On the coordinate grid, the graph of y = 3x - 1 + 3 is
What is the domain of the graphed function?
shown. It is a translation of y = 3x.
Ty
{x 1
O {y|1 < y<5}
{x x is a real number}
O {yly is a real number}
6
5
Answers
Step-by-step explanation:
the domain is the interval or set of all valid input values (values of x).
while the range is the interval or set of all valid result values (y values).
so, we don't need to look at the answer options dealing with y. the domain only concerns x.
and when you look at the graph it shows you that every number on the x-axis from all the way to the left to all the way to the right is valid (from -infinity to +infinity).
and the function itself (the cubic root of x) did not provide any theoretical limits. you can take the cubic root from any number, positive or negative.
therefore, the third answer option is correct (all x, where x is a real number).
The domain of the function is the set of all real numbers, written as:
D: {x| x ∈ R}
How to find the domain of a function?
The domain of a function f(x) is assumed to be the set of all real numbers, and then we remove the problematic points.
Problematic points can be zeros in denominators, or negative arguments in square roots, for example.
In this case, our function is:
f(x) = ∛(x - 1) + 3
As you may know, we can input any real value in a cubic root and it will not generate any problem, and we don't have any denominator here, so there are no problematic points.
Thus, the domain of this function is just the set of all real values, written as:
D: {x| x ∈ R}
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Related Questions
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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The College Board states that the average math SAT score is 514 with a standard deviation of 117. Colleen knows scores at her school are normally distributed and collects a random sample of 50 students in her graduating class. Give a 95% confidence interval for the population mean. Round to the nearest tenth.
Answers
In hypothesis testing, null hypothesis (H0) is a claim that the person conducting the research wants to test while an alternative hypothesis (H1) is a contradiction of the null hypothesis.
There are two types of tests in hypothesis testing is known.
One tailed test: In first tailed test, a claim that a parameter is greater than/ less than a value is being tested.
mean > value or mean < value.
Second tailed test: In a two tailed test, a claim that a value is equal to a value is tested,
mean = value.
Since we can see that Colleen is testing the claim that the average score of her class is the same as others against that it is different from others.
Hence, the null hypothesis is H0: mean = 514
and the alternative hypothesis is H1: mean ≠ 514
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Select the correct answer.
Which expression is equivalent to this polynomial?
(3x - √7i) ²
(3x + √7) ²
○ (3x + √7) (3x − √7)
1
(3x
+
+ √7i) (3x − √7i)
9x² + 7
Answers
The expression equal to 9x² + 7 is (3x+ √7i) (3x − √7i)
What is an expression?
An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division. The structure of an expression is: Expression = (Number, Math Operator, Number)
Given, polynomial is 9x² + 7
by expanding (3x+ √7i) (3x − √7i)
by the identity
(a+b) (a-b) = a^2-b^2
(3x+ √7i) (3x − √7i)= (3x)^2-(√7i)^2
=9x^2-7(i)^2
= 9x² + 7
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Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot with sides of lengths 119, 147, and 190 ft?
Answers
Answer:
$87,461
Step-by-step explanation:
Given that the dimensions or sides of lengths of the triangle are 119, 147, and 190 ft
where S is the semi perimeter of the triangle, that is, s = (a + b + c)/2.
S = (119 + 147 + 190) / 2 = 456/ 2 = 228
Using Heron's formula which gives the area in terms of the three sides of the triangle
= √s(s – a)(s – b)(s – c)
Therefore we have = √228 (228 - 119)(228 - 147)(228 - 190)
=> √228 (109)(81)(38)
= √228(335502)
=√76494456
= 8746.1109071 * $10
= 87461.109071
≈$87,461
Hence, the value of a triangular lot with sides of lengths 119, 147, and 190 ft is $87,461.
