Answer:
the probability that the first groupmate you meet has studied some statistics is 0.45
Step-by-step explanation:
From the information given :
A professor divided the students in her business class into three groups
Let consider then to be :
Group Statistics Class
A Never taken a statistics class
B Taken one statistics class
C Taken two or more statistics class.
If 55% of the students have never taken a statistics class,
Then ;
P(A) = 0.55
25% have taken only one semester of a statistics class
Then P(B) = 0.25
and the rest have taken two or more semesters of statistics
Then P(C) = 1 - 0.55 -0.25
P(C) = 1 - 0.80
P(C) = 0.20
The objective is to determine the probability that the first groupmate you meet has studied some statistics
The probability of the first groupmate you meet has studied some statistics = 1 - P(never taken a statistics course)
Let the probability of the first groupmate you meet that has studied some statistics be P(D)
Then P(D) = 1 - P(A)
P(D) = 1 - 0.55
P(D) = 0.45
the probability that the first groupmate you meet has studied some statistics is 0.45
A ball is thrown vertically upward from the top of a cliff. The height
of the ball is modelled by the function h(t) = 65 + 10t - 5t squared,
where h(t) is the height in metres and t is time in seconds. Determine
when the ball reaches its maximum height?
Answer:
Step-by-step explanation:
To solve this problem you have to complete the square. To do that, set the quadratic equal to 0, then move the constant over to the other side. That's 2 steps in one, but they're simple ones:
[tex]-5t^2+10t=-65[/tex]
The first picky rule that completing the square has to follow is that the coefficient on the squared term has to be a 1. Ours is a -5, so we factor it out:
[tex]-5(t^2-2t)=-65[/tex] . Now it gets even pickier. To create a perfect square binomial on the left, we take half the linear term, square it, and add it in to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is 1, so we add 1 into the set of parenthesis. BUT the -5 out front is a multiplier and refuses to be ignored. To offset the addition of the 1 inside the parenthesis, we have to multiply it by the -5 out front to get -5:
[tex]-5(t^2-2t+1)=-65-5[/tex]
The perfect square binomial on the left side and simplifying the right:
[tex]-5(t-1)^2=-70[/tex] . Now we'll move the 70 over and set the quadratic back equal to y:
[tex]-5(t-1)^2+70=y[/tex]
That's the quadratic in vertex form. The vertex here is (1, 70) which serves to answer 2 questions for us: the max height of the ball along with the time it was at that max height. For us, the ball reached a max height of 70 m after 1 second in its travels.
You could also do it the "calculus way" which is to find the derivative of the position function, which is
-10t + 10 = 0 and solve for t:
-10t = -10 so
t = 1. That's the time that the ball is at its highest point, and to find the highest point, sub that value in for t in the position function:
[tex]h(t)=-5(1)+10(1)+65[/tex] which comes to 70 m. I'm not sure what class you're taking so I did both! Calculus is way easier.
A game is played using one die. if the die is rolled and shows 6, the player wins $20. if the die shows any number other than 6, the player wins nothing.
a. if there is a charge of $4 to play the game, what is the game's expected value?
$______(round to the nearest cent)
b. choose the statment below that best describes what this value means.
Choose one!
a. over the long run, the player can expect to lose about this amount for each game played
b. over the long run, the player can expect to win about this amount for each game playedc. over the long run, the player can expect to break even.
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a charge of $1 to play the game, what is the game's expected value?
--------------------
Let random variable "x" be a count of player gain.
X-values are: 4, -1
P(x=4) = 1/6; P(x= -1) = 5/6
---------------------------------
E(x) = (1/6)(4) + (5/6)(-1)
E(x) = [4-5]/6
E(x) = -1/6 = -17 cents
=============================
Cheers,
Can someone please help me with this and show work
Answer:
29/6-16/2549/30Rationalize(1.63333333333)1*(19/30)Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2
Answer: Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
We must work with linear equations, remember that the general shape is:
y = a*x + b
where a is the slope and b is the y-intercept.
Ok, first we want to find the rate of change (or the slope) of the graphed line:
We know that for a line that passes through the points (x1, y1) and (x2, y2)
The slope is:
a = (y2 - y1)/(x2 - x1)
Then for the graphed function, we can see that it passes through the points:
(0, -2) and (4, 0)
Then the slope is:
a = (0 -(-2))/(4 - 0) = 2/4 = 1/2
Now, the slope of the second line is 15/4.
