The standard deviation of the sample of monthly salaries is 2.74
What is Standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
>Standard deviation gauges a dataset's dispersion from its mean.
>It is determined as the variance's square root.
Detailed Calculation:Mean = [tex]\frac{(8+6+12+11+13)}{5} = 10[/tex]
Variance = [tex]\frac{((8-10)^{2}+(6-10)^{2}+(11-10)^{2}+(13-10)^{2} )}{(5-1)} = 6[/tex]
Standard deviation = [tex]\sqrt{7.5} = 2.7386[/tex]
when rounded off to two decimals 2.7386≈2.74.
The standard deviation of the sample of monthly salaries is 2.74
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A natural number is choosen at random from the 100 natural number. what is the probability that number so chosen is devisible by 3?
Answer:
33/100
Step-by-step explanation:
The 100 natural numbers are from 1-100.
In order to find the total numbers divisible by 3, divide 100 by 3:
100/3 = 33.33
Put 33.33 into integer form:
33.33 ==> 33 numbers divisible by 3.
Divide 33 by 100 to get the probability: 33/100
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solve the following exponential equation. express irrational solutions in exact form and as a decimal rounded to three decimal places. 3^1-4x = 4x
The irrational solution of an exponential function, 3⁽¹⁻⁴ˣ⁾ = 4ˣ in exact form, is equals to the 0.190 in a decimal rounded to three decimal places.
Exponential function:The exponential function is a mathematical function of the form f(x) = aˣ , where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The most commonly used exponential base is the transcendental number e, which is approximately equal to 2.71828.
We have given an exponential equation is
3⁽¹⁻⁴ˣ⁾ = 4ˣ
Require to solve this Exponential equation.
Now, 3⁽¹⁻⁴ˣ⁾= 4ˣ
taking logarithm both sides we get,
ln ( 3⁽¹⁻⁴ˣ⁾ ) = ln(4ˣ)
=> (1-4x) ln(3) = xln(4) [using ln( aˣ)= x ln(a) ]
=> ln (3) - 4x ln (3) = x ln (4)
=> ln (3) = x ln(4) + 4x ln(3)
=> ln (3) = x[ ln (4) + 4 ln (3) ]
=> x = ln (3) / [ ln (4) + 4 ln (3) ]
=> x ~ 0.190
Therefore, solution set is ln (3) / [ ln (4) + 4 ln (3) ].
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There were n signers of the Declaration of Independence. The oldest was Benjamin Franklin, who was y years old.
7 is 10% of y and n is 80% of y. How many signers were there?
Answer:
There were 56 signers.
Step-by-step explanation:
First, set up the two equations for the two situations we are given.
7 is 10% of y . . . . .(1):
[tex]7 = \frac{10}{100}(y)[/tex]
n is 80% of y . . . . .(2):
[tex]n = \frac{80}{100}(y)[/tex]
Now, solve for y in the 1st equation, and substitute y in the second equation to solve for n.
[tex]7 = \frac{10y}{100}[/tex]
[tex]700 = 10y\\[/tex]
[tex]70 = y[/tex]
[tex]n = \frac{80*70}{100}[/tex]
[tex]n = \frac{5600}{100}[/tex]
[tex]n = 56[/tex]
Answer:
56 signers--------------------------------
7 is 10% of y, find y:
7 = 0.1y ⇒ y = 70n is 80% of y, find n:
n = 0.8y = 0.8*70 = 56NO LINKS!! Write the first 5 terms of the geometric sequence
a1 = 6, r = 4
a1=
a2=
a3=
a4=
a5=
Step-by-step explanation:
since it is geometric sequence we will use the formula
[tex]tn = {ar}^{n - 1} [/tex]
a = 6
r = 4
The first term
T1(a) = 6
The second term
[tex]t2 = {a \times r}^{2 - 1} [/tex]
[tex]t2 = {6 \times 4}^{1 } = 24[/tex]
The Third Term
[tex]t3 = {a \times r}^{3 - 1} = {a \times r}^{2} [/tex]
[tex]t3 = {6 \times 4}^{2} = 6 \times 16 = 96[/tex]
The fourth term
[tex]t4 = {a \times r}^{4 - 1} = {a \times r}^{3} [/tex]
[tex]t4 = {6 \times 4}^{3} = 6 \times 64 = 384[/tex]
The fifth term
[tex]t5 = {a \times r}^{5 - 1} = {a \times r}^{4} [/tex]
[tex]t5 = {6 \times 4}^{4} = 6 \times 256 = 1,536[/tex]
i hope these helped
Answer:
6, 24, 96, 384, 1536, ...
