Answer: D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .
Step-by-step explanation:
We know that for dependent events A and B , the conditional probability of getting a given that B is given by :-
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
From the given table, if A represent taking French class and B represent taking Art class.
Then P(A)=0.6
and P(B)=0.55
[tex]P(\cap B)=0.2[/tex]
Now, [tex]P(A|B)=\dfrac{0.2}{0.55}=0.036363\approx0.036[/tex]
[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.2}{0.6}=0.33333\aprox0.333[/tex]
Clearly, [tex]P(A|B)\neq P(A)[/tex]
[tex]P(B|A)\neq P(B)[/tex]
Therefore taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .[ By definition of independent events]
The correct statement is D; Taking Art class and taking French class are not independent events.
Consider A represent taking a French class and B represents taking an Art class.
The formula to determine whether two events are independent or not is P(A and B) = P(A) x P(B),
where P(A and B) is the probability of both events happening together, P(A) is the probability of event A happening, and P(B) is the probability of event B happening.
D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B).
This statement is incorrect because the formula to determine whether two events are independent or not is;
P(A and B) = P(A) x P(B),
not P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
Using the values in the table:
P(A) = 0.6 (taking French class)
P(B) = 0.55 (taking Art class)
P(A and B) = 0.2 (taking both classes)
P(A and B) ≠ P(A) x P(B)
0.2 ≠ 0.6 x 0.55
The correct statement is option D.
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Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals. Maggie keeps all the tiles on a mat with the pictures hidden and mixes them up. She then turns one tile face up and finds the picture of a plant on it. She removes this tile from the mat and turns over another tile without looking. What is the probability that the second tile that Maggie turns over has a plant on it?
Answer:6/8 - - - - simplified 3/4
Step-by-step explanation: removing the tile she just flipped over would be 6 plants and 2 animals so there would be 8 total tiles and you would putt the remaining tiles over it like so 6/8 meaning out of the remaining 8 tiles 6 of them are plants giving her a 6 in 8 chance or a 3 in 4 chance
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
We are given that Maggie has 7 tiles with pictures of plants and 2 tiles with pictures of animals .
Number of tiles with picture of plants =7
Number of tiles with picture of animals =2
Total number of tiles =7+2=9
We have to find the probability that the second tile that Maggie turns over has plant on it .
When she removes one tile of picture of plant then she has number of tiles of picture of plants =6
Total number of tiles =8
Probability,P(E)=[tex]\frac{Number\;of\;favorable\;cases}{Total\;number\;of\;cases}[/tex]
Using the formula then we get
The probability that she finds tile of picture of plant =[tex]\frac{6}{8}=\frac{3}{4}[/tex]
What is the volume of the cone shown in the picture ?
need some help
Answer:
Cone Volume = (π • radius² • height) ÷ 3
Cone Volume = (π • 8^2 * 17) /3
Cone Volume = (PI * 1,088) / 3
Cone Volume = 1,139.35 cubic centimeters
Step-by-step explanation:
which expressions have the same product as 5 * 3/4
Answer:
Step-by-step explanation:
Well let's get a couple of equivalents and you can pick the one you like best.
You could have (5 * 3)/4 = 15/4
This 15/4 will give you 3.75
You could have (2*15)/ (2*4) = 30/8 Multiply top and bottom by 2.
30/8 = 3 6/8 = 3 and 3/4
which of the following has the greatest value?
A) .4
B) .36
C) .052
D) .173
E) .0985
I need help
Answer:
0.4
Step-by-step explanation:
The way you can tell is by first looking at the left-most digit. If they are all the same, look one to the right. Keep looking until you find one with a greater number than the others.
Match the following.
1 .
multiplicative identity
the number 0; when added to any number, the value of the number does not change
2 .
multiplicative inverse
the opposite or negative of a number; the sum of a number and its additive inverse is 0
3 .
commutative property
a property of the real numbers which states that how numbers are grouped in a sum or product does not change the value
4 .
additive identity
a property of the real numbers which states that the order in which numbers are added or multiplied does not change the value
5 .
additive inverse
a(b + c) = ab + ac, or a(b - c) = ab - ac
6 .
associative property
the number 1; when multiplied by any number, the value of the number does not change
7 .
distributive property
the reciprocal of a number; the product of a number and its multiplicative inverse is 1
Answer:
1. Multiplicative identity:
The number 1; when multiplied by any number, the value of the number does not change.
