A toy store is having a sale. A video game system has an original price of $99. If it is on sale for 40% off the original price. Find the sale price of the game system. Round to the nearest CENT.

14912 years ago, the tree that was used to kill the support pole died which is one-sixth of the carbon-14 of a modern, living tree.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

One-sixth of a modern, living tree's carbon-14 is present in an ancient structure.

Assume that the half-life of carbon-14 is 5770 years

As per the given condition, the expression would be

[tex]A(t) = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\\A(t) = (0.167)A_o}[/tex]

[tex](0.167)A_o} = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]

[tex](0.167) = \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]

Take the logarithms of both sides to get:

[tex]log(0.167) =log \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]

Using logₐ(xⁿ) = n logₐx.

⇒ log 0.167= (t/5770) log (0.5)

⇒ log 0.167/ log (0.5)= (t/5770)

⇒ 3 = (t/5770)

⇒ t = 3 × 5770

⇒ t = 14912

Hence, 14912 years ago, the tree that was used to kill the support pole died.

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The trip cost per person is 6 pounds.

Unit rate is the ratio of two different units, with the denominator as 1.

It means a rate for one of something.

We have,

Total members = 40

Each minibus cost = 30 pounds

Leisure centre cost = 150 pounds

Each minibus can carry = 15 people

The number of minibusses needed to carry 40 members:

= 40 / 15

= 2.67

= 3 minibusses.

This means we need  3 minibusses to carry 40 members.

Now,

The total cost for the trip:

= 150 pounds + 3 x 30 pounds

= 150 + 90

= 240 pounds

The cost per person:

= 240 / 40

= 6 pounds

Thus the trip cost per person is 6 pounds.

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Using the expected value of a discrete distribution, it is found that:

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

For the probabilities, we consider that it is given by the number of desired outcomes divided by the number of total outcomes.

For one bet, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 578 x 5/6 - 300 x 1/6 = $431.67.

For two bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 682 x 2/3 - 300 x 1/3 = $354.67.

For three bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 945 x 1/2 - 300 x 1/2 = $322.5.

For four bets, the distribution is given as follows:

Hence the expected value is given by:

E(X) = 1312 x 1/3 - 300 x 2/3 = $237.33.

Hence, considering the greatest and the smallest expected values, we have that:

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The equation of the line that passes through the point (0,0) and is perpendicular to the line y=-2x+10 is .

We will be using the concept of slope and equation of straight line for this question. Here it has been said that the line passes through (0,0) which is the origin, so we know the point ([tex]x_{1},y_{1}[/tex]) is (0,0).This point will be required while solving the equation for the straight line. The line is said to be perpendicular to another line given by y=-2x+10. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes is equal to -1. The slope of a line can be found from the equation of the line by dividing the coeeficient of x by the coefficient of y.

Slope of y=-2x+10 is -2

mx-2=-1⇒m=1/2

equation of a straight line,

[tex](y-y_{1} )=m(x-x_{1} )\\[/tex]

⇒y-0=[tex]\frac{1}{2}[/tex](x-0)

⇒y=[tex]\frac{x}{2}[/tex]

⇒2y=x

⇒2y-x=0

Thus the equation of the line that passes through (0,0) and is perpendicular to y=-2x+10 is 2y-x=0.

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Dots sold 65 T-shirts and 13 shorts

let the x represent the number of T-shirts and y and shorts

7x + 9y= 572.......equation 1

x= 5y........equation 2

substitute 4y for x in the equation

7(5y) + 9y = 572

35y  + 9y= 572

44y= 572
y= 572/44

y= 13

substitute 13 for y in equation 2

x= 5(13)

x= 65

Hence there 65 T-shirts and 13 shorts

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Answer:

Step-by-step explanation:

it would be great if u had the image, but at least I can give some advice: use the method of rise over run to find the slope. use 2 points and count the number of squares "rising" and turn right and count the number of squares "running". left and down if it's going downward.

for the y intercept, find the x that equals 0. your coodinate should look like this: (0, *insert y*)

Answer:

Step-by-step explanation:

go pathways gives all the answers

Answer:

4 + -1 = 3, 3 - 5 = -2.

