Answer:
16
Step-by-step explanation:
an area is always calculated by multiplying 2 dimensions.
when changing the dimensions, then the change factors for EACH dimension go into the calculation too.
therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.
this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.
just think
16×a + 16×b + 16×c ... = 16×(a+b+c+...)
and you understand why.
If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?
Answer:
23
Step-by-step explanation:
We are given that
f(2)=13
[tex]f'(x)\geq 2[/tex]
[tex]2\leq x\leq 7[/tex]
We have to find the possible small value of f(7).
We know that
[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Using the formula
[tex]f'(x)=\frac{f(7)-f(2)}{7-2}[/tex]
[tex]f'(x)=\frac{f(7)-13}{5}[/tex]
We have
[tex]f'(x)\geq 2[/tex]
[tex]\frac{f(7)-13}{5}\geq 2[/tex]
[tex]f(7)-13\geq 2\times 5[/tex]
[tex]f(7)-13\geq 10[/tex]
[tex]f(7)\geq 10+13[/tex]
[tex]f(7)\geq 23[/tex]
The small value of f(7) can be 23.
A professor has learned that nine students in her class of 35 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating
Answer:
[tex]\frac{73,331}{75,516}\approx 97.11\%[/tex]
Step-by-step explanation:
The probability that she will find at least one student cheating is equal to the probability that she finds no students cheating subtracted from 1.
Each time she randomly chooses a student the probability she will catch a cheater is equal to the number of cheaters divided by the number of students.
Therefore, for the first student she chooses, there is a [tex]\frac{9}{35}[/tex] chance that the student chosen is a cheater and therefore a [tex]\frac{26}{35}[/tex] chance she does not catch a cheater. For the second student, there are only 34 students to choose from. If we stipulate that the first student chosen was not a cheater, then there is a [tex]\frac{9}{34}[/tex] chance she will catch a cheater and a [tex]\frac{25}{34}[/tex] chance she does not catch the cheater.
Therefore, the probability she does not catch a single cheater after randomly choosing ten students is equal to:
[tex]\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26}[/tex]
Subtract this from one to get the probability she finds at least one of the students cheating after randomly selecting nine students. Let event A occur when the professor finds at least one student cheating after randomly selecting ten students from a group of 35 students.
[tex]P(A)=1-\frac{26}{35}\cdot \frac{25}{34}\cdot \frac{24}{33}\cdot \frac{23}{32}\cdot \frac{22}{31}\cdot \frac{21}{30}\cdot \frac{20}{29}\cdot \frac{19}{28}\cdot \frac{18}{27}\cdot \frac{17}{26},\\\\P(A)=1-\frac{2,185}{75,516},\\\\P(A)=\boxed{\frac{73,331}{75,516}}\approx 0.97106573441\approx \boxed{97.11\%}[/tex]
Plz help me find zero x on the triangle and show work thanks
Answer:
x= 30 degrees
Step-by-step explanation:
This is an isosceles triangle as indicates by the lines on the sides.
Since the sides lengths are equal, the base angles are equal
x= 30 degrees
PLEASE HEP ME
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
9514 1404 393
Answer:
TrueTrueStep-by-step explanation:
The center of dilation (point D) is a point that doesn't move. Any line not through that point will be moved to a parallel location when a dilation factor is applied.
Any line through the center of dilation will still go through the center of dilation. Its slope does not change, so the line will appear to be the same.
AB ║ A'B' — True
AD ≅ A'D' — True
_____
You can see these relationships in the attached figure.
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle?
a) Find the radius of the circle.
b) State the equation of the circle
I am need help and an explanation on how to read these graphs.
Answer:
i think its b
Step-by-step explanation:
A golf ball is hit from ground level. Its path is modelled by the relation h(t) = -4.9 t2 + 27.2t , where h is the ball’s height above the ground, in meters, and t is the time, in seconds. Determine the time the ball is in the air.
Question 4 4 pts Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: 5 years? 10 years? 486 months?
Answer:
Step-by-step explanation:
5 years
[tex]1500(1+\frac{.06}{12})^{12*5}=2023.275229[/tex]
10 years
[tex]1500(1+\frac{.06}{12})^{10*12}=2729.095101[/tex]
486 months:
[tex]1500(1+\frac{.06}{12})^{486}=16935.47074[/tex]
round those as you please
Write a linear equation in point slope form that passes through the points (-2,18) and (1,9)
Answer:
y-18=-3(x+2)
Step-by-step explanation:
The Slope-intercept form is -3x+12
Solve for x in this equation: 3/4+|5-x|=13/4
How can the distributive property be use to solve this expression?
53x24
9514 1404 393
Answer:
= 53(20 +4) or =24(50 +3) or =(20 +4)(50 +3)
Step-by-step explanation:
Either number can be rewritten as a sum. Typically, the sum will be based on place value: 53 = 50 + 3, for example, as opposed to something like 53 = 26 +27.
The usual method of multiplication taught in grade school makes use of this sort of rewriting.
53 × 24 = 53 × (4 +20) = 53×4 +53×20 = 212 +1060 = 1272
__
Additional comment
We find this easier to multiply as 53(20 +4) than as 24(50 +3) because doubling (multiplying by 2) and doubling again (multiplying by 4) is generally easier than multiplying by 3 or 5.
In grade school, we did this digit by digit, so ...
53×24 = (3 +50)(4 +20) = 3(4 +20) +50(4 +20) = 3×4 +3×20 +50×4 +50×20
= 12 +60 +200 +1000 = 1272
Any help here please
Answer:
A
Step-by-step explanation:
JUst answered same question
A high school baseball player has a 0.305 batting average. In one game, he gets 9 at bats. What is the probability he will get at least 7 hits in the game
The probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
To solve this problem, we need to use the binomial distribution formula. The binomial distribution is used when we have a fixed number of independent trials (in this case, 9 at bats), where each trial has only two possible outcomes (hit or no hit), and the probability of success (getting a hit) is constant across all trials (0.305 in this case).
Let X be the number of hits the player gets in the game. Then X follows a binomial distribution with parameters n=9 (number of trials) and p=0.305 (probability of success).
The probability of getting at least 7 hits is equal to the sum of the probabilities of getting exactly 7, 8, or 9 hits:
P(X ≥ 7) = P(X=7) + P(X=8) + P(X=9)
Using the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
where C(n,k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
For k=7:
P(X=7) = C(9,7) * 0.305^7 * (1-0.305)^(9-7) = 0.154
For k=8:
P(X=8) = C(9,8) * 0.305^8 * (1-0.305)^(9-8) = 0.036
For k=9:
P(X=9) = C(9,9) * 0.305^9 * (1-0.305)^(9-9) = 0.002
Therefore:
P(X ≥ 7) = 0.154 + 0.036 + 0.002 = 0.192
Therefore, the probability that the player will get at least 7 hits in the game is approximately 0.192, or 19.2%.
To learn more about Probability from given link.
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Bài 2: Một công ty XNK Việt Nam nhận được tiền bán hàng từ hơp đồng XK là 35.000.000 JPY, đồng thời phải thanh toán tiền mua nguyên vật liệu NK là 3.500.000 CNY. Tại thời điểm thực hiện hợp đồng, NH niêm yết các tỷ giá giao ngay như sau: USD/JPY = 128,15/27 USD/CNY = 9,5575/91 USD/VND = 19.125/38 Hỏi tài khoản VND của công ty còn bao nhiêu tiền sau khi đã thực hiện các hơp đồng trên? Nêu ra phương án thanh toán có lợi nhất cho công ty? %3D
Answer:
Ask in English then I can help
A spinner is divided into 6 equal parts. These sections are labeled with a number 1, one section has a 2, one section has a 3, and one section has a 4. If the spinner is spun two times, what is the probability it will land on both 2 sides?
Answer:
[tex]\frac{1}{36} = 0.0278[/tex] = 2.78% probability it will land on both 2 sides.
Step-by-step explanation:
For each trial, there are only two possible outcomes. Either it lands on 2, or it does not. The probability of the spinner landing on two in a trial is independent of any other trial, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One of the six sides is 2:
This means that [tex]p = \frac{1}{6}[/tex]
If the spinner is spun two times, what is the probability it will land on both 2 sides?
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{0} = \frac{1}{36} = 0.0278[/tex]
[tex]\frac{1}{36} = 0.0278[/tex] = 2.78% probability it will land on both 2 sides.
¿COMO PUTAS SE HACE i¹⁰⁰²?
Answer:
nose
Step-by-step explanation:
A woodworker makes wooden checkerboards. her profit is a function of the price she charges. this graph shows her total profits, y, based on the sales price, x, of each checkerboard.
identify any zeros of the function, and interpret what the zeros mean in terms of the situation.
Answer:
Option B.
Step-by-step explanation:
Remember that the profit is defined as the difference between the revenue and the cost.
So, having a profit y = 0 means that the woodworker did not win nor lose anything.
Then the zeros of the function, the values of x such that the graph intersects the x-axis, are the prices such that she does not win nor loss anything.
In the graph we can see that the zeros are at:
x = 15 (the first one)
x = 70 (the second one)
so the zeros are at x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.
The correct option is B.
Answer:
x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.
Step-by-step explanation:
If x+y=6 and xy =2find x³+y³(please help me fast with explanation also please) T^T
Answer: x³+y³=180
Step-by-step explain: let's remember the formula x³+y³=(x+y)(x²-xy+y²) and also x³+y³=(x+y)³-3xy(x+y) then [tex]\displaystyle\boldsymbol{ x^3+y^3=\underbrace{(x+y)^3}_{6}-3\underbrace{xy}_{2}\underbrace{(x+y)}_6}=\\\\6^3-3\cdot 2\cdot 6=216-36=180[/tex]
Which is equivalent to 104
༡/16**?
o (10)4x
4(10)3
o (10)**
O (10)
Answer:
I think it is the last one.
Apply radical rule
= (10^1/2)3/4x
Apply exponent rule: (a^b)^c = a^bc
= 10^1/2 . 3/4x
Simplify: 1/2 . 3/4x: 3x/8
= 10^3x/8
A researcher considers two methods for collecting data to determine if store-brand laundry detergents work as well as name-brand detergents.
Method 1: The researcher surveys shoppers as they enter a grocery store. The shoppers are asked which type of detergent they use and then rate the cleanliness of their laundry on a scale from 1 to 10 (with 10 being the cleanest). The ratings of the name-brand detergents are compared to the ratings of the store-brand detergent.
Method 2: The researcher creates 10 loads of soiled fabrics and washes 5 of the loads with name-brand detergent and the other 5 with store-brand detergent. Volunteers are asked to assess the cleanliness of the fabrics using a scale from 1 to 10 (with 10 being the cleanest), and the ratings of the name-brand detergents are compared to the ratings of the store-brand detergent.
Which method describes an observational study?
Method 2 is an observational study because volunteers assess the fabrics.
Method 1 is an observational study because many people can be surveyed.
Method 1 is an observational study because no attempt is made to influence results.
Both methods are observational studies because information on both types of detergent can be collected.
Not A.
Answer:
C. Method 1 is an observational study because no attempt is made to influence results.
Step-by-step explanation:
Based on the descriptions provided: Method 1 is an observational study because no attempt is made to influence the results. Option 3 is the correct answer.
An observational study is a type of study where researchers observe and collect data without actively intervening or manipulating any variables.
Method 1 involves surveying shoppers and asking them about their detergent use and laundry cleanliness ratings. The researcher is merely collecting data without intervening or manipulating any variables. The study relies on the natural behavior of shoppers and their responses.
Method 2, on the other hand, involves actively creating soiled fabrics and washing them with different detergents. This intervention introduces an element of manipulation, making it more of an experimental study than an observational one.
To know more about observational study :
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Determine whether the three points are colinear (0,-4),(-3,-18),(2,6) are the three points colinear?
9514 1404 393
Answer:
they are not collinear
Step-by-step explanation:
A graph shows that a line through points A and C misses point B, so the points are not collinear.
__
If the points are collinear, then the slope of the segment between the first pair would be the same as the slope of the segment between the second pair.
m = (y2 -y1)/(x2 -x1)
m = (-18 -(-4))/(-3 -0) = -14/-3 = 14/3 . . . . slope of AB
__
m = (6 -(-18))/(2 -(-3)) = 24/5 . . . . slope of BC ≠ slope of AB
The points are not collinear.
_____
Additional comment
With about the same amount of computational effort, you can find the area of the triangle bounded by the three points. If it is zero, then the points are collinear. Here, it is 1 square unit, so the points are not collinear.
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? 60
60/100
60/40
40/100
Answer:
60/100
Step-by-step explanation:
Hope it helps you in your learning process
Find the volume of the cylinder in terms of [tex]\pi[/tex].
h = 6 and r = 3.
a. 27[tex]\pi[/tex] in.³
b. 108[tex]\pi[/tex] in.³
c. 54[tex]\pi[/tex] in.³
d. 324[tex]\pi[/tex] in.³
Answer:
c. 54[tex]\pi[/tex] in.³
The volume of cylinder is 54[tex]\pi[/tex] in.³
Step-by-step explanation:
Given that :-
Height of cylinder , h = 6.Radius of cylinder, r = 3.To Find :-
Volume of cylinder.Solution:-
We use formula
Volume of cylinder = π × (radius)² × h
Substitute the value of radius and height.Volume of cylinder = π × ( 3)² × 6.
Evaluate the exponent.Volume of cylinder = π × 9 × 6.
Multiply we get ,Volume of cylinder = 54[tex]\pi[/tex] in.³
The formula we use,
→ Volume of cylinder = π × r² × h
It is given that,
→ Height (h) = 6 and radius (r) = 3.
