Answer:
(f – g)(x) = - x² + 4x + 6Step-by-step explanation:
f(x) = 4x + 1
g(x) = x² – 5
To find (f – g)(x) subtract g(x) from f(x)
That's
(f – g)(x) = 4x + 1 - ( x² - 5)
Remove the bracket
(f – g)(x) = 4x + 1 - x² + 5
Group like terms
(f – g)(x) = - x² + 4x + 1 + 5
We have the final answer as
(f – g)(x) = - x² + 4x + 6Hope this helps you
A dollar bill weighs one gram. How many pounds do one million dollar bills weigh? (1000 grams
is equal to 1 kilogram and 1 kilogram is equal to about 2.205 pounds.)
Hey there! I'm happy to help!
First of all, if one bill weighs on gram, a million would weigh one million grams. Let's divide this by 1,000 to see how many kilograms it is.
1,000,000/1,000=1,000
Now, we need to convert 1,000 kilograms into pounds. We see that 1 kilogram is equal to about 2.205 pounds, so we multiply 1,000 kilograms by 2.205 to get our pounds.
1,000*2.205=2205
Therefore, one million dollar bills weigh about 2205 pounds.
Have a wonderful day! :D
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
Which graph represents exponential decay? On a coordinate plane, a straight line has a negative slope. On a coordinate plane, a graph starts at (negative 2, 0) and curves up and to the right into quadrant 1. On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2. On a coordinate plane, a graph approaches y = 0 in quadrant 2 and curves up into quadrant 1.
Answer:
The correct option is (C).
Step-by-step explanation:
The exponential function representing decay is as follows:
[tex]y=y_{0}\cdot e^{kt};\ k<0[/tex]
Here,
y = final value
y₀ = initial value
k = growth rate
t = time passed
The graph represents exponential decay is:
"On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2."
Thus, the correct option is (C).
Answer:
The answer is C
Step-by-step explanation:
I just took the test on edge
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 422 422 425 429 431 434 437
439 446 447 449 452 457 461 465
Calculate a two-sided 95% confidence interval for true average degree of polymerization.
Answer:
The 95% confidence interval for true average degree of polymerization is (431, 446).
Step-by-step explanation:
The data provided for the degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range is:
S = {418, 421, 422, 422, 425, 429, 431, 434, 437, 439, 446, 447, 449, 452, 457, 461, 465}
Compute the sample mean and sample standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{7}\times 7455=438.5294\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 3594.2353}=14.988[/tex]
As the population standard deviation is not provided use the t-statistic to compute the two-sided 95% confidence interval for true average degree of polymerization.
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]
The critical value of the t is:
[tex]t_{\alpha /2, (n-1)}=t_{0.05/2, (17-1)}=t_{0.025, 16}=2.12[/tex]
*Use a t-table.
Compute the 95% confidence interval for true average as follows:
[tex]CI=438.5294\pm 2.12\cdot\frac{14.988}{\sqrt{17}}[/tex]
[tex]=438.5294\pm 7.7065\\=(430.8229, 446.2359)\\\approx (431, 446)[/tex]
Thus, the 95% confidence interval for true average degree of polymerization is (431, 446).
use the cubic model y=x^3+x^2+x to estimate the value of y when x = 10. a 910 b. 110 c. 1210 d. 3150
Answer:
y = 1110
Step-by-step explanation:
In the above question, we are given the cubic model
y=x³ +x² + x
We are to solve for y when x = 10
Hence,
y = 10³ + 10² + 10
y = 1000 + 100 + 10
y = 1110
Therefore, the value of y when x is 10 using the cubic model of ' y =x³ +x² + x' is 1110.
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)
Answer:
√512 by √512Step-by-step explanation:
Length the length and breadth of the rectangle be x and y.
