Answer:
7/15
Step-by-step explanation:
P(appetizers with cheese) = number with cheese / total = 1/5
P(entrees with cheese) = number with cheese / total = 1/3
It is the P(a) + P(b) - P(a and b)
We cannot double count the cheese and cheese event)
P( cheese and cheese) = 1/3 * 1/5 = 1/15
1/5 + 1/3 - 1/15
3/15 + 5/15 -1/15
8/15 - 1/15
7/15
Which of the following is an equivalent trig ratio for tan 28
Cos 62
1/ tan 62
1/ tan152
Cos 28
Answer:
B
Step-by-step explanation:
tan28=tan (90-62)=cot 62=1/tan 62
Given the graph of the line, choose two points and find the slope. Construct the equations for each of the
points you chose in point slope form. Show your work and explain each step.
*The graph is in the picture *
PLEASE HELP I WILL GIVE BRAINLIST
Step-by-step explanation:
First, given that we must use point slope form, we can define that as
y - y₁ = m (x-x₁), with m being the slope .
To find the slope, we can use the equation
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Two points on the graph are (0, 1) and (1, 3). For these points, when calculating the slope, 0 and 1 represent x₁ and y₁ respectively, while 1 and 3 represent x₂ and y₂ respectively Using this formula, we can plug our points in to get
[tex]\frac{3-1}{1-0} = 2/1 = 2[/tex]
as our slope. Therefore, our equation is
y - y₁ = 2 (x-x₁).
For our first point, (0,1), we can simply plug 0 in for x₁ and 1 in for y₁ to get
y - 1 = 2(x-0) as one equation
Next, for (1,3) we can plug 1 for x₁ and 3 for y₁ to get
y - 3 = 2 (x-1) as our other equation
7(x + y) ex2 − y2 dA, R where R is the rectangle enclosed by the lines x − y = 0, x − y = 7, x + y = 0, and x + y = 6
Answer:
[tex]\int\limits {\int\limits_R {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]
Step-by-step explanation:
Given
[tex]x - y = 0[/tex]
[tex]x - y = 7[/tex]
[tex]x + y = 0[/tex]
[tex]x + y = 6[/tex]
Required
Evaluate [tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex]
Let:
[tex]u=x+y[/tex]
[tex]v =x - y[/tex]
Add both equations
[tex]2x = u + v[/tex]
[tex]x = \frac{u+v}{2}[/tex]
Subtract both equations
[tex]2y = u-v[/tex]
[tex]y = \frac{u-v}{2}[/tex]
So:
[tex]x = \frac{u+v}{2}[/tex]
[tex]y = \frac{u-v}{2}[/tex]
R is defined by the following boundaries:
[tex]0 \le u \le 6[/tex] , [tex]0 \le v \le 7[/tex]
[tex]u=x+y[/tex]
[tex]\frac{du}{dx} = 1[/tex]
[tex]\frac{du}{dy} = 1[/tex]
[tex]v =x - y[/tex]
[tex]\frac{dv}{dx} = 1[/tex]
[tex]\frac{dv}{dy} = -1[/tex]
So, we can not set up Jacobian
[tex]j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right][/tex]
This gives:
[tex]j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right][/tex]
Calculate the determinant
[tex]det\ j = 1 * -1 - 1 * -1[/tex]
[tex]det\ j = -1-1[/tex]
[tex]det\ j = -2[/tex]
Now the integral can be evaluated:
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA[/tex] becomes:
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{x^2 - y^2}} \, *\frac{1}{|det\ j|} * dv\ du[/tex]
[tex]x^2 - y^2 = (x + y)(x-y)[/tex]
[tex]x^2 - y^2 = uv[/tex]
So:
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{|det\ j|}\, dv\ du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *|\frac{1}{-2}|\, dv\ du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \int\limits^6_0 {\int\limits^7_0 {7ue^{uv}} *\frac{1}{2}\, dv\ du[/tex]
Remove constants
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 {\int\limits^7_0 {ue^{uv}} \, dv\ du[/tex]
Integrate v
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 \frac{1}{u} * {ue^{uv}} |\limits^7_0 du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 e^{uv} |\limits^7_0 du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du[/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du[/tex]
Integrate u
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0[/tex]
Expand
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)][/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}][/tex]
Open bracket
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}][/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}][/tex]
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}][/tex]
Expand
[tex]\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{1}{2}e^{42} -\frac{43}{2}[/tex]
IT ISNT THE 1st OR 2nd HELP LOOK AT IMAGE PLEASE
Answer:
Last option
Step-by-step explanation:
First method :
Red Line:
Take 2 coordinates through which the line passes. Let it be (0, 7) and (14, 0).
[tex]slope, m=\frac{ 0-7}{14-0} = -\frac{7}{14} = -\frac{1}{2}[/tex]
[tex]Equation : (y - 7) = -\frac{1}{2}(x)[/tex]
[tex]2y - 14 = -x\\2y + x = 14\\4y + 2x = 28[/tex] [tex][ multiply \ by \ 2 \ on \ both \ sides][/tex]
Blue Line:
Take coordinates through which the line passes.
Let it be (-4, -12) and (-10, -9).
[tex]slope, m = \frac{-9 + 14}{-10} = \frac{5}{-10} = -\frac{1}{2}[/tex]
[tex]equation : (y + 12) = -\frac{1}{2} (x+4)\\[/tex]
[tex]y = -\frac{1}{2}x - 2 - 12\\\\y = -\frac{1}{2}x -14\\\\2y = -x - 28\\\\-2y = x +28[/tex]
Second Method:
From the graph it is clear the lines are parallel. The slopes of line parallel to each other are equal. So convert each equation into standard line equation form :y = mx + b
And check for set of equation whose slope are same.
First set :
[tex]y = 10x - 15 \\\\=> slope = 10\\\\-9x + 2y = 10\\2y = 9x + 10\\\\y = \frac{9}{2}x + 5 => slope = \frac{9}{2}[/tex]
Slopes are not equal.
Second set :
[tex]2y = 2x + 5\\y = x + \frac{5}{2}\\slope = 1\\\\\\3x -4y = -5\\4y = 3x + 5\\\\\y = \frac{3}{4}x + \frac{5}{4}\\\\slope = \frac{3}{4}[/tex]
Slopes are not equal.
Third set :
[tex]y = 3x +10 \\slope = 3\\\\\\2x - 3y = -6\\3y = 2x +6\\\\y = \frac{2}{3}x + 2\\\\slope = \frac{2}{3}[/tex]
Slopes are not equal.
Fourth set :
[tex]2x + 4y = 28\\4y = -2x +28\\\\y = -\frac{1}{2}x + 7\\\\slope = -\frac{1}{2}\\\\\\-2y = x + 28\\\\y = -\frac{1}{2}x - 14\\\\slope = -\frac{1}{2}[/tex]
Slopes are same.
Find the mean, median, mode, range.
Answer:
1. mean: 5
2. median: 6
3. mode: 80% or 8
4. range: 7
Step-by-step explanation:
Answer:
mean = 5
median = 6
mode = 80%(aka 8)
range = 7
Step-by-step explanation:
Which of the following is not a type of correlation associated with scatterplots?
A. no correlation
B. positive correlation
C. negative correlation
D. indefinite correlation
Please select the best answer from the choices provided
The type of correlation not associated with scatterplots is an indefinite correlation
What is correlation?Correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.
Correlation can only be between -1 and 1 but not outside these values.
The types of correlation that we have to include:Hence the type of correlation not associated with scatterplots is an indefinite correlation
Learn more on correlation here: https://brainly.com/question/26172866
helppppppppppppppppppppppp
Answer:
gotta be answer A
Step-by-step explanation:
you can search up f(x) = square root of x
Find |23| absolute value
Answer:
23
Step-by-step explanation:
The absolute value of any number is just the positive version of that number. For example the absolute value of -12 is 12.
Hope this helps! :)
11. It refers to the information that supports the claim.
A. reference
B. evidence
C. cite
D. issue
Answer:
B. Evidence
Step-by-step explanation:
Reference: like when your drawing something and you want to make sure that you draw the hair the same way some other person did.
Cite: That’s when you give the credits to someone or something 90% sure
Hope this helps :)
What is the difference of the polynomials?
(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)
6r6s3 – 4r5s4 + 7r4s5
6r6s3 – 13r5s4 – r4s5
8r6s3 – 5r5s4 + r4s5 + 5r3s6
8r6s3 – 13r5s4 + r4s5 – 5r3s6
Answer:
8r6s3 – 13r5s4 + r4s5 – 5r3s6 it is D
DStep-by-step explanation:
The value of the difference of the polynomials is,
⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)
Now, We can find the difference as;
⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)
⇒ (8r⁶s³ – 9r⁵s⁴ – 4r⁵s⁴ + 3r⁴s⁵ – 2r⁴s⁵ – 5r³s⁶
⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶
Thus, The value of the difference of the polynomials is,
⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ7
according to a survey, the population of a city doubled in 12 years.
The annual rate of increase of the population of this city is approximately _____. The population will grow to three times its current size in approximately ______.
First box of answers: 2.50, 5.78, 12.0, 50.0
Second box of answers: 18, 19, 23, 24.
Answer:
5.78
19
Step-by-step explanation:
Let original population be, P = x
Growth in 12 years, A = 2x
Rate be = r
Time = 12years
Find the rate :
[tex]A = P(1 + \frac{r}{100})^t[/tex]
[tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]
The annual rate of increase of the population of this city is approximately 5.78.
Find time in which the population becomes 3 times.
That is A = 3x
P = x
R= 5.78%
[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]
The population will grow to three times its current size in approximately 19years .
5.78% ,19 years are the answers.
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0578*100=5.78%
3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years
What is an exponential growth model?
Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky
exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.
The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.
Learn more about exponential function here:https://brainly.com/question/2456547
#SPJ2
∆ABC has coordinates A(3, 1), B(5, 5) and C(4, 1). After a translation, the coordinates of A' are (0,0). What are the coordinates of B' and C'?
Answer:
B'(2,4) & C'(1,0)
Step-by-step explanation:
According To the Question,
Given, We have an ∆ABC that has coordinates A(3, 1), B(5, 5) and C(4, 1).
Now, After a translation, the coordinates of A' are (0,0) .
Then, the coordinate of B' & C' Also changes the same as like A' .
A(3,1) ⇒ A'(0,0) {here from x-axis it reduce 3 and from y-axis it reduce 1}
Same as Above,
B(5,5) ⇒ B'(2,4)
&, C(4,1) ⇒ C'(1,0) .
Please help me answer my question
Answer:
SA= 882cm^2
Step-by-step explanation:
SA=2( width*length + hight*length + hight*width )
SA=2( 9*20+ 9*20+ 9*9)
SA= 2*441
SA=882cm^2
The volume of this cone is 83.7 cubic meters. Find the DIAMETER. SHOW ALL WORK
There for the diameter is 2(4.8 )= 9.6 ft
Given: Volume of the cone is 83.7 m³
We know that:
[tex]\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}[/tex]
where r is the radius of the cone and h is the height of the cone
Given: Height of the cone = 5m
Substituting the values in the formula, we get:
[tex]\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}[/tex]
[tex]\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}[/tex]
[tex]\sf{\implies \pi r^2 = 83.7 \times 0.6}[/tex]
[tex]\sf{\implies \pi r^2 = 50.22}[/tex]
[tex]\sf{\implies r^2 = \dfrac{50.22}{\pi}}[/tex]
[tex]\sf{\implies r^2 = 16}[/tex]
[tex]\sf{\implies r = 4}[/tex]
We know that : Diameter is two times the radius
⇒ Diameter of the Cone is 8 meters
A sum of money is deposited in a bank which offers a simple interest rate of 0.325% per annum. At
the end of the 4 years, the total amount receives is $50 650. Find the sum of money deposited.
Answer:
The sum of money deposited is approximately $22,021.74
Step-by-step explanation:
The given interest and amounts of the deposit are outlined as follows;
The simple interest per annum, R = 0.325%
The number of years the money is deposited, T = 4 years
The total amount received (Interest + Initial deposit), A = $50,650
We have;
I = P × R × T
Where;
P = The principal (initial amount deposited)
R = The (annual) interest rate = 0.325%
T = The time = 4 years
Therefore;
The total amount received, A = P + I
P + I = P + P × R × T = P × (1 + R × T)
∴ A = P + I = P × (1 + R × T)
P = A/(1 + R × T)
Plugging in the values, gives;
P = 50,650/(1 + 0.325 × 4) = 506,500/23 ≈ 22,021.74
The sum of money deposited, P = $22,021.74
Please help me I would really appreciate it, If you can't that is okay but please try
Answer:
(3p+10q)
Step-by-step explanation:
9p^2 - 100q^2
Rewriting
(3p)^2 - (10q)^2
This is the difference of squares
a^2 - b^2 = (a-b)(a+b)
(3p-10q) (3p+10q)
Answer:
( 3p + 10 q)
Step-by-step explanation:
9 p ² - l00 q ²
(3p)² - ( 10 q) ²
( a ² - b ² = ( a + b) ( a - b) )
( 3p - 10 q) ( 3 p + 10 q)
Find a round to the nearest tenth 12 22 75 x x=?
