A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.
Answer: 3rd quadrant
A particular fruit's weights are normally distributed, with a mean of 275 grams and a standard deviation of 19 grams. If you pick one fruit at random, what is the probability that it will weigh between 244 grams and 305 grams?
Answer:
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 275 grams and a standard deviation of 19 grams
This means that [tex]\mu = 275, \sigma = 19[/tex]
What is the probability that it will weigh between 244 grams and 305 grams?
This is the p-value of Z when X = 305 subtracted by the p-value of Z when X = 244.
X = 305
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{305 - 275}{19}[/tex]
[tex]Z = 1.58[/tex]
[tex]Z = 1.58[/tex] has a p-value of 0.9429.
X = 244
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{244 - 275}{19}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a p-value of 0.0516
0.9429 - 0.0516 = 0.8913
0.8913 = 89.13% probability that it will weigh between 244 grams and 305 grams.
A zoo is designing a giant bird cage consisting of a cylinder of radius rr feet and height hh feet with a hemisphere on top (no bottom). The material for the hemisphere costs 2020 per square foot and the material for the cylindrical sides costs 1010 per square foot; the zoo has a budget of 45004500. Find the values of rr and hh giving the birds the greatest space inside assuming the zoo stays within its budget. Note: surface of a cylinder's side 2πrh2πrh, surface of a sphere 4πr24πr2, volume of a cylinder's side πr2hπr2h, volume of a sphere 43πr343πr3
Answer:
r = 42,32 ft
h = 84.8 ft
Step-by-step explanation:
We are going to apply Lagrange multipliers method
The greatest space means maximum volume
V(cage) = Vol. of the cylinder + volume of the hemisphere
V(cylinder ) = π*r²*h
V(sphere) = (4/3)*π*r² ⇒ V(hemisphere) = (2/3)*π*r³
V(cage) = π*r²*h + (2/3)*π*r³
Associated costs:
Costs = cost of cylinder + cost of hemisphere
Area of the cylinder = Lateral area ( no bottom no top)
Area of the cylinder = 2*π*r*h
Area of hemisphere = 2*π*r²
A(r,h) = 2*π*r*h + 2*π*r²
C(r , h ) = 10* 2*π*r*h + 20* 2*π*r² C(r , h ) = 20*π*r*h + 40*π*r²
4500 = 20*π*r*h + 40*π*r²
20*π*r*h + 40*π*r² - 4500 = 0 20*π*r*h + 40*π*r² - 4500 = g(r,h)
V(cage) = π*r²*h + (2/3)*π*r³
δV/δr = 2*r*π*h + 2*π*r² δg(r,h)/δr = 20*π*h + 80*π*r
δV/δh = π*r² δg(r,h)/δh = 20*π*r
δV/δr = λ* δg(r,h)/δr
2*r*π*h + 2*π*r² = λ* 20*π*h + 80*π*r
2*r*π* ( h + r ) = 20*π* λ* ( h + 4*r)
r* ( h + r ) = 10*λ* ( h + 4*r) (1)
δV/δh = λ* δg(r,h)/δh
π*r² = 20*λ*π*r r = 20*λ (2)
20*π*r*h + 40*π*r² - 4500 = 0 (3)
We need to sole the system of equation 1 ; 2 ; 3
r = 20*λ plugging that value in equation 1
20*λ ( h + 20*λ ) = 10*λ* ( h + 4*r)
2( h + 20*λ ) = ( h + 4*20*λ)
2*h + 40*λ = h + 80*λ
h = 40*λ
20*π*r*h + 40*π*r² - 4500 = 0
20*π*20*λ*40*λ + 40*π+400λ² - 4500 = 0
16000*π*λ² + 16000*π*λ² = 4500
32000*π*λ² = 4500
320*π*λ² = 4500
λ² = 4500/1004,8 λ² = 4.48 λ = 2.12
Then
r = 20* λ r = 42,32 ft
h = 40* λ h = 84.8 ft
\left(a+b\right)^2 hihihihihiihihihihihih
Consider, we need to find the expanded form of the given expression.
Given:
The expression is:
[tex]\left(a+b\right)^2[/tex]
To find:
The expanded form of the given expression.
Solution:
We have,
[tex]\left(a+b\right)^2[/tex]
It can be written as:
[tex]\left(a+b\right)^2=(a+b)(a+b)[/tex]
Using distributive property of multiplication over addition, we get
[tex]\left(a+b\right)^2=a(a+b)+b(a+b)[/tex]
[tex]\left(a+b\right)^2=a(a)+a(b)+b(a)+b(b)[/tex]
[tex]\left(a+b\right)^2=a^2+ab+ab+b^2[/tex]
[tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex]
Therefore, the expanded form of the given expression is [tex]a^2+2ab+b^2[/tex].
What is the y-intercept of this quadratic function? f(x)= -x^2
Answer:
x-intercept(s):
( 0 , 0 )
y-intercept(s):
( 0 , 0 )
Step-by-step explanation:
Answer:
(0,0)
Step-by-step explanation:
This has no real starting point. The x-intercept as well as the y-intercept is (0,0).
reflectiion across y=x
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The reflection across y=-x swaps the coordinates and negates both of them. The first-quadrant figure becomes a third-quadrant figure.
(x, y) ⇒ (-y, -x)
Which of the following best represents the relationship between functions f and g?
g(x) = -f(x) - 1
g(x) = f(x - 1)
g(x) = -f(x) + 1
g(x) = -f(x)
9514 1404 393
Answer:
(c) g(x) = -f(x) +1
Step-by-step explanation:
We really only need to consider one point on f(x) and/or g(x). We can look at the y-intercepts.
f(0) = 4 and g(0) = -3
Looking at the answer choices, we see ...
A. -f(0) -1 = -4 -1 = -5 ≠ g(0)
B. f(0 -1) = f(-1) = 1 ≠ g(0)
C. -f(0) +1 = -4 +1 = -3 = g(0) . . . . . matches requirements
D. -f(0) = -4 ≠ g(0)
The relation between f(x) and g(x) is g(x) = -f(x) +1.
NEED HELP ASAP!!!!!!
Answer:
It's a rhombus (if you can check more than one answer, it's also a parallelogram).
Step-by-step explanation:
A rhombus is a flat shape with 4 straight sides that are all equal length.
Also opposite sides are parallel and opposite angles are equal.
It is a type of parallelogram.
Answer:
It's a rhombus
Step-by-step explanation:
because all the 4 sides are equal
And it's like a square that it's top has been pushed
Let x be a real number such that x + (1/x) is an integer. Prove that (x^n) + 1/(x^n) is an integer for every positive integer n.
Answer:
sim eu também preciso desta respota
6. A company builds a model of its earning, and finds that its profit fits the linear model()=5―2500 Where p is the profit in dollars and q is the quantity of its product sold. a) Explain what the slope and y-intercept mean in the context of the problem. Be specific and answer in complete sentence. (2 points)
Answer:
The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.
Step-by-step explanation:
Linear function:
A linear function has the following format:
[tex]y = mx + b[/tex]
In which m is the slope, that is, by how much y changes for each unit of x, and b is the y-intercept, which is the values of y when x = 0.
In this question:
[tex]p(q) = 5q - 2500[/tex]
p is the profit in dollars and q is the quantity of its product sold.
a) Explain what the slope and y-intercept mean in the context of the problem.
The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.
Which statement is true.?
Answer:
B
Step-by-step explanation:
Please help me solve this. I keep getting the answer weong
Answer:
21 is the answer I think sike I lied ik its not im just trying get this over with
You can use this formula to work out the area of a triangle when you know two sides and the angle inbwtween them :
1/2 x a x b x sin(C)
where a and b are the two sides you know and C is the angle in between them.
So here a = 7, b = 14, C = 125.
Area = 1/2 x 7 x 14 x sin(125) = 40.138...
= 40.1 (nearest 10th)
Joe drives for 3 hours and covers 201 miles. In miles per hour, how fast was he driving?
Answer:
50
Step-by-step explanation:
I don't understand plz help
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
Triangles QST and QSR are congruent, so angle QST is congruent to angle QSR.
(3x +24)° = 30°
3x = 6 . . . . . . . . . divide by °, subtract 24
x = 2 . . . . . . . . . . divide by 3
__
Additional comment
What matters here is the relationship between the two marked acute angles. The fact that point Q is equidistant from the sides of angle TSR tells you that QS is an angle bisector and the two angles have equal measures. (The definition of an angle bisector is that it is equidistant from the sides of the angle.)
Recognition that the two triangles are congruent is another way to see that the marked acute angles have the same measure. The triangle congruence can be claimed on the basis of the HL theorem, since both are right triangles, have the same hypotenuse (QS), and have legs (QT, QR) with the same measure.
Please solve this equation
Answer:
fggggg hasdnkuw
Step-by-step explanation:
if a line intersect x axis at a point (6,0) and y axis at a point (0,-8). then what is equation of a line?
Answer: y = 4/3x -8
Step-by-step explanation:
(6,0) (0,-8)
0-(-8)/6-0 = 8/6 = 4/3
y intercept is given already
There are 9 students in a class: 7 boys and 2 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
Answer: 9/7
Step-by-step explanation:
find the value of x if 3x over 2 equals to 3
Answer:
x = 2
Step-by-step explanation:
3x/2 = 3/1
cross-multiply to get:
3x = 6
divide each side by 2 to get:
x = 2
6. a semicircle has as its diameter the hypotenuse of a right triangle shown below. determine the area of the semicircle to the nearest tenth of a square centimeter. show how you arrived at your answer.
Answer:
[tex]A = 137.3cm^2[/tex]
Step-by-step explanation:
Given
See attachment
Required
The area of the semicircle
First, we calculate the hypotenuse (h) of the triangle
Considering only the triangle, we have:
[tex]\cos(68) = \frac{7}{h}[/tex] --- cosine formula
Make h the subject
[tex]h = \frac{7}{\cos(68)}[/tex]
[tex]h = \frac{7}{0.3746}[/tex]
[tex]h = 18.7[/tex]
The area of the semicircle is then calculated as:
[tex]A = \frac{\pi h^2}{8}[/tex]
This gives:
[tex]A = \frac{3.14 * 18.7^2}{8}[/tex]
[tex]A = \frac{1098.03}{8}[/tex]
[tex]A = 137.3cm^2[/tex]
can someone help me with this?
Answer: 22
Step-by-step explanation: 44:2=22
PLEASE HELP ME WITH THIS ONE QUESTION
How many combinations without repetition are possible if n = 4 and r = 3?
A) 16
B) 12
C) 3
D) 4
Given:
[tex]n=4[/tex] and [tex]r=3[/tex].
To find:
The combinations without repetition are possible if [tex]n=4[/tex] and [tex]r=3[/tex].
Solution:
Combination of selecting r item from total n items is:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have [tex]n=4[/tex] and [tex]r=3[/tex]. By using the above formula, we get
[tex]^4C_3=\dfrac{4!}{3!(4-3)!}[/tex]
[tex]^4C_3=\dfrac{4\times 3!}{3!1!}[/tex]
[tex]^4C_3=4[/tex]
Therefore, the correct option is D.
Answer:
Step-by-step explanation:
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
9514 1404 393
Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
Choose the equation of the line that is parallel to the x-axis.
x = 4
x + y = 0
x = y
y = 4
please help thx steps too
Step-by-step explanation:
IN first triangle multiplier factor is 4
and IN second triangle multiplier factor is
[tex] \frac{3}{2} [/tex]
Can someone help me with this question please.
Answer:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
Step-by-step explanation:
The rule is to divide the weight of the bag by 4 to find the number of marbles.
Reflect (-3, 4) across the y-axis. Then reflect the result across the x-axis.
1. Determine the length and perimeter of Laura's property.
(5)
9514 1404 393
Answer:
length: 40 mperimeter: 136 marea: 653 m²volume: 6.52 m³Step-by-step explanation:
1.The outer dimensions of the property are 20 squares (length) by 14 squares. Each square is 2 m on a side, so the overall length of the property is ...
(20 squares)×(2 m/square) = 40 m . . . . length
The overall width of the property is ...
(14 squares)×(2 m/square) = 28 m . . . . width
Then the perimeter is ...
P = 2(length + width) = 2(40 +28) m = 136 m . . . . perimeter
__
Additional comment
We have computed the perimeter as though the plot were a rectangle. If you carefully consider the total length of horizontal edges and the total length of vertical edges, you see that those totals are the same as they would be for a 20×14 square (40×28 m) rectangle.
_____
2.The area of open ground is perhaps most easily computed by finding the area that must be subtracted from the overall 20×14 square rectangle. Those exclusions will be (in dimensions of squares) ...
lower right corner: 8 wide by 3 high = 24 squaresfish pond: 2 wide by 3 high = 6 squaresveranda: 4 wide by 4 high = 16 squareshouse: 9 wide by 7 high = 63 squarespavement: 4 wide by 2 high = 8 squaresThe total area of exclusions is 24+6+16+63+8 = 117 squares. The bounding rectangle is 20 by 14 = 280 squares, so the open ground is ...
280 squares - 117 squares = 163 squares
At (2 m)(2 m) = 4 m² per grid square, that's an area of ...
(163 squares)(4 m²/square) = 652 m²
The surface area of the open ground is 652 m².
_____
3.The volume is given by the formula ...
V = Bh
where B is the base area and h is the height.
1 cm = 1/100 m = 0.01 m thickness. That means the total volume is ...
V = (652 m²)(0.01 m) = 6.52 m³
6.52 cubic meters of topsoil are needed to cover the open ground to a depth of 1 cm.
Noah is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $2 per mile driven. How much would a taxi ride cost if Noah is riding for 4 miles? How much would a taxi ride cost that is mm miles long?
Answer:
$10.50
Step-by-step explanation:
We can make an equation
2.50+2x=?
x=4 because we are riding 4 miles.
so it's 2.5+2*4=?
let's solve
2.5+8=$10.50
The Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m
Given:
Pick up charge = $2.50
Charge per mile = $2
Number of miles = 4
Cost of the taxi ride for 4 miles = Pick up charge + (Charge per mile + Number of miles)
= 2.50 + (2 × 4)
= 2.50 + 8
= $10.50
Charge for m miles = Pick up charge + (Charge per mile + Number of miles)
= 2.50 + (2 × m)
= 2.50 + 2m
Therefore, Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m
Read more:
https://brainly.com/question/8957185
A local hamburger shop sold a combined total of 393 hamburgers and cheeseburgers on Thursday. There were 57 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
Answer:
H+C = 393
H - 57 = C
~~~~~~~~~~~~~~~~
H + H - 57 = 393
2H = 450
H = 225
C = 168
Step-by-step explanation:
4n-6 in as a undistributed expression
Answer:
2( 2n-3)
Step-by-step explanation:
4n-6
2*2 n - 2*3
Factor out the greatest common factor
2( 2n-3)
For each of the studies described, explain whether the study was an observational study or a randomized experiment.
a. A group of 100 students was randomly divided, with 50 assigned to receive vitamin C and the remaining 50 to receive a placebo, to determine whether or not vitamin C helps to prevent colds.
b. A random sample of patients who received a hip transplant operation at Stanford University Hospital during 2000 to 2010 will be followed for 10 years after their operation to determine the success (or failure) of the transplant.
c. Volunteers with high blood pressure were randomly divided into two groups. One group was taught to practice meditation and the other group was given a low-fat diet. After 8 weeks, reduction in blood pressure was compared for the two groups.
Answer:
B
Step-by-step explanation:
B