Answer:
4. the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers
Step-by-step explanation:
√9 = 3
3 is every kind of number except irrational. It belongs to the sets of ...
natural numberswhole numbersintegersrational numbersreal numbers
Given the following data, find the weight that represents the 53rd percentile.
Weights of Newborn Babies9.4 7.5 5.4 7.5 7.1
6.0 8.1 5.7 7.1 6.6
9.4 5.8 8.7 5.7 9.3
Answer:
Step-by-step explanation:
Rearranging the weights in ascending order, it becomes
5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4
The formula for determining the percentile is expressed as
n = (P/100)N
Where
n represents the value of the given percentile
P represents the given percentile
N represents the number of items(weights)
From the information given, the number of items, n is 15
P = 53
Therefore,
n = (53/100) × 15
n = 7.95
n = 8
Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1
53rd percentile is 7.1
Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢ 580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of GH¢2,358.60, how much was his total investment?
Answer:
GH¢2082.12
Step-by-step explanation:
Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...
t = (a) +(a +580) = 2a+580
Solving for a, we get
a = (t -580)/2
__
The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.
1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60
0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens
1.13t + 5.8 = 2358.60 . . . . . . . . . simplify
1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8
t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t
Mr. Azu's total investment was GH¢2082.12.
You have also been asked to set up the basket ball court what is the circumference of the circle
Answer: circumference of the circle is 11.31 meters
C=\pi d\\C=\pi (2r)\\C=2\pi r
Where radius (r) is half of diameter (d)
Since radius of the circle shown in 1.8m, we plug it in the formula and get:
C=2\pi r\\C=2\pi (1.8)\\C=11.31
So C = 11.31 meters
Which of the following sequence of transformations takes point J(9, 1) to J'(-3, 7)?
Answer:
Translate point J 12 units down and 6 units right.
What’s the correct answer for this?
Answer:
B and C
Step-by-step explanation:
The correct option are
B) a cross section of rectangular pyramid perpendicular to the base
C) a cross section of a rectangular prism that is parallel to it's base
e
65. the perpendicular
bisector of the
segment with
endpoints (-5/2,-2)
and (3, 5)
HELP PLEASE! Picture included!
Answer:
44x +56y = 95
Step-by-step explanation:
To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.
The midpoint is the average of the coordinate values:
((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)
The differences of the coordinates are ...
(3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)
Then the perpendicular bisector equation can be written ...
Δx(x -h) +Δy(y -k) = 0
5.5(x -0.25) +7(y -1.5) = 0
5.5x -1.375 +7y -10.5 = 0
Multiplying by 8 and subtracting the constant, we get ...
44x +56y = 95 . . . . equation of the perpendicular bisector
A, B, and C are collinear points C is the midpoint of AB AC = 5x - 6 CB = 2x Find AB
Answer:
AB = 8
Step-by-step explanation:
Since C is the midpoint, ...
AC = CB
5x -6 = 2x
3x = 6 . . . . . . . add 6-2x
x = 2
Then the length of AB is ...
AB = 2(CB) = 2(2x) = 4(2)
AB = 8
A company sells eggs whose individual weights are normally distributed with a mean of 70\,\text{g}70g70, start text, g, end text and a standard deviation of 2\,\text{g}2g2, start text, g, end text. Suppose that these eggs are sold in packages that each contain 444 eggs that represent an SRS from the population. What is the probability that the mean weight of 444 eggs in a package \bar x x ˉ x, with, \bar, on top is less than 68.5\,\text{g}68.5g68, point, 5, start text, g, end text?
Answer:
6.68% probability that the mean weight is below 68.5g.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]
Probability that the mean weight is below 68.5g:
This is 1 subtracted by the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 70}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% probability that the mean weight is below 68.5g.
Answer:
P(x ∠ 68.5) = 0.07
Step-by-step explanation:
Got it right on khan.
Using propositional logic to prove that each argument is valid.If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Kraso was not in town. If a crime was committed, then Mr. Krasov was in town. Therefore Jose did not take the jewerly. Use letters J, L, C, T.So for this question, I am very confused and would appreciate any help offerd.
Answer:
Step-by-step explanation:
We will first translate the situation to propositional logic. First, some notation is needed: [tex]\lor[/tex] is the or logical operation and [tex]\implies[/tex] is the symbol for logical implication. Define the following events:
J: Jose took the jewelry. L: Mrs Krasov lied, C: a crime was committed. T: Mr Krasov was in town.
We will symbol the propositions in logical symbols. Recall that [tex]\neg[/tex] means negation
If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed: [tex]J\lor L \implies C[/tex]
Mr. Krasov was not in town: [tex]\neg T[/tex]
If a crime was committed, then Mr. Krasov was in town: [tex]C\implies T[/tex]
We want to check if the conclusion Jose did not take the jewerly: [tex]\neg J[/tex] can be deduced from the premises.
First, recall the following:
- if [tex] a\implies b[/tex] and a is true, then b is true.
- [tex] a\implies b[/tex] is logically equivalent to [tex]\neg b \implies a[/tex]
Coming back to the problem, we have the following premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg(J\lor L)[/tex]
where the equivalence for the logical implication was applied. REcall that the negation of an or statement is g iven by
[tex] \neg( a \lor b ) = \neg a \land \neg b [/tex] where [tex] \land[/tex] is the and logical operator.
USing this, we get the premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg J\land \neg L[/tex]
Since [tex]\neg T[/tex], by having [tex]\neg T \implies \neg C[/tex], then it must be true that [tex]\neg C[/tex]. Since [tex]\neg C \implies \neg J\land \neg L[/tex], then it must be true that [tex] \neg J\land \neg L[/tex]. This final conclusion implies that it is true that [tex]\neg J[/tex] which is the statement that Jose did not take the jewelry.
5+7.(9-4)
5+7=11
11×5=55
Answer: itz 605
Step-by-step explanation:
Please Answer the following with explanation and formula with neat typing
Answer: A
Step-by-step explanation:
You want to make them both have common denominators. What number does the denominators both go into? Thats easy, its 60.
Multiply 7/12 by 5/5 to get 35/60
Now multiply 4/15 by 4/4 to get 16/60
You need to add a negative number to 35/60 in order to get 16/60
Do 16-35 to get -19/60
Find values of a. b. and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
X + y = 6
y + z = 6
x + z = 6
ax + by + cz = 0
a) a unique solution (a. b .c)=([])
b) no solution (a. b .c)=([])
c) infinitely many solutions (a. b, c) = ([])
Answer:
Step-by-step explanation:
The given equations are
x + y = 6- - - - - - - - -1
y + z = 6- - - - - - - -2
x + z = 6- - - - - - - - - 3
From equation 2, y = 6 - z
Substituting y = 6 - z into equation 1, it becomes
x + 6 - z = 6
x - z = 6 - 6
x - z = 0
x = z
Substituting x = z into equation 3, it becomes
z + z = 6
2z = 6
z = 6/2
z = 3
x = 3
Substituting x = 3 into equation 1, it becomes
3 + y = 6
y = 6 - 3
y = 3
ax + by + cz = 0
3a + 3b + 3c = 0
3(a + b + c) = 0
Therefore, it is impossible
If one angle equals 34”, then the measure of its complement angle is 56°.
True
OO
False
I need help
Answer:
True
Step-by-step explanation:
Complementary means they should sum to 90 degrees
34+56=90
Answer:
True
Step-by-step explanation:
Complementary angles are angles that add to 90 degrees, or a right angle.
If the two angles are complementary, then they will add to 90 degrees.
One angle is 34°, and it's complement is 56°.
Add the angles.
34°+56°
90°
Since they add to 90 degrees, they are complementary angles. Therefore, the statement is true.
For many years "working full-time" was 40 hours per week. A business researcher gathers data on the hours that corporate employees work each week. She wants to determine if corporations now require a longer work week. Group of answer choices Testing a claim about a single population proportion. Testing a claim about a single population mean. Testing a claim about two population proportions. Testing a claim about two population means.
Answer:
Correct option is: Testing a claim about two population means.
Step-by-step explanation:
In this provided scenario, a researchers wants to determine if corporations require a longer work week for the employees "working full-time".
