Answer:
294 grams
Explanation:
The amount of radioactive material left after t hours given that the half-life is to hours is
[tex]A=P(0.5)^{\frac{t}{t_0}}[/tex]Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives
[tex]A=2352(0.5)^{9/3}[/tex][tex]A=294g[/tex]which is our answer!
Hence, the amount of radioactive copper left after 9 hours is 294 grams.
2 × 4/3, but the answer as a fraction
The given expression is : 2 × 4/3
[tex]\begin{gathered} 2\times\frac{4}{3}=\frac{2\times4}{3} \\ 2\times\frac{4}{3}=\frac{8}{3} \end{gathered}[/tex]Answer :
[tex]2\times\frac{4}{3}=\frac{8}{3}[/tex]
Mia makes a cold drink she calls iced punch. She uses vanilla ice-cream, grape juice and
ginger ale in the ratio 1:4:5. Mia has plenty of vanilla ice-cream, but only 2250ml of grape
juice and 2750ml of ginger ale. She makes as much iced punch as she can with these
ingredients. How much of each ingredient does she use?
A road crew must repave a road that is 3/4 miles long. They can repave 1/48 miles each hour. How long will it take the crew to repave the road?Write your answer in simplest form.
Let's use a rule of three to solve this:
This way,
[tex]x=\frac{\frac{3}{4}}{\frac{1}{48}}\rightarrow x=36[/tex]The crew will take 36 hours to repave the road
The decimal equivalent Of 5/8 is a terminating decimal true or false
Answer:
This statement is True.
Step-by-step explanation:
5/8 is equal to 0.625 in decimal form. Use our fraction to decimal calculator to convert any fraction to a decimal and to know if it is a terminating or a recurring (repeating) decimal. It is, a so called, 'terminating' decimal. To convert this fraction to a decimal, just divide the numerator (5) by the denominator (8).
A stand at the farmers market sells different types of apples, as shown in the table.
Apple A Apple B Apple C
Cost ($)4.90 1.00 0.45
Weight 4 lb 10 oz 1/2 lb
Which type of apple costs the least per pound?
The apple that costs the least per pound is Apple B.
What is the least cost?The cost per pound for each apple will be calculated as:
= Cost / Weight
Apple A:
= Cost / Weight
= 4.90 / 4
= $1.25 per pound
Apple B:
= Cost / Weight
= $1 / 10
= $0.1 per pound
Apple C:
Cost / Weight
= $0.45 / 0.5
= $0.9 per pound
Therefore, apple B is the cheapest
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Dialate about the origin using a scale factor of 1/3
To determine the post image coordinates after a dilation centered about the origin, we will simply multiply each of the coordinates by the given scale factor of 1/3.
Let's start with Point A.
[tex](-12\times\frac{1}{3},24\times\frac{1}{3})\Rightarrow(-4,8)[/tex]The post image coordinate of A is at (-4, 8).
Moving on to Point B.
[tex](-30\times\frac{1}{3},0\times\frac{1}{3})\Rightarrow(-10,0)[/tex]The post image coordinate of B is at (-10, 0).
Lastly to Point C.
[tex](-36\times\frac{1}{3},36\times\frac{1}{3})\Rightarrow(-12,12)[/tex]The post image coordinate of C is at (-12, 12).
The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Yo bro, I'm just doing this for the rewards for my homework. please don't read this or take it serious
Write the coordinates of the vertex after a dilation with a scale factor of 5, centered at the origin.T(-1, 5)T' (___,___)Write your answer as a pair of numbers separated by a comma and space, like this: 4, -9
Multiply the coordinates by the scale factor (5)
T'= (-1 x 5 , 5x5) = (-5,25)
T' = (-5,25)
Solve each triangle. Round answers to the nearest tenth, if necessary.
Given the triangle DEF.
Angle E = 71.2˚
e = 29.5 cm
f = 30.3 cm
We are to solve for each triangle.
Using laws of sine:
a = b = c
sinA SinB SinC
In this case we will have:
e = f
SinE SinF
29.5 = 30.3
sin 71.2˚ sinF
cross multiply
sinF(29.5) = sin 71.2˚(30.3)
sinF = sin 71.2˚(30.3)
sin 29.5
sinF = 0.9466 * 30.3
0.4924
sinF = 58.2524
The outside temperature decreases 7*f in 3 1/2 hours.
How would you represent the temperature as unit
A temperature drop of 7 degrees Fahrenheit in 3.5 hours is represented by 2 f/hour.
What is the definition of Fahrenheit?Fahrenheit temperature scale, based on the freezing point of water at 32° and the boiling point of water at 212°, with the interval between the two divided into 180 equal parts.
