7/2 as an improper fraction
given that 4,12,x,y,324,972 is a geometric sequence. find the sum of x and y
The sum of x and y in the given geometric sequence is 144, with x being 36 and y being 108, based on the common ratio of 3.
To solve the problem, we first need to recognize that a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a constant called the common ratio. We are given a sequence 4, 12, x, y, 324, 972, and we need to find the common ratio and subsequently x and y.
Step-by-Step Solution:
Find the common ratio (r) using two known consecutive terms.
Once r is found, apply it to determine the missing terms x and y.
Calculate the sum of x and y.
Given the sequence 4, 12, x, y, 324, 972, let's use the first two terms to find the common ratio. The ratio of the second term to the first term is 12 / 4 = 3. Thus, the common ratio (r) = 3.
Now, let's find x by multiplying the second term (12) by the common ratio: x = 12 x 3 = 36.
To find y, multiply x by the common ratio: y = 36 x 3 = 108.
The sum of x and y is then: x + y = 36 + 108 = 144.
1. Which expression shows the distance on the number line between −14 and −5 ?
|−5−14|
|−14+(−5)|
|−14−5|
|−14−(−5)|
2. Which expression is equivalent to 5.9−3.8 ?
−3.8−5.9
3.8−5.9
3.8 + 5.9
−3.8+5.9
Answer: I don’t know number one but number 2 is the last one
Step-by-step explanation: Do the math in a calculator
If a stereo is sold for $59.99 and Karen pays $64.19 for it when she checks out, what is the sales tax in the area
The sales tax in the area where Karen bought the stereo is $4.20. This was calculated by subtracting the original price of the stereo ($59.99) from the total price paid ($64.19).
Explanation:To find the sales tax in this scenario, we need to subtract the original price of the stereo, which is $59.99, from the total price that Karen paid, which is $64.19. The difference will represent the sales tax that Karen had to pay at the checkout.
So we calculate: $64.19 - $59.99 = $4.20
Therefore, the sales tax that Karen paid for the stereo is $4.20.
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Is 17 1/2 to the right or left of 17 2/3 on the number line? Explain your answer.
[tex]17\frac{1}{2}[/tex] lies to the left of the number line [tex]17\frac{2}{3}[/tex]
What is number line?A number line can be defined as a pictorial representation of numbers on a straight line.
Given that, Is 17 1/2 to the right or left of 17 2/3 on the number line
17 1/2 = 17.5
17 2/3 = 17.66
17.5 < 17.66
Hence, [tex]17\frac{1}{2}[/tex] lies to the left of [tex]17\frac{2}{3}[/tex]
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What is the best estimate of 49% of
598
Nendell saw at a diner if he bought one of each item and spent $7.50, how much did the drink cost
A newly discovered planet has a mass of 4.8743 · 10 ^22 kilograms. It's estimated that there is water on the surface and that, the water's mass is only 4 · 10^ -2 percent of the planet's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
To estimate the mass of water on the planet with a mass of 4.8743 × [tex]10^{22[/tex] kg, you multiply this mass by[tex]4 * 10^{-2[/tex] percent converted to decimal (0.0004), giving a water mass of approximately 1.95 * [tex]10^{19[/tex]kg.
To estimate the mass of the planet's water, we first need to find 4% of the planet's total mass. We can do this by multiplying the planet's mass by the percentage as a decimal:
Mass of water = (4.8743 × 10^22 kg) × 0.04
Now, let's perform the multiplication:
Mass of water = 1.94972 × [tex]10^{19[/tex] kg
So, the estimated mass of the planet's water is approximately 1.95 × [tex]10^{19[/tex] kilograms.
Is 632 a multiple of 4
How many points need to be removed from this graph so that it will be a function?
Answer:
The correct option is 3.
Step-by-step explanation:
From the given graph it is noticed that the coordinates of all the points are (-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4).
So, the graph represents a relation,
R = {(-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4)}
A relation is called a function if an only if for each value of x there exist a unique value of y.
In the given relation, for each value of x we have two values of y. So it is not a function. We need to remove any of ordered pairs that have same input values.
From (-3,2) and (-3,3), we need to remove one point.
From (1,4) and (1,-4), we need to remove one point.
From (2,-2) and (2,-4), we need to remove one point.
It means total we need to remove 3 points from this graph so that it will be a function.
Therefore the correct option is 3.
Answer:
3 points
Step-by-step explanation:
got it right in Edg
Brian has reduced his cholesterol level by 12% by following a strict diet and regular exercise. If his original level was 220, what is his approximate cholesterol level now?
Final answer:
By reducing his cholesterol level by 12% from the original 220 mg/dL, Brian's current approximate cholesterol level is 193.6 mg/dL.
Explanation:
Brian has reduced his cholesterol level by 12% by following a strict diet and regular exercise. If his original level was 220, to calculate his current cholesterol level, we need to find 12% of 220 and then subtract that from 220. Here's how:
Calculate 12% of 220: (12/100) * 220 = 26.4.
Subtract the reduction from the original level: 220 - 26.4 = 193.6.
Therefore, Brian's approximate cholesterol level now is 193.6 mg/dL.
-4w less than or equal to 20
is 4.47 a rational number
Yes, 4.47 is a rational number because it can be expressed as a fraction of two integers.
Explanation:Yes, 4.47 is a rational number.
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
In this case, we can express 4.47 as the fraction 447/100, which is a quotient of two integers. Therefore, it is a rational number.
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Which property was applied to create this equivalent expression? 7x+(5+6×)--->(7x+5)+6x
Answer:
Associative property is applied
Step-by-step explanation:
7x+(5+6×)--->(7x+5)+6x
In the given expression , the terms are grouped in different order
In associative property, we can group the numbers in any order
(a+b)+c -------> a+(b+c)
first two terms are grouped on the left side
last two terms are grouped on the right side
7x+(5+6×)--->(7x+5)+6x
In the given expression, the terms are grouped in different order
So Associative property is applied
Answer:
Associative property of Addition.
Step-by-step explanation:
We are given the following information in the question:
We are given the expression:
[tex]7x + (5+6x) = (7x+5)+6x[/tex]
We have used the associative property of addition.
Associative property of addition:
The associative property states that we can add regardless of how the numbers are grouped. By grouped it is meant how you use parenthesis are used. In other words, if we are adding, it does not matter where you put the parenthesis. Whatever may be the order of addends, the sum will always be same.Use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 14x + 8 as ordered pairs.
For the equation y = 14x + 8, the ordered pairs with x values of 1, 2, 3, and 4, calculated by substituting these x-values into the equation, are (1,22), (2,36), (3,50), and (4,64).
Explanation:The equation in question is a linear equation, y = 14x + 8 , and you've been asked to use the x-values: 1, 2, 3, and 4 to write the solutions as ordered pairs. To find the corresponding y-values, substitute these x-values one by one into the equation.
For x = 1, y = 14*1 + 8 = 22, so the ordered pair is (1,22) For x = 2, y = 14*2 + 8 = 36, so the ordered pair is (2,36) For x = 3, y = 14*3 + 8 = 50, so the ordered pair is (3,50) For x = 4, y = 14*4 + 8 = 64, so the ordered pair is (4,64)
These points plotted on a graph represent the dependence of y on x.
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To determine the solutions of the equation y = 14x + 8 for x-values 1, 2, 3, and 4, each x-value is substituted into the equation to find the corresponding y-values, resulting in ordered pairs (1,22), (2,36), (3,50), and (4,64).
Explanation:To find solutions of the equation y = 14x + 8 using the x-values 1, 2, 3, and 4, we will substitute each x-value into the equation and solve for y to obtain the corresponding y-value.
These ordered pairs represent solutions for the given linear equation and show the dependence of y on x.
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How many times can 4 go into 69
Explain how you can use a model to find 6x17
Answer:
The required model is shown below:
Step-by-step explanation:
Consider the provided information.
We need to use partial products model to solve 6×17
The partial product is the product of parts of each factor.
Here Multiplicand is 6 and Multiplier is 17
We can rewrite 17 as 1 ten and 7 ones. i.e 17=10+7
Therefore,
6×17 = 6(10+7)
6×17 = 6×10+6×7 [Distributive property]
6×17 = 60+42 = 102
Hence, the required model is shown below:
What is larger
a. 3.2x10^5
b.4.2x10^3
c. 1.1x10^5
Which scatter plot shows a negative nonlinear association?
Answer:
The second option
Step-by-step explanation:
The answer is the second option because you can clearly see that it is nonlinear since there is no straight line, but you can still see it going at a negative rate.
Tammy and Jodi assembled 420 circuit boards in 8 hours. The next day they assembled 36 more circuit boards in the same amount of time. What was their average rate on the second day? A. 87 boards per hour B. 70 boards per hour C. 57 boards per hour D. 36 boards per hour
Answer:
C
Step-by-step explanation:
Pls help me I really need it
A jeweler buys a ring from a jewelry maker for $125. He marks up the price by 135% for sale in his store. What is the selling price of the ring with 7.5% sales tax?
Answer:
$315.78
Step-by-step explanation:
Does 17/20 repeat or terminate
Susie is an organic vegetable grower the perimeter of her rectangular vegetable garden is 72 yards the width of the vegetable garden is 9 yards how long is the vegetable garden
What is the equation of this line in standard form? A. −6x+7y=−11 B. −6x+5y=13 C.
−6x+7y=11 D. −7x+6y=−11
Answer:
The answer is 6x-5y=-13
Step-by-step explanation:
jamil has 3 pet lizards. the pet store owner said that jamil will need to buy a total of 36 crickets to feed his lizards if each lizard eats the numberbof crickts how many crickts does each lizard eat?
Help me I want to understand this finnall part
Round 846 divided by 11 to the nearest tenth
‘Mathnificent’ is a math tutoring service. The first year it was open, it had 5 students. If 3 new students enroll each year, which of the following equations represents how many students will be enrolled in x years?
A. y = 5x - 3
B. y = 5x + 3y
C. y = 3x - 5
D. y = 3x + 5
Final answer:
The equation representing the number of students enrolled after x years is y = 3x + 5, taking into account the initial number of students and the annual enrollment of new students.(Option D)
Explanation:
To determine the equation that represents the number of students enrolled in Mathnificent tutoring service in x years, we start with the initial condition that there were 5 students in the first year. Since 3 new students enroll each year, we add 3 to the number of students for each subsequent year. The total number of students after x years can be represented by adding the product of 3 (the number of new students enrolling each year) and x (the number of years) to the initial number of students, which is 5.
The correct equation to represent this scenario is y = 3x + 5. This equation indicates that there is a constant rate of new students enrolling each year (3), and we are adding these to the initial count (5).
Assume the $10,000 Treasury bill, 4% for 13 weeks. Calculate the effective rate of interest
To find the effective rate of interest on a 13-week Treasury bill with a 4% rate, you first convert the discount rate to an annualized rate by dividing the time period by the number of weeks in a year. As Treasury bills do not compound within the maturity period, the EAR is simply the annualized rate, which in this case is 16%.
Explanation:To calculate the effective rate of interest for a $10,000 Treasury bill with a 4% interest rate for 13 weeks, we use the formula for the effective annual rate (EAR). The formula considers the nominal annual interest rate and the number of compounding periods per year.
The nominal annual interest rate is given by the face value minus the price paid for the Treasury bill, divided by the price paid, and then multiplied by 100 to get the percentage. However, the question only provides the interest rate but not the purchase price, so I'm assuming this given interest rate is the discount rate. First, we need to calculate the annualized discount rate and then convert it to the effective annual rate since Treasury bills are typically discounted securities.
To calculate the annualized discount rate:
Convert the 13 weeks to a fraction of the year: 13/52 = 0.25 years.Multiply the stated discount rate (4%) by the annualization factor (1/0.25): 4% * (1/0.25) = 16%.Now, to convert the annualized discount rate to the effective annual rate (EAR):
EAR = (1 + nominal interest rate / number of compounding periods) ^ number of compounding periods - 1.Since Treasury bills do not have compounding within their maturity period, the number of compounding periods is 1.EAR = (1 + 0.16 / 1) ^ 1 - 1 = 0.16 or 16%.Note: If the purchase price was lower than the face value to account for the 4% interest over 13 weeks, the effective annual rate would be higher than 16%.