Step-by-step explanation:

Hope this helps!!

The value of x and y by using the given expressions is x = -5/2 and y = -15/2.

What is an expression?

An expression can be defined as the combination of variables and constants with two or more operations applied to it. The operation can be addition, subtraction, multiplication and division.

Simplifying the expressions for x and y

The given expressions are:

x - y = 5           —--- 1

x + y = -10             —---- 2

Adding the expression 1 and 2, we get,

2x = -5

x = -5/2

Subtracting the expression 1 and 2, we get,

-2y = 15

y = -15/2

Hence, the value of x and y by using the given expressions is x = -5/2 and y = -15/2.

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Answer: 40

Step-by-step explanation:

if 6 games = 24 tokens

then 1 game = 24/6=4

so 10 games = 4*10=40

Answer:

40

Step-by-step explanation:

24/6 = 4 tokens per game

4*10 games = 40

Answer:

2445

Step-by-step explanation:

it would have 2445 more costumers

Answer:

2445

Step-by-step explanation:

Subtract.

14301 - 11856 = 2445 more people on weekdays

Answer:

the answer is 7+1-7+0/xx{12

Step-by-step explanation:

the answer above stated is correctly corrected correct

Answer:

570

Step-by-step explanation:

570

The absolute difference that is between the loans paid as 570

We have the following details:

Po = $15000

loan a 5 year loan, interest = 8 percent and repayments = 304.15 dollars

Loan b

3 year loan, interest = 11 percent repayments = $491.08

Total number of repayments = 5 x 12 = 60

Total repayments = 304.15 dollars x 60

= $18249

The total interest that is paid for A would be

$18249 - $15000

= $3249

For the second loan

Total number of repayments = 3 x 12 months = 36

Total repayment = 36 x 491.08 = $17678.88

The total interest for the loan B would be: $17678.88 - $15,000

= $2678.88

Then the absolute difference between the paid loan would be

$3249 -  $2678.88 = 570.12

Hence we would have the absolute difference that is between the loans paid as 570.

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Since the pairs of y values have singular and unique x values, the following set of points are a function.

Since an increase in one unit in the x value, yields an increase in one unit in the the y value, there exists a relation between these set of points.

[tex]y (x)= x + 3 \\ D_{f} ∈ [1,3][/tex]

Option: C

Th elastic potential energy of two decimal places is    k=60×1^2 N/M

Given that,

Spring has a potential energy of =30 J

we know that,

Energy of a spring=1/2 kx^2

here, x=1cm

x^2=0.01m

30=1/2 kx^2

30=1/2 k(0.01)^2

60=k(0.01)^2

k=60/(0.01)^2

k=60×1^2N/M

Hence the potential energy of two decimal places is k= 60×1^2 N/M

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Answer:

–24x – 24 = x3 + 8x2

Step-by-step explanation:

-24x-24=x^3+8x^2

x^3+8x^2+24=-24x-24+24

x^3+8x^2+24=-24x

x^3+8x^2+24+24x=-24x+24x

x^3+8x^2+24x+24=0

Answer: x=-2

Step-by-step explanation:

[tex]-24x-24=x^3+8x^2\\-24x-24+24=x^3+8x^2+24\\-24x=x^3+8x^2+24\\-24x+24x=x^3+8x^2+24+24x\\0=x^3+8x^2+24x+24\\x^3+8x^2+24x+24=0\\x^3+8x^2+12x+12x+24=0\\(x)(x^2+8x+12)+(12)(x+2)=0\\(x)(x^2+2x+6x+12)+(12)(x+2)=0\\(x)((x)(x+2)+6(x+2))+(12)(x+2)=0\\(x+2)((x)(x+6)+12)=0\\ (x+2)(x^2+6x+12)=0\\x+2=0\\x+2-2=0+(-2)\\x=-2\\x^2+6x+12=0\\D=(-6)^2-(4)(1)(12)\\D=36-48\\D=-12\\Hence,\\The\ equation\ has\ no\ valid \ roots\\Thus,\\x=-2[/tex]

+5 degree.

