A bridge AB is to be built across a river. The point C is located 62m from B, and angle A is 80 degrees, angle C is 60 degrees. How long is the bridge
Answers
The points A, B, and C form a triangle.
From the given information in the question, the triangle ABC can be drawn to have the following parameters:
Recall the Sine Rule. Applied to the triangle above, the rule is stated as follows:
[tex]\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]The length of the bridge is AB. Given that the measures of angles A and C, and side BC are known, the following ratio is used to solve:
[tex]\frac{BC}{\sin A}=\frac{AB}{\sin C}[/tex]Substituting known values, the length of AB is calculated as follows:
[tex]\begin{gathered} \frac{62}{\sin80}=\frac{AB}{\sin60} \\ AB=\frac{62\times\sin60}{\sin80} \\ AB=54.52 \end{gathered}[/tex]The bridge is 54.52 m long.
Related Questions
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
Answers
The total points that the four students score in round 1 is 75 points.
How to calculate the value?Based on the information given, it's important to convert the numbers to while numbers and then add.
John has 19.5. This will be 20.
Adam had 21.2. This will be 21.
Peter has 23.8. This will be 24.
Grace has 10.2. This will be 10.
The total points will be:
= 20 + 21 + 24 + 10
= 75
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The points of four students are:
John 19.5
Adam 21.2
Peter 23.8
Grace 10.2
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
Factor the common factor out of each expression (GCF).-32m^5n - 36m^6n - 24m^5n^2________________________
Answers
In order to find the greatest common factor (GCF) of the terms, first let's factor the numeric values in their prime factors:
[tex]\begin{gathered} 32=2\cdot2\cdot2\cdot2\cdot2\\ \\ 36=2\cdot2\cdot3\cdot3\\ \\ 24=2\cdot2\cdot2\cdot3 \end{gathered}[/tex]The common factor between these three numbers is the product of the common prime factors, that is, 2 * 2 = 4.
Now, to find the common factor of the variables, we choose for each variable the one with the smaller exponent:
[tex]\begin{gathered} m^5,m^6,m^5\rightarrow m^5\\ \\ n,n,n^2\rightarrow n\\ \\ \\ GCF=m^5n \end{gathered}[/tex]Therefore the common factor is -4(m^5)n.
(we can put the negative signal as well, since all terms are negative).
Compute the area of each triangle. Round to the nearest tenth.
Answers
The triangle ΔDEF has the following coordinates
[tex]\lbrace D(-1,6),E(-4,-6),F(3,-5)\rbrace[/tex]To find the area of a triangle in coordinate geometry, we have a formula. Given 3 vertices A(x1, y1), B(x2,y2) and C(x3,y3), the area of this triangle is given by
[tex]Area(\Delta ABC)=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]Using this formula for our problem, we have
[tex]Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))|[/tex]Solving this equation, we have
[tex]\begin{gathered} Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))| \\ =\frac{1}{2}|(-1)((-6+5)+(-4)(-5-6)+3(6_{}+6)| \\ =\frac{1}{2}|(-1)(-1)+(-4)(-11)+3(12)| \\ =\frac{1}{2}|1+44+36| \\ =\frac{1}{2}|81| \\ =\frac{81}{2} \\ =40.5 \end{gathered}[/tex]And this is our answer Area(ΔDEF) = 40.5
Put these numbers in order from least to greatest. -27/36, 6, 18/40, 5/20
Answers
We have four numbers. We have to know that negative numbers are "smaller" than positive numbers, and when numbers are far away from zero are even "bigger".
The least number is -27/36. It is a negative number.
We can also see that we have some fractions. A fraction is a part of "a whole".
So, as we can see 6 is not a fraction. Therefore, 6 is the greatest number from this list.
So we have the least and the greatest: -27/36 and 6, respectively.
We also need to compare 18/40 and 5/20. What fraction is bigger?