A diphosphonate kit contian 180 mCi of Tc99m in 30 ml when it is prepared at 8am. Immediately, a 20 mCi dose is withdrawn for a bone scan. if the patient arrives late at 9:30 and half the volume is accidentally discharged, how much volume from the kit must now be added to the syringe to correct the dose to 20 mCi? (no other doses have been withdrawn meanwhile, and the decay factor for 1.5 hrs is 0.841)
Answers
The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = Initial activity * Decay factor
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = Initial activity - 20 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = Remaining activity * Decay factor
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30
Calculate the remaining volume at 9:30:
Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume
Let's perform the calculations step by step:
Determine the initial activity of the kit:
Initial activity = 180 mCi
Calculate the decayed activity at 9:30 (after 1.5 hours):
Decay factor = 0.841
Decay activity = 180 mCi * 0.841 = 151.38 mCi
Calculate the remaining activity after withdrawing 20 mCi at 8 am:
Remaining activity = 180 mCi - 20 mCi = 160 mCi
Calculate the remaining activity at 9:30:
Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi
Calculate the desired activity at 9:30 (20 mCi):
Desired activity at 9:30 = 20 mCi
Calculate the volume needed to achieve the desired activity:
Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30
Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml
Calculate the remaining volume at 9:30:
Remaining volume = 30 ml - (30 ml / 2) = 15 ml
Calculate the volume that needs to be added:
Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml
Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.
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Select the correct answer.
What is the solution of 5/2x-7=3/4x+14?
А.x=-6
В.x=6
C.x=8
D. r= 12
Answers
Answer:
D) x = 12
Step-by-step explanation:
we can change 5/2 to 10/4 and now have:
10/4x-7 = 3/4x + 14
we can subtract 3/4x from each side:
7/4x-7 = 14
add 7 to each side:
7/4x = 21
multiply each side by 4/7:
x = 84/7
x = 12
The 10 largest bird wingspans are 9.1, 9.8, 9.2, 9.8, 11.8, 11, 8.2, 8.2, 11, and 11.8 inches. What are the range, interquartile range, and standard deviation of the wingspans?
Answers
Answer:
The range is 3.6
Step-by-step explanation
The range is equal to the largest # - the smallest #
Which mean: 11.8 - 8.2= 3.6
Step-by-step explanation:
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Maria Krisp, a licensed physical therapist assistant, earns an hourly
rate of $18.40 and time and a half if she works any overtime. Last
week she worked 38 hours plus 6 hours overtime. What is Maria's
(a) straight-time pay, (b) overtime pay, and (c) total pay?
Answers
9514 1404 393
Answer:
straight time: $699.20overtime: $165.60total pay: $864.80Step-by-step explanation:
(a) Maria's straight time pay is ...
(38 h)×($18.40 /h) = $699.20
__
(b) Maria's overtime pay is ...
(6 h)×(1.5×$18.40 /h) = $165.60
__
(c) Her total pay is the sum of her straight time pay and her overtime pay:
$699.20 +165.60 = $864.80
3 Select the correct answer. Answer the question based on the data in the two-way table. Gender Grades Below Average Above Average Total Boy 14 23 37 Girl 16 22 38 Total 30 45 75 Which statement is true? A. P(boy|above average grades) = P(boy) B. P(above average grades|boy) = P(above average grades) C. P(boy|above average grades) P(above average grades) D. P(above average grades|boy) = P(boy) Reset Next
Answers
The probability that randomly selected girl with above average grades is 0.58
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
The above two way table shows the number of girls and boys who scored below average and above average grades.
We have to find the probability that a randomly selected girl will have above average grades.
Probability is the measure of an likelihood that an event will occur.
Probability is calculated by the formula = Favourable outcomes / total outcomes.
Total number of girls = 38
Number of girls Girls who have above average grades = 22
P(randomly selected girl with above average grades)=
= 0.58
Therefore, The probability that randomly selected girl with above average grades is 0.58
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Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answers
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
the line with a slope of 9/7 & containing a midpoint of the segment whose end points are (2, -3) & (-6, 5)
Answers
1. Find the midpoint of the segment using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
2. Use the midpoint and the slope to find the equation of the line in point-slope form. The point-slope form is given by:
y - y1 = m(x - x1), where (x1, y1) is the midpoint and m is the slope.
Substituting the values:
y - 1 = (9/7)(x - (-2))
y - 1 = (9/7)(x + 2)
y - 1 = (9/7)x + (18/7)
3. Simplify the equation to obtain the slope-intercept form:
y = (9/7)x + (18/7) + 1
y = (9/7)x + (18/7) + (7/7)
y = (9/7)x + (25/7)
So, the equation of the line with a slope of 9/7 and containing the midpoint of the segment with endpoints (2, -3) and (-6, 5) is y = (9/7)x + (25/7).
Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:
y = (9/7)x + 25/7.
Step-by-step explanation:Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
So, the midpoint of the line segment is (-2, 1).
Step 2: Write the equation of the line using the slope-intercept form.
The slope-intercept form of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given the slope as 9/7, we have:
y = (9/7)x + b
Step 3: Substitute the coordinates of the midpoint to find the value of b.
Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:
1 = (9/7)(-2) + b
1 = -18/7 + b
To find the value of b, we can solve this equation:
1 + 18/7 = b
25/7 = b
Step 4: Write the final equation of the line.
Using the value of b, the equation becomes:
y = (9/7)x + 25/7
In a game of chance there is a box filled with 20 black balls, 13 red balls, and 7 green
balls. If a single ball is drawn from the box, then what is the probability that the ball
is green?
Please help me out.
Answers
Answer:
7/40
Step-by-step explanation:
7 balls are green-->numerator
7 balls out of 40( in total) are green.
7/40
This means that out of every 40 balls picked, 7 of them should be green.
Please indicate which is the best answer to complete the figure below.
Answers
Answer:
Step-by-step explanation:
B because after having the star and the circle comes the square.
the graph of f(x) shown below has the same shape as the graph of g(x)=x^4-x^2 which contains the point
Answers
Answer:
i think the answer is B
Step-by-step explanation:
We have the function and we know that it contains the point (0,0). That is, it cuts the y axis and y = 0Then the graph of F(x) is shown in the image and we know that it is a transformation of F(x).The function F(x) cuts the y axis and y = 4.For this reason we can conclude that the function F(x) is the function G(x) displaced 4 units upwards.The transformation that shifts the graph of a function k units upwards is:Where .In this case k = 4. Therefore:The answer is Option B
(Not by me)
7. Given & right triangle ABC, with
Angle C being the right angle,
segment AC = 3, segment BC = 4,
and segment AB = 5. Find the ratio
of sin A. *
Answers
Answer:
4/5, or 0.8.
Step-by-step explanation:
Since sin is equal to opposite over hypotenuse, and the opposite of side A is BC which equals 4 and the hypotenuse is 5, we then get BC/AB, which is thus, 4/5.
Evaluate 28÷7×4
plzzzzzzzzzzzzzzzzzzzzzz
Answers
Hey there!☺
\(Answer:\boxed{16}\)
\(Explanation:\)
\(\frac{28}{7}\times4\)
Start by simplifying 28/7:
\(\frac{28}{7}=4\)
Now multiply 4 by what we have left, which is 4:
\(4\times4=16\)
16 is your answer.
Hope this helps!☺
Answer:
1
Step-by-step explanation:
28 ÷ 7 × 4
= 28/28
= 1 .....
Which expression is equal to the polynomial below 2x^4+5x^3-8x-20
Answers
The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).
The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.
We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .
Factorization by grouping:
We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.
This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)
Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).
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On 5 days, lisa swam 650 meters, 675 meters, 725 meters, 800 meters, and 900 meters. What was her average distance per day?
Answers
Answer:
Her average per day was 750 meters.
Step-by-step explanation:
To find the average, add all the numbers up in the set and divide by how many numbers there are.
650 + 675 + 725 + 800 + 900 = 3750. Divide it by 5 and you get 750
Answer:
750 meters
Step-by-step explanation:
Step 1: Add all the given data
650 + 675 + 725 + 800 + 900 = 3750
Step 2: Divide the result by the number of numbers she swam
3750/5 = 750
The average distance per day is 750 meters.
I need help with figuring out the rate of change
Answers
Explanation
Step 1
A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then
\(\text{rate of change=}\frac{change\text{ in y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1}\)then select the 2 poitns of the line, Let
P1(5,60)
p2(12,72)
Step 2
replace
\(\begin{gathered} \text{rate of change=}\frac{change\text{ in y }}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{72-60}{12-5}=\frac{12}{7} \\ \text{rate of change=12/7} \end{gathered}\)I hope this helps you
you can model the population of a certain city between 1945-2000 by the radical function P(x)+55000sqrt(x-1945) . using this model, in which year was the population of that city in 165000?
Answers
The population of the city was 165000 in the year 1954.
The population of the city in a given year, x, can be calculated using the given function:
P(x) = 55000√(x - 1945)
We want to find the year, so we need to solve for x when P(x) = 165000.
