The 80% confidence interval for the population proportion of Americans over 21 who smoke is: 0.240; 0.298.
How to find the confidence interval?First step is to find the population proportion p
Sample size = n = 383
Using this formula to find the population proportion (p)
p = x /n
Let plug in the formula
p = (383 - 280) / 383
p = 103/383
p = 0.2689
Second step is to find the Margin of error (MOE)
Value of z-score for a confidence level of 80%= 1.282
Using this formula to margin of error
MOE =( z alpha x √(p) (1-p) / n )
Let plug in the formula
MOE =( 1.282x √(0.2689)(1-.0.2689) / 383)
MOE =( 1.282 x √(0.2689)(0.7311) / 383)
MOE =( 1.282 x √0.000513297
MOE =( 1.282 x 0.0226561)
MOE = 0.02905
Third step is to find the confidence interval (CI)
Confidence interval = p ± MOE
Confidence interval = 0.2689 ± 0.02905
Confidence interval = ( 0.2689 - 0.02905) , (0.57 + 0.02905)
Confidence interval = 0.23985; 0.29795
Confidence interval = 0.240; 0.298 ( Three decimal places)
Therefore the CI is 0.240; 0.298.
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Carmelo puts $2,200.00 into savings bonds that pay a simple interest rate of 3.4%. How much money will the bonds be worth at the end of 5.5 years? (Find the total worth of the bonds in 5.5 years)
Let's begin by listing out the information given to us:
Principal (P) = $2,200, Interest rate (r) = 3.4% = 0.034, Time (t) = 5.5 years
[tex]\begin{gathered} I=P\cdot r\cdot t=2200\cdot0.034\cdot5.5 \\ I=\text{ \$414.40} \end{gathered}[/tex]The bond will be worth the sum of the Principal and the Interest:
[tex]\begin{gathered} P+I=2200+411.40 \\ \Rightarrow\text{ \$}2611.40 \end{gathered}[/tex]the dealer in a card game draws three cards from a deck of 52 cards and places them face-up on the table select all the correct probabilities
Explanation:
nCx give us the number of ways in which we can select x cards from a group of n cards.
So, the number of ways in which we can select 3 cards from 52 is:
52C3.
On the other hand, the number of ways to select 3 cards but none of them are kings is 48C3 because there are 48 cards that aren't kings. So:
[tex]P(no\text{ Kings)=}\frac{_{48}C_3}{_{52}C_3}[/tex]The number of ways to draw 2 fives is: 4C2*48C1
Because the dealer needs to draw 2 cards from the 4 that are fives and 1 card from the other 48 cards. So, P(2 fives) is:
[tex]P(\text{ 2 fives)=}\frac{_4C_2\times_{48}C_1}{_{52}C_3}[/tex]The number of ways to draw 1 heart and 2 spades is: 13C1*13C2
Because there are 13 heart cards and 13 spades cards. So, P(1 heart and 2 spades) is:
[tex]P(1\text{ Heart and 2 spades) = }\frac{_{13}C_1\times_{13}C_2_{}}{_{52}C_3}[/tex]Finally, the number of ways to select 4 aces and 1 ten is
Can someone please help me solve this problem number 9
The perimeter of the room was calculated in question 6, and it is 54 feet.
Since the borders come in 5-yard rolls, let's first convert 54 feet to yards.
Each yard has 3 feet, so we can divide the amount of feet by 3 to get it converted to yards:
[tex]\frac{54}{3}=18[/tex]Thus, the perimeter of the room is 18 yards. Since each roll has 5 yards,we will need:
[tex]\frac{18}{5}=3.6[/tex]Abou 3.6 rolls, but since we can only have whole rolls, we will have to approximate it to 4 rolls.
solve for 18 degreex 29
The given triangle is a right angle triangle. Considering angle 18 as the reference angle,
x = hypotenuse
29 = adjacent side
We would find the hypotenuse, x by applying the cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Thus, we have
Cos18 = 29/x
29 = xCos18
x = 29/Cos18 = 29/0.95
x = 30.53
At an amusement park, the two most popular rollercoasters are the Python and the Vortex. The Python is 212 feet long and the Vortex is 210 feet long. How many times as long is the Python as the Vortex?
Answer:
About 1.01 times longer
Step-by-step explanation:
we have to divide 212 by 210 since these are the lengths to get about 1.01.
