Set-builder notation: {x | x ∈ D} (where D is the domain) and {y | y ∈ R} (where R is the range), Interval notation: (a, b) (where a and b are the minimum and maximum of the domain) and [c, d] (where c and d are the minimum and maximum of the range) , Graphical notation: The domain and range are represented by a graph.
Set-builder notation is a way of representing the domain and range of a function. It uses curly brackets surrounding the domain and range variables, separated by a vertical bar. The form is {x | x ∈ D} (where D is the domain) and {y | y ∈ R} (where R is the range). This notation is useful when the domain and range are not easily written as a set of numbers.
Interval notation is another way of representing the domain and range of a function. It uses parentheses to represent the domain and square brackets to represent the range. The form is (a, b) (where a and b are the minimum and maximum of the domain) and [c, d] (where c and d are the minimum and maximum of the range). This notation is useful when the domain and range are quickly written as a set of numbers.
Graphical notation is a third way of representing the domain and range of a function. In this case, the domain and range are represented by a graph, with the x-axis representing the domain and the y-axis representing the range. This notation is useful when visualizing the relationship between the domain and range of a function.
Set-builder, interval, and graphical notations are all ways of representing the domain and range of a function. Set-builder notation is useful when the domain and range are not easily written as a set of numbers, while interval notation is useful when the domain and range are quickly written as a set of numbers. Graphical notation is useful when visualizing the relationship between the domain and range of a function.
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a jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off how many hours did the bomber take to reach the target of the fighter jet travel at 60 miles per hour
Since the jet bomber arrived over its Target at the same time as its fighter jet escorted, it took the jet bomber 0.34 h to reach the target.
To find the number of hours, we need to solve simultaneous equations.
What are simultaneous equations?Simultaneous equations are pair of equations which contain two unknowns.
How to calculate the number of hours the bomber jet took off?Let
D = distance travelled by both bomber jet and fighter jet.t = time bomber jet took off v = speed of bomber jet. T = time fighter jet took off and V = speed of fighter jet.So, D = vt
D = 500t (1)
Also, D = VT
D = 60T (2)
Since jet bomber traveling 500 mph arrived over its Target at the same time as its fighter jet escorted which left the same fate 2.5 hours after the bomb took off.
T = t + 2.5
So, D = 60(t + 2.5) (3)
The required simultaneous equationsD = 500t (1)
D = 60(t + 2.5) (3)
Equating equations (1) and (3), we have
500t = 60(t + 2.5)
500t = 60t + 150
500t - 60t = 150
440t = 150
t = 150/440
t = 15/44
t = 0.34 h
So, it took the jet bomber 0.34 hours to reach the target.
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PLEASE HELP IM STUCK
Answer:
y = 7.25 + 0.65x
Step-by-step explanation:
y = total cost
x = each mile
it starts at 7.25
any mile after that is an extra $0.65
y = 7.25 + 0.65x
The probability of winning on an arcade game is 0.568. If you play the arcade game 22 times, what is the probability of winning more than 15 times
The probability of winning 15 out of the 22 games is [tex]P = 0.099[/tex]
what is the probability of winning more than 15 times?We know that the probability of winning on the arcade game is 0.568.
Then the probability of losing is:
P = 1 - 0.568 = 0.432
The probability of winning 15 out of 22 games is given by the equation:
[tex]P = C(22, 15)*(0.568)^{15}*(0.432)^{7}[/tex]
Where C(22, 15) is the number of combinations of 15 elements that we can make with a set of 22 elements, given by:
[tex]C(22, 15) = \frac{22!}{(22 - 15)!*15!} = \frac{22!}{7!*15!} = \frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1} = 170,544[/tex]
Then the probability is:
[tex]P = 170,544*(0.568)^{15}*(0.432)^7 = 0.099[/tex]
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Using the formula: A=p(1+r)t
How much money will Mario have if he puts $1000 in a savings account earning 4% annually after 10 years?
Select one:
O a. $1004
O b. $1428.24
• c. $1000
© d. $2156.01
The amount of money Mario will have if he puts $1000 in a savings account earning 4% annually after 10 years is $1,480
Compound interestA = p(1 + r)^t
p = $1000r = 4% = 0.04t = 10 yearsA = p(1 + r)^t
= 1000(1 + 0.04)^10
= 1000(1.04)^10
= 1000(1.48)
A = $1,480
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Which of these statements is true for f(x)=(1/10)^x
A. the range of f(x) is y>1/10
B. it is always increasing
C. the graph contains (1, 1/10)
D. the domain of f(x) is x>0
Answer: C. the graph contains (1, 1/10)
Step-by-step explanation:
When x=1, [tex]y=(1/10)^1=1/10[/tex].
There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the first ticket, since 5 out of 26 letters are vogal, the probability is:
5/26.
