The domain exists on all real numbers i.e {x∈R}∈
The range exists all on real numbers except at y = 0
Domains are all input values of a function for which the function exists while ranges are all the output values for which the function exists.
Since the x-intercept of a function exists at where y = 0, this means that the point where a function does not have any x-intercepts are all other points on the graph except at y = 0.
The following statements are therefore true;
The domain exists on all real numbers i.e {x∈R}The range exists all on real numbers except at y = 0Learn more here: https://brainly.com/question/12648810
For f(x) = 4x2 + 13x + 10, find all values of a for which f(a) = 7.
The solution set is ???
i keep getting -2, -1/5 ... but it’s telling me it’s wrong. help!.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Answer:
0.84
Step-by-step explanation:
4x2+13a+10=7
13a=7-10-8
13a=-11
a=-11:13
a=0.84
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
Suppose 180 randomly selected people are surveyed to determine whether or not they plan on voting to reelect the current president. Of the 180 surveyed, 36 reported they will not vote to reelect the current president. Identify the values needed to calculate a confidence interval for the proportion that will not vote to reelect the current president at the 99% confidence level. Then find the confidence interval.
Answer:
(0.123 ; 0.277)
Step-by-step explanation:
Given :
Sample size, n = 180
x = 36
Proportion, p = x / n = 36/180 = 0.2
Confidence interval for sample proportion :
Confidence interval :
p ± Zcritical * √p(1 - p) / n
Zcritical at 99% = 2.576
0.2 ± 2.576 * √0.2(1 - 0.2) / 180
0.2 ± 2.576 * 0.0298142
0.2 ± 0.0768013792
(0.123 ; 0.277)
Which system of linear inequalities has the point (3, -2) in its solution set?
Answer:
None of the given system of linear inequalities
Step-by-step explanation:
Given
[tex](x,y) =(3,-2)[/tex]
Required
The line inequalities with the above solution
The first set of linear inequalities, we have:
[tex]y < -3[/tex]
[tex]y \ge \frac{2}{3}x - 4[/tex]
[tex]y < -3[/tex] implies that the values of y is -4,-5.....
While [tex](x,y) =(3,-2)[/tex] implies that y = -2
Hence, the first set is wrong
The second set of linear inequalities, we have:
[tex]y > - 2[/tex]
[tex]y \ge \frac{2}{3}x - 4[/tex]
[tex]y > - 2[/tex] implies that the values of y is -1,0.....
While [tex](x,y) =(3,-2)[/tex] implies that y = -2
Hence, the second set is wrong
The system of linear inequalities having the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.
What are systems of linear inequalities?A system of linear inequalities is known to be a composition of linear inequalities that can be found in the same variables.
The graph that is showing y > -3; y ≥ 2/3x - 4
-2 > -3 is true
y ≥ 2/3x - 4
-2 ≥ -2 is true
Therefore, y > -3; y ≥ 2/3x - 4 has the point (3, -2) in its solution set.
Learn more about linear inequalities from
https://brainly.com/question/12649320
A line has a slope of 9 and passes through the point (2, 8). What is its equation in slope-intercept form? Explain?
Answer:
y = 9x-10
Step-by-step explanation:
Slope-Intercept form is y = mx + b where m is the slope and b is the y intercept.
plug in what we are given
8 = 9(2) + b
solve for the y intercept (b)
8=18+b
8-18 = b
-10 = b
plug the slope (m) and y intercept (b) into our formula
y = 9x - 10
Find the slope of any line perpendicular to
the line through M(-1,5) and N(0.-3).
Answer:
1/8
Step-by-step explanation:
We want to find the slope of any line that is perpendicular to the line passing through the points M(-1, 5) and N(0, -3).
Recall that the slopes of perpendicular lines are negative reciprocals of each other. In other words, the slope of any line perpendicular to line MN must be the negative reciprocal of the slope of line MN.
Find the slope of MN using the slope formula:
[tex]\displaystyle m_{MN} = \frac{\Delta y}{\Delta x} = \frac{(-3)-(5)}{(0)-(-1)} = \frac{-8}{1}=-8[/tex]
So, the slope of line MN is -8.
The slope of any line perpendicular to MN must be its negative reciprocal. The negative reciprocal of -8 is 1/8.
Therefore, the slope of any line perpendicular to the line passing through the points M(-1, 5) and N(0, -3) is 1/8.
Jack is a discus thrower and hopes to make it to the Olympics some day. He has researched the distance (in meters) of each men's gold medal discus throw from the Olympics from 1920 to 1964. Below is the equation of the line of best fit Jack found.
y = 0.34x + 44.63
When calculating his line of best fit, Jack let x represent the number of years since 1920 (so x=0 represents 1920 and x=4 represents 1924).
