Answer:
Approximately 53 mins
Step-by-step explanation:
Yard mowed by Michael = ⅓ of the yard
Yard mowed by Mel = 1 - ⅓ = [tex] \frac{1}{1} - \frac{1}{3} = \frac{3 - 1}{3} = \frac{2}{3} [/tex]
Rate at which Mel can mow a yard = ¾ of the yard in 1 hour
That is, it would take 1 hr to mow ¾ of the yard.
If ¾ yard requires 1 hr, then,
⅔ yard would require x hr
Thus:
x*¾ = 1*⅔
[tex] \frac{3x}{4} = \frac{2}{3} [/tex]
Cross multiply
[tex] 3(3x) = 4(2) [/tex]
[tex] 9x = 8 [/tex]
Divide both sides by 9
[tex] x = \frac{8}{9} [/tex]
It would take Mel [tex] \frac{8}{9} hr [/tex] to finish mowing her part, which is approximately 53 mins. [tex] (\frac{8}{9}*60mins = 53.3mins [/tex].
Answer:
53 min
Step-by-step explanation:
Create an equation modeling the scenario. Use the equation to solve for the missing number. In your final answer, include the equation and all necessary calculations.
Twice the sum of a number and seven is three times the number. 20 points
Answer:
Number = 14
Step-by-step explanation:
It is given that,
Twice the sum of a number and seven is three times the number
Let the number be x. Twice of the number is 2x. Three times of the number is 3x.
So,
2(x+7)=3x is the equation that models the given scenario
Opening brackets on LHS,
2x+14=3x
Subtracting 2x on both the sides
2x-2x+14=3x-2x
14=x
So, the number is 14.
The number is 14.
The calculation is as follows:
Let the number be x. Twice of the number is 2x. Three times of the number is 3x.
Based on the above information, the calculation is as follows:
2(x+7)=3x
2x+14=3x
x = 14
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A stone is thrown vertically upward from a platform that is 20 feet high at a rate of 160 ft/sec. Using the quadratic function h(t) = -16t^2+160t+20 to find how long will it take the stone to reach its maximum height, and then find the maximum height. Round your answer to the nearest tenth
Answer:
5 seconds
1220 ft
Step-by-step explanation:
Step 1: Know when the stone reaches the maximum height
We know the maximum or minimum height of a parabola is at the vertex so we need to find the vertex
Step 2: Calculate the vertex
The t coordinate of the vertex can be calculated with [tex]\frac{-b}{2a}[/tex]
b = 160
a = 16
[tex]t=\frac{-(160)}{2(-16)}\\t=\frac{-160}{-32}\\t=5[/tex]
Step 3: We know the t coordinate we can find the height at that time
[tex]h_{(t)} =-16(5)^{2} +160(5)+20\\h_{(t)}=16(25)+ (800)+20\\h_{(t)}=400+ 800+20\\h_{(t)}=1220[/tex]
Therefore the stone reaches its maximum height of 1220 ft in 5 secs
Answer:
The maximum height of 420 feet is reached after 5 seconds.
Step-by-step explanation:
The CEO of a large corporation asks his Human Resource (HR) director to study absenteeism among its executive-level managers at its head office during the year. A random sample of 30 executive level managers reveals the following: Absenteeism: Sample mean = 7.3 days, Sample standard deviation=6.2 days 18 mid-level managers out of the 30 randomly selected mid-level managers, cite stress as a cause of absence. (a) Construct a 90% confidence intervalestimate for the mean number of absences for mid- level managers during the year.(b) Construct a 98% confidence intervalestimate for the population proportion of mid-level managers who cite stress as a cause of absence. (c) What sample size is needed to have 95% confidence in estimating the population mean absenteeism to within 1.5 days if the population standard deviation is estimated to be 8 days? (d) How many mid-level managers need to be selected to have 99% confidence in estimating population proportion of mid-level managers who cite stress as a cause of absence to within +0.075 if no previous estimate is available?
Answer:
Following are the answer to this question:
Step-by-step explanation:
Given:
n = 30 is the sample size.
The mean [tex]\bar X[/tex] = 7.3 days.