Given: The outside temperature drops by 7 degrees Fahrenheit in 3 1/2 hours.
We need to represent the temperature as a unit.
To do so, we must represent the temperature change per hour.
7f/3.5 hours = 2 f/hour
Therefore, the temperature that decreases by 7 degrees Fahrenheit in 3.5 hours can be represented as 2 f/hour.
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evaluate the expression, given the functions f and h: f(x)=3x-1, h(x)=-2x^2+3x-9. f(7/3)-h(-2)
The value of the function f(7/3)-h(-2) is 30
What are functions?Functions are simply defined as theorems, laws, equation or rules that holds true for the relationship between two variables in a given expression.
The variables are known as;
Independent variableDependent variableGiven the functions as;
f(x)=3x-1 h(x)=-2x^2+3x-9To determine f(73), substitute the value as x in the function, we have;
f(7/3) = 3(7/3) - 1
expand the bracket
f(7/3) = 7 -1
f(7/3) = 6
For h(-2), substitute the value as x in the function, we have;
h(-2) = -2(-2)² + 3(-2) - 9
expand the bracket
h(-2) = -8 -6 - 9
Subtract the values
h(-2) = -23
Now, f(7/3)-h(-2) = 7 --23
f(7/3)-h(-2) = 30
Hence, the value is 30
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A bicycle has a listed price of 803.98 before tax. If the sales tax is 9.5%, fins the total cost of the bicycle with sales tax included. Round to the nearest cent its necessary.
The total cost with taxes included is given by
[tex]803.98+803.98\times\frac{9.5}{100}[/tex]which is equal to
[tex]803.98(1+\frac{9.5}{100})[/tex]which gives
[tex]\begin{gathered} 803.98(1+0.095) \\ 803.98(1.095) \end{gathered}[/tex]then, we have $880.3581. By rounding to the nearest cent, the answer is $880.36
Point (-3,2) Line x + y = 3 (Question parts in the photo, sorry)
a)
The slope intercept equation of a line is expressed as
y = mx + c
where
m is the slope
c is the y intercept
The given equation is
x + y = 3
y = - x + 3
By comparing both equations,
m = - 1
If two equations are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point (- 3, 2) is - 1
We would find the y intercept by substituting x = - 3, y = 2 and m = - 1 into the slope intercept equation. It becomes
2 = - 1 * - 3 + c
2 = 3 + c
c = 2 - 3
c = - 1
By substituting m = - 1 and c = - 1 into the slope intercept equation, the equation of the line is
y = - x - 1
b) If two equations are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line Thus, the slope of the perpendicular line passing through the point (- 3, 2) is - - 1/1 = 1
We would find the y intercept by substituting x = - 3, y = 2 and m = 1 into the slope intercept equation. It becomes
2 = 1 * - 3 + c
2 = - 3 + c
c = 2 + 5
c = 5
By substituting m = 1 and c = 5 into the slope intercept equation, the equation of the line is
y = x + 5
a) y = - x - 1
b) y = x + 5
Fill in the blanks so the left side is a perfect square trinomial. That is, complete the square.x² - 6x +__ = (x -__)^2
Given:
[tex]x^2-6x+__{-----}=(x\text{ -}\_\_\_\_\rparen^2[/tex]Find: fill in the blanks.
Explanation:
[tex]x^2-6x+9=(x-3)^2[/tex]Find the slope of a line parallel to the line whose equation is x-y = 4
Answer: Slope of 1.
Step-by-step explanation:
First, we will put the equation into slope-intercept form.
x - y = 4
x = y + 4
y = x - 4
Our slope, when the line is written as y = mx + b, is the m value. Our m value here is one, so the slope of a line parallel to the line whose equation is x - y = 4 is 1.
Joe is taking an amortized loan for 85,000 to open a small business, and it's deciding between the offers if two lenders. He wants to know which one would be the better deal over the life of the small business loan, and by how much. a) His credit union had offered him a 9- year small business loan at an annual interest rate of 14.4% find the monthly payment $_b) a bank has offered him a 10-year small business loan at an annual interest rate of 12.8% find the monthly payment c) suppose Joe pays the monthly payment each month for the full term. which lender small business loan would have the lowest total amount to pay off, and how much? Credit UnionThe total amount paid would be $ less than the bank. BankThe total amount paid would be $ less than the credit union.
A building floor plan is shaped like a trapezoid, with two right angle corners. If the third corner is a 40° angle, what is the measure of the fourth angle?
