216. Factor and then calculate the value of the expression

a) a² + ab with a = 6.6, b = 3.4;


b) x2 - xu at x = 0.5, y = 2.5;


c) —5a² — 5ah at a = 4, x = -3

1) The probability that a randomly chosen penny weighs less than 2.4 grams is; 0.00621.

2) The probability that the mean weight of 15 pennies is less than 2.4 grams is; 0

The central limit theorem in statistics tells us that the sampling distribution of the mean will usually be normally distributed, provided that the sample size is large enough.

We are given the following parameter;

Population mean; μ = 2.4 grams

Standard deviation; σ = 0.04 grams

1) The probability that a randomly chosen penny weighs less than 2.4 grams is: P(X < 2.4)

Formula for z-score is;

z = (X - μ)/σ

z = (2.4 - 2.5)/0.04

z = -2.5

The p-value from z-score calculator is; p = 0.00621.

2) The standard deviation for these 15 pennies will now be;

σ' = 0.04/√15

σ' = 0.0103

The probability that the mean weight of 15 pennies is less than 2.4 grams is expressed as;

P(X' < 2.4)

z = (2.4 - 2.5)/0.0103

z = -9.709

The p-value from z-score calculator is; p = 0

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$2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.

Given that, principal = $1700, rate of interest = 2.7% and time period = 9 years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Here, simple interest = (1700×2.7×9)/100

= 41310/100

= $413.10

Amount = Principal + Simple interest

= 1700+413.10

= $2113.1

Compound interest:

[tex]Amount=P(1+\frac{R}{100} )^{nt}[/tex]

[tex]=1700(1+\frac{2.7}{100} )^{4\times9}[/tex]

[tex]=1700(1.027)^{36}[/tex]

= 1700×2.609

= $4435.3

Now, 4435.3-2113.1=$2322.2

Therefore, $2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.

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Answer:

Given

Distributive Property

Addition Property of Equality

Division Property of Equality

Step-by-step explanation:

Frist you distribute the -2 by multiplying it to everything in the parentheses.  Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4

The linear function of the table is a) g(x)=x-7

What is linear function?

 If the largest power of the variables in a function is 1, then that function is linear. A line across these two points with a straightedge is needed to complete the graph because two points determine a line. When m and b are real numbers, the slope of a linear function has the form f(x)=mx+b. To find the x-intercept, set f(x)=0 and solve for x. Because y=f(x), we can use y and f(x) interchangeably.

Here let us take g(x) as y values. In given table take any two points ,

[tex](x_1,y_1)=(0,-7)\\(x_2,y_2)=(2,-5)[/tex]

Now using slope formula ,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = 2/2 = 1

Now using equation formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y+7=1(x-0)

=> y+7=x

=> y =x-7

Then y=g(x)

=> g(x) = x-7

Therefore the linear function of the given table is g(x)=x-7 .

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Answer:

245.57

Step-by-step explanation:

[tex]P\left(1+0.05)^{10}=400 \\ \\ P=\frac{400}{(1.05)^{10}} \\ \\ P \approx 245.57[/tex]

Answer:

32 students were on each bus.

Step-by-step explanation:

First deduct 9 students from the total number: 265 - 9 = 256

Then divide the students among the total number of buses, which is 8: 256/8 = 32

So there are 32 students on each bus.

Hope this helps

Please give brainliest

The given system of linear equations has no solution. By solving the equations using substitution method we get (11, 0) where no solution exists.

How many solutions can a system of linear equation can have?

A system of linear equations is usually a set of two linear equations with two variables.

The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.

With linear systems of equations, there are three possible outcomes in terms of number of solutions:

How to identify the number of solutions?

Rewrite both equations in slope-intercept form, y = mx + b.

Compare the slopes of the lines, m, and their y-intercepts, b, to determine the number of solutions.

According to the given question:

Given system of linear equation are: y = -x + 11 and -4x -4y = 44

Rewriting the equations in slope-intercept form

        Simplifying further by dividing the equation with -4 on both side

        y = x - 11 ------ 2)

Clearly, both the equation have different m-values.

Hence the system of equation have one solution.

