Answer:
A) The y-intercept(s) is/are 2
Step-by-step explanation:
Y-intercepts are where the graph of a function cross over the y-axis. In this case, the line passes through y=2, which is the y-intercept.
1. Suppose we have a six-sided die that we roll once. Let ai represent the event that the result is i. Let Bj represent the event that the dice comes out greater than j. Let C represent the event that the result is an even number.
a) Since the number is greater than 1, what is the conditional probability that 3 is obtained? (P[A3|B1])
b) Since the number is greater than 3, what is the conditional probability that 6 is obtained?
c) Since the result is an even number, what is the conditional probability of a number greater than 3? (ie P[B3|C])
d) Since the number is greater than 3, what is the conditional probability of an even number?
Using the probability concept, it is found that there is a
a) 0.2 = 20% probability that 3 is obtained.
b) 0.3333 = 33.33% probability that 6 is obtained.
c) 0.6667 = 66.67% probability of a number greater than 3.
d) 0.6667 = 66.67% probability of an even number.
A probability is the number of desired outcomes divided by the number of total outcomes.
Item a:
There are 5 numbers greater than 1, one of which is 3, hence:
\(p = \frac{1}{5} = 0.2\)
0.2 = 20% probability that 3 is obtained.
Item b:
There are 3 numbers greater than 3, one of which is 6, hence:
\(p = \frac{1}{3} = 0.3333\)
0.3333 = 33.33% probability that 6 is obtained.
Item c:
There are 3 even numbers, two of which are greater than 3, hence:
\(p = \frac{2}{3} = 0.6667\)
0.6667 = 66.67% probability of a number greater than 3.
Item d:
There are 3 numbers greater than 3, two of which are even, hence:
\(p = \frac{2}{3} = 0.6667\)
0.6667 = 66.67% probability of an even number.
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If the numerator of a fraction is increased by 2 and the denominator by 5 it becomes 1/2. Again if the numerator is decreased by 4 and the denominator by 1 it becomes 1/3, find the fraction.
The original fraction is 10/19
Let the fraction be \(\frac{x}{y}\)
Now , according to question
\(\frac{x+2}{y+5}\) =\(\frac{1}{2}\)
⇒ 2(x+2)=y+5
⇒2x-y-1=0-------(1)
and \(\frac{x-4}{y-1}\)=\(\frac{1}{3}\)
⇒3(x-4)=y-1
⇒3x-y-11=0------(2)
subtracting 1 from 2 we get
2x-y-1
3x-y-11
- + +
⇒ x=10
putting in (1)
20-y-1=0
y=19
∴ The actual fraction was 10/19
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Use the slope-intercept form to graph the equation y=2/9x+3
we are given the following equation of a line
\(y=\frac{2}{9}x+3\)This is written in the slope-intercept form, which means it follows the general form:
\(y=mx+b\)Where "m" is the slope and "b" is the intercept. We are asked to find the graph, to do that, we can begin by using the intercept since that is the point where the line touches the y-axis, this means that it represents the point (0,b), in our case, this is: (0,3).
Now we need to find a second point, we can use the point where the line touches the x-axis, that is, the point where y = 0, so we set y = 0 in the equation for the line and solve for "x", like this:
\(\begin{gathered} y=\frac{2}{9}x+3 \\ 0=\frac{2}{9}x+3 \end{gathered}\)subtracting 3 on both sides
\(-3=\frac{2}{9}x\)multipliying by 9 on both sides
\(-3(9)=2x\)Dividing by 2 on both sides
\(\begin{gathered} \frac{-3(9)}{2}=x \\ -\frac{27}{2}=x \end{gathered}\)therefore, the second point is (-27/2,0). Now we plot both points and join them with a line, like this:
Any two points can be use to plot a line, so one could also use a different value for "x", evaluate that value in the equation for the line and get a value for "y". That point, together with the intercept can be use to plot the line.
We could use for example x = -5, if we replace that value in the equation we get.
\(y=\frac{2}{9}(-5)+3=\frac{17}{9}\)we get the point (-5,17/9), and the plot would look like this:
What is the solution of the system use substitution 3x 2y 7 y 3x 11?
Answer: The solution set of the system using substitution for 3x + 2y = 7y = -3x + 11 is ((5,-4).
Hope this helps!