The standard deviation = 6.2 days.
df = n-1
[tex]= 30-1 \\ =29[/tex]
The importance level is [tex]\alpha[/tex] = 0.10
The table value is calculated with a function excel 2010:
[tex]= tinv (\ probility, \ freedom \ level) \\= tinv (0.10,29) \\ =1.699127\\ = t_{al(2x-1)}= 1.699127[/tex]
The method for calculating the trust interval of 90 percent for the true population means is:
Formula:
[tex]\bar X - t_{al 2,x-1} \frac{S}{\sqrt{n}} \leq \mu \leq \bar X+ t_{al 2,x-1} \frac{S}{\sqrt{n}}[/tex]
[tex]=\bar X - t_{0.5, 29} \frac{6.2}{\sqrt{30}} \leq \mu \leq \bar X+ t_{0.5, 29} \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 \frac{6.2}{\sqrt{30}}\leq \mu \leq7.3 +1.699127 \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 (1.13196)\leq \mu \leq7.3 +1.699127 (1.13196) \\\\=5.37 \leq \mu \leq 9.22 \\[/tex]
It can rest assured that the true people needs that middle managers are unavailable from 5,37 to 9,23 during the years.
Density is a unit rate measured in units of mass per unit of volume the mass of the Garnett is 5.7 grams the volume is 1.5 cubic centimeters what is the density of the Garnet
Answer:
The density is 3.8 g
Step-by-step explanation:
D=M/V (Density= Mass divided by Volume)
5.7 divided by 1.5 is 3.8
Which are solutions of the equation x2 - 16 = 0? Check all that apply.
x= -8
x=-4
x=-2
x= 2
x= 4
x=8
Answer:
B) -4 and E) 4
Step-by-step explanation:
Simplify (2x)/3 + (9-x)/2 FYI. I'm pretty sure that x+27/6 isn't the answer but idk
Answer:
(27+x)/6
Step-by-step explanation:
(2x)/3 + (9-x)/2
Get a common denominator of 6
(2x)/3 *2/2 + (9-x)/2*3/3
4x/6 +3(9-x)/6
Distribute
4x/6 + (27-3x)/6
Combine like terms
(27+4x-3x)/6
(27+x)/6
A pool measures 15 feet by 17 feet. A cement walkway is added around the pool, to both the width and the length. The area of the pool and the cement walkway is now 483 square feet. What is the width of the cement walkway?
Answer:
21 feet
Step-by-step explanation:
The pool has dimension 15 feet by 17 feet, which is in the form of a rectangle.
The area of the pool = length × width
= 17 × 15
= 255 square feet
Area of the pool and cement walkway = 483 square feet
Area of walkway = area of pool and walkway - Area of pool
= 483 - 255
= 228 square feet
Let's assume that the cement walkway has equal thickness across its perimeter, so that;
the dimension of the pool and the cement walkway = 23 feet × 21 feet
The width of the cement walkway is 21 feet.
Find the exact sum or difference. 0.78 – 0.52 = A. 0.16 B. 0.26 C. 0.24 D. 0.14
Which decimals are less than 2.312? Select all that apply. A. 2.311 B. 2.4 C. 2.32 D. 2.3 E. 2.31 F. 2.313
Answer:
a c d
Step-by-step explanation:
[tex]\frac{-23}{30} + \frac{5}{48}[/tex]
Answer:
(-53)/80
Step-by-step explanation:
Simplify the following:
-23/30 + 5/48
Put -23/30 + 5/48 over the common denominator 240. -23/30 + 5/48 = (8 (-23))/240 + (5×5)/240:
(8 (-23))/240 + (5×5)/240
8 (-23) = -184:
(-184)/240 + (5×5)/240
5×5 = 25:
(-184)/240 + 25/240
-184/240 + 25/240 = (-184 + 25)/240:
(-184 + 25)/240
-184 + 25 = -159:
(-159)/240
The gcd of -159 and 240 is 3, so (-159)/240 = (3 (-53))/(3×80) = 3/3×(-53)/80 = (-53)/80:
Answer: (-53)/80
Find the distance between (-1, 4) and (1,-1).
Answer:
The answer is
[tex] \sqrt{29} \: \: units[/tex]Step-by-step explanation:
To find the distance between two points we use the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-1, 4) and (1,-1)
The distance between them is
[tex]d = \sqrt{ ({ - 1 - 1})^{2} + ({4 + 1})^{2} } \\ d = \sqrt{ ({ - 2})^{2} + {5}^{2} } \\ d = \sqrt{4 + 25} [/tex]We have the final answer as
[tex]d = \sqrt{29} \: \: \: units[/tex]Hope this helps you
The grocery store sells laundry detergent for $11.99 for 84 oz. What is the price per ounce?
Round to the nearest hundredth.
Answer:
$0.14
Step-by-step explanation:
Hello!
To find the price per ounce you divide the total cost by the number of ounces
11.99/84 = 0.1427
Round to nearest hundredth
0.14
The answer is $0.14
Hope this helps!
30 POINTS PLEASE HELP!!! 4. The following equations represent the same quadratic function written in standard, vertex, and intercept form, respectively. f (x)=0.5x^2 +x-1.5, f (x)=0.5 (x+1)^2 -2, f (x) =(0.5x+1.5) (x-1) Based on these equations, which ofthe following is a trait of the graph of f (x) ? A: the range is y>= -2 B: the line of symmetry is x=0.5 C: the graph falls toward negative infinity to both the left and right D: the y-intercept is (0, -2) Answer correctly and I'll mark Brainliest! Thank you in advance, i was caught on this practice problem
Answer:
A
Step-by-step explanation:
So we have the quadratic equation and it's written in three equivalent forms:
[tex]f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)[/tex]
Let's determine the characteristics of the quadratic equation with the given equations.
From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.
Also, the constant term is -1.5, so the y-intercept is (0,-1.5).
The second equation is the vertex form. Vertex form has the format:
[tex]f(x)=a(x-h)^2-k[/tex]
Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).
And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:
[tex][-2,\infty)[/tex]
This also means that the end behavior of the graph as a x approaches negative and positive infinity is positive infinity because the graph will always go straight up.
Also, the third form is the factored form. With that, we can solve for the zeros of the quadratic. The zeros are:
[tex]0.5x+1.5=0\text{ and } x-1=0\\0.5x=-1.5 \text{ and }x=1\\x=-3\text{ and }x=1[/tex]
Therefore, the graph crosses the x-axis at x=-3 and x=1.
So, from the three equations, we gathered the following information:
1) The graph curves upwards.
2) The roots of zeros of the function is (-3,0) and (1,0).
3) The y-intercept is (0,-1.5).
4) The vertex is (-1,-2). This is also the minimum point.
5) Therefore, the range of the graph is all values greater than or equal to -2.
6) The end behavior of the graph on both directions go towards positive infinity.
Therefore, our correct answer is A.
B is not correct because the line of symmetry (or the x-coordinate of the vertex) here is -1 and not 1/2.
C is not correct because the graph goes towards positive infinity since it shoots straight up.
And D is not correct because the y-intercept is (0,-1.5).
Step-by-step explanation:
So we have the quadratic equation and it's written in three equivalent forms:
\begin{gathered}f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)\end{gathered}
f(x)=0.5x
2
+x−1.5
f(x)=0.5(x+1)
2
−2
f(x)=(0.5x+1.5)(x−1)
Let's determine the characteristics of the quadratic equation with the given equations.
From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.
Also, the constant term is -1.5, so the y-intercept is (0,-1.5).
The second equation is the vertex form. Vertex form has the format:
f(x)=a(x-h)^2-kf(x)=a(x−h)
2
−k
Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).
And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:
Three boys cut out hundredths decimal models. Derrick does not shade any of his models. Ari shades half of one model. Wesley shades two models and one tenth of another model. What decimal represents the amount each boy shades?
Derrick's value = 0
Ari's value = 0.5
Wesley's value = 2.1
============================
Explanation:
Derrick doesn't shade anything, so his value is 0.
Ari shades half of one model, so 1/2 = 0.5 is his value
Wesley shades 2 full models, plus 1/10 = 0.1 of another one, leading to 2+0.1 = 2.1 as his value.
The fractional amount of the model shaded by each of the boys are :
Derrick = 0.0Ari = 0.005Wesley = 2.001The size of each model cut out = 1/100 = 0.01
DERRICK :
Shaded none = 0ARI :
shades half of one model = (1/100) ÷ 2 = 0.005WESLEY
shades 2 and (1/10 of another)2 + (0.1 × 0.01) = 0.0012 + 0.001 = 2.001Therefore, the amount shaded by each of the boys represented as a decimal are :
DERRICK = 0.0ARI = 0.005WESLEY = 2.001Learn more :https://brainly.com/question/13218948
What is an equation of the line that passes through the point (-4, -7) and is
parallel to the line 3x-Y = 4?
Answer:
The answer is
[tex]y = 3x + 5[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the line parallel to 3x - y = 14 we must first find the slope of 3x - y = 14.
So we have
y = 3x - 14
Comparing with the general equation above
Slope / m = 3
Since the lines are parallel their slope are also the same
So slope of parallel line = 3
Equation of the line using point ( - 4 , -7) and slope 3 is
[tex]y + 7 = 3(x + 4) \\ y + 7 = 3x + 12 \\ y = 3x + 12 - 7[/tex]We have the final answer as
[tex]y = 3x + 5[/tex]Hope this helps you
Find two consecutive integers such that the sum of the greatest integer and twice the lesser integer is 40.
