The table shows values for f and g. What is [tex]lim_{x-2} (2f(x)-3g(x))[/tex]?
[tex]\left[\begin{array}{ccc}f(2)=4&g(2)=4&\\lim_{x-2}f(x)=1 &lim_{x-2}g(x)=3 &\\\end{array}\right][/tex]
Write an equation of the line through the points (2,1) and (1,4). Write the equation in slope-intercept form.
The equation of the line through the points (2,1) and (1.4) is
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
The equation of line in slope-intercept form is found as y = -3x + 7.
What is meant by slope-intercept form?The slope-intercept part of a line is a method for writing a line's equation so that the slope and y-intercept are easily recognizable. The slope of the line is its steepness, as well as the y-intercept is where the line intersects the y-axis.For the given question;
The two passing point of the line are;
(x1, y1) = (2,1)
(x2, y2) = (1,4)
Slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (4 - 1)/(1 - 2)
m = -3
Then, the equation of the line in slope intercept form is found using two point equation.
y - y1 = m(x - x1)
y - 1 = -3(x - 2)
Simplifying,
y = -3x + 7
-3 is the slope and 7 is the y intercept.
Thus, the equation of line in slope-intercept form is found as y = -3x + 7.
To know more about the slope-intercept form, here
https://brainly.com/question/28241183
#SPJ10
Is any real number exactly 2 more than its cube?
Answer: Yes
Step-by-step explanation: The real number, which most exceeds its cube, is A 21
Macy's offers a shirt at the price $300. Then one week later, they offer the shirt at 25% off. The shirt still doesn't sell, so after another week, Macy's reduces its new price by an additional 40% off. How much does the shirt cost now?
The new cost of the shirt is $135
The new cost of the shirt can be calculated as follows ?Macy's offer a shirt at the cost of $300
One week later, they offer 25% off
25/100 × 300
0.25 × 300
= 75
300-75
= 225
The next week it was reduced by an additional 40% off
40/100 × 225
= 0.4 × 225
= 90
225-90
= 135
Hence Macy's new shirt costs $135
Read more on cost here
https://brainly.com/question/1287021
#SPJ1
Please help I’ll mark you as brainliest if correct!!
Answer:
a = 22, b = 6, c = 14, d = 8
Step-by-step explanation:
sum the elements in the leading diagonal , that is
7 + 15 + 23 = 45
then all other rows and columns and the other diagonal total 45
top row
7 + a + 16 = 45
23 + a = 45 ( subtract 23 from both sides )
a = 22
middle row
24 + 15 + b = 45
39 + b = 45 ( subtract 39 from both sides )
b = 6
left column
7 + 24 + c = 45
31 + c = 45 ( subtract 31 from both sides )
c = 14
bottom row
c + d + 23 = 45 , that is
14 + d + 23 = 45
37 + d = 45 ( subtract 37 from both sides )
d = 8
A z-score less than -2 or greater than 2 is considered unusual in a normal curve. Assuming that the data collected form normal distributions, what would data that is outside the [-2,2] range mean?
The data points from the set of collected that are outside the [-2, 2] range means that the data is an outlier or unusual data
What is a z–score?The z–score also known as standard score is the number of standard deviation a score is differs from the mean or average score
The z–score is given by the formula;
[tex]Z = \frac{x - \mu}{ \sigma} [/tex]
The Z–Score is therefore, the number of standard deviations, a data point, x is far from the mean, [tex] \mu [/tex]
The standard deviation, [tex] \sigma [/tex], is given by the formula;
[tex] \sigma = \sqrt{ \frac{ \sum {( x_{i} - \mu)}^{2} }{N} } [/tex]
As the value of [tex] \sigma [/tex] increases, the variability increases, and the Z–Score decreases, such that a Z–Score of less than -2 or greater than 2 are unusual.
From the z–score calculator, the probability that a data point has a z–score of less than -2 or more than 2 is 0.02275
Such a data point can be taken as an outlier
Therefore, data that is outside the [-2, 2] range is an unusual (outlier) data
Learn more about z–score here:
https://brainly.com/question/19125280
#SPJ1
A student took SAT (mean = 500 and standard deviation = 100) and got a score of 550. ACT is known to have a mean of 20 and a standard deviation of 5. What would this student’s score be on the ACT metric?
106 would be student's score on ACT metric.
What is mean and standard deviation?The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range. It demonstrates how different things are from the standard.
Given Data
Mean = 500
Standard deviation = 100
ACT metric
Mean = 20
Standard deviation = 5
Score = [tex]\frac{550-20}{5}[/tex]
Score = [tex]\frac{530}{5}[/tex]
Score = 106
106 would be student's score on ACT metric.
To learn more about mean and standard deviation, visit:
https://brainly.com/question/10528201
#SPJ9
PLEASE HELP NEED ANSWER
DO NOT ANSWER IF YOU DONT KNOW
If l is paralell to m solve for x and y
The given parallel lines have a transversal which passes through them.
Hence from the property of parallel lines we found the values of x and y as 16 and 10 respectively.
Given that two parallel lines are intersected by a transversal, pair of angles are created, such as:
angles that are vertically opposing and equal.
the related angle pairs that are equivalent.
the equal pairs of opposite exterior angles.
the opposite interior angle pairs that are equal.
From the diagram we have the alternate exterior angles which are equal.
Therefore, alternate angle 1 = (8x-14)°
and alternate exterior angle 2 = (5x+34)°
now equate them,
(8x-14)° = (5x+34)°
8x-14=5x+34
8x-5x=34+14
3x=48
x=48/3
x=16
now substitute x value in angle 1:
8(16)-14
= 114°
therefore angle 1 = 180°-114°
= 66°
Hence (5y+16)° = 66
5y = 66-16
5y = 50
y = 50/5
y = 10
Therefore we get the values of x and y as 16 and 10 respectively.
Learn more about Parallel lines here:
brainly.com/question/24607467
#SPJ1
There sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three
times the age of the oldest is five less than five times the middle sister's age.
(a) If x represents the age of the youngest child, then write an equation that models this scenario.
(b) Determine the ages of the three sisters.
If x represents the age of the youngest child, then the equation that models this scenario is x+3(x+4) = 5(x+2)-5 and the ages of the three sisters are 7, 9 and 11 years respectively.
According to the question,
We have the following information:
There sisters have ages that are consecutive odd integers. The sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister's age.
Age of youngest sister = x years
Middle sister = (x+2) years
Oldest sister = (x+4) years
Now, the equation according to the given situation is:
(a) x+3(x+4) = 5(x+2)-5
(b) Now, we can solve this equation:
x+3x+12 = 5x+10-5
4x+12 = 5x+5
12-5 = 5x-4x
x = 7
Middle sister = 7+2 = 9 years
Oldest sister = 7+4 = 11 years
Hence, the equation is x+3(x+4) = 5(x+2)-5 and their ages from the youngest to the oldest are 7, 9 and 11 years respectively.
To know more about equation here
https://brainly.com/question/17736923
#SPJ1
=Initial Knowledge CheckEpitaxian is a cutting edge technology company based in Florida. The company has just finisheddeveloping a prototype of a product it is calling the X-13. According to the company'sdocumentation, the X-13 must be operated in a room that is kept at a temperature of -3.8 °F.What is this temperature in degrees Celsius (°C)?Use the given formulas as necessary, and round your answer to the nearest tenth of a degree.°CX3Question 7?Formulas:C = = (F-32)5995F== 30C+32
The given temperature in degrees Celcius is -19.89°.
What is temperature?Temperature is a numerical expression of how hot a substance or radiation is.There are three different types of temperature scales: those that are defined by the average translational kinetic energy per freely moving microscopic particle, like an atom, molecule, or electron, in a body, like the SI scale; those that rely only on macroscopic properties and thermodynamic principles, like Kelvin's original definition; and those that are not defined by theoretical principles but rather by useful empirical properties of particulate matter.So, the formula for conversion from Celsius to Fahrenheit:
C = 5/9(F-32)F given is -3.8°.
