Answer:
The interval is (.0817, .118).
Step-by-step explanation:
Let's make this interval! The easy way is to go to STAT->TEST->A, 1-prop z-int, but I will show the long way.
1. Conditions
First we must check the conditions.
Randomization condition: The sample is given to be random, so we can assume independence.
Success/failure condition: Both np>10 and nq>10 must be met.
np = 1030(103/1030) = 103 ✓ nq = 1030(927/1030) = 927 ✓10% condition: The sample cannot be greater than 10% of the population.
10n < N, 10(1030) < 200000 ✓All conditions are met, so we can use a 1-proportion z-interval to represent the data.
2. Mechanics
Find [tex]\hat{p}[/tex], the sample proportion.
103/1030 = .1
[tex]\hat{q}[/tex], then, the probability of not p, is 1 - .1 = .9
Find z* (z star), the critical z-value.
You can do this on your calculator using 2nd->VARS->3 (or you can memorize it - it's 1.96. Winky face.) This is called the invNorm function, that takes the left side area under the normal curve. But what do we plug in to the invNorm function?
invNorm(.975) = 1.96
Plug values into the equation.
[tex]\hat{p}[/tex] ± z*[tex]\sqrt{\frac{\hat{p}\hat{q}}{n} }[/tex]
.1 ± 1.96[tex]\sqrt{\frac{.1*.9}{1030} }[/tex]
.1 ± 1.96(.00935)
.1 - .0183 = .0817
.1 + .0183 = .118
(.0817, .118)
3. Conclusion
Based on this sample, we are 95% confident that the proportion of people the company contacts who may buy something is between .0817 and .118. That isn't very likely, but maybe they'll make a little profit!
A bag of colored marbles contains 16 blue marbles, 12 red marbles, and 8 yellow marbles.
What is the theoretical probability of drawing a red marble?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
The theoretical probability of drawing a red marble is 1/3.
Step-by-step explanation:
1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.
2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.
3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.
The tuition at a college was $30,000 in 2012, $31,200 in 2013, and $32,448 in 2014. The tuition has been increasing by the same percentage since the year 2000.
The equation C(T) = LaTeX: 30000\cdot1.04^T
30000
⋅
1.04
T
represents the cost of tuition, in dollars, as a function of T, the number of years since 2012. Explain what the 30,000 and 1.04 tell us about this situation.
What is the percent increase in tuition from year to year?
What does C(3) mean in this situation? Find its value and show your reasoning.
a. Write an expression to represent the cost of tuition in 2007.
b. How much did tuition cost that year?
Previous Next
The meaning of each parameter is given as follows:
30,000: cost in the reference year of 2012.1.04: rate of change.Then the yearly percent increase is of:
4%.
C(3) represents the cost in 2015, which was of $33,746.
a) The expression to represent the cost in 2007 is of: C(-5).
b) The cost was of: $24,658.
How to define an exponential function?An exponential function is defined as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.For this problem, the function is defined as follows:
y = 30000(1.04)^x.
In which:
x is the number of years since 2012.y is the cost in x years after 2012.C(3) represents the cost in 2015 and is obtained as follows:
C(3) = 30000(1.04)^3 = $33,746.
C(-5) represents the cost in 2007 and is obtained as follows:
C(-5) = 30000(1.04)^(-5) = $24,658.
(as 2007 was five years before 2012).
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Solve SA = πrs + π r2 for s A) -r B) SA + r C) SA π2r3 D) SA - πr2 πr
Answer:
(SA - π r^2)/πr = s
Step-by-step explanation:
SA = πrs + π r^2
Subtract π r^2 from each side
SA - π r^2 = πrs + π r^2-π r^2
SA - π r^2 = πrs
Divide each side by πr
(SA - π r^2)/πr = πrs/πr
(SA - π r^2)/πr = s
Answer:
D
Step-by-step explanation:
SA = πrs + πr²
SA - πr² = πrs
s = (SA - πr²)/πr
For the data 20, 40, 50, 20, 10, 70. What is there mean absolute deviation?
Answer:
18.333
Step-by-step explanation:
Which phrase represents this expression?
(47−17)×4
A. 4 times the difference of 47 and 17
B. 4 times the difference of 17 and 47
C. the difference of the product of 4 times 17 and 47
D. the difference of 47 and the product of 4 times 17
Answer:
I think its A
Step-by-step explanation:
Solve the system of equations using the elimination method 4x+5y=40 6x+3y=42
Answer:
The solutions to the system of equations are [tex]y=4,\:x=5[/tex].
Step-by-step explanation:
To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]
First,
[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]
[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]
Subtract the first equation from the second equation
[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]
Solve [tex]-9y=-36[/tex] for y:
[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]
For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x
[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]
The solutions to the system of equations are:
[tex]y=4,\:x=5[/tex]
Which equation represents the black line?
Which equation represents the red line?
Explain a mathematical way to find the intersection of the lines without actually graphing the lines.
Answer:
Black Line y = 3 + 2x , y = 2x +3
Red Line y = -2 - .5x. y = -.5x -2
vice versa
Step-by-step explanation:
For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x
For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.
Ollivanders stuffed bear shop has 456 bears in stock exactly half of them Are made from wool how many wool does Mr.oillvander have in stock
Answer:
228 of them are made from wool, but there is no enough information to determine how many would he has in stock.
Step-by-step explanation:
Mr Ollivander's stuffed bear shop has 456 bears in stock, and exactly half of them are made from wool, this means that 1/2 of 456 are made from wool
1/2 of 456 = 1/2 × 456 = 456/2 = 228.
That is 228 of them are made from wool.
However, nothing tells us that this is all he has in his stock. There is no information available to determine how many would he has in stock.
Consider the triangle.
Which statement is true about the lengths of the sides?
45°
Each side has a different length.
Two sides have the same length, which is less than the
length of the third side.
D. The three sides have the same length.
D. The sum of the lengths of two sides is equal to the
length of the third side.
45°
Answer:
Assuming this is a 45 - 45 - 90 right triangle, The answer would be B) Two sides have the same length, which is less than the length of the third side
Hence statements stated true false along with reason
What is triangle?A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's interior angles equals 180 degrees is the most significant feature of a triangle.
Triangle of Isosceles: Triangle with Obtuse Angle
Triangle Inequality in the Scalene Triangle
Triangle Surface Area: Triangle with Sharp Angle
Triangle with Right Angles: Triangle Form of Pascal...
How to solve?Given a triangle and statements related to it let's check
Each side has a different length.
-This statement can't always be true as in equilateral triangle all sides are equal
Two sides have the same length, which is less than the
length of the third side.
-this statement is correct but when it is a right angles triangle where other two anges are 45degrees each then this can't be true.
The three sides have the same length.
-this statement is true for equilateral triangle
D. The sum of the lengths of two sides is equal to the
length of the third side.-
-This statement is true when we talk of only right angled triangle
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The complement of 20°17' is
Answer:69°43'
Step-by-step explanation:
Complementary angles add up to 90
Let them complement be y
y+20°17`=90°
Collect like terms
y=90-20°17' 20°17'=1217/60
y=90-1217/60
y=(60x90 -1 x 1217)/60
y=(5400-1217)/60
y=4183/60
y=69°43'
An angle whose measure is -102° is in standard position. Which quadrant does the terminal side of the angle fall?
Quadrant 1
Quadrant 2
Cuadrant 3
Cuadrant 4
Answer:3
Step-by-step explanation:
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Rewa Delta Union RugbyCEOhas become concerned about the slow pace of the rugby gamesplayed inthe current union rugby, fearing that it will lower the spectator attendance. The CEOmeets with the union rugbymanagers and refereesanddiscusses guidelines for speeding upand makingthe gamesmore interesting and lively. Before the meeting, the mean duration of the15-sided rugbygame timewas 3 hours, 5 minutes, that is, 185 minutes.This includes all the breaks and injury times during the game. A random sample of 36 of the 15-sided rugbygames after themeeting showed a mean of 179 minutes with a standard deviation of 12 minutes.Testing at the 1% significance level, can you concludethat the mean duration of 15-sided union rugbygames has decreased after the meeting?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Solve the inequality
Math question
Answer:
AAAAAAAAAAAAAAAAAAAA
Step-by-step explanation:
x < 7
Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000, select the correct answer. Note that the profit is distributed proportionally based on the respective amount each invested. A. The ratio of the investment of Bob, Paula and Sam is 11:15:10. B. The ratio of the investment of Bob, Paula and Sam is 12:17:21. C. The ratio of the investment of Bob, Paula and Sam is 12:5:4. D. The profit of Paula was $23,800
Answer:
D
Step-by-step explanation:
since sam invest the least, let a be the amount invested by sam
sam = a
paul = a + 5000
bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
a = 12000
thus sam is 12000, paul is 17000 and Bob is 21000
therefore the ratio of B:P:S is 21:17:12
profit by paula is 17/50 x 70000 = 23800
The profit by Paula is 17/50 x 70000 = 23800.
We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000
Since sam invest the least, let a be the amount invested by sam
Therefore we get,
sam = a
What is the investment of Paul?
The investment of Paul = a + 5000
Bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
divide both sides by 3 so we get,
a=36000/3
a = 12000
Therefore, sam is 12000,
paul =5000+12000=17000 and
Bob =12000+9000= 21000
Therefore the ratio of B:P:S is 21:17:12
The profit by Paula is 17/50 x 70000 = 23800.
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which expresion has a valume of 7/12
Answer:
1/1 x 7/1 x 1/12
Is there any options?
Step-by-step explanation:
Answer:6/8 adding 1/4
Step-by-step explanation: Because im right probably
Given two independent random samples with the following results: n1=8x‾1=186s1=33 n2=7x‾2=171s2=23 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Answer:
The point of estimate for the true difference would be:
[tex] 186-171= 15[/tex]
And the confidence interval is given by:
[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]
[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar X_1 = 186[/tex] the sample mean for the first sample
[tex] \bar X_2 = 171[/tex] the sample mean for the second sample
[tex]s_1 =33[/tex] the sample deviation for the first sample
[tex]s_2 =23[/tex] the sample deviation for the second sample
[tex]n_1 = 8[/tex] the sample size for the first group
[tex]n_2 = 7[/tex] the sample size for the second group
The confidence interval for the true difference is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
We can find the degrees of freedom are given:
[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]
The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:
[tex] t_{\alpha/2}= \pm 1.77[/tex]
The point of estimate for the true difference would be:
[tex] 186-171= 15[/tex]
And replacing into the formula for the confidence interval we got:
[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]
[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]
A bike tire has a diameter of 16 inches. What is the radius of the bike? What is the circumference of the bike?
Answer:
radius-8 inches cause math
circumference-50.27
Step-by-step explanation:
Greatest common factor for 30 abd 42
Answer:
6
Step-by-step explanation:
Because you are familiar with your times tables, you know that ...
30 = 6·5
42 = 6·7
The greatest common factor is 6.
Triangles BAD and BDC are right triangles with AB = 12 units, BD = 15 units, and $BC = 17 units. What is the area, in square units, of quadrilateral ABCD?
Answer:
The area of the quadrilateral ABCD is 114 square units
Step-by-step explanation:
We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD
First for the BAD right triangle:
AD = sqrt [BD ^ 2 - AB ^ 2]
AD = sqrt [15 ^ 2 - 12 ^ 2]
AD = sqrt [225-144]
AD = sqrt [81]
AD = 9
The area of a triangle is half the product of the base times the height, that is:
A1 = AB * AD / 2 = 12 * 9/2 = 54
Then for the second triangle in the right triangle BDC:
DC = sqrt [BC ^ 2 - BD ^ 2]
DC = sqrt [17 ^ 2 - 15 ^ 2]
DC = sqrt [289 - 225]
DC = sqrt [64] = 8
We calculate the area
A2 = DC * BD / 2 = 8 * 15/2 = 60
The total area then is:
AT = A1 + A2
AT = 54 + 60 = 114
Which means that the area of the quadrilateral ABCD is 114 square units
Which equation represents the hyperbola shown in the
graph?
10
8
(x - 2)2
(y + 3)
25
(-2,5) 6
(-7,3)
(1-21)
4-12-10 -8 -6 4-2
(3,3)
(x + 2)2
(y = 3) = 1
4
2 4 6
(x + 2)2
25
(y - 3)2
4
1
(232) - (7,31 = 1
(x - 2)2
25
Answer:
Step-by-step explanation:
A general equation of a hyperbola is
x^2 y^2
-------- - ------- = 1 (This applies only when the center of the hyperbola
a^2 b^2 is at (0, 0) ).
You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.
The equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
What is a hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
Given that, a graph, showing hyperbola, we need to find the equation,
We have the general equation for up - down facing hyperbola as
(y - k)² / b²- (x - h)² / a² = 1.
Let's start listing the properties of this graph -
Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).
Therefore, (h, k) = (- 4,1).
This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.
Therefore, a = 3.