2. Multiplicative inverse:
The reciprocal of a number; the product of a number and its multiplicative inverse is 1.
3. Commutative property:
a property of the real numbers which states that the order in which numbers are added or multiplied does not change the value
4. Additive identity:
The number 0; when added to any number, the value of the number does not change.
5. Additive inverse:
The opposite or negative of a number; the sum of a number and its additive inverse is 0
6. Associative property:
a property of the real numbers which states that how numbers are grouped in a sum or product does not change the value
7. Distributive property:
a(b + c) = ab + ac, or a(b - c) = ab - ac
Step-by-step explanation:
1. Multiplicative identity:
Ex: 3 × 1 = 3
2. Multiplicative inverse:
Ex: The multiplicative inverse of 2 is 1/2 ⇒ 2 × 1/2 = 1
3. Commutative property:
Ex: 2 + 3 + 5 = 10 , 3 + 2 + 5 = 10 , 5 + 3 + 2 = 10
2 × 3 × 5 = 30 , 3 × 2 × 5 = 30 , 5 × 3 × 2 = 30
4. Additive identity:
Ex: 2 + 0 = 2
5. Additive inverse:
Ex: The additive inverse of 5 is -5 ⇒ 5 + -5 = 0
6. Associative property:
Ex: 2 + (3 + 5) = (2 + 3) + 5
2× (3 × 5) = (2 × 3) × 5
7. Distributive property:
Ex: 2(3 + 5) = 2 × 3 + 2 × 5
2(5 - 3) = 2 × 5 - 2 × 3
Answer:1. Multiplicative identity:
The number 1; when multiplied by any number, the value of the number does not change.
2. Multiplicative inverse:
The reciprocal of a number; the product of a number and its multiplicative inverse is 1.
3. Commutative property:
a property of the real numbers which states that the order in which numbers are added or multiplied does not change the value
4. Additive identity:
The number 0; when added to any number, the value of the number does not change.
5. Additive inverse:
The opposite or negative of a number; the sum of a number and its additive inverse is 0
6. Associative property:
a property of the real numbers which states that how numbers are grouped in a sum or product does not change the value
7. Distributive property:
a(b + c) = ab + ac, or a(b - c) = ab - ac
Step-by-step explanation:
1. Multiplicative identity:
Ex: 3 × 1 = 3
2. Multiplicative inverse:
Ex: The multiplicative inverse of 2 is 1/2 ⇒ 2 × 1/2 = 1
3. Commutative property:
Ex: 2 + 3 + 5 = 10 , 3 + 2 + 5 = 10 , 5 + 3 + 2 = 10
2 × 3 × 5 = 30 , 3 × 2 × 5 = 30 , 5 × 3 × 2 = 30
4. Additive identity:
Ex: 2 + 0 = 2
5. Additive inverse:
Ex: The additive inverse of 5 is -5 ⇒ 5 + -5 = 0
6. Associative property:
Ex: 2 + (3 + 5) = (2 + 3) + 5
2× (3 × 5) = (2 × 3) × 5
7. Distributive property:
Ex: 2(3 + 5) = 2 × 3 + 2 × 5
2(5 - 3) = 2 × 5 - 2 × 3
Step-by-step explanation:Answer:
solve for y
13 = 6 + y
13 - 6 is 7
7 + 6 = 13
Just subtract the 2 numbers and you get your answer.
Final answer:
The equation 13 = 6 + y is solved by subtracting 6 from both sides, yielding y = 7.
Explanation:
To solve for y in the equation 13 = 6 + y, we need to isolate y on one side of the equation. We can do this by subtracting 6 from both sides of the equation.
Here is how you can solve the equation step by step:
Start with the original equation: 13 = 6 + y.
Subtract 6 from both sides: 13 - 6 = 6 + y - 6.
This simplifies to: 7 = y.
So, the value of y is 7.
Help me please urgent
PLEASE HELP MEH I REALLY NEED HELP
Answer:
find A PATTERN
Step-by-step explanation:
FIND A PATTERN IN THE NUMBERS
Answer:
The answer is 53
Step-by-step explanation:
Which statement is the correct interpretation of the inequality –5 > –6? (1 point)
Select one:
a. On a number line, −5 is located to the left of 0 and –6 is located to the right of 0.
b. On a number line, −5 is located to the right of 0 and –6 is located to the left of 0.
c. On a number line, −5 is located to the left of –6.
d. On a number line, −5 is located to the right of –6.
