In order to determine the amount of radium after 800 years, use the following formula:
[tex]N=N_oe^{-\lambda t}[/tex]where,
N: amount of radium after t years = ?
No: initial amount of radium = 50g
λ: decay constant
t = 800
The decay constant is calculated by using the following expression:
[tex]\lambda=\frac{ln2}{t\frac{_1}{2}}=\frac{ln2}{1960}\approx3.5*10^{-4}[/tex]where t1/2 = 1960 is the half-life.
Now, by replacing λ, No and t = 800 you obtain:
[tex]N=50e^{-(3.5*10-4)(800)}\approx37.68g[/tex]Hence, after 800 years there are approximately 37.68g of uranium
What does the leading term of −5x^4+4x^3−6x^2+8 tell you?
Answer this for me please Number 2 have 3 more answer choices Which are 16:57D - the number of centimeters in x inches E- the height of a swinging pendulum as a function of timeF- the height of a ball tossed in the air as a function of time
1)
Consider P to be at the same vertical distance between the maximum and minimum height the blades can reach. Therefore, at t=0, P has to be at h=0 (the maximum height is 1 and the minimum one is -1).
Then, since the fan blades rotate counterclockwise, after t=0, h has to increase until it reaches a value of 1.
Finally, a revolution is completed after 1 second; therefore, at t=1, the h has to be equal to 0 (the same height as at t=0).
Thus, the graph that models the function is option D.2)
Approximately, every year the Earth reaches its maximum distance from the sun and its minimum distance once a year, and that is a cycle that repeats almost without alteration. Furthermore, since the position of the Earth around the sun is given by an ellipse, the position of the Earth around the Sun can be expressed using trigonometric functions (because of polar coordinates).
Similarly, a rotating wheel will reach its maximum and minimum height eventually; therefore, it can be modeled using trigonometric functions which are periodic.
Finally, as for the area of a sheet of paper. Notice that the more we fold it, the less its area becomes, it does not reach its maximum anymore.
Given x inches, the number of centimeters is 2.54x, this is not a periodic function.
Due to the effects of gravity, the height of a pendulum can be expressed using a periodic function given that no energy is lost.
The trajectory of a tossed ball is given by a parabola, unless one tosses the ball again at the same initial height, option F cannot be modeled using a periodic function.
The answers to part 2 are A, B, and E.I need questions 10 , 13 , 15 , and 16 solved with steps and graph
The graphic solutions for the expressions are given as follows:
10. x = 2.667 and x = 8.
13. x = 8.
15. x < -1 or x > 8.
16. x > 3.
Item 10In item 10, we are going to solve an equation graphically, hence we have to find the points of intersection of the two curves given by:
y = |x - 4|.y = 0.5x.From the first graph given at the end of the answer, the x-coordinates of these points are given as follows:
x = 2.667 and x = 8.
Item 13Now we have to find the point of intersection of these two equations:
y = 0.75x.y = 2x - 10.They have only one intersection point, at x = 8, which is the solution to the system.
Item 15The inequality is:
x² - 7x- 8 > 0.
Hence we have to find the intervals for which the function x² - 7x - 8 is above the x-axis, and from the third graph, these intervals are described as follows:
x < -1 or x > 8.
Item 16The inequality is:
x - 5 > -2x + 4.
Combining the like terms, it can be written as;
3x > 9
x > 3.
The interval for which the increasing line is above the decreasing line is x > 3, and is shown in the fourth graph.
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Write the sentence as an inequality. The sum of 3 times a number n and 8 is at most 16. 0 3n + 8 > 16 o 31 -8 < 16 O 3 + 8n
ANSWER
[tex]3n\text{ + 8 }\leq\text{ 16}[/tex]EXPLANATION
We want to write the sentence as an inequality.
We have:
The sum of 3 times a number n and 8 is at most 16.
3 times a number n is 3 * n i.e. 3n
Adding that to 8 would yield:
3n + 8
That is at most 16.
This means that it is less than or equal to 16.
That is:
[tex]3n\text{ + 8 }\leq\text{ 16}[/tex]I need help again……..
