How do you find the domain step by step?
Answers
Using the provided function and finding the values of input for which it will provide valid output values we can find the domain.
What is the difference between domain an range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Can a function's domain and range be the same?Yes. For instance, the set of all real numbers is the domain and range of the cube root function.
Choose the input values.
Exclude any real numbers that produce a negative value in the radicand because there is an even root. Solve for x by setting the radicand to be greater than or equal to zero.
The domain of the function is the solution(s). If at all possible, format your response as an interval.
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Related Questions
5x + 3 < -7 or -2x - 6 < -8
Answers
Answer:
-2x - 6 < -8
Step-by-step explanation:
when the first one is smiplfid it gives us x<−2
when the second one is smiplfid it gives us x>1 which means it's correct because 8 is greater than 1
plz mark brainliest
Answer:
( −∞ , −2 ) ∪ ( 1 , ∞ )
Step-by-step explanation:
5x + 3 < -7 → x < −2 → ( −∞ , −2 )
-2x - 6 < -8 → x > 1 → ( 1 , ∞ )
5x + 3 < -7 or -2x - 6 < -8 → x < −2 or x > 1 → ( −∞ , −2 ) ∪ ( 1 , ∞ )
Graph 1) 5x + 3 < -7
Graph 2) -2x - 6 < -8
Graph 3) 5x + 3 < -7 or -2x - 6 < -8
simplify and Express the the result in power notation with positive exponents
a) 2-³×(-7)-³
Answers
Answer:
-1/14³Step-by-step explanation:
Use properties:
aⁿbⁿ = (ab)ⁿa⁻ⁿ = 1/aⁿSimplify:
2⁻³*(-7)⁻³ =(2*(-7))⁻³ =(-14)⁻³ =-14⁻³ =-1/14³solve/ Find the area….
Answers
Answer:
D. 195 cm^2
Step-by-step explanation:
The given is a trapezoid and to calculate the are of it we use the following formula :
(a+b)/2*h (a: base, b: base, h: height)
(9+21) / 2 * 13 = 195
If x = 0 and y> 0, where is the point (x, y) located?
on the x-axis
Or
on the y-axis
Answers
Satoko has 303030 tokens to spend at an arcade. the three lines represent the cost of playing satoko's three favorite games for various numbers of times.
Answers
Satoko has 303030 tokens to spend at an arcade, and the three lines indicate the cost of playing her favorite games. She must also consider her personal preference for each game, as enjoyment plays a crucial role.
Satoko's objective is to make the most out of her 303030 tokens while enjoying her three favorite games at the arcade. To achieve this, she needs to allocate her tokens wisely across the three games. By analyzing the cost of playing each game for various numbers of times, she can determine the optimal strategy.
First, Satoko should identify the game with the lowest cost per play. If one game stands out as the most affordable, she can prioritize it to maximize the number of plays within her token budget. However, she must also consider her personal preference for each game, as enjoyment plays a crucial role.
Next, Satoko can distribute the remaining tokens among the other two games. She should aim to strike a balance, ensuring she has a reasonable number of plays for each while still getting the most out of her tokens. It might be beneficial to allocate more tokens to the game she enjoys the most among the remaining two.
By carefully analyzing the cost per play and her personal preferences, Satoko can make informed decisions on how to allocate her 303030 tokens at the arcade. This strategic approach will help her maximize her enjoyment and extend her gaming experience within the given budget.
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How many powers of 7 are contained in 10?
Answers
There is only 1 power of 7 contained in 10.
Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.
Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.
The digit in the tens place is the same.
The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.
The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.
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There is only 1 power of 7 contained in 10.
Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.
Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.
The digit in the tens place is the same.
The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.
The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.
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0.082
0.186
( multiplying). ??
Answers
Answer:
0.015252
Step-by-step explanation:
Multiply the two together using a calulator and you will get the same answer as me.
Have a great day!
Determine whether the series is convergent or divergent. 1
2
+
3
4
+
1
8
+
3
16
+
1
32
+
3
64
+
Answers
To determine the convergence or divergence of a series, we need to analyze the behavior of its terms. In this case, the series consists of a sequence of numbers: 12, 34, 18, 316, 132, 364, and so on.
Looking at the terms of the series, we can observe that there is no clear pattern or trend in their values. The terms do not approach a specific value as we go further into the series. Instead, the terms seem to be randomly increasing and decreasing.
A convergent series is one where the terms approach a specific value as the number of terms increases, while a divergent series is one where the terms do not approach a specific value.
Since the terms in the given series do not exhibit any clear pattern or convergence, and there is no specific value that the terms are approaching, we can conclude that the series is divergent.
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The value of a company's equipment is $33,000 and decreases at a rate of 12% each year. Write an exponential decay function for the value of the equipment after t years.
Answers
Answer:
Below
Step-by-step explanation:
Value = 33000 ( .88)^t each year, t , the value is only 88% ( or in decimal: .88) of the prior year ( 12 % decrease leaves 88% )
A man has a box of coins that he uses when playing poker with friends. The box currently contains 37 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $4.18. How many of each denomination of coins does he have? ct: E Let x represent the number of pennies. Complete the table. ( Number of Coins Denomination (in dollars) 0.01 Value (in dollars) 0.01x Pennies X la .10 0.10x Dimes х 0.25 Quarters 4.18-X 0.25 4.18 po
Answers
A hiker leaves the Visitor Center traveling East-by-North East. She hikes 13 miles before
twisting her ankle and calling back to the Visitor Center. Rescue Ranger A recommends taking
the Northbound service road to rescue the hiker. Rescue Ranger B recommends taking the
Eastbound service road to rescue the hiker.
Which route is shortest? Support your answer.
What is the total distance traveled by the hiker on her walk and rescue?
Answers
Answer:
both or neither as they are the same distance to rescue her
total distance is her 13 plus 12 headed west and 5 headed south so 30
Step-by-step explanation:
Rebekah performed an experiment with a standard number cube. She rolled the cube and recorded the results in the frequency table. The frequency table is given below. Find the experimental probability of the cube landing on three.
Answers
Answer:
Step-by-step explanation:
The experimental probability of the cube landing on three is 1/10.
Use the calculator to find the product. (1. 466 × 10–8)(5. 02 × 105) What is the coefficient of the product? What is the exponent of the power in the product?.
Answers
The product of the factors in the given expression comes to be \(7.35932 *10^{-3}\).
The given expression is:
\((1.466*10^{-8} )(5.02*10^5)\)
We can rewrite the given expression as
\((1.466*5.02)(10^{-8} *10^5)\)
What is the exponent addition rule?If we have two numbers with the same base we can write the product of the numbers as a single base followed by the addition of exponents.
\(a^m*a^n = a^{m+n}\)
\(1.466*5.02=7.35932\)
\(10^{-8} *10^5 = 10^{-3}\)....from exponent addition rule
So, \((1.466*10^{-8} )(5.02*10^5)=7.35932 *10^{-3}\)
Therefore, the product of the factors in the given expression comes to be \(7.35932 *10^{-3}\).
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Answer:
7.3593 and -3
Step-by-step explanation:
Got it right on the assignment.
there are n items and a backpack that can hold max weight of w. is there a way to choose some of these n items to make the total weight exactly equal to w?
Answers
Yes, it is possible.
To determine if there is a way to choose some of the n items to make the total weight exactly equal to w, you can use the following step-by-step approach:
1. List the weights of each of the n items.
2. Create a table with columns representing the weights from 0 to w, and rows representing the items from 0 to n.
3. Initialize the first row (representing item 0) with "True" for weight 0 and "False" for all other weights.
4. Loop through each item (i) from 1 to n:
a. Loop through each possible weight (j) from 0 to w:
i. If the item's weight is less than or equal to the current weight (j), check if the remaining weight (j minus the item's weight) can be obtained using the previous items (row i-1). If yes, mark the current cell as "True".
ii. If the current item's weight is greater than the current weight (j) or the remaining weight can't be obtained using the previous items, copy the value from the cell above (row i-1) in the table.
5. Check the last cell in the table (cell [n][w]). If it is marked "True", it is possible to choose some of the n items to make the total weight exactly equal to w. If it's "False", it's not possible.
This approach uses dynamic programming to efficiently solve the problem. If the last cell in the table is "True", you can backtrack through the table to find the exact items that contribute to the total weight of w.
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The original price for a shirt is $30. It is on sale for 15% off. The sales tax is 8%. Round your
answer to the nearest cent.
Answers
Answer:$27.54
Step-by-step explanation:30 times 0.15 = 4.5
30 - 4.5 = 25.5
25.5 times 0.08 = 2.04
25.5 + 2.04 = 27. 54
heeeeeeeeeeeeelppppppppppppppp
Answers
Answer:
Step-by-step explanation:
uhhhhhhhhhhhhhhhhhhhhhhhhhh, fudge?
Answer:
Step-by-step explanation:
67
Question 1336 ptsUse the compound interest formulas A=1+ntand A = Per to solve.Find the accumulated value of an investment of $10,000 at 4% compoundedsemiannually for 5 years.O $11,040.81O $12,000.00$12,189.94O $12,166.53
Answers
Step 1: We shall state the Compound Interest formula.
\(A=P(1+\frac{r}{100\alpha})^{n\alpha}\)\(\begin{gathered} \text{Where A = amount =?} \\ P=Pr\text{incipal =\$10,000} \\ r=\text{rate = 4\%} \\ n\text{ = number of years = 5 years} \\ \alpha\text{ =number of periods per year = 2 (Since, it is semi-annually)} \end{gathered}\)Step 2: we shall substitute the values of the parameters in the formula.
\(A=10000(1+\frac{4}{100\times2})^{5\times2}\)\(\begin{gathered} A=10000(1+\frac{4}{200})^{10} \\ A=10000(1+0.02)^{10} \\ A=10000(1.02)^{10} \\ A=10000(1.21899) \\ A=12,189.944\approx\text{ \$12,189.94} \end{gathered}\)Thus, the correct answer is $12,189.94 (option
How many cups are in 20 gallons? AND how do I show my work for that?
correct=brainliest
Answers
I am not sure if this is right can someone check it ASAP please
Answers
Answer:
x=10
Step-by-step explanation:
3(4x-12) = 84
Divide each side by 3
3/3(4x-12) = 84/3
4x-12 =28
Add 12 to each side
4x-12+12 = 28+12
4x= 40
Divide each side by 4
4x/4 = 40/4
x = 10
The US household income distribution is right skewed with mean $40000 and standard deviation $20000. If we select 4 random US households, what is the probability, that their average household income is greater than $50000
Answers
The probability that the average household income of 4 randomly selected US households is greater than $50000, given a right-skewed distribution with a mean of $40000 and a standard deviation of $20000, is approximately 0.1587 or 15.87%.
How to calculate the probability of the average household income exceeding $50000 for 4 randomly selected US households, given the distribution characteristics?To calculate the probability that the average household income of 4 randomly selected US households is greater than $50000, we can use the properties of the sampling distribution of the mean.
Given that the US household income distribution is right-skewed with a mean of $40000 and a standard deviation of $20000, we can assume that the individual household incomes are independent and normally distributed.
To find the probability, we need to calculate the z-score for the given threshold of $50000 and then find the corresponding probability using the standard normal distribution.
First, we calculate the standard error of the mean (SEM) using the formula SEM = (standard deviation) / √n, where n is the sample size. In this case, n = 4.
SEM = $20000 / √4 = $10000
Next, we calculate the z-score using the formula z = (x - μ) / SEM, where x is the threshold value ($50000) and μ is the population mean ($40000).
z = ($50000 - $40000) / $10000 = 1
Now, we need to find the probability of obtaining a z-score greater than 1 from the standard normal distribution. This can be done by referring to the z-table or by using a statistical software.
From the z-table or using a software, we find that the probability of obtaining a z-score greater than 1 is approximately 0.1587.
Therefore, the probability that the average household income of 4 randomly selected US households is greater than $50000 is approximately 0.1587, or 15.87%.
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Anyone know how to do this?
Answers
Answer:
Is it 90 degrees
Step-by-step explanation:
The straight up and down line gives it away.
Justin is starting his own laundry business. Justin thinks he will do a better job than his competitors, so he thinks he can charge $15.16 per hour. If he knows he will only be able to work 50 hours per week, how much money will he earn each week?
Answers
Answer:
$758 per week
Step-by-step explanation:
15.16 x 50 = 758
Answer:$758 per week
Step-by-step explanation:Answer:15.16 x 50 = 758
This isn't a question, but if you need help with math come to me.
Answers
Answer:
Bet!! :D can i get brainliest !! please
Step-by-step explanation:
What type of number is 0.888... ?
O A rational number
O A whole number
O An irrational number
O A decimal that ends
Answers
Given f(x)=x^3-7x+k, and the remainder when f(x) is divided by x-5 is 78, then what is the value of k?
Answers
Answer:
the answer is k= -12
Step-by-step explanation:
use x-5= 0
x=5
which expression is equivalent to 4√8/3√2
Answers
Answer:
8/3
Step-by-step explanation:
The square root of 8 can actually be written \(2\sqrt2\), so \(4\sqrt2 = 4 \cdot 2\sqrt2 = 8\sqrt2\)
Now, we are looking for \(\frac{8\sqrt2}{3\sqrt2}\). Both the square root of 2s cancel, so we are left with 8/3
The sum of two numbers is 40 and the difference is 16. What are the numbers?
Answers
Answer:
28 and 12
Step-by-step explanation:
The sum of two numbers is 40 and the difference is 16. What are the number? x+y=40 Substitute for x from above. (y+16)+y=40 Subtract 16 from each side.
The two numbers whose sum is 40 and difference is 16 are 28 and 12.
Let's denote the two numbers as x and y. We are given the following information:
x + y = 40 (equation 1)
x - y = 16 (equation 2)
To solve for x and y, we can use a method called elimination or substitution. Let's use the elimination method here.
