Answer:
P(X > 112) = 0.21186.
Step-by-step explanation:
We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.
Let X = a random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 100
[tex]\sigma[/tex] = standard deviaton = 15
Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)
P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)
= 1 - 0.78814 = 0.21186
The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.
what is 25 (10 + 50) - 25?
Answer:
1,475
Step-by-step explanation:
10 + 50
= 60
60 * 25
= 1,500
1,500 - 25
= 1,475
Answer:
Hey there!
25(10+50)-25
25(60)-25
1500-25
1475
Hope this helps :)
How does the graph of y = a(x – h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. The vertex of the graph moves to a point half as far from the x-axis. The vertex of the graph moves to a point half as far from the y-axis.
Answer:
The vertex of the graph moves to a point twice as far from the y-axis.
Step-by-step explanation:
How does the graph of y = a(x – h)2 + k change if the value of h is doubled?
The vertex of the graph moves to a point twice as far from the x-axis.
The vertex of the graph moves to a point twice as far from the y-axis.because the role of h is to indicate the distance of the vertex from the y-axis.
The vertex of the graph moves to a point half as far from the x-axis.
The vertex of the graph moves to a point half as far from the y-axis.
Transformation involves changing the position of a function.
When h is doubled in [tex]\mathbf{y = a(x - h)^2 + k}[/tex], the vertex of the graph moves to a point twice as far from the y-axis.
The function is given as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
When the value of h is doubled, the new function becomes:
[tex]\mathbf{y' = a(x - 2h)^2 + k}[/tex]
Rewrite as:
[tex]\mathbf{y' = a(x - h- h)^2 + k}[/tex]
The above equation means that:
Function y will be translated to the right by h units
Assume the vertex is:
[tex]\mathbf{Vertex = (2,5)}[/tex]
The new vertex will be:
[tex]\mathbf{Vertex = (4,5)}[/tex]
Comparing the vertices, it means that:
The new function will have its vertex twice as far from the y-axis
Hence, option (b) is correct.
Read more about transformation at:
https://brainly.com/question/13801312
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. On a coordinate plane, square S has points (0, 0), (5, 0), (5, negative 5), (0, negative 5). Square S prime has points (0, 1), (0, 3), (2, 3), (2, 1). a dilation by a scale factor of Two-fifths and then a translation of 3 units up a dilation by a scale factor of Two-fifths and then a reflection across the x-axis a dilation by a scale factor of Five-halves and then a translation of 3 units up a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A dilation by a scale factor of Two-fifths and then a translation of 3 units up
Step-by-step explanation:
Given that the coordinates of the vertices of square S are
(0, 0), (5, 0), (5, -5), (0, -5)
Given that the coordinates of the vertices of square S' are
(0, 1), (0, 3), (2, 3), (2, 1)
We have;
Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)
Where;
(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices
When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;
s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5
For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)
Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2
Therefore;
The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5
The after the dilation (about the origin), the coordinates of S becomes;
(0, 0) transformed to (remains at) (0, 0) ....center of dilation
(5, 0) transformed to (5×2/5, 0) = (2, 0)
(5, -5) transformed to (2, -2)
(0, -5) transformed to (0, -2)
Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;
For (0, 0), (2, 0), (2, -2), (0, -2) we have;
(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)
(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)
For (0, 1), (0, 3), (2, 3), (2, 1) we have;
(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)
(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)
Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)
That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up
The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.
Answer:
a
Step-by-step explanation:
WILL MARK BRAINLIEST!!! EASY QUESTION!!(✿◡‿◡) Can someone please give me an example of a FIFTH DEGREE POLYNOMIAL WITH THREE TERMS IN STANDORD FORM? I just need to know what it looks like, please.
Answer:
f(x) = x⁵ + 3x³ - 2 I think, if its incorrect I apologize
Step-by-step explanation:
at the rate of 15 per 6 oz. bar of chocolate, how much would a pound
Answer:
40
Step-by-step explanation:
We know there are 16 oz in a pound
We can use ratios
15 x
----- = ----------
6 oz 16 oz
Using cross products
15 * 16 = 6x
240 = 6x
divide by 6
240/6 = 6x/6
40 =x
40 points and brainliest!!!!
In Triangle XYZ, m
triangles?
O XYZ = TUV
O XYZ = VUT
O No congruency statement can be made because only two angles in each triangle are known.
O No congruency statement can be made because the side lengths are unknown.
Answer:
Option (4).
Step-by-step explanation:
In the figure attached,
Two right triangles ΔXYZ and ΔTUV have been given,
Given:
1). m∠Y = m∠U = 30°
2). m∠Z = m∠V = 60°
3). m∠X = m∠T = 90°
For congruence of two right triangles, measure of at least one side should be known along with the measure of angles (LA, HA, LL, HL properties of congruence).
Therefore, these triangles may be similar but not congruent.
Option (4) is the correct option.
Answer:
D.No congruency statement can be made because the side lengths are unknown.
Step-by-step explanation:
EDG
on the average 5 oranges will give 3 cupful of juice. if 2 cupfuls make a pint, how many oranges must be used to make 3 gallons of juice.
Answer:
90 oranges
Step-by-step explanation:
First, find out how many cupfuls are in 3 gallons of juice.
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
16 cups = 1 gallon
48 cups = 3 gallons
For every 5 oranges, you get 3 cupfuls of juice. This gives you the ratio of 5/3. Multiply 48 cups, which is 3 gallons, by the ratio to find out how many oranges you will need.
48 × 5/3 = 90
You will need 90 oranges for 3 gallons of juice.
Answer:
80 oranges are used to make 3 gallons of juice
Step-by-step explanation:
1 gallon = 8 pint
3 gallons = 3 * 8 = 24 pint
1 pint = 2 cup full of juice
24 pint = 24 * 2 = 48 cups
Now, we have to find how many 3 cups are in 48. So, 48 ÷ 3 = 16
3 cup of juice is taken form 5 oranges.
Therefore, 16 groups of 3 cups of juice will be taken from 5 *16 = 80 oranges
Determine if the event shows uniform probability or not. You have a spinner with 8 equal spaces on it. Each space is numbered with a different integer between 1 and 8.
Answer:
it does show uniform probability.
Step-by-step explanation:
because the spaces are all equal, so there is an equal chance of every integer being picked.
a car was bought for 5500 and sold at 6500 find the percentage
Answer:
18.18%
Step-by-step explanation:
Percent change formula:
(new amount - old amount)/(old amount) * 100%
new amount: 6500
old amount: 5500
percent change:
(6500 - 5500)/5500 * 100% = 18.18%
Answer:
18.18%
Step-by-step explanation:
1000/5500 x (100) =(1000/5500)(100/1) =(2/11)(100/1)=(2)(100) (11)(1)= 200/11
=18.18%
Please answer this question now
Answer:
If it's not too late by now, the answer is 19.9 [tex]mm^{2}[/tex]
21.(03.02)
If f(x) = 7x – 1, what does f(12) represent?
Answer:
83
Step-by-step explanation:
f(x) = 7x - 1
Put x as 12.
f(12) = 7(12) - 1
f(12) = 84 - 1
f(12) = 83
What is the equation of a circle with center (0, 5) and radius 8
Answer:
See below.
Step-by-step explanation:
Recall that the equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We know the center is (0,5) and the radius is 8. Plug in the numbers:
[tex](x-(0))^2+(y-(5))^2=(8)^2[/tex]
We can remove the parentheses on the left. Therefore, the equation will be:
[tex]x^2+(y-5)^2=64[/tex]
Answer:
( x) ^2 + ( y-5) ^2 = 64
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-0) ^2 + ( y-5) ^2 = 8^2
( x) ^2 + ( y-5) ^2 = 64
A polygon with 9 sides is shown. An exterior angle has a measure of x degrees. In the regular nonagon shown, what is the measure of angle x? 36° 40° 45° 60°
Answer:
40°Step-by-step explanation:
First we must know that the sum of all the exterior angle of all polygons is 360°.
Measure of each angle of a polygon = 360°/total sides of the polygon
Since a regular nonagon has 9 sides, the measure of each angle of a polygon is expressed as thus;
Measure of each angle of a polygon = 360°/9
Measure of each angle of a polygon = 40°
Hence the measure of an exterior angle x of a nonagon is 40°
Answer:
B in Edg
Step-by-step explanation:
An oblique cylinder has a radius of 10 units and slant length of 26 units. An oblique cylinder has a radius of 10 units and a slant length of 26 units. What is the volume of the cylinder? 2,400π cubic units 2,500π cubic units 2,600π cubic units 2,700π cubic units
The volume of the oblique cylinder with the given parameters is: 2,400π
What is the Volume of an Oblique Cylinder?Volume of an oblique cylinder = πr²h
r is the radius, h is the height of the cylinder.
Given the following:
r = 10 unitsSlant height (l) = 26 unitsh = √(26² - 10²) = 24 units [Pythagorean Theorem]Volume of oblique cylinder = π(10²)(24)
Volume of oblique cylinder = 2,400π
Learn more about the volume of oblique cylinder on:
https://brainly.com/question/15940389
Answer: a
Step-by-step explanation:
Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.2. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission
Answer:
24.25
Step-by-step explanation:
The minimum admission score is at the 70th percentile of the normal distribution which, according to a z-score table, corresponds to a z-score of 0.524.
The z-score, for any given value X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
If the mean score is 21 and the standard distribution is 6.2, the minimum required score for admission is:
[tex]0.524=\frac{X-21}{6.2}\\X=24.25[/tex]
The minimum score required for admission is 24.25.
find the value of x and explain
Answer:
D
Step-by-step explanation:
The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus
[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )
120 + x = 210 ( subtract 120 from both sides )
x = 90 → D
What is the result of adding these two equations?
62 + 2y = -2
3x - 2y = -5
Answer:
x = -7/9; y = 4/3.
Step-by-step explanation:
I will assume that the top equation is 6x + 2y = -2, and the bottom one is 3x - 2y = -5.
If you add the two...
(6x + 3x) + (2y + (-2y)) = (-2 + (-5))
9x + 0 = -7
9x = -7
x = -7/9
6(-7/9) + 2y = -2
-42/9 + 2y = -18/9
2y = 24/9
y = 24/18
y = 12/9
y = 4/3
Hope this helps!
Sarah’s room is in the shape of a rectangle that is 15 feet long and 11 feet wide. Which expression can she use to find the total amount of carpeting (in square feet) that she needs to cover the floor? A.15-11 B. 11x15 C.15+11 D. 2(15+11)
Answer:
The answer is choice B , 11 x 15
Step-by-step explanation:
To find area, you multiply one side by the adjacent side
11 and 15 are both adjacent, so you multiply to find the area of Sarah's room
Hope this helps !!!! Brainliest would be appreciated
Answer:
11x15
Step-by-step explanation:
it is the answer above because the dimensions of the room are 11 by 15 so written in an expression it is the answer above
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Greetings from Brasil...
We need to use the Cosine Law in Any Triangle, so we can use Heron's formula.
AC² = AB² + BC² - 2.AB.BC.COS B
AC² = 11² + 9² - 2.11.9.COS 63
AC ≈ 10,63
Heron's Formula:
Area = √[P.(P - AB).(P - BC).(P - AC)]
where P = (AB + BC + AC)/2
P = (11 + 9 + 10,63)/2 ⇒ P ≈ 15,31
Area = √[15,31.(15,31 - 11).(15,31 - 9).(15,31 - 10,63)]
Area ≈ 44,21 u.a.what is 0.6n = $2.10
Answer: 3.5
Step-by-step explanation:
2.10/0.6=3.5
3.5x0.6=2.10
For which system of equations would you need to estimate the solution?
On a coordinate plane, 2 lines intersect at (3, 0).
On a coordinate plane, 2 lines intersect around (negative 2.1, negative 3.5).
On a coordinate plane, 2 lines intersect at (negative 2, 3).
On a coordinate plane, 2 lines intersect at (2, 2).
Answer: It is option 2 or B
Step-by-step explanation: Simple and easy, the test said it was right too.
Given that ACAB - ACED, lind the value of y to 1 dermal place
Answer:
y = 15
Step-by-step explanation:
The triangles CAB and CED are similar (Using the case AA), so we can write the following relations:
[tex]\frac{12}{28} =\frac{15}{x}=\frac{y}{35}[/tex]
Using the first two fractions, we can find the value of x:
[tex]\frac{12}{28} =\frac{15}{x}[/tex]
[tex]12x = 28*15[/tex]
[tex]12x = 504[/tex]
[tex]x = 504/12 = 42[/tex]
Using the first and last fractions, we can find the value of y:
[tex]\frac{12}{28} =\frac{y}{35}[/tex]
[tex]28y = 12*35[/tex]
[tex]28y = 420[/tex]
[tex]y = 420/28 = 15[/tex]
multiply: 4x ^3sqrt 4x^2 (2 ^3sqrt 32x^2 * x ^3sqrt 2x)
Answer:B on edge 2020 :)
Step-by-step explanation:
its b
Step-by-step explanation:
edge 2022
1 to the tenth power
Answer:
1
Step-by-step explanation:
1 to the tenth power is also 1 multiplied by 1 10 times.
1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 · 1 = 1
1 to any power will always have the answer of 1.
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answer:
Volume of the cylinder is 1521π in³
Step-by-step explanation:
Hello,
To find the volume of a cylinder, we need the know the formula used for calculating it.
Volume of cylinder = πr²h
r = radius
h = height
Data,
Radius = 13in
Height = 9in
Volume of a cylinder = πr²h
Now we need to substitute the values into the formula
Volume of a cylinder = π × 13² × 9
Volume of a cylinder = 169 × 9π
Volume of a cylinder = 1521π in³
Therefore the volume of the cylinder is 1521π in³
Answer:
1521
Step-by-step explanation:
A restaurant catered a party for 45 people. A child’s dinner (c) cost $15 and an adult’s dinner (a) cost $25. The total cost of the dinner was $1,015. How many children and adults were at the party? Use the table to guess and check.
Number of People
a
c
c + a = 45
15 c + 25 a = 1,015 dollars
9 adults and 36 children
10 adults and 35 children
34 adults and 11 children
36 adults and 9 children
Answer:
34 adults and 11 children
Step-by-step explanation:
15 times 11 is 165dollars for kids
25 times 34 adults equals 850 dollars
add it and its 1015
Answer:
34 and 11
Step-by-step explanation:
a man buys a dozen cameras for $1800.He sells them at a profit of $36 each.Express his profit as a percentage of his selling price.
Step-by-step explanation:
The solution is the document i sent please check through.
Given that (1,-8) is on the graph of f(x), find the corresponding point for the function 1/2 f(x)
Answer: 1 (-4)
Step-by-step explanation: f(x) is a function of x giving you a y value. 1/2 f(x) means you're halving every y value that plugging in x gives you.
help me please I dont remember how to do this
Answer:
A
Step-by-step explanation:
Expand brackets.
-4y - 28 = -4y - 18 - 10
Both sides have -4y, the equation has no solutions.
-4y + 4y = - 18 - 10 + 28
0 = 0
There are no solutions.
Find the zeros of y=x^2+4x-9 by completing the square.
Answer:
[tex]\boxed{x =-2 \±\sqrt{13} }[/tex]
Step-by-step explanation:
Let y = 0
0 = x^2+4x-9
x² + 4x -9 = 0
Add 9 on both sides.
x² + 4x = 9
(b/2)² = (4/2)² = 2² = 4
Add 4 on both sides.
x² + 4x + 4 = 13
Facror left side.
(x+2)² = 13
Take the square root on both sides.
x + 2 = ±√13
Subtract 2 on both sides.
x = ±√13 - 2