(a) | Masses (kg) | Frequency | Cumulative Frequency |
|-------------|-----------|---------------------|
| 15-24 | 14 | 14 |
| 25-34 | 54 | 68 |
| 35-44 | 24 | 92 |
| 45-54 | 26 | 118 |
| 55-64 | 2 | 120 |
(b) The cumulative frequency curve starts from the origin (0, 0) and moves upward and to the right, indicating that the mass of logs is increasing as we move right on the x-axis.
To construct the cumulative frequency table for the distribution of masses of 120 logs of wood, we need to add up the frequencies of each class and all the classes before it.
(b) To draw a cumulative frequency curve, we plot the cumulative frequency values against the upper class limits. The plot shows how the cumulative frequency increases with the increase in the mass of the log.
We use the same class intervals as in part (a):
- x-axis = Masses (kg)
- y-axis = Cumulative frequency
To plot the cumulative frequency curve, we mark the upper limit of each class on the x-axis, and its corresponding cumulative frequency on the y-axis. Then, we join the plotted points with a smooth curve, as shown in the graph.
The steeper the curve, the more rapid the increase in cumulative frequency, indicating that a larger number of logs fall in higher mass categories.
In the given distribution, the plot of the cumulative frequency curve shows that the majority of logs fall in the mass range of 25-34 kg, closely followed by the range of 45-54 kg.
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Cypress Middle School wants to have a fundraiser to buy art supplies. Fundraiser A will give the school $1.50 for each order placed plus $75 as a bonus. Fundraiser B will give the school $3.00 for each order placed, but no bonus. How many orders must be placed in order for the total amount of money earned by each fundraiser?
A. 150
B. 5
C. 17
D. 50
Answer:
A
Step-by-step explanation:
I don't know noya
2. The second term of an arithmetic sequence is -5, and the third term is 12. What is the first term?
Answer: -12
Step-by-step explanation:
To get from -5 to 12, you'd add 7
So to get to the first, subtract 7 from -5
The first term of an arithmetic progression whose second term is -5 and third term is 12 is -22.
What is an Arithmetic progression?
An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -
a₁ , a₂, a₃ , a₄ ...... aₙ
will be an arithmetic progression if -
a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.
Given is the second term of an arithmetic sequence which is -5 and the third term is 12.
We can calculate the nth term of an A.P. using the formula -
a[n] = a + (n - 1)d
Now -
a[2] = -5
a + (2 - 1)d = -5
a + d = - 5 ... [1]
and
a[3] = 12
a + (3 - 1)d = 12
a + 2d = 12 .... [2]
Expanding equation [2] further, we get -
(a + d) + d = 12
- 5 + d = 12
d = 17
Then -
a + d = -5
a = - 5 - d
a = -5 - 17
a = - 22
Therefore, the first term of an arithmetic progression whose second term is -5 and third term is 12 is -22.
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9. You have worked all summer long and saved $1240.
You want to buy a car that costs $5400. How much
money, m, do you need before you can buy the car?
10.
at y
you
Answer:
the answer is 4160
Step-by-step explanation:
because if you subtract 5400 by the money you worked for that is your sum yw xx.
Answer:
Step-by-step explanation:
We have to subtract the amount of money that you have earned by the amount of money that the car costs.
$5400-$1240 is $4160
So you need $4160 more money to buy the car
(Good luck getting that much money XD)
Hope this helps!
can someone help? and explain
A set of points that lie in the same plane are collinear. True O False
Answer:
Step-by-step explanation:
two lines are guaranteed to be coplanar if they lie in the same plane
Answer:
it would be true
Step-by-step explanation:
its guaranteed
The length of a side of a square is given by the expression 2x+1, and its perimeter is 56. Calculate the length of a side of the square.
Answer:
8x+4
Step-by-step explanation:
8x+4=56
56-4=52 52 divided 8 = 6.5
The formula c = 5p + 215 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending the party.
a. solve for p
b. If Allies parents are are willing to spend $300 for her party, how many people can attend. Show your work.
Answer: a. p = c/5 - 43 b. 17 people
Step-by-step explanation:
c= 5p + 215
A) a said solve for p so we will solve for p in the equation.
c= 5p + 215 First Subtract 215 from both sides
-215 -215
c - 215 = 5p Now divide both sides by 5.
p = c/5 - 43
B) If c is the total cost of hosting a birthday party then we will input 300 into the equation for c and solve for p.
300 = 5p + 215 First subtract 215 from both sides
-215 -215
85 = 5p Divide both sides by 5
p = 17
This means 17 people can attend the meeting if Allies parents are willing to spend $300.
The number of people that can attend the party will be 17
Since the formula given is represented by c = 5p + 215, to solve for p, we've to use subject of the formula and this will be:
c = 5p + 215
c - 215 = 5p
p = (c - 215)/5
p = c/5 - 43
Based on the equation given, the number of people that can attend the party will be:
c = 5p + 215
300 = 5p + 215
Collect like terms
5p = 300 - 215
5p = 85
p = 85/5
p = 17
Therefore, 17 people can attend the party.
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what the answer for this pls help me its way too complicated thank you very very much
The product of the given expressions 6 × x × y and 2 × x × 3 × y are both equivalent to 6xy.
How to find product?Multiplication is another term for product and it is the process of finding the sum of a number with itself a specified number of times, or any other analogous binary operation that combines other mathematical objects.
6 × x × y
= 6xy
2 × x × 3 × y
= 6xy
Hence, 6 × x × y and 2 × x × 3 × y equals 6xy.
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What is the intersection of plane HGY and plane GEF?
GH
Step-by-step explanation:Hi !
GH ∈ (HGY)
GH ∈ (GEF) } => (HGY) ∩ (GEF) = GH
Good luck !
Rita's water tank contains 7.8 gallons of water. Rita will begin filling her water tank at a rate of 2.1 gallons per minute. Wendy's water tank contains 97.8 gallons of water. Wendy will begin draining her water tank at a rate of 0.9 gallon per minute. After how many minutes will both water tanks contain the same amount of water? 25 min 30 min 35 min 75 min
Answer:
30 minutes
Step-by-step explanation:
Given the following :
Rita's tank contains =7.8 gallons of water
Filling rate = 2.1 gallons per minute
Wendy's tank contains = 97.8 gallons
Drain rate =. 0.9 gallons per minute
After how many minutes will both contain the same amount of water.
Let number of minutes = m
Rita is filling :
Initial + increase
7.8 + 2.1m ----(1)
Wendy is emptying:
Initial - decrease
97.8 - 0.9m - - - (2)
Equate both ;
(1) = (2)
7.8 + 2.1m = 97.8 - 0.9m
2.1m + 0.9m = 97.8 - 7.8
3m = 90
m = 90 / 3
m = 30 minutes
describe the error in graphing the function .
and correct the error
Denise is using a ladder to clean the outside of her second story windows. The ladder she is using is 24 feet long, and she puts the base of the ladder 13 feet away from the house in order to avoid her flower gardens. How high up the side of her house does the ladder reach?
La profesora de sexto grado coloca en la pizarra los siguientes números, y les pide a sus estudiantes determinar el MCD de dichas cifras:
180 - 225
¿Cuál será la respuesta correcta que darán los estudiantes?
A. 90
B. 60
C. 45
D. 15 La profesora de sexto grado coloca en la pizarra los siguientes números, y les pide a sus estudiantes determinar el MCD de dichas cifras:
180 - 225
¿Cuál será la respuesta correcta que darán los estudiantes?
A. 90
B. 60
C. 45
D. 15
15 is the GCD of 45 and 15.
The teacher of the sixth grade places the following numbers on the board and asks her students to determine the GCD of these digits:C. 45D. 15GCD (45, 15) or the Greatest Common Divisor of 45 and 15 is the largest number that divides both 45 and 15 without leaving a remainder.The prime factorization of 45 is as follows:45 = 3 x 3 x 5To get the prime factorization of a number, divide it by its smallest prime factor (which is 3 in this case) and then divide the resulting quotient by its smallest prime factor, if possible. This operation is repeated until a prime number is reached.The prime factorization of 15 is as follows:15 = 3 x 5Thus, the common factors between 45 and 15 are 3 and 5, and the highest common factor is 3 x 5 = 15, which is the Greatest Common Divisor.GCD (45, 15) = 15
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1. Two angles have the same value if they are complementary angles. TRUE FALSE
Answer: False
Step-by-step explanation: If two angles are complementary,
then the sum of their measures is 90 degrees.
In other words, any two angles whose sum is 90 when
their measures are added together are complementary angles.
Take a look at the angles below.
Do they have the same value?
Well obviously no, they don't so they aren't congruent.
However, they are still complementary because
the sum of their measures is 90 degrees.
5. A statue that cast a shadow that is 7 feet long. A 5 ſt person looking at it cast a shadow that 2.5 feet long. How tall is that person?
Question 4 of 10
Solve the inequality for x and identify the graph of its solution.
|x+31 > 2
Choose the answer that gives both the correct solution and the correct graph.
A. Solution: x < -5 or x>-1
HI
10
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
B. Solution: x>-5 and x < -1
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
C. Solution: x> 1 and x<5
H||$11
-2 -1 0 1 2 3 4
D. Solution: x<-5 or x>-1
o + +
5 6 7 8
H||$||
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2
The correct answer is option D. Solution: x < -5 or x > -1, and the correct graph would have open circles at -33 and -29 with shading to the left of -33 and to the right of -29 on a number line.
To solve the inequality |x+31 > 2|, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: x+31 > 2
In this case, we can solve the inequality by subtracting 31 from both sides:
x + 31 - 31 > 2 - 31
x > -29
Case 2: -(x+31) > 2
To solve this case, we need to flip the inequality sign when multiplying or dividing by a negative number:
x + 31 < -2
x < -33
The solution to the inequality is x < -33 or x > -29.
Now, let's analyze the given answer choices and identify the correct solution and graph:
A. Solution: x < -5 or x > -1
This answer choice does not match the solution we derived, so it is incorrect.
B. Solution: x > -5 and x < -1
This answer choice does not match the solution we derived, so it is incorrect.
C. Solution: x > 1 and x < 5
This answer choice does not match the solution we derived, so it is incorrect.
D. Solution: x < -5 or x > -1
This answer choice matches the solution we derived (x < -33 or x > -29), so it is correct.
Based on the correct solution, the graph would have an open circle at -33 and -29 on a number line, indicating that the values are not included in the solution set. The line would be shaded to the left of -33 and to the right of -29.
The correct answer is option D. Solution: x < -5 or x > -1, and the correct graph would have open circles at -33 and -29 with shading to the left of -33 and to the right of -29 on a number line.
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work out the perimeter of a semicircle with radius 3cm. give your answer in terms of pi
Answer:
[tex]\pi r + d \\ [/tex]
The circumference of a circle = 2πr
But here they asked half of the circumference = πr
By substituting this we get the answer 3π
Now add the diameter = 3π+6
Someone help pleaseeee
Step-by-step explanation:
come on, now, this is one of the (if not THE) most important formula you need to remember for the rest of your life :
a² + b² = c²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
so, in our case, we have then
x² = 5² + 12² = 25 + 144 = 169
x = sqrt(169) = 13
what is 0.000750 in scientific notation?
Answer:
7.5 × 10-4
Step-by-step explanation:
Answer: 7.5x10^-4
Step-by-step explanation:
Ms.Coreas is trying to grow some Yeast in her lab for a Bread experiment… She starts with only 1 yeast cell and needs at LEAST 4,000… If the yeast cells multiply by 4 every day, how many yeast will she have in 5 days? please hurry it is due today
Answer:
21 cells
Step-by-step explanation:
4x5+1=21
0.019 in scientific notation
Answer:
1.9x10^-2
hope this helps
Step-by-step explanation:
Answer: 1.9 • 10^-2
-----------------------------------------------------------------------------------------------------
is cube of a number ending in 5 may or may not end in 5. True or false.
Please help!!! Brainliest answer! Thank you
Answer:
112
Step-by-step explanation:
angle = 1/2(sum of Intercepted Arcs)
BFE = 1/2( 72+152)
= 1/2 ( 224)
= 112
HELP NOW What is the X and Y intercept of the graph of by+ax=c
Answer:
X int = (1,0) y int= (0,1)
Step-by-step explanation:
Х2
х
1
1
xx
1 1
What’s the area of a squarw
Could you rephrase the question a bit? We can't tell what the numbers are... :)
given allowable stresses in steel and concrete of 150mpa and 12mpa, respectively, calculate the maximum bending moment the section can carry
Given allowable stresses in steel and concrete of 150MPa and 12MPa, respectively, the maximum bending moment that the section can carry can be determined as follows:
Assuming the section is made up of steel and concrete, it is essential to consider the stresses on both materials. By considering the material properties of the section, the overall strength of the section can be obtained.
Therefore, the bending moment that a section can carry can be given by the formula:
M = σ_s * Z_s + σ_c * Z_c
Where: M = Maximum bending moment that the section can carry
σ_s = Maximum allowable stress in steel
Z_s = Section modulus of steel
σ_c = Maximum allowable stress in concrete
Z_c = Section modulus of concrete
Therefore, the maximum bending moment that the section can carry = 150*Z_s + 12*Z_c
To determine the section modulus of the steel and concrete, we can use the formula:
Z = I/y
whereZ = section modulus
I = Moment of Inertia of the section
y = distance of the neutral axis to the extreme fibre
By determining the section modulus of the steel and concrete, the maximum bending moment that the section can carry can be calculated.
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What observations do you notice about TB tests based on the tree diagram? (Hint: What do the numbers of the tree diagram represent?)
is 8 1/2 rational or irrational
viola drives 170 meters up a hill that makes an angle of 6° with the horizontal. to the nearest tenth of a meter, what horizontal distance has she covered?
a). 171.5 m
b). 169.1 m
c). 1617.4 m
d). 17.8
Viola drove 170 meters up the hill that makes an angle of 6° with the horizontal. We are to find what horizontal distance she has covered.
Let us say the horizontal distance she has covered is x meters. From the given information, we know the length of the inclined plane, which is 170 meters. Also, the angle of inclination is 6°. Hence, we know the value of opposite side and the hypotenuse.The horizontal distance she has covered is the adjacent side.Using the trigonometric formula of the tangent function, we get:
tan 6° = opposite/adjacent
tan 6° = x/170 x = 170
tan 6° Using a scientific calculator, we get
:x = 17.8 meters (nearest tenth of a meter).
Hence, the correct answer is option (d) 17.8 meters.
Viola has covered 17.8 meters horizontally.
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a card is drawn from a standard deck and replaced. after the deck is shuffled, another card is pulled. what is the probability that the first card drawn is a heart and the second card is a spade? (enter your probability as a fraction.)
If a card is drawn from a standard deck and replaced. after the deck is shuffled, another card is pulled. Then the probability that the first card drawn is a heart and the second card is a spade is 1/16.
The probability of drawing a heart on the first card is 1/4 since there are 13 hearts out of a total of 52 cards in a standard deck.
After replacing the card and shuffling the deck, the probability of drawing a spade on the second card is also 1/4 since there are 13 spades out of a total of 52 cards in the deck (assuming the deck is well-shuffled).
To find the probability of both events happening (drawing a heart and then a spade), we multiply the individual probabilities together:
Probability = (1/4) * (1/4) = 1/16
Therefore, the probability that the first card drawn is a heart and the second card is a spade is 1/16.
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