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 6r = 4Substitute the given values of a and r into the formula to create an equation for the nth term:
[tex]a_n=6(4)^{n-1}[/tex]
To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.
[tex]\begin{aligned}\implies a_1&=6(4)^{1-1}\\&=6(4)^{0}\\&=6(1)\\&=6\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2&=6(4)^{2-1}\\&=6(4)^{1}\\&=6(4)\\&=24\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3&=6(4)^{3-1}\\&=6(4)^{2}\\&=6(16)\\&=96\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_4&=6(4)^{4-1}\\&=6(4)^{3}\\&=6(64)\\&=384\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_5&=6(4)^{5-1}\\&=6(4)^{4}\\&=6(256)\\&=1536\end{aligned}[/tex]
Therefore, the first 5 terms of the given geometric sequence are:
6, 24, 96, 384, 1536, ...Simplify using order of operations.
5³+28 /7-1
Answer:
128
Step-by-step explanation:
DO the "E"
125 + 28/7 -1 do the division next
125 + 4 - 1 now do the + or - or both
128
We can use the function to estimate the total amount of daylight for an entire year. enter the function into maple and use riemann sums (using midpoints for the height of the rectangles) to estimate the total amount of daylight when: a. n ______
A right Riemann sum has the formula A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.
what is is Riemann sum?A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.
Riemann sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,
where A is the curve's area under the evaluable interval,
f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)
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Solve the equation for x
Answer:
Question 35x + 100 = 7x + 30
100 - 30 = 7x - 5x
70 = 2x
x = 35
Question 43y + 16 = 5y
16 = 5y - 3y
16 = 2y
y = 8
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-________________________________
5(x+20) = 7x + 30=> 5x + 100 = 7x + 30
=> 100 – 30 = 7x – 5x
=> 70 = 2x
=> x = 70/2
=> x = 35
The value of x is 35.
________________________________
3y + 16 = 5y=> 16 = 5y – 3y
=> 16 = 2y
=> y = 16/2
=> y = 8
The value of y is 8.
_______________________________
Find the linearization of f(x) = √ x at a = 4
Answer:
Step-by-step explanation:
To find the linearization of the function f(x) = sqrt(x) at x = a, we can use the linearization formula:
f(x) ≈ f(a) + f'(a) (x - a)
To use this formula, we first need to find the value of f(a) and f'(a). At x = a = 4, the value of f(x) is f(4) = sqrt(4) = 2. The derivative of f(x) is f'(x) = 1/(2 * sqrt(x)), so the value of f'(a) is f'(4) = 1/(2 * sqrt(4)) = 1/4.
Substituting these values into the linearization formula, we get:
f(x) ≈ 2 + 1/4 (x - 4)
This is the linearization of f(x) = sqrt(x) at x = 4. It is an approximation of the function f(x) that is valid for values of x that are close to 4.
The Beta Club plans a dance as a fund-raiser. The band costs $650, decorations cost $45, and the refreshments cost $2.20 per person. The admission tickets are $6 each.
(a) How many tickets must be sold to break even?
(b) How many tickets must be sold to clear $700?
(c) If admission tickets are $7.50 each, how many must be sold to clear $700?
183 tickets must be sold to break even. The price at which a good or service must be provided in order to recoup its expenses of production.
How many tickets must be sold to break even?The price at which an asset must be sold in order to recover its acquisition and ownership costs is known as the break-even price. It can also be used to describe the price at which a good or service must be provided in order to recoup its expenses of production.The band costs $650,
decorations cost $45
refreshments cost $2.20 per person
let x be the no of ticket
Total cost = 650+ 45+ 2.20x
break even
tickets cost = $6
6x = 650+ 45+ 2.20x
6 x - 2.20x = 695
3.8 x = 695
x = 182.89
183 tickets must be sold to break even.
tickets must be sold to clear $700
700/6 =116.6
700/ 7.5 = 93.33
117 tickets must be sold to clear $700
94 tickets must be sold to clear $700, If admission tickets are $7.50 each.
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wrate 10 as a fraction of 30
Answer:
[tex]\frac{10}{30}[/tex]
Step-by-step explanation:
Answer:
10/30
Step-by-step explanation:
Courtney would like to estimate the net worth of all people in the US. The distribution of net worth of people in the
US is strongly skewed to the right. Courtney selects an SRS of size n = 15 from this population and calculates the
sample mean. What is the shape of the distribution of the sample mean for all possible simple random samples of
size 15 from this population?
