It costs $57.19 to fill up a 19 gallon gas tank and $54.18 to fill up an
18 gallon tank.
What is the constant of proportionality that relates the cost in dollars,
y, to the number of gallons of gas, x?
Answers
Answer:
y=3.01x
Step-by-step explanation:
We can see that since 19 gallons cost $57.19 and 18 gallons cost $53.18, 1 gallon (19-18) must cost $3.01.
Therefore, y=3.01x
You can check this with algebra
Related Questions
Find the mean, median, and mode of the following data set
17, 18, 13, 15, 12, 11, 35, 18, 14
Answers
Answer: Mean- 17
Median- 15
Mode- 18
Step-by-step explanation: Your welcome. Branliest, please.
George hiked from the top of a hill to the valley floor. The elevation at the top of the hill is 127 feet above sea level. The valley floor is 52 feet below sea level. George stopped at a rest stop that is at an elevation exactly halfway between the top of the hill and the valley floor. What is the elevation, in feet, of the rest stop? Show your work
Answers
Answer:
The elevation of the rest stop is 37.5 feet above sea level.
Step-by-step explanation:
Given that the elevation at the top of the hill is 127 feet above sea level and The valley floor is 52 feet below sea level.
So, the total length from the top of the hill to the valley floor
\(l= 127+52 = 179\) feet
So, length of halfway \(= l/2=179/2=89.5\) feet ...(i)
Assuming that the stop for rest, the halfway between the top of the hill and the valley floor, is at x feet above sea level.
So, the length between the stop position and the valley floor \(= 52 +x\) feet.
As the stop position is at half-way, so by using equation (i), we have,
\(52 + x = 89.5 \\\\\Rightarrow x =89.5-52 \\\\\)
\(\Rightarrow x=37.5\) feet
Hence, the elevation of the rest stop is 37.5 feet above sea level.
The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man
Answers
Answer:
78kg
Step-by-step explanation:
76×5= 380kg
380-72-74-75-81= 78kg
x=(76.5)-302
x=380-302=78
please help xx 10 points
Answers
I uploaded the answer to a file hosting. Here's link:
bit.\(^{}\)ly/3a8Nt8n
determine the value of x in the diagram
Answers
Check the picture below.
\(x\sqrt{3}=7\implies x=\cfrac{7}{\sqrt{3}}\implies x=\cfrac{7}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies x=\cfrac{7\sqrt{3}}{3}\)
Answer:
x = 4.04
Step-by-step explanation:
\(tan30^{0}=\frac{x}{7}\)
\(x=7tan30^{0}\)
\(x=4.04\)
Hope this helps.
Solve this system of equations by using the elimination method. x+4y=9 2x-4y=-6
Answers
Answer:
\(x=6\)
\(y=\frac{3}{4}\)
Step-by-step explanation:
Given the following question:
\(x+4y=9\)
\(2x-4y=9\)
To solve using the elimination method we will add the two equations together to find the two individual values.
\(x+2x=3x\)
\(4y-4y=0\)
\(9+9=18\)
\(3x=18\)
\(\frac{3x}{3} =x\)
\(18\div3=6\)
\(x=6\)
\(x+4y=9\)
Substitute six in for x:
\(x=6\)
\(6+4y=9\)
Solve for y:
\(6-6=0\)
\(9-6=3\)
\(\frac{4y}{4} =y\)
\(3=\frac{3}{4}\)
\(y=\frac{3}{4}\)
x is equal to 6, and y is equal to 3/4.
Hope this helps.
Kami was taking a quiz and she decided to simplify the following expression Her steps are shown below. Step 1: 1.3 (5+2.3m - 2.4) Step 2: 6.3+3.6m - 1.1 Step 3: 6.3-1.1 +3.6m Step 4: 5.2+3.6m Which statement identifies and explains Kami's first mistake?
a. Kami's first mistake was in Step 4. She should have reordered the terms by writing 3.6m first and then 5.2.
b. Kami's first mistake was in Step 2. of multiplying by 1.3. She added 1.3 to each term instead
c. Kami's first mistake was in Step 2. She should only add 1.3 to 5 and not to all 3 terms.
d. Kami's first mistake was in Step 3. She should have made 3.6m negative and the 1.1 should be positive.
e. Kami's first mistake was in Step 2. She should multiply 1.3 to 5 and to -2.4 only instead of adding by 1.3 to each term.