Let's calculate the difference between the slopes:
15/4 - 1/2 = 15/4 - 2/4 = 13/4
(notice that we are calculating slope2 - slope1)
Then the correct option is:
Function 2 has a greater rate of change by 13/4
Answer:
B) Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
Please answer the question in the image below ASAP
Answer:
d. 200%
Step-by-step explanation:
( 800 ÷ 400 ) × 100
Find the term that must be added to the equation x^2−6x=7 to make it into a perfect square.
Answer:
Step-by-step explanation:
x^2-6x=7 is our equation
x^2-2*3*x= 7
So the term we will be adding is 3^2 since 3 the second term is 2*3*x
x^2-6x+9=7-9
We added 9 and substract it to keep the equation
(x+3)^2 = -2
Wich is impossible since a squared number is always positive
a coat was marked down by 60 percent from its original price of $99 . including an 8% sale tax , what is the final cost of the coat?
Answer:
i think its 42.77... might be wrong tho
Step-by-step explanation:
being marked down by 60 percent means to multiply original number by 0.4
so we get 39.6
the multiply it by 1.08 to get 42.768
Answer:
See below.
Step-by-step explanation:
To find the marked down price, multiply the total by the percentage.
[tex]99*.6=59.4[/tex]
Next, subtract the amount from the total.
[tex]99-59.4=39.6[/tex]
Then, multiply to find the sales tax.
[tex]39.6*0.08=3.168[/tex]
[tex]39.6+3.168=42.768[/tex]
Answer: $42.77
Carolina goes to a paintball field that charges an entrance fee of \$18$18dollar sign, 18 and \$0.08$0.08dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10$10dollar sign, 10 off if you spend \$75$75dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion.
Let BBB represent the number of paintballs that Carolina buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
18+0.08B \leq 7518+0.08B≤7518, plus, 0, point, 08, B, is less than or equal to, 75
(Choice B)
B
18+0.08B \geq 7518+0.08B≥7518, plus, 0, point, 08, B, is greater than or equal to, 75
(Choice C)
C
18+0.08B \leq 1018+0.08B≤1018, plus, 0, point, 08, B, is less than or equal to, 10
(Choice D)
D
18+0.08B \geq 1018+0.08B≥1018, plus, 0, point, 08, B, is greater than or equal to, 10
2) What is the smallest number of paintballs that Carolina can buy along with the entrance fee to get the promotion?
paintballs
Inequalities are used to show unequal expressions; in other words, it is the opposite of equalities.
The inequality that represents the scenario is, [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls Carolina can buy is 713
Given that:
[tex]Entrance\ Fee = \$18[/tex]
[tex]Rate = \$0.08[/tex] per ball
Let:
[tex]B \to Balls[/tex]
The amount (A) Carolina can spend on B balls is:
A = Entrance Fee + Rate * B
This gives:
[tex]A = 18 + 0.08 * B[/tex]
[tex]A = 18 + 0.08B[/tex]
To get $10, Carolina must spend $75 or more.
This means:
[tex]A \ge 75[/tex]
So, the inequality is:
[tex]18 + 0.08B \ge 75[/tex]
The smallest number of balls is calculated as follows:
[tex]18 + 0.08B \ge 75[/tex]
Collect like terms
[tex]0.08B \ge 75 - 18[/tex]
[tex]0.08B \ge 57[/tex]
Divide both sides by 0.08
[tex]B \ge 712.5[/tex]
Round up
[tex]B \ge 713[/tex]
Hence, the inequality is [tex]18 + 0.08B \ge 75[/tex] and the smallest number of balls is 713
Learn more about inequalities at:
brainly.com/question/20383699
Using a linear function, it is found that:
1. [tex]18 + 0.08B \geq 75[/tex], given by option B.2. She has to buy at least 713 paintballs.-----------
The linear function for the cost of B paintballs has the following format:
[tex]C(B) = C(0) + aB[/tex]
In which
C(0) is the fixed cost.a is the cost per paintball.-----------
Question 1:
Entrance fee of $18, thus [tex]C(0) = 18[/tex].Cost of $0.08 per ball, thus, [tex]a = 0.08[/tex]Thus:
[tex]C(B) = 18 + 0.08B[/tex]
The promotion is valid if the cost is of at least 75, thus:[tex]C(B) \geq 75[/tex]
[tex]18 + 0.08B \geq 75[/tex], given by option B.
-----------
Question 2:
The smallest number is the solution of the inequality for B, thus:[tex]18 + 0.08B \geq 75[/tex]
[tex]0.08B \geq 57[/tex]
[tex]B \geq \frac{57}{0.08}[/tex]
[tex]B \geq 712.5[/tex]
Rounding up, she has to buy at least 713 paintballs.
