Answer:
x≤14
Step-by-step explanation:
≤ = greater than/equal to(at least)
PLEASE HELP:):):):):):):):)
Answer:
[tex]Area = 8[/tex]
Step-by-step explanation:
Given
The attached figure
Required
Determine the area
The shape is a trapezium. So, the area is:
[tex]Area = \frac{1}{2} *(Sum\ of\ parallel\ sides) * Height[/tex]
From the attached,
The height is 2
The parallel sides are: 2 and 6
So, the area is:
[tex]Area = \frac{1}{2} *(2 + 6) * 2[/tex]
[tex]Area = \frac{1}{2} *8 * 2[/tex]
[tex]Area = 8[/tex]
Hence, the area is 8 units square
"A driving instructor is investigating whether the time a driver spends in a driverâs education course improves their score on the driverâs test. The instructor randomly selected 10 drivers from a driverâs education course and recorded the number of hours each driver attended the driverâs education course and their corresponding score on the driverâs test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation?"
a. A chi-square test of independence
b. A two-sample t-test for a difference between means
c. A two-sample z-test for a difference between proportions
d. A linear regression t-test for slope
e. A matched pairs t-test for a mean difference
Answer:
e. A matched pairs t-test for a mean difference
Step-by-step explanation:
When the observations from two samples are paired either naturally or by design we find the differences between the two observations of each pair.Treating the differences as a random sample from a normal population with mean ud= u1-u2 and unknwn standard deviation σd we perform one sample t- test on them. This is called the paired difference t- test or a paired t- test.
Suppose 10 young recruits are given a physical training by the Army . Their weights are recorded before and after the training. These observations constitutes natural pairing .
When we eliminate the undesireable sources of variation to take observations in pairs , this is called pairing by design.
Calculus helpppppppppppppppp
Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?
Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
Find the average number of people in these cities: New York, Philadelphia, Chicago and Detroit a. 3.35 million b. 40 million. C. 4.0 million d. 33.million
Answer:
The answer is maybe going to be D which is 33 million
Step-by-step explanation:
New york is a big city
NEED ANSWER ASAP,BRAINLIEST FOR CORRECT ANSWER. IM FAILING SCHOOL
Answer:
angle b= 86 degrees
Step-by-step explanation:
hope this helps, have a nice day :)
Find the value of x in the parallelogram below.
Answer:
B) x = 12
Step-by-step explanation:
m∡EOU = m∡TQE
m∡EOU =180 - (39+45) = 96°
m∡TQE: 7x + 12 = 96
7x = 84
x = 12
Jason rolls the die 14 times. What is the experimental probability that he will roll a 2
The experimental probability that Jason will roll a 2 is 3/14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, Jason rolls the die 14 times.
From the given table,
Number of favorable outcomes = 3
Total number of outcomes = 14
So, the probability = 3/14
Therefore, the experimental probability that Jason will roll a 2 is 3/14.
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25. Which two conversions are correct?
A. 7 mm = 70 cm
B. 7 cm = 0.07 m
C. 7,000 m = 7 km
D. 0.7 cm = 70 mm
E. 7 m = 7,000 km
Answer:
The answer is B and C
Step-by-step explanation:
1 Meter is equal to 0.001 Kilometer
1 Centimeter is equal to 0.01 Meters
The unit conversions which has the true measurements are
a) 7 cm = 0.07 m
b) 7,000 m = 7 km
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the unit conversion be represented as A
Let the first measurement be p
where the value of p is
p = 7 cm
From the unit conversion , 1 m = 100 cm
So , 7 cm = 0.07 m
And , let the second measurement be q = 7,000 m
From the unit conversion , 1 km = 1,000 m
7,000 m = 7 km
Hence , the unit conversions are solved
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13
What is the inverse of when
15
multiplying fractions?
13
A
15
15
B
13
13
C с
13
15
D
15
Answer:
Step-by-step explanation:
15x13=?
15+15+1=31
so the answer is 31
1) Madison went shopping and spent $125 she paid $45 in Texas what was the sale tax rate (percent)
Answer:
170
Step-by-step explanation:
How the sales tax de-calculator works
Step 1: take the total price and divide it by one plus the tax rate.
Step 2: multiply the result from step one by the tax rate to get the dollars of tax.
Step 3: subtract the dollars of tax from step 2 from the total price.
Pre-Tax Price = TP – [(TP / (1 + r) x r]
TP = Total Price.
Consider the given figure, which shows groups of dots arranged in increasingly larger hexagons. If the pattern continues, the next group of dots would have 61 dots. Which of
the following statements best describes the sequence that represents the number
of dots in each group?
A The sequence is arithmetic, because the first differences are constant.
B) The sequence is arithmetic, because the second differences are constant.
c) The sequence is quadratic, because the first differences are constant.
The sequence is quadratic, because the second differences are constant.
Answer:
a
hddhdhdhhdgdhdgdhf
yyeyeyehrggggdgfhfhhfbfbdbfbdfbbfhhbfbdvwshhdgnhh
The sequence is arithmetic because the second differences are constant. Then the correct option is B.
What is a sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
Consider the given figure, which shows groups of dots arranged in increasingly larger hexagons.
If the pattern continues, the next group of dots would have 61 dots.
The first difference will be
The difference between 7 and 1 is 6.
The difference between 19 and 7 is 12.
The difference between 37 and 19 is 18.
The difference between 61 and 37 is 24.
The second difference will be
The difference between 12 and 6 is 6.
The difference between 18 and 12 is 6.
The difference between 24 and 18 is 6.
Thus, the sequence is arithmetic, because the second differences are constant. Then the correct option is B.
More about the sequence link is given below.
https://brainly.com/question/21961097
The diameter of a circle is 10 ft. Find its area to the nearest tenth.
Answer:
15.70
Step-by-step explanation:
Answer:
78.5
Step-by-step explanation:
Formula: a = πr², r = d/2
Given: π = 3.14, d = 10
Sub: a = (3.14)r²
Find r.
r = 10/2
r = 5
Sub: a = (3.14)5²
Simplify: a = (3.14)25
Solve: a = 78.5
The answer is 78.5.
If this truly helped you, help me out by thanking me.
-Xax.
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
WILL MARK BRAINLIEST
Solve for x.
60
10
20
120
Answer:
x = 10
Step-by-step explanation:
Let's draw the center of the circle S and the segments SE and SD.
SE is perpendicular to EF (as EF is tangent to circle).
That means FED + DES = 90deg
We also know that DSE = 120deg
And because the SED is an isosceles triangle, we know that angle measures for DES and SDE are equal.
DES = (180deg - 120deg) / 2 = 30deg
FED = 90deg - DES = 90deg - 30deg = 60deg
7x - 10 = 60
7x = 70
x = 10
a group of students collected old newspapers for a recycling project. the data shows the mass, in kilograms, of old newspapers collected by each student.
23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55
98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.
A.) Find the range of the mass of the newspapers collected.
B.) Find the interquartile range.
Answer:
A. 107 kg
B. 49 kg
Step-by-step explanation:
To solve the equation 5sin(2x)=3cosx, you should rewrite it as___.
Answer:
A
Step-by-step explanation:
We want to solve the equation:
[tex]5\sin(2x)=3\cos(x)[/tex]
To do so, we can rewrite the equation.
Recall the double-angle identity for sine:
[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]
By substitution:
[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]
Distribute:
[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]
We can subtract 3cos(x) from both sides:
[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]
And factor:
[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.
Answer:
A. cosx(10sinx-3)=0
Step-by-step explanation:
5(2sinxcosx)=3cosx
10sinxcosx-3cosx=0
cosx(10sinx-3)=0
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Answer:
the answer is 7 feet
Step-by-step explanation:
28/4=7
Please help me I really need it
Answer:
Angle C
Step-by-step explanation:
By applying sine rule in the given triangle,
[tex]\frac{\text{sinB}}{CD}=\frac{\text{sinC}}{BD}=\frac{\text{sinD}}{BC}[/tex]
[tex]\frac{\text{sinB}}{\text{sinC}}=\frac{\text{CD}}{\text{BD}}[/tex]
Therefore, sides of the given triangle will be in the same ratio as the sine of the angles.
Since, BD > BC > CD
Therefore, Opposite angles of these sides will be in the same ratio.
∠C > ∠D > ∠B
Largest angle of the triangle is angle C.
1/3x + 2 =4 I need it ASAP
Answer:
x=1/6 or 0.16
Step-by-step explanation:
x has to be whatever makes the equation true.
does 1/3 +2= 4 alone no does it = 4 when you do the 1/3(1/6) yes
2. Which of the following is considered an
asset?
