Final answer:
In base seven, the number just before 16 is 15, and the number just after 16 is 20. These correspond to 5 and 14 in decimal notation, respectively.
Explanation:
The question asks for the base seven counting numbers just before and after 16 in base seven. In base seven, counting is similar to decimal but stops at 6 before moving to the next place value. The number 16 in base seven is written as 6 in base 10, since base seven does not have a digit for '7' or higher. Therefore, the counting sequence in base seven goes ...14, 15, 16, 20, 21... Thus, the number just before 16 in base seven is 15 (which is 5 in base 10), and the number just after 16 in base seven is 20 (which represents 14 in base 10).
In America, a person uses about 100 gallons of water each day, which is equal to 1,600 water-filled drinking glasses. How many water-filled drinking glasses would 281 Americans fill in a weeks time?
a. 449,600 water-filled glasses
b. 28,100 water-filled glasses
c. 3,147,200 water-filled glasses
d. 196,700 water-filled glasses
Answer:
c. 3,147,200 water-filled glasses
Step-by-step explanation:
The amount of water consumed by an American per day= 100 gallons
So, the amount of water consumed by an American per week = 7×100 = 700 gallons
In 100 gallons of water 1,600 drinking glasses can be filled.
In 700 gallons of water 7×1,600= 11,200 drinking glasses can be filled.
The amount of water consumed by 281 American per week = 700×281 = 196,700 gallons
As in 700 gallons of water 11,200 glasses can be filled.
So, in 1 gallons of water [tex]\dfrac{11,200}{700}=16[/tex] glasses can be filled.
So, in 196,700 gallons of water [tex]16\times 196,700=3,147,200[/tex] glasses can be filled.
Who is vladimir lenin?
Kesara Santiago purchased a riding mower for $2,746.00. She received a $49.95 rebate from the manufacturer and a $38.95 rebate from the store. What is the final price?
Answer: $2657.1
Step-by-step explanation:
Given: The price of a riding mower = $2,746.00
The amount she received by manufacturer as rebate= $49.95
The amount she received by the store as rebate = $38.95
The total amount she received as rebate =[tex]\$49.95+\$38.95=\$88.9[/tex]
Therefore, the final price of the riding mower is given by :-
[tex]\text{Final Price}=\$2746-\$88.95=\$2657.1[/tex]
A department store is having a 30% off sale for all clothing items. what is the discount price of a pair of blue jeans that normally cost $39.99?
Which equation could be used to solve this problem?
Kate weighs 3 times as much as Jen. Their total weight is 140 pounds. How much does each girl weigh?
A) 140 = 3x
B) 3x + x = 140
C) 3x - x = 140
D) x - 140 = 3x
Answer:
B
Step-by-step explanation:
y=3(1.2)x growth or decay
There are 17 goats in the barn 8 goats goes outside how many goats are still in the barn
Total number of goats still in Barn is 9 goats
Given that;
Total number of goats in Barn = 17
Number of goat go outside = 8
Find:
Total number of goats still in Barn
Computation:
Total number of goats still in Barn = Total number of goats in Barn - Number of goat go outside
Total number of goats still in Barn = 17 - 8
Total number of goats still in Barn = 9
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what is 100 x 100 ...............
The product of the given multiplication is 10000.
What is multiplication?Multiplication is when you take one number and add it together a number of times.
Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20.
Given that, multiply 100 x 100,
100 x 100 = 10000
Hence, the product of the given multiplication is 10000.
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Use the rule 4x to find the missing number on the table.
X Y
0 0
2 8
5 20
7
10 40
Answer: The missing number would be 28.
Step-by-step explanation:
Use the rule
4
to find the missing number on the table.
x y
0 0
2 8
5 20
7 28
10 40
7*4=28.
Expand and simplify 4 (2x-1) +3 (2x+5)
Also,
Find the first four terms and the 10th term
5-2n....
_ _ _ _......_
Segment BDSegment BD is a perpendicular bisector of segment ACsegment AC . AD=8x−15AD=8x−15 and DC=57DC=57 .
What is the value of x?
Only $1.87 to buy a present for Jim. Her Jim. Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling—something just a little bit near to being worthy of the honor of being owned by Jim.What inferences about Della can be made based on this excerpt Check all that apply
Della does not have much money to spend on Jim’s gift.
Della wants to buy Jim a watch chain for his watch.
Della loves her husband, Jim, very much
Della wants to buy Jim a really nice gift
Della will need to sell he
Answer:
The following are correct inferences:
1. Della does not have much money to spend on Jim’s gift.
Della is financially poor and does not have enough to gift Jim. This can be understood from the line "Only $1.87 to buy a present for Jim."