Using the line of best fit, estimate what the distance of the gold medal winning discus throw was in 1980.
71.83 meters
65.03 meters
717.83 meters
44.63 meters
Answer:
65.03 meters
Step-by-step explanation:
The line of best fit, for the distance of the winning throw, in x years after 1980 is:
[tex]y = 0.34x + 44.63[/tex]
Using the line of best fit, estimate what the distance of the gold medal winning discus throw was in 1980.
1980 - 1920 = 60, so this is y(60).
[tex]y(60) = 0.34(60) + 44.63 = 65.03[/tex]
So the answer is 65.03 meters.
Of 240 stamps that Harry and his sister collected, Harry collected 3 times as many as his sister. How many did each collected.
Answer:
Harry collected 180 stamps
Harry's sister collected 60 stamps
Step-by-step explanation:
Let X be the number of stamps that Harry's sister colleted.
The number of stamps Harry colleted is 3 time as many as his sister's
⇒ 3*X + X = 240
⇒ X = 60
⇒ 240 - 60= 180
Answer:
180 for harry and 60 for his sister
Step-by-step explanation:
Find the value of a for which there is no term independent of x in the ezlxpansion of
[tex](1 + ax {}^{2} )( \frac{2}{x} - 3x) {}^{6} [/tex]
"no terms independent of x" basically means there is no constant term, or the coefficient of x ⁰ is zero.
Recall the binomial theorem:
[tex]\displaystyle (a+b)^n=\sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]
So we have
[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 \binom 6k \left(\frac2x\right)^{6-k}(-3x)^k[/tex]
[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \left(1+ax^2\right) \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}[/tex]
[tex]\displaystyle \left(1+ax^2\right)\left(\frac2x-3x\right)^6 = \sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-6}+a\sum_{k=0}^6 2^{6-k}(-3)^k\binom 6k x^{2k-4}[/tex]
The first sum contributes a x ⁰ term for 2k - 6 = 0, or k = 3, while the second sum contributes a x ⁰ term for 2k - 4 = 0, or k = 2. The coefficient of the sum of these terms must be zero:
[tex]2^{6-3}(-3)^3\dbinom 63 + a\times2^{6-2}(-3)^2\dbinom 62 = 0[/tex]
which reduces to
2160a - 4320 = 0
2160a = 4320
a = 2
The function f(x) is shown on the provided graph. Graph the result of the following transformation on f(x). f(x) +6
Answer:
Graph the same exact curve, but move every y value up 6.
Step-by-step explanation:
A transformation to the y-values is outside of the argument of the function. i.e., outside of the parentheses.
Need answers please offering 30 points
Answer:
yefeihuerijohiftv3ugrhoerfujfy
Step-by-step explanation:
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.Number of days Absent | Probability 0 0.60 1 0.20 2 0.12 3 0.04 4 0.04 5 0.001. What is the mean number of days absent? What are the variance and standard deviation?2. For the following probability distribution: a) x|10|11|12|13|14b) P(x)|.1|.25|.3|.25|.13. Find the mean, variance and standard deviation for the following probability distribution.
Answer:
(1)
[tex]E(x) = 0.72[/tex]
[tex]Var(x) = 1.1616[/tex]
[tex]\sigma = 1.078[/tex]
(2)
[tex]E(x) = 12[/tex]
[tex]Var(x) = 1.3[/tex]
[tex]\sigma = 1.14[/tex]
Step-by-step explanation:
Solving (1):
[tex]\begin{array}{ccccccc}{Days} & {0} & {1} & {2} & {3} & {4}& {5} \ \\ {Probability} & {0.60} & {0.20} & {0.12} & {0.04} & {0.04} & {0.00} \ \end{array}[/tex]
(a): Mean
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 0 * 0.60 + 1 * 0.20 + 2 * 0.12 + 3 * 0.04 + 4 * 0.04 + 5 * 0.00[/tex]
[tex]E(x) = 0.72[/tex]
Solving (b): The variance
This is calculated as:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Where:
[tex]E(x) = 0.72[/tex]
and [tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 0^2 * 0.60 + 1^2 * 0.20 + 2^2 * 0.12 + 3^2 * 0.04 + 4^2 * 0.04 + 5^2 * 0.00[/tex]
[tex]E(x^2) = 1.68[/tex]
So, we have:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = 1.68 - 0.72^2[/tex]
[tex]Var(x) = 1.1616[/tex]
Solving (c): The standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{Var(x)}[/tex]
[tex]\sigma = \sqrt{1.1616}[/tex]
[tex]\sigma = 1.078[/tex]
Solving (2):
[tex]\begin{array}{ccccccc}{x} & {10} & {11} & {12} & {13} & {14}& { } \ \\ {P(x)} & {0.1} & {0.25} & {0.3} & {0.25} & {0.1} & { } \ \end{array}[/tex]
(a): Mean
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 10 * 0.10 + 11 * 0.25 + 12 * 0.3 + 13 * 0.25 + 14 * 0.1[/tex]
[tex]E(x) = 12[/tex]
Solving (b): The variance
This is calculated as:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Where:
[tex]E(x) = 12[/tex]
and [tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 10^2 * 0.10 + 11^2 * 0.25 + 12^2 * 0.3 + 13^2 * 0.25 + 14^2 * 0.1[/tex]
[tex]E(x^2) = 145.3[/tex]
So, we have:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = 145.3 - 12^2[/tex]
[tex]Var(x) = 1.3[/tex]
Solving (c): The standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{Var(x)}[/tex]
[tex]\sigma = \sqrt{1.3}[/tex]
[tex]\sigma = 1.14[/tex]
A rectangular room is 6 meters longer than it is wide, and its perimeter is 28
meters. Find the dimension of the room.