The distribution of the sample mean for all possible simple random samples of size 15 from the population of net worth in the US will be approximately normal, with a mean of μ and a standard deviation of σ/√15.
Courtney's estimate of the net worth of all people in the US is strongly skewed to the right. This means that the majority of the population has a net worth that is lower than the average net worth. When Courtney selects an SRS of size n = 15 from this population and calculates the sample mean, the shape of the distribution of the sample mean for all possible simple random samples of size 15 from this population will be approximately normal.
The Central Limit Theorem states that if a population has a mean of μ and a standard deviation of σ, then the sampling distribution of the sample mean will be approximately normal, no matter what the shape of the population distribution is, as long as the sample size is large enough. Since Courtney's sample size of 15 is large enough, the sampling distribution of the sample mean will be approximately normal.
The sample mean will have a mean of μ, which is the population mean, and a standard deviation of σ/√n, where n is the sample size. Since Courtney's sample size is 15, the standard deviation of the sample mean will be σ/√15. This means that the sample mean will be normally distributed with a mean of μ and a standard deviation of σ/√15.
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ANSWER NOW NEED HELP
A red die, a blue die, and a green die
are rolled. Each die is labeled 1 to 6.
Find the probability of each event:
a) a 2 on the red die, a 3 on the blue
die, and a 4 on the green die
b) a 4 on the red die, an even number
on the blue die, and a number less
then 3 on the green die
Answer:
a)1/216
b)1/36
Step-by-step explanation:
p(2r)and p(3b) and p(4g)
1/6×1/6×1/6=1/216
p(4r) and p(even b) and p(no less than 3)
1/6×3/6×2/6=1/36
Can you please help me
Answer:
(c) see below
Step-by-step explanation:
You want the graph of the compound inequality x > -6 or x > -2.
GraphsThe graph of the inequality x > -2 is shown as the top selection.
The graph of the inequality x > -6 is shown as the bottom selection.
You will notice that the bottom graph overlaps and includes the top graph. Hence the "OR" of the inequalities will look like the bottom graph, attached.
4. Caroline baked cookies from a recipe that called for 2 cup of sugar. She planned to triple the recipe.
How much sugar did she need?
Answer:
Step-by-step explanation: So First you would need to multiply 2x3 because if you need to triple two cups you have to multiply so the answer is 6 cups
3x + 2 = 5x - (2x + 1).
Answer:
No solution
Step-by-step explanation:
The Gonzalez family and the Walker family each used their sprinklers last summer. The Gonzalez family's sprinkler was used for 35 hours. The Walker family's sprinkler was used for 40 hours. There was a combined total output of 2125L of water. What was the water output rate for each sprinkler if the sum of the two rates was 55L per hour?
Gonzalez Family Sprinklers :
Walkers Family Sprinklers :
Gonzalez Family Sprinklers used 15 liters and Walkers Family Sprinklers used 40 liters.
What was the water output rate for each sprinkle?From the information, the Gonzalez family's sprinkler was used for 35 hours. The Walker family's sprinkler was used for 40 hours. There was a combined total output of 2125L of water.
Let Gonzalez = g
Let Walker = w
The equation will be:
g + w = 55 .... i
35g + 40w = 2125 ....
From equation i g = 55 - w
Put the above into equation ii
35g + 40w = 2125
35(55 - w) + 40w = 2125
1925 - 35w + 40w = 2125
Collect like terms
5w = 2125 - 1925
5w = 200
Divide
w = 200 / 5
w = 40
Walkers Family Sprinklers used 40 liters.
Since g + w = 55
g + 40 = 55
g = 55 - 40
g = 15
Gonzalez Family Sprinklers used 15 liters.
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What is an equation of the line that passes through the points (-3, 8) and (6, 2)?
Answer:
y = (-2/3)x + 6
Step-by-step explanation:
To find the equation of the line that passes through the points (-3, 8) and (6, 2), we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the slope of the line, we can use the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. Plugging in the coordinates of the two points given in the problem, we get:
m = (2 - 8) / (6 - (-3)) = -6/9 = -2/3
Next, we need to find the y-intercept of the line. This is the point where the line crosses the y-axis, which means that the x-coordinate of this point is 0. Since we know the slope of the line and one of the points that it passes through, we can use the point-slope form of the equation of a line to find the y-intercept:
y - y1 = m(x - x1)
Substituting the values we have calculated above and setting x = 0, we get:
y - 8 = (-2/3)(0 - (-3))
Solving for y, we find that the y-intercept is 8 - (2/3) * 3 = 8 - 2 = 6.
