Answer:
-1/4x² + 3
Step-by-step explanation:
Given that:
Path of sprinkler is modeled by the quadratic function :
w(x) = -1/4(x^2 -12 )
w(x) = height of the water, in meters, at position x
The height of ceiling as a constant or Coefficient = w(x)
Expanding w(x)
-1/4(x^2 -12 )
-1/4 * x² + 1/4 * 12
-1/4x² + 3
The height of ceiling is -1/4x² + 3
Q3a) How many lengths of string, each 53 cm
long can be cut from a ball containing 25
meters? (2 mks)
b) What length of string, in millimeters
remains? (2 mks)
Part (a)
1 meter = 100 cm
25 meters = 2500 cm .... multiply both sides by 25
Divide the 2500 cm over the 53 cm to get 2500/53 = 47.1698
Ignore the stuff after the decimal point. This means we can cut exactly 47 smaller bits of string, each 53 cm long
Answer: 47====================================================
Part (b)
We found that we can cut exactly 47 smaller bits of string, each 53 cm long. That takes up 47*53 = 2491 cm overall
The leftovers would be 2500 - 2491 = 9 cm which isn't longer than 53 cm
Convert 9 cm to mm by multiplying by 10 (because 1 cm = 10 mm).
9 cm = 90 mm
Answer: 90 mmThe sequence is defined recursively. Write the first four terms.
a 1 = -10; a n = n - a n - 1
Answer:
-10, 12, -9 and 13
Step-by-step explanation:
Given the recursive sequence
a1 = -10
an = n - an-1
a2 = 2 - a1
a2 = 2 - (-10)
a2 = 2+10
a2 = 12
a3 = 3 - a2
a3 = 3 - (12)
a3 = -9
a4 = 4 - a3
a4 = 4 - (-9)
a4 = 4+9
a4 = 13
Hence the first 4 terms are -10, 12, -9 and 13
Which statements are true of the given function?
Check all that apply.
9514 1404 393
Answer:
B, E
Step-by-step explanation:
The table tells you that f(0) = 3/2. (0 is found in the x-column; 3/2 is found in the f(x) column.)
__
You can find f(4) by evaluating the formula.
f(4) = 1/2·4 +3/2 = 4/2 +3/2
f(4) = 7/2 . . . . agrees with last answer choice
Answer:
A ,B and E ;)
Step-by-step explanation:
Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival time may be modeled by the random variable T, such that
f(T = t) = {3/5 (5/t)^4 , t ≥ 5
0, otherwise
If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?
А. 62%
B. 73%
C. 88%
D. 91%
E. 96%
Answer:
D. 91%
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Less than 15 minutes.
Event B: Less than 10 minutes.
We are given the following probability distribution:
[tex]f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5[/tex]
Simplifying:
[tex]f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}[/tex]
Probability of arriving in less than 15 minutes:
Integral of the distribution from 5 to 15. So
[tex]P(A) = \int_{5}^{15} = \frac{375}{t^4}[/tex]
Integral of [tex]\frac{1}{t^4} = t^{-4}[/tex] is [tex]\frac{t^{-3}}{-3} = -\frac{1}{3t^3}[/tex]
Then
[tex]\int \frac{375}{t^4} dt = -\frac{125}{t^3}[/tex]
Applying the limits, by the Fundamental Theorem of Calculus:
At [tex]t = 15[/tex], [tex]f(15) = -\frac{125}{15^3} = -\frac{1}{27}[/tex]
At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]
Then
[tex]P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}[/tex]
Probability of arriving in less than 15 minutes and less than 10 minutes.
The intersection of these events is less than 10 minutes, so:
[tex]P(B) = \int_{5}^{10} = \frac{375}{t^4}[/tex]
We already have the integral, so just apply the limits:
At [tex]t = 10[/tex], [tex]f(10) = -\frac{125}{10^3} = -\frac{1}{8}[/tex]
At [tex]t = 5[/tex], [tex]f(5) = -\frac{125}{5^3} = -1[/tex]
Then
[tex]P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}[/tex]
If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087[/tex]
Thus 90.87%, approximately 91%, and the correct answer is given by option D.
There are 25 black cars, 15 blue cars, 21 red cars and 30 white cars what is the probability of getting a red car
25 points!!!!!!!!
Solve the system of equations.
4x + 3y + 5z = 6
6x + 8y + 62 = 4
4x + 2y + 62 = 8
please select the best answer from me the choices provided
a. (x = 1, y = - 1,2 = 1)
b. (x = 3, y = -3, z = 3)
(x = 0, y = 0, z = 2)
d. (x = 2, y = -2, z = 0)
Answer:
A is your answer, my guy
Step-by-step explanation:
4x1=4
3x-1=-3
5x1=5
4+(-3)+5=6
6x1=6
8x-1=-8
6x1=6
6+(-8)+6=4
4x1=4
2x-1=-2
6x1=6
4+(-2)+6=8
picture down below please help
Answer: please add the picture
Step-by-step explanation:
Find the zeroes of this quadratic (5b – 4)(b + 3) = 0
Answer:
b=4/ 5
Step-by-step explanation:
What means the same as 6 x 5?
What means the same as 3 + 3 + 3 + 3?
65
35
5 + 5 + 5 + 5 + 5
3 X 3
6 + 6 + 6 + 6 + 6
3 X 4
COMPLETE
COMPLETE
What means the same as 657
What means the same as 2.2.2.2. 2?
5.5.5.5.5
25
6.6.6.6.6
2 x 5
6 + 6 + 6 + 6 + 6
52
COMPLETE
COMPLETE
Answer:
6x5 can also be 6+6+6+6+6
3+3+3+3 can also be 3x4
5+5+5+5+5 can also be 25
3x3 can be 3+3+3
Step-by-step explanation:
Answer:
Here were your Answers
Step-by-step explanation:
Good Job you got it right you must be new to this app because your suppose to ask a question then someone will come and see your question and answer it for you maybe look around at other people's question's and how to use this app. Have a Nice day :) happy face This is for
omar2566 and for everyone!
Will Mark Brainlest help please
Answer:
g(-1 )=-1 and g(2)+g(1)=7
Step-by-step explanation:
If g(x) = x^3+x^2-x-2 find g(-1)
if we find g(-1)
we substitute all the x's in the function with -1
-1^3+-1^2-(-1)-2
-1^3 = -1
-1^2 = 1
-1+1+1-2
(two minuses make a plus)
-1+1 = 0
0+1 = 1
1-2 = -1
if x=-1, g(-1) is -1
g(2)+g(1)
substitute the x's in the function with 2 and 1 and add your results
2^3+2^2-2-2
2^3 = 8, 2^2 = 4
8+4-2-2
8+4= 12, 12-2 = 10, 10-2 = 8
g(2)=8
g(1) now
1^3 + 1^2-1-2
1^3=1, 1^2 = 1
1+1-1-2
1+1 = 2, 2-1 = 1, 1-2 = -1
g(3) = -1
g(2) (which equals 8) + g(3) (which equals -1) =
8+(-1) = 7
g(2)+g(3)=7
Which descriptions from the list below accurately describe the relationship
between AXYZ and AUVW? Check all that apply.
Answer:
Same shape
Similar
Answer:
B. Same shape
C. Similar
Step-by-step explanation:
The three angles in ∆XYZ are congruent to the corresponding three angles in ∆UVW.
Also, the ratio of the corresponding side lengths of ∆XYZ to ∆UVW are the same. i.e. WU/XY = VW/XZ = UW/XZ = 2
Therefore, we can conclude that they are similar because they have the same shape even though their sizes are different.
Using the diagram below, which of the following parts of the triangles are
congruent?
9514 1404 393
Answer:
B. ∠A ≅ ∠E
Step-by-step explanation:
The similarity statement tells you the corresponding angles are ...
ΔCAB ~ ΔCED
∠C ≅ ∠C . . . . listed first in the similarity statement
∠A ≅ ∠E . . . . listed second in the similarity statement
∠B ≅ ∠D . . . . listed third in the similarity statement
The relationship between angles A and E is properly shown in answer choice B.
Consider function g.
6,
-8 < x <-2 2
g(x) =
0,
-2
-4, 4 < x < 10
What are the values of the function when x = -2 and when r = 4?
gl-2)
=
3
g(4)
=
N
[tex]x = - 2 \: then \: g( - 2) = 0 \\ x = 4 \: then \: g(4) = - 4.[/tex]
Hence, The values of the function when x = -2 is g(x) = 0 and x = 4 is
g(x) = - 4.
What is composite function?A composite function is created when one function is substituted into another function.
