Step-by-step explanation:
To answer this question we must understand what does each percentge mean :
80 percent alcohol mrans that in one liter we have 0.8 l of alcohol and 0.2 liter of water for example 65 percent ⇒0.65 liter of alcohol and 0.35 liter of waterFor 71 percent alcohol we have the quantity wich is 15 liter
so :
15 liter⇒ 100 percent
x( the unkhown quantity)⇒ 71 percent
x = (15*71)/100 )= 10.65 liter of alcohol
so we want 10.65 liter of alcohol
here is a way :
lat's take 10 L of 80 percent alcohol and 4liters of the other one
10*0.8+4*0.65 = 10.6
we just need 0.05 liter of alcohol
add 0.0625 L of the 80 percent liter alcohol to get 10.65
Find the lengths of the remaining sides of the triangle. a = 18 a is 60 degrees b is 30 degrees b = c =
Answer:
b= 10.39
c = 20.79
Step-by-step explanation:
a = 60 °
b = 30°
c= 180-(60+30)
c = 180-(90)
c = 90°
Length facing angle a = 18
Let's look for length facing angle b
b/sinb = a/sin a
b/sin 30 = 18/sin 60
b =( 18 * sin30)/sin 60
b = (18*0.5)/0.8660
b = 9/0.8660
b= 10.39
Let's look for c
c/sin c = a/sin a
c/sin 90 = 18/sin 60
c = (18 * sin 90)/sin 60
c =18/0.8660
c = 20.79
the sum of the interior angles of a triangle is sometimes, but not always , 180 degrees
Answer:
180 degrees
Step-by-step explanation:
The sum of all the interior angles in a triangle is always equal to 180 degrees.
Answer:
The correct answer is TRUE.
Step-by-step explanation:
Find the measure of x.
Begin by setting up an equation of the five angles equal to 180°.
x + 37° + 41° + 29° + 51° = 180° • The sum of the angles is 180°.
x + 158° = 180° • Add the known values on the left side.
x = 22° • Subtract 158° from both sides.
The measure of angle x is 22°.
HELP ASAP PLEASE!!!! SHOW WORK D = child’s dosage in milligrams a = age of the child M = adult dosage in milligrams The child weighs 55 lbs. Convert the child’s weight in pounds (lbs.) to kilograms (kg).
Answer:
24.95 kg
Step-by-step explanation:
one pound =0.45356 kg
55 lbs=55*45356 =24.95 kg
Samples of aluminum-alloy channels were tested for stiffness. the following frequency distribution was obtained. The distribution is assumed to be normal.stiffness frequency2480 232440 352400 402360 332320 21a) What is the approximate mean of the population from which the sample were taken?b) What is the approximate standard deviation of the population from which the samples were taken?c) What is the approximate probability that stiffness would be less than 2350 for any given channel section?
Answer:
The answer is explained below
Step-by-step explanation:
stiffness frequency
2480 23
2440 35
2400 40
2360 33
2320 21
a) The mean for the population is calculated using the formula:
[tex]mean (\mu)=\frac{\Sigma f_ix_i}{\Sigma f_i} \\=\frac{x_1f_1+x_2f_2+.\ .\ .+x_nf_n}{x_1+x_2+.\ .\ . +x_n} \\=\frac{(2480*23)+(2440*35)+(2400*40)+(2360*33)+(2320*21)}{23+35+40+33+21} =\frac{365040}{152}=2401.6[/tex]
b) The standard deviation is given by:
[tex]\sigma=\sqrt{ \frac{\Sigma f_i(x_i-\mu)^2}{\Sigma f_1} } \\=\sqrt{ \frac{f_1(x_1-\mu)^2+f_2(x_2-\mu)^2+.\ .\ .+f_n(x_n-\mu)^2}{f_1+f_2+.\ .\ .+f_n} } \\=\sqrt{ \frac{23(2480-2401.6)^2+35(2440-2401.6)^2+40(2400-2401.6)^2+33(2360-2401.6)^2+21(2320-2401.6)^2}{23+35+40+33+21 }}\\=\sqrt{\frac{390021.12}{152} }= 50.7[/tex]
c) We have to find the z score for x = 2350. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2350-2401.6}{50.7}=-1.02[/tex]
From the z table:
The probability that stiffness would be less than 2350 for any given channel section = P(x < 2350) = P(z < -1.02) = 0.1539 = 15.39%
Sue has $1.80 in dimes and nickels. If she has 9 more dimes than nickels, How many of dimes and nickels does she have?
Answer:
15 dimes6 nickelsStep-by-step explanation:
Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...
10d +5(d-9) = 180
15d -45 = 180 . . . . . simplify
d -3 = 12 . . . . . . . . . .divide by 15
d = 15
15 -9 = 6 = number of nickels
Sue has 15 dimes and 6 nickels.
Answer:
15 dimes, 6 nickels
Step-by-step explanation:
D = # of dimes, and N = # of nickels
10D + 5N = 180
D = N + 9
Substitute:
10 (N + 9) + 5N = 180
10N + 90 + 5N = 180
15N = 90
N = 6
D = 15
Pleaseeeee help, I need this now...
Answer:
7/16.
Step-by-step explanation:
The first triangle has no shading.
The second triangle has 1/4 shaded.
The third has 3/9.
The fourth has 6/16.
Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.
The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.
So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.
Hope this helps!
The unconditional probability of event A is 1/2. The unconditional probability of event B is 1/3. Say whether each of the following is true or false, and explain why.
(a) If A and B are independent, the chance that they both happen must be 1/2 x 1/3 = 1/6.
(b) If A and B are independent, the chance that at least one of them happens is 1/2 + 1/3 = 5/6.
(c) A and B cannot be both independent and mutually exclusive. The case is not possible.
need answer asap helpppp!!!
Answer:
A.
Step-by-step explanation:
Minor arcs are arcs that are less than 180°. If that is the case, then our only option would be A.
Consider the matrices. A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢−27−35−12⎤⎦⎥ What is the result of A−B? Enter your answer by filling in the boxes.
Answer:
Step-by-step explanation:
hello
[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
hope this helps
If two matrices are given as,
[tex]X=\begin{bmatrix}a & b\\ c & d\end{bmatrix}[/tex] and [tex]Y=\begin{bmatrix}h & k\\ l & m\end{bmatrix}[/tex]
Then [tex]X-Y=\begin{bmatrix}a-h & b-k\\ c-l & d-m\end{bmatrix}[/tex]
Following this rule answer will be → [tex]A-B=\begin{bmatrix}6 & 2\\ -10 & 9\\ -2 & -4\end{bmatrix}[/tex].
It's given in the question,
Two matrices, [tex]A=\begin{bmatrix}4 & 7\\ -3 & 8\\ -5 & -2\end{bmatrix}[/tex] and [tex]B=\begin{bmatrix}-2 & 5\\ 7 & -1\\ -3 & 2\end{bmatrix}[/tex]
Therefore, [tex]A-B=\begin{bmatrix}4+2 & 7-5\\ -3-7 & 8+1\\ -5+3 & -2-2\end{bmatrix}[/tex]
[tex]A-B=\begin{bmatrix}6 & 2\\ -10 & 9\\ -2 & -4\end{bmatrix}[/tex]
Learn more,
https://brainly.com/question/14302687
Help me pls pls pls pls
Answer:
The valid point is (5/2, 5)
Step-by-step explanation:
In order to check which ones are valid we will apply all of them to the expression.
(5,15):
[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}5 - \frac{1}{5}15 \geq 0\\\\-1 \geq 0[/tex]
False.
(1/2, 5):
[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{1}{2} - \frac{1}{5}5 \geq 0\\\\-\frac{4}{5} \geq 0[/tex]
False.
(5/2, 5):
[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{5}{2} - \frac{1}{5}5 \geq 0\\\\0 \geq 0[/tex]
True.
(2,5):
[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}2 - \frac{1}{5}5 \geq 0\\\\-\frac{1}{5} \geq 0[/tex]
False
(-1,0):
[tex]\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}(-1) - \frac{1}{5}0 \geq 0\\\\-\frac{2}{5} \geq 0[/tex]
False.
The difference of m2 + n2 and m + n is
A square matrix is called a permutation matrix if it contains the entry 1 exactly once in each row and in each column, with all other entries being 0. All permutation matrices are invertible. Find the inverse of the following permutation matrix.
A = [0 0 1 0, 0 0 0 1, 0 1 0 0, 1 0 0 0]
The inverse of the given permutation matrix A is
[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]
To find the inverse of the given permutation matrix A:
[tex]\[ A = \begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\\end{bmatrix} \][/tex]
Utilize the concept that the inverse of a permutation matrix is its transpose.
Therefore, the inverse of matrix A is:
[tex]\[ A^{-1} = A^T \][/tex]
Taking the transpose of matrix A, gives
[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]
Learn more about Matrix here:
https://brainly.com/question/29132693
#SPJ6
Is the selection below a permutation, a combination, or neither? Explain your reasoning. Upper A group of 5 senators is chosen to be part of a special committee.
Answer:
Combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation
Step-by-step explanation:
The first thing to keep in mind is the difference between combination and permutation.
The main difference is that in the combinations the order does not matter, whereas in the permutations the order does matter.
Combination example:
Choose 7 people for a project.
Example of permutation:
Choose 5 men for each specific role in a soccer team.
Therefore, "group of 5 senators is chosen to be part of a special committee" is a combination, but keep in mind that if the committee had two open positions, say President and Secretary, it would be a permutation.
Brent counted 10 red cards, 10 black cards, and 20 blue cards in a deck of cards. What is the ratio of red cards to other cards? Answers: A) 1:1 B) 1:2 C) 2:1 D) 1:3
Answer:
1:3
Step-by-step explanation:
10 red cards, 10 black cards, and 20 blue cards
We want the ratio of red to other cards
red : blue and black
10 : 10+20
10 : 30
Divide each side by 10
10/10 : 30/10
1:3
Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 y2
Answer:
hello your question is incomplete here is the complete question
Use cylindrical coordinates Find the volume of the solid that lies within both the cylinder x^2 + y^2=16 and the sphere x^2 + y^2 + Z^2= 81
Answer : [tex]\frac{4 \pi }{3} [729 - 65\sqrt{65} ][/tex]
Step-by-step explanation:
The given data
cylinder = x^2 + y^2 = 16
sphere = x^2 + y^2 +z^2 = 81
from the given data the solid is symmetric around the xy plane hence we will calculate half the solid volume above the plane then multiply the sesult by 2
Note : we are restricting our attention to the cylinder x^2 + y^2 = 16 and also finding the volume inside the sphere which gives bound on the z-coordinate as well
the r parameter goes from 0 to 4
ATTACHED IS THE REMAINING PART OF THE SOLUTION
showing the integration
Identify the vertex of the function. PLEASE HELP!!!
Answer:
Step-by-step explanation:
y-|x|+3
y=|x|+3
vertex=(0,3)
y=|x-4|-7
vertex(4,-7)
ABC and ADC are triangles. The area of triangle ADC is 52m^2
Given that,
ABC and ADC are triangles.
The area of ΔADC is 52 m².
Suppose , AD is the median.
According to figure,
We need to find the area of ΔABC
Using theorem of triangle
[tex]\bigtriangleup ADB +\bigtriangleup ADC=\bigtriangleup ABC[/tex]
Here, Δ ADB = Δ ADC
So, [tex]2 \bigtriangleup ADC=\bigtriangleup ABC[/tex]
Put the value of Δ ADC
[tex]\bigtriangleup ABC =2\times52[/tex]
[tex]\bigtriangleup ABC = 104\ m^2[/tex]
Hence, The area of ΔABC is 104 m².
In the figure below, what is the value of xº?
Answer:
[tex] \boxed{\sf x \degree = 62 \degree} [/tex]
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
[tex] \sf \implies x \degree + 38 \degree = 100 \degree \\ \\ \sf \implies x \degree + (38 \degree - 38 \degree) = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 100 \degree - 38 \degree \\ \\ \sf \implies x \degree = 62 \degree[/tex]
In the given figure, the value of x is 62°.
What is angle ?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
The given angles are,
x°, 38° and 100°.
To find the value of angle x, use exterior angle property.
According to exterior angle property,
The sum of two interior angles is equal to exterior angle.
Since, 100° is the exterior angle of x and 38.
x + 38 = 100
x = 100 - 38
x = 62.
The required value of angle x is 62°.
To learn more about Angle on:
https://brainly.com/question/28451077
#SPJ5
At a DBE lecture of 100 students there are 29 women and 23 men. Out of these students 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture.
Answer:
The number of women teachers attending the lecture is 1
Step-by-step explanation:
Let M denotes men , W denotes women and T denotes teachers.
Number of women = n(W)=29
Number of men = n(M)=23
Number of teachers=n(T)=4
We are given that 24 are either men or teachers.
So,n(M∪T)=24
We are supposed to find the number of women teachers attending the lecture.
n(M∪T)=n(M)+n(T)-n(M∩T)
24=23+4-n(M∩T)
n(M∩T)=3
So,No. of teachers those are men is 3
Total number of teachers = 4
So, the number of women teachers attending the lecture= 4-3 = 1
Hence the number of women teachers attending the lecture is 1
Previous 20 Two groups leave on different flights from the same airport. Group A flies 200 miles due south, then turns 68° toward west and flies 75 miles. Group B flies 75 miles due north, then turns 51° toward east and flies 200 miles. Which group is farther from the airport?
Answer:
Group B is farther from the airport.
Step-by-step explanation:
To find the distance of each group to the airport we can use the law of cosines in the triangle created with the two movements done and the resulting total distance.
Law of cosines:
[tex]c^2 = a^2 + b^2 - 2ab*cos(angle)[/tex]
For group A, we have the sides of 200 miles and 75 miles, and the angle between the sides is (180-68) = 112°, so the third side of the triangle is:
[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(112)[/tex]
[tex]c^2 = 56863.198[/tex]
[tex]c = 238.46\ miles[/tex]
For group B, we also have the sides of 200 miles and 75 miles, and the angle between the sides is (180-51) = 129°, so the third side of the triangle is:
[tex]c^2 = 200^2 + 75^2 -2*200*75*cos(129)[/tex]
[tex]c^2 = 64504.612[/tex]
[tex]c = 253.98\ miles[/tex]
The distance from group B to the airport is bigger, so group B is farther from the airport.
find domain and range using interval notation
Hey there! :)
Answer:
D: [8, 12].
R: [-10, -6].
Step-by-step explanation:
Notice that the endpoints of the graph are closed circles. This means that square brackets will be used:
The graphed equation is from x = 8 to x = 12. Therefore, the domain of the function is:
D: [8, 12].
The range goes from y = -10 to -6. Therefore:
R: [-10, -6].
Answer:
D: [8 , 12]
R: [-10 , -6]
Step-by-step explanation:
Well for this parabola domain and rage are acttually limited because of the solid dots you see on the graph.
So first things first, what is range? Well range is the amount of y values on a line or anything in a graph.
And what’s domain? Domain is the amount of x values on a line or whatnot.
So let’s do domain first.
On the parabola the first x value is 8 and the last is 12 so we have to write this in interval notation which is [8 , 12].
Now for range the lowest y value is -10 and the highest is -6 so in interval notation it is [-10 , -6].
) Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when r − 2. (c) Show that the rate of change of the area of a circle with respect to its radius (at any r) is equal to the circumference of the circle. Try to explain geometrically why this is true by drawing a circle whose radius is increased by an amount Dr. How can you approximate the resulting change in area DA if Dr is small?
Answer and Step-by-step explanation:
The rate of change of an area of a circle in respect to tis radius is given by:
ΔA / Δr = [tex]\frac{\pi(r_{1}^{2} - r_{2}^{2}) }{r_{1} - r_{2}}[/tex]
(i) 2 to 3:
ΔA / Δr = [tex]\frac{\pi(3^{2} - 2^{2}) }{3-2}[/tex] = 5π
(ii) 2 to 2.5
ΔA / Δr = [tex]\frac{\pi(2.5^{2} - 2^{2}) }{2.5-2}[/tex] = 4.5π
(iii) 2 to 2.1
ΔA / Δr = [tex]\frac{\pi(2.1^{2}-2^{2})}{2.1-2}[/tex] = 4.1π
Instantaneous rate of change is the change of a rate at a specific value. In this case, it wants at r = 2, so take the derivative of area and determine the area with the specific radius:
[tex]\frac{dA}{dr}[/tex] = π.r²
A'(r) = 2.π.r (1)
A'(2) = 4π
Note that expression (1) is the circumference of a circle, so it is shown that to determine the instantaneous rate of change of the are of a circle, is the circumference of any given radius.
The circles in the attachment shows a circle with radius r (light green) and a circle with radius r + Δr (darker green).
The rate of change between the two circles is the area shown by the arrow:
ΔA = π,[r² - (r+Δr)²]
ΔA = π.[r² - r² + 2rΔr + Δr²]
ΔA = π.(2rΔr + Δr²)
If Δr is too small, Δr² will be approximately zero, so
Δr²≈0
ΔA = π.(2rΔr)
The rate of change with respect to its radius will be:
ΔA / Δr = π.(2rΔr) / Δr
ΔA / Δr = 2.π.r
which is the circumference of a circle, so, this is the geometrical proof.
A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing. What is the expected number (mean) of sales of this store from this sample of 30?
Answer:
The expected number of sales of this store from this sample of 30 is 6.
Step-by-step explanation:
For each prospect, there are only two possible outcomes. Either there is a trade, or there is not. Prospects are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability.
This means that [tex]p = 0.2[/tex]
Suppose 30 prospects are randomly selected from a city-wide mailing.
This means that [tex]n = 30[/tex]
What is the expected number (mean) of sales of this store from this sample of 30?
[tex]E(X) = np = 30*0.2 = 6[/tex]
The expected number of sales of this store from this sample of 30 is 6.
The expected number (mean) of sales of this store from this sample of 30 is 6.
Calculation of the expected number or mean:Since A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.
So here the expected mean should be
= 20% of 20
= 6
Hence, The expected number (mean) of sales of this store from this sample of 30 is 6.
Learn more about mean here: https://brainly.com/question/797669
Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water. She thinks the solution is a little strong, so she drains 100 mL from the beaker, adds 100 mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains 100 mL from the beaker, and adds 100 mL of water. How many mL of water are now in the beaker?
Answer:
350 mL of water
Step-by-step explanation:
Well she starts with 200mL of water and there is 800 mL of acid of water.
She drains 100 mL of acid and adds 100 mL of water so there is 300 mL of water.
And she stirs meaning the compounds have mixed.
Then she drains 100 mL and she they are mixed she drains half of acid and half of water so she has 250 mL of water.
The she adds 100 mL of water so now there’s 350 mL of water left.
Find the velocity. Please help. Thank you!
