Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.
What is the exponential function for the amount of the substance?It is given by, after t years:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
It will reach an amount of 7 parts per million when A(t) = 7, hence:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
[tex]7 = 14(2.71)^{-0.016t}[/tex]
[tex](2.71)^{-0.016t} = 0.5[/tex]
[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]
[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]
[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]
t = 43.5.
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Charlotte is running at a rate of 9 KM/H.
What is Charlotte's speed in M/S?
Answer: 5/2 M/S
Answer:
Step-by-step explanation:
[tex]9~km/h=\frac{9 \times ~1000}{1 \times 60 \times 60}=\frac{5}{2} m/s}[/tex]
Fine the IRQ of the data set. 11,13,9,4,6,5,8,10
PLEASE HELP!!!!!!!!!!!!!!
Answer:
5
Explanation:
Data Set : {11, 13, 9, 4, 6, 5, 8, 10}
Arrange ascendingly: {4, 5, 6, 8, 9, 10, 11, 13}
Quartiles:
Q1 --> 5.5Q2 --> 8.5Q3 --> 10.5Interquartile Range: Q3 - Q1 = 10.5 - 5.5 = 5
Proper ascending ordered set
{4,5,6,8,9,10,11,13}Q1
6+5/2=5.5Q3
11+10/2=10.5IRQ
Q3-Q1=10.5-5.5=5If A=P+I make the subject as P
Answer:
[tex]P = A - I[/tex]
Step-by-step explanation:
A = P + I (Given)[tex]\implies P = A - I[/tex]Weights of four-year-olds are Normally distributed, with a mean of 40 pounds and a standard deviation of 1.3 pounds. At his four-year checkup, Marlon’s weight is measured to be greater than 30% of boys his age. How much does Marlon weigh?
Find the z-table here.
37.6 pounds
38.4 pounds
38.7 pounds
39.3 pounds
Picture posted below
Marlon's weight is 39.3 pounds with a mean weight of 40 pounds and a standard deviation of 1.3 pounds.
We know that the formula for calculating a z-score is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Given that mean weight = 40 pounds.
and standard deviation = 1.3 pounds.
Also given that Marlon is heavier than 30% of boys his age on average, according to measurements.
The z value of 30% is -0.524.
We can put this value in the formula.
-0.524 = (x - 40)/1.3
i.e. (-0.524) * 1.3 = x - 40
i.e. - 0.6812 = x - 40
i.e. x = 40 - 0.6812 = 39.3188
Therefore, we can conclude that Marlon's weight is 39.3 pounds with a mean weight of 40 pounds and a standard deviation of 1.3 pounds. So, the last option is correct.
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4. Three weeks later, you find a scooter on sale for $399.99, which reflects a discount rate of 30%.
What percentage of the original price is $399.99? Show the proportion to solve the equation.
What was the original price? (Hint, you will need to perform subtraction, similar to the
example).
Answer:
70%
$571.41
Step-by-step explanation:
100% means 1, or a whole thing.
Since the discount is 30% of the original price, and the original price is 100% of the original price, then
100% - 30% = 70%
With a 30% discount, you actually pay 70% of the original price.
$399.99 is 70% of the original price.
399.99 / 70% = x / 100%
70x = 100 × 399.99
x = 571.41
The original price was $571.41.
1. Henry is working in a pack room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs. Which of the following weights are allowable? Circle all allowable weights.
a. 34
b. 36
C. 29
d. 40
The allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Henry is working in a packed room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs.
Weight of the bag = 35 lbs
Tolerance = ± 5 lbs
Allowable weights = 35 ± 5
= 35 + 5 = 40 lbs
= 35 - 5 = 30 lbs
Thus, the allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.
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Normal annual capacity for star company is 36,000 machine hours, with fixed factory overhead budgeted as Rs. 16,920 and an estimated variable factory overhead rate of Rs. 2.10 per hour, During October actual production required 2,700 machine hours, with a total factory overhead of Rs. 7,400. Required: Compute: 1) The applied factory overhead 2) The over-or underapplied factory overhead amount for October,
The applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
Applied and under applied factory overhead1. Applied factory overhead:
Predetermine overhead rate=Fixed overhead/Machine hours
Predetermine overhead rate=16,920/36,000
Predetermine overhead rate=0.47
Applied overhead=Machine hours×Rate
Variable=2700×2.10 per hour= $5,670
Fixed=2700×0.47 per hour=$1,269
Total overhead applied=$6,939
($5,670+$1,269)
2. Under applied overhead
Total overhead applied $6,939
Less Total factory overhead $7,400
Under applied overhead -$461
($6,939-$7,400)
Therefore the applied factory overhead is $6,939 and the over-or underapplied factory overhead amount for October is $461.
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Describe the end behavior for the graph of y=-x³- ax + 3, if a is a constant.
Answer: Choice C
As [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]
As [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]
Check out the diagram below.
========================================================
Explanation:
The leading term is the term with the largest exponent. That would be the term of [tex]-\text{x}^3[/tex]. The leading term directly determines the end behavior. The other terms will not play a role.
What this means is that the end behavior of [tex]\text{y} = -\text{x}^3 - \text{ax} + 3[/tex] is the exact same as the end behavior of [tex]\text{y} = -\text{x}^3[/tex]
As x gets really big in the positive direction, we'll have [tex]-\text{x}^3[/tex] get really small in the negative direction. For instance, x = 10 leads to [tex]-\text{x}^3 = -10^3 = -1000[/tex] and x = 100 leads to [tex]-\text{x}^3 = -100^3 = -1,000,000[/tex]
Therefore, as [tex]\text{x} \to \infty[/tex] then [tex]\text{y} \to -\infty[/tex]
Visually the graph goes forever downward when we move to the right. We can consider this as "falls to the right".
--------------------------------
The graph "rises to the left" because as [tex]\text{x} \to -\infty[/tex] then [tex]\text{y} \to \infty[/tex]
Here's a small table to give numeric examples:
[tex]\begin{array}{|c|c|} \cline{1-2}x & y\\\cline{1-2}-1 & 1\\\cline{1-2}-10 & 1000\\\cline{1-2}-100 & 1,000,000\\\cline{1-2}\end{array}[/tex]
As x gets more negative, y becomes more positive. We have this opposite nature going on similar to the previous section.
This graph goes uphill when moving to the left.
Check out the graph below. In the diagram I used a = 2, but you could use any value of 'a' you want to get the same end behavior.
help me with this please i will gave u bralinet answer who ever answer first
Answer:
[tex]\fbox {5 times}[/tex]
Step-by-step explanation:
Days where both will be done :
⇒ 2nd day × 3rd day
⇒ 6th day
Number of times in September :
⇒ The month has 30 days
⇒ Number of times = 30/6
⇒ Number of times = 5
Answer:
5 times
Step-by-step explanation:
• Calculate the lowest common multiple (LCM) of 2 and 3 to find the first day of the month in which she will do both:
LCM (2 and 3) = 2 x 3
= 6
This means, she will do both every 6th day.
• There are 30 days in September. To find how many days she will do both in September, we have to calculate how many 6-day blocks there are in 30 days:
⇒ 30 ÷ 6
= 5 times
A paramedic maintains a time card for hours she works on the rescue squad. How many hours did she work per week ?
39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:
We can write a mixed fraction in a fraction:
6 1/2 = 13/2
8 1/2 = 33/2
7 3/4 = 31/4
8 1/12 = 97/12
8 5/12 = 101/12
Adding all the fractions:
[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]
[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]
[tex]=23+\dfrac{64}{4}[/tex]
= 39 hours
Thus, 39 hours; she works per week if the paramedic maintains a time card for hours she works on the rescue squad.
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Find limit (x / 3x+2) as x approach 1
Answer:
x/ 3x + 2
x approach 1
1/3 (1) + 2
1/ 5.
Evaluate each expression for r=9 n t=14 enter in your numerical answer
Answer:
1764
Step-by-step explanation:
[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]
Hii!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]
1764
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
Stick in the values: 9 for r and 14 for t, and simplify.
[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]
[tex]\bullet[/tex] Square 14 first
[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]
[tex]\bullet[/tex] Multiply the numbers
[tex]\twoheadrightarrow\sf 1764}[/tex]
[tex]\bullet[/tex] Great job! We found the answer
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
What is a necessary step for constructing perpendicular lines through a point off the line?
Answer:
Find another point on the perpendicular line.
Step-by-step explanation:
Given an original line "m", and a point off the line "Q", in order to construct a second line "p", meant to be perpendicular to "m" through the point "Q", fundamentally, the only truly necessary step to construct a perpendicular line through is to find another point on the yet-to-be-found perpendicular line.
Most often, this is accomplished by exploiting the fact that "p" is the set of all points that are equidistant from any pair of points that are symmetric about "p".
Since the symmetry must be about "p", and we don't even know where "p" is, one often finds two points on "m" that are equidistant from "Q".
This can be accomplished by adjusting a compass to a fixed radius (larger than the distance from "Q" to "m"), and making an arc that intersects "m" in two places. Those two places will be equidistant from "Q", and are simultaneously on line "m". Thus, these two points, "A" & "B" are symmetric about "p".
Since "A" & "B" are symmetric about "p", they are equidistant from "p", and are on "m". One could try to find the point of intersection between "p" and "m" through construction, but this is unnecessary. We need only find a second point (besides "Q") that is equidistant from "A" & "B", which will necessarily be a point on "p", to form the line perpendicular to "m".
To do this, fix the compass with any radius, and from "A" make a large arc generally in the direction of "B", and make the same radius arc from "B" in the direction of "A" such that the two arcs intersect at some point that isn't "Q". This point of intersection we can call point "T", and the line QT is line "p", the line perpendicular to the original line, necessarily containing "Q".
Which of the following demonstrates the Distributive Property?
3(4a + 2) = 12a + 6
3(4a + 2) = 12a + 2
3(4a + 2) = 4a + 6
3(4a + 2) = 7a + 5
Answer:
[tex]\fbox {3(4a + 2) = 12a + 6}[/tex]
Step-by-step explanation:
⇒ 3(4a + 2)
⇒ 3(4a) + 3(2)
⇒ 12a + 6
Answer:
A) 3(4a + 2) = 12a + 6
Step-by-step explanation:
This is the correct answer because the distributive property is where you break up all the numbers and pretty much that is what you do in A.
3 * 4a = 12a
3 * 2 = 6
So then, as you can see, the answer would be 12a + 6.
This is another explanation, even though they are LITERALLY the same.
Apply the distributive property.
3 (4a) + 3 ⋅ 2
Multiply 4 by 3.
12a + 3 ⋅ 2
Multiply 3 by 2.
12a + 6
Brainliest pls
Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?
Find the value of c that makes the expression a perfect square trinomial. x2 + 9 4 x + c
A) 9/16
B) 9/64
C) 81/16
D) 81/64
The value of c is 81/64 for the expression a perfect square trinomial.
What is an Expression?An expression can be defined as a mathematical statement that consists of variables, constants and mathematical operators simultaneously.
It is given that an expression
x² +9/4x +c is a perfect square polynomial
c =?
(a+b)² = a² +2ab+b²
2ab = 9/4
b = 9/8
c = b² = 81/64
Therefore the value of c is 81/64 for the expression a perfect square trinomial.
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10% of the library books in the fiction section are worn and need replacement. 20% of the nonfiction holdings are worn. The library's holdings are 60% fiction and 40% nonfiction. The probability to get a worn book is?
Answer: 14%
Step-by-step explanation:
Let's assume that there are 100 books in total.
So there are 60 fiction books and 40 nonfiction books.
10% of 60 is 6.
20% of 40 is 8.
So there are 14 books out of 100 that are worn.
This is 14%
What is the mode of 1,1,2,2,3,3,4,4
Answer: There is no mode.
Step-by-step explanation:
The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.
I hope this helped!! :)
Answer:
1, 2, 3, 4
or none
Step-by-step explanation:
Mode is the value or values in the data set that occurs most frequently.
example:
For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.
in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode
hope this helps:)
Which statements are true about the ordered pair (-1,-4) and the system of equations? x-y=3 and 7x-y=-3
Answer:
when (-1, -4) is substituted into the first equation it's true
when (-1, -4) is substituted into the second equation it's true
the ordered pair (-1, -4) is a solution to the systems of equation
Step-by-step explanation:
original equation
x-y=3
multiply both sides by 7
7x-7y = 21
add 7y to both sides
7x=7y + 21
substitute into second equation
(7y+21)-y=-3
simplify
6y+21=-3
subtract 21 from both sides
6y=-24
y=-4
substitute y into original equation
x-(-4) = 3
cancel out negative signs
x+4=3
subtract -4 from both sides
x=-1
Mr. Rijo bought 49 bags of soil one week and 28 bags of soil the next week. Which expression correctly applies the
distributive property to show equivalent expressions for the number of bags of soll he bought?
49 + 28 = 4(7 + 7)
59 + 28 - (7)(7) + (14)(2))
19 + 28 - (7)(14) + (7)(7)
49 + 28 - 7(7+ 4)
Answer:
49 + 28 = 7(7 + 4)
Step-by-step explanation:
49 bags of soil one week
28 bags of soil the next week
49 + 28 bags of soil purchased in total
Find the GCF (Greatest Common Factor) of 49 and 28.
49/7 = 7
28/7 = 4 (GCF is 7 since it is the largest number that can divide both 49 and 28 equally)
Factor out the GCF + rewrite division above (optional for visualization)
49/7 = 7 -> 49 = 7 * 7
28/7 = 4 -> 28 = 7 * 4
49 + 28 = 7(7 + 4)
Let me know if you have any questions!
An expression is shown below:
4ck2 + 10k2 − 16ck − 40k
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Part A:
The greatest common factor is 2k
2k(2ck + 5k - 8c - 20)
Part B:
factor by grouping
2k (k(2c + 5) - 4(2c + 5))2k(k - 4)(2c + 5)2k(k - 4)(2c + 5) is the final factored form
A water wheel is designed in the shape of a regular octagon. What is the perimeter of the water wheel?
The graph shows an eight-sided polygon. Some major points are (0, 4), (3, 3), (4, 0), (3, minus 3), (0, minus 4), (minus 3, minus 3), (minus 4, 0), and (minus 3, 3).
A.
B.
C.
D.
Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,
Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58
Now, the perimeter of the octagon is 8 times of√58.
Perimeter = 8 ×√58 = 8√58
Hence, the perimeter of the regular octagon is 8√58 units.
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I need to use factorial the! When you use the binomial probability formula and I need to show step-by-step for for a through c
Given the number of trials and the probability of success, determine the probability indicated: (Hint use binomial distribution formula use factorials ! in showing your work)
n = 15, p = 0.4, find P(4 successes)
n = 12, p = 0.2, find P(2 success )
n = 20, p = 0.05, find P(at most 3 successes)
(hint for c.
P (at most 3 successes) = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)
Using the binomial distribution, it is found that the probabilities are:
P(X = 4) = 0.1268.P(X = 2) = 0.2835.[tex]P(X \leq 3) = 0.9841[/tex]What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Exercise 1:
The parameters are:
n = 15, p = 0.4, x = 4.
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228[/tex]
Exercise 2:
The parameters are:
n = 12, p = 0.2, x = 2.
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835[/tex]
Exercise 3:
The parameters are:
n = 20, p = 0.05.
The probability is:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Using the binomial formula for each value and adding them:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841[/tex]
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Question is attached………
Answer:
D
Step-by-step explanation:
the cordinate is at (-3,2)
The legs of a 90-45-45 triangle are 3 and 7. What is the hypotenuse?
Answer:
The hypotenuse is [tex]\sqrt{58}[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2 + 7^2 = c^2
9 + 49 = c^2
58 = c^2
Taking the square root of each side
[tex]\sqrt{58} = \sqrt{c^2}[/tex]
[tex]\sqrt{58} =c[/tex]
Can someone help me? I’ll give Brainliest to whoever answers correctly first
Answer:Angle C=68 degrees
Step-by-step explanation:
The solution is in the
3x² - 2x + 1 = [?]
x=4
Answer:
3(4)² - 2(4) + 1 = 48 - 8 +1 = 41
x = 4
[tex] {3x}^{2} - 2x + 1 \\ \\ 3 \times {4}^{2} - 2 \times 4 + 1 \\ \\ 3 \times 16 -8 + 1 \\ \\ 48 - 8 + 1 \\ \\ 41.[/tex]
urgent help needed algebra 2
The solution of the given equation 4(3x - 4) - 7( 2x + 3) = 3 is -20.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
The given equation is;
4(3x - 4) - 7( 2x + 3) = 3
To solve;
4(3x - 4) - 7( 2x + 3) = 3
Solve the parentheses using the distributive property;
12x - 16 - 14x - 21 = 3
we need to get the like terms together;
12x - 14x -16 - 21 = 3
-2x - 37 = 3
Add 37 both sides, we get;
-2x = 40
Divide both sides by -2
x = -20
Hence, the solution of the given equation is -20.
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Guys i just cant do this my brain doesnt work right now
Answer:
[tex] \frac{1}{4} [/tex]
Step-by-step explanation:
To find the gradient of the graph, we use the formula,
[tex]gradient \: (m) = \frac{(y2 - y1)}{(x2 - x1)} [/tex]
From the graph, we obtain values for x and y
x1 = 4, x2 = 8
y1 = 2, y2 = 3
Substitute the values into our formula.
[tex]m \: = \frac{(3 - 2)}{(8 - 4)} \\ = \frac{1}{4} [/tex]
Therefore, the gradient, m, =
[tex] \frac{1}{4} [/tex]
Note:-
Use the above formula when determining the gradient of the graph.Obtain the values of x and y then subtract [∆y] and [∆x].Divide the twohow do i solve this??
-6 ≤ x < -2
Step-by-step explanation:
[ => this shows ≤ sign
) => this shows < sign