A similar problem is given at https://brainly.com/question/24583430
pls let me know what you get for this question
Answer:
[tex]h=13\,\sqrt{3}[/tex]
[tex]x=52[/tex]
Step-by-step explanation:
Using the triangle formed in the far left, we can use the Pythagorean theorem to solve for h:
[tex]h^2+a^2=y^2\\h^2+39^2=(26\,\sqrt{3} )^2\\h^2=26^2\,(3)-39^2\\h^2=507\\h=\sqrt{507}\\h=13\,\sqrt{3}[/tex]
Now, using the right angle triangle on the right we solve for x:
[tex](x-a)^2+h^2=z^2\\(x-39)^2+507=26^2\\(x-39)^2=676-507\\(x-39)^2=169\\x-39=+/-13\\x=26\,\,\,or\,\,\,x=52[/tex]
since x has to be larger than "a" (39), we use the second answer:
[tex]x=52[/tex]
The Hernandez family ordered one jumbo pizza with a diameter of 20 inches, cut it into 15 equal slices, and had 3 slices left over after dinner. The Mullins family ordered two medium pizzas, each with a diameter of 12 inches, cut them into 8 equal slices each, and had 6 slices left over after dinner. How much pizza did the Mullins family eat as a fraction of the pizza the Hernandez family ate?
Answer: Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex] , where r is the radius
Given, Diameter of Hernandez family's pizza = 20 inches
Radius = [tex]\dfrac{20}{2}[/tex] = 10 inches
Area of Hernandez family's pizza = [tex]\pi (10)^2=100\pi \text{ in.}^2[/tex]
Since, they divide pizza into 15 pieces , area of each slice = [tex]\dfrac{100\pi}{15}=\dfrac{20}{3}\pi\text{ in.}^2[/tex]
They left with 3 slices i.e. they ate 12 slices, area of all 12 slices = 12 x (area of each slice)
= [tex]12\times\dfrac{20}{3}\pi\text{ in.}^2= 80\pi\text{ in.}^2[/tex]
Diameter of Mullins family's pizza = 12 inches
Radius = [tex]\dfrac{12}{2}[/tex] = 6 inches
Area of Mullins family's pizza = [tex]\pi (12)^2=144\pi \text{ in.}^2[/tex]
Since, they divide pizza into 8 pieces , area of each slice = [tex]\dfrac{144\pi}{8}=18\pi\text{ in.}^2[/tex]
They left with 6 slices i.e. they ate 2 slices, area of all 2 slices = 2 x (area of each slice)
= [tex]2\times18\pi\text{ in.}^2=36\pi\text{ in.}^2[/tex]
Since, [tex]\dfrac{36\pi}{80\pi}=\dfrac{9}{20}[/tex]
Hence, Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.
What is the value of y in the solution to the system of equations? One-thirdx + One-fourthy = 1 2x – 3y = –30 –8 –3 3 8
Answer:
8 hopefully
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
PLSSS HELP What is the formula for the following arithmetic sequence? -2, 3, 8, 13, ... an = -2n + 3 an = -2n + 7 an = 5n + 3 an = 5n - 7
Answer:
an = 5n -7
Step-by-step explanation:
Try the offered formulas with n= 1 and see which gives you the first term of the sequence.
an = -2n +3
-2(1) +3 = 1 . . . . not -2
an = -2n +7
-2(1) +7 = 5 . . . . not -2
an = 5n +3
5(1) +3 = 8 . . . . not -2
an = 5n -7
5(1) -7 = -2 . . . . this is the formula you want
_____
If you recognize the common difference of the sequence to be 5, then you can automatically eliminate any formulas that don't contain 5n.
The Venn diagram shows the results of two events resulting from rolling a number cube.
Answer:
Option B.
Step-by-step explanation:
From the given venn diagram it is clear that
[tex]A={1,2}[/tex]
[tex]B={1,2,3,4,5,6}[/tex]
[tex]A\cap B={1,2}[/tex]
Since the intersection of A and B is non-empty, therefore by conditional probability
[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]P(B|A)\cdot P(A)=P(A\cap B)[/tex]
[tex]P(A\cap B)=P(B|A)\cdot P(A)[/tex]
Therefore, the correct option is B.
What happens to the diagonal of a rectangle when the rectangle is reflected across a line of symmetry? What does this suggest about the diagonals of rectangles?
When you reflect a diagonal over a line of symmetry, the diagonal will land perfectly on the other diagonal (and vice versa). This suggests that one diagonal is a mirror copy of the other.
Another way to put it: The vertex points of the rectangle will swap when we reflect over a line of symmetry. A diagonal is simply the opposite vertex points joined together. So this is why the diagonals swap places (because the vertices line up perfectly when you apply the reflection).