A Savings account
B Credit card debt
C Personal loan
D Mortgage
Answer:
A
Step-by-step explanation:
All of the rest you have to pay off. A savings account is a good place to keep money safe for the future, and you can also make interest.
Find g(-6) when g(x)
= x+3/x-1
Answer: The answer would be 3/7.
Step-by-step explanation:
PLEASE HELP ASAP GEOMETRY I AM LITERALLY DYING!! 100 POINTS REAL ANSWERS ONLY OR YOU WILL BE REPORTED AND GET NO POINTS!
Let’s design a new ferris wheel!! Create a sketch of a new Ferris wheel. This new ferris wheel must have an arc length measuring 3 25π feet. What is the equation of your new ferris wheel if the center must be at least 60 feet from the ground? Be sure to show and explain all work.
9514 1404 393
Answer:
x^2 +(y -61)^2 = 625/36
Step-by-step explanation:
The graph of the above equation is attached.
If the circumference of the wheel is 25π/3 feet, the diameter is ...
d = C/π = (25/3π)/π = 25/3 . . . feet, about 8.33 feet
The radius will be half that value, or 25/6 feet.
For a center point (h, k) and radius r, the equation of a circle is ...
(x -h)^2 +(y -k)^2 = r^2
You want the center to be more than 60 feet from the ground, so we can make it be 61 feet. The horizontal location is not specified, so we can make it zero.
This means we apparently want the equation for a circle of radius 25/6 feet with a center that is (x, y) = (0, 61). The equation of this circle is ...
x^2 +(y -61)^2 = 625/36
g(x)=x^2-5x
f(x)=2x+1
Find (g-f)(x)
Answer:
(g-f)(x) = x²-7x -1
Step-by-step explanation:
hello :
g(x)=x²-5x f(x)=2x+1
(g-f)(x) =g(x) - f(x) = x²-5x- ( 2x+1 ) = x²-5x - 2x-1
(g-f)(x) = x²-7x -1
State of the given functions are inverses
Answer:
1) They are not inverses
2) They are inverses
Step-by-step explanation:
We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.
1)
Let's find f[g(x)] and simplify.
[tex]f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{7}{2}-\frac{3}{4}x[/tex]
As f[g(x)] is not equal to x, these functions are not inverses.
2)
Let's find f[g(x)] and simplify.
[tex]f[g(n)]=\frac{-16+(4n+16)}{4}[/tex]
[tex]f[g(n)]=\frac{-16+4n+16}{4}[/tex]
[tex]f[g(n)]=\frac{4n}{4}[/tex]
[tex]f[g(n)]=n[/tex]
Now, we need to find the other composition function g[f(x)]
Let's find g[f(x)] and simplify.
[tex]g[f(x)]=4(\frac{-16+n}{4})+16[/tex]
[tex]g[f(x)]=-16+n+16[/tex]
[tex]g[f(x)]=n[/tex]
Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.
I hope it helps you!
Find the area of the trapezoid.
22.2 cm
9.86 cm
8.52 cm
[? ]cm2
Enter the exact answer. Do not round
Answer:
151.4496
Step-by-step explanation:
it has not been rounded or anything that is the exact answer
Answer: 151.45 (151.4496)
Step-by-step explanation:
Formula: A = (a+b)/2 * h
Base = 22.2
Base = 8.52
Height = 9.86
Do the following:
(22.2+8.52)/2 * 9.86 = 151.4496
Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?
Answer:
He would save $4.40
Step-by-step explanation:
And in total he would pay 17.60
What fraction of 2 minutes is 6
seconds?
Answer:
1/20 of 2 minutes = 6 seconds
Answer:
1/20; 0.05; 5%
Step-by-step explanation:
Well, 2 minutes is 120 seconds, 6/120 simplified is 1/20, and decimal form would be 0.05, which is 5%
Given that these triangles are similar, what is the perimeter of triangle PQR? Show your work.
If someone could answer fr this time that would be great.
Answer:
24
Step-by-step explanation:
I use the Pythagoras theorem.
[tex]\sqrt{a^{2} +b^{2} } =c^{2}[/tex]
[tex]4^{2}{x}6^{2} = c^{2}[/tex]
16 x 36= 576
[tex]\sqrt{576} = 24[/tex]
I need help with slopes!!
Answer:
The slope of this line is -4