It is given that for many years "working full-time" was 40 hours per week.
The researchers researcher gathers data on the hours that corporate employees work each week.
It is quite clear that the researcher wants to determine whether the number of hours worked per week must be increased from 40 hours or not.
A test for the difference between two population means would help the researcher to reach the conclusion.
Thus, the correct option is: Testing a claim about two population means.
THIS QUESTION IS KILLING ME
Calculate the volume of the object by using the triple integral.
The volume of the solid (call it S) in Cartesian coordinates is
[tex]\displaystyle\iiint_S\mathrm dV=\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{(x^2+y^2)^2-1}^{4-4(x^2+y^2)}\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
but I suspect converting to cylindrical coordinates would make the integral much more tractable.
Take
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=z\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]
Then
[tex]4-4(x^2+y^2)=4-4r^2=4(1-r^2)[/tex]
[tex](x^2+y^2)^2-1=(r^2)^2-1=r^4-1[/tex]
and the integral becomes
[tex]\displaystyle\iiint_S\mathrm dV=\int_0^{2\pi}\int_0^1\int_{r^4-1}^{4(1-r^2)}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\pi\int_0^1r(4(1-r^2)-(r^4-1))\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^1r(5-4r^2-r^4)\,\mathrm dr[/tex]
[tex]=\displaystyle2\pi\int_0^15r-4r^3-r^5\,\mathrm dr[/tex]
[tex]=2\pi\left(\dfrac52-1-\dfrac16\right)=\boxed{\dfrac{8\pi}3}[/tex]
A toy car is placed on the floor He moves in a straight line starting from rest and travels with a constant acceleration for three seconds reaching a velocity of 4 meters per second it then slows down with constant deceleration of 0.5 meters per second squared For four seconds before hitting the wall and stopping draw a velocity time graph for the toy car what is the total distance travelled by the toy car
Answer:
18 meters.
Step-by-step explanation:
There is a constant acceleration for 3 seconds, reaching 4 m/s. This, when drawn on a velocity/time graph, creates a diagonal line. The area underneath this line, which is the distance it travels, is found by the following: 0.5(l*h), the formula used to find the area of a triangle.
0.5(3*4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2*4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find the area of it.
2*4=8m
Finally, we add each of these up.
6m+4m+8m=18m
Sorry if the step by step process was poorly explained, I'm not the best at explaining. Hope this helped, though. :^)
The total distance traveled by the toy car is 18 meters.
What is acceleration?Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.
For three seconds, there is a steady acceleration that reaches 4 m/s. This yields a diagonal line when drawn on a velocity/time graph. The following formula can be used to determine the region beneath this line, or the distance it travels:
The triangle area is calculated using the formula:-
A = 0.5(l x h).
A = 0.5(3 x 4)=6m
There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.
0.5(2 x 4)=4m
Now, all that remains is a rectangle of height 2 and a length of 4, so we find its area of it.
2 x 4 = 8m
Finally, we add each of these up.
6m+4m+8m=18m
Therefore, the total distance traveled by the toy car is 18 meters.
To know more about acceleration follow
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work out the length of the container. Giver your answer to the nearest whole centimetre.
Dennis is making a container for tomato plant. The container will be in the shape of a cuboid.
missing length ? 40cm by 55cm.
The capacity of the container will be 180 litres.
1 Litre =1000cm cuboid.
Answer:
Length of the container = 82 cm
Step-by-step explanation:
Given:
Breadth of the container is 40 cm and height of the container is 55 cm
Volume of the container is 180 litres
To find: length of the container
Solution:
A container is in the shape of the cuboid.
Volume of cuboid = length × breadth × height
Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]
(as 1 litre = 1000 [tex]cm^3[/tex] )
Therefore,
[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]
The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from the base of the trunk.what is the lenght of the broken part of the tree to the nearest tenth of a foot
Answer:
14.3 feet.
