Answer: the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.
Step-by-step explanation:
since f(x) = x + 4 and g(x) = x - 1
then f/g = x + 4/x - 1
the denominator of a function cannot be zero since a fraction with a denominator of zero is undefined.
∴ x - 1 ≠ 0
the value of x when g(x) = 0 is
x - 1 = 0
x = 1
∴ x ≠ 1
Therefore the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.
A little kid running a lemonade stand sells small and large beverages. Each small beverage sells for $2 and each large beverage sells for $5. Small beverages require 4 lemons and 6 tablespoons of sugar each. Large beverages require 5 lemons and 10 tablespoons of sugar each. She has 100 lemons and 180 tablespoons of sugar. How many of each beverage should she sell to maximize her earnings?
Answer:
No. of Small Beverage = x = 10
No. of Large Beverage = y = 12
Step-by-step explanation:
Analyzing the given situation, we can form two algebraic equations.
Since, she has 100 lemons and 4 lemons are required for small beverage, while 5 lemons are required for large beverage. So, we can form the equation:
4x + 5y = 100 --------- eqn (1)
where,
x = No. of small beverages sold
y = No. of large beverages sold
Similarly, she has 180 table spoons of sugar and 6 table spoons are required for small beverage, while 10 table spoons are required for large beverage. So, we can form the equation:
6x + 10y = 180 -------- eqn (2)
From eqn (1):
x = (100 - 5y)/4 ------- eqn (3)
Substituting this value of x in eqn (2)
(6)(100 - 5y)/4 + 10y = 180
10 y - 7.5 y= 180 - 150
2.5 y = 30
y = 30/2.5
y = 12
Using this value of y in eqn (3)
x = [100 - (5)(12)]/4
x = 10
Therefore, in order to maximize the earnings the kid should sell following number of each beverage:
No. of Small Beverage = x = 10
No. of Large Beverage = y = 12
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
A) 26
E) 12
Step-by-step explanation:
11x ≥ 132
x ≥ 12
The solution set would include numbers greater than or equal to 12
Two figures are arranged as shown. Which of the following can be used to the area of the figure
shaded light gray?
9
9
Answer:
[tex]9^{2} -x^{2}[/tex]
Step-by-step explanation:
The figure is shown in the image attached.
Notice that the shaded light gray area can be calculated by the difference of the bigger square and the smaller square.
The area of the bigger square is: [tex]A_{big}=9^{2}[/tex]
The area of the smaller square is: [tex]A_{small}: x^{2}[/tex]
The difference between these areas is: [tex]A=9^{2} -x^{2}[/tex]
Therefore, the expression that can be used to find the light gray area is: [tex]9^{2} -x^{2}[/tex]
Additionally, the expression [tex]x(9-x)+9(9-x)[/tex] is also a right answer, because it's equivalent to the first answer.
[tex]x(9-x)+9(9-x)=9x-x^{2} +81-9x=81-x^{2} =9^{2} -x^{2}[/tex]
Is OCD and perfectionism the same thing. I need an explanation thanks
Answer: ocd can be characterized as an extreme form of perfectionism, where anything can lead to anxiety fear, and distress. perfectionism is a personality trait where one drives for flawless ness, it becomes ocd when those strives cause literal disorder in ones life
Step-by-step explanation:
A bakery sells cakes for $23 and a dozen cupcakes for
$18. In one day they sold 72 items and made a total of
$1446. Which system is an appropriate model of the
problem?
A.23x + y = 72
18x+ y = 1446
B.x+y=72
23x18y=4600
C.23x + 18y = 72
x + y = 1446
D. 23x + y = 1446
x + 18y = 72
Answer:
23x + 18y = 1446
x + y = 72
Step-by-step explanation:
The bakery made $1446 total. We represent this as the cost of each cake ($23) times the number of cakes sold (x) plus the cost of each dozen cupcakes ($18) times the number of cupcakes sold (y).
Thus, 23x +18y = $1446.
The bakery sold 72 items total. We represent this as the number of cakes sold (x) plus the number of each dozen cupcakes sold (y).
Thus, x + y = 72.
The Australian Open is the first of the four Grand Slam professional tennis events held each year. Victoria Azarenka beat Maria Sharapova to win the 2012 Australian Open women’s title. During the tournament Ms. Azarenka serve speed reached kilometers per hour. A list of the Women’s Singles serve speed for the 2012 Australian Open is provided below. Player Serve Speed (km/h) S. Williams 192 S. Lisicki 192 M. Keys 191 L. Hradecka 188 J. Gajdosova 187 J. Hampton 187 B. Mattek-Sands 185 F. Schiavone 185 P. Ormaechea 185 P. Parmentier 185 N. Petrova 183 G. Arn 183 V. Azarenka 182 A. Ivanovic 182 P. Kvitova 179 M. Krajicek 179 V. Dushevina 178 S. Stosur 176 S. Cirstea 176 M. Barthel 175
a. Compute the mean, variance, and standard deviation for the serve speeds.
b. A similar sample of the 20 Women’s Singles serve speed leaders for the 2011 Wimbledon tournament showed a sample mean serve speed of 182.5 kilometers per hour. The variance and standard deviation were 33.3 and 5.77, respectively. Discuss any difference between the serve speeds in the Australian Open and the Wimbledon women’s tournaments.
Answer:
asnwer is B
Step-by-step explanation:
mark BRAINLIEST
James rented a car for 4 days plus $0.25 per mile. He took the collision waiver for $19.95 per day. He drove the car 352 miles. Gasoline cost $41.38. What was the total cost of renting the car?
1 point
$61.58
$149.33
$413.33
$209.18
Answer:
$209.18
Step-by-step explanation:
352 miles*$0.25 per mile = $88 for mileage.
$19.95 per day * 4 days = $79.80
88+ 79.80 + 41.38 for gass = $209.18 Total Cost
Sebastian got estimates from 7 companies for his kitchen remodel: $ 27,500 ; $31,000 ; $36,000 ; $92, 000; $29,000 ; $30,500 ; $28,500. Which measure of center best describe the data, is it the mean or the median?
We have been given that Sebastian got estimates from 7 companies for his kitchen remodel: $ 27,500 ; $31,000 ; $36,000 ; $92,000; $29,000 ; $30,500 ; $28,500. We are asked to find the best measure of center for the given data.
We can see that our given data set has a large valued data point that is $92,000.
We know that mean is very much affected by large valued outliers. The data point $92,000 will increase the mean. Therefore, mean is not a best measure of center for given data.
We know that median is very less affected by outliers, therefore, median will be best measure of center for the given data.
A researcher planned a study in which a crucial step was offering participants a food reward. It was important that three food rewards were equal in appeal. Thus, a pilot study was designed in which participants were asked which of the rewards they preferred. The observed frequencies are as follows:
Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots.
1. The appropriate statistical test for this problem is (be specific): ________.
2. What are the expected frequencies for this question?
3. What is the cutoff on the comparison distribution (step 3)?
4. What is the correct calculation for chi-square (step 4)?
Answer:
Step-by-step explanation:
Hello!
A pilot study was conducted to test if three food rewards are equally appealing to the participants.
Of 60 participants surveyed:
16 preferred cupcakes (CC)
26 preferred candy bars (CB)
18 preferred dried apricots (DA)
If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3
1.
The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. [tex]X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex] Where k= number of categories of the variable.
For this example the statistical hypotheses are:
H₀: P(CC)=P(CB)=P(DA)= 1/3
H₁: At least one of the proportions isn't equal to the others.
2.
To calculate the expected frequencies for each category you have to use the formula: [tex]E_i= n* P_i[/tex] where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.
[tex]E_{CC}= n* P(CC)= 60*1/3= 20[/tex]
[tex]E_{CB}= n*P(CB)= 60*1/3= 20[/tex]
[tex]E_{DA}= n* P(DA)= 60* 1/3= 20[/tex]
3.
The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:
Assuming α: 0.05
[tex]X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378[/tex]
The rejection region is then X²₂ ≥ 7.378
4.
[tex]X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8[/tex]
I hope this helps!
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply.
