Convert this rational number to its decimal form and round to the nearest thousandth 5/7
The rational number, 5/7 converted to a decimal is 0.714.
What is the decimal?A rational number is a number that can be expressed as a fraction of two integers.
A decimal is a non-integer in which the integers are separated from the non integers by a point. In order to convert the fraction to a decimal, divide the numerator by the denominator.
5/7 = 0.714
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Wendy keeps her hamster, Fluffy, in a cage shaped like a rectangular prism that is 20 inches long, 14 inches wide, and has a volume of 4,340 cubic inches. Kenneth keeps his hamster, Speedy, in a cage that is the same length, but is 15 inches wide and has a volume of 5,250 cubic inches.
Speedy cage is 2 inches taller than fluffy cage.
How to find the volume of a rectangular prism?The volume of rectangular prism = lwh
where
l =lengthh = heightw = weightTherefore,
height of fluffy cage can be calculate as follows:
4340 = 20 × 14 × h
4340 = 280h
h = 4340 / 280
h = 15.5 inches
height of Kenneth cage can be calculate as follows:
5250 = 20 × 15 × h
5250 = 300h
h = 5250 / 300
h = 17.5 inches
height difference = 17.5 - 15.5 = 2.0 inches
Hence, speedy cage is 2 inches taller than fluffy cage.
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The equation of a line is -2x+5y=-20.
What is the x-intercept of the line?
The x intercept of the given line is (10, 0)
Finding the x intercept of a lineThe x intercept of a line is the point where the line crosses the x-axis
It is the point where the value of y is zero
Given the equation of a line -2x+5y = -20
Substitute y = 0 into the equation
-2x +5(0) = -20
-2x = -20
x = 10
Hence the x intercept of the given line is (10, 0)
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A number m is formed by writing all the prime numbers between 0 and 10 in ascending order. another number n is formed by writing all the square numbers between 0 and 10 in descending order: a)find m -n b)express(m-n) as a product of its prime factors
Answer:
(a) 1416
(b) 2 × 2 × 2 × 3 × 59
Step-by-step explanation:
The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357
The square numbers between 0 and 10 are 1, 4, 9 and in descending order 9,4.1so n = 941
m - n = 2357 - 941 = 1416
Unique prime factors of 1416 are 2,3,59
1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59
If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at
The vertex U' is located at (-4, -5)
How to determine the location of U'?The vertices are given as:
U = (-4, 5)
V = (-6, 2)
The rule of transformation is given as:
Reflection across the x-axis
This is represented as:
(x, y) => (x, -y)
So, we have:
U' = (-4, -5)
Hence, the vertex U' is located at (-4, -5)
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Complete question
Quadrilateral UVWX is reflected over the x-axis to form quadrilateral U′V′W′X′. If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at
Please answer correctly
[tex]\displaystyle\lim_{t\to \infty}(20+100(0.3)^{0.2t})=20+100\lim_{t\to \infty}0.3^{0.2t}=20+100\cdot 0=20[/tex]
I need help ASAP !?!?!?!?!!?!?!!??!
Answer:
First, do 15/12 then take that and divide by 500!
Step-by-step explanation:
(6+√-64)(3-√-16) Multiply. This is urgent, please explain this to me!
Answer:
50
Step-by-step explanation:
[tex]\sqrt{-64}[/tex] and [tex]\sqrt{-16}[/tex] can be expressed in complex form, with [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-64}[/tex] = [tex]\sqrt{64(-1)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{-1}[/tex] = 8i
[tex]\sqrt{-16}[/tex] = [tex]\sqrt{16(-1)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] = 4i
the factors can then be expressed as
(6 + 8i)(3 - 4i) ← expand using FOIL
= 18 - 24i + 24i - 32i² [ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 ]
= 18 - 24i + 24i + 32 ← collect like terms
= 18 + 32 + 0
= 50
How many solutions does the equation ||2x-3|-m|=m have if m>0?
There are three solutions of the equation ||2x-3|-m|=m have if m>0.
We have to estimate the number of solutions of the equation ||2x - 3| - m| = m where m > 0.
As we know in the modulus function
|x|= x if x>0
-x if x<0
0 if x=0
here given m > 0
if |2x-3|-m>0 then the modulus value will be ||2x-3|-m|= |2x-3|-m
Then, |2x - 3| - m = m
⇒|2x - 3| = m+m= 2m
⇒2x - 3 = 2m or -(2x-3)=2m
⇒2x - 3 = 2m or 2x-3=-2m
⇒2x = 3 ± 2m
⇒x = (3 ± 2m)/2
⇒x= (3 + 2m)/2 or (3 - 2m)/2
If |2x-3|-m<0 then then the modulus value will be | |2x-3|-m| = -(|2x-3|-m)
-(|2x-3|-m)=m
⇒m-|2x-3|=m
⇒-|2x-3|= m-m
⇒ |2x - 3| = 0
⇒2x = 3
⇒x = 3/2
Therefore The solution of the equation will be (3 + 2m)/2, (3 - 2m)/2, and 3/2.
Therefore there are three solutions of the equation ||2x-3|-m|=m have if m>0.
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can someone answer this question for me pls n thanks
Answer:
Mean: 29.5; Median: 26; Modes: 25, 26
Step-by-step explanation:
Add 10+12+25+25+26+26+30+31+33+34+47+55 = 354
Then divide it by 12 354/12 = 29.5
Mode are numbers that appear most often which in this case are 2 numbers, 25 and 26.
What assumption do we need to make to find a valid 99% confidence interval for the mean number of all workplace homicides per year
We have to assume that the sample mean is given , distribution is normal and sample size is also given.
Given confidence level 99%.
We have to answer the assumptions that are needed to make a valid 99% confidence interval.
Confidence interval can be made by formula of margin of error.
Margin of error is the difference between actual values and the calculated values.
Upper level of confidence interval=Mean+ margin of error
Lower level of confidence interval= Mean - margin of error.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the corresponding z value for the confidence level given ,
σ is population mean and n is sample size.
Hence to calculate the confidence interval we need population mean, sample size.
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In the following exercises, solve
635. The price that Tyler pays for gas varies directly with the number of gallons he buys. If 24 gallons cost him $59.76, what would 30 gallons cost?
Answer:
The cost of 30 gallons of gas is $74.7.
Step-by-step explanation:
Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.The cost 24 gallons is $59.76 to him.Now we need to find the cost of 30 gallons.To solve this problem use a direct variation formula.Solve for constant variation.Step 1 of 3
Here we need to find the cost of 30 gallons.
Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.
The cost of 24 gallons is $59.76 to him.
Let, x be the number of gallons and y be the cost or price for gas.
Use the formula for direct variation which is given by y=kx.
Step 2 of 3
Now substitute the value y=$59.76 and x=24.
Put value in y=kx, we get
[tex]$$\begin{aligned}&59.76=k \times 24 \\&k=2.49\end{aligned}$$[/tex]
Substitute value of k is y=kx, we get y=2.49x
Step 3 of 3
Now we need to find the value of y that is the cost for 30 gallons.
Again use direct variation formula y=kx and value of k and x, we get [tex]$y=2.49 \times 30$[/tex]
[tex]$$y=74.7$$[/tex]
Verbal
3. Can a function be its own inverse? Explain.
Answer:
The function can have its own inverse, that is, [tex]$f^{-1}(x)=f(x)$[/tex] and this type of function is called an involution. Example f(x)=6-x.
Step-by-step explanation:
A statement that a function can be its own inverse is given.
It is required to explain whether a function has its own inverse. Then explain whether the given statement satisfies the condition.
Step 1 of 3
Consider a function is f(x)=6-x.
This function is a continuous function for all values of x. This function is also a linear function. So, every continuous linear function is a one-to-one function.
So, this function is one-to-one.
Step 2 of 3
Consider f(x) as y and rewrite the equation.
The equation becomes [tex]$y=6-x$[/tex]
Solve the rewritten equation.
Add -6 on both sides of the equation.
[tex]$$\begin{aligned}&y=6-x \\&y-6=6-x-6 \\&y-6=-x\end{aligned}$$[/tex]
Step 3 of 3
Multiply by -1 on both sides.
[tex]$$\begin{aligned}&y-6=-x \\&(-1)(y-6)=(-x)(-1) \\&-y+6=x \\&x=6-y\end{aligned}$$[/tex]
Interchange x and y in solved equation.
[tex]$$\begin{aligned}&x=6-y \\&y=6-x\end{aligned}$$[/tex]
So, the inverse of the given function is [tex]$f^{-1}(x)=6-x$[/tex].
The function and inverse of the function are the same, that is, [tex]$f^{-1}(x)=f(x)$[/tex]
So, a function can have its own inverse. This type of function is called an involution.
Angela and Michelle shared some money in the ratio 4: 9 then Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20. Work out how much money was originally shared.
Using a system of equations, it is found that £52 was originally shared.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Angela's share.Variable y: Michelle's share.Variable z: Daniel's share.Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:
[tex]x = \frac{4t}{13}[/tex].[tex]y = \frac{9t}{13}[/tex]Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:
[tex]\frac{x}{2} + \frac{y}{3} = 20[/tex]
[tex]\frac{4t}{26} + \frac{9t}{39} = 20[/tex]
[tex]\frac{12t + 18t}{78} = 20[/tex]
30t = 20 x 78
t = 20 x 78/30
t = £52.
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For the following exercises, graph the absolute value function. Plot at least five points by hand for each graph.
37. y = | x − 1 |
The points used in plotting the graph of the absolute function as given are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).
What are the points to be used to plot the graph of the absolute function?The absolute function given is; y = | x − 1 |
Hence, by consider x-values; -2,-1,0,1,2....it follows that the corresponding y-values which are all positive by virtue of the absolute value symbol are; 3, 2, 1, 0, 1.
Hence, the points are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).
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An open-top rectangular box with square base is to be made from 100 square feet of material, as shown.
What is the largest possible volume of the box?
The largest possible volume of the given box is; 96.28 ft³
How to maximize volume of a box?Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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The length of a pencil, l cm, varies directly with its mass m g and inversely with its area of cross section A cm square when m=4 and A=0.4 l=18
The equation connecting L, m, A is L = [tex]\frac{1.8m}{A}[/tex]
What is a Variation?Variation is a mathematical relationship that shows how a certain variable behaves when other variables depending on it increase or decrease.
The types of variation are: Direct, indirect, joint and partial.
Analysis:
L ∝ [tex]\frac{m}{A}[/tex]
introducing a constant K to replace the proportionality sign,
L = [tex]\frac{Km}{A}[/tex]
when L = 18, m = 0.4, A = 0.4
18 = [tex]\frac{K(4)}{0.4}[/tex]
4K = 0.4 x 18
k = 1.8
Therefore the equation connecting the three variables is,
L = [tex]\frac{1.8m}{A}[/tex]
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vA sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.
[0.3105, 0.3695] expect to buy a new car next year.
These are the answer choices -
A) [0.3074, 0.3726]
B) [0.3105, 0.3695]
C) [0.3140, 0.3660]
D) [0.3392, 0.3408]
It is given that a sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year.
For large random samples, a confidence interval for a population proportion is given by
[tex]sample proportion[/tex] ± [tex]z * \frac{\sqrt{sample proportion (1 - sample proportion)} }{n}[/tex]
where z* is a multiplier number that comes from the normal curve and determines the level of confidence (see Table 9.1 for some common multiplier numbers).
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Given the legs of a right triangle are 8 and 4, what is the measure of the hypotenuse?
Answer:
Hypotenuse = 8.94
Step-by-step explanation:
Consider a TV set that consumes 120 W of electric power when it is on, and is kept on for an average of 6 h per day. For a unit electricity cost of 23 cents per kWh, determine the cost of electricity this TV consumes per month (30 days). The cost of electricity the TV consumes per month is $
The cost of electricity consumed by the TV per month is $4.968.
In the question, we are given that a TV set consumes 120W of electric power when switched on. It is kept on for a daily average of 6 hours per day. The number of days in the month is given to be 30 days. The cost per unit of electricity is 23 cents per kWh.
We are asked to find the cost of electricity the TV consumes in the month.
The daily energy consumed by the TV = Power*Daily time = 120*6 Wh = 720 Wh.
The monthly energy consumed by the TV = Daily energy*Number of days in the month = 720*30 Wh = 21600 Wh = 21600/1000 kWh = 21.6 kWh.
Hence, the total cost of electricity the TV consumes = Monthly energy*Per unit cost = 21.6*23 cents = 496.8 cents = $496.8/100 = $4.968.
Therefore, the cost of electricity consumed by the TV per month is $4.968.
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Probabilities that can be estimated from long-run relative frequencies of events are called _____ probabilities.
Probabilities that can be estimated from long-run relative frequencies of events are called objective probabilities.
What is Objective Probability?In contrast to intuition or guessing, objective probability refers to the chances or odds that an event will occur based on the examination of certain measurements. Each metric is based on factual observation, a documented observation, or a long history of data collection.
Instead of being dependent on anecdotes, firsthand knowledge, or hunches, the objective probability is based on statistics, experiments, and mathematical measures. Using objective probability is crucial in the realm of finance to prevent making irrational investment decisions.
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Raj was friends with his waitress so he left her a 90 percent tip.
Percents
Total
90%
10%
100%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
x
If his tip was $27.54, what is the value of x in the table above?
The value on the table above will be $30.6. Then the correct option is D.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Raj was friends with his waitress, so he left her a 90 percent tip.
If his tip was $27.54.
Then the value in the table above will be
⇒ $27.54 / 0.90
⇒ $30.6
Then the correct option is D.
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What is the degree of the polynomial?
The degree of the polynomial is 2
How to determine the degrees?The root of the polynomial is given as:
Root = x - 3i
The above expression is a complex root.
This means that the conjugate is also a root of the polynomial
So, we have
Roots = x - 3i and x + 3i
Multiply the roots
f(x) = (x - 3i)(x + 3i)
This gives
f(x) = x^2 + 9
The degree of the above equation is 2 i.e. the highest power
Hence, the degree of the polynomial is 2
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Hey Guys! I need some help. This is the question... Sara travels often for her job. The miles she traveled for the last seven work days are shown.
88, 72, 91, 65, 86, 93, 97
Which is the interquartile range of Sara's daily miles?
Using the median concept, it is found that the interquartile range of Sara's daily miles is of 21 miles.
What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the quartiles.The ordered data-set is given as follows:
65, 72, 86, 88, 91, 93, 97
There are 7 elements, hence the median is the 4th element, of 88. Then:
The first half is 65, 72, 86.The second half is 91, 93, 97.Since the quartiles are the medians of each half, the have that:
The first quartile is of 72 miles.The third quartile is of 93 miles.The interquartile range is of 93 - 72 = 21 miles.More can be learned about the median of a data-set at https://brainly.com/question/3876456
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^
Find (ff)(0).
f(x) = 3x - 2
a. 1
b. 0
Please select the best answer from the choices provided
ABCD
Answer:
a
Step-by-step explanation:
go it right on a mastery test
What is the value of the expression below?
Answer: 6
Step-by-step explanation:
This is a direct application of the exponent rule [tex](a^b)^c=a^{bc}[/tex].
15. Jeff packed tins in cartons standing upright and Sammy packed lying along the width of the carton. How many more tins are packed standing upright than lying along the width?
I think the answer is D
☆...hope this helps...☆
_♡_mashi_♡_
2. The name of the 1500-meter gold medal winner for each of the Olympics
from 1896 to 2000 is placed in a jar. (If a man has won the race more than
once, his name will be included for each race he won.)
A. If one name is drawn from the jar, which country has the best chance
of having a name drawn?
B. Three names are drawn without replacing the name after it is drawn.
What is the probability that the three winners will be from either
New Zealand or Australia?
pLEASE HELP
The probability shows that when one name is drawn from the jar, the country that has the best chance of having a name drawn is Great Britain.
How to calculate probability?It should be noted that Great Britain has won 6 golds in the 1500 meters Olympics and the next placed country is Kenya. In this case, the country that has the best chance of having a name drawn is Great Britain.
Note that New Zealand has 3 gold medals while Australia has 2 gold medals. Also, the Olympics has taken place 29 times.
The probability that the winners will be from either New Zealand or Australia will be:
= 3/29 + 2/29
= 5/29
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Answer
A. Great Britain
B. 3/29+2/29=5/29
please give me the brainliest.
In the xy-coordinate plane, point (1, 4) is on the line whose equation is y = 3x + b. What is the value of b ?
Answer:
b = 1
Step-by-step explanation:
since the point (1, 4 ) lies on the line then it satisfies the equation , that is
3(1) + b = 4
3 + b = 4 ( subtract 3 from both sides )
b = 1
help me find x please
Step-by-step explanation:
x² + (2x)² = (√180)²
x² + 4x² = 180
5x² = 180
x² = 180/5
x² = 36
x = √36 (and no - √36 because x ≥ 0)
x = 6