Therefore, the equation of the line that passes through the points (-3, 8) and (6, 2) is:
y = (-2/3)x + 6
f(x) = 6x + 2 g(x) = -5x -9 Find the product of f and g.
Answer:30x^2 - 54x - 18
Step-by-step explanation: To find the product of f and g, we can simply multiply the expressions for f and g together. The product of f and g is:
(f * g)(x) = (6x + 2)(-5x - 9)
= -30x^2 - 54x - 18
So, the product of f and g is -30x^2 - 54x - 18
Elizabeth has a 1,200-word report to be finished in 3 weeks.
During the first week, she wrote every day (Sunday to Saturday) and wrote a total of 525 words. For the second week, she plans to write every day according to the equation y = 55z where y is
the total number of words written after x days.
Use the drop-down menus to correctly complete the statements below.
Last week, Elizabeth wrote at a pace of
This week, she plans to write at a pace of
She will still need to write To complete report
Answer:
Step-by-step explanation: for the first part, 525/7 = 75.
for the second part, 55y = x, which means 55 words per day for a total of (55*7) or 385
for the third part, 1200-525-385=290, not totally sure, but I think this is the answer, the text was a bit blurry and I couldn't understand everything, try not to following this blindly and just see if it makes sense. Hope I could help
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer: the answer is A
Step-by-step explanation:
The average mass of Stephen, Shamsul and Saravanan is 64 kg. Stephen's mass is 72 kg Shamsul's mass is 1.5 times Saravanan's mass Calculate Shamsul's mass in kg.
Answer:
72kg
Step-by-step explanation:
Stephen = 72
Saravanan = x
Shamsul = (x • 1.5) since Shamsul's mass is 1.5 times Saravanan's mass
1. make an equation:
( 72 + x + (x • 1.5) ) ÷ 3 = 64
2. solve it:
( 72 + x + (x • 1.5) ) ÷ 3 = 64
( 72 + x + (x • 1.5) ) = 64 • 3
( 72 + x + (x • 1.5) ) = 192
x + 1.5x = 192 - 72
2.5x = 120
x = 120 ÷ 2.5
x = 48
Thus shamsul's mass is:
48 • 1.5 = 72kg
Given the following piecewise function, evaluate ƒ(–2).
f(x) =
50+4 r
3x+3 x
2
2
Answer:
2
Step-by-step explanation:
The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 349 and a standard deviation of 24. According to the standard deviation rule, approximately 95% of the students spent between _____$ and _____$ on textbooks in a semester.
Question 12
Type numbers in the boxes.
1 points
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 16. According to the standard deviation rule, ______% of people have an IQ between 52 and 148. Do not round.
Question 13
Type numbers in the boxes.
10 points
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13. According to the standard deviation rule, only _____% of people have an IQ over 139.
Question 14
Type numbers in the boxes.
10 points
The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 310 and a standard deviation of: σ= 36.
According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester? _____
(b) is the correct response. the students spend on textbooks in a semester between $250 and $2,000
The Gaussian distribution is another name for the normal distribution. It is a typical continuous probability distribution with a standard deviation of one and a mean of zero.
The tails of the curve are asymptotic, extending to infinity without touching the horizontal axis, and the curve is unimodal and symmetric about the mean. Since the majority of observations are centered on the mean, mean=mode=median.
99.7% of the area under the curve is approximately -3, or 3 standard deviations from the mean, according to the 68-95-99.7 rule. The z score is determined utilizing the accompanying recipe:
For z=3, solve for both x by equating the z score formula with -3 and 3.
3 = x 235 5 x = (3 5) + 235 x = 250 for z=-3:
3 = x 235 5 x = (3 5) + 235 x = 220 A student spends between $220 and $250 on textbooks each semester.
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Full Question = The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $5. According to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?
a. Between 230 and 240 dollars.
b. Between 220 and 250 dollars.
c. Between 175 and 295 dollars.
d. Less than 220 dollars or more than 250 dollars.
e. Less than 230 dollars or more than 240 dollars.