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Hey can you help me with my homework also can you tell me the points so I can put them into the graphs
Step 1
Find the equation of f(x)
[tex]\begin{gathered} The\text{ absolute value function is;} \\ y=a|x-h|+k \end{gathered}[/tex][tex]From\text{ the graph the vertex \lparen h,k\rparen is 3,3}[/tex][tex]\begin{gathered} h=3,k=3 \\ y=1,x=5 \end{gathered}[/tex][tex]1=a|5-3|+3[/tex][tex]\begin{gathered} 1=2a+3 \\ 2a=1-3 \\ 2a=-2 \\ \frac{2a}{2}=-\frac{2}{2} \\ a=-1 \end{gathered}[/tex]Thus f(x) will be;
[tex]y=-1|x-3|+3[/tex]Step 2
Find the equation of y= -f(x) then plot the graph
[tex]\begin{gathered} y=-(-1|x-3|+3) \\ y=1\left|x-3\right|-3 \end{gathered}[/tex]Thus the graph using the points below will look like;
[tex](-4,4),(0,0),(3,-3),(6,0),(8,2)[/tex]Introduction to Chord LengthsINPlace the following expressions so that they can be used to solve for X11 781211 7.8 1211 INN111712
SOLUTION
We know that the diameter of the circle is 18.8.
Therefore the value of its radius will be.
[tex]\frac{18.8}{2}[/tex]And we also know that the radius from the diagram is:
[tex]x+4.2[/tex]So we can equate both equations together to have an idea of what will give us the value of x.
[tex]\begin{gathered} \frac{18.8}{2}=x+4.2 \\ \text{Collect like terms} \\ \frac{18.8}{2}-4.2=x \end{gathered}[/tex]So going by the above solutions, the answers we will drag into the two boxes will be the 4th expression and the 6th expression
THAT IS:
[tex]\begin{gathered} \frac{18.8}{2} \\ \text{and} \\ -4.2 \end{gathered}[/tex]Identify the normal equations of an exponential curve.ΣxY = AΣx + BΣx2 and ΣY = nA + BΣxΣxY = AΣx + BΣx2 and ΣY = A + BΣxΣxY = AΣx - BΣx2 and ΣY = nA + BΣxΣxY = AΣx + BΣx2 and ΣY = nA - BΣx
Given
The normal equations of an exponential curve.
Solution
[tex]The\text{ exponential equation is y=ax}^b[/tex]taking logarithm on both sides, we get
[tex]\begin{gathered} log10y=log10a+blog10x \\ \\ Y=A+bXwhereY=log10y,A=log10a,X=log10x \end{gathered}[/tex]which linear in Y,X
So the corresponding normal equations are
[tex]\begin{gathered} ∑Y=nA+b∑X \\ \\ ∑XY=A∑X+b∑X2 \end{gathered}[/tex]The final answer
Option A
Given vector v equals open angled bracket negative 11 comma negative 5 close angled bracket comma what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.
We will begin by finding the magnitude of a vector, denoted |v|.
The formula we can use is
[tex]|v|=\sqrt{a^2+b^2}[/tex]where a and b represent the vector components. Since we are given the vector <-11,-5>, we will let a be -11 and b is -5.
Substituting those values, we have
[tex]\begin{gathered} |<-11,-1>|=\sqrt{(-11)^2+(-5)^2} \\ \sqrt{121+25} \\ \sqrt{146} \\ \approx12.083 \end{gathered}[/tex]So far, your answer is either the first option or the second option.
Next, we want to find the direction of the vector. We can use another helpful formula:
[tex]\tan\theta=\frac{b}{a}[/tex]Substituting our original values for a and b, we have:
[tex]\tan\theta=\frac{-5}{-11}[/tex]Be careful here! Since the both the a-value and b-value are negative, we are going to be in the third quadrant. After finding our angle (which will be in quadrant 1), we will need to add 180 degrees.
Take the inverse tangent of both sides to get the angle:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{-5}{-11}) \\ \theta\approx24^{\circ} \end{gathered}[/tex]We'll add 180 degrees to get our final angle:
[tex]24+180=204[/tex]Since our final angle is 204 degrees, the correct answer is the second option.
Answer:
12.083; 24°
explanation:
Magnitude of v = sqrt((-11)^2 + (-5)^2)
Direction of v = atan(-5 / -11)
Calculating these values:
Magnitude of v = sqrt(121 + 25) ≈ 12.083 (rounded to the thousandths place)
Direction of v = atan(-5 / -11) ≈ 0.435 radians
Converting radians to degrees:
The direction of v ≈ 0.435 * (180 / π) ≈ 24.881° ≈ 24° (rounded to the nearest degree)
Therefore, the correct answer is 12.083; 24°.
calculate the surface area of a tetrahedron with four faces and a base of 1 square foot and a height of 0.866 foot
The surface area is given by:
[tex]SA=B+\frac{1}{2}ph[/tex]Where:
B = Area of the base
h = height
p = Perimeter of the base
so:
[tex]\begin{gathered} SA=1+\frac{1}{2}(4)(0.866) \\ SA=2.732ft^2 \end{gathered}[/tex]What is the the musical instrument that is a pair of clash cymbals, originating in the Indian subcontinent, which makes high- pitched percussion sounds?