Answer:
me again. hope it can help.lol
Answer:
See below
Step-by-step explanation:
For this equation to have non-real roots, the discriminant (b^2 - 4ac) of the Quadratic Formula must be < zero
b^2 - 4ac < 0 b = 5 a = (n-2) c = -2
5^2 - 4 ( n-2)(-2) <0
25 + 8n - 16 <0
8n + 9 < 0
8n < -9
n < - 9/ 8
NO LINKS!! Please help me with this probability 1c
Answer: Choice A) [tex]\boldsymbol{78.67\% \ \pm \ 9.46\%}[/tex]
======================================================
Explanation:
phat = 59/75 = 0.7867 = 78.67% approximately is the sample proportion
n = 75 is the sample size
Your teacher doesn't mention a confidence level, so I'll assume it's the default 95%.
Let's compute the margin of error at 95% confidence
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.7867*(1-0.7867)/75)
E = 0.0927 approximately
E = 9.27% approximately
Unfortunately the margin of error 9.27% isn't listed among the four answer choices, but let's change the z = 1.96 to z = 2 instead.
Recalculate the margin of error.
E = z*sqrt(phat*(1-phat)/n)
E = 2*sqrt(0.7867*(1-0.7867)/75)
E = 0.0946 approximately
E = 9.46% approximately
This margin of error is listed among the four answer choices.
------------------
We found that
phat = 78.67% approximatelyE = 9.46% approximatelyThe confidence interval in the format [tex]\text{phat} \ \pm \ \text{E}[/tex] is approximately [tex]78.67\% \ \pm \ 9.46\%[/tex] which points us to choice A as the answer.
Answer:
[tex]\textsf{a)} \quad 78.67\% \pm 9.46\%[/tex]
or d) None of the answers are correct. (Please see notes below).
Step-by-step explanation:
P-hat is the probability that a given outcome will occur given a specified sample size.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{P-hat formula}\\\\$\hat{p}=\dfrac{X}{n}$\\\\where:\\\phantom{ww}$\bullet$ $\hat{p}$ is the probability. \\ \phantom{ww}$\bullet$ $X$ is the number of occurrences of an event. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]
Given:
X = 59n = 75Substitute the given values into the formula to find p-hat:
[tex]\implies \hat{p}=\dfrac{59}{75} =0.78666666...[/tex]
The critical value for a 95% confidence level using normal distribution is:
[tex]z=1.9600\;\;\sf (4\;d.p.)[/tex]
[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Margin of error}\\\\$ME=z \cdot \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$\\\\where:\\\phantom{ww}$\bullet$ $z$ is the critical value. \\ \phantom{ww}$\bullet$ $\hat{p}$ is the sample proportion. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]
Substitute the given values into the margin of error formula:
[tex]\implies ME=1.9600 \cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]
[tex]\implies ME=0.092715036...[/tex]
Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) is:
[tex]\implies \hat{p}\pm ME[/tex]
[tex]\implies 0.7867\pm 0.0927[/tex]
[tex]\implies 78.67\% \pm 9.27\%[/tex]
This result if not given in the list of answer options. However, the final result depends on the accuracy of the z-score and p-hat used in the calculations.
If we round the critical value to the nearest integer then:
[tex]\implies z=2[/tex]
Substitute the rounded z-value into the margin of error formula:
[tex]\implies ME=2\cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]
[tex]\implies ME=0.094607180...[/tex]
Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) using z = 2 is:
[tex]\implies 78.67\% \pm 9.46\%[/tex]
Note: It is likely that this question required the critical value to be rounded to the nearest integer, however please note that this is not normal practice as it produces a different result, as evidenced above.
Find the value of x in the given right triangle. 12. x = [?] 62° х Enter your answer as a decimal rounded to the nearest tenth. Enter
EXPLANATION
Let's see the facts:
We can use the Law of Cosines to calculate the unknown value:
[tex]\cos \alpha\text{ = }\frac{\text{Adjacent cathetus}}{\text{Hypothenuse}}[/tex]Replacing terms:
[tex]\cos 62\text{ = }\frac{x}{12}[/tex]Isolating x:
[tex]x\text{ = 12}\cdot\cos 62\text{ = 6}[/tex]Answer is x=6.
I need help on this Homework question and also please give the steps on what lead to the answer.
The function is given by:
[tex]f(x)=x(x^2+7)(x^2-8)[/tex]The three quantities are zero then it follows:
[tex]\begin{gathered} x=0;x^2+7=0;x^2-8=0 \\ x=0;x^2=-7;x^2=8 \\ x=0,x=\pm\sqrt[]{7}i;x=\pm2\sqrt[]{2} \end{gathered}[/tex]Option D is correct.
what is the scale factor form polygon ABCD to the polygon PQRS
The scale factor in this polygon comparison can easily be found as 1.5 because when we divide the length of for example side PS (3 units) by the size of side AD (its pre-image which measures 2 units) we get:
3/2 = 1.5
We could try also the same with any other of the sides in image and pre-image, like PQ comared to AB. PQ has a length of 1.5 units, while AB has a length of 1 unit. Then:
PQ/AB = 1.5/1 = 1.5
Which of the expressions are equivalent to the one below? Check all thatapply.5•(3 + 7)A. 5•(7+3)B. 5.3 + 5.7C. (5.3) +7D. (3+7)5
Concept
To solve the question you will use the associative property.
a . ( b + c ) = a . b + a . c
The expressions that is equivalent to 5 .(3 + 7) = 5 . 3 + 5 . 7 , ( 3 + 7 ) 5 , 5 . (
Fi
(2, y) for all real y
[if solved and correct give 30 points+ brainliest]
Answer:
You actually cannot find Y using this knowledge!
Step-by-step explanation:
( 2, y ) It only shows how X is 2, you need more information to find y. If you can respond, try to give me more information, I am willing to help!
QUESTION 9 1 POINTSimplify: ( 12 + 1/2 m)÷ 0, where + #0.4 2If the given expression is undefined enter Ø as your answer.Provide your answer below:Content attribution
Given
[tex](\frac{1}{4}+\frac{1}{2}m)\div0[/tex]Find
Simplify
Explanation
[tex]\begin{gathered} (\frac{1}{4}+\frac{1}{2}m)\div0 \\ \\ (\frac{1+2m}{4})\div0 \end{gathered}[/tex]as we know , any number divided by zero is infinity because division by zero is undefined and infinity does not really exist.
so , the solution is undefined.
Final Answer
Hence , the solution is undefined. so , the answer is
[tex]\emptyset[/tex]The table lists several points that form a line on a coordinate plane. x y 4 6 12 8 16 9 28 12 Based on the information in the table, what are the y-intercept and slope of the line described by these points?
A.y-intercept: = 2; slope: m = 4
B.y-intercept: = –20; slope: m =14
C.y-intercept: = 5; slope: m = 4
D.y-intercept: = 5; slope: m =14
Slope is 1/4 (0.25) while y-intercept is 5.
Here, we are interested in getting the y intercept and slope of the line joining the given points.
We can get the slope by using any two points
Let’s say (4,6) and (12,8)
Mathematically; slope
= (y2-y1)/(x2-x1) = (8-6)/(12-4) = 2/8 = 1/4 = 0.25
To get the y-intercept, we proceed
kindly recall that the equation of a straight line is;
y = mx + c
where m is the slope and c is the y-intercept
Let’s take any of the points (28,12)
Thus:
12 = 0.25(28) + c
12 = 7 + c
c = 12-7
c = 5
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simplify for 4^n
4^11/4^-8
Answer: 4^3
Step-by-step explanation:
Answer: 4^3.
Step-by-step explanation:
factored form of y=x2-x-12
The factored form of y = x² - x + 12 will be (x + 3)(x - 4).
What is factor?It should be noted that a factor simply means the number than can be multiplied by another number to get the original number. The factored form is when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form can be restated in standard form.
This will be illustrated as:
x² - x - 12
x² - 4x + 3x - 12.
x(x - 4) + 3(x - 4)
(x + 3)(x - 4)
The factored form is (x + 3)(x - 4).
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the freshman class is selling popcorn and candles as a fundraiser popcorn and sell them for $5 a bag and candle sell $15 each a total of 824 items were sold and 5555 was raised how many of each item was sold
Step 1. Define our variables.
[tex]undefined[/tex]Multiple choice math pls help urgent
The correct option R avg(x) = 100 - 5x, shows the average revenue function.
What is termed as the revenue function?The average revenue demonstrates how much money is made per unit of output. In other words, it computes how much revenue a company earns on average from each unit of product sold. To find the average revenue, multiply the total revenue by the number of output units.Total revenue income is the money earned by a company from the sale of a specific amount of output. Total revenue is calculated by multiplying the price by the number of units sold.For the given question;
The revenue function is given by the equation,
R(x) = 100x - 5x²
Let the
Let the total revenue be 'x'.
Then,
Average revenue function = revenue function/ total revenue
Average revenue function = (100x -5x²)/x
Average revenue function = 100 - 5x
Thus, the average revenue function is given by the equation 100 - 5x.
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I need help with number two please and thank you
Given:
Karla has a garden that is 14 feet long.
To convert feet into yards:
We know that,
[tex]\begin{gathered} \text{3 fe}et=1\text{ yard } \\ \text{1 fe}et=\frac{1}{3}\text{yard} \end{gathered}[/tex]So, for the 14 feet,
[tex]\begin{gathered} \text{14 fe}et=\frac{1\times14}{3}\text{yard} \\ =4\frac{2}{3}yards \end{gathered}[/tex]Hence, the answer is,
[tex]4\frac{2}{3}\text{ yards (or) 4.67 yards}[/tex]B
Find the slope for each line then determine if they are parallel, perpendicular, and neither.
Points on lines E & F;
Line E: (-1,-4) (5, -3) & Line F: (14, 3) (15,-3)
O Perpendicular
O Not Enough Information
O Parallel
ONeither
A basket holds m apples you pick 2n-3 apples and your friends picks n+4 how many baskets do you need to carry all the apples.
Answer: The number of baskets = (3n+1)/m
Step-by-step explanation:
The total number of apples picked:
yours (2n-3) + your friend (n+4)
Divide the combined total by the number in one basket (m):
((2n-3)+(n+4))/m
Simplify:
(3n+1)/m
If the interest rate changed from 10%
to 2%, what would happen to
borrowing?
A. Debtors would less likely want to borrow.
B. There would be a government law against rising
interest rates.
C. There would be no impact on borrowing.
D. There would be an increase in borrowing.
Consequently, borrowing would increase with the change in interest rate from 10 % to 2 %. The correct answer is Option D.
What happens to interest rates when borrowing becomes more expensive?The greater the ability of banks to lend, the greater the amount of credit available to the economy. And as the supply of credit expands, so does the cost of borrowing (interest). The amount of credit available to the economy decreases as lenders decide to postpone loan repayment.What effect does a change in interest rates have on business borrowing?Higher interest rates make it more expensive for businesses to borrow money through loans and lines of credit, and they also affect how much interest you pay on credit card or home purchase purchases.
Given that the interest rate has risen from 10% to 2%.
Borrowers can easily borrow by paying less interest now that the interest rate has dropped from 10% to 2%.
As a result, borrowing would increase with the decrease in interest rates. Option D is thus correct.
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Write an equation in point-slope form for the line that satisfies the given set of conditions.
slope of 0, passes through (0, -10)
y + 5x = 0 is the line's equation in point-slope form.
Given is a line with a slope of 0 and a point at (0, -10) on it. We must determine the line's point slope form equation.
What shape does a line's point slope take?The line's point-slope shape is ( y -[tex]Y_{1}[/tex] ) = m ( x - [tex]X_{1}[/tex] ).
According to the query, slope (m) = 0 and
the line is going through ( [tex]X_{1}[/tex] , [tex]Y_{1}[/tex] ) = ( 0 , -10 )
∴ ( y - [tex]Y_{1}[/tex] ) = m ( x - [tex]X_{1}[/tex] )
y + 10 = 0 ( x - 0 )
y + 10 = 0
y + 5x = 0
As a result, the equation for the line in point-slope form will be
y + 5x = 0.
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A scuba diver is swimming at -30 feet the divers depth then changes to 5 feet where could the diver be explain
The scuba driver will be 25 ft below the surface water after his position changed by 5 ft.
What is depth of a river?
The depth of a river is the vertical distance measured in straight line towards the center of earth from the surface of earth indicating to what level below the lithosphere does the sea beds exist.
Given is a scuba diver who is swimming at - 30 feet. The divers depth then changes to 5 feet.
