Answer:
x = -3
Step-by-step explanation:
expand -23x + 36 = 105
subtract 36 from both sides -23x +36 -36 = 105 - 36
Simplify -23x = 69
Divid both sides by -23: -23x / - 23 = 69 / -23
x = -3
17.
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) Compute P(all four are red).
(b) Compute P(exactly two are red and exactly two are green).
(c) Compute P(exactly two are red or exactly two are green).
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
Complete Question
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
Answer:
(a) The probability that all four balls are red is
0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
1.398
Step-by-step explanation:
An urn contains
Red balls = 8
White balls = 6
Green balls = 4
Total number of balls = 18 balls
(a) The probability that all four balls are red is?
The probability that a ball drawn is red = 8/18
The probability of drawing a ball that is not red = 1 - 8/18 = 10/18
The probability that all the 4 balls drawn are red = 8/18 × 7/17 × 6/16 x 5/15
= 1680/73440
= 0.022875817
Approximately = 0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
There are 6 ways by which this can be achieved. Where R = Red balls and G = Green Balls
RRGG
GGRR
RGRG
GRGR
RGGR
GRRG
P(Exactly two red balls and two green balls) = P(Exactly two red balls × Exactly two green balls)
=[ (8/18 × 7/17) ×( 4/16 × 3/15)] × 6 ways
= 672/73440 × 6 ways
= 0.0091503268 × 6 ways
= 0.0549019608
Probability of drawing out exactly two two red balls and two green balls is
= 0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
P(Exactly two red balls or two green balls) = P(Exactly two red balls + Exactly two green balls)
P(Exactly two red balls or two green balls) = P(Exactly two red balls or Exactly two green balls)
=[ (8/18 × 7/17) + ( 4/16 × 3/15)] × 6 ways
=0.1830065359 + 0.05
= 0.2330065359 × 6 ways
= 1.3980392154
≈1.398
The temperature on Monday was 5 Degrees. The temperature on Thursday was - 8 degrees. Was the overall change in the temperature positive, negative, or 0? Why ? *
Answer:
Negative change
Step-by-step explanation:
Given
[tex]Monday\ Temperature = 5\ deg[/tex]
[tex]Thursday\ Temperature = -8\ deg[/tex]
First, we need to calculate the overall change in temperature
This is calculated by subtracting the initial temperature from the final temperature
[tex]Overall\ Change = Thursday\ Temperature - Monday\ Temperature[/tex]
[tex]Overall\ Change = -8\ deg - 5\ deg[/tex]
[tex]Overall\ Change = -13\ deg[/tex]
The overall change shows a negative change in the temperature.
This is as a result of a drop in temperature from Monday to Thursday
Evaluate the following iterated integral by converting to polar coordinates.
∫8 −8∫0^(64−x^2)1/2 sin(x^2+y^2) dydx
Integration
IntegralsIntegration TechniquesIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Double Integrals
Polar Coordinates Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle x^2 + y^2 = r^2[/tex]Integral Conversion [Polar Coordinates]:
[tex]\displaystyle \iint_T {f(x, y)} \, dA = \iint_R {f(r, \theta)r} \, dr \, d\theta[/tex]
The formatting of the question was thrown off, so I have defined it down below.
We are given an integral and asked to convert to polar coordinates as well as evaluate it:
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx[/tex]
It would be quite difficult to evaluate the given integral using conventional methods, so we apply polar conversion to evaluate the integral. Let's start out by converting the function and the bounds.
[Bounds] Cartesian to Polar:
[tex]\displaystyle \left \{ {{-8 \leq x \leq 8} \atop {0 \leq y \leq \sqrt{64 - x^2}}} \right \longrightarrow \left \{ {{0 \leq r \leq 8} \atop {0 \leq \theta \leq \pi}} \right[/tex]
[Function] Cartesian to Polar:
[tex]\displaystyle f(x ,\ y) = \sin(x^2 + y^2) \longrightarrow f(r ,\ \theta) = \sin r^2[/tex]
Now that we've converted to polar coordinates, we can convert the integral using our integral conversion listed under "Multivariable Calculus":
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx \longrightarrow \int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta[/tex]
We can now evaluate the polar integral using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \int \limits^{\pi}_{0} \underbrace{\int \limits^{8}_{0} r \sin r^2 \, dr \, }_{u = r^2 ,\ du = 2r \, dr} d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{8}_{0} 2r \sin r^2 \, dr \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \int \limits^{r = 8}_{r = 0} \sin u \, du \, d\theta \\\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos u \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos r^2 \bigg) \bigg| \limits^{r = 8}_{r = 0} \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( - \cos 64 + 1 \bigg) \, d\theta \\& = \frac{1}{2} \int \limits^{\pi}_{0} \bigg( 1 - \cos 64 \bigg) \, d\theta \\\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\int \limits^{\pi}_{0} \int \limits^{8}_{0} r \sin r^2 \, dr \, d\theta & = \frac{1}{2} \bigg(1 - \cos 64 \bigg) \bigg( \theta \bigg) \bigg| \limits^{\pi}_{0} \\& = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }\end{aligned}[/tex]
∴ the integral equals:
[tex]\displaystyle \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]
[tex]\displaystyle \int \limits^{8}_{-8} \int \limits^{\sqrt{64 - x^2}}_{0} \sin(x^2 + y^2) \, dy \, dx = \boxed{ \frac{\pi}{2} \bigg( 1 - \cos 64 \bigg) }[/tex]
___
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Topic: Multivariable Calculus
Unit: Double Integrals
Let f(x)=5x-13 what ordered pair in f corresponds to the equation f(x)=7 ? Recall y=f(x).
Answer:
(4,7)
Step-by-step explanation:
f(x)=5x-13
Let this equal to 7
7=5x-13
Add 13 to each side
7+13 = 5x-13+13
20 = 5x
Divide by 5
20/5 = 5x/5
4 =x
The ordered pair is
(4,7)
cual de estos tipos de mentalidad puede contribuir a superar situaciones de no inclusión porque
La mentalidad de crecimiento, ya que a diferencia de la mentalidad fija, nos permite ver en otras personas la mentalidad de mejorar y perseverar.
Solve the following equation algebraically
Answer:
the right answer is d
Step-by-step explanation:
please give 5 star i need it
A diagonal of a rectangle is 8cm and forms an angel measuring 30 with one side.Find the area of the rectangle.
Answer:
16 * √3 cm² or approximately 27.71 cm²
Step-by-step explanation:
Given the 8 cm length of the diagonal and the 30° (π/6 radians) angle with one of the sides, we can calculate the width and height of the rectangle using:
8 * cos(π/6) = 8 * ((√3)/2) = 4 * √3
8 * sin(π/6) = 8 * (1/2) = 4
Multiply those two values together to get the area and you get
16 * √3 cm²
the sides of an angle are
Answer:
the vetrex
Step-by-step explanation:
What is the solution to the equation by -2(y + 1) = 3(y – 2) + 6?
Answer: y= -2.5
Step-by-step explanation:
Distribute the -2 and 3 into the parentheses. -6 + 6 cancels out so you are left with 3y on the right side. Add 2y to the right side leaving you with -2=5y. Divide both sides by -2
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ y = - 0.4}}}}[/tex]Step-by-step explanation:
[tex] \sf{ - 2(y + 1) = 3(y - 2) + 6}[/tex]
Distribute -2 through the parentheses
Similarly, Distribute 3 through the parentheses
⇒[tex] \sf{ - 2y - 2 = 3y - 6 + 6}[/tex]
Since two opposites add up to zero , remove them
⇒[tex] \sf{ - 2y - 2 = 3y}[/tex]
Move 3y to Left hand side and change it's sign
Similarly, move -1 to right hand side and change it's sign
⇒[tex] \sf{ - 2y - 3y = 2}[/tex]
Collect like term
⇒[tex] \sf{ - 5y = 2}[/tex]
Divide both sides of the equation by -5
⇒[tex] \sf{ \frac{ - 5y}{ -5 } = \frac{2}{ - 5} }[/tex]
Calculate
⇒[tex] \sf{ - 0.4}[/tex]
Hope I helped!
Best regards!
What is the solution to the equation to 0.5x+3.5=6
Answer:
x = 5
Step-by-step explanation:
0.5x + 3.5 = 6
0.5x = 6 - 3.5
0.5x = 2.5
x = 2.5 / 0.5
x = 5
Which type of transformation is shown?
Answer:
Translation
Step-by-step explanation:
The object is only moved, which is what happens when a translation occurs
Given the true/false statements are true (facts), select the best logical induction made from thoses statements: Mo likes oranges, jai likes oranges, Ben like oranges.
Answer:
People like oranges
Step-by-step explanation:
Given:
Mo likes oranges. Jai likes oranges. Ben likes oranges.
We have a few different options;
Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given people who like oranges.
Option B: People on like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.
Option C: People like oranges. This can be possible because Mo, Jai, and Ben likes oranges
Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not
People like oranges.
What is Induction?the action or process of inducting someone to a position or organization.
How to determine?We have a few different options;
Option A: People don't like other fruit, such as apples. This can't be possible because we have only been given to people who like oranges.
Option B: People like oranges. This can't be possible because only is the case where people do not like any fruit except oranges, and we are not sure of this.
Option C: People like oranges. This can be possible because Mo, Jai, and Ben like oranges
Option D: People like fruit. This can't be possible because we are not sure if people like all fruits or not
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What is the ratio of 2 feet to 4 yards?
Answer:
1:6
Step-by-step explanation:
1 yard = 3 feet. 4 yards = 12 feet.
Ratio of 2 feet:12 feet = 1:6 Ans D
The ratio of 2 feet to 4 yards is 1 : 6
How to determine the ratio?The ratio is given as:
Ratio = 2 feet : 4 yards
Convert yard to feet
Ratio = 2 feet : 4 * 3 feet
Evaluate
Ratio = 2 feet : 12 feet
Divide the ratio
Ratio = 1 : 6
Hence, the ratio of 2 feet to 4 yards is 1 : 6
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HII PLEASE HELP ME IN THIS
Step-by-step explanation:
(i) Sum the forces at point M in the x direction.
∑F = ma
-T sin 30° − T sin 30° + 5 N = 0
2T sin 30° = 5 N
T = 5 N
(ii) Sum the forces on the ring in the x direction.
∑F = ma
T sin 30° − N = 0
N = 2.5 N
Sum the forces on the ring in the y direction.
∑F = ma
T cos 30° − mg − Nμ = 0
Nμ = T cos 30° − mg
2.5 μ = 5 cos 30° − 2
μ = 0.932
(iii) Sum the forces on the ring in the y direction.
∑F = ma
T cos 30° − m₁g − m₂g + Nμ = 0
m₂g = T cos 30° − m₁g + Nμ
m (10) = 5 cos 30° − 2 + (2.5)(0.932)
m = 0.466 kg
what is equal to -3/2
Answer:
-1.5
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
-1.5
-1 1/2
-6/4
after running 3/5 of a race the runner only has 4 miles left how long was the race
Answer:
10 miles
Step-by-step explanation:
3a/5 + 4 = a
a = race long
4 = a - 3a/5
4 = 5a/5 - 3a/5
4 = 2a/5
4*5/2 = a
a = 10
The length of the entire race is 10 miles.
Let length of race = r
Miles left after running 3/5 of race :
r - 3r/5 = 4We can solve the expression thus :
r - 3r/5 = 4
r - 3r = 4 * -5
r - 3r = -20
-2r = -20
divide both sides by -2 to isolate r
r = 10
Hence, the length of the entire race is 10 miles.
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Damien worked at a grocery store earning $9.00 an hour. He worked 30 hours a week and was paid every two weeks. He paid $62 in taxes and had a $50 savings account deduction. How much were Damien's taxes and deductions?
Answer:
Answer: $428.00
Step-by-step explanation: First, we need to calculate the person’s total hours, (30 x 2 = 60 hours) then the money per hour (60 x 9) then take away the taxes and account deductions.
Charmaine can knit 15 rows in 22 minutes. Create a ratio table and then estimate about how many full rows could she knit in 90 minutes?
Answer:
61 rows
Step-by-step explanation:
Set up a proportion:
[tex]\frac{15}{22}[/tex] = [tex]\frac{x}{90}[/tex]
Cross multiply:
22x = 1350
x = 61.36
= approx. 61 rows
Which equation can pair with X- y=-2 to create a consistent and dependent system?
O 6x + 2y = 15
0 -3x + 3y = 6
O _8x – 3y = 2
O 4x – 4y = 6
m and n are both integers. Select all the statements that are true if m and n are also equal to each other. m - n = n - m OR +m (- n) = m - n
OR 0 = m - n OR m + n = 0
Answer:
The true statements are;
(i) m - n = n - m
(ii) +m (-n) = m - n
(iii) 0 = m - n
Step-by-step explanation:
We are given that m and n are both integers and we have to select all the statements that are true if m and n are also equal to each other.
(i) The given situation is: m - n = n - m
LHS = m - n
= m - m {because m and n are equal}
= 0
RHS = n - m
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(ii) The given situation is: +m (- n) = m - n
LHS = +m (- n)
= m - n
= m - m {because m and n are equal}
= 0
RHS = m - n
= n - n {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iii) The given situation is: 0 = m - n
LHS = 0
RHS = m - n
= m - m {because m and n are equal}
= 0
Hence, the given statement is true because LHS = RHS = 0.
(iv) The given situation is: m + n = 0
RHS = 0
LHS = m + n
= m + m {because m and n are equal}
= 2m
Hence, the given statement is not true because LHS [tex]\neq[/tex] RHS.
#1) m - n = n - m
#2) +m (-n) = m - n
#3) 0 = m - n
hope this HELPS!!!!!!!
The equation $y = -6t^2 + 51t$ describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 108 feet in height?
Answer:
4 OR 4.5 SECONDS
Step-by-step explanation:
2 What operation should be done first to solve 6x + 5 = 35?
o
Subtract 5
O Add 5
Multiply by 6
O Divide by 6
Answer:
subtract 5
Step-by-step explanation:
subtract 5 from each side of the equal sign..
Answer:
the answer is subtract 5
Step-by-step explanation:
If the side of an equatorial triangle is L then express the perimeter of the triangle in terms of L.
Answer:
3L
Step-by-step explanation:
Perimeter is the sum of side lengths
Since the triangle is equilateral, it has all sides equal and each has length of L
So perimeter is:
P= L+L+L = 3LConsider a group of students playing a game of tug-of-war, in which two teams pull on a rope to find which team is strongest. Each of the statements that follows describes what happens during the tug-of-war. Evaluate each statement and select the statements that are accurate.
Jeremy bought $2,500 worth of gold this week. If the price of gold appreciates at the rate of 5.5%
each year, what will his gold be worth in 7 years?
Answer:
$3,636.70
Step-by-step explanation:
Given the following:
Initial price of Gold (A) = $2500
Rate of appreciation (r) = 5.5% = 0.055
Worth of gold in 7 years will be?
Period (p) = 7
Using the compound interest formula :
Let F = final amount
F = A( 1 + r/n)^nt
n = number of times Appreciation occurs per period.
Since rate compounds yearly, then, n = 1
F = $2500( 1 + 0.055/1)^(7*1)
F = $2500(1 + 0.055)^7
F = $2500(1.055)^7
F = $2500(1.454679161133794609375)
F = $3636.6979
Amount in 7 years = $3,636.70
The area of rectangular is 46 square inches.if the length is 4 times the width . Then find the dimensions of the rectangular
Answer:
the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
Step-by-step explanation:
Recall that the area of a rectangle is Length times Width
If we name the length "L" and the width "W", we have:
L * W = 46
Also: "the length is 4 times the width" can be written in math form as:
L = 4 * W
and now we can replace the length L by 4 * W in the formula for the area:
[tex]L\,*\,W = 46\\(4\,W) \,W = 46\\4\,W^2=46\\W^2=\frac{46}{4} =11.5\\W=\sqrt{11.5} \\W\approx 3.39[/tex]
and now we find the value of L:
[tex]L=4\.(3.39) = 13.56[/tex]
Therefore, the rectangle's width is approximately 3.39 inches
and the length is approximately 13.56 inches.
Multiply
11 x 34.12
I’m so confused?
Answer:
[tex]34.12 * 11 = 375.32[/tex]
Step-by-step explanation:
Given
11 * 34.12
Required
Multiply
To start with, we have to ignore the decimal points;
So, we have
3412
* 11
---------------
3 4 1 2
3 4 1 2
------------------------
3 7 5 3 2
The next step is as follows;
34.12 is in 2 decimal places
11 is has no decimal (0 decimal place)
Add the decimal places together
[tex]Decimal\ Place = 2 + 0 = 2[/tex]
This implies that the result will be in 2 decimal placed;
Hence:
[tex]34.12 * 11 = 375.32[/tex]
Part A.) in another baseball game division, one team had a winning percentage of 0.444... what fractions of the game did the team win? *with full steps please* Part B.)How do you know what power of 10 to multiply by in the second step at the right?
Answer:
4/9
Step-by-step explanation:
0.4444... can be written as a geometric series with first term 0.4 and common ratio 0.1. Each new digit is 0.1 times the previous digit.
0.4
Then 0.4444... = ------------ = 0.4/0.9 = 4/9
1 - 0.1
You may check this result by dividing 4 by 9 on a calculator.
Find (f-g)(x) for the following functions. f(x) = x2-2x-24 g(x) = x+4
Answer:
(f-g)(x) = x² - 3x - 24Step-by-step explanation:
f(x) = x² - 2x - 24
g(x) = x + 4
To find (f-g)(x) subtract g(x) from f(x)
That's
(f-g)(x) = x² - 2x - 24 - ( x + 4)
(f-g)(x) = x² - 2x - 24 - x - 4
Group like terms
We have
(f-g)(x) = x² - 2x - x - 24 - 4
Simplify
We have the final answer as
(f-g)(x) = x² - 3x - 28Hope this helps you
20 POINTSSSSSSSSSSS AND BRAINLIESTTTTTTTTTTTTTSSSSSSSSSSSSSS
Answer:
C
Step-by-step explanation:
Since the exponent on the 10 is negative, we need to move the decimal point to the left instead of the right. After moving the decimal point on the 2.5 to the left 4 places, we see that the answer is 0.00025.