Answer: OPTION D.
Step-by-step explanation:
The symbol of the inequality ">" means "greater than". Then, -5 is greater than -6.
If a negative number -a is greater than other negative number -b , then the distance between -a and zero is shorter than the distance between -b and zero.
You can see in the number line attached that -5 is closer to 0 than -6. Therefore, -5 is located to the right of -6.
Answer:
D
Step-by-step explanation:
A computer cost £900. It is on sale for 25% off. You also need to pay 6% sales tax. What is the final price of the computer?
First we have to find 25% of 900 pounds (i hope that's the right currency). so 900 x .25 = 225
so we subtract 225 from 900 and get 675 pounds.
to find sales tax we have to find 6% of 675, so 675 x .06 = 40.50
675 + 40.50 = 715.5 pounds
Choose the third degree polynomial. 2x-5 3x2+2x-5 x3-3x2+2x-5 5x4+x3-3x2+2x-5
ANSWER
[tex] {x}^{3} - 3 {x}^{2} + 2x - 5[/tex]
is the third degree polynomial.
EXPLANATION
The third degree polynomial has the highest degree to be 3.
All the polynomials were written in standard form.
[tex]2x - 5[/tex]
is a first degree polynomial.
[tex]3 {x}^{2} + 2x - 5[/tex]
is a second degree polynomial .
[tex] {x}^{3} - 3 {x}^{2} + 2x - 5[/tex]
is a third degree polynomial.
[tex]5 {x}^{4} + {x}^{3} - 3 {x}^{2} + 2x - 5[/tex]
is a fourth degree polynomial.
Answer:
[tex]x^3-3x^2+2x-5[/tex]
Step-by-step explanation:
Since, the degree of a polynomial is the highest power of its monomial with non zero coefficient,
In the polynomial 2x - 5,
The highest power is 1,
So, its degree is 1,
In the polynomial [tex]3x^2+2x-5[/tex],
The highest power is 2,
So, its degree is 2,
In the polynomial [tex]x^3-3x^2+2x-5[/tex],
The highest power is 3,
So, its degree is 3,
In the polynomial [tex]5x^4+x^3-3x^2+2x-5[/tex]
The highest power is 4,
So, its degree is 4.
Write and solve an equation to answer the question,
"5 is 5% of what number w?"
An equation is blank =0.05 blank .
The solution is w= blank.
The mathematical representation of '5 is 5% of what number?' is 5 = 0.05w. To solve for w, we divide 5 by 0.05, which gives us a value of w=100.
Explanation:To solve the question, '5 is 5% of what number w?', we can set up the equation as 5 = 0.05w. This equation represents the statement '5 is 5% of some number w' in mathematical terms. To find the value of w, we divide both sides of the equation by 0.05. The calculation goes like this:
Set up the equation: 5 = 0.05wDivide both sides by 0.05: w = 5 / 0.05Perform the division to find the value of w: w=100Learn more about Math Percentage here:
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The equation to find the number for which 5 is 5% is: 5 = 0.05w. The solution to the equation is w = 100.
To write and solve the equation that represents the given statement, we can let 'w' represent the unknown number.
The equation is:
5 = 0.05w
Solving for w, we divide both sides by 0.05:
w = 5 / 0.05
w = 100
Therefore, the solution to the equation is w = 100. This means that 5 is 5% of 100.
if the radius of a circle is 15 units abs the center of the circle is (-3,2), what is the equation of the circle?
Answer:
[tex]\large\boxed{(x+3)^2+(y-2)^2=225}[/tex]
Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have r = 15 and the center (-3, 2). Substitute:
[tex](x-(-3))^2+(y-2)^2=15^2\\\\(x+3)^2+(y-2)^2=225[/tex]
HELP QUICKY
Which statement is true about the end behavior of the function?
As the x-values go to positive infinity, the function's values go to positive infinity.
Answer: D, As the x values go to positive infinity, the functions values go to positive infinity.
Step-by-step explanation:
This is true for just about any [tex]y=x^{3}[/tex] graph. As the value of the input (x) get larger, the value of the output (y) will get exponentially larger.