Recall that the interior angles of a regular quadrilateral add up to 360 degrees, and a right angle has a measure of 90 degrees.
Let x° be the measure of the fourth angle, then we can set the following equation:
[tex]40^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}.[/tex]Adding like terms we get:
[tex]220^{\circ}+x^{\circ}=360^{\circ}.[/tex]Subtracting 220 degrees from the above result we get:
[tex]\begin{gathered} 220^{\circ}+x^{\circ}-220^{\circ}=360^{\circ}-220^{\circ}, \\ x^\circ=140^\circ. \end{gathered}[/tex]Answer:
[tex]140^{\circ}.[/tex]If $16,000 is invested at 8% for 12 years, find the future value if the interest is compounded
semiannually.
Please round the answer to the nearest cent.
The future value is $
t - the number of years the money is invested for
P = $16,000
m =2
t = 12 yr
r = 8% or .08
FV = 16,000* ( 1+ .08/2) 2*12 = 16000 (1.04) 24 = 16000* (2.5633041) = $41012.8656
FV - the future value of the investment = $41012.87 is answer
Given the scatter plot on the graph below. What is the slope of the line of fit
Hello there. To solve this question, we'll have to remember some properties about scatter plots and slope of a line.
Given the scatter plot of the data information, we have to determine the slope of the line.
For this, we could determine it numerically using the least squares method, if we knew the data (the coordinates of the points we're plotting the best fit).
In this case, we simply need to find, by inspection, two points contained in the line and use the slope formula.
Given two points (x0, y0) and (x1, y1) that a line L passes through, then the slope m of this line is given by:
[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]By inspection, we can easily spot the points (16, 12) and (28, 20).
Plugging these coordinates in the formula, we get:
[tex]m=\frac{20-12}{28-16}[/tex]Add the numbers and simplify the fraction
[tex]m=\frac{8}{12}\overset{:4}{=}\frac{2}{3}[/tex]This is the slope of this line.
Consider the two expressions (6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)/(2x + 3 - 7x - 11) and 4x^2 - 7 + 1/(2x + 3 - 7x - 11)
a) Show that the two expressions represent equal numbers when x = 10
b) Explain why these two expressions do not represent equal numbers when x = -3/2
c) Show that these two expressions represent equal numbers for all x other than -3/2.
Step-by-step explanation:
a)
(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)
[tex] \sf \frac{(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)}{(2x + 3 - 7x - 11)}[/tex]
[tex] \sf = \frac{(6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8)}{(2(10) + 3 - 7(10) - 11)}[/tex]
[tex] = \frac{ - 5175}{58}[/tex]
4x^2 - 7 + 1/(2x + 3 - 7x - 11)
[tex] \sf{ 4x^2 - 7 + \frac{1}{(2x + 3 - 7x - 11)}}[/tex]
[tex] \sf{ 4(10)^2 - 7 + \frac{1}{(2(10) + 3 - 7(10) - 11)}}[/tex]
[tex] = \sf \frac{22793}{58}[/tex]
√ 3 ⋅ √ 5 ⋅ √ 13 simplified answer
Answer: √195 or 13.96424004
Step-by-step explanation:
Answer:
[tex]\sqrt{195}[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{13}[/tex]
[tex]\textsf{Apply the radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]
[tex]\implies \sqrt{3 \cdot 5 \cdot 13}[/tex]
[tex]\implies \sqrt{15 \cdot 13}[/tex]
[tex]\implies \sqrt{195}[/tex]
This cannot be simplified any further.
Question 4 of 10
Solve 2x + 6 8 or 2x + 8 > 12.
A. x2 or x > 6
B. x
1 or x > 6
C.
2 and x > 2
1 ora > 2
OD. x
SU
The value is x≤1 or x>2
What is inequalities?Equations don't always need to have a "equal to" symbol on both sides to be balanced. Sometimes it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
2x +6≤8 or 2x + 8 > 12
2x +6≤8
2x ≤2
x≤1
2x +8>12
2x>4
x>2
The value is x≤1 or x>2
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College Algebra
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 hours, while the outlet pipe can empty it in 8 hours. How long will it take to fill the vat if both pipes are left open?
It will take__ hours.
(Simplify your answer. Do not round.)
Answer:
3 1/13
Step-by-step explanation:
rate(time) of one pipe + rate(time) of the other pipe = 1 job
The rate would be the the number of jobs over the time
The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.
Together:
1/5t + 1/8t = I job
t(1/5 + 1/8) = 1
t(8/40 + 5/40) = 1
t(13/40) = 1 multiply each side by 40/13
t(40/13)(13/40) = 1(40/13)
t = 40/13
t = 3 1/13
I need help with finding the area and the perimeter for a trapezoid thank you
From the figure given in the question, we are asked to find the area and perimeter.