Then we have to,
find the volume of the cylinder,
→ π × r² × h
→ π × 3² × 6
→ π × 9 × 6
→ 54π in.³
Thus, option (c) is the answer.
A ladder is leaning against a building so that the distance from the ground to the top of the latter is 1 foot less than the length of the latter find the length of the latter is the distance from the bottom of the ladder to the building is 7 feet
Answer:
[tex]25\text{ feet}[/tex]
Step-by-step explanation:
The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.
For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ([tex]a^2+b^2=c^2[/tex]), where [tex]c[/tex] is the hypotenuse.
Let the length of the ladder be [tex]\ell[/tex] (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as [tex]\ell -1[/tex].
From the Pythagorean Theorem, we then have:
[tex]7^2+(\ell-1)^2=\ell^2[/tex]
Expand using [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]49+\ell^2-2\ell+1=\ell^2[/tex]
Subtract [tex]\ell[/tex] from both sides and add [tex]2\ell[/tex] to both sides:
[tex]49+1=2\ell[/tex]
Combine like terms:
[tex]50=2\ell, \\2\ell =50[/tex]
Divide both sides by 2:
[tex]\ell=\frac{50}{2}=\boxed{25\text{ feet}}[/tex]
Therefore, the length of the ladder is 25 feet.
help I was never taught how to do this im confused
Answer:
36
Step-by-step explanation:
Area of a triangle = (bh)/2
Where b = base length and h = height
Given base length: 18ft
Given height: 4ft
This being known let's define the variables
b = 18
h = 4
Now to find the area we simply plug in these values into the formula
Area = (18)(4)/2
Simplify multiplication 18 * 4 = 72
Area = 72/2
Simplify division
Area = 36
a baceball team won 11 on its first 18 games at this rate how many games will the team win in a 162 game season
Answer:
Step-by-step explanation:
Set up the following proportion. x is the number of games you should win.
11/18 = x / 162
11*162 / 18 = x
x = 99 You likely would be out of the playoffs with a number like this.
If there is a song that is 2 minutes and 58 seconds long and it plays 40 times how long does it play convert answer into seconds.
Answer: I got 7120 seconds
Step-by-step explanation:
There's 178 seconds in the song (for more context, I just converted the 2 minutes into seconds and added it with 58) then I multiplied it by the total amount of times it played (in this case, 40)
Hope this helps
in the given figure poq is a line. if x=30 then find qor and ros
Answer:
[tex]2y + 3y + x = 180 \\ 5y + 30 = 180 \\ 5y = 180 - 30 \\ 5y = 150 \\ y = 30[/tex]
QOR =3Y
=3×30
=90°
ROS = 2Y
=2×30
=60°
The slope of the line below is 2. Which of the following is the point-slope form
of the line?
Answer:
y+1 = 2(x-1)
Step-by-step explanation:
Point slope form for a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
We are given the point(1,-1)
y --1 = 2(x-1)
y+1 = 2(x-1)
A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division in which employees worked affected their choice of method. Below is a table summarizing the data.
Sales Quality Operations Total
Traditional 16 10 8 34
Online 35 23 44 102
Total 51 33 52 136
Required:
a. What is the probability that an employee chose online training?
b. What is the probability that an employee is in the Quality division and chose online training?
c. What is the probability that an employee chose online training given that he/she is in the Sales division?
Answer:
(a) [tex]P(Online\ Training) = 0.750[/tex]
(b) [tex]Pr = 0.169[/tex] --- Quality Division and Online Training
(c) [tex]P(A\ |\ B) = 0.686[/tex] --- Online Training given Sales Division
Step-by-step explanation:
Given
The two-way table
Solving (a): P(Online Training)
The total employee is:
[tex]Total = 136[/tex]
The employees for online training is:
[tex]Online\ Training = 102[/tex]
So, the probability is:
[tex]P(Online\ Training) = \frac{102}{136}[/tex]
[tex]P(Online\ Training) = 0.750[/tex]
Solving (b): P(Quality Division and Online Training)
The number of employees that choose quality Division and online training is 23
So, the probability is:
[tex]Pr = \frac{23}{136}[/tex]
[tex]Pr = 0.169[/tex]
Solving (c): P(Online Training | Sales Division)
This is calculated as:
Let:
[tex]A \to[/tex] Online training
[tex]B \to[/tex] Sales division
So, we have:
[tex]P(A\ |\ B) = \frac{n(A\ n\ B)}{n(B)}[/tex]
From the table:
[tex]n(A\ n\ B) =35[/tex]
[tex]n(B) = 16 + 35 = 51[/tex]
So, the probability is:
[tex]P(A\ |\ B) = \frac{35}{51}[/tex]
[tex]P(A\ |\ B) = 0.686[/tex]
