Graphing y = 4 and the focus, we clearly see that the equation we need has the form (x - h)^2 = 4a(y - k).
We need to find a, h and k.
The focus is half way between the vertex and directrix.
You know that y = 4 is 2 units away from the focus and the focus is 2 units down from the focus. So, our vertex is (-3, 0).
From the vertex to the directrix, there are 4 units. Half that distance is the value of a. So, a = 2.
We have all that is needed to form our equation.
(x - (-3))^2 = 4(2)(y - 0)
(x + 3)^2 = 8y
Done.
Answer:
i think this will help (x - (-3))^2 = 4(2)(y - 0)
(x + 3)^2 = 8y
Step-by-step explanation:
PLEASE HELP!!! Consider this bag of marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things?
https://lh3.googleusercontent.com/HGdB_Oa4buUyXgZbq38nPvDmZEK9J5FLEqrQ1NsfckiHy9N2VTd3wEpjuEpI8rrp5LtZMw=s100
Answer:
Probabilities are usually given in percentages.
Odds can have a value of 0-infinity & are in the form of a ratio. Odds can be given in 2 different ways: Odds in favor & Odds against.
*Probability of drawing a green
marble is 50%
*Odds if drawing a green marble
are 5:5
The probability of drawing a green marble is 1/2 and the odds are 1:1. The difference between probability and odds is explained.
The probability of drawing a green marble from the bag can be calculated by dividing the number of green marbles by the total number of marbles in the bag. In this case, there are 5 green marbles and a total of 10 marbles, so the probability is 5/10 or 1/2.
Odds, on the other hand, represent the ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, since there are 5 green marbles and a total of 5 marbles that are not green (3 blue marbles and 2 red marbles), the odds of drawing a green marble are 5:5 or 1:1.
The difference between probability and odds is that probability is a measure of the likelihood of an event occurring, while odds represent the ratio of favorable to unfavorable outcomes.
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The probable question may be:
Consider this bag of marbles, where we have 5 green marbles, 3 blue marbles and 2 red marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things?
The picture shows a lorry driver standing next to his lorry.
The lorry driver and the lorry are drawn to the same scale.
The lorry driver wants to drive the lorry into a car park.
The entrance to the car park is 3.1 meters high.
Can the lorry driver safely drive the lorry into the car park?
You must clearly show how you got your answer, explaining any
assumptions you have made.
Answer: no its too big it wont fit
Step-by-step explanation:
its just too big
An unknown radioactive element decays into non-radioactive substances. In 30 days the radioactivity of a sample decreases by 12%. When will a sample of 50 mg decay to 10 mg? Round your final answer to 1 decimal place.
Answer:
Time to decay will be 377.7 days.
Step-by-step explanation:
Decay of an radioactive element is represented by the formula
[tex]A_{t}=A_{0}e^{-kt}[/tex]
where [tex]A_{t}[/tex] = Amount after t days
[tex]A_{0}[/tex] = Initial amount
t = duration for the decay
k = decay constant
Now we plug in the values in the formula
[tex](1-0.12)x=xe^{-30k}[/tex]
[tex](0.88)x=xe^{-30k}[/tex]
[tex]0.88=e^{-30k}[/tex]
Now we take natural log on both the sides
ln(0.88) = [tex]ln(e)^{-30k}[/tex]
ln(0.88) = -30k(lne)
-30k = -0.1278
k = [tex]\frac{.1278}{30}[/tex]
k = [tex]4.261\times 10^{-3}[/tex]
Now we have to calculate the duration for the decay of 50 mg sample to 10 mg.
[tex]A_{t}=A_{0}e^{-kt}[/tex]
We plug in the values in the formula
10 = 50[tex]e^{-4.261\times 10^{-3}\times t}[/tex]
[tex]e^{-4.261\times 10^{-3}\times t}=\frac{10}{50}[/tex]
[tex]e^{-4.261\times 10^{-3}\times t}=0.2[/tex]
We take (ln) on both the sides
[tex]ln(e^{-4.261\times 10^{-3}\times t})=ln(0.2)[/tex]
[tex]-4.261\times 10^{-3}\times t=-1.6094[/tex]
t = [tex]\frac{1.6094}{4.261\times 10^{-3} }[/tex]
t = 0.37771×10³
t = 377.7 days
Therefore, time for decay will be 377.7 days.
Suppose that the domain of the propositional function P(x) consists of −5, −3, −1, 1, 3, and 5. Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions.a) ∃xP (x) b) ∀xP (x) c) ∀x((x ≠ 1) → P (x)) d) ∃x((x ≥ 0) ∧ P (x)) e) ∃x(¬P (x)) ∧ ∀x((x < 0) → P (x))
Answer:
a) ∃xP (x)
P(-5) v P(-3) v P(-1) v P(1) v P(3) v P(5)
(at least one of them is true)
b) ∀xP (x)
P(-5) ^ P(-3) ^ P(-1) ^ P(1) ^ P(3) ^ P(5)
(all of them are true)
c) ∀x((x ≠ 1) → P (x))
P(-5) ^ P(-3) ^ P(-1) ^ P(3) ^ P(5)
d) ∃x((x ≥ 0) ∧ P (x))
P(1) v P(3) v P(5)
e) ∃x(¬P (x)) ∧ ∀x((x < 0) → P (x))
[¬P(-5) v ¬P(-3) v ¬P(-1) v ¬P(1) v ¬P(3) v ¬P(5)] ^ [P(-5) ^ P(-3) ^ P(-1)]
[¬P(1) v ¬P(3) v ¬P(5)] ^ [P(-5) ^ P(-3) ^ P(-1)]
Here are the given statements expressed without quantifiers: a) P(-5) OR P(-3) OR P(-1) OR P(1) OR P(3) OR P(5), b) P(-5) AND P(-3) AND P(-1) AND P(1) AND P(3) AND P(5), c) P(-5) AND P(-3) AND P(-1) AND P(3) AND P(5), d) (1 ≥ 0 AND P(1)) OR (3 ≥ 0 AND P(3)) OR (5 ≥ 0 AND P(5)), and e) ((¬P(-5) OR ¬P(-3) OR ¬P(-1) OR ¬P(1) OR ¬P(3) OR ¬P(5)) AND (P(-5) AND P(-3) AND P(-1))).
Explanation:To express your statements without quantifiers, we would consider using disjunctions (OR), conjunctions (AND) and negations (NOT). Here are your statements expressed accordingly:
a) ∃xP (x) becomes P(-5) OR P(-3) OR P(-1) OR P(1) OR P(3) OR P(5).
b) ∀xP (x) becomes P(-5) AND P(-3) AND P(-1) AND P(1) AND P(3) AND P(5).
c) ∀x((x ≠ 1) → P (x)) becomes P(-5) AND P(-3) AND P(-1) AND P(3) AND P(5).
d) ∃x((x ≥ 0) ∧ P (x)) becomes (1 ≥ 0 AND P(1)) OR (3 ≥ 0 AND P(3)) OR (5 ≥ 0 AND P(5)).
e) ∃x(¬P (x)) ∧ ∀x((x < 0) → P (x)) becomes ((¬P(-5) OR ¬P(-3) OR ¬P(-1) OR ¬P(1) OR ¬P(3) OR ¬P(5)) AND (P(-5) AND P(-3) AND P(-1))).
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For homework, Brooke has 15 math problems, 5 social studies problems, and 9 science problems. Use mental math to determine how many problems she has for homework. Tell which property you used.Answer Property
Answer:
29 homework problems
Addition Property was used
Step-by-step explanation:
15+5=20+9=29
Addition
By using the associative property of addition, we calculate that Brooke has 29 problems for homework. This total is found by adding 15 math problems, 5 social studies problems, and 9 science problems together.
Explanation:To calculate how many problems Brooke has for homework, we need to add together the numbers of math, social studies, and science problems. This operation is typically done using the property of addition. The property of addition we've applied here is known as the Associative Property of Addition. This property states that the way numbers are grouped does not change their sum.
So, if Brooke has 15 math problems, 5 social studies problems, and 9 science problems, we calculate the total as follows: 15 (math) + 5 (social studies) + 9 (science) equals 29 problems. So, Brooke has 29 problems to do for her homework.
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Find the equation in slope/intercept form that is perpendicular to 2x - 3y = 4 and passing through (-1/7, 4).
Answer:
y = -1½x + 3 11⁄14
Step-by-step explanation:
First convert from Standard Form to Slope-Intercept Form:
2x - 3y = 4
-2x - 2x
____________
-3y = -2x + 4
___ _______
-3 -3
y = ⅔x - 1⅓ >> Slope-Intercept Form
↑
slope
Now, Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes], so since the slope is ⅔, the opposite multiplicative inverse of that would be -1½, or -3⁄2. Anyway, do the following:
4 = -1½[-⅐] + b
3⁄14
-3⁄14 - 3⁄14
_______________
3 11⁄14 = b
y = -1½x + 3 11⁄14 >> New equation
I am joyous to assist you anytime.