For the second ticket, since there is no replacement, the probability is:
4/25.
The probability of both tickets is:
[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]
0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
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Work out the area of the triangle.
Answer:
555.75m²Step-by-step explanation:
Triangle Area = 1/2b*h
1/2 57 * 19.5 =
28.5 * 19.5 =
555.75m²
A scientist observes the bacteria’s growth. In the first observation, there were 12 bacteria, 24 in the second observation, 48 in the third and so on. How many bacteria will be there in the 8th observation? Use the explicit formula.
1,536
28
126
27
Answer:
Step-by-step explanation:96 in the fourth since they are adding the answer itself two times before you get the other like 12 bacteria and then 24 so that means 12 + 12 is 24 and the third one 48 so 24 +24 =48
fourth 48 + 48=96
fifth 96+96=192
sixth 192+192=384
seventh 384+384=768
last but not least 768+768 = 1536
so your answer is 1,536
If someone can help with this that would be great
Answer:
p ≈ 7.3 m
Step-by-step explanation:
using the Sine Rule in the triangle
[tex]\frac{p}{sinP}[/tex] = [tex]\frac{r}{sinR}[/tex] ( substitute values )
[tex]\frac{p}{sin40}[/tex] = [tex]\frac{10}{sin62}[/tex] ( cross- multiply )
p × sin62° = 10 × sin40° ( divide both sides by sin62° )
p = [tex]\frac{10sin40}{sin62}[/tex] ≈ 7.3 m ( to the nearest tenth )
Answer:
[tex]\fbox {p = 7.3 m}[/tex]
Step-by-step explanation:
Applying the Law of Sines :
[tex]\boxed {\frac{sin R}{PS} = \frac{sin P}{RS}}[/tex]
Substitute the values :
sin 62° / 10 = sin 40° / pp = sin 40° × 10 / sin 62°p = 0.64278761 × 10 / 0.882947593p = 7.3 m (nearest tenth)WILL MAKE BRAINLIEST!!
Complete the congruence statement for the figure below.
Determine the unknown length or angle measurement. Round each answer to the nearest whole number
(a) The value of the unknown length, a, is 18 cm
(b) The value of the unknown angle measurement, θ, is 39°
From the question, we are to determine the unknown length and angle measurement
(a)
A + B + C = 180° (Sum of angles in a triangle)
A = 180° - (B + C)
A = 180° -(68° + 59°)
A = 53°
Using the law of sines
[tex]\frac{a}{sin A}=\frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 53^\circ}=\frac{19.5}{sin 59^\circ}[/tex]
[tex]a=\frac{19.5 \times sin 53^\circ}{sin 59^\circ}[/tex]
[tex]a= 18.168[/tex]
[tex]a \approx 18 cm[/tex]
(b)
[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]
[tex]\frac{sin \theta}{15}=\frac{sin 57^\circ}{20}[/tex]
[tex]sin \theta=\frac{15 \times sin 57^\circ}{20}[/tex]
[tex]sin \theta=0.6290[/tex]
[tex]\theta=sin ^{-1} (0.6290)[/tex]
[tex]\theta=38.976 ^\circ[/tex]
[tex]\theta \approx 39^\circ[/tex]
Hence, the value of the unknown length, a, is 18 cm
The value of the unknown angle measurement, θ, is 39°
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please help with this.
Answer:
R = $2,120
Ticket price = $11
Step-by-step explanation:
Finding revenue when t = 10 :
R = -6(10)² + 132(10) + 1440R = 1400 + 1320 - 600R = 2720 - 600[tex]\fbox {Revenue = 2,120 dollars}[/tex]The vertex of the graph will have the maximum revenue.
Vertex = (h, k)h = -b/2ah = -132/2(-6)h = 132/12h = 11Hence, the revenue is maximum when the ticket price is $11.
The measure of one angle of an octagon is twice the measure of one of the other seven congruent angles. What is the measure of each angle?
Each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees
How to find the angle of octagon?The angle of an octagon can be found as follows;
An octagon is a polygon that has 8 sides.
The sum of angles in an octagon is 1080 degrees.
Therefore,
x + x + x + x + x + x + x + 2x = 1080
Hence,
9x = 1080
divide both sides by 9
x = 1080 / 9
x = 120
Therefore, each one of the smaller angles x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees
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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.15 gallons. A previous study found that for an average family the variance is 3.61 gallons and the mean is 19.4 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
The minimum sample size required to estimate the mean usage of water = 2225.07
What is Standard deviation?