(x + 10)(3x² + 5x - 2)
To expand the expression (x + 10)(3x² + 5x - 2), we can use the distributive property, which states that for any numbers a, b, and c, the product (a + b)(c) can be written as a * c + b * c. Applying this property to the given expression, we get (x + 10)(3x² + 5x - 2) = (x * 3x² + 10 * 3x²) + (x * 5x + 10 * 5x) + (x * -2 + 10 * -2) = 3x³ + 30x² + 5x² + 50x - 2x - 20. Combining like terms, we get 3x³ + 35x² + 51x - 20. Thus, the expanded form of the expression (x + 10)(3x² + 5x - 2) is 3x³ + 35x² + 51x - 20.
a regular pentagon with side lengths of 9 units is translated 2 units to the left. what is the length of one side of the pentagon after translation, in units? 2
9
5
8
The length of one side of the pentagon after translation is 9 units
Step-by-step explanation:
To be clear, "A translation is an isometry that translates all points of a figure the same distance in the same direction." The dimensions of any geometric figure will never change as a result of translation. The figure's measurements won't change; it will simply be moved from one location to another.
This means that even after being translated 2 units to the left, a regular pentagon with sides of 9 units will still have a side length of 9 units.
The length of one side of the pentagon after translation is 9 units(option B)
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Solve for h. If you answer, you get 14 points
Answer: 24
Step-by-step explanation:
Answer:
h = 24
Step-by-step explanation:
Find the width (in m) of the river in the illustration. (Round your answer to three significant digits.)
44°
100 m
Answer:
[tex]w \approx 96.6 \, \textrm{m}[/tex]
Step-by-step explanation:
See the attached image for my labeled diagram.
To solve for [tex]w[/tex], we can use the trigonometric ratio tangent.
[tex]\tan(\theta)=\dfrac{\textrm{opposite}}{\textrm{adjacent}}[/tex]
[tex]\tan(44\textdegree)=\dfrac{w}{100 \, \textrm{m}}[/tex]
↓ multiply both sides by 100m
[tex]100 \, \textrm{m} \cdot \tan(44\textdegree)=w[/tex]
↓ plug [tex]100\, \textrm{m} \cdot \tan(44\textdegree)[/tex] into a calculator
[tex]96.56887 \, \textrm{m} \approx w[/tex]
[tex]w \approx 96.56887 \, \textrm{m}[/tex]
↓ round to 3 significant figures
[tex]w \approx 96.6 \, \textrm{m}[/tex]
Which of the following sets represents a function? {(3, 5), (-1, 7), (3, 9)} {(1, 2), (3, 2), (5, 7)} {(1, 2), (1, 4), (1, 6)} unlimited attempts remain
The set {(1, 2), (1, 4), (1, 6)} represents a function because each value of x corresponds to only one value of y.
In contrast, the sets {(3, 5), (-1, 7), (3, 9)} and {(1, 2), (3, 2), (5, 7)} do not represent functions because they contain multiple values of x that correspond to the same value of y. Specifically, the set {(3, 5), (-1, 7), (3, 9)} contains two values of x (3 and -1) that correspond to the same value of y (7), while the set {(1, 2), (3, 2), (5, 7)} contains two values of x (3 and 1) that correspond to the same value of y (2).
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Help guys!!!!! This is due tomorrow morning!! :)
Answer:
Step-by-step explanation:
we are told that JK and KL sides are the same (b/c of the marks) so set them equal and solve for x
8x = 13x-15
8x - 8x + 15 = 13x - 8x -15 + 15
15 = 5x
divide by 5
3 = x
Use the fact that it's 180° around the interior angles of the triangle to solve for y
180 = 5y -3 + 52 + 76
52 = 5y - 3
55 = 5y
11 = y
4.
a) Find four consecutive even integers such that twice the sum of the second and third exceeds 3 times the first by 32.
b) The difference between two numbers is 24. Find the numbers if their sum is 88.
5.
a) Separate 60 into two parts so that 3 times the smaller added to 6 more than 6 times the smaller = 60.
b) A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of: Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.
1) 50 mph
2) 70 mph
3) x mph
4) (x+10)mph
5) (x-5)mph
The first, second, third, and fourth consecutive even integers must be greater than 10, 12, 14, and 16 respectively.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the four consecutive even integers be n, (n + 2), (n + 4) and (n + 6).
Such that twice the sum of the second and third exceeds 3 times the first by 32.
2{(n + 2) + (n + 4)} > 3(n) + 32.
2n + 4 + 2n + 8 > 3n + 32.
4n - 3n > 32 - 12.
n > 10.
So, the consecutive even numbers must all be greater than 10.
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