Confidence interval is written as
point estimate ± margin of error
In this case, the point estimate is the sample mean
the formula for calculating margin of error is expressed as
[tex]\text{margin of error = z }\times\frac{\sigma}{\sqrt[]{n}}[/tex]where
σ = population standard deviation
n = sample size
z is the z score corresponding to a 95% confidence level. From the standard normal distribution table, z = 1.96
From the information given,
σ = 15
n = 50
sample mean = 244
By substituting these values into the formula,
[tex]\text{margin of error = 1.96 }\times\frac{15}{\sqrt[]{50}}\text{ = 4.16}[/tex]Thus,
confidence interval = 244 ± 4.16
Lower limit of conidence interval = 244 - 4.16 = 239.84
Upper limit of conidence interval = 244 + 4.16 = 248.16
Conclusion: We estimate with 95% confidence that the mean weight of all elephants is between 239.84 pounds and 248.16 pounds
In 2005 there were 744 radio stations, by 2015 that number had increased by 13.8%. How many radio stations in 2015?
Answer: We have to find the radio stations in 2015, which is 13.8% more than the radio stations in 2005 which were 744:
[tex]\begin{gathered} x=\text{ Radio stations in 2015} \\ \\ x=(1.138)\times(744) \\ \\ x=846.672 \\ \\ x\approx847 \end{gathered}[/tex]Use the quadratic function fly)=-22 +53411 to answer the following questions,a) Use the vertex formula to determine the vertes.The verteris(Type an ordered pair Simplify your answer.)
The vertex of a quadratic function can be found by using the following expression:
[tex]x=\frac{-b}{2a}[/tex]Where "a" is the number multiplying x² and b is the number multiplying x. For this function a = -2 and b = 5. Applying these on the problem we have:
[tex]x=\frac{-5}{2\cdot(-2)}=\frac{-5}{-4}=\frac{5}{4}=1.25[/tex]To find the y coordinate of the vertex we need to use the value for x that we found above. We have:
[tex]\begin{gathered} f(x)=-2x^2+5x+11 \\ f(\frac{5}{4})=-2\cdot(\frac{5}{4})^2+5\cdot(\frac{5}{4})+11 \\ f(\frac{5}{4})=-2\frac{25}{16}+\frac{25}{4}+11 \\ f(\frac{5}{4})=\frac{-50}{16}+\frac{25}{4}+11 \\ f(\frac{5}{4})=-3.125+6.25+11=14.125 \end{gathered}[/tex]The ordered pair for this function's vertex is (1.25, 14.125)
5. Graph the system of inequalities. Then, identify a coordinate point in the solution set.2x -y > -3 4x + y < 5
We have the next inequalities
[tex]\begin{gathered} 2x-y>-3 \\ 4x+y<5 \end{gathered}[/tex]as we can see if we graph these inequalities we will obtain the next graph
where the red area is the first inequality and the blue area is the second inequality
and the area in purple is the solution set of the two inequalities
one coordinate point in the solution set could be (0,0)
SOMEONE PLEASE HELP ME QUICKLY WITH THIS,ITS AN EMERGENCY!!!!! pls explain how you get the solution as well, sorry!
Thank you <3
The statement that reflects the running rates is Pepe ran 9/8 mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.
What is the speed?Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.
Speed = distance / time
Speed if Paul ran 1/5 mile in 4/15 hour
Speed = 1/5 ÷ 4/15
1/5 x 15/4 = 3/4 miles per hour
Speed if Pepe ran 8/10 mile in 1/4 of an hour
Speed = 8/10 ÷ 1/4
8/10 x 4 = 16/5 = 3 1/5 mile per hour
Difference in speeds =
[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]
Speed if Paul ran 4/15 mile in 1/5 hour
Speed = 4/15 ÷ 1/5
4/15 x 5 = 4/3 = 1 1/3 miles per hour
Speed if Pepe ran 1/4 mile in of 8/10 an hour
Speed = 1/4 ÷ 8/10
1/4 x 10/8 = 5 / 16
Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]
Speed if Paul ran 1/3 mile in 19/24 hour
Speed = 1/3 ÷ 19 / 24
1/3 x 24/19 = 8/19 miles per hour
Speed if Pepe ran 1/2 mile in of 9/8 an hour
Speed = 1/2 ÷ 9/8
1/2 x 8/9 = 4/9 mile per hour
Difference = 4/9 - 8/19 = 4/171
Speed if Pepe ran 9/8 mile in 1/2 hour
Speed = 9/8 ÷ 1/2
9/8 x 2 = 2 1/4 miles per hour
Speed if Paul ran 19 / 24 mile in of 1/3 an hour
Speed = 19 / 24 ÷ 1/3
19 / 24 x 3 = 2 3/8 miles per hour
Difference =
[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]
[tex]\frac{3 - 2}{8}[/tex] = [tex]\frac{1}{8}[/tex] miles per hour
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helpppppp!!!!!!!!!!!!!!!!!!!!