Now solving by substitution method

Substituting 2) in 1)

x - 11 = -x + 11 (since y = x -11 from 2))

2x = 22

∴ x = 11

Now substituting x = 11 in equation 2) to get the value of y

y = 11 - 11

∴ y = 0

So, the system of equation has no solution at (11, 0).

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The required expression is Total = 152+x .

What is expression ?

  Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

Here,

The number of bottles Enrique collected = 152

Let us take number of bottles  collected by Latasha as x. Then,

Total number of bottles collected by the is ,

=> Total = Number of bottles collected  + Number of bottle collected

                by Enrique                                   By Latasha.

=> Total = 152+x

Hence the required expression is Total = 152+x.

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Answer:

It will take 7.5 days to complete the job.

Step-by-step explanation:

First, find how many total hours the ten men worked to complete the job

10 x 6 = 60 hours a day

12 x 60 = 720 hours total

Now compare that with the 8 men's hours

8 x 12 = 96 hours a day

720 / 96 = 7.5 days

The numbers matched with its divisibility numbers is

for 60 the divisibility numbers are 2,3,5,10 .

for 48 the divisibility numbers are 2,3    and

for 81 the divisibility numbers are 3,9 .

In the question ,

three numbers are given as 60 , 48 and 81

we need to match them with their , respective divisibility numbers that are given in the option  

For the first number 60 ,

we see that 60 is divisible by 2 , 3 , 5 and 10 because

30*2 [tex]=[/tex] 60  , 3*20 [tex]=[/tex] 60 , 5*12 [tex]=[/tex] 60 and 10*6 [tex]=[/tex]60 ,

So, for 60 the divisibility numbers are 2,3,5,10

that is option(c)

For the second number 48 ,

we see that 48 is divisible by 2 and 3  because

2*24 [tex]=[/tex] 48 , 3*16 [tex]=[/tex] 48 ,

So , for 48 the divisibility numbers are 2,3

that is option(b)

For the third number 81

we see that 81 is divisible by 3 and 9  because

3*27 [tex]=[/tex] 81 , 9*9 [tex]=[/tex] 81

So , for 81 the divisibility numbers are 3 an 9

that is option(a)

Therefore , The numbers matched with its divisibility numbers is

for 60 the divisibility numbers are 2,3,5,10 .

for 48 the divisibility numbers are 2,3    and

for 81 the divisibility numbers are 3,9 .

The given question is incomplete , the complete question is

Match the numbers 60 , 48 and 81  with its divisibility numbers

(a) 3,9

(b) 2,3

(c) 2,3,5,10

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The last sample range in this table is missing,the missing value is 2.

Given:

The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and Elise (age 5).

Sample(n = 2)    A, B      A, C    A, D    Α, Ε  B, C ........ D,E

Ages                 15, 10    15,9    15,7    15, 5  10,9 .......  7,5

Sample range      5          6         8       10      1  ...........  

Let x be the sample range missing.

sample range = ages difference

= Age of D - Age of E

= 7 - 5

= 2

Therefore The last sample range in this table is missing,the missing value is 2.

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Answer:

answer is 2 i did it and got it right

Step-by-step explanation:

The kilograms of dough that Emmett prepare if he worked for 4 hours is 20 kilograms.

A proportional relationship simply means the relationship that has an equivalent ratio as well as a constant.

In this case, Emmett prepared 10 kilograms of dough after working 2 hours. The kilograms per hour will be:

= 10/2

= 5 kilograms per hour

Therefore, in 4 hours, the kilograms will be:

= Number of hours × 5 kilograms

= 4 × 5

= 20 kilograms

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Answer:

x = 11

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{3}[/tex] (2x + 5) = 3 , then

2x + 5 = 3³ = 27 ( subtract 5 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11

The interest on the borrowed amount after 7 years is $486.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

Given that,

The amount borrowed is  P = $200.

Rate of interest is r = 18% per annum compounded quarterly.

Total time is t = 7 years

Then, the rate of interest for quarterly compounding is given by,

r  = 18 / 4%

  = 4.5%

And, total time period for compounding is,

n = 7 × 4

  = 28

The formula for compound interest is given as,

P[(1 + r / 100)ⁿ - 1]

Substitute the respective values to get,

200 × [(1 + 4.5 / 100)²⁸ - 1]

= 200 × 2.43

= 486

Hence, the interest due on the loan is given as $486.