Given
Composite Function g
g(x) = 6, -8 ≤ x ≤ -2
g(x) = 0, -2 ≤ x ≤ 4
g(x) = -4, 4 ≤ x ≤ 10
The values of the function when x = -2
x is between -2 and 4
g(x) = 0, -2 ≤ x ≤ 4
Thus, The values of the function when x = -2 is g(x) = 0
The values of the function when x = 4
x is between 4 and 10
g(x) = -4, 4 ≤ x ≤ 10
Thus, The values of the function when x = 4 is g(x) = - 4
Hence, The values of the function when x = -2 is g(x) = 0 and x = 4 is
g(x) = - 4.
Learn more about composite function here
https://brainly.com/question/20379727
#SPJ2
A local grocery store charges for oranges
based on weight as shown in the graph below.
Find the price (dollars per kilogram) of
oranges at the grocery store.
dollars per kilogram
Answer:
3 dollars
Step-by-step explanation:
Khan academy said so
In practice, the most frequently encountered hypothesis test about a population variance is a _____. a. two-tailed test, with equal-size rejection regions b. two-tailed test, with unequal-size rejection regions c. one-tailed test, with rejection region in upper tail d. one-tailed test, with rejection region in lower tail
Answer:
c. one-tailed test, with rejection region in the upper tail.
Step-by-step explanation:
One tailed test is statistical test in which critical area of distribution is one sided and greater or less than certain value. One tailed test can be left or right sided depending on the population distribution. Rejection region of the one tailed test will determine whether to accept or reject the null hypothesis.
Side View of a Waterslide
Select the points you need to calculate the
average rate of change from the beginning of the
slide to when the slide has covered a horizontal
distance of 15 feet.
800
O
(0, 80)
60
(5, 40)
OOO
Height (ft)
(10, 20)
(15, 10)
DONE
20
20
10
Horizontal Distance (ft)
Answer:
(0, 80)
(15, 10)
Step-by-step explanation:
The initial point the beginning of the point and the point where the horizontal distance covered is 15 ft are the two points needed to calculate the average rate of change required.
From the graph,
Initial point = (0, 80)
The point of the slide when distance covered is 15 ft = (15, 10)
These are the points needed.
HELP FAST PLS
Factor x2 - 7x + 8.
O (X + 8)(x - 1)
O Prime
O (x - 3)(x - 1)
O (X + 8)(x + 1)
The 12th term of GP whose
1
first term is 1/8 and second
term is 1/2is
Answer:
jjanation:jdgjdjgdjgjkdkidjgjghdjjghhkd
which geometric figures are shown in the diagram
Answer:
A circle to start off, encompassing almost the entire figure, then a triangle, with D, A and C as its vertices, then a fan (a sector of a circle), with C, E and B as its vertices. Next, a chord (DA) which serves as a line segment at the same time, and finally three rays, starting from C and ending in A, B and E respectively. In total, six geometric figures.
Step-by-step explanation:
Hope this helped!
Determine the equation of the circle graphed below.
10
8
10
-10
-8
-6
2
-2
-4
-6
-8
-10
Answer:
Equation = (x - 6 )² + ( y + 3 )² = 9
Step-by-step explanation:
The circle passes through ( 6, 0) and ( 6 , -6)
They are the coordinates of the diameter.
Using this we can find the centre of the circle.
Find the centre of the circle.
Centre of the circle is the mid- point of (6, 0) and ( 6, -6)
[tex]Centre = (\frac{x_1+x_2}{2} , \frac{y_1 + y_2}{2})[/tex]
[tex]=(\frac{6 + 6}{2}, \frac{0 + (-6)}{2})\\\\=(6, -3)[/tex]
Find the radius of the circle.
[tex]Radius = \frac{Diameter }{2}[/tex]
Diameter is the distance between the points (6 , 0) and ( 6, - 6)
[tex]Diameter = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2\\}[/tex]
[tex]=\sqrt{(6-6)^2 + (-6 -0)^2}\\\\=\sqrt{0 + 36} \\\\= 6[/tex]
Therefore,
[tex]Radius ,r = \frac{6}{2} = 3[/tex]
Standard equation of a circle:
[tex](x - a)^2 + (y - b)^2 = r^2 \ where \ (a , b) \ is \ the\ centre \ coordinates.[/tex]
Therefore , equation of the circle ;
[tex](x - 6)^2 + (y + 3)^2 = 3^2\\\\(x -6)^2 + (y + 3)^2 = 9[/tex]
Round the following as specified.
153.38519 to the nearest thousandth.
Answer:
153.3852
Step-by-step explanation:
After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2
Answer:
153.385
Step-by-step explanation:
153.38519
153.38519
The digit to the right of the thousandth (the the one, which is bolded) is less than or equal to 4, which means we round down.
153.38519 ≈ 153.385
Hope this helps.
In the figure below net of cube is show
Find the surface area of cube.
3 in
Answer:
Surface Area = 54 in^2
Step-by-step explanation:
SA = [tex]6a^{2}[/tex]
SA = [tex]6(3)^2[/tex] Solve for the exponents first
SA = 6(9) Then multiply
SA = 54 square inches
How many quarts of pure antifreeze must be added to 8 quarts of a 10% antifreeze solution to obtain a 60% antifreeze solution
Answer:
10 quarts
Step-by-step explanation:
.1(8) + 1(x) = .6(x + 8)
.8 + x = .6x + 4.8
.4x = 4
x = 10
10 quarts
tiệm cận ngang của đồ thị y= 2-x/x+3
tiệm cận ngang của đồ thị 3/x+3
PLEASE HELP QUICK!! WILL GIVE BRAINLIEST ANSWER!!!!!!!
Answer:
X = 32
Step-by-step explanation:
Angle BEC = 43 degrees
You find X by setting up the equation 137 = 3x+41
Solve for x
You find angle BEC by subtracting 137 from 180, finding the acute angle that brings the obtuse angle up to 180 degrees (a flat line)
Answer:
x = 32 degree and angle BEC = 43 degree
Step-by-step explanation:
3x + 41 = 137 degree (being vertically opposite angles)
3x = 137 - 41
x = 96/3
x = 32
angle BEC be y
137 + y =180 degree (being linear pair)
y = 180 - 137
y = 43 degree
therefore angle BEC = 43 degree
what are the first five terms of the recursive sequence
Answer: Choice D
9, 30, 93, 282, 849
============================================================
Explanation:
The notation [tex]a_1 = 9[/tex] tells us that the first term is 9
The notation [tex]a_n = 3*(a_{n-1})+3[/tex] says that we multiply the (n-1)st term by 3, then add on 3 to get the nth term [tex]a_n[/tex]
So if we wanted the second term for instance, then we'd say
[tex]a_n = 3*(a_{n-1})+3\\\\a_2 = 3*(a_{2-1})+3\\\\a_2 = 3*(a_{1})+3\\\\a_2 = 3*(9)+3\\\\a_2 = 27+3\\\\a_2 = 30\\\\[/tex]
If we want the third term, then,
[tex]a_n = 3*(a_{n-1})+3\\\\a_3 = 3*(a_{3-1})+3\\\\a_3 = 3*(a_{2})+3\\\\a_3 = 3*(30)+3\\\\a_3 = 90+3\\\\a_3 = 93\\\\[/tex]
and so on.
The terms so far are: 9, 30, 93
You should find the fourth and fifth terms are 282 and 849 respectively if you keep this pattern going.
Therefore, the answer is choice D
Solve the equation ln(x - 3) + ln(x + 1) = ln(x + 7)
x = 5, or x = ???
Answer:
x = 5 or x = - 2
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log (xy)
log x = log y ⇒ x = y
Given
ln(x- 3) + ln(x + 1) = ln(x + 7) , then
ln (x - 3)(x + 1) = ln (x + 7) , so
(x - 3)(x + 1) = x + 7 ← expand left side using FOIL
x² - 2x - 3 = x + 7 ( subtract x + 7 from both sides )
x² - 3x - 10 = 0 ← in standard form
(x - 5)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 2 = 0 ⇒ x = - 2
A rectangle is 6 centimetres longer than its width
If the perimeter of the rectangle is 28 centimetres, form an equation
involving x and solving it to find the width
of the rectangle
do u mean rectangle is longer or rectangles lenght is longer
Write in standard form 4.91E-2
Answer:
4.91e-2 in decimal form is 0.0491
One kilogram equals 2.2 pounds. If a paitent weighs 79.5kg, his weight is what in pounds?
Answer:
174.9
Step-by-step explanation:
since 1 kg is 2.2 lbs
79.5 times 2.2
they weight 174.9 lbs
Answer:
174.9 pounds
Step-by-step explanation:
Create a proportion where x is his weight in pounds:
[tex]\frac{1}{2.2}[/tex] = [tex]\frac{79.5}{x}[/tex]
Cross multiply:
x = 79.5(2.2)
x = 174.9
So, his weight in pounds is 174.9 pounds