An aquarium I’d 8 feet long , 5 feet wide, and 5.5 feet deep . What is the volume of the tank?
Answer:
V = 220 feet³
Step-by-step explanation:
Formula: V = LWH
(8ft) (5ft) (5.5ft) = 220 ft^3
Luke is x years old. Kate is half of Luke's age. Adam is 6 years younger than Kate. Adam is 4 years old. How old is Luke?
Answer: luke is twenty
Step-by-step explanation: Adam is 4 plus 6 is 10 ten times two is twenty
Answer:
luke is 20
Step-by-step explanation:
because you had 6 and 4 and multiply it by 2
How would you find # 3 HELP ASAP PLZZ
Answer:
24 = AE
How to find it
AB = 26 and BD = 20 find AE
Because its a rhombus point is the midpoint of BD so BE is 1/2 BD so BE is 10
Now we no longer need to use BD and instead we use BE
Now since ∠BEA is 90° we can use the Pythagorean Theorem
AB²-BE²=AE²
26²-10²=AE²
676-100=AE²
576=AE²
[tex]\sqrt{576}[/tex]=AE
24 = AE
Consider the matrix shown below:
What are the dimensions of A.
3 X 4
4 X 3
12
A and B
Answer:
Dimensions of a matrix:
r × c
Where r is the no. of rows and c is the no. of columns
If A has 4 rows (horizontal) and 3 columns (vertical),
Dimensions are: 4 × 3
If A has 3 rows (horizontal) and 4 columns (vertical),
Dimensions are: 3 × 4
1. There are 65 adults and 15 children in a movie theater. Of these people, 41 adults and 6 children bought popcorn.
a) What is the probability that a randomly selected person in the theater is a child or someone who bought popcorn.
b) What is the probability that a randomly selected person is an adult or someone who did not buy popcorn.
My answers are 0.70 and 0.925 respectively. My friends believe otherwise.
Answer:
a. 7/10
b. 79/240
Step-by-step explanation:
Please see the attached files for details
Answer:
a) 0.70
b) 0.925
You are right and your friends are wrong.
Step-by-step explanation:
- 65 adults and 15 children in a movie theater
- 41 adults and 6 children bought popcorn
Number of children in the theatre = 15
Number of adults in the theatre = 65
Number of children that bought popcorn = 6
Number of children that did not buy popcorn = 15 - 6 = 9
Number of adults that bought popcorn = 41
Number of adults that did not buy popcorn = 65 - 41 = 24
Total number of persons that bought popcorn = 41 + 6 = 47
Number of people that did not buy popcorn = 80 - 47 = 33
Total number of persons in the theatre = 65 + 15 = 80
a) The probability that a randomly selected person in the theater is a child or someone who bought popcorn.
Required probability
= (number of children or people that bought popcorn) ÷ (total number of people)
There 15 children, and 47 people that bought popcorn, but of the 47, there are still 6 children amongst them.
Hence, the number of children or people that bought popcorn = 15 + 47 - 6 = 56
Total number of people = 80
Required probability = (56/80) = 0.70
b) The probability that a randomly selected person is an adult or someone who did not buy popcorn.
Required probability
= (number of adults or people who did not buy popcorn) ÷ (total number of people)
There are 65 adults, and 33 people that did not buy popcorn, but of the 33, there are still 24 adults amongst them.
Hence, the number of adults or people who did not buy popcorn
= 65 + 33 - 24 = 74
Total number of people = 80
Required probability = (74/80) = 0.925
You are right and your friends are wrong.
Hope this Helps!!!
5 2/3 x 4 1/2 make sure your anser is correct
(-1,-4) and (6,10) x intercept write as ordered paid
Answer:
y=2x-2 I hope this helps
Step-by-step explanation:
Slope intercept form, y=mx+b
What if you wanted a smaller margin of error in your interval for the proportion of left-handed people (say plus or minus 2%)? How many people would you need to survey in order to get a margin of error of 2% ? You can use the LaTeX: \hat{p} p ^ that you already calculated as your estimate in the sample size formula.
Answer:
The sample size n= 2500
A survey with 2500 left-handed people guarantees the given margin error is 2%
Step-by-step explanation:
Explanation:-
The margin of error = [tex]\frac{2 S.D}{\sqrt{n} }[/tex]
here for proportions , the standard deviation (σ) = [tex]\sqrt{p(1-p)} \leq \frac{1}{2}[/tex]
[tex]Margin of error = \frac{2 S.D}{\sqrt{n} } \leq \frac{2(\frac{1}{2}) }{\sqrt{n} }[/tex]
[tex]Margin of error = \frac{1}{\sqrt{n} }[/tex]
now The necessary sample size is
[tex]n= \frac{1}{(M.E)^{2} }[/tex]
Given data the survey in order to get a margin of error of 2%
M.E = 0.02
[tex]n= \frac{1}{(0.02)^{2} } = 2500[/tex]
Conclusion:-
The sample size n= 2500
A survey with 2500 left-handed people guarantees the given margin error is 2%
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0).
What is the area of the circle?
Select the appropriate response:
A) 3
B) 9
C) 18
D) 25
Answer:
18pi or 56.52 units²
Step-by-step explanation:
Radius² = (-3-0)² + (2-5)²
= 18
Area = pi × r²
3.14 × 18
56.52
The area of the circle is 57.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
To find the area of the circle, we need to know the radius.
The radius can be determined using the distance formula between the center of the circle (2, -3) and the point on the circle (5, 0).
The distance formula is given by:
d =√(5 - 2)² + (0 - (-3))²
= √3²+ 3²
=√9 + 9
=√18
The radius is the distance between the center and a point on the circle, which is the square root of 18.
Now, we can calculate the area of the circle using the formula:
Area = π × radius²
Area = π ×√18²
= 18π
= 56.52
Hence, the area of the circle is 57.
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The angle shown is in standard position. Select the possible measures of the angle. –450° –360° –270° –90° 90° 270° 360° 450° On a coordinate plane, 2 rays are shown. One ray is on the x-axis between quadrants 1 and 4, and the other ray is on the y-axis between quadrants 3 and 4.
Answer: a, d,f
On edge.
Step-by-step explanation:
The possible measures of the angle are -450°, -90° and 270°
What is terminal side?An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.
In any standard position, the vertex of the angle is on the origin (0, 0) of the x and y-axis. Therefore, one side of the angle is always fixed along the positive x-axis, namely, going to the right along the axis in the 3 o'clock direction. This is called the initial side of the angle. The other side of the angle is called the terminal side.
Hence, the angles that match the figure above are the measures of the angle. That is:
-450°
-90°
270°
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A house was built in 1985 and cost $62000. It was sold in 2003 for $310000.
(a) Work out the 1985 price as a percentage of the 2003 price.
(b)Calculate the percentage increase in the price from 1985 to 2003.
Answer:
a) 20%
b) 400%
Step-by-step explanation:
In a) you firts do
$310000=100% what about $62000.Then cross multiply
$62000×100%=6200000÷310000=20%
In b) you first do
$62000=100% what about $248000.Then cross multiply
$248000×100=$24800000÷62000=400%
The 1985 cost of the house is 20% of the 2003 price. There was a 400% increase in price from 1985 to 2003.
Explanation:To answer both parts of this question, we will use the concept of percentages.
(a) First, we calculate the 1985 price as a percentage of the 2003 price by dividing the cost of the house in 1985 by the cost in 2003, and then multiply the result by 100 to give a percentage. So we have (62000/310000)*100 = 20%. Therefore, the 1985 house cost represents 20% of the 2003 price.
(b) To calculate the percentage increase from 1985 to 2003, we take the difference in prices from 1985 to 2003, divide this by the original price in 1985, and then multiply the result by 100. So we have ((310000-62000)/62000)*100 = 400%. Hence, there was 400% increase in the price from 1985 to 2003.
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the number 0.7777 repeats forever therefore it is irrational true or false?
Answer:
It's false, this number is a rational number.
Step-by-step explanation:
It's false, the kind of decimal where the same digits repeats forever are known as periodic decimals and they can be represented with fractions therefore they are a part of the rational numbers. To represent this number in a fraction form we need to first identify the part that repeats, in this case it's 7, since it's only one number we can insert it in the numerator and the denominator will have a 9, if it were two numbers the denominator would have a 99 and so on. So in this case:
7/9 = 0.7777...