165000 = 55000√(x - 1945)
Dividing both sides by 55000:
3 = √(x - 1945)
Squaring both sides:
9 = x - 1945
Adding 1945 to both sides:
x = 1954
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what is The greatest common factor of 42 and 96? I need it to be broken down for me to understand. thanks
Answers
Answer:
GCF is 6
Step-by-step explanation:
42 :
2 | 42
3 | 21
7 | 7
| 1
; 42 = 2 x 3 x 7
96 :
2 | 48
2 | 24
2 | 12
2 | 6
3 | 3
| 1
; 96 = 2 x 2 x 2 x 2 x 2 x 3
here, common factors are 2 x 3 = 6
Hence, the GCF of 42 and 96 is 6.
Solve using the square root property
x2 - 12 = 0
Answers
Situation 1. ROCKET RIDE.
The Rocket Coaster has 10 cars, some that
hold 4 people and some that hold 8 people.
There is room for 56 people altogether.
How many 4-passenger cars are there?
How many 8-passenger cars are there?
Let x= number of 4-passenger cars
Let y = number of 8-passenger cars
equation #1:
equation #2:
Solution:
Answers
In Jayce's favorite video game, he collects stars to earn points. Today, he collected 80 silver stars and earned 160 points. He also collected 30 gold stars and earned 150 points. How many more points per star does Jayce earn from gold stars?
Answers
Jayce earns 3 more points from gold stars than from silver stars.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Jayce collected 80 silver stars and earned 160 points.
He collected 30 gold stars and earned 150 points.
Therefore,
The points per star Jayce earns from silver stars
160/80=2,
The points per star Jayce earns from gold stars
150/30=5
Hence, Jayce earns 3 more points from gold stars than silver stars.
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What equation of the line which passes through the point (-1, 2) and is parallel to the line y=x+4
Answers
Answer:
Thus, the equation of line for point (-1, 2) is y = x + 3.
Step-by-step explanation:
Answer:
The equation of the line is y = x + 3.
Step-by-step explanation:
A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.
y = mx + b
y = 1 * -1 + b
y = -1 + b
b = y + 1
b = 2 + 1
b = 3
a biologist wants to compare the proportions of rainbow trout infected with whirling disease (an illness of trout and salmon caused by a microscopic parasite) coming from two separate watersheds. for each watershed, the biologist will collect a random sample of trout and record the proportion infected in the sample. the biologist intends to estimate the difference for all trout in the two watersheds. assuming all conditions for inference are met, which of the following is the most appropriate method for the biologist to use to analyze the results?
Answers
The following is the most appropriate method for the biologist to use to analyse the results:
"A two-sample z-interval for a difference in population proportions "
What is proportion?
A proportion is a mathematical formula that makes two ratios equal. For instance, you could write the ratio as 1: 3, which indicates that there are 34 girls and 14 boys in the population overall. This ratio indicates that there are three girls for every one boy.
A biologist is comparing how many rainbow trout from two different watersheds are affected by whirling disease, a salmon and trout illness brought on by a microscopic parasite.
A random sample of trout will be taken by the biologist, who will then note the percentage of infected fish in the sample. For all trout in the two watersheds, the biologist plans to estimate the difference.
According to the posed question, the two-sample z-interval for a difference in population proportions will be the most suitable method for the biologist.
Because it's important for biologists to compare the percentages of rainbow trout with whirling disease and determine how the populations of these fish in two watersheds differ.
As a result, the correct answer is Statement D, "A two-sample z-interval for a difference in population proportions."
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Solve for m: 1/3 klm
Answers
Answer:75
Step-by-step explanation:
Choose the expression that completes the equation. 30 ÷ 2 + 10 = ________ 7(2 + 1) 6(3 + 7) 5(4 + 1) 3(2 + 3)
Answers
Answer:
5(4 + 1)
Step-by-step explanation:
5 times 4 = 20. 5 times 1 =5. Add the 20 and 5 you'll get 25
Answer: 5(4+1)
Step-by-step explanation:
Yes
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
Answers
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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You work for a rock-climbing gym and need to purchase 330 feet of climbing rope to arrive in three days for an event. The online retailer SportsStuff.com charges $5.50 per yard of rope and offers free three-day shipping. The same rope at OutdoorHaven.com costs $5.20 per yard, plus a $12.25 rush delivery fee. What is the cheapest price you can pay for the rope you need for your gym?
Answers
Answer:pls brainly award
Step-by-step explanation:
The 330 feet of rope is equivalent to 330/3 = 110 yards.
The cost of the rope at SportsStuff.com is 110 * $5.50 = $605.
The cost of the rope at OutdoorHaven.com is 110 * $5.20 + $12.25 = $604.45.
Therefore, the cheapest price you can pay is $604.45.