A shape with a line of symmetry will land on itself, when reflected across the line of symmetry. The true statements are:
The diagonals of the rectangle will land perfectly on each otherThe diagonals of a rectangle are lines of symmetryFrom the question, we understand that; the rectangle is reflected across the line of symmetry
When this is done, the half of the rectangle will land directly on the other half.
This means that, the diagonal of the rectangle will land perfectly on the other diagonal
The statement above suggests that, the diagonal of a rectangle is also a line of symmetry of the rectangle.
Read more about lines of symmetry and diagonals at:
https://brainly.com/question/1045307
The temperature in Chicago when the plane left was 22°F. When the plane arrived in Atlanta it was 46°F. What was the difference in temperature?
Answer:
24
Step-by-step explanation:
46 - 22 = 24
find the value of a and explain
Answer:
D
Step-by-step explanation:
The triangle is an isosceles triangle which means that two sides are the same, A is the same size of the equal side so A is D.
Answer:
The answer is D.
What is the measure of ∠XBC? m∠XBC = m∠BAC + m∠BCA 3p – 6 = p + 4 + 84 3p – 6 = p + 88 2p – 6 = 88 2p = 94 m∠XBC
Alguien que sepa cómo se resuelve ésto que me ayudé a solucionarlo,es urgente,doy 25 puntos
38 42 34 54
Step-by-step explanation:
7have the best mayonnaise bianco babi naive albino pig is this real or not be a posible and I am a great day for 53feet
(6) Find a and b as well as the ratio c:d in the
figure below.
Answer:
i have a Similar question I’m stuck on, just remember z rule, vertically opposite etc.
A percent measures a rate
answer = no it does not measure a rate
Answer:
NO
Step-by-step explanation:
Percent is just a number out of 100
Simplify the following:
1.√7 × √7
2.√18 × √2
3.√45
4.√50/5
5.2√2 × 4√5
6.√48 - √12
7.(2-√3) (1+√3))
Answer:
1. 7
2. 6
[tex]3. 3\sqrt{5}[/tex]
4?
5. [tex]8\sqrt{10}[/tex]
6.[tex]5\sqrt{3}[/tex]
7. [tex]-1+\sqrt{3}[/tex]
Step-by-step explanation:
1. [tex]\sqrt{7} *\sqrt{7} =\sqrt{49}=7[/tex]
2. [tex]\sqrt{18}*\sqrt{2} =\sqrt{36}=6[/tex]
3.[tex]\sqrt{45}=\sqrt{9^{2}*5 }=3\sqrt{5}[/tex]
4. here there are two cases
[tex]\sqrt{\frac{50}{5} }=\sqrt{10}[/tex]
[tex]\frac{\sqrt{50} }{5} =\frac{5\sqrt{2} }{5} =\sqrt{2}[/tex]
5. [tex]2\sqrt{2} *4\sqrt{5} =8\sqrt{10}[/tex]
6. [tex]\sqrt{48}- \sqrt{12} =4\sqrt{3} -2\sqrt{3} =2\sqrt{3}[/tex]
7. [tex](2-\sqrt{3} )(1+\sqrt{3} )=2+2\sqrt{3}-\sqrt{3} -3=-1+\sqrt{3}[/tex]
pls help me do this (atleast one) using quadratic formula
i neeeed help quickkkk
Answer:
20 hours
Step-by-step explanation:
If your computer can download a movie in 5 hours, then it downloads [tex]\frac{1}{5}[/tex] of a movie in 1 hour.
The extra processor in 1 hour, reduces the time down to 5 hours, so it downloads [tex]\frac{1}{4}[/tex] of the movie in 1 hour.
The time that the extra processor will spend to download a whole movie added to [tex]\frac{1}{5}[/tex] will equal [tex]\frac{1}{4}[/tex] .
So our equation is [tex]\frac{1}{5} + \frac{1}{x} = \frac{1}{4}[/tex].
To simplify this, lets multiply all sides by 20x.
[tex](\frac{1}{5}+\frac{1}{x} \cdot 20x) = \frac{1}{4}\cdot20x\\ 4x + 20 = 5x[/tex]
Now we can simplify this equation.
[tex]20 = 5x-4x\\\\20 = x\\x = 20[/tex]
So the extra processor alone would take 20 hours to download the movie.
Hope this helped!
PLEASE help me with this question ASAP!!!!