Now, insert the value in the formula to find the temperature in Celcius.
C = 5/9(F-32)C = 5/9(-3.8 -32)C = 5/9(-35.8)C = -179/9C = -19.88888After rounding off: 19.89Therefore, the given temperature in degrees Celcius is -19.89°.
Know more about temperature here:
https://brainly.com/question/25677592
#SPJ9
Find the measure of the angle indicated. Round to the nearest tenth. Make sure that your calculator mode is degrees
Answer:
The correct answer is c, 24.2°.
Step-by-step explanation:
[tex] { \tan}^{ - 1} ( \frac{7.2}{16}) = 24.2 [/tex]
2:5:4=n:8 so please do this for me
The mismatch in the number of variables in the ratio, implies that the ratio is undefined
How to evaluate the ratio?The ratio expression is given as:
2 : 5 : 4 = n : 8
In the above ratio expression, we have the following observations:
Right-hand side: Two variablesLeft-hand side: Three variablesIf the ratio expression is to represent an equivalent expression, then the number of variables on both sides of the expression must be the same
This in other words implies that
When the number of variables on either sides of the ratio expression, then the ratio is either incorrect or undefined
In this case, we can conclude that the ratio is undefined
Hence, the value of n in the ratio given as 2 : 5 : 4 = n : 8 is undefined
Read more about ratio at
https://brainly.com/question/2784798
#SPJ1
Please help I’ll mark you as brainliest if correct!!
Answer: The answer is 5
Step-by-step explanation:
There are 16 boys and 12 girls in the running club. What is the ratio of girls to boys?
3:4
16:12
4:3
12:16
Answer:
4:3
Step-by-step explanation:
it will be 16:12 and when you divide both by 3 it will be 4:3
Find the value of x.
Homework: 3.410 of 15 (10 complete)Score: 0 of 1 ptX 3.4.34A certain lottery has 27 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)There are different ways the numbers can be selected.(Simplify your answer.)Enter your answer in the answer box and then click Check AnswerClear Allshowing
equations help me please
Solve the equation and check
___________________
-89 = 11 - 4x
4x = 89 +11
x = 100/ 4
x= 25
________________
Can you see the updates?
___________________
Verifying
if x= 25
so then
-89 = 11- 4*(25)
-80
The formula that represents the image is:
ANSWER:
[tex]2p+5=21[/tex]STEP-BY-STEP EXPLANATION:
Let p be the figure of the pentagon.
We can establish the following equation:
[tex]\begin{gathered} 2p+5=10+10+1 \\ 2p+5=21 \end{gathered}[/tex]Therefore, the correct answer is the 4th option a) 2p + 5 = 21
If f(x)and f−1(x)
are inverse functions, which of the following must be true? Select all that apply.
Group of answer choices
The graphs are reflections of each other across the line y=x.
f(x)= f−1(x)
f−1(f(x))=x
f(f−1(x))= x
Both functions are base graphs.
The option (A) the graphs are reflections of each other across the line y=x, and option (D) f(f⁻¹(x)) = x are correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the b is related to exactly one value in the range.
The functions f(x) and f⁻¹(x) are inverses of each other.
As we know, the graph of the function and inverse function are reflections of each other about y = x.
From the property of the inverse of function:
f(f⁻¹(x)) = x
Thus, the option (A) the graphs are reflections of each other across the line y=x, and option (D) f(f⁻¹(x)) = x are correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
(c) If sand and cement are mixed in the ratio of 2:5,find the part of them in fraction
Answer:
The sand is 2/5 and the cement is 5/7
Step-by-step explanation:
You need to get the total parts of both by adding the numerator and the denominator, and then divide the amount of parts by the total amount of parts.
[tex] \rm \int_{0}^{1} \sqrt{ \frac{2 - {x}^{2} }{1 - {x}^{2} } } dx \\ [/tex]
Substitute [tex]x=\sin(t)[/tex] and [tex]dx=\cos(t)\,dt[/tex], and recall the definition of the elliptic integral of the second kind,
[tex]\displaystyle E(k) = \int_0^{\pi/2} \sqrt{1 - k^2 \sin^2(\theta)} \, d\theta[/tex]
Then the integral has a value of
[tex]\displaystyle \int_0^1 \sqrt{\frac{2-x^2}{1-x^2}} \, dx = \int_0^{\pi/2} \sqrt{2-\sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \sqrt2 \int_0^{\pi/2} \sqrt{1 - \frac12 \sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~= \boxed{\sqrt2 E\left(\frac1{\sqrt2}\right)}[/tex]
Write an augmented matrix for the following system of equations and give its size.- 8x + 3y = 1 4x - 7y = 4What is the augmented matrix?
SOLUTION:
The equation is;
[tex]\begin{gathered} -8x+3y=1 \\ \text{ }4x-7y=4 \end{gathered}[/tex]Writing in matrix form, we have;
[tex]\begin{bmatrix}{-8} & {3} \\ {4} & {-7}\end{bmatrix}\begin{bmatrix}{x} & {} \\ {y} & {}\end{bmatrix}=\begin{bmatrix}{1} & {} \\ {4} & {}\end{bmatrix}[/tex]The augmented matrix is thus;
[tex]\begin{bmatrix}{-8} & {3} & |{\text{ }1} \\ {4} & {-7} & |{\text{ }4} \\ {} & {} & \end{bmatrix}[/tex]What is the product of 83 and 4.5 \times 10^64.5×10
6
expressed in scientific notation?
The product of 83 and 4.5 \times 10^64.5×106 is expressed in scientific notation is 830*10^-12.
What is scientific notation?Scientific notation can be described as the representation of the large numbers or very small numbers in the standard form which can be seen in the final answer of this question , it do make the handling of numbers to be easier when making a calculation.
From the question, we are asked for the product of 83 and 4.5 \times 10^64.5×10^6,
Then we can multiply 10^6 * 4.5×10^6 which is (4.5*10^11)
Then 4.5/(4.5*10^11) = 10 *10^-12
Then we can found the product expression as (83* 10 *10^-12) = 830*10^-12.
Read more about scientific notation at:
https://brainly.com/question/5756316
#SPJ1
There are about 146 million sheep in China and 101 million sheep in Australia. The number of sheep in Australia is what percent less than the number of sheep in China?
Answer: 4500% i think
Step-by-step explanation: no explanations pls
If a person shoots a basketball overhand from a position 8 feet above the floor, then the path of the basketball 2 through the hoop can be modeled by the parabola y = +1.15x+8, where v is the initial velocity of the ball in 0.434v ft/sec, y is the height of the ball and x is the distance away from the person. (a) If the basketball hoop is 10 ft high and 11 ft away, what initial velocity v should the basketball have?
Basketball should have 20.64 ft/s initial velocity.
What is velocity?When an object is moving, its velocity is the direction at which it is moving as a measure of how quickly its location is changing as seen from a certain point of view and as measured by a specific unit of time. velocity. It is the quickness, swiftness, or speed of movement, action, or operation. A measurement of a body's rate of motion in physics is the rate at which its location changes over time in a certain direction.
Given Data
The parabola y=(-16x2/0.434v2)+1.15x+8 can be used to represent the ath of a basketball through a hoop, where v is the ball's speed in feet per second, y is the hoop's height, and x is the distance from the hoop. When the basketball hoop is 10 feet high and 17 feet away, the following is true:
y = (-16x⁰.434v²)+1.15x+8
10 = [-16(17)⁰.434v²] + 1.15(17) + 8
v = 24.64 ft/s
To learn more about velocity, visit:
https://brainly.com/question/2386084
#SPJ9
Kira and her mom want to make matching pairs of polka-dotted pajama pants. So, they go to the craft store to pick out fabric. Kira needs 4 feet of fabric for her pajamas, and her mom needs 6 feet of fabric. But, the store only sells fabric by the yard. If they buy 4 yards of fabric, how many feet will be left over?
Answer:
2
Step-by-step explanation:
One yard = 3 feet
4+6 =10
4 times 3 is 12
12 - 10 = 2
Imagine you were a dairy products processor planning for production in 2001. Describe how you would allocate the milk you buy, in terms of bottling whole milk and 0–1% fat milk.
With the full question now given (see attached image), I would allocate equal resources to Whole Milk and 0-1% fat milk. This exercise is about the Allocation of Resources in a free economy with the help of market trends. See further explanation below.
What is the Allocation of Resources?The allocation of available resources to diverse purposes is referred to as resource allocation in economics. In the framework of a whole economy, resources can be distributed through a variety of mechanisms, including markets and planning.
Note that in the attached graph, the demand for Whole Milk has been falling while the demand for 0-1% fat is dropping. While the reasons for this trend is beyond the scope of this exercise, suffice it to say that it is reasonably expected that the consumption data in 2001 will most likely be equal to each other.
1980 to 1985 the movement in 0-1% fat milk was negligible but it shot up the next 5 year period.
It is logical to expect that this pattern will reoccur since the demeand has been stable for the last 10 years (hence a reoccurring pattern).
On the other hand, every 5 years, the demand (consumption) for Whole Milk has consistently dropped. Hence the reason for the decision.
Learn more about Market Trends:
https://brainly.com/question/2926894
#SPJ1
Which of the following expressions illustrates how you can use the
associative property of addition to solve 13+6.2+5.8 more simply?
a. 13+5.8+6.2
b. (13+6.2)+5.8
c. 13+(6.2+5.8)
d. (13+6.2)+(13+5.8)
Answer:
c.
Step-by-step explanation:
13+6.2+5.8
= 13+(6.2+5.8)
- the sum in the parentheses is easy to calculate (it = 12).
Store A sold a total of 36 cups and plates. Store B sold twice as many cups and half as many plates for a total of 39 cups and plates. How many cups did store A sell?
By solving a system of equations we will see that 8 cups were sold on store A.
How many cups did store A sell?Let's define:
c= cups sold on store A.
p = plates sold on store A.
pᵇ = plates sold on store B
cᵇ = cups sold on store B.
For "Store B sold twice as many cups and half as many plates"
We can write:
pᵇ = 0.5*p
cᵇ = 2*c
We can write the system of equations:
c + p = 36
0.5*p + 2*c = 39
We want to solve this for c, so we isolate p on the first equation and replace that in the second one.
p = 36 - c
0.5*(36 - c) + 2c = 39
18 + 1.5*c = 30
1.5*c = 30 - 18
1.5*c = 12
c = 12/1.5 = 8
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
Im trying to finish this problem and couldn’t figure it out
Answer: Option A. 18.2
Explanation:
Step 1. The two polygons are similar. To find the length of BC, we will first identify the corresponding sides of the polygon, which are shown here in the same color:
Step 2. There must be a proportion between corresponding sides:
[tex]\frac{AB}{PQ}=\frac{BC}{RQ}=\frac{CD}{RS}[/tex]In this case, using only the first and second part of the proportion:
[tex]\begin{gathered} \begin{equation*} \frac{AB}{PQ}=\frac{BC}{RQ} \end{equation*} \\ \downarrow\downarrow \\ \frac{6.5}{10}=\frac{BC}{28} \end{gathered}[/tex]Step 3. From the last equation, we can solve to find BC. Move 28 to multiply on the left-hand side of the equation:
[tex]\frac{6.5}{10}\times28=BC[/tex]Solving the operations:
[tex]\begin{gathered} 0.65\times28=BC \\ 18.2=BC \end{gathered}[/tex]The length of BC is 18.2. This result is shown in option A.
Answer: Option A. 18.2