That gives asymptotes. Now remember that it will be in the form
y = ± b / a.
We already know a = 3, so we have to find b.
Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).
Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x.
Therefore, b = 2.
Let's substitute to equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1
Hence, the equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
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The complete question is attached
1).
A) supplementary
B) complementary
C) comesponding
D) alternate interior
Nora made 15 gallons of lemonade for a community picnic.
Part A
Which of the following can be used to find the number of pints of lemonade that Nora made?
15 × 2 × 2
15 × 4 × 2
15 × 3 × 2
15 × 4 × 3
Part B
How many pints of lemonade did Nora make?
Enter your answer in the box.
pints
Answer:
I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!
Answer:
B
Step-by-step explanation:
Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of
modeled by the function r(s)=315, where sis time in seconds.
The area of the spill when s=5 seconds is
1 square inches.
Reset
Reset
Next
Next
Answer:
[tex]45\pi$ square inches[/tex]
Step-by-step explanation:
The radius, r of the expanding circle of oil is modeled by the function:
[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.
When s=5
Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]
Area of a circle [tex]=\pi r^2[/tex]
Therefore, the area of the oil spill when s=5 seconds
[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]
The area of the spill when s=5 seconds is 45pi square inches.
log 10(x + 3) – log 10(x-3) = 1
Answer:33/9
Step-by-step explanation:
Log10(x+3)-Log10(x-3)=1
Log10((x+3)/(x-3))=1
(x+3)/(x-3)=10^1
(x+3)/(x-3)=10
Cross multiply
x+3=10(x-3)
Open brackets
x+3=10x-30
Collect like terms
10x-x=30+3
9x=33
Divide both sides by 9
9x/9=33/9
x=33/9
simplify [tex]\sqrt{.49x^{18} }[/tex] where x<0
Answer:
-7x⁹
Step-by-step explanation:
[tex]\sqrt{49x^{18}} = \sqrt{(7^2)(x^9)^2} =\sqrt{(7x^{9})^2} = |7x^9|[/tex]
Since x < 0 ,then |7x⁹| = -7x⁹
What is the simplest form of this expression?
(2x + 1)(x2 - 9X+11)
Answer:
2x³ - 17x² + 13x + 11
Step-by-step explanation:
(2x + 1)(x² - 9x + 11) Distribute the 2x then the 1
2x³ - 18x² + 22x + x² - 9x + 11 Combine like terms
2x³ - 17x² + 13x + 11
If this answer is correct, please make me Brainliest!
The Empire State Building weighs about 7.3×108pounds. The One World Trade Center building weighs about 88,200,000 pounds. What is the total weight, in pounds, of these two buildings? Expressing your answer in scientific notation in the form a×10b, what are the values of a and b?
Answer:
[tex]8.182X10^8 $pounds[/tex]
a=8.182 and b=8
Step-by-step explanation:
Weight of the Empire State Building =[tex]7.3X 10^8[/tex] pounds.
Weight of the One World Trade Center building= 88,200,000 pounds.
=[tex]8.82 X 10^7[/tex]
The addition of the two:
[tex]=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds[/tex]
Comparing with the form: [tex]aX10^b[/tex]
a=8.182 and b=8
How many solutions does the equation -2a + 2a + 7 = 8 have
Step-by-step explanation:
-2a + 2a + 7 = 8
Solving like terms
7 = 8
= 8 - 7 = 1
Has one solution
¿1 y media taza x 9?
Answer: [tex]1\frac{1}{2} *9=\frac{3}{2}*9=\frac{27}{2}=13\frac{1}{2}[/tex]
Step-by-step explanation:
Answer: 27
-------
2
Step-by-step explanation:
1. Solve the system of equations
-x+y=0
4x - 3y=-3
I
=
Answer:
x = -3
y = -3
Step-by-step explanation:
To solve this system of equations, you can use the elimination method, which is to have one of the variables match, but be the opposite sign of the other:
- x + y = 0
4x - 3y = -3
The easier one to match is the 1st equation, and to make it match oppositely, you multiply the whole equation by 4:
4(-x + y = 0)
-4x + 4y = 0
4x - 3y = -3
-4x and 4x cancel each other out:
4y = 0
-3y = -3
_______
y = -3
Then plug in -3 for y, into one of the equations:
- x + y = 0
- x - 3 = 0
Add 3 to both sides:
- x = 3
Divide both sides by -1:
x = -3