In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
We can find the minimum sample size required to estimate the mean usage of water as shown below:
Standard deviation [tex]\sigma =3.61[/tex]
Margin of error E=0.15
Critical value for 95% confidence interval = 1.96
Required minimum sample size: [tex]n=(\frac{Z_{\frac{\alpha}{2}}.\sigma }{E} )^2[/tex]
[tex]=(\frac{1.96\times 3.61}{0.15} )^2[/tex]
=2225.07
Hence, the minimum sample size required to estimate the mean usage of water = 2225.07
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It took an hour to now a lawn using a mower with 14 inches blade. How long will it take using a mower with 12 inches wide
If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.
What is width?
The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.
How to calculate time?
We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:
It will be as 14/12* 1 hour
=14/12
=1.167
=1.17 hour
Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.
Answer:
70 mins
Step-by-step explanation:
This is called inverse proportion.
1hr : 14in
x hr : 12in
Ask yourself, what do you do to 14 to get 12? To find this out, we do:
14 / 12 = 1.16666667
Since the blade is smaller, it will take longer. So, we times 1hr by 1.16666667 to get
1.16666667 hrs =
1.17 hours (rounded)
This is 70.2 mins, or 1hr 10 mins
Hope this helps!
A procedure for using sample data to find the estimated regression equation is _____. Group of answer choices point estimation interval estimation the least squares method extrapolation
c. the least squares method.
Regression equation:
In simple linear regression, the predicted value of the dependent variable is given by the equation = b0 + b1x. The values of b0 and b1 are calculated from the data so that the line = b0 + b1X minimizes the total sum of squared errors (error is the difference between the predicted value and the actual value of y).
Least squares method:
The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.
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 What property is used to do…
-2y + 15 = -23
Answer:
-2y= -23-15
-2y=-38
-y= -38/2
-y=19 proved
Identify an equation in point slope form for the line parallel to y=-2/3×+8 that paases through (4,-5)
Answer:
y=-2/3x-7/3
Step-by-step explanation:
a parallel line has the same slope but different y intercept
so we need to solve for y=-2/3x+b
since it passes through 4,-5 we can plug it in for x and y
-5=-2/3(4)+b
-5=(-8/3)+b then add 8/3 to both sides
-5 is also -15/3
-7/3=b
so answer is y=-2/3x-7/3
1. what are the peaks of a periodic function?
a. the highest points of the graph
b. the lowest points of the graph
c. the extremes of the graph
d. the x-intercepts of the graph
Answer:
A. The Highest Points Of The Graph
Step-by-step explanation:
A nonperiodic function is one that generates a graph without a regular recurring pattern over a fixed time interval. A repeating section of a graph is called the period.
Three friends owe 18 dollars to another friend for gas if they plan to split the cost evenly which of the following expressions could they use to find how much they each owe
If they plan to split the cost evenly, the expression that could be used to find how much they each owe is 18/3
How to determine the amount paid by each?The given parameters are:
Total amount owed = 18 dollars
Number of friend = 3
If they plan to split the cost evenly, the expression that could be used to find how much they each owe is represented as:
Amount = Total/Friends
This gives
Amount = 18/3
Hence, the expression is 18/3
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x: -1/2
-6(x-2):
por favor necesito una respuesta
The value of the expression if x = -1/2 is 15
Function and valuesGiven the expression below shown;
f(x) = -6(x - 2)
If the value of x is -1/2, hence;
f(-1/2) = -6(-1/2 - 2)
Simplify
f(-1/2) = -6(-5/2)
f(-1/2) = 6 * 5/2
f(-1/2) = 3 * 5 = 15
Hence the value of the expression if x = -1/2 is 15
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Which of the following is equal to the expression below?
(4^-5)^3
A. -4^2
B. 1/4^15
C. -4^15
D. 1/4^2
Answer: B
Step-by-step explanation:
[tex](4^{-5})^3=4^{-15}=\frac{1}{4^{15}}[/tex]
Zoe went out to her garden and cut 19 roses from the first rose bush, 28 roses from the second rose bush, 37 roses from the third rose bush, and 46 roses from the fourth rose bush. What kind of sequence is this?