Area of the rectangle A = Length * breadth
Perimeter P = 2(Length + Breadth)
A = xy and P = 2(x+y)
If the area of the rectangle is 512m², then 512 = xy
x = 512/y
Substituting x = 512/y into the formula for calculating the perimeter;
P = 2(512/y + y)
P = 1024/y + 2y
To get the value of y, we will set dP/dy to zero and solve.
dP/dy = -1024y⁻² + 2
-1024y⁻² + 2 = 0
-1024y⁻² = -2
512y⁻² = 1
y⁻² = 1/512
1/y² = 1/512
y² = 512
y = √512 m
On testing for minimum, we must know that the perimeter is at the minimum when y = √512
From xy = 512
x(√512) = 512
x = 512/√512
On rationalizing, x = 512/√512 * √512 /√512
x = 512√512 /512
x = √512 m
Hence, the dimensions of a rectangle is √512 m by √512 m
PLEASE ANSWER QUICK A manufacturing facility pays its employees an average wage of $4.50 an hour with a standard deviation of 50cents. If the wages are normally distributed, what is the percentage of workers getting paid between #3.75 and $5.00 an hour? A. 80.4% B.77.4% C.70.5% D.65.4%
Answer:
B.77.4%
Step-by-step explanation:
Mean wage (μ) = $4.50
Standard deviation (σ) = $0.50
For nay given salary X, the z-score is given by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $3.75, the z-score is:
[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]
For X = $5.00, the z-score is:
[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]
A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:
[tex]P=84.13-6.68\\P=77.45\%[/tex]
The answer is alternative B.77.4%
What linear function defines the following Arithmetic Sequence?
-8, -4, 0, 4, 8, ...
A : an = -8 + 4(n - 1)
B : an= 8 + 4(n - 1)
C : an = -8 - 4(n - 1)
D : an = 8 - 4(n - 1)
The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, the sequence is -8, -4, 0, 4, 8, ...
a = -8
d = +4
The expression for the nth term will be written as,
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
To know more about arithmetic progression follow
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The lowest temperature ever
recorded on earth was -89°C
in Antarctica. The average
temperature on Mars is about
-55°C. Which is warmer?
Write an inequality to support
your answer
Answer:
Mars
Step-by-step explanation:
America
What is the solution to the quadratic equation x2 + x - 30 = 0?
Answer:
try 3x=30 or 10
Step-by-step explanation:
How many games are played in a 4 team round robin tournament? (Each team
plays every other team only once.)
Answer: 6
Step-by-step explanation:
If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.
We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total
Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.
Now we have already included D playing every other team so we don't include any other pairings.
In total, now every team has played every other team giving a total of 6.
(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.
Answer:
6 games.
Step-by-step explanation:
The answer is the number of combinations of 2 from 4
= 4*3 / 2*1
= 6.
Please answer the followings: W^mW^n=
Step-by-step explanation:
[tex]W^m=\underbrace{W\cdot W\cdot W\cdot...\cdot W}_{m}\\\\W^n=\underbrace{W\cdot W\cdot W\cdot...\cdot W}_{n}\\\\W^mW^n=\underbrace{(W\cdot W\cdot W\cdot...\cdot W)}_{m}\underbrace{(W\cdot W\cdot W\cdot...\cdot W)}_{n}\\\\=\underbrace{W\cdot W\cdot W\cdot...\cdot W}_{m+n}=W^{m+n}[/tex]
From the following given equation, the answer to W^mW^n = [tex]\mathbf{W^{m+n}}[/tex]
The laws of indices provide us with the rules and principles for simplifying mathematical computations or algebraic expressions that include powers of the same base.
The example of the question given can be solved by using the multiplication rule. The multiplication rule states that we sum up the power of the integers if they have the same base.
From the given information
W^mW^n = [tex]\mathbf{W^{m+n}}[/tex]
Learn more about indices here:
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There are 50 mangoes 20 of which are unriped another basket contains 40 mangoes 15 unripe if we take 1 mangoes from each basket Find the probability of getting both are ripe Find the probability of getting both are unripe Find the probability of getting one ripe and one unripe Find the probability of at least one right Find the probability of at least one uripe
Answer:
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.375
Probability of one ripe and one unripe
=0.234375
Probability of at least one unripe
=0.625
Step-by-step explanation:
50 mangoes 20 of which are unriped in the first basket .