2. Della loves her husband, Jim, very much.
Della has been saving for months to gift her husband something rare and unique that his husband is worth for.
"Something fine and rare and sterling—something just a little bit near to being worthy of the honor of being owned by Jim." these lines shows her love and affection for her husband.
3. Della wants to buy Jim a really nice gift.
"Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling—" These lines show that Della needs to buy something for Jim.
A popular video game claims that the average time needed to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours. James thinks that he and his four friends are more skilled than the average gamer because it took them an average of only 2.5 hours. Which of the following is the most restrictive level that would validate his claim?
a. 1%
b. 2.5%
c. 5%
d. 10%
Answer:
a
Step-by-step explanation:
1%
Final answer:
The z-score calculation for James and his friends' gaming performance indicates that their claim would be validated at even the most restrictive level of significance, which is 1%.
Explanation:
To determine which level of significance validates James and his friends' claim of being more skilled gamers, we use the concept of hypothesis testing in statistics. Given that the average time to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours, and James and his friends have an average of 2.5 hours, we can calculate the z-score to see how many standard deviations their average is from the population mean.
The formula for the z-score is: Z = (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size. Plugging in the values, we get:
Z = (2.5 - 3) / (0.4 / √5) = -6.25
This z-score is significantly below the mean. Looking at the z-table, a z-score of -6.25 falls well beyond the typical critical values for common levels of significance (1%, 2.5%, 5%, and 10%). Thus, James's claim would be validated at even the most restrictive level.
Therefore, the answer is:
a. 1%
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7-x^2 .
What are the dimensions of such a rectangle with the greatest possible area?
The rectangle with the maximum area that can be inscribed within the parabola y=7-x^2 has dimensions length 2√(7/3) and height 14/3.
Explanation:The problem is asking to find the dimensions of a rectangle inscribed within a parabola with maximum area. This is an example of an optimization problem in calculus. Here, the parabola given by y=7-x^2 suggests that the rectangle's corners on the x-axis lie at (-x, 0) and (x, 0). The corners on the parabola would be located at (-x, 7-x^2) and (x, 7-x^2). The dimensions of the rectangle would be 2x for the length (base) and 7-x^2 for the height.
For the maximum area, we need to take the derivative of the area function A = length*width = (2x)*(7-x^2) and set it equal to zero, thus defining the critical points.
The derivative of A is given by A' = 14 - 6x^2. Setting A' equal to zero gives: x = √(14/6) which simplifies to x = √(7/3).
Finally, as we are looking for the dimensions of the rectangle, the length (base) is 2*x = 2√(7/3) and the height is given by y = 7 - x^2 = 7 - (7/3) = 14/3.
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Find the ordered pairs for the x- and y-intercepts of the equation 3x − 2y = 18 and select the appropriate option below.
The x-intercept is (0, 6); the y-intercept is (–9, 0).
The x-intercept is (6, 0); the y-intercept is (0, –9).
The x-intercept is (3, 0); the y-intercept is (0, –2).
The x-intercept is (0, 3); the y-intercept is (–2, 0).
Answer:
The x-intercept is (6, 0); the y-intercept is (0, –9).
Step-by-step explanation:
explain why you can use subtraction to solve a division problem.
Final answer:
Subtraction can be used to solve division problems as division can be thought of as repeated subtraction. In scientific notation, dividing numbers involves subtracting exponents, underscoring the relationship between subtraction and division, especially with exponent rules.
Explanation:
Subtraction can be used to solve a division problem because division essentially involves determining how many times a number (the divisor) can be subtracted from another number (the dividend) until nothing is left or a remainder is obtained. This concept is similar to repeated subtraction, and understanding this helps clarify why we subtract exponents when dividing numbers in scientific notation. For example, when dividing $10^6$ by $10^3$, you are essentially finding out how many times $10^3$ can be subtracted from $10^6$, which can be intuitively understood as reducing the exponent by 3 (hence $10^{(6-3)}$ or $10^3$).
When working with scientific notation, the operation of division is handled by dividing the coefficients (the numbers in front of the exponents), and then subtracting exponent of the divisor from the exponent of the dividend. This subtraction of exponents is based on the properties of powers where dividing two numbers with the same base results in a power with the base raised to the difference of the exponents. Division and subtraction are intimately related in mathematics, particularly in dealing with exponent rules which require a deep conceptual understanding, not just a mechanical execution of operations.
What type of number is
- square root 81?
Select all that apply.