In order to compare them, we need to have two fractions with the same denominator. Then, the fraction with the greatest numerator is "bigger" than the other fraction.
Let us see:
If we divide the numerator and the denominator of 18/40 by 2, we have:
18/2 = 9
40/2 = 20
Then, the equivalent fraction is 9/20 (or 9/20 is equivalent to 18/40). Now, we can compare them:
9/20 and 5/20. So, which one is the greatest? The one with the greatest numerator: 9/20.
Our final list is this way, from least to the greatest as follows:
-27/36, 5/20, 18/40 (9/20), 6.
(1 point) For each trigonometric expression A,B,C,D, E, choose the expression from 1,2,3,4,5 that completes a fundamental identity. Enter the appropriate letter (A,B,C,D, or E) in each blank.
Answers
Answer:
Step-by-step explanation:
I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.
1 - this corresponds with C as sin^2(x)+cos^2(x)=1
1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)
cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.
sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.
tan(x) - this is sin(x)/cos(x), choice D.
What is 150% of 38.
Answers
We are asked to find 150% of 38
Step 1:
Convert the 150% to decimal by removing the % sign which means dividing by 100.
150/100 = 1.5
Step 2:
Now simply multiply the decimal percentage with the number 38
1.5×38 = 57
Therefore, 150% of 38 is found to be 57
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chefwants to make 370 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
Answers
Assuming these are volume percentages and the volumes don't change when you mix them, we can calculate this using a system of equations.
But first we need to identify each equation and variable.
let x be the volume of 7% vinegar used and y be the volume of 12% vinegar used.
The total volume is the sum of those and it must be equal to 370 mL, so:
[tex]x+y=370[/tex]The amount of vinegar in the x volume of 7% vinegar can be calculated by multiplying x by the 7%, that is, by 0.07:
[tex]0.07x[/tex]Similarly, the amount of vinegar in y is:
[tex]0.12y[/tex]So, the total amount of vinegar after the mixture is:
[tex]0.07x+0.12y[/tex]Since the percentage of the final mixture is 8%, the amount after the mixture can also be calculated by taking 8% of the final volume of 370mL, that is:
[tex]0.08\cdot370=29.6[/tex]The two ways of calculating the amount of vinegar in the mixture must be the same, so we have got our second equation:
[tex]0.07x+0.12y=29.6[/tex]So, the system of equations is:
[tex]\begin{gathered} x+y=370 \\ 0.07x+0.12=29.6 \end{gathered}[/tex]We can solve this by substitution:
[tex]\begin{gathered} x+y=370 \\ x=370-y \end{gathered}[/tex]Thus:
[tex]\begin{gathered} 0.07x+0.12y=29.6 \\ 0.07(370-y)+0.12y=29.6 \\ 0.07\cdot370-0.07y+0.12y=29.6 \\ 25.9+0.05y=29.6 \\ 0.05y=29.6-25.9 \\ 0.05y=3.7 \\ y=\frac{3.7}{0.05} \\ y=74 \end{gathered}[/tex]And, going back to the first equation:
[tex]\begin{gathered} x=370-y \\ x=370-74 \\ x=296 \end{gathered}[/tex]if the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
Answers
since n, mand r are the constants for a, b,c n=6
Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume (000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
a.
What is the yield to maturity of the bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. What is the current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Answers
a) The yield to maturity of the IOU Corporation's bond is -0.39%.
b) The current yield of the IOU Corporation's bond is 5.58%.
What is the yield to maturity?The bond's yield to maturity (YTM) is the total rate of return earned by a bondholder with all interest payments and the original principal repaid.
We can compute the yield to maturity using the following YTM formula:
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
Where:
FV = Face Value of the Bond
Price = Current Market Price
Maturity = Maturity Period.
