To solve the expression 64.3-3x2 to the third power divided by 2, simplify inside the parentheses, raise the result to the third power, and divide by 2.
Explanation:To solve the expression 64.3-3x2 to the third power divided by 2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and division from left to right.
First, let's simplify the expression inside the parentheses: 64.3-3x2 = 64.3-6 = 58.3
Next, we raise the result to the third power: 58.3^3 = 19671.327
Finally, we divide the result by 2: 19671.327 / 2 = 9835.6635
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.
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.
Is 22/15 less than 14/31?
Is 19/35 greater than 27/19
Is 15/25 greater than 22/44
Is 30/25 less than 29/30
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%.
Joshua has a baseball card collection.84 cards make up 70% of his collection how many cards are in his total collection
Help me I want to understand this finnall part
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.
A cone has a diameter of 18 units and height of 8 units. What is its volume?
Answer:
289
Step-by-step explanation:
btw i need the point pls dont use this
Final answer:
The volume of a cone with a diameter of 18 units and height of 8 units is approximately 678.58 cubic units, calculated using the formula V = 1/3πr²h.
Explanation:
The student is asking about the volume of a cone with a given diameter and height. To calculate the volume (V) of a cone, you can use the formula:
V = ⅓πr²h
where π (pi) is approximately 3.14159, r is the radius of the base of the cone, and h is the height of the cone.
The diameter is given as 18 units, so the radius (r) is half of the diameter, which is 9 units. The height (h) is given as 8 units. By substituting these values into the formula, the calculation for the volume is:
V = ⅓π(9 units)²(8 units)
V = ⅓π(81 units²)(8 units)
V = ⅓π(648 units³)
V = 216π units³
When we calculate this using the approximate value of π, the volume is:
V = 216 × 3.14159 units³
V = 678.58464 units³
The volume of the cone is approximately 678.58 cubic units.
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:
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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There are two containers of milk. There is twice as much milk in the first container as in the second. After using 2 gal. of milk from the second container and 3 gal. of milk from the first container, the second container had 4.5 times less milk than the first. How many gallons of milk were in both containers originally?
Let us say that:
V1 = initial gallons in first container
V2 = initial gallons in second container
From the problem statement, we can create the equations:
V1 = 2 V2
V1 – 3 = 4.5 (V2 – 2)
Combining the two:
2 V2 – 3 = 4.5 (V2 – 2)
2 V2 – 3 = 4.5 V2 – 9
2.5 V2 = 6
V2 = 2.4 gallons
V1 = 2 V2 = 4.8 gallons
So there are 4.8 gallons in the 1st container while 2.4 gallons in the 2nd container.
What is larger
a. 3.2x10^5
b.4.2x10^3
c. 1.1x10^5
I really need help on this.
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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The formula f=n/4+37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. Use the formula to estimate the temperature when n = 18 chirps/min. Round to the nearest whole number, if necessary. 41 42 37 46
[tex]f=\dfrac{n}{4}+37\\\\\text{substitute the value of n = 18 to the expression}\\\\f=\dfrac{18}{4}+37=4.5+37=41.5\approx42[/tex]
Answer: f = 42.
By using substitution of value n, temperature F in degree Fahrenheit is 42.
What is substitution method?"The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables."
Given
Formula to estimate the temperature F in degree Fahrenheit
f = [tex]\frac{n}{4} +37[/tex]
n = 18 chirps/min
Substituting n in the formula
f = [tex]\frac{n}{4} +37[/tex]
⇒ f = [tex]\frac{18}{4}+37[/tex]
⇒ f = 4.5 + 37
⇒ f = 41.5 ≅ 42 (nearest whole number)
Thus, temperature F in degree Fahrenheit is 42.
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Nendell saw at a diner if he bought one of each item and spent $7.50, how much did the drink cost
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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What is the best estimate of 49% of
598
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
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:
Round 846 divided by 11 to the nearest tenth
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.
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.What is 57.15% rounded to the nearest whole percent?
The number we would get when we round 57.15% to the nearest whole number is: A. 57%.
What is Nearest Whole Percent?Nearest whole percent means the number has no fractional part of decimal.
Given the number, 57.15%, to round it to the nearest whole number, digits 1 and 5 would be removed since the last number closer to the whole number is less than 5.
Thus, we would have 57%.
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-4w less than or equal to 20
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:
Is 632 a multiple of 4
‘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).
Does 17/20 repeat or terminate
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