Answer: width = 4 and length = 10
Step-by-step explanation:
Width = w and length = w + 6
2(w) + 2 (w + 6) = 28
2w + 2w + 12 = 28
4w = 28 - 12
W = 16/4
W = 4 (width)
Length = w + 6
4 + 6 = 10
If mZACB = 180°, and m2DCB = 1350,
then mZDCA = [? ]°
Answer:
m<DCA=45°
Step-by-step explanation:
m<DCA=m<ACB-m<DCB
m<DCA=180°-135°
m<DCA=45°
Help on this question Please
Answer:
After 7 years, the value would be $9,046.
After 13 years, the value would be $3,660
Step-by-step explanation:
Find the time required for an investment to double in value if invested in an account paying 3% compounded quarterly.
Answer: [tex]6.12\ \text{years}[/tex]
Step-by-step explanation:
Given
Rate of interest is [tex]r=3\%[/tex] compounded quarterly
So, annually it is [tex]r=12\%[/tex]
Suppose [tex]P[/tex] is the Principal and A is the amount after certain time period.
Amount in Compound interest is given by
[tex]\Rightarrow A=P[1+r\%]^t[/tex]
for given conditions
[tex]\Rightarrow 2P=P[1+0.12]^t\\\Rightarrow 2=(1.12)^t\\\\\Rightarrow t=\dfrac{\ln (2)}{\ln (1.12)}\\\\\Rightarrow t=6.116\approx 6.12\ \text{years}[/tex]
It take [tex]6.12\ \text{years}[/tex] to double the invested amount.
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker plz simple for class 5 pleeease
Answer:
$150
Step-by-step explanation:
discount=60%
let the price=x
(100-60)% of x=$60
40% of x=60
x=60×(100/40)=150
oliver walks 5/8 of a mile in 1/6 of an hour. What is his unit rate in miles per hour?
Answer:
3.75 miles per hour
Step-by-step explanation:
(5/8)/(1/6)=3.75 mph, or you could do 5/8 x 6, since 1/6 x 6 equals one hour
Answer:
3 3/4 miles per hour
Step-by-step explanation:
Take the miles and divide by the hours
5/8 ÷ 1/6
Copy dot flip
5/8 * 6/1
Rewriting
5/1 * 6/8
5/1 * 3/4
15/4
3 3/4
Sadie plans to install new bookcases along a wall in her room her wall measures 12 2/5 feet long and each bookcase measures 3 3/4 feet in length how many bookcases can Sadie fit along her wall. Asap!!!!!Before 8:00pm.
Answer:
3 bookcases
Step-by-step explanation:
The perimeter of a collage basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions? HELP MEEEEE
Answer:
width = 17 m ; length = 31 m
Step-by-step explanation:
w = width
l = length
perimeter of a rectangle = (length + width) * 2
l = 14 + w
(14 + w + w) * 2 = 96
(14 + 2w) * 2 = 96
28 + 4w = 96
4w = 68
w = 17 m
l = 14 + 17 = 31 m
Calculate the exact slope m (rather than a decimal approximation) of the straight line through the given pair of points, if defined. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.)
(6, 7) and (7, 1)
Answer:
m = -6
Step-by-step explanation:
The slope of a line is calculated as the change in y divided by the change in x.
Teachers use the phrase "rise over run". In this case the rise is negative as the line moves from a higher y value to a lower y value as x increases.
(y-final - y-initial)/(x-final - x-initial)
You are given two points on the line and just plug them in.
(1-7)/(7-6) = -6/1 = -6
can somone help me with this please
Answer:
undefined
0
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
m = (-7 -5)/(-6 - -6)
= (-7-5)/(-6+6)
-12 /0
undefined
m = (y2-y1)/(x2-x1)
m = (-3 - -3)/(7 - -8)
= (-3+3)/(7+8)
= 0/15
= 0
Slope Formula: (y2 - y1) / (x2 - x1)
#1.
Point 1 = (-6,5)
Point 2 = (-6,-7)
Slope = (-7 - 5) / (-6 - -6) = -12 / 0 = undefined
#2.
Point 1 = (-8,-3)
Point 2 = (7,-3)
Slope = (-3 - - 3) / (7 - - 8) = 0 / 15 = 0 slope
Hope this helps!
Sketch a graph of f (x) = −1
Answer:
Step-by-step explanation:
f(x) = -1 is actually the same as y = -1. Find y = -1 on the y axis and then draw a horizontal line through this point. The resulting graph is that called for here.
1,547,489 which digit is in the thousandsths place
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Starting from right to left...
9 is in the ones place
8 is in the tenths place
4 is in the hundreds place
7 is in the thousands place.
I hope this helps!
If g(x) = x2 – 4, find g(5).
6
О
14
21
O
29
[tex]\boxed{ \sf{Answer}} [/tex]
[tex]\sf \: g(x) = {x}^{2} - 4 \\ \\ \sf \: x = 5 \\ \\ \sf \: g(5) = {5}^{2} - 4 \\ \sf \: g(5) = 25 - 4 \\ \sf \: g(5) =\underline 2\underline1[/tex]
Answer ↦21 [Option C]
[tex]\tt \: g(x) = {x}^{2} - 4[/tex]
Substitute the value of x as 5 (given) in the above equation. The equation changes too..
[tex]\tt \: g(5) = {5}^{2} - 4[/tex]
Now you can easily solve the equation.
[tex]\tt \: g(5) = {5}^{2} - 4 \\\tt g(5) =( 5 \times 5) - 4 \\ \tt \: g(5) = 25 - 4 \\ \tt \: g(5) = 21[/tex]
Answer - [tex]\boxed{\sf{21}}[/tex]
One 8.3 ounce can of Red Bull contains energy in two forms: 27 grams of sugar and 80 milligrams of caffeine. One 23.5 ounce can of Jolt Cola contains 94 grams of sugar and 280 milligrams of caffeine. Determine the number of cans of each drink that when combined will contain 457 grams sugar and 1360 milligrams caffeine. We need cans of Red Bull, and cans of Jolt.
on monday, sammy the storekeeper decided the increase the price of avocados by 20%. on tuesday he increases this price by another 25%. what percent of the original avocados after both increases? on Wednesday, sammy decides to return the avocados to their original price. by what percent must he decrease the tuesday price?
Answer:
I think 55%
Step-by-step explanation:
Answer:
Increases = 50%On Wednesday, sammy must decrease 50% to return to original priceStep-by-step explanation:
price on monday go to: 100% + 20% = 120% = 1,2 x first price
price on tuesday go to: 125% of 120% = 1,25 x 1,2 = 1,5 x first price
Increases = 50%
on Wednesday, sammy must decrease 50% (of price after second increases) to return to original price
For example for understanding:
If original price is $100
firs increase: new price: $100 + $20 = $120
second increase: new new price: $120 + $30 = $150
final price - original price = $150 - $100 = $50
And icreases/original = $50/$100 =0,5 = 50%
For return to orignial price, sammy must have to reduce 50% the price of avocados in wednesday
Mr. Mason’s class is going on a field trip. There are 27 students. There will be 1 adult for every 9 students. Mr. Mason wants to know how many adults (n) are needed for the field trip. Which of the following equations should he use?
A. 9n + 27
B. 27 – 9n
C. 9n = 27 - 1
D. 9n = 27
Answer:
D. 9n = 27
Step-by-step explanation:
If we need one adult for every 9 students, we can represent that as 9n:
if n is the number of adults.
Because we have 27 students, the equation 9n = 27 works.
A better way of formatting the equation is:
n = 27/9
Because it directly shows what the number of adults is, but with some reformatting, it is clearly the same equation.
A girl has 9 skirts, 8 blouses, and 7 pairs of shoes. How many different skirt-blouse-shoe outfits can
she wear? (Assume that each item matches all the others, so she is willing to wear any combination.)
Answer:
She could wear 7 different outfits
Need the answer plz.