Bond's face value = $2,000
Current date = April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume
(000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
Annual interest = $126 ($2,000 x 6.3%)
Maturity period = 16 (2037 - 2021)
Price = $2,259.4 ($2,000 x 112.97/100)
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
= [$126 + {($2,000 - $2,259.4)/16}] / [($2,000 + 2,259.4)/2]
= [$126 -$259.4)/16] / [($4,259.4)/2]
= -8.3375/2,129.7
= -0.39%
Current yield = Annual Coupon/Current Price
= 5.58% ($126/$2,259.4 x 100)
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Shown below are the scatter plots for four different data sets.Answer the questions that follow. The same response may be the correct answer for more than one question.
Answers
Solution:
Given the scatter plots below:
A scatter plot will have a negative correlation if the points form line that slants from from left to right. In other words, the variable y decreases, as x increases.
When the line formed slants from right to left, the scatter plot will have a positive correlation. In other words, the variable y increases as variable x increases.
When the points are scattered randomly, there's no correlation or relationship between the variables in the scatter plot.
Thus,
1. Dataset that indicates the strongest positive linear relationship between its two variables.
Answer: The dataset in figure 4
2. Dataset that whose correlation coefficient is closest to zero.
Answer: The dataset in figure 1.
3. Dataset that whose correlation coefficient is closest to -1.
Answer: The dataset in figure 2.
Consider the following loan. Complete parts (a)-(c) below.An individual borrowed $67,000 at an APR of 3%, which will be paid off with monthly payments of 347$ for 22 years.a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.The amount borrowed is $____ the annual interest rate is ____, the number of payments per year is _____, the loan term is _____ years, and the payment amount is _____$ b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?There are ____ payments toward the loan and the total amount paid is ____$ c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?The percentage paid toward the principal is _____% and the percentage paid for interest is ____%.(Round to the nearest tenth as needed.)
Answers
b) There are 12 payments per year for 22 years; multiply 12 by 22 to get the total number of payments:
[tex]12\times22=264[/tex]To find the total amount paid, multiply the number of payments by the payment amount:
[tex]264\times347=91,608[/tex]There are 264 payments toward the loan and the total amount paid is $91,608c) Toward principal: $67,000
Toward interest: subtract the principal from the payment amount:
[tex]91,608-67,000=24,608[/tex]Let 91,608 be the 100%, use a rule of three to find the % corresponding to the principal and interest:
[tex]\begin{gathered} Principal: \\ x=\frac{67,000\times100}{91,608}=73.1 \\ \\ Interest: \\ x=\frac{24,608\times100}{91,608}=26.9 \end{gathered}[/tex]The percentage paid toward the principal is 73.1% and the percentage paid for interest is 26.9%А ВC D0 2 4 68 10 12Which point best represents V15?-0,1)A)point AB)point Bpoint CD)point D
Answers
We have to select a point that is the best representative of the square root of 15.
We can calculate the square root of 15 with a calculator, but we can aproximate with the following reasoning.
We know that 15 is the product of 3 and 5. If we average them, we have 4.
If we multiply 4 by 4, we get 16, that is a little higher than 15.
If we go to the previous number (3) and calculate 3 by 3 we get 9, that is far from 15 than 16.
So we can conclude that the square root of 15 is a number a little less than 4.
In the graph, the point B is the one that satisfy our conclusion, as it is a point in the scale that is between 3 and 4, and closer to 4.
The answer is Point B
What is the value of the expression below?2,816 x 714,57214,67219,61219,712
Answers
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 middle school football game has four 12-minute quarters. Jason plays 8 minutes in each quarter.Which ratio represents Jason's playing time compared to the total number of minutes of playing time possible?1 to 3 2 to 33 to 24 to 1I’m
Answers
The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is
[tex]\frac{32}{48}[/tex]Simplifying it, we have
[tex]\frac{32}{48}=\frac{16}{24}=\frac{8}{12}=\frac{4}{6}=\frac{2}{3}[/tex]So, the playing ratio is 2 to 3 for Jason.