Answer:
B
Step-by-step explanation: it is a quadratic equation it can only have two intercepts
what is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4
Answer:
2
Step-by-step explanation:
For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.
The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...
f'(1) = 2(1) = 2
The average rate of change of f(x) on [-2, 4] is 2.
__
Alternate solution
The average rate of change is the slope of the line between the end points of the interval:
m = (y2 -y1)/(x2 -x1)
m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2
The average rate of change on [-2, 4] is 2.
_____
The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.
Do you remember the difference between a row and a column
in Math?
Answer:
Rows are the steps - they go left to right and are numbered 1,2,3,... Columns are the columns - they go up and down and are lettered A,B,C,... Cells are defined by the row and column they are in.
Step-by-step explanation:
if a rectangular prism has a volume of 550 cm squared and its dimensions are all tripled, then what would be the new volume?
Answer:
The new volume would be 14,850cm³.
Step-by-step explanation:
The volume of a rectangular prism is:
[tex]V = l*w*h[/tex]
In which l is the length, w is the width and h is the height.
Dimensions tripled.
So [tex]l = 3l, w = 3w, h = 3h[/tex]
The modified volume will be:
[tex]V_{m} = 3l*3w*3h = 27*l*w*h = 27V[/tex]
Volume of 550 cm³ before the dimensions are tripled.
This means that [tex]V = 550[/tex]
New volume:
[tex]V_{m} = 27*550 = 14850[/tex]
The new volume would be 14,850cm³.
if a punnet of strawberrier weighs 100g
how many punnets would weigh 1 kg
Answer:
10
Step-by-step explanation:
1 kg = 1000 g
1000/100=10
Which is the same as moving the decimal point 3 places to the right in a decimal number
Answer:
Moving the decimal 3 places to the right in a decimal number is the same as multiplying the number by 1000.
HELPPP PLEASEEEEE!!!!!!!!!
Answer:20
Step-by-step explanation:
Since it is a right angled triangle we can use Pythagoras principle to get the missing length
Let the missing length be h
h=√(16^2+12^2)
h=√(16x16+12x12)
h=√(256+144)
h=√(400)
h=20
If you flip a coin ten times, how many different sequences of heads and tails are possible? a. 2 Superscript 9 Baseline = 512 b. 10 squared = 100 c. 10 squared = 1024 d. 2 Superscript 10 Baseline = 1024
Answer:
1024
Step-by-step explanation:
I don't know what this superscript is but the answer is above.
Answer:OPTION D: 2^10 = 1024
Step-by-step explanation: I just took the quiz on edge.hope this helps :)
What’s the volume of the solid ?
Answer:
I think its 70in hope it helps
Step-by-step explanation:
What is 256/6561 as a power
Answer:
(2/3)^8
Step-by-step explanation:
Note that 2^8 = 256, and that 3^8 = 6561.
Then 256/6561 = (2/3)^8
what is the area of the triangle shown below?
Answer: Please provide the triangle
Plz answer BRAINLIEST Choose the statement that is true of both triangles.
9514 1404 393
Answer:
A. Side lengths of 4 units and 2 units and a nonincluded angle of 30°
Step-by-step explanation:
Both triangles have sides marked 2 units and 4 units, but the angle is not between them. The angle is opposite the short side in one triangle (which will be a right triangle), and opposite the long side in the other triangle (which will be an obtuse triangle). The sides and angles of the two triangles will not have the same measures, and neither will have an angle of 100°.
The first description is appropriate:
Side lengths of 4 units and 2 units and a nonincluded angle of 30°
Difference between-9°C and -21°C
Answer:
12
Step-by-step explanation:
21-9=12 hope this helps :)
Do you remember the difference between a row and a column
in Math?
Answer:
Rows are the steps - they go left to right and are numbered 1,2,3,... Columns are the columns - they go up and down and are lettered A,B,C,... Cells are defined by the row and column they are in.
