Answer:
626.968
Step-by-step explanation:
EMDAS rule
solve the absolute value 4=1+(2-1/4w)
Consider the functions f and g in the tables below. f(x) = 90x2 + 180x + 92 x y 0 92 1 362 2 812 3 1,442 4 2,252 5 3,242 g(x) = 6x x y 0 1 1 6 2 36 3 216 4 1,296 5 7,776 Which of the following statements is true? A. At approximately x = 4.39, the rate of change of f is equal to the rate of change of g. B. As x increases, the rate of change of g exceeds the rate of change of f. C. As x increases, the rate of change of f exceeds the rate of change of g. D. For every value of x, the rate of change of g exceeds the rate of change of f.
Answer:
As x increases, the rate of change of g exceeds the rate of change of f.
Step-by-step explanation:
Given
[tex]f(x) = 90x^2 + 180x + 92[/tex]
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} \ \end{array}[/tex]
[tex]g(x) = 6^x[/tex]
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} \ \end{array}[/tex]
Required
Which of the options is true?
A. At [tex]x \approx 4.39[/tex], f(x) has the same rate of change as g(x)
Rate of change is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For f(x)
[tex]f(x) = 90x^2 + 180x + 92[/tex]
[tex]f(4.39) = 90*4.39^2 + 180*4.39 + 92 = 2616.689[/tex]
So, the rate of change is:
[tex]m = \frac{2616.689}{4.39} = 596.06[/tex]
For g(x)
[tex]g(x) = 6^x[/tex]
[tex]g(4.39) = 6^{4.39} = 2606.66[/tex]
So, the rate of change is:
[tex]m = \frac{2606.66}{4.39} = 593.77[/tex]
The rate of change of both functions are not equal at x = 4.39. Hence, (a) is false.
B. Rate of change of g(x) is greater than f(x) with increment in x
Using the formula in (a), we have:
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} & m &\infty & 362 & 406 & 480 & 563 &648.4\ \end{array}[/tex]
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} & m & \infty & 6 & 18 & 72 & 324 & 1555 \ \end{array}[/tex]
From x = 1 to 4, the rate of change of f is greater than the rate of g.
However, from x = 5, the rate of change of g is greater than the rate of f.
This means that (b) is true.
The above table further shows that (c) and (d) are false.
Answer:
Step-by-step explanation:
C
find two number nearest to 8888888 which are exactly divisible by 2915
Step-by-step explanation:
Given problem is to find nearest number,
= 8888888/2915
quotient = 3049
remainder= 1053
Now, 2915-1053 = 1862
8888888+1862 = 8890750
8888888-1053 = 8887835
Two numbers nearest to 8888888 which are exactly divisible by 2915 is 8887835 and 8890750
urgent image below for the question
Answer:
240 ft²
Step-by-step explanation:
Surface area of a rectangular prism is,
2(lw+wh+hl)
= 2(7×6+6×6+6×7)
= 240 ft²
If 3(nP2 + 24)=2nP2, find the positive value of n
Answer:
[tex]n = 8[/tex]
Step-by-step explanation:
Given
[tex]3(^nP_2 + 24) = ^{2n}P_2[/tex]
Required
Find n
To do this, we simply apply permutations formula
[tex]nP_r = \frac{n!}{(n -r)!}[/tex]
So, we have:
[tex]3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}[/tex]
Expand
[tex]3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}[/tex]
[tex]3 * [n * (n - 1) + 24] = 2n * (2n - 1)[/tex]
[tex]3 * [n^2 - n + 24] = 4n^2 - 2n[/tex]
Open bracket
[tex]3n^2 - 3n + 72 = 4n^2 - 2n[/tex]
Collect like terms
[tex]3n^2 - 4n^2- 3n+2n + 72 = 0[/tex]
[tex]-n^2- n + 72 = 0[/tex]
Expand
[tex]-n^2 -9n + 8n + 72 = 0[/tex]
Factorize
[tex]-n(n +9) - 8(n + 9) = 0[/tex]
Factor out n + 9
[tex](-n -8)(n + 9) = 0[/tex]
Split
[tex](-n -8)= 0 \ or\ (n + 9) = 0[/tex]
Solve for n
[tex]n =8\ or\ n = -9[/tex]
The positive value is [tex]n = 8[/tex]
What is the distance from point N to LM in the figure below?
N
8.4
8.1
7.8
O
O A. 3.11
B. 0.8
C. 8.1
D. 2.18
E. 7.8
F. 8.4
Answer:
the answer to your question is 7.8 (E)
The distance from point N to LM is 7.8, 8.1 and 8.4 unit.