Manny opened a savings account 7 years ago the account earns 9%interest compounded monthly if the current balance is 400.00 how much did he deposit initially
Answers
We have the following:
The formula for compound interest is as follows
[tex]\begin{gathered} A=P(1+r)^t \\ \end{gathered}[/tex]A is amount (current balance 400), P is the principal ( deposit initially), r is the rate (0.07) and is the time ( 7 years)
replacing:
[tex]\begin{gathered} 400=P(1+0.07)^{7^{}} \\ P=\frac{400}{(1.07)^7} \\ P=249.09 \end{gathered}[/tex]Which means that the initial deposit was $ 249.09
Recall that two angles are complementary if the sum of their measures is 90°.
Find the measures of two complementary angles if one angle is 18° more than two times
the other angle.
The smaller angle measures
...
Answers
Complementary angles - The smaller angle is 24 degrees in size.
what are complementary angles?
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
Let x equal the first angle's measurement for the sake of explanation.
Let y be the size of the first angle's complement.
One angle, which we'll refer to as y, is 18 more than twice as large as another, x.
y = 18 + 2x
Complementary angles add up to 90 degrees.
x + 18 + 2x = 90
By substituting for y,
we get x + 18 + 2 x = 90.
Putting like phrases together and taking 18 off on both sides...
3x + 18 = 90
- 18 -18
3x = 72
By dividing both sides by 3, you get
3x/3 = 72/3
24 degrees is the angle between the two that is smaller. and the other angle would be,
y= 18+2x
=18+2(24)= 66 degrees.
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The value of an IBM share one day was $ 74.50 more than the value of an AT&T share.
Answers
An algebraic expression we can use to compare the price of IBM shares as being $74.50 more than AT&T shares is x + 74.50, where x is the value of AT&T shares.
What is an algebraic expression?An algebraic expression consists of variables, terms, constants, and mathematical operations, including addition, subtraction, multiplication, division, and others.
The five algebraic expressions include monomial, polynomial, binomial, trinomial, multinomial.
We can also describe algebraic expressions as falling under the following categories:
Elementary algebraAdvanced algebraAbstract algebraLinear algebraCommutative algebra.An example of an algebraic expression is 2x + 3y.
Let the value of AT&T share = x
Let the value of IBM share = x + 74.50
Thus, we can, algebraically, conclude that AT&T's share price is x while the price of IBM's share is x + 74.50 on that particular day.
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“John is buying carpet for his house. He pays $1.30 per square foot for the first 1000 square feet. He pays $1.00 peradditional square foot after 1000 square feet.Part A: Write an equation for the total price when John buys less than 1000 square feet of carpet. Let c representthe amount of carpet needed in square feet, and p represent the total price in dollars.Enter vour equation in the first response boxPart B: John calculates that the total price will be $1500. How many square feet of carpet will he buy?Place your answer in the second response box”
Answers
EXPLANATION:
Given:
We are told that John pays $1.30 per square foot for the first 1000 square feet of carpet he buys. Then he pays $1.00 per additional square foot after the first 1000 square feet.
Required:
We are required to write an equation to represent the total price when he buys less than 1000 square feet.
Step-by-step solution;
Take note that he pays $1.30 per square foot for the first 1000 square feet. The amount spent, that is the price would be represented by p while, c would represent the amount of carpet to be bought.
Hence, for buying less than 1000 square feet;
[tex]p=1.30c[/tex]Next we note that John calculates that the total price would be $1500.
If John pays the amount of $1.30 for the first 1000 square feet, then he would have paid;
[tex]p=1.30(1000)[/tex][tex]p=1300[/tex]However, we are told that John calculates a total of $1500. This simply means that he will buy more than 1000 square feet of carpet.
He is going to spend an extra $200 (that is 1500 minus 1300). The cost of any extra foot after the first 1000 is $1.00. That means;
[tex]Extra\text{ }carpet=\frac{200}{1.00}[/tex][tex]Extra\text{ }carpet=200ft^2[/tex]That means John would be paying the sum of $1500 to buy 1,200 square feet of carpet.