Based on the given scenario, the kind of sequence explained is an arithmetic sequence
SequenceFirst bush = 19 rosesSecond bush = 28 rosesThird bush = 37 rosesFourth bush = 46First term, a = 19
Second term, a + d
28 = 19 + d
28 - 19 = d
9 = d
Common difference, d = 9Third term, a + 2d
= 19 + 2(9)
= 19 + 18
= 37
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please answer quickly
1a. 10. 24
1b. 125/243
2a. 0. 0048
2b. 32/3125
3a. 0. 64
3b. 0. 0031
4a. 2/5
4b. 48. 735
5a. 2. 36
5b. 1. 39
How to determine the values
1a. Given the values
(2/5)^2/(1/2)^6
Multiply both the numerator and denominator by the powers
⇒ [tex]\frac{\frac{4}{25} }{\frac{1}{64} }[/tex]
To find the common ration, multiply thus;
⇒ [tex]\frac{4}{25}[/tex] × [tex]\frac{64}{1}[/tex]
⇒ [tex]\frac{256}{25}[/tex]
= 10. 24
1b. (5/7)^2 × (5/7)^1
= [tex]\frac{25}{49}[/tex] × [tex]\frac{5}{7}[/tex]
= [tex]\frac{125}{343}[/tex]
= 125/243
2a. 0. 6^1 × 0. 2^3
= 0. 6 × 0. 008
= 0. 0048
2b. (2/5)^3 × (2/5)^2
= [tex]\frac{8}{125}[/tex] × [tex]\frac{4}{25}[/tex]
= [tex]\frac{32}{3125}[/tex]
= 32/ 3125
3a. 1^99 - 0. 6^2
= 1 - 0. 36
= 0. 64
3b. (0. 2 ) ^1 × (1/8)^2
= 0. 2 × 1/64
= 0. 2 × 0. 016
= 0. 0031
4a. (1/2)^2/ (5/8)^1
= [tex]\frac{\frac{1}{4} }{\frac{5}{8} }[/tex]
Take the inverse of the denominator
= [tex]\frac{1}{4}[/tex] × [tex]\frac{8}{5}[/tex]
= 2/5
4b. 7^2 - 0. 5^3
= 49 - 0. 125
= 48. 875
5a. 3^1 - 0. 8 ^2
= 3 - 0. 64
= 2. 36
5b. 0. 7^2 + 0. 9^1
= 0. 49 + 0. 9
= 1. 39
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Calculate how long it would take for an investment of R9000 to double if the simple interest rate is 11% per annum.
Answer:
9.09 years
Step-by-step explanation:
Use the simple interest formula
A=P(1+rt)
18000=9000(1+.11*t), solve for t
t = 9.0909
A doctor asked a patient to reduce his medication by a regular number of tablets per week. The reduction plan begins one week after the visit to the doctor. If 10 weeks after the visit to the doctor the person is taking 40 tablets and 20 weeks after the visit the person is taking 30. Find the weekly reduction in his consumption of tablets.
1 tablet weekly reduction in his consumption of tablets.
What is an algebraic expression?Algebraic expression is a set of variable, constant and algebraic operations like addition, subtraction, multiplication and division. for example 3x^2+2x+3=0
Tablet after 10 week of doctor visit = 40 tablet
Tablet after 20 week of doctor visit= 30
In 10 week there is a difference of (40-30) 10 tablets.
in 10 week there is reduction of 10 tablets its mean there is reduction of 1 tablet per week
so, the weekly reduction of 1 tablet per week.
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You have 1 blue suit, 2 black suits, and 1 brown suit, You also have 2 blue ties, 3 red ties, and 3 pink ties. What is the probability that you pick a striped shirt AND a blue suit AND a pink tie
The probability that you pick a striped shirt AND a blue suit is 1/4 AND a pink tie is 3/8.
According to the statement
Number of blue suit = 1
Number of black suit = 2
Number of brown suit = 1
Number of blue ties = 2
Number of red ties = 3
Number of pink ties = 3
Now we find the probability by its formula
Probability that picked suit is blue = blue suits/ total number of suits
Probability = 1/4
Now,
Probability that picked tie is pink = Pink tie / total number of ties
Probability = 3/8
So, The probability that you pick a striped shirt AND a blue suit is 1/4 AND a pink tie is 3/8.
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What make 6 6 6 6=9 true
Answer:
Step-by-step explanation:
6^0 + 6^0 + 6^0 + 6
= 1+1+1+6
= 9.
PLEASE HELP IM STUCK
Answer:
-70
Step-by-step explanation:
We are given this arithmetic sequence:
-2, -6, -10, -14, ...
And we want to find the 18th term in it.
The 18th term can be found using this formula:
1st term + common difference(desired term-1)
The desired term is the term that we are looking for. In this case, it would be the 18th term, so substitute 'desired term' with 18.
1st term + common difference(18-1)
So, let's find the first term and the common difference.
The 1st term is the first term (number) that appears in the sequence. In this case, that number would be -2.
The common difference can be found by doing second term minus first term.
Remember that we know that the first term is -2. The second term is the second number that appears in the sequence, which would be -6.
So, do -6 subtract -2.
-6 - - 2
-6 + 2
-4
The common difference is -4.
So, we can plug -2 and -4 into the formula.
-2 - 4(18-1)
Now, doing the order of operations, first, subtract 1 from 18.
-2-4(17)
Now multiply -4 and 17 together.
-2 -68
Subtract -68 from -2.
-70
The 18th term of the sequence is -70.
Find the surface area of the pyramid. Round to the nearest tenth.
Answer:
279
Step-by-step explanation:
The area of the square base is 9² = 81.
The area of each triangular face is (1/2)(9)(11)=99/2.
So, the total surface area is 4(99/2)+81=279