Answer
D. Observations of constellations show that stars have moved over time.
Explanation:
A scientific claim is basically an observation in science.
Constellation changes there position over time because of earth's rotation around sun. So, observation of constellations shows that stars have moved over time is a scietific claim. If stars would not move then constellation will not form.
Use the graph of 'f' in the figure below to answer the following questions. 1. State the domain and range of 'f'.2. Find the average rate of change of 'f' over the interval [0,6].
The domain of the given function corresponds to:
[tex]\lbrack-4,-2)\cup(-2,6)[/tex]And the range of the function is:
[tex](-2,6)[/tex]The average rate of change of f over the interval [0,6] is:
[tex]\frac{5.5-(-2)}{0-6}=\frac{7.5}{-6}=-\frac{5}{4}=-1.25[/tex]43/1/2 divided by 1/1/4
When 43/1/2 is divided by 1/1/4 , the value will be 34 4/5.
What is a fraction?A fraction simply means a numbers that's represented as a/b where a = numerator and b = denominator
In this case, the division of the fraction will be:
43 1/2 ÷ 1 1/4
= 87/2 ÷ 5/4
= 87/2 × 4/5
= 174 / 5
= 34 4/5
This shows the. concept of fractions.
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Question 2-22
A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his wealty rate of eating the cale
5
36
.
B
TH
cakesliveek
er
9
Using the concept of Fraction, the weekly rate of Jake eating the cake is 11.2.
What is Fraction?Fraction represents parts of a whole or group of objects. A fraction consists of two parts. The numerator is the number at the beginning of the line. It specifies the number of equal parts taken from the whole or collection. The number below the line is the denominator. It shows the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.
We know that,
The cake is cut into 12 equal slices.
After 3 days Jake eats 5 slices then,
For 1 day = [tex]\frac{5}{3}[/tex]
= 1.6
Then for 7 days,
1.6 × 7 = 11.2
Hence, Jake's weekly rate of eating the cake is 11.2.
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The complete question would be
'A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?'
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.The number of ducks and pigs in a field totals 37. The total number of legs among them is 98. Assuming each duck has exactly two legs and each plg has exactly fourlegs, determine how many ducks and how many pigs are in the field.ducks?pigs?
Lets call x to the number of ducks
and y the number of pigs.
Then:
[tex]2x+4y=98[/tex]Because there are 2 legs per duck and 4 legs per pig.
If the total of animals is 37, then:
[tex]x+y=37[/tex]Then:
[tex]x=37-y[/tex]And replacing on the first equation we get:
[tex]2(37-y)+4y=98[/tex][tex]74-2y+4y=98[/tex][tex]2y=98-74[/tex][tex]2y=24[/tex][tex]y=\frac{24}{2}[/tex][tex]y=12[/tex]There are 12 pigs and therefore 25 ducks.
2x + 37 = 7x + 42x = ???
Solve;
[tex]\begin{gathered} 2x+37=7x+42 \\ \text{Collect all like terms and you'll have,} \\ 2x-7x=42-37 \\ \text{Note that a positive number becomes negative once it crosses the equality sign} \\ \text{And vice versa for a negative number} \\ 2x-7x=42-37 \\ -5x=5 \\ \text{Divide both sides by -5} \\ \frac{-5x}{-5}=\frac{5}{-5} \\ x=-1 \end{gathered}[/tex]Therefore, x = -1
cuántos cifras tiene el cociente de 900÷25
Given the expression
I’m not firmiliar with the sun or difference of cubes (HW assignment)
Given:
[tex]125r^3-216[/tex]Find-: Factor using the formula of the sum or difference of cube.
Sol:
Factoring sum and differences of cubs is:
[tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ x^3+y^3=(x+y)(x^2+y^2-xy) \end{gathered}[/tex]Apply for the given information.