Step-by-step explanation:
Ramesh examined the pattern in the table. Powers of 7 Value 7 Superscript 4 2,401 7 Superscript 3 343 7 Superscript 2 49 7 Superscript 1 7 7 Superscript 0 1 7 Superscript negative 1 StartFraction 1 Over 7 EndFraction Ramesh says that based on the pattern 7 Superscript negative 5 = negative 16,807. Which statement explains whether Ramesh is correct? Ramesh is correct because 7 Superscript negative 5 is equivalent to Negative 7 times (negative 7) times (negative 7) times (negative 7) times (negative 7), which has the same value as Negative 16,807. Ramesh is correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = negative 16,807. Ramesh is not correct because 7 Superscript negative 5 is equivalent to StartFraction 1 Over 7 Superscript 5 EndFraction, which has the same value as StartFraction 1 Over 7 Superscript 4 EndFraction divided by 7 = StartFraction 1 Over 7 cubed EndFraction = StartFraction 1 Over 343 EndFraction. Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = StartFraction 1 Over 16,807 EndFraction. NEED HELP NOW PLEASE I HAVE ONLY SEEN WRONG ANSWERS
Answer:
D
Step-by-step explanation:
Answer:
D.- Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7^-5 = 1 ÷ 7 ÷ 7 ÷ 7 ÷ 7 ÷ 7 = 1/16,807.
6th grade math help me :))
Answer:
(30*20)+200
Step-by-step explanation:
27 to 30
18 to 20
172 to 200
Please help worth 20 points!!
Answer:I would think u would
Step-by-step explanation:42,500×26
Answer:
1634.62$
Step-by-step explanation:
P=S/n
P=42500/26=1634.62
On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).
What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
(40, 96)
(85, 105)
(80, 104)
(96, 72)
Answer:
the answer is (40,96)
Step-by-step explanation:
Point P on the directed line segment from K to J has x and y coordinates that are three-fifths of the length of the line segment from K to J
(85, 105).
What are coordinates?The coordinates point to any point can be found by using the following formula.
X = [m/(m + n)](x₂ - x₁) + x₁
Y = [m/(m + n)](y₂ - y₁) + y₁
Given, On a coordinate plane, a line is drawn from point K to point J. Point K is at (160, 120) and point J is at (negative 40, 80).
The x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J is;
X = [m/(m + n)](x₂ - x₁) + x₁
X = [3/(3 + 5)](- 40 - 160) + 160.
X = - 75 + 160.
X = 85.
Y = [m/(m + n)](y₂ - y₁) + y₁
Y = [3/(3 + 5)](80 - 120) + 120.
Y = - 15 + 120.
Y = 105
As a result, point P's x and y coordinates are such that P is three-fifths the length of the directed line segment from K to J (85, 105).
learn more about co-ordinates here :
brainly.com/question/13847533
#PJ6
Mr.Lipps flips a coin 20 times how many times can he expect heads
Answer:
Mr. Lipps would expect it to land on heads 10 times
Step-by-step explanation:
hope this helps :)
You have 9 pets:
4 fish,
1 cat,
2 dogs
and 2 birds. What is the probability a pet chosen at random is a dog or a four legged pet?
Answer:
1/3
Step-by-step explanation:
4 fish, 1 cat,2 dogs,and 2 birds = 9
dogs or 4 legged = cats and dogs = 1+2 = 3
P(dog or 4 legged) = number of dogs or 4 legged / total
=3/9
=1/3
Answer:
⅓
Step-by-step explanation:
Total pets:
4+1+2+2 = 9
Dog or four legged pets: 2 + 1 = 3
Probability: 3/9 = 1/3
How would you write "4/1000" In decimal form?
Answer:
0.004
Step-by-step explanation:
Since 4/10 is 0.4 and 4/100 is 0.04, 4/1000 must be 0.004
Answer:
0.004
Step-by-step explanation:
[tex]\frac{4}{1000}[/tex] is basically [tex]4 \cdot 10^{-4[/tex] (if you've learned scientific notation), so all you have to do is move the decimal to the left four times. That gives us
[tex]4.0\\0.4\\0.04\\\boxed{0.004}[/tex]
More depth:
[tex]10^{-4[/tex] also equals 0.001, so [tex]4 \cdot 0.001 = \boxed{0.004.}[/tex]
*You may do division and find the answer too. However, these ways are quicker.
