Answer:
16 units
Step-by-step explanation:
RST was dilated by a scale factor of 1/2. This means R'S'T' has sides that are 1/2 the length of the sides of RST.
Since the legs of R'S'T' are 8 units, this gives us the equation
8 = 1/2x
Divide both sides by 1/2:
8÷1/2 = x
8 × 2/1 = x
16 = x
Each leg in RST is 16 units.
A polygon has 13 sides calculate the sum of the interior angle measure of each polygon
You purchase a new desktop computer for $2,200. you put a 6% down payment and $100 per month on a 24 month purchase plan. determine the total finance
What is the interquartile range of this data? A.6 B.7 C.8 D.9
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.
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%.
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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.
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
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.
Which correlation coefficient obtained from modeling advertising and sales data of tutti frutti ice cream expresses the strongest correlation of the data?
a.r = .10
b.r = .50
c.r = .75
d.r = .90
Answer:
d) r=0.90
Step-by-step explanation:
When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation nearerto -1 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation.
Correlation coefficient measures the strength of association between two variables.
It may be positive or negative.
If nearer to 1 or - there is strong correlation
Since here is it 0.90 positive and nearer to 1 out of all 4 options
option d is correct
Can you use elimination to solve a system of linear equations with three equations
How many atoms of carbon are in a single molecule of sugar?
What constant term should be used to complete the square? x 2 - 5x + _____ = 7
25/4 is the anwser. i just took this test
Rent-a-car rents compact cars for a fixed amount per day plus a fixed amount for each mile driven Benito rented a car for 6 days drove it 550 miles and spent $337. Lisa rented the same car for 3 days drove it 350 miles and spent $185. What is the charge per day and charge per mile for the compact car?
Please show all work! TYSM! ☺♥♫
The charge per day and charge per mile for the compact car is $36 and $0.22 respectively
let
x = charge per day
y = charge per mile
6x + 550y = 337 (1)
3x + 350y = 185 (2)
multiply (2) by 2
6x + 700y = 370 (3)
6x + 550y = 337 (1)
subtract (1) from (3)
700y - 550y = 370 - 337
150y = 33
y = 33/150
y = 0.22
substitute y = 0.22 into (2)
3x + 350y = 185
3x + 350(0.22) = 185
3x + 77 = 185
3x = 185 - 77
3x = 108
x = 108/3
x = 36
Therefore, charge per day and charge per mile for the compact car is $36 and $0.22 respectively
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what is the 14 letter word with the definition of an example showing a statement is not true. it is c--n-e-t--m-l-
$8000 at 3% annually for 4 years
Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 – 7x + 4 has. Which best describes the discriminant and the number of zeros?
How many differnet points could a parabola intersect a ircle?
A party store sells large plates in packs of 12 and small plates in packs of 8 . In order to have an equal number of both , what is the least amount of large plants that would have to be purchased
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.
find the base of a parallelogram with an area of 18 square inches and a height of 2 inches
Can Someone PLEASE help me
And if you can show your work.
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 :)
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.
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]
The length of a rectangle with length 12 yd and width 11 yd is divided by 6.
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
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
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
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?