Answer:
Step-by-step explanation:
So a few things to know before hand. Slope ntercept form is y = mx + b where m is the slope, and in this form that will always make b the y intercept.
A perpendicular slope is pretty easy to find. Of course, perpendicular means it intersects that first line at a 90 degree angle. So the x and y axis themselves are perpendicular. Anyway, if you know the slope of the line, a perpendicular slope is -1/m where m is the slope. S taking the simplest example, in the graph of just x, the slope is 1, so the perpendicular slope is -1/1 or just -1.
The last thing is to know how to write the equation of a linear function when you know a point and its slope. if you have the slope m and a point on the graph (a,c) you can use the point slope form which is this. y - c = m(x - a) where you solve for y. x an y stay as variables here.
Now knowing all that we can start. First we want to put the original graph into slope intercept form, which is pretty easy. Just manipulate the equation.
2x - 3y = 4
2x -4 = 3y
y = (2x - 4)/3
y = 2/3 x - 4/3
so m = 2/3 and b = -4/3
Now, we have the slope of this line and want the slope of a perpendicular line. Like I mentioned before the slope is -1/m so in this case that's -1/(2/3) = -3/2 Let me know if you don't get how that was gotten.
Now that we kno the perpendicular slope, we can make a perpendicular line. How do we make a line when we know the slope and a point? Keep in mind the point is (-1/7, 4)
y - c = m(x-a)
y - 4 = -3/2(x + 1/7)
y - 4 = -3/2 x - 3/14
y = -3/2 x + 53/14
If it weren't in slope intercept form you'd have to put it in that, but I took care of it in the process, so here's the answer. Let me know if there's anything you don't understand.
Which of the following expressions is incorrect?
a) Sales revenue - cost of goods sold - Operating expenses = Net income
b) Gross profit - Operating expenses = Net income
c) Net income + Operating expenses = Gross profit
d) Operating expenses - Cost of goods sold = Gross profit
Answer:
d) Operating expenses - Cost of goods sold = Gross profit
Step-by-step explanation:
first of all when you say gross in accounting it means the totality so gross profit would never be a subtraction.
And finally operating expenses usually go with a negative sign {-} because it means costs or something goes opposite to the revenue of the firm.
Answer:
d) Operating expenses - Cost of goods sold = Gross profit
Step-by-step explanation:
The formula of Net income is
Sales revenue
- cost of goods sold
= Gross profit
- Operating expenses
= Net income
So, we are going to analyze each option
a) Sales revenue - cost of goods sold - Operating expenses = Net income CORRECT
b) Gross profit - Operating expenses = Net income CORRECT
c) Net income + Operating expenses = Gross profit CORRECT
d) Operating expenses - Cost of goods sold = Gross profit INCORRECT
Gabi wants to drive to and from the airport. She finds two companies near her that offer short-term car rental service at different rates and then sets up the equation 0.22m+7.20=0.1m+8.40 to find out after how many miles, m, the companies will charge the same amount. What is the difference in per-mile costs for the two companies?
Answer:
The difference in per-mile costs for the two companies is $0.12
Step-by-step explanation:
Gabi sets up the equation [tex]0.22m+7.20=0.1m+8.40[/tex] to find out after how many miles, m, the companies will charge the same amount.
The first company charges [tex]c_1=0.22m+7.20[/tex] for m miles driven.
The second company charges [tex]c_2=0.1m+8.40[/tex] for m miles driven.
In both these functions, numbers 7.20 and 8,40 represent the initial fee the companies charge.
Numbers 0.22 and 0.1 represent per-mile costs.