What is perpendicular?Perpendicular lines are those that cross at a straight angle to one another. Examples include the opposite sides of a rectangle and the steps of a straight staircase. the icon used to represent two parallel lines.
Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle.
Given:
In ΔNOM
The Perpendicular distance is 7.8 unit
and, Hypotenuse distance id 8.1 unit
Now, In ΔNOL
The Perpendicular distance is 7.8 unit
and, Hypotenuse distance id 8.4 unit
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The lengths of pregnancies in a small rural village are normally distributed with a mean of 264.1 days and a standard deviation of 12.9 days. In what range would you expect to find the middle 95% of most pregnancies
Answer:
The range of the 95% data (X) = 238.3 days < X < 289.9 days
Step-by-step explanation:
Given;
mean of the normal distribution, m = 264.1 days
standard deviation, d = 12.9 days
between two standard deviation below and above the mean is 96% of all the data.
two standard deviation below the mean = m - 2d
= 264.1 - 2(12.9)
= 238.3 days
two standard deviation above the mean = m + 2d
= 264.1 + 2(12.9)
= 289.9 days
The middle of the 95% of most pregnancies would be found in the following range;
238.3 days < X < 289.9 days
Can anyone help? I am terrible at math!!
A class of 40 students visits a farm they tour the farm in group of 5 how many groups of 5 can they make?
Answer:
8
Step-by-step explanation:
40 grouped into 5 = 40/5 = 8
Find the focus and directrix of the parabola y = .5(x + 2)2 – 3
Answer:
comparing equation with standard equation x 2 =4aya=2/5co-ordinates of focus =(o,a) i.e. (0, 2/5)equation of directrix=y=-a i.e. y=-(2/5)length of latus rectum= 4a i.e. 8/5co-ordinates of latus rectum=(-2a,a) and (2a,a) i.e. (-4/5,2/5) and (4/5,2/5)..Step-by-step explanation:
And please marks me as brainliests..please and follow me...find the slope of the line (-3,-2) (1,6)
Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (1, 6)
m = [tex]\frac{6-(-2)}{1-(-3)}[/tex] = [tex]\frac{6+2}{1+3}[/tex] = [tex]\frac{8}{4}[/tex] = 2
write 10 toolbars on the keyboard
Answer:
WINKEY + D. ...
WINKEY + SPACE. ...
SHIFT + Mouse Click on a taskbar button. ...
CTRL + SHIFT + Mouse Click on a taskbar button. ...
SHIFT + Right Mouse Click on a taskbar button. ...
SHIFT + Right Mouse Click on a grouped taskbar button. ...
CTRL + Mouse Click on a grouped taskbar button. ...
WINKEY + T.
ctrl + X = cut
ctrl + c = copy
make me brainliest
is the multiplicative identity for rational number
Answer:
The rational number 1 is the multiplicative identity for rational numbers.
Step-by-step explanation:
I hope this will help you buddy
Please help me with this
Answer:
6
Step-by-step explanation:
c(2)=(-9/2)*(-4/3)^(2-1)=(-9/2)*(-4/3)=6
Determine the intervals on which the function is increasing, decreasing, and constant.
A. Increasing x>0; Decreasing x<0
B. Decreasing on all real numbers
C. Increasing on all real numbers
D. Increasing x<0; Decreasing x>0
Answer:
Option A, increasing x>0; decreasing x<0
how do i establish this identity?
RHS
[tex]\\ \sf\longmapsto \frac{2 \tan( \theta) }{ \sin(2 \theta) } \\ \\ \sf\longmapsto \frac{ \frac{2 \sin( \theta) }{2 \cos( \theta) } }{ \sin(2 \theta) } \\ \\ \sf\longmapsto \frac{1}{ \cos {}^{2} ( \theta) } \\ \\ \sf\longmapsto {sec}^{2} \theta[/tex]
Expand and simplify the following expressions. a. (2 − 3)( − 6)
Answer:
your answer should be six I hope this help
Answer:
the should be 6
Step-by-step explanation:
(2-3)(-6)
-12+18
=6
What type of line is PQ?
A. median
B. altitude
C. angle bisector
D. side bisector
I need help with this question to pass a test
Answer:
Option C, angle bisector
Answered by GAUTHMATH
The area of a square is 64 cm2 then find it's perimeter.
Answer:
32cm
Step-by-step explanation:
The area of sqaure is a^2
Side will be
underroot of 64 =8
Premeter of sqaure is 4a = 4×8 = 32cm
first we need to find length.
here.