Answer:
13 and 14.
Step-by-step explanation:
So we have two consecutive integers.
Let's call the first integer a.
Since the integers are consecutive, the other integer must be (a+1) (one more than the last one).
We know that the sum of the greatest integer (or a+1) and twice the lesser integer (a) is 40. Therefore, we can write the following equation:
[tex](a+1)+2(a)=40[/tex]
The first term represents the greatest integer. The second term represents 2 times the lesser integer. And together, they equal 40.
Solve for a. Combine like terms:
[tex]a+1+2a=40\\3a+1=40[/tex]
Subtract 1 from both sides. The 1s on the left cancel:
[tex](3a+1)-1=(40)-1\\3a=39[/tex]
Divide both sides by 3:
[tex]\frac{3a}{3}=\frac{39}{3}\\a=13[/tex]
Therefore, a or the first integer is 13.
And the second integer is 14.
And we can check:
14+2(13)=14+26=40
Let the two consecutive integers be x and x + 1.
According to the question,
★ Greatest integer = x + 1
★ Lesser integer = x
The sum of the greatest integer and twice the lesser integer is 40. [ Given ]
⇒ ( x + 1 ) + 2 ( x ) = 40
⇒ x + 1 + 2x = 40
⇒ 3x + 1 = 40
⇒ 3x = 40 - 1
⇒ 3x = 39
⇒ x = 39/3
⇒ x = 13
★ x + 1 = 13 + 1 = 14
Can someone please help me find the answer for this please. Thank you.
Answer:
3
Step-by-step explanation:
Write down the expression exactly as it is given.
[tex] \dfrac{3y - 9}{x} = [/tex]
Now write the expression again, but replace x with 3, and replace y with 6.
[tex] = \dfrac{3 \times 6 - 9}{3} [/tex]
Now simplify the numerator using the correct order of operations.
[tex] = \dfrac{18 - 9}{3} [/tex]
[tex] = \dfrac{9}{3} [/tex]
Now divide 9 by 3.
[tex] = 3 [/tex]
Answer: 3
A book sold 33,200 copies in its first month. Suppose this represents 7.4% of the number of copies sold to date. How many copies have been sold to date?
Answer:
448,648
Step-by-step explanation:
33,200/.074 = 448,648
Answer: 448648
Step-by-step explanation:
33,200 copies represent 7.4% of the total amount
-----------------------------------------------------
#1 33,200 ÷ 7.4%
- this is because how we get 33,200 by calculation is use the total amount and times 7.4% to get 33,200. So we are just working backwards. Since it was times before, then we divide after.
33,200÷7.4%
=33,200÷0.074
≈448648 (you can't round up when the real amount is less the exact amount)
Find the pattern and use inductive reasoning to predict the next number in the sequence 100,120,60,80,40
Answer:
The next number going up or down?
Step-by-step explanation:
Down
20
5
Up
180
Answer:
60
Step-by-step explanation:
The sequence is to first add 20 and then divide by 2. To find the next number in the sequence, add 20. This means the next number in the sequence is 40+20=60.
(3xy2x2y−3)2(9xy−3x3y2)−1.
Answer:
-18x square y -+36xy square + 54 xy - 1
Step-by-step explanation:
collect the terms, calculate the product, collect the terms, then distribute
. In a study about the relationship between the age of a person and the preference for digital vs analog watches, which of the following could be valid data sets? (Choose all that apply) A.height of a person B.watch preference for those who are less than 30 years C.the quality of the strap of the watch D.type of watch, digital or analog D.age of a person
Answer:
B and the first d and second one.
Step-by-step explanation:
The age is a big factor and b can showing the preference per age
find the unknown angle please help
Answer:
60
Step-by-step explanation:
The exterior angle is the sum of the opposite interior angles.
120 = x + the other angle next to x but not the one next to 120
Since it is an isosceles triangle
120 = x + x
120 = 2x
60 = x
Hope that helped!!! k
A line segment (DE) joining the midpoints of two sides of a triangle is
parallel
to the third sid
Answer:
This is called a mid segment theorem in which the al ine segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side.
Step-by-step explanation:
Suppose we have a triangle ABC. Then the midpoints can be located as D, E and F. If we join D , E and F another triangle is formed.
From the figure we can see that
AE≅ CE
AD≅DB
BF≅CF
BECAUSE all the given points are the midpoints which divide the lines into two equal halves.