Answer:
By law of Sines[tex]\frac{Sin75^o}{22} =\frac{Sinx}{12}[/tex][tex]\frac{Sin75}{22}(12)=\frac{Sinx}{12} (12)[/tex][tex]0.5268=Sinx[/tex][tex]Sin^(0.5268)=x[/tex][tex]x=31.789[/tex][tex]x=31.79^o[/tex]-----------------------hope it helps..have a great day!!PLEASE HELPP MEEE ASAPPPPP
Answer:
D) 24,32,40
Step-by-step explanation:
Sense this is a right triangle, I will use the Pythagorean theorem to solve this problem. Use the following formula: a^2 + b^2 = c^2. 40 would be c. 40 x 40 = 1600. 32 x 32 = 1024. 24 x 24 = 576. Since 576 + 1,024 equals 1600, this means the answer would be D. Remember, that you can only use the Pythagorean Theorem method on right triangles.
1,600 = 576 + 1024.
Note:
Pls notify me if my answer is incorrect, for the other users that will see this message.
-kiniwih426
A function g is described below:
· g(2) = 2 ( 23 – 3) = 5
• domain is all real numbers greater than 0
The range of g is all real numbers greater than or equal to
Answer:
A≈1075.21
d Diameter
37
d
r
r
r
d
d
C
A
Using the formulas
A=
π
r
2
d=
2
r
Solving forA
A=
1
4
π
d
2
=
1
4
π
37
2
≈
1075.21009
Step-by-step explanation:
A swimmer breaks a world record by 0.07 seconds. The old record was 49.51 seconds. What is the swimmer's new world record?
a. 49.58 seconds
b.49.44 seconds
c.48.81 seconds
d.48.58 seconds
Answer:
B
Step-by-step explanation:
Simply subtract 0.07 from 49.51 too get 49.44.
Hope that this helps!
Please answer this fasttt
gavin and play a game with 20 numbered balls. The 20 balls are numbered from 1 to 20. Write down the probability that the score is a multiple of 3.
Step-by-step explanation:
6/20
3/10 (simplified)
do you want the percentage?
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
The multiplies of 3 from 1-20 are:
3, 6, 9, 12, 15, 18
Since there are [tex]20-1+1=20[/tex] numbers from 1-20 inclusive, the probability that a ball is a multiple of 3 is [tex]\frac{6}{20}=\boxed{\frac{3}{10}}[/tex]
Each year the Mannel Department Store has a big end-of-summer
sale. At the sale, they give customers an additional 25% off on all
marked-down merchandise.
a. A beach towel had an original price of $22.00. It was marked
down 10%. What is the final price after the additional
25% discount?
b. A patio table and four chairs originally cost $350.00. They were
marked down 50%. What is the final cost of the table and chairs
with the additional discount?
Answer:
Es ydjwj rjsbt djeiweke
can someone pls help me find the gradient and y-intercept of the last 2 questions . tysm i will give brainliest !
please help me :(
I am in Great trouble:(
Answer: (I am not a maths moderator)
x=4
Step-by-step explanation:
Multiply the exponents
(2x-4)^12=(4^2)^6 (exponents multiply so)
(2x-4)^12=4^12
4^12 = 16777216
(2x-4)^12= 16777216
Take the 1/12 exponent for both sides
that will remove the ^12 exponent from the left side and will take the 12th root for the right.
2x-4=4
add 4 to both sides
2x=8
divide both sides by 2
x=4
Help me pls i'm struggling need help fast!
Dan earns $9.50 per hour as a dishwasher. Determine the fewest number of hours he must work to earn
more than $408.
Answer:
43 hours
Step-by-step explanation:
[tex]\frac{y}{1} :\frac{408}{9.5}[/tex]
y × 9.5 = 408 × 1
9.5y = 408
9.5y ÷ 9.5 = 408 ÷ 9.5
[tex]y=42\frac{18}{19}[/tex]
43 hours
Confused on this work
We know that :
⊕ Sum of the interior angles in a Pentagon should be equal to 540°
⇒ x° + (2x)° + (2x)° + 90° + 90° = 540°
⇒ (5x)° = 540° - 180°
⇒ (5x)° = 360°
[tex]\sf{\implies x^{\circ} = \dfrac{360^{\circ}}{5}}[/tex]
⇒ x° = 72°
MARKING BRAINLIEST
PLS HELP
Answer:
25
Step-by-step explanation:
Moving it down does not change the length.
BRAINLIEST IF CORRECT You choose a movie at random from a list containing 8 comedy movies, 5 science fiction movies, and 7 adventure movies. What is the theoretical probability that the movie is not a comedy?
Select all that apply.
0.60
50%
252 fifths
353 fifths
60%
Answer:
0.60 & 60%
Step-by-step explanation: