The rule of the length of an arc is
[tex]L=\frac{x}{360}\times2\pi\text{ r}[/tex]Where L is the length of the arc
x is the central angle subtended by the arc
r is the radius of the circle
∵ BC = r
∵ BC = 16 ft
∴ r = 16
∵ < ABC is a central angle subtended by the arc AC
∴ ∵ < ABC = 51 degrees
∴ x = 51
→ Substitute the values of x and r in the rule above to find The length of arc AC
[tex]\begin{gathered} AC=\frac{51}{360}\times2\times3.14\times16 \\ AC=14.23466667 \end{gathered}[/tex]→ Round it to 2 decimal places
∴ AC arc = 14.23 ft
A tub of theater popcorn has 247.5 grams of popcorn, which is 275% larger than a regular bag of popcorn. How many grams of popcorn would be in a regular sized bag.
Let's begin by listing out the information given to us:
A tub has this: 247.5 grams of popcorn = 275%
regular-sized bag: x grams = 100%
We will solve using simple proportion
[tex]\begin{gathered} 247.5g=275 \\ xg=100 \\ \text{Cross Multiply, we have:} \\ 247.5\cdot100\cdot g=275\cdot x\cdot g \\ \text{Make x the subject of formula (divide by 275g)} \\ \frac{247.5\cdot100\cdot g}{275\cdot g}=\frac{275\cdot x\cdot g}{275\cdot g} \\ 0.9\cdot100=x\Rightarrow x=900 \\ x=900g \end{gathered}[/tex]a. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?
In this case
[tex]\begin{gathered} 48=45+3 \\ 51=45+2(3) \end{gathered}[/tex]Therefore, the percentage that lies between 45 and 48 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]And, the percentage that lies between 45 and 51 is given by
[tex]\frac{68}{2}=34\text{ \%}[/tex]Find the area of a regularpolygon with 5 sides that has aside length of 6 inches and anapothem of 9 inches. Area = ?
SOLUTION
Write out the formula
[tex]\text{area of regular polygon=}\frac{A\text{ }\times P}{2}[/tex]where A= apothem and P= perimeter of the regular polygon
[tex]\begin{gathered} A=9in \\ P=6(5)=30in \\ \text{perimeter of the regular polygon is sum of all the lenght} \\ \text{the number of sides }\times the\text{ lenght of a side } \end{gathered}[/tex]The area of the regular polygon is
[tex]\frac{9\times30}{2}=9\times15=135in^2[/tex]How do you convert 313313 yards to inches? Use the drop-down menus to explain your answer.Since there are inches in 11 yard, 313313 by .So, 313313 yards = inches.
Given:
[tex]3\frac{1}{3}\text{yards}[/tex]Aim:
We need to convert yards into inches.
Explanation:
[tex]3\frac{1}{3}\text{yards}=\frac{3\times3+1}{3}\text{ yards}[/tex]
[tex]3\frac{1}{3}\text{yards}=\frac{10}{3}\text{ yards}[/tex]
Recall that
[tex]1\text{ yard =}36\text{ inches}[/tex]Multiply 10/3 on both sides, we get
[tex]\frac{10}{3}\text{ yards =}\frac{10}{3}\times36\text{ inches}[/tex][tex]\frac{10}{3}\text{ yards=}120\text{ inches}[/tex][tex]3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]We know that
[tex]3\frac{1}{3}\times36=120[/tex]Final answer:
Since there are 36 inches in 1 yard.
[tex]\text{ multiply 3}\frac{1}{3}\text{ by 36.}[/tex][tex]\text{ So, }3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]what is 1x2x3x4x5x6x7x8x9
Answer:
1x2x3x4x5x6x7x8x9 = 362880
you could also break it down
1x2x3=6
4x5x6=120
7x8x9=504
6 x 120 x 504 = 362880
The solution to the given question [tex]1\times 2\times {3\times 4\times \5\times 6\times 7 \times \ 8\times 9\times 10[/tex] will be[tex]3,628,800[/tex].
The process of making a mathematical expression simpler (usually shorter) is termed simplification.
example :
37 - [5 + {28 - (19 - 7)}]
here using the BODMAS rule we will get the simplified value of this expression.
[tex]=[1\times 2\times {3\times 4\times (5\times 6\times 7 )\times \ 8\times 9\times 10][/tex]
firstly we will solve the small brackets, thus we get the value
[tex]=[1\times2\times3\times{4\times210 \times8}\times9\times10][/tex]
on multiplying again all the terms by itself we get
=[tex]3,628,800[/tex]
thus the solution of the given expression using simplification will be [tex]3,628,800[/tex].
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Which expression is equivalent to (6 – 3x) + 9x ? 1 A. 8x + 2 B. 8x + 3 C. 10x-2 D. 10x - 6
Given to solve the expression:
[tex]\frac{1}{3}(6-3x)+9x[/tex]step 1: Expand the bracket by multiplying each term by the factor outside
[tex]\begin{gathered} (\frac{1}{3}\times6)-(\frac{1}{3}\times3x)+9x \\ 2-x+9x \end{gathered}[/tex]step 2: Simplify the expression obtained in step 1
[tex]\begin{gathered} 2-x+9x\text{ } \\ =2+8x \\ =8x+2 \\ \\ \text{The answer is \lbrack{}Option }A\rbrack \end{gathered}[/tex]The given diagram shows the steps for constructing a parallel line to line AB and passing through point P, but an error has occurred in the construction
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
The error occurred in the construction.
Explanation:
The procedure is,
The first arc must be drawn centred at C.
The second must be drawn centred at P.
Finally, the third arc must be drawn centred at F.
But here, the third arc is drawn centred at D. This is wrong.
Therefore, the correct step is that the third arc must be centred at F.
Final answer:
The third arc should be drawn centred at F.
Here is a system of equations.y=-3x+3y=-x-1Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many solutions.-6
From the given system, we can observe that the y intercepts of the equations are 3 and -1 respectively.
Also we can find the x intercepts by replacing y for 0 and solving for x:
[tex]\begin{gathered} 0=-3x+3 \\ -3=-3x \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} 0=-x-1 \\ 1=-x \\ x=-1 \end{gathered}[/tex]It means that the x intercepts of the lines are 1 and -1 respectively.
Using these points we can graph both lines, this way:
According to this graph, the intersection of these lines is at (2, -3). This represent the solution of the system, therefore, the solution of the system is x=2 and y=-3.
A loaded S-sided de is loaded so that the number 4 occurs 3/10 of the time while the other numbers occur with equal frequency. What is the expected value of this die? CASS 08.44 OC.48 Next O My
The probablity of obtain a 4 is= 3/10
The probablity of obtain a 1,2,3,5,6,7,8= 1-3/10=7/10
The expect value is:
[tex]E(p)=X1*p1+X2*p2+X3*p3+...+X8*p8[/tex]And p(1)=p(2)=p(3)=p(5)=p(6)=7/10
All have the same frequency, therefore
p(1,2,3,5,6,7,8)=7/10*1/5=7/50=1/10
Where x=1, 2 ,3,4,5,6 and p=3/10 if is 4 and 7/10 for any other number.
Replacing:
[tex]\begin{gathered} E=(1+2+3+5+6)*\frac{7}{50}+4*\frac{3}{10} \\ \\ E=2.38+1.2=3.58\approx4 \end{gathered}[/tex]A basketball player scored 24 times during one game. she scored a total of 38 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
The number of two-points shots made is 14
The number of free throws made is 10
What is the number of two-points shots and free throws made?The first step is to formulate a set of linear equations that represent the information in the question:
x + y = 24 equation 1
2x + y = 38 equation 2
Where:
x = number of two-point shots made y = number of free throws madeThe linear equations would be solved using the elimination method.
In order to determine the value of x, take the following steps:
Subtract equation 1 from equation 2
x = 14
Substitute for x in equation 1
14 + y = 24
Combine similar terms:
y = 24 - 14
Add similar terms together
y = 10
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
5/8-3/8 S = two minus S
The value of S in the expression 5/8-3/8 S = two minus S is 2 1/5.
How to illustrate the information?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, this is illustrated thus:
5/8 - 3/8S = 2 -S
Collect like terms
-3/8S + S = 2 - 5/8
5/8S = 1 3/8
Divide
S= 1 3/8 ÷ 5/8
S = 11/8 × 8/5
S = 11/5
S = 2 1/5
This illustrates the concept of expression.
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with regard to promoting standards of excellence, lafasto and larson (2001) identified three rs that help improve performance: require results, review results, and ______.
With regard to promoting standards of excellence, Lafasto and Larson (2001) identified three Rs that help improve performance:
require results, review results, and Reward Results.What did the Larson and LaFasto 1989 study capture?
The LaFasto and Larson Model investigated team effectiveness. It is founded on the premise that, while individuals might be highly competent and talented, teams solve the most challenging issues.
It doesn't matter how skilled an individual is if they can't operate as part of a team.
They studied the traits of 75 highly successful teams. They discovered that high standards of excellence were a critical component in team performance.
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I need help with a question
8c + 3 = 5c + 12
5c is adding on the right, then it will subtract on the left
3 is adding on the left, then it will subtract on the right
8c - 5c = 12 - 3
3c = 9
3 is multiplying on the left, then it will divide on the right
c = 9/3
c = 3
A golf course charges you $54 for a round of golf using a set of their clubs, and $42 if you have your own clubs. You decide to buy a set of clubs for $280 and your friend wants to just use the course's clubs.a. Write an equation to describe the cost for x number of rounds for you.b. write an equation to describe the cost for x number of rounds for your friend.c. How many rounds must you play to recover the cost of the clubs? (Find the break-even point).
Answer
You must play 24 rounds to recover the cost of the club
Step-by-step explanation:
The amount golf charged for using their set clubs = $54
They charged $42 for using personal course
let x be the number of rounds played
let y be the total cost of the clubs
Since you will be buying a set of clubs worth $280
Then, the first equation is
a. y = 280 + 42x
b. y = 54x
c . Calculate the number of rounds that must be played to recover the cost of the clubs
To calculate this, we need to equate equations a and b together
280 + 42x = 54x
Collect the like terms
280 = 54x - 42x
280 = 12x
Isolate x by dividing through by 12
280/12 = 12x/12
x = 23.3333
Hence, you must play 24 rounds to recover the cost of the club
Can you please help me solve this and the test statistics and p value
The claim is that the population mean for the smartphone carrier's data speed at airports is less than 4.00 Mbps
The parameter of the study is the population mean, symbolized by the Greek letter mu "μ"
The researchers believe is that his value is less than 4, you can symbolize this as:
[tex]\mu<4[/tex]This expression does not include the "=" symbol, which indicates that it represents the alternative hypothesis. The null and alternative hypotheses are complementary, so if the alternative hypothesis represents the values of μ less than 4, then the null hypothesis, as its complement, should represent all other possible values, which are those greater than and equal to 4. You can represent this as:
[tex]\mu\ge4\text{ or simply }\mu=4[/tex]The statistical hypotheses for this test are:
[tex]\begin{gathered} H_0\colon\mu=4 \\ H_1\colon\mu<4 \end{gathered}[/tex]Option A.
In the display of technology, you can see the data calculated for the test.
The second value shown in the display corresponds to the value of the test statistic under the null hypothesis, you have to round it to two decimal places:
[tex]t_{H0}=-2.432925\approx-2.43[/tex]The value of the test statistic is -2.43
The p-value corresponds to the third value shown in the display.
The p-value is 0.009337
To make a decision over the hypothesis test using the p-value you have to follow the decision rule:
- If p-value ≥ α, do not reject the null hypotheses.
- If p-value < α, reject the null hypotheses.
The significance level is α= 0.05
Since the p-value (0.009337) is less than the significance level of 0.05, the decision is to reject the null hypothesis.
Conclusion
So, at a 5% significance level, you can conclude that there is significant evidence to reject the null hypothesis (H₀: μ=4), which means that the population mean of the smartphone carrier's data speed at the airport is less than 4.00 Mbps.
solve the proportion 4/3 is equal to 9 / X
We need to solve for X.
The proportion is:
[tex]\frac{4}{3}=\frac{9}{X}[/tex]To solve for X, we cross multiply and then use algebra to solve. The process is shown below:
[tex]\begin{gathered} \frac{4}{3}=\frac{9}{X} \\ 4\times X=3\times9 \\ 4X=27 \\ X=\frac{27}{4} \end{gathered}[/tex]AABC - ADEF? Explain your reasoning. E 6 units C 40° 9 units 4 units 6 units er your answer and explanation.
Side-Angle-Side Theorem states that triangles are congruent if any pair of corresponding sides and their included angle are congruent.
How do we know that their sides are congruent, by similarity ratios, means a ratio of the lengths of the sides to see if they have the same ratio or scale factor:
[tex]\begin{gathered} \frac{9}{6}=1.5 \\ \frac{6}{4}=1.5 \end{gathered}[/tex]Then, since their sides are congruent and they have the same angle, they are congruent by SAS.
Andre is looking at apartments with 1 of his friends. They want the monthly rent to be no more than $1000. If the roommates split the rent evenly among the two of them, what is the maximum rent each will pay?
We have the next inequality
[tex]2x\le1000[/tex]where x is the rent of each person
[tex]\begin{gathered} x\le\frac{1000}{2} \\ x\le500 \end{gathered}[/tex]The maximum rent each will pay is $500
simplify -5m²n³ × 15m⁴ n⁶
To simplify the given expression we will use the following property of exponents:
[tex]a^n\times a^m=a^{n+m}.[/tex]Using the above property we get:
[tex]-5m^2n^3\times15m^4n^6=(-5\times15)m^{2+4}n^{3+6}=-75m^6n^9.[/tex]Answer:
[tex]-5m^2n^3\times15m^4n^6=-75m^6n^9.[/tex]Given m||n, find the value of x.50°Click heredismiss)
Let's recall that If a set of 2 parallel lines, line m and line m, are crossed or cut by another line, line T, in our question, we say "a set of parallel lines are cut by a transversal.
Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection.
These are matched in measure and position with a counterpart at the other parallel line.
At each of the parallel lines, there are two pairs of vertical angle. Each angle in the pair is congruent to the other angle in the pair.
In our question, the angle that measures 145 degrees is congruent with the opposites angles of angle x.
Let's recall that x and 145 degrees are adjacent supplementary angles. And these angles add up to 180 degrees. Then, for solve for x, we have:
x = 180 - 145
x = 35 degrees
y=-2x+6x+8 how do i find the vertex
Then the vertex is (3/2, 25/2)
A general equation of a parabola is:
[tex]y=ax^2\text{ + bx + c; the vertex of a parabola is the point (h,k) where h = -b/2a}[/tex]This way you find the value of h
Since h is a value of x, you can find the corresponing value of y by using the original equation:
[tex]y=ah^2\text{ + bh + c}[/tex]and this will be the value of K
Melissa standing 40 feet from a tree the angle of elevation from where she is standing on the ground to the top of the tree is 50° how tall is the tree round the final answer to the nearest 10th.
Given:
• Melissa standing 40 feet from a tree.
,• The angle of elevation from where she is standing on the ground to the top of the tree is 50°.
Required: To determine the height of the tree.