What is the perimeter of triangle ABC ?
Answer:
The perimeter is equal to [tex](y+39)\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of the triangle is equal to the sum of the length of its sides.
so
[tex]P=AB+BC+AC[/tex]
substitute the values
[tex]P=(y+7)+18+14[/tex]
[tex]P=(y+39)\ units[/tex]
An someone please help.
This is a special right triangle with 3 sides that are 5, 12, 13. You should remember this triangle.
[tex] {13}^{2} = {x}^{2} + {12}^{2} \\ {x}^{2} = {13}^{2} - {12}^{2} \\ x = \sqrt{ {13}^{2} - {12}^{2} } = \sqrt{169 - 144} = \sqrt{25} = 5[/tex]
Solve 2,401 = 76 – 2x.
Answer:
its 1.
Step-by-step explanation:
What is the volume of the square pyramid with base edges 16m and height 24m?
Answer:
192
Step-by-step explanation:
1/2 of 24 times 16=192
oof IDK anymore look above at the picture
Answer:
V=120 in^3
Step-by-step explanation:
Height x Width x Length
If a leg of a 45-45-90 triangle is 11 then the hypotenuse is...
a)11
b)11√3
c)11√2
d)5.5
Include work if possible :)
Answer:
c)11√2
Step-by-step explanation:
Given that two of the angles are equal ,each measuring 45 degrees then two legs will be equal as well each measuring 11 units. We have a right angled triangle with two sides given and we are required to determine the hypotenuse. We use Pythagoras theorem;
hypotenuse^2 = 11^2 + 11^2
hypotenuse ^2 = 242
hypotenuse = [tex]\sqrt{242}[/tex]
hypotenuse = [tex]11\sqrt{2}[/tex]
Answer:
a) 11
Step-by-step explanation:
Pete played 18 tennis matches in a week. Jack played 6 fewer matches than Pete.
How many times the number of matches pete played is the number of matches jack played?
Answer:
Pete played 1.5 times the number of matches that Jack played.Step-by-step explanation:
Pete played 18 tennis matches in a week.
P = 18
Jack played 6 fewer matches than Pete.
J = P - 6
J = 18 - 6
J = 12
How many times the number of matches pete played is the number of matches jack played?
18 / 12 = 1.5
Pete played 1.5 times the number of matches that Jack played.
Answer:
Pete played 1.5 times the amount of matches Jack did.
Step-by-step explanation:
In order to find this, first find the number that Jack played. Since he played 6 fewer than Pete we can solve by subtracting 6 from Pete's number.
18 - 6 = 12
Now to find how many more times higher it is, divide the number Pete does by Jack's number. 18/12 = 1.5
What is the volume of this rectangular prism
Answer:
V = 5/8 cm^3
Step-by-step explanation:
V= l*w*h
V = 3/4 * 1/3 * 5/2
The numerator = 3*1*5 = 15
The denominator = 4*3*2 = 24
V = 15/24 cm^3
We can simplify the fraction by divide the top and bottom by 3
V = 5/8 cm^3
Which graph represents the multiplication of 3(-4)
Answer:
Step-by-step explanation:
Unfortunately, you haven't shared the graphs from which you're supposed to choose.
I would draw a number line. Place a dot at 0. Now move 4 spaces to the left and place another dot. Repeat this twice. Your final dot will represent 3(-4).
Answer:
Look at the photo provided above
The difference between the two roots of the equation 3x2+10x+c=0 is 4 2/3 . Find the solutions for the equation.
Answer:
x1 = - 4
x2 = 2/3
Step-by-step explanation:
Divide the equation by 3 to give
x^2 + 10x/3 + c/3 = 0
The sum of the two roots = - 10/3
So
x1 + x2 = -10/3
x1 - x2 = 4 2/3 Add these two equations.
2x1 = -10/3 + 4 2/3 Change 4 2/3 to an improper fraction
2x1 = -10/3 + 14/3 Combine the right
2x1 = 4/3 Divide by 2
2x1/2 =4/3//2
x1 = 2/3
=====================
x1 + x2 = - 10/3
2/3 + x2 = - 10/3
x2 = - 10/3 - 2/3
x2= -12/3
x2 = - 4
=================
(x - 2/3)(x +4) = 0 Multiply through by 3
(3x - 2)(x + 4) =0
==============
Check
(3x - 2)(x + 4) = 0
3x^2 + 12x - 2x - 8 =0
3x^2 + 10x - 8 = 0
Write the equation of the line in slope-intercept form using the two points: E(-1, 3) and F(-2, -3).
