we can do a subtraction to calculate the savings
[tex]14.99-11.53=3.46[/tex]will save 3.46 buying store-brand laundry detergent
and your savings from using the coupon are 1.95
We make a subtraction between the savings to know how much you save more with one method than with the other
[tex]3.46-1.95=1.51[/tex]she save $1.51 more buying store-brand
A deep-dish pizza is cut into twelve equal slices. If you eat four slices, how manydegrees of pizza do you eat?240°120°45°90°
The shape of the pizza is circular. This means that the total angle possible is 360 degrees.
Since the pizza have 12 equal slices
Then each slice will represent
[tex]\frac{360}{12}=30^0[/tex]Therefore, If you decide to eat 4 four slices, then
you will eat
[tex]4\times30^0=120^0[/tex]Answer = 120 degrees
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
The length of BC is 29 units (solved using trigonometry and its applications).
What is trigonometry?
Trigonometry (from Ancient Greek v (trgnon) 'triangle' and (métron)'measure') is a field of mathematics that explores the correlations between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. The Greeks concentrated on chord computation, whereas Indian mathematicians established the first-known tables of values for trigonometric ratios (also known as trigonometric functions) such as sine. Trigonometry has been used throughout history in geodesy, surveying, celestial mechanics, and navigation. Trigonometry is well-known for its many identities. These trigonometric identities are frequently used to rewrite trigonometrical expressions with the goal of simplifying an expression, finding a more usable form of an expression, or solving an equation.
Let the point where AB is cut through line from C be D
This can be solved using trigonometry and its applications.
In triangle ACD,
tan 45° = CD/AD
or, CD = tan 45° x AD
= 1 x 20
= 20 units
In triangle CDB,
tan Ф = CD/BD
or, Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
or, BC = CD/sin 43.6°
= 20/0.689
= 29 units
The length of BC is 29 units.
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Answer:
29
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/SQRT2
4. McKenzie wants to determine which ice cream option is the best choice. The chart below gives the description and prices for her options. Use the space below each item to record your findings. Place work below the chart. A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter. A cone has a 2-inch diameter and a height of 4.5 inches. A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches. a. Determine the volume of each choice. Use 3.14 to approximate pi. b. Determine which choice is the best value for her money. Explain your reasoning. (That means some division, you decide which.) $2.00 $3.00 $4.00 One scoop in a сир Two scoops in a cup Three scoops in a cup Half a scoop on a cone filled with ice cream A cup filled with ice cream (level to the top of the cup)
McKenzie wants to determine which ice cream option is the best choice.
Part (a)
Volume of Scoop:
A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter.
The volume of the sphere is given by
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]Where r is the radius.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a scoop of ice cream is
[tex]V_{\text{scoop}}=\frac{4}{3}\cdot3.14\cdot(1)^3=\frac{4}{3}\cdot3.14\cdot1=4.19\: in^3[/tex]Therefore, the volume of a scoop of ice cream is 4.19 in³
Volume of Cone:
A cone has a 2-inch diameter and a height of 4.5 inches.
The volume of a cone is given by
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the cone.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{2}{2}=1[/tex]So, the volume of a cone of ice cream is
[tex]V_{\text{cone}}=\frac{1}{3}\cdot3.14\cdot(1)^2\cdot4.5=\frac{1}{3}\cdot3.14\cdot1^{}\cdot4.5=4.71\: in^3[/tex]Therefore, the volume of a cone of ice cream is 4.71 in³
Volume of Cup:
A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches.
The volume of a right circular cylinder is given by
[tex]V=\pi\cdot r^2\cdot h[/tex]Where r is the radius and h is the height of the right circular cylinder.
We know that radius is half of the diameter.
[tex]r=\frac{D}{2}=\frac{3}{2}=1.5[/tex]So, the volume of a cup of ice cream is
[tex]V_{\text{cup}}=3.14\cdot(1.5)^2\cdot2=3.14\cdot2.25\cdot2=14.13\: in^3[/tex]Therefore, the volume of a cup of ice cream is 14.13 in³
Part (b)
Now let us compare the various given options and decide which option is the best value for money
Option 1:
The price of one scoop in a cup is $2
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{4.19}{\$2}=2.095\: [/tex]Option 2:
The price of two scoops in a cup is $3
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{2\cdot4.19}{\$3}=2.793\: [/tex]Option 3:
The price of three scoops in a cup is $4
The volume of one scoop of ice cream is 4.19 in³
[tex]rate=\frac{3\cdot4.19}{\$4}=3.1425[/tex]Option 4:
The price of half a scoop in a cone is $2
The volume of one scoop of ice cream is 4.19 in³
The volume of one cone of ice cream is 4.71 in³
[tex]rate=\frac{\frac{4.19}{2}+4.71}{\$2}=\frac{2.095+4.71}{\$2}=\frac{6.805}{\$2}=3.4025[/tex]Option 5:
The price of a cup filled with ice cream is $4
The volume of a cup is 14.13 in³
[tex]rate=\frac{14.13}{\$4}=3.5325[/tex]As you can see, the option 5 (a cup filled with ice cream) has the highest rate (volume/$)
This means that option 5 provides the best value for money.