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Answer:

A is shown in the attached image.

B. 5/6

C.  P(A or B)

Step-by-step explanation:

B. 1/2 + 2/3 - 1/3 = 5/6 or 3/6 + 4/6 - 2/6 = 5/6

C. P(A or B) = 5/6. P(A) + P(B) - P(A and B) = 5/6. Therefore, P(A) + P(B) - P(A and B) = P(A or B).

Answer:

two times x plus two

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The x's go up by 1 (1, 2, 3, 4, 5)

The y's go up by 4's. 0, 4, 8, 12, 16

There is a rule to find the y's from the x's instead:

times by 4 and minus 4.

y = 4x - 4

y = 4(5) - 4

y = 20 - 4

y = 16

Answer: The image is for an idea of what you should look for

Step-by-step explanation:

The surface area of the cylinder in term of π is 6764πmm^2

A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.

The total surface area of a cylinder is 2πr(r+h)

Where r is the radius and h is the height of the cylinder

therefore T.S.A= 2×38π(38+51)

T.S.A=76π×89

The total surface area(T.S.A) of the cylinder =6764πmm^2

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Answer:

2 1/5

Step-by-step explanation:

8 4/5=44/5

(44/5)/(4)=(44/5)*(1/4)

(44/5)*(1/4)=44/20

44/20=2 1/5

Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

The percentage decrease in population is 17%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply it by 100. percentage . The word per cent means per 100. It is represented by the symbol “%”.

percentage decrease in population= (0riginal population- new population)÷ original population × 100

%decrease in population = (181000 - 150230) ÷ 181000× 100

=( 307770×100)/181000

= 17%

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17%

Step-by-step explanation:

i tried it it worked

The function notation when the function was shifted right 6 is f(x-6).

Given that, the function was shifted right 6 units.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

So, the transformation from the original function to new function is

f(x-6)

Therefore, the function notation when the function was shifted right 6 is f(x-6).

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The simple interest on $1,200, 3.9%, 8 months is $31.356.

From the informationm, we want to calculate the simple interest of the amount that is given.

The simple interest is calculated thus:

Simple interest = PRT / 100

where

P = Principal = $1200

R = Rate = 3.9%

T = Time = 8 months = 8/12 = 0.67 years

The interest will be:

Simple interest = PRT / 100

Simple interest = (1200 × 3.9 × 0.67) / 100

Simple interest = 31.356

The interest is $31.356.

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Complete question

Calculate the simple interest on $1,200, 3.9%, 8 months

Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here, the given line is

2x + 5y = 10

5y = -2x + 10

[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]

Slope of the given line is [tex]-\frac{2}{5}[/tex]

Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]

The line passes through (-2, -3)

Equation of the required line

[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]

Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

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Answer:

x>=3 make the inequality false

Step-by-step explanation:

4x-2x<12-6

2x<6

x<3

Answer:

Any number higher than 3

Ex. 4, 5, 6, 7, 8, 9, 10, etc

Step-by-step explanation:

4x + 6 < 2x + 12

-2x        -2x

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

2x + 6 < 12

      -6    -6

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

2x < 6

÷2   ÷2

-----------

x < 3

Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4

4(4) + 6 < 2(4) + 12

16 + 6 < 8 + 12

22 < 20 (false)

I hope this helps!

Answer:

1.7 gallons

Step-by-step explanation:

You would chand the 1/2 and 4/5 into tenths by multiplying 1/2 by 5 getting 5/10 then multiplying 4/5 by 2 to get 8/10 so you would have 13 5/10- 11 8/10 to get 1.7 gallons left.

Answer:

Strings packs cost $14 each

Step-by-step explanation:

Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?

Lenny: 2s

Lashae: 2s + b

when b = $16 then these equations are:

Lenny: 2s

Lashae: 2s + 16

together they spent $72 so:

lenny + Lashae = $72 or:

2s + 2s + 16 = 72

subtract 26 from both sides:

2s + 2s + 16 - 16 = 72 - 16

2s + 2s = 56

combine s terms:

4s = 56

divide both sides by 4:

4s/4 = 56/4

s = $14