Adding equation 1 and equation 2, we eliminate the y term:
(x + y) + (x - y) = 40 + 16
2x = 56
x = 28
Now we can substitute the value of x back into equation 1 to solve for y:
28 + y = 40
y = 40 - 28
y = 12
Therefore, the two numbers are 28 and 12.
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When 30 passengers, each with average mass of 80 kg , board the car, how much does the car move down on its spring suspension? assume that each wheel supports 1 / 8 the weight of the car.
Answers
The car move down on its spring suspension by the length of 0.0001501 m.
Define the term spring constant?The spring's stiffness is indicated by the spring constant, k. Higher spring constants are found in stiffer (harder to stretch) springs. An object's displacement is a distance calculation that expresses the deviation from its equilibrium or normal position.Acceleration due to gravity g = 9.81 m/s²
Spring constant k = 2.8×10⁷N/m.
Compression of spring x.
Force (F) = mg
Mass of the car is ;
m = 80 x 30
m = 2400 kg
Mass supported by the each spring,
m = 2400/8 = 300 kg
Put the value in force of spring;
F = kx
x = F/k = mg/k
x = (300 x 9.81)/ 2.8×10⁷
x = 0.0001501 m
Thus, the car move down on its spring suspension by the length of 0.0001501 m.
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The complete question is-
A passenger railroad car has a total of 8 wheels. Springs on each wheel compress--slightly--when the car is loaded. Ratings for the car give stiffness per wheel (the spring constant, treating the entire spring assembly as a single spring) as 2.8×10⁷N/m.
When 30 passengers, each with average mass of 80 kg, board the car, how much does the car move down on its spring suspension? Assume that each wheel supports 1/8 the weight of the car.
Write an algebraic equation for each question below and then solve the equation.
5. Jerry sold 50 rare coins from his collection. He now has 225 rare coins. How many coins were originally in his collection?
Answers
Let the original number of rara coins that Jerry had back then be x.
now if he sold 50 rare coins, the coins left will be x - 50
x - 50 = 225x = 225 + 50x = 275The following is a set of data from a sample of
n=5.
4 −9 −4 4 6
a. Compute the mean, median, and mode.
b. Compute the range, variance, standard deviation, and coefficient of variation.
c. Compute the Z scores. Are there any outliers?
d. Describe the shape of the data set.
Answers
a. The mean is -0.6, the median is 4, and there is no mode in the data set.
b. The range is 15, the variance is 35.2, the standard deviation is approximately 5.93, and the coefficient of variation is approximately -0.988.
c. The Z-scores for the data set are -0.68, -1.69, -0.68, -0.68, and 1.37. There are no outliers as none of the Z-scores exceed the threshold of ±3.
d. The shape of the data set is skewed to the left, indicating a negative skewness.
a. To calculate the mean, we sum up all the values and divide by the sample size:
Mean = (4 - 9 - 4 + 4 + 6) / 5 = -0.6
The median is the middle value when the data is arranged in ascending order:
Median = 4
The mode is the value that appears most frequently, but in this data set, none of the values are repeated, so there is no mode.
b. The range is calculated by finding the difference between the maximum and minimum values:
Range = Maximum value - Minimum value = 6 - (-9) = 15
The variance measures the average squared deviation from the mean:
Variance = ((4 - (-0.6))^2 + (-9 - (-0.6))^2 + (-4 - (-0.6))^2 + (4 - (-0.6))^2 + (6 - (-0.6))^2) / (5 - 1) = 35.2
The standard deviation is the square root of the variance:
Standard Deviation ≈ √35.2 ≈ 5.93
The coefficient of variation is the standard deviation divided by the mean, expressed as a percentage:
Coefficient of Variation ≈ (5.93 / 0.6) × 100 ≈ -0.988
c. The Z-score measures how many standard deviations a data point is away from the mean. To calculate the Z-scores, we subtract the mean from each data point and divide by the standard deviation:
Z1 = (4 - (-0.6)) / 5.93 ≈ -0.68
Z2 = (-9 - (-0.6)) / 5.93 ≈ -1.69
Z3 = (-4 - (-0.6)) / 5.93 ≈ -0.68
Z4 = (4 - (-0.6)) / 5.93 ≈ -0.68
Z5 = (6 - (-0.6)) / 5.93 ≈ 1.37
Since none of the Z-scores exceed the threshold of ±3, there are no outliers in the data set.
d. The shape of the data set can be determined by analyzing the skewness. A negative skewness indicates that the data is skewed to the left, which means that the tail of the distribution extends towards the lower values. In this case, the negative skewness suggests that the data set is skewed to the left.
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