[tex]\begin{gathered} =125r^3-216 \\ \\ =(5r)^3-(6)^3 \end{gathered}[/tex][tex]\begin{gathered} x^3-y^3=(x-y)(x^2+y^2+xy) \\ \\ (5r)^3-(6)^3=(5r-6)((5r)^2+(6)^2+(5r)(6)) \\ \\ =(5r-6)(25r^2+36+30r) \end{gathered}[/tex]Find the area of each figure. Round to the nearest 10th if necessary.
1.
First, divide the figure into 3 different figures.
Find the area of each figure, and then add them:
A1 is a rectangle:
Area of a rectangle: Lenght x width
A1 = 8 x 5.3 = 42.4 in2
A2 is also a rectangle:
Lenght = 4
width = 8 - 5.3 = 2.7
A2 = 4 x 2.7 = 10.8 in2
A3 is a triangle:
Area of a triangle = (base x height) / 2
base = 2.7
Height = 8-4 = 4
A3= ( 2.7 x 4 ) / 2 = 5.4 in2
Total area = A1 + A2 + A3 = 42.4 + 10.8 + 5.4 = 58.6 in2
Answer = 58.6 in2
can someone please help me find the answer to the following?
We are given a tangent and a chord of a circle. The angle ABC form by the intersection of the tangent and the chord is half the arc they both intersect, therefore, we must find the major arc of the circle, we can do that with the fact that the total arc of the circle is 360, therefore:
[tex]\begin{gathered} \text{arcAB}=360-50 \\ \text{arcAB}=310 \end{gathered}[/tex]Therefore, the angle is:
[tex]\begin{gathered} \angle ABC=\frac{1}{2}\times310 \\ \angle ABC=155 \end{gathered}[/tex]Angle ABC is 155 degrees.
The vertex of a quadratic function is (2, -1) and its y-intercept is 7. Find the function,
Given:-
[tex]\text{vertex}=(2,-1),y-intercept=7[/tex]To find:-
The function.
So the formula is,
[tex]y=a\mleft(x-h\mright)^{2}+k[/tex]So substituting we get,
[tex]y=7(x-2)^2-1[/tex]So the value. we get,
[tex]\begin{gathered} y=7(x-2)^2-1 \\ y=7(x^2-4x+4)-1 \end{gathered}[/tex]Since the value of x is,
[tex]\begin{gathered} y=7x^2-28x+28-1 \\ y=7x^2-28x+27 \end{gathered}[/tex]So the value,
[tex]y=7x^2-28x+27[/tex]x equals 6 y equals 1 y = x + ?
The given information is
help meeeee pleaseeeee!!!
thank you
Step-by-step explanation:
what is the problem ?
first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.
just simple calculation !
(a)
R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200
$200 million
(b)
R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500
$500 million
there ! that's all that was needed.
Solve the system of equations.y= x2 - 3x + 6y = 2x + 6
We have the following:
[tex]\begin{gathered} y=x^2-3x+6 \\ y=2x+6 \end{gathered}[/tex]We subtract the equations:
[tex]\begin{gathered} y-y=x^2-3x+6-2x-6 \\ 0=x^2-5x \\ 0=x(x-5) \\ x=0;x=5 \end{gathered}[/tex]for y:
[tex]\begin{gathered} y=2\cdot0+6 \\ y=6 \\ y=2\cdot5+6 \\ y=16 \end{gathered}[/tex]therefore, the answer is:
(0,6) and (5,16), the option D.
A chemist needs to mix a 12% acid solution with a 20% acid solution to obtain 160 ounces of a 15% acid solution. How many ounces of each of the acid solutions must be used?
Answer:
100 ounces of 12% solution and 60 ounces of the 20% solution.
Step-by-step explanation:
Let x ounces be the amount of 12% solution, then there will be 160-x ounces of the 20% solution.
So, we have the equation:
0.12x + 0.20(160 - x) = 0.15* 160
0.12x - 0.20x + 32 = 24
-0.08x = -8
x = 100.
So, it is 100 ounces of 12% solution and 60 ounces of the 20% solution.
you pull with 45nm on a torque wrench of 1m what's the tourqe at the end
The torque at the end is equal to 45 Nm.
What is torque?Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.
Mathematically, torque can be calculated by using this formula:
τ = Fd
Where:
τ represents the torque.F represents the force.d represents the perpendicular distance.In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.
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Find g(x), where g(x) is the translation 4 units left of f(x)=|x|.
The equation for the translated function is:
g(x) = |x + 4|
How to find g(x)?
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.if N < 0, the translation is to the right.Here we have:
f(x) = |x|
And the translation is of 4 units to the left, so the translated function is:
g(x) = f(x + 4) = |x + 4|
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8x - 3x + 4x = -36x = ?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
8x - 3x + 4x = -36
x = ?
Step 02:
We must apply the algebraic rules to find the solution.
8x - 3x + 4x = -36
12x - 3x = - 36
9x = - 36
x = - 36 / 9
x = - 4
The answer is:
x = - 4
Solve the system using the elimination method. State your final answer as an ordered pair. DO NOT include any spaces in your answers.
Given:-
let
5x-4y=1 be the equation 1
-5x-10y=-15 be the equation 2
step 1-
add equation 1 and 2
we get=
-14y=-14
y=1
this is required value of y
we are going to put this value of y in equation 1
we get
5x-4(1)=1
5x-4=1
5x=1+4
5x=5
x=1
this is required value of x
hence value of x and y are(1,1)
2. The Venn diagram shows the sets U, X and Y.UXY.34 246..9.512:31List the elements of the following sets:(a) X(b) Y(c) U(d) XUY(e) XnY(g) X\Y(h) Y\X(f) X'(1) (XY)2:31
Given the Venn diagram in the question, we can proceed to answer the questions as follow
[tex]\begin{gathered} X=\text{members of the subset X} \\ This\text{ gives: 1,2,3,4, and 5} \end{gathered}[/tex][tex]\begin{gathered} QuestionA\text{ } \\ X=1,2,3,4,and\text{ 5} \\ \end{gathered}[/tex]Question B
Y= members of subset Y
Y =2,4,6, and 8
Question C
U means that we should list all elements in the universal set
U = ALL members of the set
U = 1,2,3,4,5,6,7,8, and 9
Question D
This is the union of both sets X and Y. This means we will list all the members that are found in the 2 subsets
[tex]\text{XUY}=1,2,3,4,5,6,\text{ and 8}[/tex]Question E
[tex]\begin{gathered} \text{XnY means we are to find the elements that are common to both X and Y} \\ \text{XnY}=2\text{ and 4} \end{gathered}[/tex]Question F
X' means that we should find all members of the set except that of X
[tex]X^{\prime}=6,7,8,\text{ and 9}[/tex]Question G
X\Y means that we should list the elements of X that are not found in Y
X\Y= 1,3, and 5
Question H
Y\X means that we should list the elements of Y that are not found in X
Y\X= 6, and 7
Question I
To solve (XnY)' we will follow the steps below
Step 1: Find (XnY)
[tex]\text{XnY}=2\text{ and 4}[/tex]Step 2: Find (XnY)'
[tex]We\text{ will list all elements aside (XnY)}[/tex][tex](XnY)^{^{\prime}}\Rightarrow1,3,5,6,7,8,\text{and 9}[/tex]
Khalid is investigating two linear functions. The first linear function is defined by the equation 2x + 3y = 12. The second linear functionpasses through the points (3,-2) and (-2, k).For the case where the two linear functions have the same y-intercept, what must be the value of k?k=
According to the given data we have the following:
first linear function is defined by the equation 2x + 3y = 12
second linear function passes through the points (3,-2) and (-2, k)
the two linear functions have the same y-intercept
k?
To calculate k first we have to do the following:
we would have to use the formula y=mx +b
the two linear functions have the same y-intercept, therefore, b=12.
So, y=mx +12
As second linear function passes through the points (3,-2) we are going to substitue the x and y with 3 and -2.
So, -2=m*3+12
-2-12=m*3
-14=m*3
m=-14/3
m=-4
Finally we would calculate k by writiing the equation of the line that passes through each pair of points as follows:
y2-y1/x2-x1=m
So
[tex]\frac{k\text{ -(-2)}}{\text{-2 - 3}}\text{ }=\text{ -4}[/tex]So, k +2/-5=-4
k+2=20
k=20-2
k=18
Identify the side lengths that form a right triangle.a. 12, 13, 16b. 15, 20, 21c. 9, 40, 42d. 10, 24, 26Identify the side lengths that form a right triangle.a. 3, 4, 8b. 30, 40, 45c. 5, 12, 13d. 6, 12, 133. do the side lengths of 8, 10, and 13 form a right triangle? 4. Determine if ▼ABC is a right triangle if AB=36, AC=48 and BC=60
Answer:
d. 10, 24, 26
Explanation:
To identify the side lengths that form a right triangle, we check if it satisfies the Pythagorean theorem.