Riped = 50-20= 30
Probability of unripe = 20/50
Probability of unripe= 0.4
Probability of ripe = 30/50
Probability of ripe = 0.6
40 mangoes of which 15 are unripe In the second basket
Number of riped= 40-15= 25
Probability of unriped= 15/40
Probability of unriped= 0.375
Probability of riped= 25/40
Probability of riped= 0.625
probability of getting both are unripe
= 0.4*0.375
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.6*0.625
= 0.375
Probability of one ripe and one unripe
= 0.625*0375
= 0.234375
Probability of at least one unripe
= 1- probability of no unripe
= 1 - probability of both ripe
= 1-0.375
= 0.625
what is the answer. plz heelp 5h+2(11-h)= -5
Answer:
h = -9
Step-by-step explanation:
5h+2(11-h)= -5
Distribute
5h +22 -2h = -5
Combine like terms
3h +22 = -5
Subtract 22 from each side
3h +22-22 = -5-22
3h = -27
Divide by 3
3h/3 = -27/3
h = -9
State sales tax S S is directly proportional to retail price p p . An item that sells for 142 142 dollars has a sales tax of 12.32 12.32 dollars. Find a mathematical model that gives the amount of sales tax S S in terms of the retail price p p .
Answer: [tex]S=0.087p[/tex] .
Step-by-step explanation:
Equation for direct proportion:
y=kx
, where x= independent variable ,
y=dependent variable.
k= proportionality constant
Here, State sales tax S is directly proportional to retail price p.
Also, dependent variable= S, independent variable =p
Required equation: S= kp
Put S= 12.32 and x= 142
[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]
Hence, the required equation is [tex]S=0.087p[/tex] .
how do you slove 21 - 4d for d= 5
Consider the following estimated regression equation based on 10 observations y 29.1270 5906x, 4980x2 011
a. Develop a point estimate of the mean value of y when x 1 = 180 and x 2-310 (to 3 decimals).
b. Develop a point estimate for an individual value of y when x 1 180 and x 2-310 (to 3 decimals)
Answer:
no tiene mas informaion?
Step-by-step explanation:
∫ ex (sec x + tan²x) dx = ? a) eˣsec²x b) eˣsecx c) eˣtan²x d) eˣtanx
None of these options seem to be correct. You can check each result by differentiation:
[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]
[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]
[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]
[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]
But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...
Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4
Answer:
option 3
Step-by-step explanation:
4x+8<-16
x<-6
4x+8_>-16
x_>-1
(it's more and equal .so the circle has to be shaded and move to the right of -1)
Answer:C
Step-by-step explanation:
The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in meters) and t is the time (in seconds). What is the domain and range? Domain:
Answer:
Step-by-step explanation:
when h(t)=0
-4.9 t²+19.6t=0
4.9t(-t+4)=0
either t=0 or t=4
so domain is 0≤t≤4
for range
h(t)=-4.9t²+19.6t
=-4.9(t²-4t+4-4)
=-4.9(t-2)²+19.6
so range is 0≤h≤19.6
Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.
Range = 0<h<19.6, again, use less than or equal to signs.
Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
i think its b
???
Step-by-step explanation:
im sorry if im wrong im not very confident on my answer :(
Answer:
D
Step-by-step explanation:
Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.
A gift package contains 6 wedges of cheese . If each wedges is 2/3 onuce what is the totel weight in pounds of cheese?
Answer:
4 ounces
Step-by-step explanation:
6x2/3= 4
The diagram shows the floor plan for Harry's new tree house. The entry terrace on the tree house is shaped like an isosceles trapezoid.
Answer:
what do you need help with its not really clear
Answer
1. 48 2. 308
Step-by-step explanation:
Evaluate the following integrals
Answer:
a. (24 ln 2 − 7) / 9
b. x tan x + ln|cos x| + C
Step-by-step explanation:
a. ∫₁² x² ln x dx
Integrate by parts.
If u = ln x, then du = 1/x dx.
If dv = x² dx, then v = ⅓ x³.
∫ u dv = uv − ∫ v du
= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)
= ⅓ x³ ln x − ∫ ⅓ x² dx
= ⅓ x³ ln x − ¹/₉ x³ + C
= ¹/₉ x³ (3 ln x − 1) + C
Evaluate between x=1 and x=2.
[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]
⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C
⁸/₉ (3 ln 2 − 1) + ¹/₉
⁸/₃ ln 2 − ⁸/₉ + ¹/₉
⁸/₃ ln 2 − ⁷/₉
(24 ln 2 − 7) / 9
b. ∫ x sec² x dx
Integrate by parts.
If u = x, then du = dx.
If dv = sec² x dx, then v = tan x.
∫ u dv = uv − ∫ v du
= x tan x − ∫ tan x dx
= x tan x + ∫ -sin x / cos x dx
= x tan x + ln|cos x| + C
Which of the following is equivalent to (3)/(x)=(6)/(x-4)
Answer:
[tex]3(x - 4) = 6x[/tex]Option A is the correct option.
Step-by-step explanation:
[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]
Apply cross product property:
[tex]3(x - 4) = 6 \times x[/tex]
[tex]3(x - 4) = 6x[/tex]
Hope this helps...
Best regards!!
Answer:
3 * (x - 4) = 6 * x.
Step-by-step explanation:
3 / x = 6 / (x - 4)
3 * (x - 4) = 6 * x
3x - 12 = 6x
6x = 3x - 12
6x - 3x = -12
3x = -12
x = -4.
Hope this helps!
Circle A has center of (4,6) and a radius of 5, and circle B has a center of (1,0) and a radius of 15. What steps will help show that circle A is similar to circle B? Dilate circle Dilate circle A by a scale factor of 3. translate Circle A using the rule (x - 3, y + 6). Rotate circle A 180° about the center. reflect circle A over the y-axis.
The answer is A. Dilate circle A by a scale factor of 3
I took the test :)
What's the common denominator of this equation?
3 - b = 6-7
Answer:
b = 4
Step-by-step explanation:
3 - b = 6 - 7
3 - b = -1
-b = -1 -3
-b = -4
b = 4
Which statement is true about the function f(x)= -x?
O The domain of the graph is all real numbers.
The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
The range of the graph is all real numbers less than or equal to 0.
Answer:
The domain of the graph is all real numbers less than or equal to 0.
Step-by-step explanation:
Hello,
We know that we cannot take square root of negative numbers, so we must have
[tex]-x\geq 0 \ \text{ ***multiply by -1, it changes the inequality, so*** } \\ \\\large \boxed{\sf \ \ x\leq0 \ \ }[/tex]
So the domain of the graph is all real numbers less than or equal to 0.
For information, I attached the graph so that we can verify it.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
what's the thickness of a rectangle prism with a height of 12 inches, a width of 8 inches and surface area 992 square inches?
Answer:
Thickness of rectangle prism is 20 inches.
Step-by-step explanation:
Given:
Surface area of rectangular prism, A = 992 sq inches.
Height, h = 12 inches
Width, w = 8 inches
To find:
Thickness / length of prism, [tex]l[/tex] = ?
Solution:
First of all, let us learn the formula for surface area of a rectangular prism.
Formula for surface area of a prism is given as:
[tex]A=2(wl+hl+hw)[/tex]
As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.
Putting all the given values in the formula to find the value of [tex]l[/tex]:
[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]
So, the answer is Thickness of rectangle prism is 20 inches.
In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
Answer:
I believe the interquarrile range is 5