Thus, the difference in per-mile costs is [tex]0.22-0.1=0.12[/tex]
Another way to solve this problem is to find the cost per mile driven for each company:
1. Cost per-mile 1st company
[tex]c_1(0)=0.22\cdot 0+7.20=7.20\\ \\c_1(1)=0.22\cdot 1+7.20=7.42\\ \\c_1(1)-c_1(0)-7.42-7.20=0.22[/tex]
2. Cost per-mile 2nd company
[tex]c_2(0)=0.1\cdot 0+8.40=8.40\\ \\c_2(1)=0.1\cdot 1+8.40=8.50\\ \\c_2(1)-c_2(0)=8.50-8.40=0.1[/tex]
3. Difference:
[tex]0.22-0.1=0.12[/tex]
An equation that expresses a relationship between two or more variables, such as Upper H equals nine tenths left parenthesis 220 minus a right parenthesis , is called _______. The process of finding such equations to describe real-world phenomena is called mathematical _______. Such equations, together with the meaning assigned to the variables, are called mathematical _______.
Answer:
An equation that expresses a relationship between two or more variables, such as Upper H equals nine tenths left parenthesis 220 minus a right parenthesis , is called Formula.
A formula is an equation that expresses a relationship between two or more variables.
The process of finding formulas to describe real-world phenomena is called mathematical modeling.
Such equations, together with the meaning assigned to the variables, are called mathematical models.
A mathematical equation expresses a relationship between variables, and the process of finding such equations is called mathematical modeling.
Explanation:An equation that expresses a relationship between two or more variables is called a mathematical equation. The process of finding such equations to describe real-world phenomena is called mathematical modeling. These equations, together with the meaning assigned to the variables, are called mathematical models.
For example, if we have an equation like Upper H equals nine tenths left parenthesis 220 minus a right parenthesis, this equation represents a relationship between a variable H and the expression nine tenths left parenthesis 220 minus a right parenthesis. We can use this equation to calculate the value of H given a specific value for the expression.
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if (x, y) maps to (x + 2, y - 3), how did the object transform?
A. The object slid 2 units right and 3 units down.
B. The object reflected over the x-axis.
C. The object rotated 2 times counter clockwise 3 degrees.
D. The object was dilated 2 times horizontally and 3 times vertically.
Mrs. Grundy has two children. Given that Mrs. Grundy has at least one child born on a Monday, what is the probability that both her children were born on Mondays?
Answer: Ok, the chanche of both children were born on a monday is [tex]\frac{1}{7}[/tex]
Step-by-step explanation: Well, we alredy know that one of her children was born on a monday, when they ask the probability of both children were born on a monday, we only need to see the case of the second kid.
So, the week has 7 days, ence the probability for each day (in this case a monday) is 1/7.
Iliana multiplied 3p – 7 and 2p2 – 3p – 4. Her work is shown in the table. The expression (3 p minus 7)(2 p squared minus 3 p minus 4) is shown above a table with 3 columns and 2 rows. First column is labeled 2 p squared, second column is labeled negative 3 p, the third column is labeled negative 4. First row is labeled 3 p with entries 6 p cubed, negative 9 p squared, negative 12 p. Second row is labeled negative 7 with entries negative 14 p squared, 21 p, 28. Which is the product? 6p3 + 23p2 + 9p + 28 6p3 – 23p2 – 9p + 28 6p3 – 23p2 + 9p + 28 6p3 + 23p2 – 9p + 28
Answer:
the answer is C
Step-by-step explanation:
Answer:
The correct option is C) [tex]6p^3-23p^2+9p+28[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]3p - 7[/tex] and [tex]2p^2 - 3p - 4[/tex]
According to the provided information the table will be like this.
[tex]2p^2[/tex] -3p -4
3p [tex]6p^3[/tex] -9p² -12p
-7 [tex]-14p^2[/tex] 21 p 28
The above table shows the terms after multiplication.
To find the product you just need to add the terms as shown.
[tex]6p^3-9p^2-12p-14p^2+21p+28[/tex]
[tex]6p^3-9p^2-14p^2-12p+21p+28[/tex]
[tex]6p^3-23p^2+9p+28[/tex]
Hence, the product is [tex]6p^3-23p^2+9p+28[/tex].
You can verify this by product as shown.
[tex]3p-7(2p^2-3p -4)[/tex]
[tex]6p^3-9p^2-12p-14p^2+21p+28[/tex]
[tex]6p^3-23p^2+9p+28[/tex]
Hence, the correct option is C) [tex]6p^3-23p^2+9p+28[/tex]
Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 65.30 miles apart. If one travels 14 miles per hour slower than the other, what is the rate of the slower train? (Round your answer to the nearest integer)
Answer:
15 miles per hour is the speed of the slower train.
Step-by-step explanation:
As given in the figure attached,
Let the speed of train 1 is v and train 2 is u.
Therefore, distance traveled in 2 hours by train 1 will be = 2v miles
and distance traveled by train 2 will be = 2u miles
Now we can see in the figure a right angle triangle is formed by the two trains.
AB² + BC² = AC²
(2v)² + (2u)²= (65.30)²
4v² + 4u² = 4264.09
Now we divide this equation by 4
v² + u² = 1066.02
If speed of the slower train is v miles per hour then as per statement of the question.
u = v - 14
v = u + 14
By putting the value of v in the equation
(u + 14)² + u² = 1066
u² + 196 + 28u + u² = 1066
2u² + 28u + 196 = 1066
2u² + 28u + 196 - 1066 = 0
2u² + 28u - 870 = 0
By diving this equation by 2
u² + 14u - 435 = 0
u² + 29u - 15u - 435 = 0
u(u + 29) - 15(u + 29) = 0
(u + 29)(u - 15) = 0
u = -29, 15
Since speed can not be with negative notation so u = 15 miles per hour will be the speed.
Therefore, 15 miles per hour is the speed of the slower train.
Consider the following information.
1 hour = 3.6 · 103 seconds
1 day = 24 hours
1 year = 3.65 · 102 days
Use scientific notation to calculate the number of seconds in 3 days.
Answer:
2.592×10^5 seconds
Step-by-step explanation:
[tex]3\,days\cdot\dfrac{24\,h}{1\,day}\cdot\dfrac{3.6\cdot 10^3\,s}{1\,h}=3\cdot 24\cdot 3.6\cdot 10^3\,s=2.592\cdot 10^5\,s[/tex]
Answer:
Corrected answer is 8.64 x 10^4 seconds in one day
Step-by-step explanation:
Find a cubic function with the given zeros. (2 points)
squared 6 , negative squared 6 , -3
Select one:
a. f(x) = x3 - 3x2 - 6x - 18
b. f(x) = x3 + 3x2 - 6x - 18
c. f(x) = x3 + 3x2 + 6x - 18
d. f(x) = x3 + 3x2 - 6x + 18
Answer:
b. f(x) = x³ +3x² -6x -18
Step-by-step explanation:
You want the cubic function with zeros ±√6 and -3.
ZerosEach zero p gives rise to a factor (x-p). This means the factored form of f(x) will be ...
f(x) = (x -√6)(x +√6)(x -(-3))
Standard formExpanding this product gives ...
f(x) = (x² -6)(x +3)
f(x) = x³ +3x² -6x -18 . . . . . . . matches choice B
Assume that one day's labor in Argentina can produce either 20 units of cloth or 2 units of wine, while in Chile one day's labor can produce either 24 units of cloth or 12 units of wine. If Argentina transfers 2 units of labor from wine to cloth and Chile transfers 1 unit of labor from cloth to wine, the increase in combined output by those two workers will be: A. 16 wine; 8 cloths B. 16 wine; 16 cloths C. 12 wine; 12 cloths D. 8 wine; 16 cloths
(D). 8 Wine, 16 Cloth
Step-by-step explanation:Cloth production by Argentina = 20 units
Wine production by Argentina = 2 units
Cloth production by Chile = 24 units
Wine production by Chile = 12 units
Now,
2 units of labor was transferred by Argentina from Wine to Cloth and 1 unit of labor was transferred by Chile from Cloth to Wine.
Therefore,
Increase in Cloth production = Argentina's total cloth produced - Cloth produced by Chile (before transfer)
Now,
We can say that total cloth produced by Argentina is = 2 x 20 = 40 units
So,
Increase in Cloth production = 40 - 24 = 16 units
Therefore, the increase in Cloth Production is 16 units.
Similarly,
Increase in Wine production = Chile's total Wine produced - Wine produced by Argentina (before transfer)
Now,
We can say that total Wine produced by Chile is = 1 x 12 = 12 units
Wine produced by Argentina before transfer = 2 x 2 = 4 units
So,
Increase in Wine production = 12 - 4 = 8 units
Therefore, the increase in Wine Production is 8 units.
Hence, the correct option is (D).
Meg constructed triangle POQ and then used compass and straight edge to accurately construct line segment OS, as shown in the figure below. Which could be a measure of POS and angle POQ?
Answer:
The answer is C
Step-by-step explanation:
The measurement of angle POS is 20 and POQ is 40
OS is an angle bisector of ∠POQ. This means it splits ∠POQ into two congruent pieces.
This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.
If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.
Answer:
The correct option is C) m∠POS = 20°, m∠POQ = 40°,
Step-by-step explanation:
Consider the provided figure.
Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS.
From the given figure it is clear that OS is angle bisector of POQ,
[tex]\angle POQ=\angle POS+\angle QOS[/tex]
[tex]\angle POS=\angle QOS[/tex] ∴ angle bisector
[tex]\angle POQ=\angle POS+\angle POS=2\angle POS[/tex]
Thus, the measure of ∠POQ is double the measure of ∠POS.
There is only one option in which m∠POQ is double the m∠POS.
Therefore, the correct option is C) m∠POS = 20°, m∠POQ = 40°,
Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance. In a study of a weight loss program, 4 subjects lost an average of 48 lbs. It is found that there is about a 32% chance of getting such results with a diet that has no effect.
Answer:
Step-by-step explanation:
Given that in a study of a weight loss program, 4 subjects lost an average of 48 lbs.
It is found that there is about a 32% chance of getting such results with a diet that has no effect.
The results do not appear to have statistical significance. The reasons are
1) Sample size of 4 is very small not even meeting the bare minimum
2) Sample of 4 cannot be taken to represent the population
3) Whether bias was there in the selection of sample is not known.
4) Std deviation is not considered which is very important while concluding results.
Need help with this im confused
Answer:
[tex]-\frac34 -\frac14 i[/tex]
Step-by-step explanation:
Let's start with distributing: [tex]\frac1{4i}-\frac{3i}{4i}[/tex] Simplify i with i in the second term, and rearrange.[tex]-\frac34 +\frac1{4i}[/tex]. Since i in the denominator looks ugly, let's multiply top and bottom by i. [tex]-\frac34 +\frac i{4i^2} = -\frac34 +\frac i{4(-1)} =-\frac34 -\frac14 i[/tex]. The middle passage is based on the fact that, by definition, [tex]i^2=-1[/tex]
Consider the numbers 0, 10, 20, 30, and 40. Multiply each by 4 and compare the result to 60 to determine into which of the following intervals the answer to the question "What number can you multiply by 4 and then add 8 to the product to get 60?" should fall.
Select the interval into which the answer should fall.
a) 0 to 10
b) 10 to 20
c) 20 to 30
d) 30 to 40
Answer:
b) 10 to 20
Step-by-step explanation:
You have to multiply each of the given numbers by 4, and add 8 to that result.
So:
0*4+8 = 810*4+8 = 4820*4+8 = 8830*4+8 = 12840*4+8 = 168And 60 is between the result of 10 and 20, so that's the interval you have to select.
The correct answer is b) 10 to 20
Please please help me with this
Answer: y= -1/2x + 3/4
Step-by-step explanation: For a line in the for of y=mx + b, the slope is m and y intercept is b.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 6x + 12y = 9 into this form
Subtract 6x from both sides
12y = - 6x + 9 ( divide all terms by 12 )
y = - [tex]\frac{6}{12}[/tex] x + [tex]\frac{9}{12}[/tex], that is
y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{4}[/tex]
Earth's oceans have an average depth of 3800 m, a total area of 3.63 × 108 km2, and an average concentration of dissolved gold of 5.8 × 10−9 g/L. How many grams of gold are in the oceans?
Answer:
grams of gold=8x10^12 g
Step-by-step explanation:
first we calculate the volume of the ocean this is achieved by multiplying the area by the depth
A=3.63x10^8 km^2=3.63x10^14 m^2
V=AxL
V=3.63x10^14 x 3800=1.3797x10^18m^3=1.3797x10^21L
then we multiply the volume in liters by the concentration of gold in the ocean per liter
grams of gold=1.3797x10^21 x 5.8x10^-9=8x10^12 g
Answer:
8.00 *10¹² g
Step-by-step explanation:
We must calculate the grams of gold in the ocean.
We are given the concentration of dissolved gold as grams per Liter.
So we need to first calculate the Liters of the ocean, that is, the volume.
We can calculate the volume of the ocean assuming a prism shape as:
Volume = Area x Depth
Depth = 3800 mArea = 3.63 x10⁸ km²We should first convert the area from km² to m² so that the units are consistent:
[tex]3.63 *10^{8} km^{2} * (\frac{1000 m}{1 km} )^{2} = 3.63 *10^{14} m^{2}[/tex]
So the volume:
Volume = 3.63 x10¹⁴ m² * 3800 m = 1.38 x10¹⁸ m³
Since we have the concentration given in Liters, lets convert the volume to Liters, knowing that 1 L = 1000 m³:
[tex]1.38 *10^{18} m^{3} *\frac{1000 L}{1 m^{3} } = 1.38 *10^{21} L[/tex]
Knowing that the concentration of gold is 5.8 *10⁻⁹ grams per Liter, we can multiply this value by the Liters of the ocean to calculate the grams of gold:
5.8 *10⁻⁹ g/L x 1.38 *10²¹ L = 8.00 *10¹² g
There are 8.00 *10¹² grams of gold in the ocean
A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.
Answer:
57120
Step-by-step explanation:
Total number of people in a committee = 17
We need to select a president, a vice-president, a secretary, and a treasurer from the committee .
We need to find the number of ways in which these four positions can be filled .
Also, assume that a committee member can hold at most one of these offices.
For post of president , we can choose from 17 people
For post of vice - president , we are left with 16 choices only as one person has already been selected for post of president .
For post of a secretary , we are left with 15 choices only as two persons have already been selected for post of president and vice - president .
For post of a treasurer , we are left with 14 choices only as three persons have already been selected for post of president , vice - president and treasurer .
So, number of ways in which these four positions can be filled = [tex]17\times 16\times 15\times 14 = 57120[/tex]
To determine the number of ways to fill four distinct positions from 17 people where each person can only hold one position, we calculate the permutations, resulting in 17 x 16 x 15 x 14 = 40,320 different ways.
Explanation:The question pertains to a combinatorial mathematics problem, specifically involving permutations. Given a committee consisting of 17 people, we need to determine in how many different ways four distinct positions (president, vice-president, secretary, and treasurer) can be filled. To solve this, we assume that no person can hold more than one office.
To choose the president, there are 17 possible candidates. Once the president is chosen, there are 16 remaining candidates for the vice-president. Similarly, there are 15 candidates for the secretary position after the president and vice-president have been chosen, and finally, 14 candidates for the treasurer. The number of permutations is the product of these choices, which is calculated as 17 x 16 x 15 x 14.
The calculation yields 40,320 different ways to fill the four positions. This calculation is an example of using factorial notation in permutations where the general formula is n!/(n-r)!, with n representing the total number to choose from, and r is the number to be chosen.
suppose Tinsel Town Videos lowers the price of its movie club membership by 10 percent and as a result, CineArts Videos experienced a 16 percent decline in its movie club membership. What is the value of the cross- price elasticity between the two movie club memberships
Answer: The value of cross price elasticity is 1.6.
Step-by-step explanation:
Since we have given that
Percent change in price = 10%
Percent change in quantity = 16%
So, we need to find the cross price elasticity between the two movie club memberships.
As we know the formula for cross price elasticity :
[tex]\dfrac{\%\text{change in demand}}{\%\text{change in price}}\\\\=\dfrac{16}{10}\\\\=1.6[/tex]
Hence, the value of cross price elasticity is 1.6.
What is the length of Line segment A C? Round to the nearest tenth. Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters. 10.5 m 12.3 m 18.3 m 21.4 m
Answer:
10.5
Step-by-step explanation:
got it on the test
The length of line segment AC in triangle ABC is 12.3 meters, derived using the sine function and the given angle and side.
Explanation:To find the length of Line segment AC in the given right angle triangle ABC, we can use the trigonometry functions. Since we are given the length of side CB and the measure of angle BAC, we can apply the sine function. The sin of an angle in a right angle triangle is the length of the opposite side (which in this case is the length of AC we're trying to find) divided by the length of the hypotenuse (which in this case is length CB = 15 m).
So, sin(55 degrees) = Length of AC / 15 m. Solving this equation for Length of AC produces: Length of AC = 15 m * sin(55 Degrees). Plugging in the value of sin(55 degrees) approximately as 0.819 gives a Length of AC approximately equal to 12.3 m. "So the length of the line segment AC is 12.3 m".
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Wilson Rooeboker brokers sales agreements for a major home builders chain. He is paid a straight commission of 1.5% of the contract plus an annual bonus of 2.5% of total contracts over $1,500,000 per year. What is his total pay for a year in which he had total contracts for $2,555,500?
Answer:
$64,720
Step-by-step explanation:
The straightforward way to figure this is ...
total pay = straight commission + annual bonus
= 1.5% × 2,555,500 + 2.5% ×(2,555,500 -1,500,000)
However, this expression can be simplified a little bit to ...
2,555,500 × (1.5% +2.5%) -2.5% × 1,500,000
= 4% × 2,555,000 -2.5% × 1,500,000
= 102,220 -37,500
total pay = $64,720
15=3n+6p solve for n
15=3n+6p
We need to isolate n.
15 - 6p = 3n
(15 - 6p)/3 = n
5 - 2p = n
To solve for n in the equation 15 = 3n + 6p, isolate n by subtracting 6p from both sides, and then divide both sides by 3.
Explanation:To solve for n in the equation 15 = 3n + 6p, we can start by isolating the variable n. First, subtract 6p from both sides of the equation to get 15 - 6p = 3n. Then, divide both sides by 3 to solve for n, yielding: n = (15 - 6p) / 3.
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If AD = 12 units, BD = 15 units, and AC = 4 units, what is the length of BC?
Answer:
The answer to your question is: BC = √65 or 8.05 u
Step-by-step explanation:
Data
AD = 12 u
BD = 15 u
AC = 4 u
BC = ?
First calculate the length of AB using the pythagorean theorem
BD² = AB² + AD²
AB² = BD² - AD²
AB² = 15² - 12²
AB² = 225 - 144
AB² = 81
AB = 9 u
Now, use the pythagorean theorem to find BC
AB² = BC² + AC²
BC² = AB² - AC²
BC² = 9² - 4²
BC² = 81 - 16
BC² = 65
BC = √65 or 8.05 u
help fast thanks In the figure, prove that m∥n
Complete the proof below by providing the reasons in each blank.
Blank # 1
Blank # 2
Blank # 3
Answer:
See below
Step-by-step explanation:
a + 133 = 180 because they are supplementary angles. (adjacent angles that form a straight angle)
a = 47 (you substract 133 at each side of the previous equation, leaving that a = 47)
m || n Since "a" measure the same as the angle in the figure that measures 47 both are corresponding angles, therefore m and n are parallels
Answer:
Step-by-step explanation:
It is called adjacent angles to all pairs of angles (2 angles) that are consecutive (that is, have the vertex and one side in common) and supplementary ( the sum of both angles results in 180 °; that is, a straight angle). Graphically, two opposite semi-lines are observed. You can see two adjacent angles in the image.
A case of consecutive angles is shown between a"" and 133 °, because they form a straight angle and are separated by a common side. Then "a" and 133 ° add up to 180 °. In this way you can know what is the value of "a".
a+133°=180°
a=180°-133°
a=47°
The relative position of the angles with respect to the straight lines makes those angles receive specific names. Thus, it is called corresponding angles to those that are located on the same side of the parallels and on the same side of the transversal. These angles are equal.
Note that the other angle given as data is 47 °. This angle has the same value as "a" and as both angles are on the same side of the transverse, so that they are corresponding m must be parallel to n.
A researcher reports that the time (in minutes) it takes children who are "picky eaters" to finish their vegetables is negatively skewed, with children finishing their vegetables in 4.2±1.0 (M±SD) minutes. Based on Chebyshev's theorem, we can conclude that68% of children finished their vegetables in 3.2 to 5.2 minutes.50% of children finished their vegetables in at least 3.2 minutes.99.7% of children finished their vegetables in 2.2 to 6.2 minutes.At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.
Answer:
Option d) Chebyshev's rule
Step-by-step explanation:
The Chebyshev's rule state that for a data that is not distributed normally,
atleast [tex](1 - \frac{1}{k^2})\% \text{ of data lies within the interval}~(Mean \pm (k)Standard ~Deviation)[/tex].
Here, k cannot be 1 and is always greater than 2.
For k = 2,
[tex](1 - \frac{1}{4})\times 100\% = 75\%[/tex] of data lies within the range of [tex](\mu \pm 2\sigma)[/tex]
Atleast 75% of children finished their vegetables in [tex](\mu \pm 2\sigma) = (4.2 \pm (2)1.0) = (2.2,6.2)[/tex]
For k = 3,
[tex](1 - \frac{1}{9})\times 100\% = 88.912\%[/tex] of data lies within the range of [tex](\mu \pm 3\sigma)[/tex]
Atleast 89% of children finished their vegetables in [tex](\mu \pm 3\sigma) = (4.2 \pm (3)1.0) = (1.2,7.2)[/tex]
Thus, option d) is correct.