SOLUTION:
Step 1:
In this question, we are asked to find the musical instrument that is a pair of clash cymbals, originating in the Indian subcontinent, which makes high- pitched percussion sounds.
Step 2:
The details of the solution are as follows:
The Taal is a pair of clash cymbals, originating in the Indian subcontinent, which makes high-pitched percussion sounds. In its simplest form, it consists of a pair of small hand cymbals.
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GIVEN: P(N) = 0.25 and P(R) = 0.6If the probability of P(N R) = 0.15, are N and Rindependent events?a) Yes, because P(N) + P(R) +0.15b) No, because P(N).P(R) +0.15c) Yes, because P(N) X P(R) = 0.15d) Not enough information
P(N∩R) represents the probability of A and B.
When two events are independent events, the joint probability is calculated by multiplying their individual probabilities.
P(N∩R) For independent events:
[tex]P\mleft(N\cap R\mright)=P(N)\times P(R)[/tex]Substituting the known values for P(N) and P(R):
[tex]\begin{gathered} P(N\cap R)=0.25\times0.6 \\ P(N\cap R)=0.15 \end{gathered}[/tex]0.15 is the value of P(N∩R) given by the problem, and since we get the same result using the formula for independent events, we can affirm that N and R independent events.
Answer:
c) Yes, because P(N) X P(R) = 0.15
the sum of three consecutive integers is 267.what is that largest interger
The sum of three consecutive integers is 267. If the first one is a, then the second would be a + 1, while the third would be a + 2. Therefore, you would have;
[tex]\begin{gathered} a+(a+1)+(a+2)=267 \\ a+a+1+a+2=267 \\ 3a+3=267 \\ \text{Subtract 3 from both sides} \\ 3a=264 \\ \text{Divide both sides by 3} \\ a=88 \end{gathered}[/tex]The largest (third) integer is a + 2, therefore
[tex]\begin{gathered} a+2=88+2 \\ a+2=90 \end{gathered}[/tex]The largest integer therefore is 90.
Find the perimeter of each circle. Use 3 for pi.
Part 1
We need to find the perimeter of a circle with a diameter of 18 inches.
The relation between the perimeter P and the diameter d is given by:
[tex]P=\pi d[/tex]Since d = 18 inches and we need to use 3 for π, we obtain:
[tex]P=3\cdot18\text{ inches }=54\text{ inches}[/tex]Therefore, the ribbon needs to be 54 inches long.
Part 2
We need to find the perimeter of a semicircle with a radius of 8 in.
The perimeter of this semicircle is the sum of half the perimeter of the whole circle and the line segment formed by two radii.
The relation between the perimeter P and the radius r of a circle is:
[tex]P=2\pi r[/tex]Thus, half the perimeter is:
[tex]\frac{P}{2}=\pi r[/tex]Since we need to use 3 for π and r = 8 in, we obtain:
[tex]\frac{P}{2}=3\cdot8\text{ in }=24\text{ in}[/tex]And the line segment measures:
[tex]2\cdot8\text{ in }=16\text{ in}[/tex]Therefore, the perimeter of the calzone is:
[tex]24\text{ in }+16\text{ in }=40\text{ in}[/tex]Answer: 40 in.
The glass portion of a small window is 12 inches by 24 inches. The framework on each side adds on x inches. Express the area of the entire window as a function of x. 72 + x square inches 36+x square inches x² + 36x + 288 square inches 288 + x² square inches
The area of the entire window expressed as a function of x is x²+36x+288 square inches
How to express the area of the window as a function of x?
Given that: The glass portion of a small window is 12 inches by 24 inches
The framework on each side adds on x inches
That means (x+12) by (x+24) inches. This is the representation of the area of the entire window as a function of x. Thus:
(x+12)(x+24) = x(x+24) + 12(x+24) (Clear the brackets)
= x²+24x+12x+288 (Add like terms)
= x²+36x+288 in²
Therefore, the area of the entire window as a function of x is x²+36x+288 square inches
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1 Write the missing power of ten.0.04 x 10 = 0.4
Notice that in the number 0.4, the decimal point appears shifted one place to the right with respect to the number 0.04. When we multiply a number by the power 10^n, the decimal point is shifted n places to the right. Therefore, the power of 10 needed to move the decimal point from 0.04 one place to the right to get 0.4 is 1.
Therefore, the missing power of the base 10 is:
[tex]1[/tex]So, we can write:
[tex]0.04\times10^1=0.4[/tex]options 1. a (-3,50) b (-2,0) c (0,-4) d (1,-6) 2. a (-3,50) b (0,-4) c (-1,-6) d (2,0)3. a (-3,50) b (-2,0) c (0,-4) d (2,0)
Answer:
The x-intercepts shown in the table are (-2, 0) and (2, 0).
The y-intercept shown in the table is (0, -4)
Explanation:
The x-intercepts are the points where the value of f(x) is 0. Then, these points are (-2, 0) and (2, 0)
Additionally, the y-intercept is the point where the value of x is 0, so the y-intercept is (0, -4).
Then, the answers are:
The x-intercepts shown in the table are (-2, 0) and (2, 0).
The y-intercept shown in the table is (0, -4)
Suppose that a regression line for some data transformed with logarithmspredicts that when y equals 8, log(%) will equal 1.603. What does theregression line predict y will equal when y equals 8? Round your answer to thenearest whole number.
Given the relationship between y and x to be
[tex]y=a^x\text{ ------ equation 1}[/tex]Take the logarithm of both sides,
[tex]\begin{gathered} \log y=\log ^{}_{}a^x \\ \Rightarrow\log \text{ y = x }\times\text{ log a ---- equation 2} \end{gathered}[/tex]But when x = 8, log y = 1.603.
Thus, substituting the above values into equation 2, we have
[tex]\begin{gathered} 1.603\text{ = 8 }\times\text{ log a} \\ \text{divide both sides by 8} \\ \log \text{ a= }\frac{1.603}{8} \\ \Rightarrow\log \text{ a =0.2}004 \\ \text{Thus, } \\ a=1.586 \end{gathered}[/tex]From equation 1,
[tex]\begin{gathered} y=a^x \\ \Rightarrow y=1.586^x\text{ ----- equation 3} \end{gathered}[/tex]Thus, when x = 8
[tex]\begin{gathered} y=1.586^x \\ y=1.586^8 \\ \Rightarrow y=40.03 \end{gathered}[/tex]Thus, the value of y will be 40 (to the nearest whole number)
The correct option is D
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $15. For one performance,there were 50 tickets sold in all, and the total amount paid for them was $1275. How many tickets of each type were sold?
Given:
there are two types of tickets to a show: advance and same-day
Let the number of tickets from the type of Advance = x
And the number of tickets from the type of Same-day = y
there were 50 tickets sold in all
So,
[tex]x+y=50\rightarrow(1)[/tex]Advance tickets cost $30 and same-day tickets cost $15.
the total amount paid for them was $1275
So,
[tex]30x+15y=1275\rightarrow(2)[/tex]Solve the equations (1) and (2) to find (x) and (y)
[tex]\begin{gathered} x+y=50\rightarrow(\times-15) \\ 30x+15y=1275 \\ ============= \\ -15x-15y=-750 \\ 30x+15y=1275 \\ ============= \\ 15x=525 \\ x=\frac{525}{15}=35 \\ y=50-x=50-35=15 \end{gathered}[/tex]So, The answer will be:
The number of tickets from the type of Advance = x = 35
And the number of tickets from the type of Same-day = y = 15
Determine algebraically if f(x)=x^2-8 is a function even, odd, or neither.
For a function to be even, it has to meet the following condition:
[tex]f(x)=f(-x)[/tex]To check if the given is an even function, evaluate the function at x and -x:
[tex]\begin{gathered} f(x)=x^2-8 \\ f(-x)=(-x)^2-8=x^2-8 \\ f(x)=f(-x) \end{gathered}[/tex]It means that the function is even.
For a function to be odd, it has to meet this condition:
[tex]f(-x)=-f(x)[/tex]We already know the values of f(-x) and f(x) and from this we can state that the function is not odd.
. Kelly makes $475 per week as an assistant I the human resource department of a law firm. What is her annual salary?
Week salary = $475
In a year there are 52 weeks
Use a rule of three to find the answer
1 week --------------------$475
52 weeks ----------------- x
x = (52 x 475) / 1
x = $24700
Her annual salary is $24700
what would the length of segment BC have to be in order for line BC to be tangent to circle
Given data:
The first given length is AC=53.
The second given length is AB= 45.
The expression for the Pythagoras theorem is,
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ (45)^2+BC^2=(53)^2 \\ BC^2=784 \\ BC=28 \end{gathered}[/tex]Here, consider only positive sign of BC length as side cannot negative.
Thus, the BC length is 28.
how many FULL cases of oil can you get from a 150-gallon oil tank?
Given
The job is to fill the quart size of bottles, from a full 150 gallon oil tank.
And, the oil is packed into 24 quart's of oil.
To find the number of full cases of oil.
Explanation:
It is given that,
The total amount of oil is 150 gallon.
The number of cases it has to be filled is, 24.
Then, the number of the full cases of oil is,
[tex]\begin{gathered} Number\text{ of full cases of oil}=\frac{150}{24} \\ =\frac{50}{8} \\ =\frac{25}{4} \\ =\frac{24}{4}+\frac{1}{4} \\ =6+\frac{1}{4} \\ =6\frac{1}{4} \end{gathered}[/tex]Hence, the number of full cases of oil is 6.
identify the beginning of a sample period for the function
Given:
[tex]f(t)\text{ = 2csc\lparen t + }\frac{\pi}{4})-1\text{ }[/tex]The graph of f(t) is shown below:
From the graph, we can see that
[tex]x=\text{ }\frac{\pi}{4}\text{ is a good start for the period of f\lparen t\rparen}[/tex]Answer: Option D
Write a recursive definition for the following function. 40, 120,360,1080,3240
The recursive definition of the given geometric series is [tex]40 \times (3)^n[/tex]
What is geometric series?
Geometric series are those series in which ratio between the consecutive terms of the series are same.
Here the series is in geometric progression with a common ratio of 3
and first term 40
So the recursive definition of the given geometric series is [tex]40 \times (3)^n[/tex]
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What are the solution(s) to the quadratic equation 9x² = 4?O x = and x = -- 90x = ² and x = -1/33O= and x = --X=no real solutionM/NK
Given:
The quadratic equation is:
9x² = 4
Required:
Find the solutions to the given equation.
Explanation:
The given equation is:
[tex]9x²=4[/tex]Divide both sides by 4.
[tex]x^2=\frac{4}{9}[/tex]Take the square root on both sides.
[tex]\begin{gathered} x=\pm\sqrt{\frac{4}{9}} \\ x=\pm\frac{3}{2} \end{gathered}[/tex]the solutions to the equation are
[tex]x=\frac{3}{2}\text{ and x =-}\frac{3}{2}[/tex]Final Answer:
Option third is the correct answer.
Find the slope of the line that goes through the points (14,-13) and (2,3).
Answer
The slope of the line is -4/3
Step-by-step explanation:
Given the following coordinates point
(14, -13) and (2, 3)
Slope = rise / run
rise = y2 - y1
run = x2 - x1
Slope = y2 - y1 / x2 - x1
Let; x1 = 14, y1 = -13, x2 = 2, and y2 = 3
Slope = 3 - (-13) / 2 - 14
Slope = 3 + 13 / - 12
Slope = 16 / -12
Slope = -4/3
Hence, the slope of the line is -4/3
Use the Law of Cosines to determine the indicated angle 0. (Assume a = 65.01, b = 36.38, and c = 42.05. Round your answer to two decimal places.)
a = 65.01, b = 36.38, and c = 42.05.
And it is required to find the measure of angle 0 which will be the angle B
Using the law of cosine
[tex]\begin{gathered} b^2=a^2+c^2-2\cdot a\cdot c\cdot\cos B \\ \cos B=\frac{a^2+c^2-b^2}{2\cdot a\cdot c}=\frac{65.01^2+42.05^2-36.38^2}{2\cdot65.01\cdot42.05}=0.854 \\ \end{gathered}[/tex][tex]\angle\emptyset=\angle B=\cos ^{-1}0.854=31.31[/tex]the answer is rounded to two decimals
I need help with my math
help!!! thanks :))))))
The length of given sides BC = 38 and EF = 38.
Given:
ΔABC ≅ ΔDEF
BC = x + 30 , EF = 4x + 6
we know that
BC = EF
x + 30 = 4x + 6
30 - 6 = 4x - x
24 = 3x
divide by 3 on both sides
3x/3 = 24/3
x = 8
BC = x + 30
= 8 + 30
= 38
EF = 4x + 6
= 4*8 + 6
= 32+6
= 38
Therefore the length of given sides BC = 38 and EF = 38.
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