Answer:
His final velocity is 48.03 m/s
Step-by-step explanation:
Using SI units (m, kg, s)
a = 3.7
x0 = 25
x1 = 300
v0 = 16.5
Apply kinematics formula
v1^2 - v0^2 = 2a(x1-x0)
solve for v1
Final velocity
v1 = sqrt(2a(x1-x0)+v0^2)
= sqrt( 2(3.7)(300-25)+16.5^2) )
= 48.03 m/s
Not sure how I would solve this
The first ordered pair is ( -4 , -3 )
The second ordered pair is ( 8, 3 )
=================================================
Explanation:
The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x
x-2y = 2
x-2(-3) = 2 ... replace every y with -3; isolate x
x+6 = 2
x = 2-6
x = -4
The first point is (-4, -3)
---------------------------
We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y
x-2y = 2
8-2y = 2
-2y = 2-8
-2y = -6
y = -6/(-2)
y = 3
The second point is (8, 3)
Apply the product rules to determine the sign of each expression
Answer:
Step-by-step explanation:
1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]
[tex]=-\frac{7}{9}[/tex] [Negative]
2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]
[tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]
[tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]
3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)
= (-1)⁴(3)⁵
= (3)⁵ [Positive]
4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]
= [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]
= [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]
5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]
[tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]
[tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]
6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]
[tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]
Question 1 (1 point)
A CODE has 4 digits. you remember that the 4 digits are 1, 3, 5, and 7, but you
cannot remember the sequence. What is the probability that you guess the code
correctly on the first try?
Answer:
24 ways
Step-by-step explanation:
There are 4!=24 ways to make distinct codes with the given distinct digits. So the probability of guessing it the first time is 1/24.
The probability that you guess the code correctly on the first try will be 1/24.
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
If the code is arranged then the total number of ways possible is;
⇒4!
⇒4×3×2×1
⇒24
Possible outcome = 1
Total outcome = 24
Probability = Possible outcome/total outcome
Probability = 1/24
Hence the probability that you guess the code correctly on the first try will be 1/24.
To learn more about probability, refer to the link: https://brainly.com/question/795909.
#SPJ2
Two cylindrical cans of beef stew sell for the same price. One can has a diameter of 8 inches and a height of 4 inches. The other has a diameter of 6 inches and a height of 7 inches. Which can contains more stew & is , therefore ,a better buy?
Answer:
Can 1 will contain more stew
Step-by-step explanation:
Can -1diameter= 8
radius=d/2=4
height=4
therefore volume= [tex]\pi[/tex] r2 h= 201.06
Can-2Diameter= 6
radius=d/2=3
height= 7
therefore volume= [tex]\pi[/tex] r2 h= 197.92
The cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
The more volume of a can is, the more stew it can store.
For first can:
Height = 4 inches, diameter of base = 8 inches.Since radius = diameter/2, so radius of base = 8/2 = 4 inches.
Thus, volume of first can: [tex]V = \pi (4)^2 (4) = 64\pi \: \rm unit^3[/tex]
For second can:
Height = 7 inches, diameter of base = 6 inches.Since radius = diameter/2, so radius of base = 6/2 = 3 inches.
Thus, volume of first can: [tex]V = \pi (3)^2 (7) = 63\pi \: \rm unit^3[/tex]
Thus, as π > 0, so first can can contain more stew.
Thus, the cylindrical can that contains more stew is the first can which has a diameter of 8 inches and a height of 4 inches.
Learn more about volume of cylinder here:
https://brainly.com/question/12763699
Find the inverse of the function f(x)=4+ \sqrt{x-2}
Answer:
y = (x - 4)² + 2 , x ≥ 4.
Step-by-step explanation:
Finding the inverse of
f(x) = 4 + √(x - 2)
Begin by swapping the x and y variables in the equation:
x = 4 + √(y - 2)
Subtract 4 from both sides:
x - 4 = √(y - 2)
Square both sides:
(x - 4)² = y - 2
Add 2 to both sides to get your equation:
y = (x - 4)² + 2
However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.