The statement is false. The number 0.7777 repeating is not an irrational number, but a rational number, as it can be expressed as the fraction 7/9.
Explanation:The statement is false. The number 0.7777 repeating is not an irrational number. An irrational number is a number that cannot be expressed as a/b, where a and b are integers and b ≠ 0. However, the number 0.7777 repeating can be expressed as a fraction, specifically, as 7/9. Therefore, it does not meet the definition of an irrational number and is, in fact, a rational number.
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A circle with radius of 5 cm sits inside a 11 cm * 11 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
42.43 [tex]cm^{2}[/tex]
Step-by-step explanation:
Given:
A circle with a radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Question asked:
What is the area of the shaded region as shown in the figure ?
Solution:
First of all calculate area of circle and then area of rectangle:-
[tex]Area\ of\ cirle=\pi r^{2}[/tex]
[tex]=\frac{22}{7} \times5\times5\\ \\ =\frac{550}{7}\\ \\=78.571\ cm^{2}\\[/tex]
As here length an width both are 11 cm, we can say that this is a square.
[tex]Area\ of\ square=(Side)^{2}[/tex]
[tex]=11\times11=121\ cm^{2}[/tex]
Now, area of shaded region = Area of square - Area of circle
= 121 - 78.571 = 42.429 [tex]cm^{2}[/tex]
Therefore, the area of the shaded region will be 42.43 [tex]cm^{2}[/tex]
write 5/57 as a percentage and round to the nearest tenth
Answer: 8.8%
Convert the fraction to a decimal, then multiply by 100
8.77192982 rounded to the nearest 10 is 8.8%
8.8% is the answer
When 125 is subtracted from one third of a number the result is 2 what is the number
Answer:
381
Step-by-step explanation:
Let n be the number
When 125 is subtracted from one third of a number the result is 2
1/3n - 125 = 2
Add 125 to each side
1/3n -125+125 = 2+125
1/3n = 127
Multiply each side by 3
1/3n *3 = 127*3
n =381
What expression represents the volume of the prism, in cubic units?
Final answer:
Volume of a prism is represented in cubic units as length x width x height. The SI unit of volume is cubic meter (m³) and a common unit is the liter (L), equivalent to a cubic decimeter (dm³).
Explanation:
Volume is defined as the amount of space occupied by a solid in cubic units, and for a prism that is length x width x height. In the case of volume, it goes like length cubed, represented as V = L³.
The SI unit of volume is cubic meter (m³), equal to the space occupied by a cube of 1m on each edge. A more commonly used unit of volume is the liter (L), which is equivalent to a cubic decimeter (dm³).
Suppose a population of 200 crickets doubles in size every month the function f(x) equals 200×2 to the X power gives the population after X months how many crickets will there be after three years
Answer:
≈ 1.37 * [tex]10^{13}[/tex]
Step-by-step explanation:
Given the exponental function is:
F(x) = 200*[tex]2^{x}[/tex] where:
200 is initial value of crickets 2 is the base number (doubles in size every month) x is the number of monthsHow many crickets will there be after three years?
3 years = 12*3 = 36 so x = 36. Substitute x into the function we have:
F(x) = 200*[tex]2^{36}[/tex] ≈ 1.37 * [tex]10^{13}[/tex]
So the number of crickets after three years is: ≈ 1.37 * [tex]10^{13}[/tex]
Answer: There will be 1.37 x 10^13 crickets after 3 years.
Step-by-step explanation:
Hi, to answer this question we simply have to replace x in the formula by the number of months in 3 years.
f (x) = 200 (2^x)
Where x is the number of months
Since one year has 12 months,
for 3 years: 3 x 12 = 36 months
Substituting x= 36 on the function
f (36) = 200 (2^36)
f (36) = 200 (2^x)
f(36) = 1.37 x 10^13
Feel free to ask for more if needed or if you did not understand something.
Brian just bought 9 bags of 14 cookies each. He already had 8 cookies in a jar. How many cookies does Brian have now?
Answer: 134 cookies
Step-by-step explanation: First we want to find the total amount of cookies Brain bought. Simply multiply 14 x 9 to find the total amount of cookies bought.
14 x 9 = 126 cookies.
Since Brian already had 8 cookies in the jar, we will simply add the new amount of cookies he bought to the cookies in the jar left.
126 + 8 = 134 total cookies that Brain has now.
(3 × 9) + (5 + 8) + (33 ÷ 3) =
Answer:
Step-by-step explanation:
(3 x 9) + (5 + 8) + (33/3) = 51
27 + 13 + 11 = 51
Answer:
51
Step-by-step explanation:
use PEMDAS
Question 1 (1 point)
The ordered pairs in the table below represent a linear function.
Xy
23
9 h
What is the slope of the function?
1/2
Oo oo
1/4
Do ya'll know how to do this? (grade 10)
Please help im stranded :(
(15 Points)
Answer:
a.) (-16,0)(0,12)
b.) (-3,0)(0, 3/2)
Step-by-step explanation:
Plug it in for each.
y= 3/4x+12 (Lets plug in our x intercept of (x,0) and our y intercept of (0,y)
x-intercept
0=3/4x+12
-12 -12
-12=3/4x
-12/(3/4)=x
-16=x
SO, your x intercept is -16 which is point (-16, 0)
Now to do your y intercept in lets plug x in as 0 instead this time:
y = 3/4(0)+12
y = 12
Your y intercept is 12
Now for b its the same process of plugging 0 in for the values let
y-int=-2(0)-4y+6=0
-6 -6
-4y/-4=-6/-4 <- divide both sides by 4
y = 3/2 <- Simplified answer
y int = (0, 3/2)
x-int = -2x-4(0)+6 = 0
+6 +6
-2x = 6
x = 6/-2 <-- Divide both sides by -2
x = -3 <-- Simplify
x-int = (-3, 0)
The drama club members at Millie's middle school are selling tickets to the school play. Millie wants to determine the average
number of tickets sold. First, she surveyed the club members in her homeroom, and then she surveyed every third member of
the club in her physical education class. Which sampling technique should produce a more representative sample?
Answer:
Every third member of the club in her physical educations class
Step-by-step explanation:
The reasoning behind this is because if Millie surveys her club members who are hosting the school play, she wouldn't be able to get an accurate average number of tickets sold because the club member have a bias in terms of purchasing the tickets as they run the club. Meanwhile the physical education class has a more random assessment because every third person in the class may or may not have an interest in the play the same way the club would.
Answer:The answer is
Neither sample will be representative. B on edge
Step-by-step explanation:):):):):):):):):):) I GOT IT RIGHT
A logical argument arranged with statements and reasons.
The answer is Two column proof
What is the value of b in the equation below? 9^-8 x 9^-2 = a^b
-10
-6
9
16
Answer:
-10
Step-by-step explanation:
9^-8 x 9^-2 = a^b
We know that x^y * x^z = x^(y+z)
9^-8 x 9^-2 = 9^(-8+-2) = 9^(-10)
a= 9
b = -10
A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want 90% confidence in our estimate of the percentage of American adults who approve of cloning endangered animals.
Answer:
The margin of error for the survey is 0.016
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 1024
Sample proportion:
[tex]\hat{p} = 89\% = 0.89[/tex]
We have to find the margin of error associated with a 90% Confidence interval.
Formula for margin of error:
[tex]z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]
Putting the values, we get:
[tex]M.E = 1.64\times (\sqrt{\dfrac{0.89(1-0.89)}{1024}})\\\\M.E=0.016[/tex]
Thus, the margin of error for the survey is 0.016
The margin of error for the given survey, when wanting a 90% confidence level, is approximately 1.58%. This means that the true proportion of American adults who approve of cloning endangered animals is likely to be within 1.58% above or below the survey's result of 89%.
Explanation:The subject matter of this question is in the field of statistics, specifically exploring concepts of confidence intervals and margin of error. A 90% confidence interval implies that we are 90% certain that the true population proportion lies within the calculated range, whereas the margin of error gives us the range that this estimate might deviate from the actual value.
In your scenario, you have a sample size of 1024 adults with 89% approving cloning of endangered animals. To compute the margin of error in this case, we first need to find the standard error. The standard error (SE) for a proportion is calculated as √[P(1 - P) / n] where P is the sample proportion and n is the total sample size. Let's compute this:
SE = √[0.89(1 - 0.89) / 1024] = 0.0096For a 90% confidence interval, the critical value from the z-table is 1.645 ((double-tail distribution). Therefore, the margin of error (E) is calculated as:
E = z * SE = 1.645 * 0.0096 = 0.01579, approximately 1.58%To interpret this value, you could say that with 90% confidence, the true proportion of American adults in favor of cloning endangered animals is within the range of 1.58% above or below 89%.
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A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12
A 1/100
B 1/12
C 11/100
D 12/100
Answer:
c
Step-by-step explanation:
If there are 100 cards and you can only pick numbers less then 12, you then could only have a number between 1 and 11
Answer:
its c
Step-by-step explanation:
the point A (6,3) maps onto A'(2,1) under a dilation with respect to the origin. what is the constant of dilation
Answer:
[tex]k = \frac{1}{3}[/tex]
Step-by-step explanation:
The coeficcient of dillation is:
[tex](6,3)[/tex]
[tex](3\cdot 2, 3\cdot 1)[/tex]
[tex]3\cdot (2,1)[/tex]
The constant of dilation is [tex]k = \frac{1}{3}[/tex].
Final answer:
To find the constant of dilation for a point A (6,3) mapping onto A\'(2,1) under dilation with respect to the origin, the coordinates are compared resulting in a constant of dilation of 1/3.
Explanation:
The question involves finding the constant of dilation when a point A (6,3) maps onto A\'(2,1) under a dilation with respect to the origin.
The constant of dilation can be found by comparing the coordinates of A with those of A\'.
For point A with coordinates (x,y) mapping to A\' with coordinates (x\',y\'), the dilation factor (k) is found by the formula k = x\'/x = y\'/y when the dilation is centered at the origin (0,0).
In this case, for the x-coordinates: k = 2/6 = 1/3, and for the y-coordinates: k = 1/3 which confirms our calculation, as the dilation factor must be consistent across both coordinates.
Therefore, the constant of dilation is 1/3.
Amber is trying to solve 3x^2-4x=0 using a graphical method. She therefore starts by drawing the graph of y=3x^2 on a grid she now intends to complete her method by drawing a straight line graph in the same grid. complete Ambrrs method to solve 3x^2-4x=0
You can rewrite the equation as
[tex]3x^2-4x=0 \iff 3x^2=4x[/tex]
So, you draw the graph of [tex]y=3x^2[/tex] (the parabola), and then the graph of [tex]y=4x[/tex] (the line), and see where they intersect.
To solve the equation 3x^2 - 4x = 0 graphically, Amber can draw the graph of y=3x^2 and a straight line that intersects the parabola. The x-values where the line intersects the parabola are the solutions to the equation.
Explanation:To solve the equation 3x^2 - 4x = 0 using a graphical method, Amber starts by drawing the graph of y=3x^2. This is a parabola that opens upwards with a vertex at the origin (0,0). Since she wants to find the x-values that satisfy the equation, she needs to draw a line that intersects the parabola. The line should be a straight line that crosses the x-axis at the values of x that make the equation true.
To draw this line, she needs to find two points that lie on the line. Since the equation is linear, she can choose any two points to draw the line. Let's choose two points that are easy to calculate. For example, when x=0, y=9 and when x=1, y=12. Plot these two points on the graph.
Next, draw a straight line that passes through these two points. Extend the line so that it intersects the parabola. The x-values where the line intersects the parabola are the solutions to the equation 3x^2 - 4x = 0. In this case, the line intersects the parabola at x=0 and x=4/3.
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Find the height of the giraffe in the diagram below
the giraffe is 18 feet tall.
A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 15 feet.
Answer:
The length of ladder is 17 feet .
Step-by-step explanation:
Refer the attached figure .
Let the length of ladder AC be h
We are given that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder.
So ,Perpendicular = AB = h-9
Distance from the bottom of the ladder to the building= BC = Base =15 feet.
Using Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2\\h^2=(h-9)^2+15^2\\h^2=h^2+81-18h+225\\18h=306\\h=\frac{306}{18}\\h=17[/tex]
Hence The length of ladder is 17 feet .