(a) Area:
Since the figure is a trapezoid, the formula for the area of a trapezoid is:
Area = (a + b)h
2
Where:
a = 2
b = 5
h = 4
Area = (2 + 5)4
2
Area = 7/2 * 4
Area = 3.5 * 4
Area = 14 cm²
(b) Perimeter:
To get the perimeter, we will have to add all the side length.
But we will have to find the missin side length first.
Using pythagoras:
a² + b² = c²
Where:
a = 4
b = 3
c² = 4² + 3²
c² = 16 + 9
c² = 25
Taking square of both sides:
c = √25
c = 5
Since we have gotten the missing side length as 5cm, we can now add all the given side length to get the perimeter.
Perimeter = 4 + 2 + 5 + 5
Perimeter = 16 cm
I need help with statistical problem I have got the answer of 0.3354 because I subtracted 0.9991 - 0.146 I wanted to know if that was correct I kept getting the answer wrong
Data:
• Cumulative probability of -2.18 ,: 0.0146
• Cumulative probability of 3.74 ,:, ,0.9999
Procedure:
0. Using the following formula we can get our probability.
[tex]P(-2.182. Replacing the values previously got from a Standard Normal Table.[tex]P(-2.18Answer: 0.9853
An agent lists a sellers house for 6% commission. The final agreed sales price is $205,000. How much commission did the seller pay?
Out of $205000, the total commission earned by the agent will be $12300.
What is Commission?
A commission is a fee paid to a salesperson in exchange for services in facilitating or completing a sale transaction. Mathematically -
Commission [C] = Sales revenue [R] x commission rate [rc]
Given is an agent who lists a sellers house for 6% commission. The final agreed sales price is $205,000.
The total sales price = [P] = $205000
The commission on house = [C] = 6%
Now, the money agent gets as a commission will be = [M] -
[M] = 6% of 205000
[M] = (6/100) x 205000
[M] = 6 x 2050
[M] = 12300
Therefore, out of $205000, the total commission of the agent will be $12300.
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I need help solving for x and y
[tex]\cos \theta=\frac{x}{16} \implies x=16 \cos \theta \\ \\ \sin \theta=\frac{y}{16} \implies y=16 \sin \theta[/tex]
Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."cos(x) + cos(x) = 4cos(x) + 4
The solutions to the quadratic trigonometric equation are given as follows:
x = kπ, k = ± 1, ± 3, ± 5, ± 7.
How to solve the quadratic trigonometric equation?The quadratic trigonometric equation is defined as follows:
cos²(x) + cos(x) = 4cos(x) + 4.
Then the following transformation is applied to solve the equation:
y = cos(x).
Hence:
y² + y = 4y + 4
y² - 3y - 4 = 0
(y - 4)(y + 1) = 0.
Applying the Factor Theorem, the solutions are given as follows:
y - 4 = 0 -> y = 4.y + 1 = 0 -> y = -1.However, we want the solutions for x, hence they are obtained as follows:
cos(x) = 4.
x = arccos(4), which has no solution, as there are no angles with a cosine of four.
cos(x) = -1.
x = arccos(-1)
x = kπ, k = ± 1, ± 3, ± 5, ± 7
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solve the equations and verify the answer
The value of m is -6/5.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Given:
2m -3 = 3/10 (5m - 12)
Now, cross multiplying
10( 2m -3)= 3( 5m -12)
20m -30 = 15m - 36
20m- 15m= -36 + 30
5m = -6
Divide both side by 5
m= -6/5
Verification:
LHS = 2m-3
=2(-6/5)-3
=-12/5-3
=-27/5
and, RHS
= 3/10( 5m -12)
=3/10(5 x (-6/5) -12)
=3/10 (-6 - 12)
=3/10 x -18
= -54/10
= -27/5
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Can you please help me out with a question
Note:
For similar shapes, the ratio of their areas is equal to the square of the ratio of sides.
That is:
[tex]\text{ ratio of areas of similar shapes = (ratio of sides )}^2[/tex][tex]\begin{gathered} \frac{846}{376}\text{ = (}\frac{X}{24})^2 \\ \frac{846}{376}\text{ = }\frac{x^2}{576} \\ \text{cross multiply} \\ 376X^2=\text{ 576 x 846} \\ 376X^2=487296 \\ X^2=\frac{487296}{376} \\ X^2=1296 \\ X=\sqrt[]{1296}\text{ = 36} \end{gathered}[/tex]The value of X is 36