Answers
The statement that shows kemi first mistake is that
' Kemi first mistake was in step 2 , instead of multiplying 1.3 with all terms , she added 1.3 to each term instead'. (optionB)
What is simplification of expression?Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler. For example;
5( 2x+6) can be simplified by using distributive law. i.e 5× 2x + 5× 6
= 10x + 30
Similar simplifying 1.3 (5+2.3m - 2.4), we use distributive law to simplify.
1.3 × 5 + 1.3 × 2.3m -2.4 × 1.3
= 6.5 + 2.99m - 3.12
The next step is to collect like terms
= 6.5-3.12 + 2.99m
= 3.38 + 2.99m
Instead of using the distributive law, Kami added 1.3 to all the terms in parentheses.
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Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (1, 5), and the x-axis.
Answers
The area of the region bounded by the parabola is \(\frac {5}{12} $\).
Area of the region bounded by y=f(x) and x axis between x=a and x=b is given by \($\int_a^b f(x) d x$\). The coordinates of all the points mentioned are first calculated and then finally the area of required region OAC is calculated.
The area of the region bounded by the parabola y=\(5x^{2}\).
The area that needs to be calculated is the area enclosed by OAC as shown in figure.
From the figure, it is clear that
Area of region OAC=area of region OAB-area of region ABC......(1) let us first calculate the equation of the tangent at(1,5).
⇒\($\frac{d y}{d x}=10 x \Rightarrow \frac{d y}{d x}(1,5)=10$$\)
Equation of tangent is y-5=10(x-1).
This tangent intercepts x axis at \($x=\frac{-5}{10}+1=\frac{1}{2}$\) (Putting y=0 in equation of tangent)
Hence, coordinates of C is (0.5,0) and B is (1,0).
⇒BC=OB−OC⇒BC=1−0.5=0.5
The area of region ABC is \($\frac{1}{2} * B C * A B=\frac{1}{2} * 0.5 * 5=\frac{5}{4}$\)
Now area of region OAB is given by \($\int_0^1 5 x^2 d x \Rightarrow\left[\frac{5}{3} x^3\right]_0^1=\frac{5}{3}$\)
Area of region OAB is thus \($\frac{5}{3}$\)
Now using equation (1) area of region OAC \(=\frac{5}{3}-\frac{5}{4}=\frac{5}{12}$\)
The area of region OAC is \(\frac {5}{12} $\).
Therefore, the area of the region is \(\frac {5}{12} $\).
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Solve.
11. Antoine measured a tree in his yard to be
4 meters tall. Each meter is equivalent to
100 centimeters. How tall, in centimeters,
was the tree that Antoine measured?
Answers
If the tree is 4 meters tall and each meter is 100 centimeters, then multiply 4 by 100 to get 400 centimeters.
Meg plotted the graph below to show the relationship between the temperature of her city and the number of people at a swimming pool:
Main title on the graph is Swimming Pool Population. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of People at the Pool. Dots are made at the ordered pairs 2.5, 1 and 5, 2 and 7.5, 2 and 7.5, 3 and 7.5, 4 and 10, 5 and 10, 6 and 12.5, 6 and 15, 7 and 15, 8 and 17.5, 5 and 17.5, 7 and 20, 9 and 22.5, 7 and 22.5, 9 and 25, 11 and 27.5, 12.
Part A: In your own words, describe the relationship between the temperature of the city and the number of people at the swimming pool. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Answers
Answer:
Step-by-step explanation:
Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.
Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):
Slope (m) = (change in y) / (change in x)
= (12 - 1) / (12 - 2.5)
= 11 / 9.5
≈ 1.16
To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):
1 = 1.16 * 2.5 + b
1 = 2.9 + b
b ≈ -1.9
Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.
Which number sentence is true?A) -1/12 x 6/7 = -1/14B) -1/12 x (-6/7) = -1/14C) 1/12 x 6/7 = 1/14D) 1/12 x (-6/7) = 1/14
Answers
Let's check each option:
a.
\(\begin{gathered} \frac{-1}{12}\cdot\frac{6}{7}=\frac{-1\cdot6}{12\cdot7}=\frac{6}{84} \\ \text{We can rewrite the expresion:} \\ \frac{6}{84}=\frac{6\cdot-1}{6\cdot14} \\ \text{Simplify the common term }\frac{6}{6}=1,\text{ Then} \\ =\frac{-1}{14} \end{gathered}\)b.
\(\begin{gathered} \frac{-1}{12}\cdot\frac{-6}{7}=\frac{(-1)(-6)}{(12)(7)}=\frac{6}{84} \\ \text{We can rewrite the expresion:} \\ \frac{6\cdot1}{6\cdot14} \\ \text{Simplify the common term }\frac{6}{6}=1,\text{ then:} \\ =\frac{1}{14} \end{gathered}\)c.
\(\begin{gathered} \frac{1}{12}\cdot\frac{6}{7}=\frac{1\cdot6}{84} \\ \text{We can rewrite as:} \\ =\frac{1\cdot6}{6\cdot14} \\ \text{Simplify the common term }\frac{6}{6}=1,\text{ then:} \\ =\frac{1}{14} \end{gathered}\)d.
\(\begin{gathered} \frac{1}{12}\cdot\frac{-6}{7}=\frac{(1)(-6)}{84} \\ \text{We can rewrite as:} \\ =\frac{1\cdot-6}{6\cdot14} \\ \text{Simplify the common term }\frac{6}{6}=1,\text{ then:} \\ =\frac{-1}{14} \end{gathered}\)Hence, the correct answers are options A and C.
Pls help solve all 3 questions
Thank you :)
Answers
Answer:
Q18: x = 21, y = 15
Q19: x = 16, y = 10
Q20: x = 24, y = 19
Step-by-step explanation:
Q18:
(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)
9x - 9 = 180
9x = 189
x = 21
11y - 32 = 6x + 7 (vertically opposite angles)
11y - 32 = 6(21) + 7
11y - 32 = 133
11y = 165
y = 15
Q19:
8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)
3x = 48
x = 16
(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)
8(16)-14 + (5y + 16) = 180
114 + 5y + 16 = 180
5y + 130 = 180
5y = 50
y = 10
Q20:
47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)
5x + 60 = 180
5x = 120
x = 24
5y - 23 = 3x (corresponding angles)
5y - 23 = 3(24)
5y - 23 = 72
5y = 95
y = 19
Mr. Walker is looking at the fundraiser totals for the last five years. How does the mean of the totals compare to the median? the median is $1. 60 greater than the mean. The mean is $1. 60 greater than the median. The median is $2. 82 greater than the mean. The mean is $2. 82 greater than the median.
Answers
The mean is $1.60 greater than median So, Option B is correct
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this.
The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.
According to the question,
Five year data is given:
For calculating mean,
Total number of year = 5
Sum of all year = 896 + 925 + 880 + 963 + 914
=> 4573
Mean = sum / total number
=> mean = 4578/5
=> 915.6
For calculating Median,
Arrange all the data in a ascending order
880 , 896 , 914 , 925 , 963
The middle value is 914
Therefore , median = 914
Difference of mean and median = 915.6 - 914
=> 1.6
Hence , Mean is $1.60 greater than median
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please help me this is due tomorrow
Answers
Answer:
Step-by-step explanation:
This graph represents the line of best fit for some dataset.
It is reduced to a linear function in this instance with a constant slope, where x represents the independent variable and y, the dependent variable. This shows us quiz score is supposedly directly proportional to the time spent on homework per week in hours.
To find the amount of time someone should expect to study to get a 96% on their quiz you need to resolve the linear function modeled by y=mx+b which is in slope-intercept form. where m is the slope and b is the y-intercept. the y-intercept can be found when x = 0 which is shown in the graph to be 63, to solve for slope you can use the equation \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\) which is rise/ run. then plug in any 2 points I will use (1,69) and (2,75) \(\frac{75-69 }{2-1 }\) or 6 which means m = 6, therefore, our equation is y = 6x + 63 and because we know that y must be 96 for this question, we can solve for x using inverse operations. 96 = 6x + 63 subtract 63 from both sides and 6x = 33 then divide by 6 and 33/6 = 5.5 so a person should expect to study 5.5 hours to get a quiz score of 96%
the pre image of a line has the equation y=-7x. this line is translated -5 units along the x-axis and the 8 units along the y-axis. which is the equation of the image of this line?
ill mark you brainliest if youre right
Answers
Answer:
(b) y = -7x -27
Step-by-step explanation:
When x and y in the equation y = f(x) are replaced by (x-h) and (y-k), the function graph is translated h units right and k units up. The translated function can be written as ...
y -k = f(x -h)
y = f(x -h) +k . . . . . . add k
__
Your function is ...
y = -7x
and you want to translate it by (h, k) = (-5, 8). That makes it ...
y' = -7(x -(-5)) +8 = -7x -35 +8
y' = -7x -27
Find the sum: xy+6xy
Answers
Answer:
7xy
Step-by-step explanation:
If your family goes for a bike ride each weekend, what are you likely to do when you are living on your own?
Answers
We will likely do exercise regularly as part of your weekly schedule.
What are exercises?Exercise is defined as any bodily activity that improves or maintains physical fitness as well as overall health and wellness.It is done for a variety of reasons, including aiding growth and improving strength, developing muscles and the cardiovascular system, honing athletic skills, weight loss or maintenance, improving health, or simply for fun. Many people prefer to exercise outside, where they can congregate in groups, socialize, and improve their physical and mental health.In terms of health benefits, the amount of exercise recommended depends on the goal, the type of exercise, and the person's age. Even a small amount of exercise is preferable to none.As there are so many benefits of exercise, so we will likely do exercise regularly as part of your weekly schedule.
Therefore, we will likely do exercise regularly as part of your weekly schedule.
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Identify the equations below that are true. The video Powers and Roots, Part 3, reviews the ideas you'll need for this part.
Select all that apply.
1. 3^4 X 3^5 = 3^4+5
2. 3^4 divided by sign 3^5 =3^4-5
3. 9^-3 X 9^-6 = 9^-3+(-6)
4. Square root 2 X square root 2 = 2 1/2+1/2
5. 12^2/12^3 = 12^2-3
6. (7^-2)^3 = 7^-2X3
Answers
The true equations are:
\(3^4 X 3^5 = 3^4+5\) and
\(9^-3 X 9^-6 = 9^-3+(-6).\)
To identify the true equations from the given options, let's evaluate each statement:
\(3^4 X 3^5 = 3^4+5\)
This equation is true because when multiplying two exponential expressions with the same base, the exponents are added:
\(3^4 X 3^5 = 3^(4+5)\)
\(= 3^9.\)
3⁴ divided by sign 3⁵ = 3⁴⁻⁵
This equation is false. When dividing two exponential expressions with the same base, the exponents are subtracted:
\(3^4 ÷ 3^5 = 3^(4-5)\)
= 3⁻¹
= 1/3.
\(9^-3 X 9^-6 = 9^-3+(-6)\)
This equation is true. When multiplying two exponential expressions with the same base, the exponents are added:
\(9^-3 X 9^-6 = 9^(-3+(-6))\)
\(= 9^(-9).\)
Square root 2 X square root
2 = 2 1/2+1/2
This equation is false. The square root of 2 multiplied by the square root of 2 is equal to 2, not 2 1/2+1/2.
\(12^2/12^3 = 12^2-3\)
This equation is false. When dividing two exponential expressions with the same base, the exponents are subtracted:
\(12^2 ÷ 12^3 = 12^(2-\)3)
= 1/12.
\((7^-2)^3 = 7^-2 X 3\)
This equation is false. When raising an exponential expression to a power, the exponent is multiplied by the power:
\((7^-2)^3 = 7^(-2 X 3)\)
\(= 7^(-6).\)
Therefore, the true equations are:
\(3^4 X 3^5 = 3^4+5\)
\(9^-3 X 9^-6 = 9^-3+(-6)\)
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Say, for example, the correlation is 0.75 between fat content (measured in grams) and cholesterol level (measured in milligrams) for 20 different brands of American cheese slices. If cholesterol level were changed to being measured in grams (where 1 gram = 1000 milligrams), what effect would this have on the correlation?
Answers
If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.
This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.
The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.
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a multple choice question has 5 answer options of which two are correct what is thw probablliry of randomly choosng the correcty pair
Answers
The probability of randomly choosing the correct pair from a multiple-choice question with 5 options, where 2 options are correct, is 0.1 or 10%.
How to calculate probability of choosing correct pair?In a multiple-choice question with 5 answer options, where two options are correct, we need to determine the probability of randomly selecting the correct pair.
To calculate this probability, we first consider the number of correct pairs. Since there are two correct options, there is only one possible correct pair (selecting both correct options together).
Next, we need to find the total number of possible pairs. Using the combination formula (nCr), we calculate the number of ways to select 2 options out of the 5 available. In this case, C(5,2) = 10, meaning there are 10 possible pairs.
Therefore, the probability of randomly choosing the correct pair is given by 1 (the number of correct pairs) divided by 10 (the total number of possible pairs). This simplifies to 1/10 or 0.1, which represents a probability of 10%.
In summary, when randomly choosing a pair of options in this multiple-choice question, there is a 10% chance of selecting the correct pair.
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. a construction zone on a highway has a posted speed limit of 40 miles per hour. the speeds of vehicles passing through this construction zone are normally distributed with a mean of 46 mph and a standard deviation of 4 mph. (around your answer to 2 decimal places) b) if the police wish to ticket only those drivers whose speed falls in the upper 20th percent, what is the minimum speed of a driver that will be ticketed?
Answers
a. A speed of 40 mph is 1.5 standard deviations below the mean.
b. The minimum speed of a driver that will be ticketed is approximately 49.36 mph.
What is standard deviation?The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.
a) We can use the z-score formula to find out how many standard deviations away from the mean a speed of 40 mph is:
z = (40 - 46) / 4 = -1.5
This means that a speed of 40 mph is 1.5 standard deviations below the mean.
b) To find the minimum speed of a driver that will be ticketed, we need to find the z-score that corresponds to the 80th percentile (since we want to find the speed for the upper 20th percentile):
z = invNorm(0.8) ≈ 0.84
Using the z-score formula again, we can solve for the speed:
z = (x - 46) / 4
0.84 = (x - 46) / 4
x - 46 = 3.36
x ≈ 49.36 mph
Therefore, the minimum speed of a driver that will be ticketed is approximately 49.36 mph.
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Milo's Ice Cream Factory sold more than 45 waffle cones yesterday. Which of the following inequalities represents the number of waffle cones Milo's Ice Cream Factory sold yesterday?
A.
x 45
D.
x < 46
Answers
Answer:
I believe the answer would be x<46
Answer:
I'm fairly sure that it would be D, or the final answer.
Step-by-step explanation:
Since he sold more than 45 waffle cones, x would not equal 45. This is why D is correct. Hope it helps!
Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 and deposits $66 per month into his account. Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 and deposits $66 per month into his account
Answers
it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit amount at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).
To solve this problem, we can start by finding the monthly difference in their deposits:
Muhammad: $59/month
Connor: $66/month
Since Muhammad's monthly deposit is lower than Connor's, we need to find out how many months it will take for Muhammad's balance to catch up to and surpass Connor's. We can set up an equation to represent this situation:
$158 + $59x = $74 + $66x
where x is the number of months elapsed.
We can simplify and solve for x:
$158 + $59x - $74 - $66x = 0
$84 - $7x = 0
$7x = $84
x = 12
Therefore, it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit money at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).
the complete question is :
Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 in his bank account and deposits $66 per month into his account. If Muhammad and Connor continue to deposit money into their accounts at the same rate, how long will it take for Muhammad's account balance to surpass Connor's?
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Please help !!!
x 0,5,10
g(x) 325,400,475
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 12 days? (2 points)
Answers
By applying the linear equation concept, it can be concluded that:
A. The slope of the line is 15
B. The standard form of the equation is 15x - y + 325 = 0
C. The function notation of the equation is g(x) = 15x + 325
D. The balance in the bank account after 12 days is $505
Linear equation is an equation that contains one or more variables, where each variable has the power of one.
The standard form of a linear equation is y - y₁ = m(x - x₁) or ax + by + c = 0, where m is the slope of the function.
Slope of the function represents the change in y (Δy) over the change in x (Δx). m = Δy / Δx
We have the following table:
x 0 5 10
g(x) 325 400 475
A. To find the slope of the line, we calculate the value of Δy dan Δx:
Δy = y₂ - y₁
= 400 - 325
= 75
Δx = x₂ - x₁
= 5 - 0
= 5
m = Δy / Δx
= 75 / 5
= 15
B. To find its standard form, we can input the value of one point into y - y₁ = m(x - x₁):
y - y₁ = m(x - x₁)
y - 325 = 15 (x - 0)
y - 325 = 15x - 0
15x - y + 325 = 0
C. function notation changes the y to g(x), so we get:
15x - y + 325 = 0
15x - g(x) + 325 = 0
g(x) = 15x + 325
D. The balance in the bank account after 12 days can be calculated by substituting the value of x = 12 into the function:
g(x) = 15x + 325
= 15 · 12 + 325
= 180 + 325
= $505
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Write the equation of the ellipse using the given information. The ellipse has foci (4, 1) and (8, 1) and major vertices (1, 1) and (11, 1).
Answers
from the foci, it is clear that the center is at (6,1) and
c = 2
Since the major axis has length 10, a=5
b^2 = 25-4 = 21
so, the equation is
(x-6)^2/25 + (y-1)^2/21 = 1
Can you help me solve this!
Answers
Hello!
surface area
= 2(6*2) + 2(4*2) + 4*6
= 2*12 + 2*8 + 24
= 24 + 16 + 24
= 64 square inches
Add
2x+1/x + -3/x^2+3x
Answers
Answer:
it hi
Step-by-step explanation:
I need some help please
Answers
Answer:
Step-by-step explanation:
I think is x-1
It is because you need to find f(1) and the formula of x-1 when x is greater and equal to 1.
If in a population the rate of mutation that converts the A allele to the a allele is 10^-6 and the current frequency of the A allele is 0.75 and the a allele is 0.25, then the frequency of the A and a alleles in the next generation will be
Multiple Choice
O A: 0.74 a: 0.26
O A: 0.75000075 a: 0.24999925
O A: 0.75 a: 0.25
O A: 0.74999925 a: 0.25000075
Answers
The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m
where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925
And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075
Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.
This is option D.
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The time of a pendulum varies as the square root of its length. If the length of a pendulum which beats 15 seconds is 9 cm. Find
(A) the length that beats 80 seconds
(B)the time of a pendulum with length 36 cm
Answers
(A) The length that beats 80 seconds is 256 cm.
(B) The time of a pendulum with length 36 cm is 30 seconds.
(A) According to the given information, the time of a pendulum varies as the square root of its length. Let's denote time as T and length as L. Therefore, T ∝ √L. To find the constant of proportionality, we can use the provided data: T1 = 15 seconds and L1 = 9 cm. So, we have T1 / √L1 = k, where k is the constant. Now, let's find k: k = 15 / √9 = 15 / 3 = 5.
Now, we want to find the length (L2) of a pendulum that beats 80 seconds (T2). We can use the formula T2 = k * √L2. Substituting the values, we get 80 = 5 * √L2. To find L2, we can rearrange and solve for it: L2 = (80 / 5)² = 16² = 256 cm.
(B) To find the time (T3) of a pendulum with a length of 36 cm (L3), we can use the same formula with the known constant k: T3 = k * √L3. Substituting the values, we get T3 = 5 * √36 = 5 * 6 = 30 seconds.
In conclusion, the length of a pendulum that beats 80 seconds is 256 cm, and the time of a pendulum with a length of 36 cm is 30 seconds.
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