Answer:
see below
Step-by-step explanation:
D miles / M miles per gallon = gallons used
Rewrite in simplest terms: -3(7n+5n+8)-8n
Answer:
28n+24
Step-by-step explanation:
3 ( 7 n + 5 n + 8 ) - 8 n
combine 7n and 5n to get 12n
3 ( 12n + 8 ) - 8
distribute 3 to 12n +8
36n+24-8n
combine like terms
28n+24
since ypu cant simply any more it stays like thats
*by the way there is an app that helps with equation and explains the process, its Microsoft Math Solver. hope it helped
find two consecutive even integers such that 8 times the first equals 7 times the second
Answer:
Step-by-step explanation:
let the consecutive even integers be 2x,2x+2
8×2x=7(2x+2)
16x=14x+14
16x-14x=14
2x=14
x=14/2=7
so numbers are 2×7,2×7+2
or
14,16
Find integra of xlnxdx
Answer:
[tex]\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Increase the power by 1, then divide by the new power.
Given indefinite integral:
[tex]\displaystyle \int x \ln x \:\: \text{d}x[/tex]
To integrate the given integral, use Integration by Parts:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
[tex]\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]
[tex]\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}[/tex]
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Consider the given figure. Two right angled triangles R T S, and U T S with their hypotenuse side intersecting at the point Q. The opposite side of both triangle have the same length. Using the SSS congruence criterion, what additional information is needed to show that ΔRST ≅ ΔUTS? A. RT ≅ US B. ∠S ≅ ∠T C. RQ ≅ QS D. ∠R ≅ ∠U\
Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U
When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.
From the given question, the following can be deduced:
RT ≅ US (given: opposite sides are equal)
and TS is a common side for the two triangles.
<TRS ≅ <RSU (alternate angle property)
<RTS ≅ <UST (right angle property)
<RTU ≅ <SUT (alternate angle property)
Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R ≅ <U.
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Answer:
Step-by-step explanation:
Cost of a CD: $19.95
Markup: 70%
Answer:
$33.915 for the cd
Step-by-step explanation:
70% of 19.95 = 13.965
19.95 + 13.965= 33.91
The express elevator in a skyscraper goes up 51 floors in 123/4 seconds. How many floors does the elevator go up in 1 second
The express elevator will go 4 floors per seconds.
How to find rate?We have to find the rate of the express elevator before we can find how many floors one can go in one seconds.
time = 12 3 / 4 = 51 / 4 seconds
number of floor = 51 floors
rate = 51 / 51 / 4
rate = 51 × 4 / 51
rate = 4 floors per seconds
Therefore, the elevator will go 4 floors per seconds.
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Which equation can be used to solve the problem? 10 is 50 percent of what number? StartFraction 10 divided by 1 Over 50 divided by 1 EndFraction = StartFraction 10 Over 50 EndFraction StartFraction 100 times 2 Over 50 times 2 EndFraction = StartFraction 200 Over 100 EndFraction StartFraction 10 divided by 2 Over 50 divided by 2 EndFraction = StartFraction 5 Over 25 EndFraction StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction Mark this and return
The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number.
According to the problem.
50% of x = 10
x = 10 ÷ 50%
= 10×(50/100)
= (50÷5)/(100÷5) = 10/20
Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
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mrs.darby works at the local bakery as a cake decorator if it takes her 1 1/3 hours to decorate one cake how many cakes can she dcorate in a 30-hour week.
The number of cakes Mrs Darby can decorate in a 30-hour week is 22.5 cakes.
Number of cakes to decorateTime taken to decorate a cake = 1 1/3 hoursTotal time for decoration per week = 30 hoursTime conversion
1 hour = 60 minutes
1 1/3 hours = 60 × 1 1/3
= 60 × 4/3
= 240/3
= 80 minutes
30 hours = 30 × 60
= 1800 minutes
Number of cakes decorated = 1800 / 80
= 22.5 cakes
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Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a
function?
Select all correct answers.
Select all that apply.
□ {(-1,6), (4,4), (7, 13), (4,8)}
{(3,6), (3, 5), (9, 12), (0, -3)}
{(-5,0), (6, 8), (3,-5), (-5,-3)}
{(7,9), (8,4), (-2,4),(-3, 14)}
{(8,3), (3, 7), (6,4), (5,4)}
C
Answer:
D, E
Step-by-step explanation:
A set of ordered pairs represents a function if no x-value is repeated in the set.
Examine choices{(-1,6), (4,4), (7, 13), (4,8)} . . . . . not a function
{(3,6), (3, 5), (9, 12), (0, -3)} . . . not a function
{(-5,0), (6, 8), (3,-5), (-5,-3)} . . . . not a function
{(7,9), (8,4), (-2,4),(-3, 14)} . . . . no repeated x-values; is a function
{(8,3), (3, 7), (6,4), (5,4)} . . . . . .no repeated x-values; is a function
I need some help please
Answer:
[tex]2261.9cm^{2}[/tex]
Step-by-step explanation:
Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]
Note: Do not get tricked by the 24cm (taking 24cm as the radius), that is the diameter.
To find r, radius = [tex]\frac{1}{2} d[/tex]
=[tex]\frac{1}{2} (24)\\[/tex]
= 12cm
Now we know r = 12cm, h = 18cm
Now we substitute r and h into the formula to find the total surface area.
Total Surface Area of Cylinder = [tex]2\pi (12)(18)+2\pi (12)^{2} \\=432\pi +288\pi \\=720\pi cm^{2} \\=2261.9cm^{2}[/tex]
Please help!! If........
Answer:
26
Step-by-step explanation:
[tex]f(x)=3x^{2} -5x+4\\f(-2)=3(-2)^{2} -5(-2)+4\\=3(4)+10+4\\=12+10+4\\=26[/tex]
Answer:
26
Step-by-step explanation:
3(-2)^2 = 12
5(-2) = -10
So 12 - (-10) + 4 = 26
How much should you put in an investment paying simple interest rate of 8% if you need 4000 in six months?
The amount you should put is 3846
How to determine the principal amount?The given parameters are:
Amount, A = 4000
Rate, r = 8%
Time = 0.5 year i.e. 6 months
The amount on simple interest is calculated as:
A = P(1 + RT)
This gives
4000 = P * (1 + 8% * 0.5)
Evaluate the product
4000 = P * (1 + 0.04)
Evaluate the sum
4000 = P * (1.04)
Divide both sides by 1.04
P= 3846
Hence, the amount you should put is 3846
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which expression is equivalent to 6 to the power of 4 x 6 to the 3rd power
Answer:
6^4 * 6^3
Step-by-step explanation:
If cos = 3/5 and is in quadrant IV, Sin2=
Using a trigonometric identity, it is found that the sine of the angle is given as follows:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
Which trigonometric identity relates the sine and the cosine of an angle?Considering an angle [tex]\theta[/tex], the identity is given as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem, the cosine is given as follows:
[tex]\cos{\theta} = \frac{3}{5}[/tex]
Hence the sine is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]
[tex]\sin^2{\theta} = \frac{16}{25}[/tex]
[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]
In quadrant IV, the sine is negative, hence:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
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what is numrical in math and complex function?
[tex] \sqrt{ - i} [/tex]
Answer:
Step-by-step explanation:
[tex]\sqrt{- i} =\sqrt{(-1)i} =\sqrt{i^2i} =i\sqrt{i}[/tex]
There are 520 bridges on the freight rail network in the province of Ostenborg. Of these, 200 are classified as “old” rail bridges (i.e., 50 years or more in age). Past records indicate that 50% of all rail bridges in the state exhibit visible signs of structural distress. Of the bridges 70% are old or exhibit structural distress.
Find the probability that a randomly selected rail bridge will exhibit structural distress given that it is old.
Answer:
The probability that a selected randomly rail bridge will exhibit structural distress given that it is old
= (200/520) * 0.5 * 0.7 * 100
= 0.1346154 * 100
= 13.46154 %
Solve |√2-y| = |y-√2|
Answer:
Step-by-step explanation:
|√2-y|=|y-√2|
√2-y=±(y-√2)
when √2-y=y-√2
y+y=√2+√2
2y=2√2
y=√2
when √2-y=-(y-√2)
√2-y=-y+√2
or 0=0
it gives no value of y.
so only possible value is y=√2
Inferential statistics
Answer:
Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics
Step-by-step explanation:
hope this helps (﹡ˆ﹀ˆ﹡)♡
Can someone help me answer this
Duplicate don't answer!
Find the HCF of x³y² and x^2
Answer:
[tex]x^2[/tex]
Step-by-step explanation:
Hello!
The HCF or the highest common factor (sometimes also known as the greatest common factor, GCF), is the greatest factor between terms.
First, let's expand both terms:
[tex]x^3y^2 = x*x*x*y*y[/tex][tex]x^2 = x*x[/tex]If we keep them on top of another, we can see that the overlapping variables are [tex]x*x[/tex], meaning that the greatest common factor between them is [tex]x^2[/tex].
In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 67.2 grams.
I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.
Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?
The percentage of gold will be equal to 39.7%
What are percentages?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
1. First find the density of your chain
Density = mass / volume
Volume = displaced water volume
= Volume of Final level of water - initial level of water
= 20 ml - 15 ml = 5 ml
Mass = 66.7 g
Density = 66.7g / 5 ml = 13.34 g/ml
2. Second, write the density of the chain as the weighted average of the densities of the other metals:
Mass of gold x density of gold + mass of other metals x density of other metals, all divided by the mass of the chain.
Calling x the amount of gold, then the amount of other metals is 66.7 - x:
[(19.3x+(9.7)(66.7-x)] / 66.7 = 13.34
19.3x + 635.66 - 9.7x = 889.778
9.6x = 254.118
x = 26.47
Then, there are 26.47 grams of gold in 66.7 grams of chain, which yields a percentage of:
(26.47 / 66.7) x 100 = 39.7%
Therefore the percentage of gold will be equal to 39.7%
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Maths Trigonometry Question
100 points up for grabs!
Will give brainliest to whoever answers
Answer:
14) 21.136505024965 m
15) 43.076759215619 km
Step-by-step explanation:
14)
let h be the height of the lighthouse:
tan(41.3) = 18.7/h
Then
h = 18.7÷tan(41.5)
= 21.136505024965 m
………………………………………
15)
90-71.4 =18.6
Let s be the distance that the plane flew
towards the south:
tan(90 - 71.4) = s/128
Then
tan(18.6) = s/128
Then
s = tan(18.6)×128
= 43.076759215619 km
14.)
See the diagram below.
Here use tan rule:
[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(41+ \frac{30}{60} ) = \dfrac{18.7}{adjacent}[/tex]
[tex]\sf adjacent = \dfrac{18.7}{tan(41.5)}[/tex]
[tex]\sf adjacent = 21.14[/tex]
The height of the lighthouse is 21.14 m.
15.)
See the diagram below.
Here use tan rule:
[tex]\sf tan(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf tan(18.6) = \dfrac{opposite}{128}[/tex]
[tex]\sf opposite = 128 tan(18.6)[/tex]
[tex]\sf opposite = 43.08[/tex]
The plane travelled 43.08 km far south.
How would you answer this?: z^3/z^9
Hello !
Answer:
[tex]z {}^{ - 6} [/tex]
Step-by-step explanation:
[tex] \frac{z {}^{3} }{z {}^{9} } = z {}^{3 - 9} = z {}^{ - 6} [/tex]
the sum of all even numbers in 3 digit
it will mark as topper
Answer
sum of all 3 digit even number = 247050
The series is 100 + 102 + 104 + .... + 998
which by using formula Sn = N/2 ( a + an)
where N = number of terms
a = first term = 100
an = last term = 998
Which number sentence matches the question below?
For how many days did Curtis practice juggling, if he practiced for 87 hours in all and for 3 hours each day?
A.
n ÷ 87 = 3
B.
3 ÷ n = 87
C.
87 ÷ n = 3
D.
n ÷ 3 = 87
The equation which represent number of days is 87 ÷ n = 3
What is Division?It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here,
total hour practicing = 87 hours
Daily hours for practicing = 3 hours
total number of days = n days
Now, according to question;
n X 3 = 87
87 ÷ n = 3
Thus, the equation which represent number of days is 87 ÷ n = 3.
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Slope is -4/5 and passes through the point (2, -3).
5
Answer:
y = (-4/5)x - 7/5
Step-by-step explanation:
The general equation of the line is slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of the slope (m = -4/5). To find the y-intercept, use the slope and values from the Point (2,-3) to isolate "b".
y = mx + b <----- Slope-intercept form
y = (-4/5)x + b <------ Plug -4/5 in "m"
-3 = (-4/5)(2) + b <----- Plug in "x" and "y" values from Point
-3 = -8/5 + b <------ Multiply -4/5 and 2
-15/5 = -8/5 + b <----- Assign common denominator
-7/5 = b <----- Add 8/5 to both sides
Now that you have the slope and y-intercept, you can construct the equation.
y = (-4/5)x - 7/5
8. What is 3x times (3x² - 5)?
a.3x² + 5x -5
b.9x³-5
c.9x³ - 15x
d.15x³ - 25x
Answer:
9x^3-15x
Step-by-step explanation:
Lynn’s cruise lasted 11 days and 7 hours. Convert the time to hour
Here is conversion chart
1 day=24hr
so the equation to solve this would look like this
(24*11)+7
Therefore the answer is 271 hr
Which equation can be used to solve the problem? 10 is 50 percent of what number? StartFraction 10 divided by 1 Over 50 divided by 1 EndFraction = StartFraction 10 Over 50 EndFraction StartFraction 100 times 2 Over 50 times 2 EndFraction = StartFraction 200 Over 100 EndFraction StartFraction 10 divided by 2 Over 50 divided by 2 EndFraction = StartFraction 5 Over 25 EndFraction StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction Mark this and return
The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number.
According to the problem.
50% of x = 10
x = 10 ÷ 50%
= 10×(50/100)
= (50÷5)/(100÷5) = 10/20
Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
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James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 2 cm. One tray makes 6 spheres.
What is the total volume of ice the tray can make at one time?
The ice cube tray can make 200.96 cubic centimeters of ice.
How to get the total volume?For a sphere of radius R, the volume is:
[tex]V = \frac{4}{3}*3.14*R^3[/tex]
In this case, we have 6 spheres, each one with a radius of 2cm.
Then the total volume of ice that the ice cube tray can make at one time is:
[tex]volume = 6*V = 6*(\frac{4}{3} *3.14*(2cm)^3) = 200.96cm^3[/tex]
The ice cube tray can make 200.96 cubic centimeters of ice.
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