Determine the equation of the line given by the graph.
A) y = 2 3 x − 1
B) y = 3 2 x − 1
C) y = −2 3 x − 1
D) y = −3 2 x − 1
Answer:
A. [tex]y=\frac{2}{3}x-1[/tex]Step-by-step explanation:
The given graph belongs to a linear function, because it's a line.
To find its equation, we first need to find the slope of the line using two points and the formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
We are gonna use points (0,-1) and (3,1), because the lines crosses through them. Replacing these points in the formula, we have
[tex]m=\frac{1-(-1)}{3 -0 }=\frac{1+1}{3}\\m=\frac{2}{3}[/tex]
Now, we use one points and the point-slope formula
[tex]y -y_{1} =m(x-x_{1} )\\y-(-1)=\frac{2}{3}(x-0)\\ y+1=\frac{2}{3}x\\y=\frac{2}{3}x-1[/tex]
Therefore, the right answer is A.
[tex]y=\frac{2}{3}x-1[/tex]
How many atoms of carbon are in a single molecule of sugar?
Can Someone PLEASE help me
And if you can show your work.
What constant term should be used to complete the square? x 2 - 5x + _____ = 7
25/4 is the anwser. i just took this test
Ten percent of all dynamite mints candies are orange and 45 percent of all holiday mints candies are orange. two independent random samples, each of size 25, are selected⎯one from dynamite mints candies and the other from holiday mints candies. the total number of orange candies in the two samples is observed. what are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?
The mean and standard deviation of the sample of orange sweets can be ibtaide using the binomial approximation relation. Hence, the mean and standard deviation are 13.75 and 2.905
Mean = np
Sample size, n = 25 Proportion, pDynamite mints :
25 x 0.1 = 2.5Holiday mints:
25 x 0.45 = 11.25Total orange candies = (2.5 + 11.25) = 13.75
2.)
Standard deviation, σ = √(npq)
q = 1 - pDynamite mints :
√[25 x 0.1 × (1 - 0.1)] = 1.5
Holiday mints :
√[25 x 0.45 (1 - 0.45)] = 2.4874
Combined standard deviation : s²(x + y) = s²(x) + s²(y)
Std = √(1.5²2 + 2.4874²) = 2.905
Therefore, the mean and sample standard deviation are 13.75 and 2.905 respectively.
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what is the value of x in the equation 1,331x^4-216=0?
a) -6/11
b) 11/6
c) 1/6
d) 6/11
At a shoe store a sales person earns a weekly salary of $150.a salesperson is also paid $2.00 for each pair of shoes he or she sells during the week what is the algebraic expression
Answer:
150 + (2x)
Step-by-step explanation:
At a shoe store a sales person earns a weekly salary = $150.
He or she also paid for the sale of each pair of shoes = $2.00
Let the number of pairs of shoes sold be 'x'
the commission on the shoes sold = 2(x)
So the algebraic expression for her/his weekly pay would be
150 + (2x)
The length of a rectangle with length 12 yd and width 11 yd is divided by 6.
How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get a 70% acid solution?
Final answer:
To obtain a 70% acid solution, mix 4 gallons of pure acid with the existing 6 gallons of 50% acid solution.
Explanation:
To find out how much pure acid should be mixed with 6 gallons of a 50% acid solution to obtain a 70% acid solution, we use the concept of mixtures in percentage problems. Let x be the number of gallons of pure acid to be added.
Firstly, the amount of pure acid in the initial solution is 50% of 6 gallons, which is 3 gallons. When we add x gallons of pure acid, the total volume of the mixture becomes x + 6 gallons, and the total amount of pure acid is x + 3 gallons.
To have a 70% acid solution:
The total amount of pure acid divided by the total volume should equal 70%.
Therefore, the equation is:
(x + 3) / (x + 6) = 0.70
By solving for x:
x + 3 = 0.70(x + 6)
x + 3 = 0.70x + 4.20
x - 0.70x = 4.20 - 3
0.30x = 1.20
x = 1.20 / 0.30
x = 4 gallons
You need to mix 4 gallons of pure acid with the 6 gallons of 50% acid solution to end up with a 70% acid solution.
3)
Write a function to represent the set of ordered pairs.
{(2, 2), (3, 7), (4, 14), (5, 23)}
A) f(x) = x
B) f(x) = 4x - 6
C) f(x) = x2 - 2
D) f(x) = 2x2 - 6
Answer:
C
Step-by-step explanation:
f(x) = x2 - 2
A pair of dice is rolled. find the probabilities of the given events. the sum is 6, given that the sum is less than 8.
Given the condition that the sum of the dice rolled is less than 8, the probability of the dice having a sum of 6 is found by considering all outcomes where the sum is less than 8 and outcomes that result in a sum of 6. The probability turns out to be 20%.
Explanation:This question involves the concept of conditional probability in mathematics. For a pair of six-sided dice, there are 36 equally likely outcomes (Because 6 faces of one die times 6 faces of the other). We are interested in the event of getting a sum of 6, given the sum is less than 8.
We first consider all the outcomes where the sum of two dice is less than 8: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,5), (4,1), (4,2), (4,3), (4,4), (5,1), (5,2), (5,3), (6,1), (6,2). There are 25 equally likely outcomes where the sum is less than 8.
Then, consider all the outcomes where the sum of the two dice is equal to 6: (1,5), (2,4), (3,3), (4,2), (5,1). There are 5 equally likely outcomes. So given the condition that the sum is less than 8, the probability of getting a sum of 6 is 5/25 or 20%.
Learn more about Conditional Probability here:https://brainly.com/question/32171649
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If the relationship is linear do the variables have a positive or negative association?
a. the variables have a positive association.
b. the variables have a negative association.
c. the relationship is not linear.
Bromine-82 has a half of about 35 hours. After 140 hour, how many milliliters of an 80 mL sample will remain? A,65mL B.20mL C.10mL D.5mL
Final answer:
After 140 hours, which is equivalent to 4 half-lives, the amount of bromine-82 remaining from an 80 mL sample will be 5 mL, as the amount is halved after each half-life period of 35 hours.
Explanation:
The question involves the half-life of a radioactive isotope, which is a concept in Chemistry specifically related to nuclear chemistry and radioactive decay. Since bromine-82 has a half-life of about 35 hours, after 140 hours, which is equivalent to 4 half-lives, the amount of the element remaining in the sample will be reduced by a factor of two after each half-life. To calculate this, we start with the initial 80 mL and reduce it by half 4 times.
After the first half-life (35 hours), 40 mL remains.
After the second half-life (70 hours), 20 mL remains.
After the third half-life (105 hours), 10 mL remains.
After the fourth half-life (140 hours), 5 mL remains.
Therefore, the correct answer is D. 5mL.
Final answer:
After 140 hours, which is four half-lives of Bromine-82, only 5 mL of an initial 80 mL sample will remain, making the correct answer D. 5mL.
Explanation:
The question is asking how much of a radioactive isotope will remain after a certain amount of time, given its half-life. In this example, the half-life of Bromine-82 is about 35 hours, and we want to know how much of an 80 mL sample will remain after 140 hours. To solve this, we will use the concept of half-life, which is the time it takes for half of the radioactive atoms in a sample to decay.
Since 140 hours is equal to 4 half-lives (140 hours ÷ 35 hours/half-life), we can calculate the remaining amount of Bromine-82 in the sample by halving the initial amount repeatedly, four times:
After the first half-life (35 hours), the remaining amount is ⅓ × 80 mL = 40 mL.
After the second half-life (70 hours in total), the remaining amount is ⅓ of 40 mL = 20 mL.
After the third half-life (105 hours in total), the remaining amount is ⅓ of 20 mL = 10 mL.
After the fourth half-life (140 hours in total), the remaining amount is ⅓ of 10 mL = 5 mL.
The correct answer is D. 5mL.
Can you use elimination to solve a system of linear equations with three equations
What is the factorization of the polynomial below?
–x2 – 15x – 54
A. (x – 9)(x + 6)
B. (x + 9)(x + 6)
C. –1(x + 9)(x + 6)
D. (x + 9)(x – 6)
Answer:
Option C, -(x + 9)(x + 6) or,
-1(x + 9)(x + 6)
Explanation:
We can begin the factorization process by factoring out the negative -1 from each term in the polynomial. This changes the expression to:
-1(x² + 15x + 54)
This factored-out negative will follow all the way to the answer so any answer not containing a -1 factored out can eliminated. Options A, B, and D do not have this negative. Therefore, they are ruled out. But let's continue to confirm Option C.
With the polynomial within the parentheses in quadratic expression ax² + bx + c form, we start by finding which factor pair for the product and coefficient a and constant c has a sum equating to coefficient b. This may sound complicated but this is not the case in practice.
Coefficient a = 1
Constant c = 54
Coefficient b = 15
The product of a and b = 1(54) = 54
Now, we list factors of 54. I like to list them as factor pairs:
1, 54; 2, 27; 3, 18; 6, 9
Next, find which factor pair has a sum of 15. That would be 6 and 9. We now substitute these values as the coefficients b, separate the terms into pairs as binomials, and factor out their greatest common factors (GCF).
-(x² + 6x + 9x + 54)
-[(x² + 6x) + (9x + 54)]
The GCF between x² and 6x is x. The GCF between 9x and 54 is 9. So:
-[x(x + 6) + 9(x + 6)]
If the binomial within each set of parentheses matches, you have found the factors for your polynomial. They are the polynomial within the binomial within the parentheses and the GCFs that were factored out of each:
-x² - 15x - 54 = -(x² + 15x + 54) = -(x + 9)(x + 6)
Final answer:
The factorization of the polynomials [tex]-x^2 - 15x - 54[/tex] is obtained by finding two numbers that multiply to -54 and add up to -15, which are -9 and -6. The factored form is -1(x + 9)(x + 6).
Explanation:
The factorization of the polynomial [tex]-x^2 - 15x - 54[/tex] can be approached by looking for two numbers that multiply to give the product of the coefficient of x2 (which is -1) and the constant term (which is -54), and at the same time, add up to give the coefficient of x (which is -15). After finding such numbers, we can then express the polynomial in its factored form.
In this case, the numbers that satisfy these conditions are -9 and -6. Multiplying these gives 54 (which is the negative of the constant -54 when considering the leading negative sign of the polynomial), and adding them gives -15.
Therefore, the polynomial can be factored as -1(x + 9)(x + 6), which corresponds to answer option C.
Help ???!!!! ThankYou !!!
A scatter plot is shown:
A scatter plot is shown. Data points are located at 0 and 0, 1 and 0.25, 2 and 1, 3 and 2, 4 and 3, 5 and 4, 5.5 and 5, 6 and 6, 6.4 and 7, 6.7 and 7.8, 7 and 9.
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
The correct option is 2.
Step-by-step explanation:
From the given graph it is noticed that the data points are located at (0,0), (1,0.25), (2,1), (3,2), (4,3), (5,4), (5.5,5), (6,6), (6.4,7), (6.7,7.8) and (7,9).
The rate of change from first two data points is
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{0.25-0}{1-0}=0.25[/tex]
The rate of change from next two data points is
[tex]m_2=\frac{2-1}{3-2}=1[/tex]
[tex]m_1\neq m_2[/tex]
The rate of change it not constant, therefore the given data points are non linear.
The value of y increases as the value of x-increases. It means there is a positive relation between x and y.
Therefore the graph represent a Nonlinear positive association between x and y. Option 2 is correct.
Answer:
The correct answer is 2.
a physics student stands at the top of a hill that has an elevation of 56 meters. He throws a rock and it goes up in the air and then falls back past him and lands on the ground below the path of the rock can be modeled by the equation y=-0.04x^2+1.3x+56 where x is the horizontal distance in meters from the starting point on top of the hill and y is the height in meters of the rock above the ground. How far horizontally from the starting point will the rock land? Round to the nearest hundredth.
Evan graphs the function h(x)=x^2+4. Victor graphs the function g(x)=(x+4)^2. Which statments are true regarding the two graphs? Check all that apply.
How many differnet points could a parabola intersect a ircle?
Yun is making some investments in the stock market. Stock for Company A has a 30% chance of losing $12,000, a 45% chance of breaking even, and a 25% chance of earning Yun $11,000. Assuming Yun would like the odds to be in favor of her gaining money, should she invest in Company A? Explain.
a. no, 7,700 > 3,600
b. yes, 7,700 > 3,600
c. yes, 3,600 > 2,750
d. no, 3,600 > 2,750
We have been given that company A has a 30% chance of losing $12,000.
Let us calculate the amount that Yun can loose.
[tex]\frac{12000\times 30}{100} \\ \\ =\$3600[/tex]
Now, 45% chance of breaking even. It means neither loss nor profit.
Then, 25% chance of earning Yun $11,000.
Let us calculate the amount of profit
[tex]\frac{11000 \times 25}{100} \\ \\ =\$2750[/tex]
Since, 3,600 > 2,750. It means that Yun will be in loss on investing in the company.
Hence, she will not invest in the company A.
d is the correct option.
d. no, 3,600 > 2,750
1) Which rate is the lowest price?
$2.50/5lb
$2.40/6lb
$3.00/6lb
$2.40/4lb
2)Select all that apply
Which rates are equivalent to 25 miles per gallon?
150miles/6gallons
50miles/1.5gallons
100miles/3.8gallons
75miles/3gallons
3) which speed is the fastest?
30miles/1hour
90miles/2hours
180miles/3hours
240miles/6hours
Please ASAP thank you:)
Answer:
5 points for this bruuuh
Step-by-step explanation:
Juan visited a candy store and purchased 7 pounds of candy consisting of Atomic Fireballs and Gummi Bears. Atomic Fireballs cost $4.25 per pound and Gummi Bears were on sale for $1.25 per pound. Juan spent a total of $14.75, before taxes. Let x represent the number of pounds of Atomic Fireballs and y represent the number of pounds of Gummi Bears uan purchased. Which of the following graphically represents this situation?
Answer:
The 2nd graph correctly represents the situation.
Step-by-step explanation:
Let the number of Atomic Fireballs= x and the number of Gummi bears= y.
Now, Juan purchased total 7 pounds of candies.
So, [tex]x+y=7[/tex]
Also, the cost of Atomic Fireballs and Gummi bears is $4.25 and $1.25 per pound respectively.
Since, Juan spent total $14.75 before taxes.
Then, [tex]4.25x+1.25y=14.75[/tex]
That is, the system of equations is given by,
[tex]x+y=7[/tex]
[tex]4.25x+1.25y=14.75[/tex]
Plotting the equations, we get that,
The 2nd graph shown below correctly represents the situation.
There’s a positive correlation between the price a passenger pays for a train ticket and the number of stops the train makes during their trip.
Which variable is most likely the lurking variable that explains the correlation?
age of passenger
outside temperature
distance being traveled
expected time of arrival
Answer:
The variable that is most likely the lurking variable that explains the correlation is:
Distance being traveled.
Step-by-step explanation:
As we know that a lurking variable is a variable that correlates between the dependent and independent variable in a scatter plot or some other statistical model.
Hence, here as the distance traveled increases the number of stops would also increase and more passengers would come and hence the cost of ticket will increase.
Hence, the lurking variable is:
Distance being traveled.
The most likely lurking variable that explains the positive correlation between the price a passenger pays for a train ticket and the number of stops the train makes during their trip is distance being traveled.
Distance being traveled: Longer trips generally cost more, and longer trips are also more likely to include more stops. Therefore, the distance being traveled is a common factor influencing both the price of the ticket and the number of stops, leading to the observed positive correlation.The other variables are less likely to explain the correlation:
Age of passenger: This does not directly affect the number of stops or the ticket price.Outside temperature: This is unrelated to the ticket price and the number of stops a train makes.Expected time of arrival: While it could be related to the overall trip duration, it doesn't directly influence the number of stops or the price independently of the distance being traveled.Hence, the distance being traveled is the lurking variable most likely explaining the correlation between ticket price and the number of stops.
which of the following describe the given graph of the function over the interval [2,6]
•increasing
•constant
•decreasing
•decreasing to increasing
Answer:
Increasing
Step-by-step explanation:
We know that, a function can be increasing, decreasing, constant or a mix of these three i.e. a function is:
1. Increasing: if for x < y, f(x) < f(y).
2. Decreasing: If for x < y, f(x) > f(y).
3. Constant: If for any two numbers say x and y, f(x) = f(y).
As we can see from the graph, between [2,6], the value of function at 2 is less than the value of function at 6.
i.e. As 2 < 6, f(2) < f(6).
Which satisfies the definition of an increasing function.
Hence, the graph of the function over [2,6] is increasing.
A polygon has 13 sides calculate the sum of the interior angle measure of each polygon
If a storage tank that measures 12 feet by 9 feet by 8 feet is designed to store gas that costs $1.82 per cubic foot, what does it cost to fill the tank to one-half of its capacity?
Find the following measure for this figure.
Volume =
275 cubic units
91 2/3 cubic units
36 2/3 cubic units
Answer:
Step-by-step explanation:
the right answer is B. 91 2/3 Cubic units i got it right on my geometry test :)
Here is the sample space for three tosses of a coin. {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} calculate te probability that all three coin tosses will give a tails result
The probability is 0.125
find the base of a parallelogram with an area of 18 square inches and a height of 2 inches