The initial depth of the scuba driver = [D] = - 30 ft
Now, as the depth of the scuba driver changes by +5 feet, then the scuba driver will be at -
- 30 + 5
- 25 ft
Hence, the scuba driver will be 25 ft below the surface water after his position changed by 5 ft.
Therefore, the scuba driver will be 25 ft below the surface water after his position changed by 5 ft.
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Let F(x) = f(x ^ 5) * ndG(x) = (f(x)) ^ 5 You also know that a ^ 4 = 3 , f(a) = 2 , f^ prime (a)=13 , f^ prime (a^ 5 )=2
Given the functions:
[tex]\begin{gathered} F(x)=f(x^5) \\ \\ G(x)=(f(x))^5 \end{gathered}[/tex]Additionally, we know that:
[tex]\begin{gathered} a^4=3 \\ f(a)=2 \\ f^{\prime}(a)=13 \\ f^{\prime}(a^5)=2 \end{gathered}[/tex]We use the chain rule to find the derivatives of F(x) and G(x):
[tex]\begin{gathered} F^{\prime}(x)=f^{\prime}(x^5)\cdot(x^5)^{\prime}=5x^4\cdot f^{\prime}(x^5) \\ \\ G^{\prime}(x)=5(f(x))^4\cdot f^{\prime}(x) \end{gathered}[/tex]Finally, evaluating for x = a and using the results stated before:
[tex]\begin{gathered} F^{\prime}(a)=5\cdot a^4\cdot f^{\prime}(a^5)=5\cdot3\cdot2 \\ \\ \therefore F^{\prime}(a)=30 \end{gathered}[/tex][tex]\begin{gathered} G^{\prime}(a)=5\cdot(f(a))^4\cdot f^{\prime}(a)=5\cdot2^4\cdot13 \\ \\ \therefore G^{\prime}(a)=1040 \end{gathered}[/tex]Write a function rule to model each situation.
1 You are starting a yard-care business. You
decide to charge a flat fee of $15 plus a rate
of $8 per hour. Write a function rule in which
x is the number of hours and y is the total
amount you charge.
The function rule of the scenario is f(x) = 15 + 8x
How to determine the function rule?From the question, the given parameters are:
Flat fee = $15
Rate = $8
To determine the function rule of the scenario, we make use of the following template equation
f(x) = Flat fee + Rate * Number of hours
Where
f(x) = total and x = number of hours
So, we have
f(x) = Flat fee + Rate * x
This gives
f(x) = 15 + 8x
Hence, the function rule is f(x) = 15 + 8x
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Find 3 ratios that are equivalent to the given ratio. 30:42 Find three ratios that are equivalent to the given ratio. DA. 60:84 B. 5:126 DC. 60:7 D 90:7 DE. 60:126 OF 90:126 O G. 5:84 OH 5:7
The The 3 ratios are;
A=60: 84
F=90:126
H=5:7
For each calculation choose the correct answer written in standard form.
a) (7 × 10⁵ ) × (3× 10²)
A 21 × 10¹⁰
B 21 ×10⁷
C 2.1 × 10¹¹
D 2.1 × 10⁸
b) ( 2 × 10⁵) ÷ ( 4 × 10² )
A 2 × 10 ³
B 5 × 10²
C 0.5 × 10³
D 2 × 10²
Answer:
A car travels at average speed of 4m/s and covers a distance of 2.4km calculate the time take help me
please help asap !!!!
What is the solution of the equation [tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1[/tex] ?
x=4
How is the given equation solved?
[tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1\\\\\frac{2}{3} x-\frac{2}{3} -\frac{2}{5} x+\frac{3}{5}=1\\\\\frac{2}{3} x-\frac{2}{5}x =1+\frac{2}{3}- \frac{3}{5}\\\\\text{Taking LCM},\\\\\frac{10x-6x}{15} =\frac{15+10-9}{15} \\\\4x= 16\\\\x=4[/tex]
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics.Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.To learn more about equation solving, refer:
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How many degrees mustFigure A be rotatedcounterclockwise aroundthe origin in order to lineup with Figure B?АBA. 90B. 180C. 270D. 360
The answer is A 90 degrees
For a standard normal distribution, find:P(z > 1.74)
Solution
Using Z score calculator
P(x>Z) = 0.04093