Perform the operation. Enter your answer in scientific notation. 7 × 102 − 5.6 × 102 =
Cody donated $15 to the local Humane Society his brother donate at four dollars less than twice the amount that Cody donated how much money did Cody’s brother donate
Answer:
$26
Step-by-step explanation:
15 * 2= 30
30-4= 26
Does the expression x^3-1 divided by x^2 -1 simplify to x?
No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.
To simplify the expression, let's first factorize both the numerator and denominator.
The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).
The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).
Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:
[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]
The (x - 1) terms cancel out, leaving us with:
x^2 + x + 1 / (x + 1)
So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.
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8/3 X 7/10 X 6/1 plz help me
Answer:
are you mutiplying?
Step-by-step explanation:
When Alvin woke up in the morning, it was
–
9°F. By the afternoon, the temperature had risen to
–
2°F.
What was the change in temperature from the morning to the afternoon?
Answer:
The answer to this question is: 7
The change in temperature from the morning to the afternoon is 7°F.
Given that, Alvin woke up in the morning, it was –9°F. By the afternoon, the temperature had risen to –2°F.
We need to find what was the change in temperature from the morning to the afternoon.
What is the change in temperature?Temperature change is a process whereby the degree of hotness of a body (or medium) changes.
You subtract the final temperature from the starting temperature to find the difference.
Now, change in teperature=-2-(-9)
=-2+9=7
Therefore, the change in temperature from the morning to the afternoon is 7°F.
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A
B
C
D
37. What is the length of side P in the figure below?
6.7 cm
11 cm
15 cm
45 cm
20 cm
25 cm
P
The length of the side P is 15 cm. And the right option is C.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
To calculate the length of side P we use Pythagoras theorem's formula
Pythagoras formula:
a² = b²+c²......................... Equation 1Where:
a = Diagonal of the rectangleb = Length of the rectanglec = Width of the rectangleFrom the diagram,
Given:
a = 25 cmb = 20 cmc = p cmSubstitute these values into equation 1
25² = 20²+p²p² = 25²-20²p² = 225p = √225p = 15 cmHence, the right option is C 15 cm.
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I'm Waiter at diner and the dinner cost the customer $50.00 they give me $200 how much change do I get or how much change customer gets
Answer:
$150
Step-by-step explanation:
200 - 50 = 150
Solve the inequality.
Answer: x>-5
Step-by-step explanation:
For this problem there are 2 ways to solve for x.
Solution 1
6((x/2)+4)≥9 [distribute 6 to x/2 and 4]
3x+24≥9 [subtract 24 on both sides]
3x≥-15 [divide both sides by 3]
x≥-5
-----------------------------------------------------------------------------------
Solution 2
6((x/2)+4)≥9 [divide both sides by 6]
(x/2)+4≥1.5 [subtract 4 on both sides]
x/2≥-2.5 [multiply 2 on both sides]
x≥-5
a cylinder has a volume of (x+5) (x^2+10x+25)pi and a diameter of 2x+10. Find the height. PLEASE HELP
Answer:
Height = (x² + 10x + 25)
Step-by-step explanation:
We are given;
volume of cylinder; v = (x+5)•(x² + 10x + 25)π
Diameter = 2x + 10
So radius;r = diameter/2 = (2x + 10)/2 = x + 5
Now,formula for volume of cylinder is;
V = πr²h
Where r is radius and h is height
Plugging in the relevant values, we have;
(x+5)•(x² + 10x + 25)π = π(x + 5)*h
Dividing both sides by π(x + 5) gives us;
h = (x² + 10x + 25)
Please answer this correctly without making mistakes
Answer:
The second coupon
Step-by-step explanation:
Answer:
First coupon ($250.00)
Step-by-step explanation:
Figure out the new price with first coupon:
$453.00 - $250.00 = $203.00Figure out the new price with second coupon:
55% of $453 = \(\frac{55}{100}\) × \(\frac{453}{1} = \frac{24915}{100} = 249.15\) Because we now know that 55% ($249.15) is less than $250.00, we automatically know that the first coupon will save Braden more moneyI hope this helps!
what numbers add up to 6 but multiply to 77
Answer:
one
Step-by-step explanation:
one is the only number that evenly adds up to six and multplys to 77
solve the question below
Answer:
The answer is below
Step-by-step explanation:
1) A triangle is a polygon with three sides and three angles. There are different types of triangles such as obtuse, scalene, right angle, equilateral and isosceles triangle.
Given that triangle ABC is right angled and AC = 25 cm = hypotenuse and BC = 15 cm. Using Pythagoras:
AC² = BC² + AB²
25² = AB² + 15²
AB² = 25² - 15²
AB² = 400
AB = √400
AB = 20 cm
Using sine rule:
\(\frac{sin(B)}{AC}=\frac{sin(A)}{BC}=\frac{sin(C)}{AB}\\\\But\ \angle B= 90^o(right\ angle)\ hence:\\\\ \frac{sin(B)}{AC}=\frac{sin(A)}{BC}\\\\\frac{sin(90)}{25}=\frac{sin(A)}{15}\\\\sin(A)=\frac{sin(90)}{25}*15\\\\sin(A)=0.6\\\\A=sin^{-1}(0.6)\\\\A=36.87^o\)
2)
Using Pythagoras:
hypotenuse² = 8² + 6²
hypotenuse² = 100
hypotenuse = √100
hypotenuse = 10
Using sine rule:
\(\frac{sin(x)}{8}=\frac{sin(90)}{10}\\\\sin(x)=\frac{sin(90)}{10}*8\\\\sin(x)=0.8\\\\x=sin^{-1}(0.8)\\\\x=53.13 ^o\)
Answer below
Brainliest
Answer:
25 remainder of 4
Step-by-step explanation:
Answer:
here hope this will be you ^^"
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
What is the volume of an 8-inch by 4-inch by 4
1) 2-inch rectangular box?
Answer________ cubic inches
Answer is 128 cubic inches
The volume of the given box is 64 inch³
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.
The length, width, and height of a rectangular box are multiplied to get its volume.
As a result, the following formula may be used to determine the volume of an 8 inches by 4 inches by 2 inches rectangular box:
Volume is calculated using the formula LWH.
Volume is =8 * 4 * 2 inches.
64 cubic inches is the volume.
The rectangular box measures 8 by 4 by 2 inches and thus has a volume of 64 cubic inches.
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2 3/4 of 500grams in step by step calculator
Answer:
To calculate 2 3/4 of 500 grams, follow these steps:
1. Convert the mixed number to an improper fraction:
2 3/4 = (2 x 4 + 3)/4 = 11/4
2. Multiply the improper fraction by 500:
11/4 x 500 = (11 x 500)/4 = 2,750/4
3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:
2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2
Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.
Step-by-step explanation:
-3x^2+33=48x complete the square
The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75
Completing the square:
To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.
In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.
Here we have
- 3x² + 33 = 48x
Keep 'x' terms on one side and constant terms sides on another side
=> - 3x² - 48x = - 33
Divide by - 3 on both sides
=> -3(x² + 4x)/3 = - 33/3
=> x² + 16x = 11
Take half of the 'x' term and square it and add on both sides
=> x² + 2(8x) (x) + (8)² = 11 + (8)²
Which is in the form of x² + 2bx + b² = (x + b)²
=> [x + 8]² = 75
Therefore,
The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75
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HELP ME ASAP!!! YOU WILL BE BRAILIEST!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
\(P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\\)
This is 25% (for each one, equally)
b) The experimental probability is given by:
\(P(A)= \frac{32}{150} =0.2133\)
\(P(B)= \frac{38}{150} =0.2533\)
\(P(C)= \frac{35}{150} =0.2333\)
\(P(D)= \frac{45}{150} =0.3000\)
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
You start to watch a warm crawling across the ground the worm is traveling 3 feet every minute the worm had already traveled 1 foot when you started watching how long did it take the worm to crawl 10 feet
how many ft is equal to 1.66m
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
What is the value of x? A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees. (1 point)
A –19
B 125
C 19
D 55
The value of x in the angles is 19.
How to find angles in intersecting lines?When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.
Therefore, let's find the value of x in the intersecting lines.
Hence,
7x - 8 = 6x + 11 (vertically opposite angles)
Vertically opposite angles are congruent and they share the same vertex point.
Hence,
7x - 8 = 6x + 11
subtract 6x from both sides of the equation
7x - 8 = 6x + 11
7x - 6x - 8 = 6x - 6x + 11
x - 8 = 11
add 8 to both sides of the equation
x - 8 + 8 = 11 + 8
x = 19
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explain why the statement x < 3 or > 5 cannot be written 5 < x < 3
Answer:
This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.
Step-by-step explanation:
x < 3 or x > 5
This means, x is less than 3, but greater than 5.
Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.
A rectangular poster is 50 centimeters long and 25 centimeters wide. If 1 centimeter is approximately 0.4 inches, which of the following best represents the area of the poster in inches?