ANSWER:
[tex]\begin{gathered} Part\text{ }A: \\ p=1.30c \end{gathered}[/tex][tex]\begin{gathered} Part\text{ }B: \\ 1200ft^2 \end{gathered}[/tex]Two students are painting strips of wood to make scenery for the school play. Henry has painted 14 strips of wood. He can paint 3½ strips of wood per minute. Sandy has painted 10 strips of wood. She can paint 4 strips of wood per minute. After how many minutes will both students have painted the same number of strips of wood? Let m represent the number of minutes. Select the correct values to write an equation to represent the situation.
Answers
The number of minutes when they would both paint the same strip of wood is 8 minutes.
In how many minutes would they paint the same strip of wood?The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)
14 + (3½x m)
14 + 3½m
The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)
10 + (4 x m)
10 + 4m
When both people paint the same strip of wood, the two above equations would be equal.
10 + 4m = 14 + 14 +3½m
4m - 3½m = 14 - 10
0.5m = 4
m = 4 / 0,5 = 8
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Help!!!! (Show ur work)
There are two questions
Answers
Answer:
Question 1: 3
Question 2: $120
Step-by-step explanation:
Set up a proportion
[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex] fill in the numbers that you know and solve for the unknow.
[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex] Cross multiply
5x =7.5(2)
5x = 15 Divide both sides by 5
x = 3
If we take 40% off that means that we leave 60% on
Percent means per hundred
[tex]\frac{60}{100}[/tex] When you divide by hundred, you move the decimal two places to the left.
200(.6)
$120.00
6. Tyrion's hourly rate is $16 an hour. He worked for 30 hours this week. 5 of those hours wereon a holiday, and his company pays twice the hourly rate for holidays. What was the total on hispaycheck? Show your calculations.
Answers
For the diagram below, if < 4 = 4x - 2, and < 6 = 2x + 14, what is the value of x?Select one:a.8b.16c.4d.5
Answers
x = 8
ExplanationsFrom the line geometry shown, the line a and b are parallel lines while line "t" is the transversal.
Since the horizontal lines are parallel, hence;
[tex]\angle4=\angle6(alternate\text{ exterior angle})[/tex]Given the following parameters
[tex]\begin{gathered} \angle4=4x-2 \\ \angle6=2x+14 \end{gathered}[/tex]Equate both expressions to have:
[tex]\begin{gathered} 4x-2=2x+14 \\ 4x-2x=14+2 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence the value of x is 8
What is the largestNumber of these wooden Els that can be packed in a box that is 2 cm x 4 cm x 6 cm
Answers
The largest number of the wooden Els with it's total surface area that can be packed in the 2cm×4cm×6cm box is 2 wooden Els.
Total Surface Area of Solid ShapesIn finding the total surface area of a solid cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) and use the formula, SA=2(lw+lh+hw), to find the surface area.
For the box, l=2cm, w=4cm and h=6cm
total surface area of box=2(2×6+2×4+6×4) cm square units
total surface area of box=2(44) cm square units
total surface area of box=88cm square units
For the top cuboid of the wooden El, l=3cm, w=1cm and h=2cm
total surface area of top El cuboid=22cm square units
For the bottom cuboid of the wooden El, l=1cm, w=1cm and h=2cm
total surface area of bottom El cuboid=10cm square units
total surface area of the El=32cm square units
(88cm²/32cm²)=2.75
This implies that only two(2) whole Els with total surface area of 32cm² can be packed in the box.
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hello can you help me with this math question and this a homework assignment
Answers
We know that two vectors are ortogonal if and only if:
[tex]\vec{v}\cdot\vec{w}=0[/tex]where
[tex]\vec{v}\cdot\vec{w}=v_1w_1+v_2w_2[/tex]is the dot product between the vectors.
In this case we have the vectors:
[tex]\begin{gathered} \vec{a}=\langle-4,-3\rangle \\ \vec{b}=\langle-1,k\rangle \end{gathered}[/tex]the dot product between them is:
[tex]\begin{gathered} \vec{a}\cdot\vec{b}=(-4)(-1)+(-3)(k) \\ =4-3k \end{gathered}[/tex]and we want them to be ortogonal, so we equate the dot product to zero and solve the equation for k:
[tex]\begin{gathered} 4-3k=0 \\ 4=3k \\ k=\frac{4}{3} \end{gathered}[/tex]Therefore, for the two vector to be ortogonal k has to be 4/3.
use the number line to find the distance between -3 and -9
Answers
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Answer:
a) 6
b) 6
-6
c) 6
6
Explanation:
a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;
Distance = -3 - (-9)
Distance = -3 + 9
Distance = 6units
b) -3 - (-9)
= -3 + 9
= 6
c) -9 - (-3)
= -9 + 3
= -6
d) For the modulus
|-3 - (-9)|
= |-3 + 9|
= |6|
Since the modulus of a value returns a positive value, |6| = 6
e) |-9-(-3)|
= |-9+3)|
= |-6|
Since the modulus of a negative value gives a positive value, hence;
|-6| = 6
Here are the exam scores for the 15 students in Mr. Kirk's statistics class:
72 75 75 78 81 83 85 89 90 90 90 91 95 95 98
Karen was at the 20th percentile of the distribution. What score did Karen earn on the exam?
(A) 75
(B) 78
(C) 81
(D) 83
Answers
The diameter of a planet at its equator is 5790 kilometers.Estimate using scientific notation:
Answers
Explanation
Step 1
divide the number by 1000
remember:
[tex]1000=10^3[/tex][tex]\frac{5790}{1000}=5.79[/tex]Step 2
input the value of cubic ten instead of 100
[tex]\begin{gathered} 5790=5.79\cdot1000 \\ 5.79\cdot1000=5.79\cdot10^3 \end{gathered}[/tex]then, the answer is
[tex]5.79x10^3\text{ kilometers}[/tex]
Chris took four math quizzes and achieved a 68, 90, 95, and 75. What is his mean quiz average?
Answers
The average of a set is computed as follows:
[tex]\text{Average = }\frac{Tota\text{l sum of all numbers}}{\text{ number of items in the set}}[/tex]In this case,
[tex]\text{Average =}\frac{68+90+95+75}{4}=\frac{328}{4}=82[/tex]What is 5 5/7 divided by 1 3/5 divided by 4 2/3 in simplest form?
Answers
The simplest form of the given division is,[tex][tex]\frac{550}{13}[/tex][/tex].
What is division?
The opposite of multiplication is division. Dividing a sum of numbers into equal pieces. A number is divided in division, which is a straightforward procedure.
Given that: (55/7)/(13/5)/(42/3)
First to simplify:
[tex](13/5)/(42/3)[tex]\frac{(\frac{13}{5}) }{(\frac{42}{3}) } = \frac{(\frac{13}{5}) }{14} \\[/tex] [tex]= \frac{13}{(5)(14)} \\= \frac{13}{70}[/tex][/tex]
So, expression becomes,
[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )}[/tex][/tex]
Now to simplify this expression.
Using:[tex][tex]\frac{(\frac{a}{b} )}{(\frac{c}{d} )} = \frac{ad}{bc}[/tex][/tex]
Then,[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )} = \frac{(55)(70)}{(7)(13)} = \frac{3850}{91} = \frac{550}{13}[/tex][/tex]
Therefore, [tex][tex]\frac{550}{13}[/tex][/tex] is the simplest form of the given division.
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An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?
Answers
Step 1
Given;
Step 2
When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).
[tex]\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}[/tex]checking properly, the sample proportion =0.30, because
[tex]\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}[/tex]Answer; Option D
[tex]0.30[/tex]