Therefore, McKenzie should choose "a cup filled with ice cream level to the top of cup" for the best value for money.
Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }
The Solution:
The given expression is
[tex]\frac{8}{1-\sqrt[]{17}}[/tex]Rationalizing the expression with the conjugate of the denominator, we have
[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]This becomes
[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]Thus, the correct answer is
[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]What is the value of the expression below?2,816 x 714,57214,67219,61219,712
The given expression is
[tex]2,816\times7[/tex]We just have to multiply.
[tex]2,816\times7=19,712[/tex]Hence, the right answer is D.A scale drawing of a game room is shown below:A rectangle is shown. The length of the rectangle is labeled 2 inches. The width of the rectangle is labeled 4.5 inches. The scale is 1 to 30.What is the area of the actual game room in square feet? Round your answer to the nearest whole number.9 ft223 ft256 ft2270 ft
The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.
Since the length is labeled 2 inches, the real length of the room is:
[tex]2in\times30=60in[/tex]Since the width is labeled 4.5 inches, the real with of the room is:
[tex]4.5in\times30=135in[/tex]1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:
[tex]\begin{gathered} 60in=60in\times\frac{1ft}{12in}=5ft \\ \\ 135in=135in\times\frac{1ft}{12in}=11.25ft \end{gathered}[/tex]Multiply the width and the length to find the area of the room:
[tex]A=(5ft)(11.25ft)=56.25ft^2\approx56ft^2[/tex]Therefore, to the nearest whole number, the area of the game room is 56ft^2.
gabrielle opened a savings account and deposited $800.00 . the account earns 2% interest compounded annually.
We need the actual question. I can write the compounded interest accrued value equation for this, but if no question about number of years the deposit is kept, there is no question to be solved. Please continue the formulation of the question. What is it we need to find? what amount of money she needs to collect?
The formula for accrued value with compounded interest would be written as:
[tex]A=P(1+r)^t[/tex]with the information on the account, we can write it as:
[tex]A=800(1+0.02)^t[/tex]but we cannot do anything with it unless you give:
1) the time to keep the account collecting interest,
OR
2) the total amount of money she needs to obtain.
What is the value of that new bicycle she wants?
Well, you have the equation needed. If you don't give me more info on what is needed, I cannot help you solve the equation. We need an extra piece of information.
The information now provided is that the person wants to keep the savings account for 2 years. So we use t = 2 in the equation above to obtain the answer:
[tex]A=800(1.02)^2=832.32[/tex]At the end of the two years she will have a total of $832.32
PLEASE HELP I JUST NEED TO KNOW THE POINTS AND HOW THE GRAPH LOOKS LIKE
You have the following function:
[tex]g(x)=2x^2-4x-16[/tex]the x coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]in this case, a = 2 and b = -4. Replace these values into the previous expression and simplify:
[tex]x=-\frac{-4}{2(2)}=1[/tex]next, replace the previous values of x into the function g(x):
[tex]\begin{gathered} g(1)=2(1)^2-4(1)-16 \\ g(1)=-18 \end{gathered}[/tex]then, the vertex is (1,-18)
In order to graph, calculate another point for any value of x, for instance, for x = 0:
g(0) = 2(0)^2 - 4(0) - 16
What is f(2) - f(0) answer choices:A) 1B) 2C) 3D) 4
The points of the graph of a function f(x) have the form (x,f(x)). This means that the values of f(0) and f(2) are the y-values of the points in the graph that have 0 and 2 as their x-values. If you look at the graph you'll notice that the points (0,1) and (2,4) are part of the graph which implies that:
[tex]\begin{gathered} (0,f(0))=(0,1)\rightarrow f(0)=1 \\ (2,f(2))=(2,4)\rightarrow f(2)=4 \end{gathered}[/tex]Then we get:
[tex]f(2)-f(0)=4-1=3[/tex]AnswerThen the answer is option C.
Find the equation for the line through points (-3,1) and (4,7) use y=Mx+b
A = (-3, 1) and B = (4,7)
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{7-1}{4-(-3)}=\frac{6}{7}[/tex][tex]y=\frac{6}{7}x+b[/tex]Now, for b, using point B
[tex](7)=\frac{6}{7}(4)+b[/tex][tex]b=7-\frac{6}{7}(4)\rightarrow b=\frac{25}{7}[/tex][tex]y=\frac{6}{7}x+\frac{25}{7}[/tex]Perform the indicated operation of multiplication or division on the rational expression and simply.
The rational expression is given as,
[tex]\frac{15x}{2y^3}\cdot\frac{12y^2}{5x}[/tex]Performing the division and multiplication in the given rational expression,
[tex]\frac{15x}{2y^3}\cdot\frac{12y^2}{5x}=\frac{3\times6\times y^3}{y^2}[/tex][tex]\frac{3\times6\times y^3}{y^2}=\frac{18}{y}[/tex]The rational expression after using the indicated operation we get,
[tex]\frac{18}{y}\text{.}[/tex]I need help please and thank you and you have to graph it
From the graph provided we can determine two points which are;
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(2,0) \end{gathered}[/tex]For the equation of the line given in slope-intercept form which is;
[tex]y=mx+b[/tex]We would begin by calculating the slope which is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can now substitute the values shown above and we'll have;
[tex]\begin{gathered} m=\frac{(0-\lbrack-3\rbrack)}{2-0} \\ m=\frac{0+3}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;
[tex]\begin{gathered} y=mx+b \\ \text{Where;} \\ x=0,y=-3,m=\frac{3}{2} \end{gathered}[/tex]We now have the equation as;
[tex]\begin{gathered} -3=\frac{3}{2}(0)+b \\ -3=0+b \\ b=-3 \end{gathered}[/tex]We now have the y-intercept as -3. The equation now is;
[tex]\begin{gathered} \text{Substitute m and b into the equation,} \\ y=mx+b \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]The graph of this is now shown below;
We shall now draw lines to indicate the 'rise' and 'run' of this graph.
ANSWER
Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).
This clearly defines the slope of the equation that is;
[tex]\frac{\Delta y}{\Delta x}=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{3}{2}[/tex]Write a pair of complex numbers whose sum is -4 and whose product is 53
The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.
How to calculate the he value?Let the numbers be represented as a and b.
Therefore a + b = -4 .....i
a × b = 53 ........... ii
From equation I, a = -4 - b
Put this into equation ii
ab = 53
(-4 - b)b = 53
-b² - 4b = 53
Equate to 0
-b² - 4b - 53 = 0
The value can be found using the Almighty formula
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This is lines, functions and systems. Graph the line with slope 2/3 passing through the point (2, 1).
Note that the slope is expressed as :
[tex]\text{slope}=\frac{\text{rise}}{\text{run}}[/tex]From the given, the slope is 2/3
[tex]\text{slope}=\frac{\text{rise}}{\text{run}}=\frac{2}{3}[/tex]So it means that from the point (2,1)
You need to rise 2 units upward and run 3 units to the right
It will be look like this :
Next step is to connect these two points by drawing a line.
That's it, the line is in blue line.
In the past, Johnny got paid $111,180 annually. Since switching to a new career, he has been making 154.1% more. How much does Johnny make now?
The amount of money that Johnny makes now = $282,508.38
What is annual payment?Annual payment is the type of payment that is done every 12 month and by the end of the year.
The initial annual payment received by Johnny= $111,180
The new career pays the rate of 154.1% more that is;
( 154.2% of $111,180 ) + $111,180 Which is;
= (154.1/100 × 111,180) + $111,180
= (17,132,838/100) + $111,180
= $ 171,328.38 + $111,180
= $282,508.38.
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how many millielters are in 1/5 liters
We know,
1 liter=1000 milliter.
So, millilters in 1/5 liters is,
[tex]\frac{1}{5}liter\times\frac{1000\text{ milliter}}{1\text{ liter}}=200\text{ milliter}[/tex]Therefore, there are 200 milliters in 1/5 liters.
fred had a tray of brownies for his birthday. he ate 1/6 of the brownies by himself and his family ate 1/3 of the brownies how many brownies did fred and his family eat altogether
We want to know how many brownmies did Fred and his family eat together.
We will call to the total of the brownies by 1. On this case, after Fred ate 1/3 of the brownies, he will have:
[tex]1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}[/tex]This means that he has left 2/3 of the brownies. After his family ate 1/6 of the brownies:
[tex]\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}[/tex]This means they will have left 1/2 of the tray of brownies, and that they ate half of it.
Solve for x
4x = -5
Put the answer in its simplest form.
Answer:
[tex] \sf x=-1.25 [/tex]
[tex]\sf--------------------------------------------------------------------- [/tex]
Step-by-step explanation:
4x = -5
Divide both sides by 4 to single out the variable
4x/4 = -5/4
x = -1.25
I don’t know how to find the value of x. Geometry is so confusing too me, i can never understand it no matter how many times i re-read my instructions.
The value of x = 40°
Explanation:To solve for x, we will use an illustration:
When two lines intersect, the angles opposite each other are vertical angles. Vertical angles are equal.
The angles marked in magenta are equal.
The angle by the right in magenta colour will also be 52°.
The sum of angles in a triangle = 180°
x° + 52° + 88° = 180°
x + 140 = 180
subtract 140 from both sides:
x + 140 - 140 = 180 - 140
x = 40°
A baker need 2/3 cup of sugar,but he can only find a 1/2 cup measure,so he decides to estimate, Which of the following would result in the correct amount of sugar?A)One Full scoop plus 1/3 of a scoopB)One Full scoop plus 1/2 of a scoop C) Two ScoopsD)3/4 of a scoop
He needs 2/3 cup of sugar . But he can only find 1/2 cup measures.
[tex]6x - 9y - 7x + - 6y[/tex]simplify please
6x - 9y - 7x + -6y
To simplify the expression add the like terms
The like terms are the terms which have the same variable and same degree
6x, -7x are like terms
-9y, -6y are like terms
So let us add them
(6x + -7x) + (-9y + -6y)
6 + -7 = -1
6x + -7x = -x
-9 + - 6 = -15
-9y + -6y = -15y
(6x + -7x) + (-9y + -6y) = -x + -15y
Remember (+)
I Need some help on this assignment Also the second half to the problem how much will be spent on the job from the 10 to 20th day
Explanation
[tex]f(x)=4.1x+1.9[/tex]
where x is the number of days since the start of the job
and f(x) is the rate of change
Step 1
a)find the total expenditure if the job takes 12 days
so, as x represents the number of days, just replace and calculate
let x= 12
[tex]\begin{gathered} f(x)=4.1x+1.9 \\ f(12)=4.1(12)+1.9 \\ f(12)=49.2+1.9 \\ f(12)=51.1 \end{gathered}[/tex]so
a) 51.1
Step 2
now, let's find the total spent on the job from the 10 to 20th day
a) find the x value ( number of days since the job started)
x= 20 days-10dys= 10
so
x= 10
The convex polygon below has 8 sides. Find the value of x.140°11801270153013401561170
Explanation
The formula for calculating the sum of interior angles in a polygon is ( n − 2 ) × 180 ∘ where is the number of sides.
[tex](n-2)\cdot180=\text{ Sum of internal angles}[/tex]Step 1
find the sum of the internal angles in the given polygon
Let
number of sides = 8
Now, replace
[tex]\begin{gathered} (n-2)\cdot180=\text{ Sum of internal angles} \\ (8-2)\cdot180=\text{ Sum of internal angles} \\ 6\cdot180=\text{Sum of internal angles} \\ 1080=\text{Sum of internal angles}\rightarrow equation(1) \end{gathered}[/tex]Step 2
now, we have the other angles, so
sum of internal angles is:
[tex]\text{angle}1+\text{angle}2+\text{angle}3+\text{angle}4+\text{angle}5+\text{angle}6+\text{angle}7+\text{angle}8=\text{ sum of the internal angles}[/tex]replace
[tex]\begin{gathered} 127+140+118+153+156+117+x+132=\text{ Sum of internal angles} \\ x+943=\text{Sum of internal angles}\rightarrow equation\text{ (2)} \end{gathered}[/tex]hence
[tex]x+945=1080[/tex]subtract 945 in both sides to solve for x
[tex]\begin{gathered} x+945=1080 \\ x+945-945=1080-945 \\ x=135 \end{gathered}[/tex]i hope this helps you
Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
The correct option is negative 23 over 14 times j plus negative 1 over 15
Given,
The expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
The expression; -1/7j + 2/5 - 3/2j + 7/15
negative one seventh j = - 1/7j
two fifths = 2/5
three halves j = 3/2 j
seven fifteenths = 7/15
Now,
Substitute the values;
- 1/7j + 2/5 - 3/2j - 7/15
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Therefore,
The correct option is negative 23 over 14 times j plus negative 1 over 15
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g(n) = n2 − 4
h(n) = n − 5
Find g(n) · h(n)
g(x) = 4x + 4
f(x) = x3 − 1
Find (g ◦ f)(x)
The value of
g(n) · h(n) = n³ - 5n² - 4n + 20 (g ◦ f)(x) = 4x³What is function?The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
g(n) = n² − 4, h(n) = n − 5
g(n).h(n)
= (n² − 4).(n-5)
= n³ - 5n² - 4n + 20
and, g(x) = 4x + 4, f(x) = x³ − 1
(gof)(x)
=g(f(x))
=g(x³-1)
= 4(x³-1) + 4
= 4x³ - 4 + 4
= 4x³
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can anyone help me i have a picture of my math question
Answer:
-8, -5, -2, 1, 4
Explanation:
The given sequence is an arithmetic sequence -8, -5, -2 ....
The nth term of the sequence is expressed as;
Tn = a+ (n-1)d
a is the first term = -8
d is the common difference = -5 -(-8) = -2-(-5)
d = -5+8 = -2+5 = 3
Get the 4th term;
n = 4
T4 = -8+(4-1)*(3)
T4 = -8+3(3)
T4 = -8+9
T4 = 1
Get the 5th term:
n = 5
T5 = -8 + (5-1)*3
T5 = -8+4(3)
T5 = -8 + 12
T5 = 4
Hence the next two terms of the sequence are 1 and 4
The ice skating rink charges $5 for a skate rental and $3 for every hour that you skate. What would be the equation you would use to determine how much you would need to pay?
If we use the variable t to represent the number of hours skating, the fixed price is $5 and the variable price is $3 per hour, that is, we have a variable cost of 3t.
So the final cost (variable C) is the sum of the fixed and variable costs:
[tex]C=5+3t[/tex]A box is filled with shoe boxes. Each shoe box has a volume of 1 cubic foot. Six shoe boxes can fit in each layer and the height of the box is 4 feet. What is the volume of the box?
shoe box = 1 cubic foot = 1 * 1 * 1
1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot
Box height = 4 feet
Box volume = 6*4*1 = 24 feet
Rebecca makes four payments a year of $255 each for life
insurance; two payments of $455.35 each for real estate taxes;
and six payments of $66.21 each for auto insurance. How
much must Rebecca put into fixed savings each month to
cover her annual expenses for life insurance, auto insurance
and real estate taxes?
The amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes is $ 194.
Given that:-
Amount invested in life insurance = $ 255
Number of payments in life insurance = 4
Amount invested in real estate taxes = $ 455.35
Number of payments in real estate taxes = 2
Amount invested in auto insurance = $ 66.21
Number of payments in auto insurance = 6
We have to find the amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes.
Hence,
Total amount put by Rebecca in a year = 255*4 + 455.35*2 + 66.21*6 = 1020 + 910.70 + 397.26 = $ 2,327.96
Amount put by Rebecca in a month = 2327.96/12 = $ 193.997 ≈ $ 194
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(b) Construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone. Round the answers to at least three decimal places.
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24
who have an Android phone is
SEE PHOTO
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.
In the given question,
We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.
A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is
..............< p <...............
We have to construct the 90% confidence interval.
From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.
So the total number of cell phone owners aged 18 - 24 is 240.
So n=240
From them 108 have an android phone.
So x=108
Estimation of sample proportion([tex]\hat p[/tex]) = x/n
Now putting the value
Estimation of sample proportion([tex]\hat p[/tex]) = 108/240
Estimation of sample proportion([tex]\hat p[/tex]) = 0.45
Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone
C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]
As we know that
[tex]\hat p=0.45[/tex]
Now finding the value of [tex]z_{\alpha /2}[/tex]
We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90
So [tex]\alpha[/tex] = 1-0.90
So [tex]z_{\alpha /2}=z_{0.10 /2}[/tex]
[tex]z_{\alpha /2}=z_{0.05}[/tex]
From the standard z table
[tex]z_{0.05}[/tex] = 1.645
Now putting the value in the
C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})[/tex]
Simplifying
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})[/tex]
C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})[/tex]
C.I. = [tex](0.45 \pm 1.645\sqrt{0.001031})[/tex]
C.I. = [tex](0.45 \pm 1.645\times0.0321)[/tex]
C.I. = [tex](0.45 \pm 0.053)[/tex]
We can write it as
C.I. = {(0.45+0.053),(0.45-0.053)}
C.I. = (0.503,0.397)
Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is
0.503 < p < 0.397.
To learn more about confidence interval link is here
https://brainly.com/question/24131141
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