The area of the poster in inches is,
⇒ A = 4 inches²
We have to given that;
A rectangular poster is 50 centimeters long and 25 centimeters wide.
Here, 1 centimeter is approximately 0.4 inches
Hence, Lenght = 50 cm
Lenght = 50 x 0.4
= 2 inches
Width = 25 cm
= 25 x 0.4
= 1 inches
Thus, The area of the poster in inches is,
⇒ A = 1 x 4
⇒ A = 4 inches²
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Answer both please
Find the domain of the function. (Enter your answer using interval notation.)
f(x) =
4x³-3
x² + 4x - 5
7. [-/3 Points]
f(-8)
=
Evaluate f(-8), f(0), and f(4) for the piecewise defined function.
f(x) =
x+4 if x < 0
2-x if x 20
f(0) =
f(4) =
The solution is, the domain is: x ∈ (-∞, ∞).
Here, we have,
When we have two functions, f(x) and g(x), the composite function:
(f°g)(x)
is just the first function evaluated in the second one, or:
f( g(x))
And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:
f(x) = 1/(x + 1)
where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.
Now, we have:
f(x) = x^2
g(x) = x + 9
then:
(f ∘ g)(x) = (x + 9)^2
And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:
x ∈ (-∞, ∞)
(g ∘ f)(x)
this is g(f(x)) = (x^2) + 9 = x^2 + 9
And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:
x ∈ (-∞, ∞)
(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4
And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:
x ∈ (-∞, ∞)
(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18
And again, there are no values of x that cause a problem here,
so the domain is:
x ∈ (-∞, ∞)
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complete question:
Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat
Which ordered pair makes both inequalities true?
y> -3x +3
y22x-2
O (1,0)
O (-1,1)
O (2,2)
O (0,3)
None of the ordered pairs (1, 0), (-1, 1), (2, 2), and (0, 3) make both inequalities true.
To determine which ordered pair makes both inequalities true, we can substitute the given values into the inequalities and check for validity:
1. (1, 0):
For y > -3x + 3: 0 > -3(1) + 3 -> 0 > 0, which is not true.
For y < 2x - 2: 0 < 2(1) - 2 -> 0 < 0, which is not true.
Therefore, (1, 0) does not satisfy both inequalities.
2. (-1, 1):
For y > -3x + 3: 1 > -3(-1) + 3 -> 1 > 6, which is not true.
For y < 2x - 2: 1 < 2(-1) - 2 -> 1 < -4, which is not true.
Therefore, (-1, 1) does not satisfy both inequalities.
3. (2, 2):
For y > -3x + 3: 2 > -3(2) + 3 -> 2 > -3, which is true.
For y < 2x - 2: 2 < 2(2) - 2 -> 2 < 2, which is not true.
Therefore, (2, 2) does not satisfy both inequalities.
4. (0, 3):
For y > -3x + 3: 3 > -3(0) + 3 -> 3 > 3, which is not true.
For y < 2x - 2: 3 < 2(0) - 2 -> 3 < -2, which is not true.
Therefore, (0, 3) does not satisfy both inequalities.
None of the given ordered pairs satisfy both inequalities simultaneously.
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Which expressions are equivalent to -6.3x - 4.2?
-4.7 - 2.3x + 0.5 - 4x
-5.3x - 4.2 - x
-3.4 - 6.3x - 0.8
-6.2x - 4.2
-4.2x - 6.3
-3.7 - 5.3x + 0.5
multiple choice.
Answer:
(1): -4.7 - 2.3x + 0.5 - 4x
(2):-5.3x-4.2-x
(3):-3.4-6.3x-0.8
Step-by-step explanation:
By Collecting like terms and adding the answer I get -6.3x - 4.2
(1):-4.7-2.3x+0.5-4x
Collect like terms
-2.3x-4x-4.7+0.5
-6.3x-4.2
(2):-5.3x-4.2-x
Collect like terms
-5.3x-x-4.2
-6.3x-4.2
(3): -3.4-6.3x-0.8
Collect like terms
-6.3x-3.4-0.8
-6.3x-4.2
Answer:
The first 3 are equivalent the last 3 aren't.
Step-by-step explanation:
Why do we choose 5% as a risk of making error and not 1%
In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.
The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.
In general, the choice of significance level depends on the specific application and context of the statistical analysis.
The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.
The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.
A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.
A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.
For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.
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