By the theorem:
[tex]\begin{gathered} a^2=b^2+c^2 \\ a\text{ is the hypotenuse, the longest side.} \end{gathered}[/tex]a. 12, 13, 16
[tex]\begin{gathered} 16^2=12^2+13^2 \\ 256=144+169 \\ 256\neq313 \end{gathered}[/tex]These side lengths do not form a right triangle.
b. 15, 20, 21
[tex]\begin{gathered} 21^2=15^2+20^2 \\ 441=225+400 \\ 441\neq625 \end{gathered}[/tex]These side lengths do not form a right triangle.
c. 9,40,42
[tex]\begin{gathered} 42^2=9^2+40^2 \\ 1764=81+1600 \\ 1764\neq1681 \end{gathered}[/tex]These side lengths do not form a right triangle.
d. 10, 24, 26
[tex]\begin{gathered} 26^2=10^2+24^2 \\ 676=100+576 \\ 676=676 \end{gathered}[/tex]These side lengths form a right triangle since both sides of the equation are the same.
reduce the square root of -360
reduce the square root of
[tex]\begin{gathered} \sqrt[]{-360} \\ 360=36\cdot10=6^2\cdot10 \\ \end{gathered}[/tex]There is no square root for the negative number
so, this is represent a complex number
So,
[tex]\begin{gathered} \sqrt[]{-360}=\sqrt[]{-1}\cdot\sqrt[]{360} \\ =i\cdot\sqrt[]{6^2\cdot10} \\ =i\cdot6\sqrt[]{10} \\ =6\sqrt[]{10}\cdot i \end{gathered}[/tex]
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 17 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 112 million dollars? Round your answer to four decimal places.
0.8413 is the probability that a random selected firm will earn less than 112 million dollar
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Let X be a random variable represents the income of the firm in the industry
Hence
X~ N (mean =u= 95 , standard deviation= d = 17 )
We must determine the likelihood that a randomly chosen company will make fewer than 112 million dollars in earnings ie.
P(X<112) = P(X-u/d < 112-95/17)
Z=X-u/d = 112 - 95/17 = 1
P(X<112) = P(Z-1)=0.8413
Using the standard normal probability table.
P(X<112) = 0.8413
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Two people out of a group of 75 will win tickets to an upcoming concert. How many different groups of two are possible?
To calculate the combinations of groups of 2, since the order doesn't matter, we can use combination. In this case we have a total of 75 to choose from and will choose 2, so this is "75 choose 2".
The equation to use is (n choose k):
[tex]C(n,k)=\frac{n!}{(n-k)!k!}[/tex]In this case, we have n = 75 and k = 2, so:
[tex]C(75,2)=\frac{75!}{73!2!}[/tex]For the property of factorials, 75! / 73! = 75*74, because the terms less or equal 73 cancel out. so:
[tex]C(75,2)=\frac{75\cdot74}{2!}=\frac{75\cdot74}{2}=75\cdot\frac{74}{2}=75\cdot37=2775[/tex]So, there are 2775 different groups of 2 in this case.
Another way of doing this calculation is by thinking of choosing one at a time.
At first, we can choose from 75 possible people, so we start at 75.
When we choose the second one, we already picked the first, so there are only 74 people left. So we get:
[tex]75\cdot74[/tex]This are the two first people, but, in this way we are considering too many groups, since here we considere the order matter, to fix this we divide by k!, where k is the number of picks, which is 2 in this case (so, permutation of 2). So:
[tex]\frac{75}{2}\frac{74}{1}=\frac{75\cdot74}{2}=2775[/tex]45. (09.01) Let A = {1, 2, 3, 4, 5} and B = {2,4}. What is A n B? O {2,4) O {1, 2, 3) O {1, 2, 3, 4 } O {1, 2, 3, 4,5)
Answer:
{2,4}
Explanation:
Given sets A and B defined below:
[tex]\begin{gathered} A=\mleft\{1,2,3,4,5\mright\} \\ B=\mleft\{2,4\mright\} \end{gathered}[/tex]The set A Π B is the set of elements common to sets A and B.
[tex]A\cap B=\{2,4\}[/tex]