰/479001600

Solving further, we have

P(x = 12) = 0.0948

Hence, the probability is 0.0948

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Answer: say can't help

Step-by-step explanation:

Answer:

4:2 and 14:7

Step-by-step explanation:

The ratios equivalent to 8:4 would be:

4:2

14:7

5:10 wouldn't be equivalent because if you simplify that, it is 1/2 and if you simplify 8/4, it is 2. 1/2 and 2 are not the same.

:D

Answer:

They are all equivalent except for 5:10

Step-by-step explanation:

You can write ratios as fractions

[tex]\frac{8}4}[/tex]   [tex]\frac{4}{2}[/tex]  [tex]\frac{14}{7}[/tex]   [tex]\frac{5}{10}[/tex]  If I simplify each fraction, I can see that they all equal 2 expect for the the last one.

2   2   2   1/2

We will determine the area of the green section as follows:

Here alpha is the angle [In radians] and r is the radius-

*First: We determine the angle:

Now, we transform it to radians:

*Second: We replace on the equation:

So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]

Answer:

A ≈ 43.4 cm²

Step-by-step explanation:

the area (A) of the green sector is calculated as

A = area of circle × fraction of circle

  given d = 12 then r = 12 ÷ 2 = 6 cm

the central angle of the green sector = 180° - 42° = 138°

then

A = πr² × [tex]\frac{138}{360}[/tex] ( simplify fraction by dividing numerator/denominator by 6 )

   = π × 6² × [tex]\frac{23}{60}[/tex]

   = 36π × [tex]\frac{23}{60}[/tex]

   = [tex]\frac{36\\pi (23) }{60}[/tex]

   ≈ 43.4 cm² ( to the nearest tenth )

When 2 to the power of hundred is divided by 5 it show s remainder of 1

2 to the 100th power is solved as follows

2 ^ 100 = 1.2676506 * 10^30

This is solved using a calculator and the solution means that

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2   (2 multiplying itself till the number of 2's are up to 100)

This gives the value = 1.2676506 * 10^30

Division of the  2^100, by 5

2^100 / 5

2^1 / 5 remainder =2

2^2 / 5 remainder = 4

2^3 / 5 remainder = 3

2^4 / 5 remainder = 1

2^5 / 5 remainder = 2

2^6 / 5 remainder = 4

2^7 / 5 remainder = 3

2^8 / 5 remainder = 1

2^9 / 5 remainder = 2

2^10 / 5 remainder = 4

2^11 / 5 remainder = 3

It can be seen that it generates a pattern which is

The pattern counts in 4's. If we follow the pattern and count to 2^30

= 100 / 4

= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1

This is to say

2^97 / 5 remainder = 2

2^98 / 5 remainder = 4

2^99 / 5 remainder = 3

2^100 / 5 remainder = 1

Hence 2^100 divided by 5 will give a remainder of 1

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Answer:

16°F

Step-by-step explanation:

The temperature is −4°F. What will the temperature be if the temperature rises 20°F?

-4 + 20 = 16

so:

16°F

After simplifying i^61 we get the answer is i

Define Complex number

Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labelled i sometimes known as the imaginary unit, and satisfying the equation i² = 1.

We have the given expression : i ^ 61

Rewrite it,

i ^ 61 as (i^4)^15 * i

we know, i² = -1

so, i ^ 4 = i² * i² = -1 * -1 = 1

so, put i ^ 4 value,

⇒1^15 * i

power 1 to the 15 is 1,

⇒1 * i

⇒ i

Hence, the answer is ' i '

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Given:

a.) A person had 14,000 infested in two accounts.

b.) One paying 9% simple interest.

c.) One paying 10% simple interest.

Let,

x = the amount invested at 9% simple interest

y = the amount invested at 10% simple interest

1.) We know the total amount of money invested is $14,000. We get,

x + y = 14,000

2.) We know that the total interest for the year for the two accounts is $1432. We get,

0.09*x + 0.1*y = 1,339

Let's equate the two equations,

x = 14,000 - y (Substitute for x)

0.09*(14,000 - y) + 0.1*y = 1,339

1,260 - 0.09y + 0.1y = 1,339

0.1y - 0.09y = 1,339 - 1,260

0.01y = 79

0.01y/0.01 = 79/0.01

y = 7,900

Therefore, $7,900 was invested at the rate of 10% simple interest.