Area= 64cm^2
or, 64= l^2
using formula area = length × length
therefore solving we get ,
length = 8 cm.
now,
perimeter = 4l
= 4 × 8 cm.
= 32 cm..........
F(x) = 3x+5 G(x)= 4x^2-2 H(x) = x^2-3x+1 Find f(x) +g(x) -h(x)
Answer:
Step-by-step explanation:
f(x) + g(x) = 3x + 5 + 4x^2 - 2
f(x) + g(x) = 4x^2 + 3x + 3
f(x) + g(x) - h(x) = 4x^2 + 3x + 3 - (x^2 - 3x + 1) Remove the brackets.
f(x) + g(x) - h(x) = 3x^2 +3x + 3 - x^2 + 3x - 1 Collect like terms
f(x)+g(x) - h(x) = 2x^2 + 6x + 2
Answer:
f(x)=3x^2+6x+2
Step-by-step explanation:
Need to know Anwser yes or no
Answer:
Reflective symmetry over the line y = 4 is No
Reflective symmetry over the line y = 1/7x + 3 is Yes
Find the derivative on the value of x=-4
[tex]y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=(6x-5)\sqrt{8x-3}[/tex]
[tex]\\ \sf\longmapsto y=6(-4)-5\sqrt{8(-4)-3}[/tex]
[tex]\\ \sf\longmapsto y=-24-5\sqrt{-32-3}[/tex]
[tex]\\ \sf\longmapsto y=-29\sqrt{-35}[/tex]
[tex]\\ \sf\longmapsto y=-29\times 35i[/tex]
[tex]\\ \sf\longmapsto y=-1015i[/tex]
The maximum and minimum values of a quadratic function are called as________of the function.
Vertex is the point where the function is at its maximum/ minimum.
A(6, -5) and B(-1, 2) in the ratio of 2:5
Answer:
p(x,y)= (4,-3)
Step-by-step explanation:
all explainations are in the picture below.
4.Siti and Janice spent 3h 25min altogether in Shopping malls A and B. If they spent 1h 45min in Shopping mall A, how long did they spend in Shopping mall B?
Answer:
1 hour and 40 minutes
Step-by-step explanation:
→ Convert 3 hr and 25 minutes to minutes
( 3 × 60 ) + 25 = 205 minutes
→ Convert 1 hr and 45 minutes to minutes
( 1 × 60 ) + 45 = 105 minutes
→ Minus the answers from each other
205 - 105 = 100 minutes
→ Convert 100 minutes to hours and minutes
1 hour and 40 minutes
One third of number is four times eleven. What is half of that number
Answer:
One third of a number is four times eleven. What is the half of that number?
Explanation:
Four times 11 = 11 X 4 = 44
One third (1/3) of the number = 44
The number is = 44 X 3 = 132
Therefore half of the number 132 = 66
Answer:
66
Step-by-step explanation:
11 X 4 = 44
One third (1/3) of the number = 44
The number is = 44 X 3 = 132
Therefore half of the number 132 = 66
The length of a rectangle is 4 units more than its width. The area of the rectangle is 25 more than 4 times the
width. What is the width of the rectangle?
A А 9
B -5
С. 3
D 5
Please select the best answer from the choices provided
Answer:
D
Step-by-step explanation:
let the width = w
w = w
L = 4 + w
Area = 4*w + 25 = L * w
4w + 25 = L * w Substitute for the length
4w + 25 = (w*(w + 4))
4w + 25 = w^2 + 4w Subtract 4w from each side
w^2 = 25 Take the square root.
w = +/- 5
- 5 has no meaning.
w = 5
what is symmetrical line
Answer:
assuming youre asking for line of symmetry, it's a line that cuts a shape exactly in half.
for example, a square has 4 lines of symmetry
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x – 9y = -72
the slope-intercept form of the given equation is y = x/3 + 8.
What is the slope?The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.
The slope-intercept form of a line is Y = m*X +C.
Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.
3x-9y = -72
9y = 3x + 72
y = 1/3 * x + 8
Therefore y = x/3 + 8 is the slope-intercept form of the given equation. where its slope is 1/3.
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Of the respondents, 502 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment?
Answer:
The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]
Step-by-step explanation:
Incomplete question, so i will suppose this is a sample of 1000.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of the n respondents, 502 replied that America is doing about the right amount.
Supposing [tex]n = 1000[/tex], so [tex]\pi = \frac{502}{1000} = 0.502[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 - 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.461[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 + 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.543[/tex]
The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]