This is achieved thus:
First, we represent the given information diagrammatically as follows:
Using the diagram above, in relation to the given angle, we can determine the height of the tree by using the tangent ratio as follows:
[tex]\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ \therefore\tan50\degree=\frac{h}{40} \\ h=40\tan50\degree \\ h\approx47.7ft \end{gathered}[/tex]Hence, the answer is:
[tex]47.7ft[/tex]I can't solve them 15 here and 15 on another post
6. Measure of angle 1 is 60 degrees because it congruent to angle 4 because they are opposed by the vertex
7. Measure of angle 3 is equal to 180 - angle 1 - angle 2 = 180 - 60 - 40 = 80 because these three angles sum 180 degrees
8. Measure of angle 5 is 40 degrees because it congruent to angle 2 because they are opposed by the vertex
9. Measure of angle 6 is equal to angle 3, because they are congruent, so it measures 80 degrees
10. Mesure of angle 7 is equal to the sum of angles 1 and 2 because they are congruent, so measure of angle 7 is 100
11. 80
12. 60
13. 120
14. 60
15. 120
1 pointThe 5 consecutive integers below add up to 175. What is the value of x?x-3x-2X - 1ХX + 1
Then x=36.
The first three terms of a sequence are given. Round to the nearest thousandth (ifnecessary).15, 18, 108/5. find the 8th term
SOLUTION
The following is a geometric series
We will use the formula
[tex]T_n=ar^{n-1}[/tex]Where Tn is the nth term of the series,
n is the number of terms = 8,
a is the first term = 15
And r is the common ratio = 1.2 (to find r, divide the second term, 18 by the first term which is 15
Now let's solve
[tex]\begin{gathered} T_n=ar^{n-1} \\ T_8=15\times1.2^{8-1} \\ T_8=15\times1.2^7 \\ T_8=15\times3.583 \\ T_8=53.748 \end{gathered}[/tex]So the 8th term = 53.748
Devon saw 19 adults wearing hats
Answer:
please add rest of question?
Step-by-step explanation:
Ryan's car used 9 gallons to travel 396 miles. How many miles can the car go on one gallon of gas?On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Given:
At 9 gallons, it can travel 396 miles.
Find: At one gallon, it can travel ___ miles.
Solution:
First, let's fill in the number line with the information we have.
Then, to find the missing value ?, let's do cross multiplication.
[tex]\begin{gathered} ?\times9=1\times396 \\ ?\times9=396 \end{gathered}[/tex]Then, divide both sides of the equation by 9.
[tex]\begin{gathered} \frac{?\times9}{9}=\frac{396}{9} \\ ?=44 \end{gathered}[/tex]Therefore, on 1 gallon of gas, the car can travel 44 miles.
Not sure on how to do this. Would really like some help.
Given:
[tex]\cos60^{\circ}[/tex]To find:
The value
Explanation:
We know that,
[tex]\cos\theta=\sin(90-\theta)[/tex]So, we write,
[tex]\begin{gathered} \cos60^{\circ}=\sin(90-60) \\ =\sin30^{\circ} \\ =\frac{1}{2} \end{gathered}[/tex]Final answer:
[tex]\cos60^{\circ}=\frac{1}{2}[/tex]A country with 16 states and a population of 615529 contains 128 seats in a House of Representatives.What is the average number of seats assigned per state?
Since there are 128 seats available and these 128 seats will be filled in by people from 16 states, we will divide 128 by 16 to get the average number of seats assigned per state.
[tex]128\div16=8[/tex]Therefore, the average number of seats assigned per state is 8.
The number of milligrams D (h) of a certain drug that is in a patients bloodstream h hours after the drug is injected is given by the following function. D (h)=40e ^0.2h When the number of milligrams reaches 9, the drug has to be injected again. How much time is needed between injections? Round your answer to the nearest tenth, and do not round any intermediate computations.
we need to find the value of h when D is 9, so we need to replace D by 9 and find h:
