Answers
Answer:
68
Explanation:
We start with the mode:
[tex]\text{Mode}=l+\frac{(f_1-f_0)\times h}{(2f_1-f_0-f_2)}[/tex]Where the terms are defined as follows:
[tex]\begin{gathered} l=\text{lower limit of the modal class} \\ f_1=\text{frequency of the modal class} \\ f_0=\text{frequency of the class before the modal class} \\ f_2=\text{frequency of the class after the modal class} \\ h=\text{size of the class interval} \end{gathered}[/tex]From the table, the modal class is 65-69.
Therefore:
[tex]\begin{gathered} l=\text{6}5 \\ f_1=\text{1}9 \\ f_0=\text{1}0 \\ f_2=\text{1}3 \\ h=\text{5} \end{gathered}[/tex]We substitute into the formula:
[tex]\begin{gathered} \text{Mode}=65+\frac{(19-10)\times5}{(2\times19-10-13)} \\ =65+\frac{9\times5}{15} \\ =65+\frac{45}{15} \\ =65+3 \\ =68 \end{gathered}[/tex]The mode of the given data is 68.
Related Questions
solve the right triangle and round decimal answers to the nearest tenthi know its either option a or c but im not 100% sure which one
Answers
Step 1
Name all sides
Hypotanuse = 16 side facing right angle
Opposite = y side facing given angle
Adjacent = x
90 +
Step 2
Find the values of x and y
[tex]\begin{gathered} \theta\text{ = 76} \\ \sin \theta\text{ = }\frac{\text{Opposite}}{\text{Hypotanuse}} \\ \sin 76\text{ = }\frac{y}{16} \\ 0.97\text{ = }\frac{y}{16} \\ \text{Cross multiply} \\ y\text{ = 0.97 x 16} \\ y\text{ = 15.52} \\ y\text{ = 15.5} \end{gathered}[/tex][tex]\begin{gathered} \cos \theta\text{ = }\frac{adjacent}{\text{hypotanuse}} \\ \cos 76\text{ = }\frac{x}{16} \\ 0.24\text{ = }\frac{x}{16} \\ \text{Cross multiply} \\ x\text{ = 0.24 x 16} \\ x\text{ = 3.8}5 \\ x\text{ = 3}.9 \end{gathered}[/tex]6) The volume of a cylinder is 753.6 units and the height is 15, determine thelength of the radius (round to the nearest whole number)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
cylinder:
volume = 753.6 units³
height = 15 units
Step 02:
geometry:
volume of cylinder = π r² h
[tex]\begin{gathered} 753.6\text{ = }\pi *r^2*15 \\ \\ \frac{753.6}{15*\pi}=r^2 \end{gathered}[/tex][tex]\sqrt{15.99}=r[/tex]r = 3.999
The answer is:
r = 4 units
If a submarine is 80 m below sea level if it dives another 15 m, how far below sea level is the submarine now?
Answers
ANSWER
EXPLANATION
The submarine is initially 80 m below sea level.
It then dives another 15 m.
That means it goes 15 m lower than its original position.
Sea level is equivalent to 0 m.
Therefore, the submarine being initially 80 m below sea level means that it was at -80 m.
Now, it goes 15 m lower,
1500.000 to the nearest hundredth
Answers
1500.000 to the nearest hundredth is 1500.00
Given that there is a zero in the thousandths position, the zero in the hundredths position is rounded to zero.
Geometry - Triangles > Interior angles of a trlangle 20. The three angles of a triangle measure x°, yº and 17. Which of the following statements must be true? y=180- x+y=17 y+x= 180 - 17 y=x+ 17
Answers
Given:
Three angles of a triangle are x°, y° and 17°.
The objective is to select the correct statement.
By the angle sum property of triangle, the sum of all the angles of a triangle will be 180°.
Then, the sum of given three angles will be,
[tex]\begin{gathered} x\degree+y\degree+17\degree=180\degree \\ x\degree+y\degree=180\degree-17\degree \end{gathered}[/tex]Hence, the correct statement is y+x=180-17.
Using the chart above of 500 people go in for surgery how many are going for eye surgery?
Answers
From the graph (a pie chart), we have that the percent of people that go to Eye Surgery is 5%.
We have that total is 500 people. We, therefore, need to get the 5% of 500 to get the number of those that go for eye surgery, then:
[tex]\frac{5}{100}\cdot500\text{ = 25}[/tex]Then, for eye surgery, we have 25 people in total, according to chart.
Find the points of inflection. f(x) = x3 + 3x2 - X - 24 O (-1,3) 0 (-1,0) O (1,8) 0 (-1, -21)
Answers
whats 9 9/35- 6 8/10
Answers
You have the following expression:
9 9/35 - 6 8/10
In order to simplify the prevous expression, first convert the mixed number to normal fractions, just as follow:
9 9/35 = 9/1 + 9/35 = (315 + 9)/(35) = 324/35
6 8/10 = 6/1 + 8/10 = (60 + 8)/10 = 68/10 = 34/5
next, subtract the previous result:
324/35 - 34/5
multiply the second fraction by 7/7 to obtain two homogeneus fractions:
(34/5)(7/7) = 238/35
then, you have
324/35 - 34/5
= 324/35 - 238/35
= (324 - 238)/35
= 86/35
Hence, the simplied expression is 86/35
Answer:
For decimals, it is: 2.45714285714
For fractions, it is: [tex]2\frac{22857142857}{50000000000}[/tex]
Step-by-step explanation:
Please brainliest.
On a construction site, a winch is used to wind cable onto the drum of the winch
Answers
Solution
Formula
[tex]P=\frac{K}{D}[/tex]Given parameters
[tex]\begin{gathered} P=8400 \\ D=3 \end{gathered}[/tex][tex]3in\text{ =0.25foot}[/tex]Now, substitute the given parameters into the formula
[tex]\begin{gathered} 8400=\frac{K}{3} \\ \\ K=8400\times0.25 \\ K=2100 \end{gathered}[/tex]The final answer
2100 foot -pounds
Sanford's gym coach made him run 20 laps on a 600-m track. How many kilometers did he run? How many miles? Round youranswers to two decimal places, if necessary.wSanford rankilometers, which ismiles.Х5HELP?? Stuck
Answers
First, determine how far he ran in meters
20 laps * 600 meters
12000 meters
We can find the number of kilometers by using the conversion factor 1000meters = 1 km
12000meters * 1 km/1000m = 12 km
Now we can convert km to miles
1 km = .62137119 miles
12 km * .62137119 miles/ 1 km
7.45645428
Rounding to 2 decimal places
7.46 miles
I dont know how to find the mean or what a mean is
Answers
To find the mean simply add all the numbers, and then divide by how many numbers are.
We have 6 values (numbers)
-54 + (-32)+ (-70)+(-25)+(-65)+(-42)
-288
-288 /6 = -48
Stan and Olga are considering buying a sheep farm. A surveyorhas supplied them with the given accurate sketch. Find the areaof the property, giving your answer in:km2
Answers
The approximate area of the property is;
[tex]75km^2[/tex]Here, we want to calculate the area of the property
Firstly, we can see that the farm is divided into two shapes (two triangles actually)
By finding the areas of the two triangles, adding tehm up, we will have the area of the farm
Firstly, we need to get all the sides of the triangles
Let us start with the triangle below
It is simply the length of the diagonal QS
We can find this by the use of cosine rule
We have this as;
[tex]\begin{gathered} p^2=q^2+s^2-2qsCosP \\ p^2=8^2+12^2\text{ -2(8)(12)Cos70} \\ p^2\text{ = 64 + 144 - 65.67} \\ p\text{ = 11.93 km} \end{gathered}[/tex]Now, by using this calculated diagonal, we can get the missing side of the top triangle
We have the missing side calculated as follows;
[tex]\begin{gathered} q^2=r^2+s^2-2rsCosQ \\ q^2=11.93^2+10^2-2(11.93)(10)Cos30 \\ q^2\text{ = 35.69} \\ \text{q = 5.97 km} \end{gathered}[/tex]So, we now use Heron's formula for each of the two triangles before adding up
For triangle QPS, we have;
[tex]\begin{gathered} A\text{ = }\sqrt[]{s(s-a)(s-b)(s-c)} \\ a,b\text{ and c are the sides} \\ \text{s = }\frac{a+b+c}{2}\text{ = }\frac{8+12+11.93}{2}\text{ = 15.965} \\ \\ A\text{ = }\sqrt[]{15.965(15.965-8)(15.965-12)(15.965-11.93)} \\ A\text{ = }\sqrt[]{15.965(7.965)(3.965)(4.035)} \\ A=45.105km^2 \end{gathered}[/tex]For triangle QRS, we have;
[tex]\begin{gathered} A\text{ = }\sqrt[]{s(s-a)(s-b)(s-c)} \\ a,b,c\text{ are the sides} \\ s\text{ = }\frac{a+b+c}{2}\text{ = }\frac{10\text{ + 5.97+11.93}}{2}\text{ = 13.95} \\ \\ A\text{ = }\sqrt[]{13.95(13.95-10)(13.95-5.97)(13.95-11.93)} \\ A=29.803km^2 \end{gathered}[/tex]The area of the sheep farm is the sum of both areas
We have this as;
[tex]\text{Total area = 29.803 + 45.105 = 74.908 km}^2[/tex]Evaluate the function below. Round to four decimal places, if necessary. f(x)=1.2e^{2x}-0.3, for f(3)f(3)= Answer
Answers
To evalueate a function f(x) on f(3), we simply has to substitute all x with 3 and evaluate the expression:
[tex]\begin{gathered} f(x)=1.2e^{2x}-0.3 \\ f(3)=1.2e^{2\cdot3}-0.3 \\ f(3)=1.2e^6-0.3 \\ f(3)=1.2\cdot403.4287935\ldots-0.3 \\ f(3)=484.1145522\ldots-0.3 \\ f(3)=483.8145522\ldots\approx483.8146 \end{gathered}[/tex]So, the answer is approximately 483.8146.
The owner of a restaurant determines she can spend no more than $1600 to buy coffee for the next month. At wholesale prices, the regular coffee she uses costs $4.50 per pound and the decaffeinated coffee costs $6.00 per pound. The owner estimates she will need at least 60 pounds of coffee for the month. Which system of inequalities represents the possible combinations of the number of pounds of regular coffee, x, and the number of pounds of decaffeinated coffee, y, that meet these conditions? A 4.5x + 6y < 1600x + y > 60 B. 4.5x + 6y < 1600 x + y < 60 C. 4.5+ 6y < 60 x +y > 1600 D 4.5x + 6y > 1600 x + y > 60
Answers
Answer:
A) 4.5x + 6y < 1600, x + y > 60
Explanation:
Let the number of pounds of regular coffee = x
Let the number of pounds of decaffeinated coffee = y
Cost of regular coffee = $4.50 per pound
Cost of decaffeinated coffee = $6.00 per pound.
If she can spend no more than $1600 to buy coffee for the next month, then:
[tex]4.50x+6.00y\le1600[/tex]The owner estimates she will need at least 60 pounds of coffee for the month..
Therefore:
[tex]x+y\ge60[/tex]Therefore, the inequalities that meet these conditions are:
[tex]\begin{gathered} 4.5x+6y<1600 \\ x+y>60 \end{gathered}[/tex]a) what is KN+IKb)What is the coordinate of midpoint GO
Answers
Given the figure of a number line
a) We will find the value of KN+IK
As shown in the figure:
[tex]\begin{gathered} K=0 \\ N=3 \\ I=-2 \\ So, \\ KN+IK=0\times3+(-2)\times0=0+0=0 \end{gathered}[/tex]So, the answer will be KN+IK = 0
b) )What is the coordinate of midpoint GO
As shown:
[tex]G=-4,O=4[/tex]The midpoint =
[tex]\frac{-4+4}{2}=\frac{0}{2}=0[/tex]So, the answer will be the midpoint will be k = 0
b.) What does the point (2.1, 18.6) represent? Select]
Answers
Based on the information of the graph, you can notice that the point (2.1 , 18.6) corresponds to point B.
The point (2.1 , 18.6) means that for 2.1 free throw attemps per game, there are approximately 18.6 points per game.
Pystems - Elimination O Answer each of the questions below. Show all work. Highlight/Circle your answers. Use the system of equations below to answer the questions 1-5. (4x – 2y = 4 | 2x + y = 6 1) What value should you multiply the second equation by? 2) Which of the following problems is created by using the elimination method on the system above a) 6x= 10 b) 8x = 12 c) 8x = 16 d) 2x = 10 3) Find the value of x. Show ALL work. W P
Answers
Answer
1) The value to multiply the second equation by is 2.
2) The problem created by using the elimination method on the system above is 8x = 16
3) x = 2
y = 2
Explanation
4x - 2y = 4
2x + y = 6
In order to solve this system of equation, we will try to eliminate y. To do this, we will multiply equation 2 by 2
4x - 2y = 4
2x + y = 6
4x - 2y = 4
4x + 2y = 12
Adding the two equations now, we have
4x + 4x - 2y + 2y = 4 + 12
8x + 0 = 16
8x = 16
To find the value of x, we will divide both sides by 8
(8x/8) = (16/8)
x = 2
We can then solve for y
2x + y = 6
2(2) + y = 6
4 + y = 6
y = 6 - 4
y = 2
Hope this Helps!!!
Which expression uses the commutative property to make it easier to evaluate ( – 5). 11. ? 3 5 11 O A. (-). 11 $). O B. (-6).3. OC. . 11.(-5) O D. (-5) 5.11 SUBN
Answers
I’m here to help you. Just give me a few mins to look over your question.
Step 01:
Data
(-6/5) *11 * 3/5
Commutative property
Step 02:
We must analyze the expressions to find the solution.
Commutative property
[tex]\frac{5}{3}\cdot11\cdot(-\frac{6}{5})[/tex]That is the solution .
Find the equation of a line where slope is -1/2 and goes through points (-10, 1)
Answers
We need to use two forms of the line:
* The point-slope form is:
y = m(x - h)+ k
* The slope-intercept form is:
y = mx + b
Where m is the slope, b is the y-intercept, and (h, k) is a point of the line.
We are given the slope m = -1/2 and the point (-10, 1). Using the point-slope form:
[tex]y=-\frac{1}{2}(x+10)+1[/tex]Operating:
[tex]\begin{gathered} y=-\frac{1}{2}x-5+1 \\ \\ y=-\frac{1}{2}x-4 \end{gathered}[/tex]I need help with this practice from my trigonometry prep book I attempted this previously, struggling, I got two answers and I’m not sure if I’m correct so I would like more clarification
Answers
Therefore:
[tex]\cos (\alpha-\beta)=-\frac{63}{65}[/tex]A mountain bike has a cash price of $600,00. Eric purchases the bike by making a down payment of $18.00 and 24 payments of $33.71 Find the finance charge.O A $58200B. $227.04OC. $291.00 D. $18.00
Answers
From the statement, we know that:
• the original price of the bike is $600.00,
,• Eric purchases the bike by making a down payment of $18.00,
,• and 24 payments of $33.71.
The final price of the bike is the sum of the down payment and the 24 payments:
[tex]FP=\text{ \$18.00 }+24\times\text{\$33.71}=\text{ \$827.04.}[/tex]The finance charge is the difference between the final price and the original price:
[tex]FC=FP-OP=\text{ \$827.04}-\text{\$600.00}=\text{ \$227.04.}[/tex]AnswerB. $227.04
Addison Rae Drank 3.5 bottles of water Yesterday. Each bottle Contained 1.2 pints of water what was the number of pints of water Addison rae drank yesterday
Answers
given BD is the angle bisector of ABC complete the flowchart proof below .Note that the last statement and reason has been filled for you
Answers
Box 1:
Statement
[tex]\bar{BD}\text{ bisects }\angle ABC[/tex]Reason
Given
Box 2 (left):
Statement
[tex]\bar{AD}\cong\bar{CD}[/tex]Reason
A segment bisector divides a segment into two congruent segments
Box 3:
Statement
[tex]\bar{BD}\cong\bar{BD}[/tex]Reason
Reflexive property
Box 4:
Statement
[tex]\angle ADB\text{ }\cong\text{ }\angle CDB[/tex]Reason
All right angles are congruent
mrs. Ruiz planted 14 flowers in three plots she planted 4 flowers in 1 blue pot and split the rest equally between 2 red plots add symbols to the equation below then solve the equation to find the number of flowers mrs. Ruiz planet and each of the two red plots
Answers
Total numbers of flowers = 14
4 flowers in the blue pot
Then, 14 - 4 = 10 plants
10 plants were equally planted in 2 red pots.
10 = 2r
r = 5 flowers
Mrs Ruiz planted 4 flowers in the blue pot and 5 flowers in each of the red pots.
A sporting goods salesperson sells 2 fishing reels and 5 rods for $365. Thenext day, the sales person sells 4 reels und 2 rods for S290. How much does each cost?(Solve by Setting-up a system of two equations in two variables)
Answers
Let's use the variable x to represent the cost of one fishing reel and the variable y to represent the cost of one rod.
If 2 fishing reels and 5 rods cost $365, we have the equation:
[tex]2x+5y=365[/tex]Then, if 4 reels and 2 rods cost $290, we have the second equation:
[tex]4x+2y=290[/tex]Let's divide the second equation by 2 and isolate the variable y:
[tex]\begin{gathered} 2x+y=145 \\ y=145-2x \end{gathered}[/tex]Then, let's use this value of y in the first equation:
[tex]\begin{gathered} 2x+5(145-2x)=365 \\ 2x+725-10x=365 \\ -8x=365-725 \\ -8x=-360 \\ x=45 \\ \\ y=145-2\cdot45 \\ y=145-90 \\ y=55 \end{gathered}[/tex]So the cost of one reel is $45 and the cost of one rod is $55.
Which ordered pair is a solution to the system of equations?Note: Use the substitution method.{x=1/4y+2 and −4x+3y=4 (−1/12, −2/63 )(7/2, 6 )(5/4, 3 )(−1/4, 1 )
Answers
Given the system of equations
[tex]\begin{gathered} x=\frac{1}{4}y+2 \\ -4x+3y=4 \end{gathered}[/tex]Substitute x =1/4y+2 in the second equation
[tex]-4(\frac{1}{4}y+2)+3y=4[/tex]Simplify
[tex]\begin{gathered} -y-8+3y=4 \\ 2y-8=4 \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} 2y-8+8=4+8 \\ 2y=12 \\ \frac{2y}{2}=\frac{12}{2} \\ y=6 \end{gathered}[/tex]Then substitute y = 6 in x
[tex]x=\frac{1}{4}(6)+2=\frac{6}{4}+2=\frac{7}{2}[/tex]Answer: (7/2, 6)
Martina purchased a prepaid card for $30. Long distance calls cost 11 cents a minute using this card. Martina used her card only once to .ake a long distance call. If the remaining credit on her card is $28.46, how many minutes did her call last.
Answers
we get that
[tex]\begin{gathered} 28.46+0.11t=30 \\ t=\frac{30-28.46}{0.11}=14 \end{gathered}[/tex]so her call last 14 minutes
Gerd is considering an account that earns 6% interest per annum compounded monthly. What is the annual percentage yield (APY)? Give your answer as a percent rounded to the nearest tenth (e.g. 5.1%). Do not include the percentage sign (%) in the answer box below.
Answers
Data
Interest = 6%
Annual percentage yield = ?
APY = (1 + r/n)^n -1 12 is because a year has 12 months
6% = 0.06
APY = (1 + 0.06/12) ^12 - 1
APY = (1 + 0.005)^12 - 1
APY = (1.005)^12 - 1
APY = 1.062 - 1
APY = 0.062 or 6.2%
A taxi service charges a pick-up fee plus a charge for each mile driven. the equation y=1.8x+5 gives the total cost y to travel x miles in the taxi
Answers
Part A
The equation that gives the total cost, y to travel x miles is:
[tex]y=1.8x+5[/tex]When x=0
[tex]\begin{gathered} y=1.8(0)+5=0+5 \\ y=5 \end{gathered}[/tex]When x=10
[tex]\begin{gathered} y=1.8(10)+5=18+5 \\ y=23 \end{gathered}[/tex]When x=20
[tex]\begin{gathered} y=1.8(20)+5=36+5 \\ y=41 \end{gathered}[/tex]When x=30
[tex]\begin{gathered} y=1.8(30)+5=54+5 \\ y=59 \end{gathered}[/tex]When x=40
[tex]\begin{gathered} y=1.8(40)+5=72+5 \\ y=77 \end{gathered}[/tex]We can then fill the table using these values.
Part B
The y-intercept is the point at which x=0
From the table above, when x=0, y=5
• Therefore, the y-intercept is 5.
To use the table to find the slope, first, pick any two pair of points.
• For an example, I pick the points (0,5) and (10,23).
Then find the slope using the formula below:
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{23-5}{10-0} \\ =\frac{18}{10} \\ m=1.8 \end{gathered}[/tex]26cm/s= m/min please explain
Answers
26cm/s to m/min
1 centimeter = 100 meters
60 seconds = 1 minute
Divide 26 cm by 100 to obtain meters
(26 cm/s) / 100 = 0.26 m/s
Multiply 1 second by 60 ( 1 minute)
0.26 m/s x 60 = 15.6 m/min