Let's determine x, substituting y = 7,900 in x + y = 14,000.

x + y = 14,000

x + 7,900 = 14,000

x = 14,000 - 7,900

x = 6,100

Therefore, $6,100 was invested at the rate of 9% simple interest.

The equation used to find the amount of time Emmet answers phone calls is t +25= 45

An equation is an expression that shows the relationship between two or more numbers and variables.

The amount of time Emmet answers phone calls = 20

She spends delivering flowers to patient's room= 25 minutes

She spends meetings volunteering at the hospital=  45

Let t be the amount of time Emmet answers phone calls in the hospital

Hence the equation used to calculate the amount of time spent on calls;

t + 25= 45

Now collect the like terms;

t= 45-25

t= 20

Hence, The equation used to find the amount of time Emmet answers phone calls is t +25= 45

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Answer:

a: 120 = 2x + 40

80 = 2x

x = 40

b: (3x + 10) + (x-30) = 180

4x - 20 = 180

4x = 200

x = 50

c: 105 = 2x - 11

116 = 2x

58 = x

d: 8y + 36 = 14y - 24

-6y = -60

y = 10

64 = 48 + x

16 = x

y = 10, x = 16

e: 75 + (2x - 5) = 180

70 + 2x = 180

2x = 110

x = 55

2(55) - 5 =y

y = 105

f: (2x + 8) + (3x + 17) = 180

5x + 25 = 180

x = 31

3(31) + 17 = 5y + 15

110 = 5y + 15

95 = 5y

y = 19, x = 31

The conservationist expects to be in the lake would be; 142 trouts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.  

We have to find conservationists who expect to be in the lake.

Now, initially, trout count = 200

Then, again 56 trouts caught then, trout count = 200 + 56

But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.

So, trout count = 200 + 56 – 14  = 142.

Hence, the conservationist expects would be; 142 trouts.

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I will ask my question here

is p(x)

bye :)

The blue graph is represented by the equation g(x) = (x - 5)²

The possible graph that completes the question is added as an attachment

From the attached graph, we have the following parameters

Also from the graph, we have the equation of the function f(x) to be

f(x) = x²

Solving further, we can see that:

The only difference is that, f(x) is shifted to the right by 5 units

This means that

g(x) = f(x - 5)

So, we have

g(x) = (x - 5)²

Hence, the blue graph equation is g(x) = (x - 5)²

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The total price of that Ingrid has to pay is $52.90.

From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

Sales price = $48.90

Amount needed to be paid = 8.5% of $48.90 + $48.90

= 4.15 + $48.90

= $52.90

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Using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.

So, more pink sand is available to each girl:

Sand available to each girl:

Pink sand more to each girl:

Therefore, using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.

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For the standardized dataset , the value of median = mean , which is equal to 7

The mean of the close friends people have = 7

The variance = 100

Standard deviation can be found using the formula

                   v = σ²

where  v is the variance and

            σ is the standard deviation

Then ,                  σ² = 100

                            σ  = √100

                            σ  = 10

Therefore , the standard deviation for the close friends have is 10

The standard score for these vales can be found using the formula

                         Z = (X - μ) / σ

where Z is the standard score

           X is the raw score

           μ is the mean

           σ is the standard deviation

Using this formula, the standard score of any raw score can be calculated.

For, the standardized dataset , the value of median will be equal to value of median.

                           Median = mean

                           Median = 7

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we have the quadratic equation

we have that

a=1

b=-1

c=-12

Applying the formula to solve a quadratic equation

The values of u are

u=4 and u=-3

therefore

The answer is

A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x,y).

y= 3 / 10x + 8

y=mx+b, where

y=mx+b

y=3/ 10x+8

m=3/10  b=8

Slope: 3/ 10, and the y-intercept is at (0, 8).

x           y

0         8

10        11.

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