If we increase the line DE to a point L we find out that DL is parallel to BC i.e. it does not meet at any point with BC. ( the two lines do not meet)
(1)
If we join C with L we find out that the the line DE is half in length to the line BC.
AS
AE= CE (midpoints dividing into equal line segements.)
LE= DE
Triangle CEL= Triangle DEF
so
DL= BC
But DE = 1/2 DL
therefore
DE= 1/2 BC (2)
Therefore from 1 and 2 we find that a line segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side
which expression is equivalent to the given expression 8 square root of 6
Answer:
[tex]\sqrt{384}[/tex]
Step-by-step explanation:
[tex]\sqrt{384}[/tex] is equivalent to [tex]\sqrt[8]{6}[/tex]
An equivalent expression to the given expression [tex]8\sqrt{6}[/tex] is [tex]\sqrt{384}[/tex]
What is expression?"It is a mathematical statement which consists of numbers, variables and some mathematical operations."
What are equivalent expressions?"The expressions that work the same even though they look different."
For given question,
We have been given an expression [tex]8\sqrt{6}[/tex]
We know, for a positive real number a, [tex]\sqrt{a^2}=a[/tex]
So, we can write 8 as [tex]8=\sqrt{8^2}[/tex]
So, given expression becomes [tex]\sqrt{8^2}\sqrt{6}[/tex]
We know, for any positive real numbers m, n, [tex]\sqrt{m} \sqrt{n}=\sqrt{mn}[/tex]
[tex]\sqrt{8^2}\sqrt{6}[/tex]
= [tex]\sqrt{8^2\times 6}[/tex]
= [tex]\sqrt{64\times 6}[/tex]
= [tex]\sqrt{384}[/tex]
So, an expression [tex]8\sqrt{6}[/tex] is equivalent to expression [tex]\sqrt{384}[/tex]
Therefore, an equivalent expression to the given expression [tex]8\sqrt{6}[/tex] is [tex]\sqrt{384}[/tex]
Learn more about equivalent expressions here:
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Circle O is shown. Line segments A C and B D are diameters. The measure of arc A B is (3 x minus 70) degrees and the measure of arc D C is (x + 10) degrees. What is mArc B C? 50° 80° 100° 130° In circle O, AC and BD are diameters. In circle O, AC and BD are diameters.
Answer:
Option (4)
Step-by-step explanation:
From the given circle O,
AC and BD are the diameters intersecting at point O.
∠AOB ≅ ∠COD [Vertical angles]
Therefore, length of intercepted arcs by these central angles will be same.
[tex]m(\widehat{AB})=m(\widehat{CD})[/tex]
(3x - 70) = (x + 10)
3x - x = 70 + 10
2x = 80
x = 40
Since, [tex]m(\widehat{AB})+m(\widehat{BC})=180[/tex] [Since AC is a diameter]
(3x - 70) + [tex]m(\widehat{BC})[/tex] = 180°
3(40) - 70 + [tex]m(\widehat{BC})[/tex] = 180°
[tex]m(\widehat{BC})[/tex] = 180° - 50°
= 130°
Therefore, Option (4) will be the correct option.
Answer:
130 degrees
Step-by-step explanation:
List the next three numbers for the sequence: 25, 75, 300, 1500, ...
Answer: 2000
Step-by-step explanation:
Assuming that the Chinese population continues to grow at the same rate, how many years until the population reaches 1.5 billion?
Answer:
29 years
Step-by-step explanation:
The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method
after x years, the population will be
1.3 * 1.0049^x
so you just need to solve
1.3 * 1.0049^x = 1.5
1.0049^x = 1.5/1.3
x log 1.0049 = log(1.5/1.3)
x = log(1.5/1.3)/log(1.0049)
x = 0.062 / 0.002122
x = 29.25 years
Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn
least to greatest again? I can't visualize this one.. -11/5, -2.4, 1.6, 15/10, -2.25 Thanks
Answer:
Hey again! Just remember about the number lines. If it's easier, you can use a calculator to divide the fractions to make them easier to visualize in decimal form.
The answer to this one is:
-2.4
-2.25
-11/5 (which is -2.2)
-15/10 (1.5)
-1.6
What is the answer ?
Answer:
according to circle theorem the angle in the center is twice of the angle of the angle form by the cords of the circle.
Since, the center circle is 90 theta is 45 degrees
Step-by-step explanation:
*Another approach
Given the following probability distribution, what is the expected value of the random variable X? X P(X) 100 .10 150 .20 200 .30 250 .30 300 .10 Sum 1.00
Answer: 1
Step-by-step explanation: