Answer: the number of multiple choice questions in the test is 12.
the number of short response questions in the test is 8.
Step-by-step explanation:
Let x represent the number of multiple choice questions in the test.
Let y represent the number of short response questions in the test.
The total number of questions in the test is 20. It means that
x + y = 20
The multiple choice questions are worth 3 points each and the short response question are worth 8 points each. The total number of points is 100. It means that
3x + 8y = 100 - - - - - - - - - - 1
Substituting x = 20 - y into equation 1, it becomes
3(20 - y) + 8y = 100
60 - 3y + 8y = 100
- 3y + 8y = 100 - 60
5y = 40
y = 40/5 = 8
x = 20 - y = 20 - 8
x = 12
The longest human power sporting event is the tour de France cycling race in a particular year the average speed for the winner of the this race was 23.66 mph in that same year of the race was 2292 miles long how long did it take the winner to complete the race
Answer:
The winner completed the race in 96 hours and 52 minutes.
Step-by-step explanation:
Given:
Distance of the cycling race = 2292 miles
Average speed of the winner = [tex]23.66\ mph[/tex]
We need to find time required by winner to complete the race.
Solution:
Now we know that;
Time required can be calculated by dividing Total Distance from the Average speed.
framing in equation form we get;
time required by winner to complete the race = [tex]\frac{2292}{23.66} = 96.87\ hrs[/tex]
Now converting [tex]0.87\ hrs[/tex] into minutes we get;
[tex]0.87\times 60= 52.2\approx 52\ mins[/tex]
Hence the winner completed the race in 96 hours and 52 minutes.
x and y vary inversely, and y =7 when x = 4. What is the constant of variation?
Answer:
Y doesn't vary directly with x
Answer:28
Step-by-step explanation:
X varies inversely as y
X©1/y
X=k/y
4=k/7
Cross product
We get 4×7=k×1
28=k
Therefore constant (k)=28
Tony sells 50.5 ounces of lemonade for a total of $20.20. Find the unit price in dollars per ounce. If necessary, round your answer to the nearest cent.
The unit price in dollars per ounce will be $0.4 per ounce.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Division means the separation of something into different parts, sharing of something among different people, places, etc.
Tony sells 50.5 ounces of lemonade for a total of $20.20.
The unit price in dollars per ounce will be calculated as,
Rate = $20.20 / 50.5
Rate = $0.4 per ounce
The unit price in dollars per ounce will be $0.4 per ounce.
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Tony's lemonade has a unit price of $0.40 per ounce.
Tony sells 50.5 ounces of lemonade for a total of $20.20.
To find the unit price in dollars per ounce, we divide the total cost by the total number of ounces.
The calculation looks like this: $20.20 ÷ 50.5 ounces = $0.40 per ounce.
Therefore, the unit price of Tony’s lemonade is $0.40 per ounce. If rounding is necessary, this answer is already precise to the nearest cent.
The variables x and y are proportional.Use the vaules to find the constant aof proportonality.Then write the equation that relates x and y. When y=72, and x=3
Answer:
Constant of proportionality = 24
Equation: [tex]y=24x[/tex]
Step-by-step explanation:
Given:
'x' and 'y' are proportional to each other.
At [tex]x=3,y=72[/tex]
Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.
Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:
[tex]k=\frac{y}{x}\\\\k=\frac{72}{3}=24[/tex]
Therefore, the constant of proportionality is 24.
Now, a proportional relationship in 'x' and 'y' is given as:
[tex]y=kx[/tex]
Now, plug in the given value of 'k' and complete the equation. This gives,
[tex]y=24x[/tex]
Therefore, the equation that relates 'x' and 'y' is [tex]y=24x[/tex]
There is a stack of sweaters at the store. Six sweaters have 5 buttons each. One sweater has 4 buttons. How many buttons do the sweaters have altogether?
Answer:
29 buttons
Step-by-step explanation:
6 x 5 - 1
Answer:
Step-by-step explanation: 29
Lines a and b are parallel.
what is the measure of angle b
enter in the box
B=
Answer:
Ans _ angle b = 79
Hope it helps
∠B4 = ∠A2
b° = 79°
hope this helps :)
Right △EFG has its right angle at G, EF=8 , and FG=6 .
What is the value of the trigonometric ratio of an angle of the triangle?
Drag a value to each box to match the trigonometric ratio with its value.
Answer:
[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]
[tex]Cos\ F = \frac{3}{4}[/tex]
[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]
Step-by-step explanation:
Given
EF = 8
FG = 6
We need to find the trigonometric ratios.
Solution:
First we will find the length of the third side.
Now we know that;
△EFG is a right angled triangle with right angle at G.
Now applying Pythagoras theorem which states.
"The sum of square of the two legs of the triangle is equal to square of the hypotenuse."
so we can say that;
[tex]FG^2=EF^2+EG^2\\\\EG^2=FG^2-EF^2[/tex]
Substituting the given values we get;
[tex]EG^2=8^2-6^2=64-36=28[/tex]
Taking square roots on both side we get;
[tex]\sqrt{EG^2} =\sqrt{28}=\sqrt{4\times7}\\ \\EG = 2\sqrt{7}[/tex]
Now we will find the trigonometric values.
[tex]secE=\frac{Hypotenuse}{Adjacent\ side}[/tex]
Here Hypotenuse = EF = 8
Adjacent side of E = EG = [tex]2\sqrt{7}[/tex]
[tex]secE=\frac{8}{2\sqrt{7}} =\frac{4}{\sqrt{7}}[/tex]
Now rationalizing the denominator by multiplying numerator and denominator by [tex]\sqrt{7}[/tex] we get;
[tex]secE=\frac{4\times \sqrt{7} }{\sqrt{7}\times \sqrt{7} }\\\\secE = \frac{4\sqrt{7} }{7}[/tex]
Now,
[tex]Cos F = \frac{Adjacent \ side}{Hypotenuse}[/tex]
Adjacent side to F =GF = 6
Hypotenuse = EF = 8
[tex]Cos\ F = \frac{6}{8}\\\\Cos\ F = \frac{3}{4}[/tex]
Now,
[tex]Tan F = \frac{opposite \ side}{adjacent\ side}[/tex]
Here Opposite side of F = EG = [tex]2\sqrt{7}[/tex]
Adjacent side of F = GF = 6
[tex]Tan\ F= \frac{2\sqrt{7}}{6}\\\\Tan\ F =\frac{\sqrt{7}}{3}[/tex]
Hence Below are required details.
[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]
[tex]Cos\ F = \frac{3}{4}[/tex]
[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]
The value of the trigonometric ratio of an angle of the triangle is;
[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]
Given
Right △EFG has its right angle at G, EF=8, and FG=6.
Pythagoras theoremThe Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.
In right-angle △EFG, in which E is a right angle.
[tex]\rm EF^2=FG^2-EG^2\\\\8^2=6^2-EG^2\\\\EG^2=8^2-6^2\\ \\EG^2=64-36\\\\EG^2=28\\\\EG = 2\sqrt{7}[/tex]
The value of the trigonometric ratio of an angle of the triangle is;
[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠K.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠K = °
Answer:
Step-by-step explanation:
[tex]tan K=\frac{2}{3} \\m \angle K=tan^{-1} (\frac{2}{3} ) \approx 33.7 ^\circ[/tex]
How do you do this problem?
Answer:
A) g is increasing, and the graph of g is concave up.
Step-by-step explanation:
g'(x) = ∫₀ˣ e^(-t³) dt
Since e^(-t³) is always positive, ∫₀ˣ e^(-t³) dt is positive when x > 0. So the function is increasing.
Find g"(x) by taking the derivative using second fundamental theorem of calculus:
g"(x) = e^(-x³)
g"(x) is always positive, so the function is always concave up.
The Sweet Shoppe wishes to sell a special mix for Valentine’s Day that consists of Dark Chocolate that costs $4.00 per lb and Milk Chocolate that costs $2.00 per lb. How much of each should be used to get a 50 lb mix that costs $2.60 per lb?
Answer: Quantity of Dark Chocolate used = 15 lb
Quantity of Milk Chocolate used = 35 lb
Step-by-step explanation:
Let x = Quantity of Dark Chocolate.
y = Quantity of Milk Chocolate.
As per given , we have the following system of equations:
[tex]x+y= 50-------------(1)\\\\ 4x+2y=50\times2.60\\\\ 4x+2y=130-----------(2)[/tex]
Multiply equation (1) by 2 , we get
[tex]2x+2y= 100-------(3)[/tex]
Eliminate equation (3) from equation (2) , we get
[tex]2x=30\\\Rightarrow\ x=15[/tex]
Put x= 15 in (1) , we get [tex]15+y=50[/tex]
⇒ y=35
Therefore , Quantity of Dark Chocolate used = 15 lb
Quantity of Milk Chocolate used = 35 lb
Please help ASAP. Will give Brainliest and 50 points
A jar contains 5 green, 3 black, and 2 red marbles. Brandi draws a marble from the jar and then puts it back. She then draws
another marble. What is the probability that Brandi draws
a. 2 greens
b. 2 reds
c. 1 black and 1 green
d. 1 green and 1 red
Step-by-step explanation:
a. 5/10 x 5/10 = 25%
b. 2/10 x 2/10 = 4%
c. 3/10 x 5/10 = 15% (Probability for getting black then green)
5/10 x 3/10 = 15% (Probability of getting green then black)
Thus, probability of getting green and black in any order is 30%
d. SIimilarly,
5/10 x 2/10 = 10% (Green then red)
2/10 x 5/10 = 10% (Red then green)
Green and red in any order 20%
Answer:
Depending on the remaining of the question. C is the answer
Step-by-step explanation:
5/10 x 5/10 = 25%
2/10 x 2/10 = 4%
3/10 x 5/10 = 15% Probability for getting black then green
5/10 x 3/10 = 15% Probability of getting green then black
green and black in any order is 30% the changes are higher in this case.
5/10 x 2/10 = 10% (Green then red)
2/10 x 5/10 = 10% (Red then green)
Green and red in any order 20%
Alden paid to have some programs printed for the football game last weekend. The printing cost per program was 54 cents, and the plan was to sell them for 75 cents each. Poor weather kept many fans away from the game, however, so unlucky Alden was left with 100 unsold copies, and lost $12 on the venture. How many programs did Alden have printed?
Answer:
300 programs
Step-by-step explanation:
Let’s work with cents to make this easier. We convert the $12 to cents, making 1200 cents
Let the number of copies Alden printed be x. His total printing cost would be x * 54 = 54x cents.
He sold at 75 cents each and still had left 100 copies. This means his total sale would be (x - 100)75
He lost $12 on the venture. This means his cost price minus his selling price is $12 since it’s a loss.
Computing this:
54x - 75(x - 100) = 1200
54x - 75x + 7500 = 1200
-21x = 1200 - 7500
-21x = -6,300
x = 6300/21 = 300 programs
Ena's income is $1900 a month, and she plans to budget 29 of her income for entertainment and 15 of her income for groceries. Step 1 of 2 : What fraction of her income does she plan to spend each month on these two items together? Express your answer in lowest terms.
Answer:
2/10 of her income will go to these items
Step-by-step explanation:
29 +15 = 41
41/1900 equal 2/10
Final answer:
Ena plans to spend 29% of her income on entertainment and 15% on groceries, which is a total of [tex]\(\frac{44}{100}\)[/tex]of her income. Simplifying this to its lowest terms gives us [tex]\(\frac{11}{25}\)[/tex] of her income spent on these two items together.
Explanation:
To find the fraction of Ena's income that is spent on entertainment and groceries together, we need to sum the fractions of income allocated to each category. Ena plans to spend 29% of her income on entertainment and 15% on groceries. In fractional terms, 29% is the same as 29/100 and 15% is equivalent to 15/100. Adding these fractions together:
[tex]\(\frac{29}{100} + \frac{15}{100} = \frac{44}{100}\)[/tex]
Now, we simplify the fraction to its lowest terms:
[tex]\(\frac{44}{100} = \frac{44 \div 4}{100 \div 4} = \frac{11}{25}\)[/tex]
Thus, Ena plans to spend [tex]\(\frac{11}{25}\)[/tex]of her income on entertainment and groceries together.
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y = x^2 +2x -5
Answer:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y -intercept(s): ( − 1 + √ 6 , 0 ) , ( − 1 − √ 6 , 0 ) y-intercept(s): ( 0 , − 5 )
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
A warehouse worker ships 25 boxes each day. Every box contains 3 shipping labels. Inventory has 500 shipping labels. How many days will it take to use the inventory of shipping labels? round to the nearest whole.
Answer: It will take 7 days to use the inventory of shipping labels.
Step-by-step explanation:
Given : Total boxes shipped by warehouse worker per day = 25
Every box contains 3 shipping labels.
Inventory has 500 shipping labels.
Then, the total number of boxes can be made = (Total shipping labels) ÷ (labels in each box)
500 ÷ 3 =166.67≈166
Number of days it will take to use the inventory of shipping labels= (total number of boxes can be made) ÷ (Total boxes shipped per day)
= 166÷ 25=6.64≈7
Hence, it will take 7 days to use the inventory of shipping labels.
It will take about 7 days to use the inventory of shipping labels.
Explanation:To find how many days it will take to use the inventory of shipping labels, we need to divide the total number of shipping labels by the number of shipping labels used per day.
The total number of shipping labels is 500 and the worker ships 25 boxes each day, with each box containing 3 shipping labels.
So, the worker uses 25 x 3 = 75 shipping labels per day.
Dividing the total number of shipping labels (500) by the number of shipping labels used per day (75), we get 500 / 75 = 6.67.
Rounding to the nearest whole number, it will take about 7 days to use the inventory of shipping labels.
The sum of two numbers is 29
and their product is 180.
Find the numbers.
Final answer:
To find the two numbers with a sum of 29 and product of 180, we set up a system of equations, solve for one variable in terms of the other, and then factor a quadratic equation to find that the two numbers are 20 and 9.
Explanation:
The student's question is about finding two numbers based on their sum and product. To solve this, we can set up two equations based on the given information: let's call our numbers x and y. The first equation based on their sum is x + y = 29, and the second equation based on their product is xy = 180.
We can find one number in terms of the other using the first equation: y = 29 - x. We then substitute this into the second equation to get x(29-x) = 180. Simplifying, we have x² - 29x + 180 = 0. Factoring the quadratic equation, we get (x - 20)(x - 9) = 0, which gives us two possible values for x: 20 or 9. Thus, the two numbers are 20 and 9.
Please help me, Geometry is really hard for me.
Answer:
Step-by-step explanation:
the answers c.
Barry runs at an average rate of 8 mi/hr. He walks at an average rate of 3 mi/hr. If x represents the time spent running and y represents the time spent walking, write a linear equation that relates the time he could spend running and walking if he travels a total distance of 16 miles
============================
Work Shown:
x = number of hours spent running
8x = distance he runs (since he runs at 8 mph)
y = number of hours spent walking
3y = distance he walks (he walks at a speed of 3 mph)
8x+3y = total distance = 16 miles
8x+3y = 16
This equation is in standard form Ax+By = C
--------
Extra Info
Solving for y will get
8x+3y = 16
3y = -8x+16
y = (-8x+16)/3
y = (-8x)/3+16/3
y = (-8/3)x+16/3
This is in slope intercept form y = mx+b
m = -8/3 is the slope
b = 16/3 is the y intercept
Significant Figures PracticeName________________________ Date_____________ Section________________
1. State the number of significant digits in each measurement. 1) 2804 m2) 2.84 km3) 5.029 m4) 0.003068 m5) 4.6 x 105 m 6) 4.06 x 10-5 m7) 750 m8) 75 m 9) 75,000 m 10) 75.00 m 11) 75,000.0 m 12) 10 cm 2. Round the following numbers as indicated:To four figures:3.68241721.860051375.6523112.51145.4673To one decimal place:1.35112.4735.6875247.5558.235To two decimal places:22.49479.25880.030623.412541.866323. Solve the following problems and report answers with appropriate number of significant digits.1) 6.201 cm + 7.4 cm + 0.68 cm +12.0 cm =
2) 1.6 km + 1.62 km +1200 km =
3) 8.264 g - 7.8 g =
4) 10.4168 m - 6.0 m =
5) 12.00 m+15.001 kg=
6) 1.31 cm x 2.3 cm =
7) 5.7621 m x 6.201 m = 8) 20.2 cm / 7.41 s =
Answer:1)2804m^2=4s.f
2)84Km^3=2s.f
3)5.029m=4s.f
4)0.00003068m=4s.f
5)4.6×10^5m=2s.f
6)4.06×10^-5m=3s.f
7)750m=3s.f
8)75m=2s.f
9)75,000.0m=5s.f
10)75.00m=2s.f
11)75,000.00m=5s.f
12)10cm=2s.t
B) to four significant figures
1)3.682
2)860100
3)375.7
4)51150
5)4673
C to 1 decimal places
1)1.4
2)4735.0
3)687524.0
4)7.6
5)235.0
Dto 2d.p
1)22.49
2)25880.00
3)30623.00
4)412541.00
5)866323.00
E)
1)6.201cm+7.4cm+0.68cm+12.0cm=26.281cm
2)1.6km+1.62km+1200km=1203.22km
3)8.264g-7.8g=0.464g
4)10.4168m-6m=4.4168m
5)12.00m+15.001kg=12.00m+15.001kg
6)1.31cm×2.3cm=3.013cm^2
7)5.7621m×6.201m=35.7308m^2
8)20.2cm/7.41s=2.726cm/s
Step-by-step explanation:
S.f means significant figures or Digits.
2)cm +kg is impossible because they are unlike termsi.e they do not have any thing in common, hence 12.00m+15.001kg cannot be added up.
This detailed answer involves the concept of significant figures, rounding off significant figures, and performing calculations while maintaining the appropriateness of significant figures in measurement.
Explanation:Number of significant digits
Significance figures involve the digits in a number that carry meaningful information about its precision.
2804 m - 4 significant digits2.84 km - 3 significant digits5.029 m - 4 significant digits0.003068 m - 4 significant digits4.6 x 10^5 m - 2 significant digits4.06 x 10^-5 m - 3 significant digits750 m - 2 significant digits75 m - 2 significant digits75,000 m - 2 significant digits (trailing zeros in a whole number do not count as significant figures)75.00 m - 4 significant digits (trailing zeros in a decimal number do count as significant figures)75,000.0 m - 6 significant digits.10 cm - 1 significant digit
Rounding off to Significant Figures
To round to a certain number of significant figures, start from the first non-zero number and count the number of digits required, rounding the last one if necessary. Here are your rounded numbers:
To four figures: 3.6825; 21.86; 375.7; 112.5; 45.67.To one decimal place: 1.4; 2.5; 5.7; 248; 8.2.To two decimal places: 22.49; 79.26; 80.03; 23.41; 41.87.
Performing Calculations
In adding or subtracting numbers, the result should retain the smallest number of decimal places in the input values. In multiplication or division, the result should retain the smallest number of significant figures in the input values. Here are your answers:
6.2 cm + 7.4 cm + 0.68 cm +12.0 cm = 26.3 cm.1.6 km + 1.62 km +1200 km = 1204 km.8.264 g - 7.8 g = 0.46 g.10.4168 m - 6.0 m = 4.4 m.Cannot add metres and kilograms - invalid calculation.1.31 cm x 2.3 cm = 3.0 cm^2.5.7621 m x 6.201 m = 35.728 m^2.20.2 cm / 7.41 s = 2.7 cm/s.Learn more about Significant Figures here:https://brainly.com/question/37022020
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The explicit formula for a sequence is
an=−1+3(n−1)
What is the 55th term of the sequence?
Step-by-step explanation:
[tex] \because \: a_n = - 1 + 3(n - 1) \\ \\ \therefore \: a_{55} = - 1 + 3(55 - 1) \\ \\ \therefore \: a_{55} = - 1 + 3 \times 54 \\ \\ \therefore \: a_{55} = - 1 + 162\\ \\ \huge \blue { \boxed{\therefore \: a_{55} = 161}}\\ \\ [/tex]
Hence, the 55th term of the sequence is 161.
Tv emporium had a huge sale in the morning 5/12 of the flat screen televisions were sold in the afternoon one-third of the flat screen televisions were sold how many flat screen televisions were sold all together
Answer:
Total number of flat screen sold is 3/4
Step-by-step explanation:
Let the total number of the flat screen sold be y
y = number of flat screen sold in the morning + number of the flat screen sold in the afternoon.
Number sold in the morning = 5/15
Number sold in the afternoon = 1/3
Y = 5/12 + 1/3
Find the LCM of 12 and 3
Y = (5 + 4)/12
Y = 9/12
Y = 3/4
Total number of flat screen sold is 3/4
5/12
+1/3
=9/12
Reduce to 3/4
Step-by-step explanation:
The equation R= -0.028t +20.8 can be used to predict the world record in the 200 meter dash, where R stands for the record in seconds and t for the number of years since 1920. In what year did the record become 19.68 seconds?
Final answer:
To find the year when the record became 19.68 seconds, substitute the value of R into the equation. Solve for t and add 1920 to get the year.
Explanation:
To find the year when the record became 19.68 seconds, we need to substitute the value of R into the equation:
R = -0.028t + 20.8
19.68 = -0.028t + 20.8
Solving for t:
Subtract 20.8 from both sides: -0.028t = -1.12
Divide both sides by -0.028: t = 40
Since t represents the number of years since 1920, we add 1920 to the result to get the year:
t + 1920 = 40 + 1920 = 1960
Therefore, the record became 19.68 seconds in the year 1960.
A researcher records the family relationship (brother, son, father, cousin, etc.) of the
people who stay in regular contact with loved ones in a nursing home. What type of measure
is family relationship?
A) Quantitative and discrete
B) Qualitative and discrete
C) Qualitative and continuous
D) Quantitative and continuous
Answer:
The correct option is B) Qualitative and discrete.
Step-by-step explanation:
Consider the provided information.
Quantitative variable is the variables that can be determined by counting or measuring something.
Qualitative variable is the variables that can't be determined by counting or measuring something.
If the value is obtained by counting then it is called discrete variable, If the value obtained by measuring then it is called continuous variable.
Since the relationship can't be measure by counting so it it qualitative variable.
We can calculate the regular contact days so it is discrete variable.
Therefore, the correct option is B) Qualitative and discrete.
To determine customer opinion of their safety features, Daimler - Chrysler randomly selects 110 service centers during a certain week and surveys all customers visiting the service centers. What type of sampling is used? a.Simple b.random c.Convenience d.Cluster e.Systematic f.Stratified
Simple sampling - A method where individuals are chosen randomly from a larger set.
Convenience sampling - The sample is being chosen as per ease of access thus it is not a random sampling.
Systematic sampling - Probability method where elements are chosen from a target population.
Stratified sampling - Method where population were divided into different groups called strata and the sample is then drawn from each group.
Cluster sampling - Population is where population were divided into different groups known as clusters. The clusters were then chosen randomly as the samples.
Answer: D (cluster sampling) - The service centers refer as the clusters and it is chosen randomly.
Final answer:
The Daimler - Chrysler survey method is an example of cluster sampling, where random groups (service centers) are selected and all members within these groups are surveyed.
Explanation:
The type of sampling used by Daimler - Chrysler when they randomly select 110 service centers during a certain week and survey all customers visiting those service centers is cluster sampling. In cluster sampling, the overall population is divided into groups, or clusters, and a random selection of these clusters is chosen.
All members (or customers, in this case) within these selected clusters are surveyed. This method is often more practical and cost-effective than surveying the entire population. It is important that the clusters themselves are representative of the population to ensure that data obtained is not biased.
PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTURE !
answer is C: [tex]\frac{EF}{DF}[/tex]
Answer:option C is the correct answer
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle,
DF represents the hypotenuse of the right angle triangle.
With m∠θ as the reference angle,
EF represents the adjacent side of the right angle triangle.
DE represents the opposite side of the right angle triangle.
To determine Cos ∠θ, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos θ = EF/DF
A baker started out with 13 cups of flour.She had 9 and 1 four cups of flour left after the first batch of batter she made.She have 6 and 1 half cups of flour left after the second batch of batter she made.If she makes two more batches of batter,how many cups of flour will be left?
Question is wrong; Correct question is given below;
A baker started out with 12 cups of flour she had 9 1/4 cups of flour left after the first bunch of batter she made she had 6 1/2 cups of flour left after the second bunch of batter she made if she makes two more batches of batter how many cups of batter will be left?
Answer:
Baker will be left with 1 cups of Flour.
Step-by-step explanation:
Given
Amount of flour baker started with = 12 cups
Amount of flour left after making first batter = [tex]9\frac14\ cups[/tex]
[tex]9\frac14\ cups[/tex] can be Rewritten as [tex]\frac{37}4\ cups[/tex]
Amount of flour left after making first batter = [tex]\frac{37}4\ cups[/tex]
Now we can say that;
Amount of flour used to make first batter is equal to Amount of flour baker started with minus Amount of flour left after making first batter
Thus, the Amount of flour she use to make first batter = [tex]20-\frac{37}{4}[/tex]
Now we will use LCM to make the denominator common we get;
Amount of flour she use to make first batter = [tex]\frac{20\times4}{4}-\frac{37\times1}{4\times1} = \frac{48}{4}-\frac{37}{4}[/tex]
Now denominator common so we will solve the numerator we get;
Amount of flour she use to make first batter = [tex]\frac{48-37}{4}=\frac{11}{4}\ cups.[/tex]
Now Given:
Amount of flour left after the second batch of batter = [tex]6\frac12\ cups[/tex]
[tex]6\frac12\ cups[/tex] can be Rewritten as [tex]\frac{13}2\ cups[/tex]
Amount of flour left after the second batch of batter = [tex]\frac{13}2\ cups[/tex]
Thus, the quantity she use to make second batter = [tex]\frac{37}{4}-\frac{13}{2}[/tex]
Now we will use LCM to make the denominator common we get;
Amount of flour she use to make Second batter = [tex]\frac{37\times1}{4\times1}-\frac{13\times2}{2\times2}=\frac{37}{4}-\frac{26}{4}[/tex]
Now denominator common so we will solve the numerator we get;
Amount of flour she use to make Second batter = [tex]\frac{37-26}{4}=\frac{11}{4}\ cups[/tex]
Thus, she use [tex]\frac{11}{4}\ cups[/tex] of flour for each batter.
Amount of Flour used in making 2 more batter = [tex]2\times\frac{11}{4}= \frac{11}{2}\ cups[/tex]
Now we can say that;
Cups of flour left will be equal to Amount of flour left after the second batch of batter minus Amount of Flour used in making 2 more batter.
framing in equation form we get;
Cups of flour left = [tex]\frac{13}{2}-\frac{11}{2}=\frac{13-11}{2}=\frac{2}{2}=1\ cup[/tex]
Hence Baker will be left with 1 cups of Flour.
Three numbers, of which the third is equal to 12, form a geometric progression. If 12 is replaced with 9, then the three numbers form an arithmetic progression. Find these three numbers.
Final answer:
To find the three numbers, we determine 'a' and 'r' using a system of equations derived from the conditions that they form a geometric progression with 12 and an arithmetic progression with 9. By solving these equations, we obtain the three numbers in sequence.
Explanation:
The question requires us to find three numbers that form a geometric progression with the third being 12, and when the third number is changed to 9, the numbers form an arithmetic progression.
Let's denote the first number as 'a' and the common ratio of the geometric progression as 'r'. The three numbers in the geometric progression can be represented as 'a', 'ar', and 'ar^2'. Given that the third number is equal to 12, we have 'ar^2 = 12'.
When 12 is replaced with 9 to form an arithmetic progression, the common difference 'd' can be found by subtracting the first term from the second term. The three numbers in this sequence are 'a', 'a + d', and 'a + 2d'. Given that the third number is now 9, we have 'a + 2d = 9'.
To find 'a' and 'r', we can set up a system of equations using the fact that the second number in both progressions is the same. So 'ar = a + d'. We have the following system:
ar^2 = 12 (1)
a + 2d = 9 (2)
ar = a + d (3)
From equation (3), we can solve for 'd' in terms of 'a' and 'r': 'd = ar - a = a(r - 1)'. Substituting 'd' in equation (2), we get 'a + 2(a(r - 1)) = 9', which simplifies to 'a(2r + 1) = 9'.
Using this new equation along with equation (1), we solve for 'a' and 'r' to find the three numbers:
a(2r + 1) = 9 (4)
ar^2 = 12 (1)
From equation (1), 'a = 12/r^2'. Substituting this into equation (4) gives us a single equation: '12/r^2(2r + 1) = 9', which we can solve to find 'r', and subsequently, 'a'. After solving these, we find the three numbers that form both the geometric and arithmetic progressions.
what is the graph of the inequality in the coordinate plane x ≥ 1
Answer: basically it would be whatever side the x is one indicating x is greater than 1
Step-by-step explanation:
S is between B and C. True or false
I would say false.
B is on top of S.
I'm using common sense here but If you were to draw a line from B and C.
S would not be marked in between that line.
The claim "S is between B and C" is false.
Is the statement true or false?S is between B and C only if the 3 points are collinear, and S is between the other poitns in that line.
In the triangle we can see that CS and SB are perependicular lines, so the 3 points are not collinear, and thus, the statement "S is between B and C" is false.
Learn more about collinear points.
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I need help with this practice problem
Answer:
a. see below
b. Rita: 300; John: 900; Rodell: 925
c. Rita: L; John: 3L; Rodell: 3L+25
d. L +3L +(3L+25) = 2125
e. Rita: $600; John: $1800; Rodell: $1850
Step-by-step explanation:
Since John's number of laps is expressed in terms of Rita's number of laps, it makes a certain amount of sense to use Rita's laps as a unit of measure. We don't yet know what that unit of measure is, but we can use it to describe both John's laps and Rodell's laps. Rodell will have 25 additional laps added to the 3 units that match John's laps.
Altogether, these 7 units +25 laps will match the total of 2100 +25 laps. It is pretty clear that 1 unit will be 2100/7 = 300 laps. This is shown in the attachment.
__
a) The attachment matches the above description.
__
b) 1 unit of 300 laps is the number of laps Rita swam. Then John's 3 units correspond to 3×300 = 900 laps, and Rodell's laps will be 25 more than John's, so 925.
__
c) In this part, we define 1 unit as L, so the three contributors are ...
Rita: LJohn: 3LRodell: 3L+25__
d) The equation shows that the sum of the parts is equal to the whole:
L + 3L + (3L+25) = 2125
__
e) The numbers of part (b) get multiplied by $2, so are ...
Rita: $600John: $1800Rodell: $1850