Formula for Length Change due to Thermal Expansion: The formula for calculating the change in length of a substance due to thermal expansion is ΔL=αLΔT Δ L = α L Δ T where L is the original length of the substance and ΔT is the change in temperature of the substance either in degrees Celsius or in Kelvin.

For comparision of temperature -

Subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C.

Given data

temperature of tuesday = 55 degree

temperature of saturday = 60 degree

Difference between temperature  = 60 -55 = 5 degree.

Hence, 5 degree more colder was Tuesday then Saturday.

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The translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).

We are given the translation as:

(x , y)  → (x - 5 , y + 1)

Now we have some points:

Z (−3, –4)

K (−2, −1)

M (0, -1)

We need to translate these points.

For Z (−3, –4), we get the translation as:

Z (−3, –4) = Z' ( - 3 - 5 , - 4 + 1)

Z (−3, –4) = Z' ( - 8 , - 3 )

For K (−2, −1), we get the translation as:

K (−2, −1) = K' ( - 2 - 5 , - 1 + 1)

K (−2, −1) = K' ( - 7 , 0 )

For M (0, -1), we get the translation as:

M (0, -1) = K' ( 0 - 5 , - 1 + 1)

M (0, -1) = K' ( - 5 , 0 )

Therefore, we get the translation of the points as Z' ( - 8 , - 3 ), K' ( - 7 , 0 ) and K' ( - 5 , 0 ).

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Answer:

i don't know how to attach the file

1683 доллара - 102% . Найдем 1  процент и умножим его на 100%, тем самым получив ответ:

1) 1683 / 102 = 16.5 доллара - 1 % от всей зарплаты

2) 16.5 * 100 = 1650 - изначальная сумма, которую получал Андрей до повышения.

Ответ : 1650 $

The equation when solved for t gives d/r

Subject of formula can be defined as a variable or element expressed in terms of other variables in an equation.

Iris also known as the variable that is being worked out in equation.

From the information given, we have the equation as;

d = rt

Where;

Now, let's make 't' the subject

Divide both sides by the coefficient of t

d/r = rt/r

t = d/r

Thus, the equation when solved for t gives d/r

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The complete question:

The formula below relates distance, rate, and time. Solve this formula for t.

d = rt

Answer: Irrational Number

Step-by-step explanation: It's Irrational because it cant be represented as a simple fraction.

Answer:

9x

Step-by-step explanation:

=9x+8x+9x-8x-9x

=9x

Answer:

8 pizzas

Step-by-step explanation:

Answer:

Subscribe to itsIceboiiYT

Answer:

[tex] \large \sf \: x=30[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

5/9 = x/54

Step 1: Cross-multiply.

5/9 = x/54

(5)*(54)=x*(9)

270=9x

Step 2: Flip the equation.

9x=270

Step 3: Divide both sides by 9.

9x/9 = 270/9

x=30

Solution:

A.) [tex](-4-\sqrt{13},-4+\sqrt{13})[/tex]

Hope this helps!

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

For the given function :

[tex]\qquad \sf  \dashrightarrow \: f(x) = \dfrac{7}{x - 10} - 7[/tex]

f(x) is defined for all real values of x, except the value of x for which the denominator becomes 0, because if denominator is 0, the function at that instant will be undefined.

that is : f(x) is not defined when :

[tex]\qquad \sf  \dashrightarrow \: x - 10 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 10[/tex]

Hence, f (x) is defined for all real values of x except 10

It can be represented as :

[tex]\qquad \sf  \dashrightarrow \: f(x) : x \in R \sim \{10 \}[/tex]

Answer:

He now has 64 marbles.

Step-by-step explanation:

This is because 1/5 of 80 is 16.