14.3 feet
Step-by-step explanation:
The problem forms a right triangle in which:
The Vertical Leg of the Right Triangle = 3 feet
The Horizontal Leg of the Right Triangle =14 feet
We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.[/tex]
What’s the correct answer for this? Select all that apply
Answer:
B and C
Step-by-step explanation:
The correct options are :
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
In both the cases the length and the width of the section are equal
Select the action you would use to solve x/3=12. Then select the property that justifies that action
Answer:
To solve this I would multiply both sides by 3
Step-by-step explanation:
i would use the multiplication property of equality
The property that justifies that action x/3=12 is a linear question using reciprocal law.
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.explanation:-
x/3= 12
x = 12*3 ( using reciprocal)
hence x = 36
solving this we will get the valve of Y if x is given.
Learn more about linear equations here:-https://brainly.com/question/14323743
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0.2x + (-0.9) + 1.7 = 9.6
0.2x + 0.8 = 9.6
X=
WHAT DOES x =
Answer:
x =44
Step-by-step explanation:
0.2x + (-0.9) + 1.7 = 9.6
Combine like terms
.2x +.8 = 9.6
Subtract .8 from each side
.2x +.8 -.8 = 9.6 -.8
.2x = 8.8
Divide each side by .2
.2x/.2 = 8.8/.2
x =44
The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?
Answer:
4.6%.
Step-by-step explanation:
The probability that a can of paint contains contamination(C) is 3.23%
P(C)=3.23%
The probability of a mixing(M) error is 2.4%.
P(M)=2.4%
The probability of both is 1.03%.
[tex]P(C \cap M)=1.03\%[/tex]
We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]
In probability theory:
[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]
The probability that a randomly selected can has contamination or a mixing error is 4.6%.
A sample of 1100 computer chips revealed that 77% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 76% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]
Step-by-step explanation:
Information given
n=1100 represent the random sample taken
[tex]\hat p=0.77[/tex] estimated proportion of chips that fall in the first 1000 hours of their use
[tex]p_o=0.76[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Solution
We need to conduct a hypothesis in order to check if the true proportion is equal to 0.76.:
Null hypothesis:[tex]p=0.76[/tex]
Alternative hypothesis:[tex]p \neq 0.76[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]
The histogram represents the daily low and high temperatures in a city during March. Which comparison of the distributions is true?
A)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is nearly symmetric.
B)The distribution of low temperatures is skewed right, and the distribution of high temperatures is nearly symmetric.
C)The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is skewed right.
D)The distribution of low temperatures is skewed right, and the distribution of high temperatures is skewed right.
Answer:
ITS C
Step-by-step explanation:
The other answer is wrong, I just tried it.
Answer:
It's C on EDG
Step-by-step explanation:
I need help solving this
Answer:
The answer is the first one on the bottom left.
Step-by-step explanation:
The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rate of change of the volume when r = 9 inches. in.3/min (b) Find the rate of change of the volume when r = 37 inches. in.3/min
Answer:
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Step-by-step explanation:
given data
radius r of a sphere is increasing at a rate = 3 inches per minute
[tex]\frac{dr}{dt}[/tex] = 3
solution
we know volume of sphere is V = [tex]\frac{4}{3} \pi r^3[/tex]
so [tex]\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}[/tex]
and when r = 9
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
and
when r = 37 inches
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Help! Best Answer = brainiest!
Answer:
30 or younger
Step-by-step explanation:
Pythagorean theorem please help
Answer:
4√73
Step-by-step explanation:
x^2= 12^2 + 32^2
x^2= 144+ 1024
x^2=1168
x= 4√73
Solve for x
A)9
B)33
C)45
D)62
Answer:
A) 9
Step-by-step explanation:
R=7x+17
S=4x-6
Q=180-110=70
4x-6+7x+17+70=18011x+81=19011x=180-8111x=99x=99/11x=9Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
73 mph
Step-by-step explanation:
The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).
We have that the model would be:
y = 43.81 - 0.395 * x
We need to solve for x, if y = 15
Replacing:
15 = 43.81 - 0.395 * x
Solving for x we have:
0.395 * x = 43.81 - 15
0.395 * x = 28.81
x = 28.81 / 0.395
x = 72.9
We are asked to round to the nearest number therefore x = 73.
The car will average 15 miles per gallon at the speed of 73 miles per hour.