Answer:
[tex]\large\boxed{y=6x+9}[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points E(-1, 3) and F(-2, -3). Substitute:
[tex]m=\dfrac{-3-3}{-2-(-1)}=\dfrac{-6}{-2+1}=\dfrac{-6}{-1}=6[/tex]
Therefore the equation of a line is:
[tex]y=6x+b[/tex]
Put the coordinates of the point E(-1, 3) to the equation and solve it for b:
[tex]3=6(-1)+b[/tex]
[tex]3=-6+b[/tex] add 6 to both sides
[tex]9=b\to b=9[/tex]
Finally we have:
[tex]y=6x+9[/tex]
Simplify the expression 4(2x - 3y) ASAP
Answer:
8x - 12y
Step-by-step explanation:
4(2x-3y)
Distribute/multiply the 4 to everything in the parentheses
4 * 2x = 8x 4 * -3y = -12y
8x - 12y
Answer:
[tex]4(2x-3y)=8x-12y[/tex]
Step-by-step explanation:
The given expression is
[tex]4(2x-3y)[/tex]
We expand using the distributive property to obtain;
[tex]4(2x-3y)=4\times2x-4\times3y[/tex]
This implies that;
[tex]4(2x-3y)=8x-12y[/tex]
A cake recipe calls for 425 g of flour about how many pounds of flour do you need use the conversion factors
You'd need 0 pounds and 14 ounces of flour.
Please help with this normal distribution problem
900 = 750 + 2*75. In other words, 900 is 2 standard deviations away from the mean. Similarly, 975 is 3 standard deviations from the mean. So
[tex]P(900<X<975)=P(2<Z<3)[/tex
where [tex]X[/tex] is the random variable for the lifespan of a light bulb with the given normal distribution, and [tex]Z=\dfrac{X-750}{75}[/tex] with the standard normal distribution.
We get
[tex]P(2<Z<3)\approx0.0214=2.14\%[/tex]
If you don't have a calculator/lookup table available, you can invoke the empirical rule, the one that says
[tex]\begin{cases}P(-1<Z<1)\approx68\%\\P(-2<Z<2)\approx95\%\\P(-3<Z<3)\approx99.7\%\end{cases}[/tex]
The normal distribution is symmetric about its mean, so we also know
[tex]\begin{cases}P(0<Z<1)\approx34\%\\P(0<Z<2)\approx47.5\%\\P(0<Z<3)\approx49.85\%\end{cases}[/tex]
Then
[tex]P(2<Z<3)=P(0<Z<3)-P(0<Z<2)\approx2.35\%[/tex]
Answer:
0.021
Step-by-step explanation:
One way in which to approach this problem solution is to use a calculator that has statistical distribution functions built in. My old TI-83Plus has the function "normalcdf," which does the job nicely.
Typing in normalcdf(900,975,750,75) results in the probability 0.021 that a light bulb chosen at random will last between 900 and 975 hours.
Using a table of z-scores would be a good alternative approach. Note that the z-score corresponding to 750 hours is 0; that for 900 is +2; and that for 975 is +3. Find the area under the standard normal curve to the left of 975 (z = 3) and that to the left of 900 (z = 2), and then subtract the two results. It will be 0.021, as before.
find the radius of a circle with an area of 89 sqaure feet.
Answer:
5.32255
Step-by-step explanation:
if the circle's surface area is 89 square feet. The circle's radius will then be 5.32 feet.
What is the area of a circle?It is the closely curving line drawn from the center to an equally distant point. The distance separating a circle's center and perimeter is its radius.
Let r be the radius of the circle. Then the area of the circle is written as,
A = πr² square units
The area of the circle is 89 square feet. Then the radius of the circle will be given as,
89 = πr²
Simplify the equation, then the radius is written as,
πr² = 89
r² = 28.34
r = 5.32 feet
if the circle's surface area is 89 square feet. The circle's radius will then be 5.32 feet.
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which place value chart represents the number 450,803
Answer:
3 = ones
0 = tens
8 = hundreds
0 = thousands
5 = ten-thousands
4 = hundred-thousands
Answer
C. 4508
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