Step-by-step explanation:
I believe the answer is
The fuction roughly matches the data
Answer:
The function fits very well
Step-by-step explanation:
The equation for the stats is
y=-0.039866x²+3.99375x-0.4785714
HELP ASAP The graph of a function h is shown below. Use the graph to find its average rate of change from x=-7 to x=-5. Simplify your answer as much as possible
Answer:
The average rate of change from x=-7 to x=-5 is -3
Step-by-step explanation:
In order to calculate average rate of change we would have to make the following calculation:
According to the given data we have the following:
x=-7 so, f(-7) is to be calculated in the graph y
x=-5 so, f(-5) is to be calculated in the graph y
Therefore, average rate of change=f(-5)-f(-7)/-5-(-7)
average rate of change=3-9/2
average rate of change=-6/2
average rate of change=-3
The average rate of change from x=-7 to x=-5 is -3
The average rate of change of a function is the unit change of the function.
The average rate of change from x = -7 to x = -5 is -3
The average rate of change is calculated as:
[tex]\mathbf{f'(x) = \frac{f(b) - f(a)}{b - a}}[/tex]
The interval is given as: x = -7 to x = -5.
This means that:
a = -5 and b = -7
So, we have:
[tex]\mathbf{f'(x) = \frac{f(-7) - f(-5)}{-7 - -5}}[/tex]
This gives
[tex]\mathbf{f'(x) = \frac{f(-7) - f(-5)}{-2}}[/tex]
From the graph
f(-7) = 9 and f(-5) = 3.
So, we have:
[tex]\mathbf{f'(x) = \frac{9 - 3}{-2}}[/tex]
Subtract
[tex]\mathbf{f'(x) = \frac{6}{-2}}[/tex]
Divide
[tex]\mathbf{f'(x) = -3}[/tex]
Hence, the average rate of change from x = -7 to x = -5 is -3
Read more about average rate of change at:
https://brainly.com/question/23715190
Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t is the time in seconds. For which interval of time is the height of the ball less than 17 feet?
Answer:
Step-by-step explanation:
We are given the position function and need to find the value of t when h<17.
Create an inequality that represents this situation:
[tex]-16t^2+81<17[/tex] The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.
The simplest way to solve this is to subtract 81 from both sides:
[tex]-16t^2<-64[/tex] then divide both sides by -16:
[tex]t^2>4[/tex] Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is
t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.
Answer:
A on edg
Step-by-step explanation:
you are going to give each customer 12fl oz of lemonade.If you have 15 gallons of lemonade prepared, how many customers will you be able to serve?
Answer:
160
Step-by-step explanation:
so 1 gallon is 128 fluid ounces
how many is 12fl oz
so (1×12)/128=0.09375gallons per person
and you have 15 so if one consumes 0.09375 how many can consume 15
so 15/0.09375
what is the value of the digit 6 in the number 48.061?
Answer:
The hundredths place.
Step-by-step explanation:
48 is the whole number, and .061 is the decimals. As you probably know, this is the whole numbers place value.
ones, tens, hundreds, thousand, 10 thousand, 100 thousand, million...ect.
The decimal places are different
in this case the 0 is the tenths
the 6 is the hundredths
and the 1 is the thousandths.
Mostly, the decimal points are just with added ths to the end.
Hope this helped :D
As per the given number, the place value of 6 is that it is at hundredths place.
What is Place Value?Place value is the value assigned to each digit in a number. Depending on its location, each digit in such a number has a unique value. Because a digit's value relies on where it appears in an integer, it is possible for an amount to have two equivalent digits with different values.
The decimal equivalent of 48 is .061. The entire number is 48. This is the entire integer's place value, as you are surely aware.
The decimal places are different
In the given question, the 0 is at tenths place ,6 is the hundredths place and 1 is the thousandths place.
The decimal points are typically only inserted at the end.
To know more about Place Value:
https://brainly.com/question/27734142
#SPJ3
A waffle cone has a height of 7 inches and a diameter of 3 inches. What is the volume of ice cream that can be contained within the cone? Use 3.14 to for pi. Round your answer to the nearest hundredth.
15.43 in^3
16.49 in^3
17.86 in^3
18.89 in^3
Hey there! I'm happy to help!
To find the volume of a cone, we multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find a circle, you square the radius and then multiply by pi (or 3.14 in our case).
Radius is half of the diameter.
3/2=1.5
We square this.
1.5²=2.25
We multiply by 3.14
2.25×3.14=7.065
Now, we multiply this base area by the height.
7.065×7=49.455
We divide by 3.
49.455/3=16.485
Therefore, if we round this, our answer is 16.49 in³.
Now you can find the volume of a cone! Have a wonderful day! :D
Answer:
16.49
Step-by-step explanation:
PLs help I need to know what 11 is I will mark u as brianlist