Whole number
Integer
Rational
Irrational
The square root of 81 is 9. Hence, it falls under the categories of Whole number, Integer, and Rational number since it can be a positive whole number without any fractional part and can be written as a ratio.
Explanation:The square root of 81 is 9. Now, considering the types of numbers, 9 is a Whole number, because it is not a fraction, and it does not have a decimal point. It is also an Integer, which are numbers that can be written without a fractional component, including both positive and negative whole numbers plus zero. Lastly, 9 is a Rational number, a number that can be written as a fraction. So, the square root of 81 is all three: Whole number, Integer, and Rational number. It is not an Irrational number, which is a number that cannot be expressed as a ratio of two integers.
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Final answer:
The square root of 81 is 9, which makes it a whole number, an integer, and a rational number. It is not an irrational number.
Explanation:
The type of number the square root of 81 is can be determined simply by calculating the square root. The square root of 81 is 9, since 9 multiplied by 9 equals 81. Now, let's classify this number:
Whole number: Yes, because whole numbers include all the non-negative numbers (0, 1, 2, 3...), and 9 falls into this category.
Integer: Yes, because integers are all whole numbers, both positive and negative, including zero (-3, -2, -1, 0, 1, 2, 3...), so 9 is also an integer.
Rational number: Yes, because rational numbers are ratios of integers (like 2/1 or -3/4), and 9 can be expressed as 9/1.
Irrational number: No, because irrational numbers cannot be expressed as ratios of integers. Examples of irrational numbers include √2 or π.
Therefore, the square root of 81 is a whole number, an integer, and a rational number, but it is not irrational.
in the rectangle below, what is x?
Business: the charge on isongs is $4.50 per song. for his birthday, jason is allowed to spend at most $50 worth of music. write the inequality that describes how many songs he can buy; then solve the equation
(x-2)(x+2) Find The Product?
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A standard showerhead in Marty's house dispenses 7 gallons of water per minute. Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead.
y = 3x
How much water does Marty save each day with the change in showerheads if he uses the shower for 8 minutes each day?
4 gallons
12 gallons
32 gallons
53 gallons
Answer:
the answer would be 32
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Krystal bought a refrigerator from a rental center for $1,050. She makes 16 monthly payments of $112.75 with her credit card. The rental center charges $1.25 for every payment made with a credit card. What is the total cost of the refrigerator?
$1,050
$1,804
$1,824
$2,052
Description
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Let
n--------> number of monthly payments
x-------> amount of monthly payments with Kristal's credit card
y-------> charges for every payment made with a credit card
T-------> total cost of the refrigerator
we know that
[tex] n=16\\x=\$112.75\\ y=\$1.25\\[/tex]
the total cost of the refrigerator is equal to
[tex] T=n(x+y) [/tex]
substitute the values in the formula
[tex] T=16*(112.75+1.25) [/tex]
[tex] T=16*114 [/tex]
[tex] T=\$1,824 [/tex]
therefore
the answer is
the total cost of the refrigerator is equal to [tex] \$1,824 [/tex]
In a scatter plot or diagram, what is it called when all the points lie approximately along a straight line?
A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend. Which expression uses the distributive property to show equivalent expressions for this situation?
Answer:
D.) 54 + 42 = 6(9+7)
Step-by-step explanation:
This shows the distributive property as, when the 6 is distributed to the 9 you get 54 (pumpkins), and when distributed to the 7 you get 42 (pumpkins).
Suppose that the area of a square is eight times its perimeter. find the length of a side of the square.
Final answer:
To solve the problem, an equation is set where the area of the square (a²) is equal to eight times its perimeter (8(4a)). Solving for a, we find the side length of the square to be 32 inches.
Explanation:
The student is presented with a problem where the area of a square is stated to be eight times its perimeter. Let the side length of the square be a inches. The area of a square is given by a², and the perimeter of a square is given by 4a. According to the problem, we have a² = 8(4a).
Firstly, we set up the equation based on the given information:
a² = 8(4a)
Solving for a:
a² = 32a
a² - 32a = 0
a(a - 32) = 0
Therefore, the side length a can be 0 or 32. Since the side length cannot be 0, the length of a side of the square is 32 inches.
Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is -3/4?
Calculate dy/dx
You need not expand your answer.
y=3x^2-9x+13/2x+4 ...?
Which of the following points does not lie on the line whose equation is x+ y = 7?
(-10, 17)
(13/3, 8/3)
(-1, -6)
What is 2.5 in expanded and word form?
Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = 144 – 16t2, where t is the number of seconds it takes the car to travel down to each point on the ride. For which interval of time is Greg’s car moving in the air?