Using proportions, it is found that the scale of the drawing is of 1 ft:0.4 cm.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that 35 cm represent 87.5 ft. How many cm represent a ft?
The rule of three is given by:
35 cm - 87 ft
x cm - 1 ft
Applying cross multiplication:
[tex]87x = 35[/tex]
[tex]x = \frac{35}{87}[/tex]
[tex]x = 0.4[/tex]
Hence, the scale of the drawing is of 1 ft:0.4 cm.
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HELP PLZ; 20 POINTS
At a fair, each person can spin two wheels of chance. The first wheel has the numbers 1, 2, and 3. The second wheel has the letters A and B. (a) List all the possible outcomes of the compound event. (b) If you spin both wheels, what is the probability that you get either a 1 or an A? Explain. Answer:
(a) All the possible outcomes of the compound event are {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}
(b) Probability is 2/3.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
Given that,
At a fair, each person can spin two wheels of chance.
The first wheel has the numbers 1, 2, and 3.
The second wheel has the letters A and B.
(a) 1 can be followed by A and B, 2 can be followed by A and and B and so is 3.
Possible outcomes = {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}
(b) Total possible outcomes = 6
Number of outcomes which has either 1 or A = 4
Probability = 4/6 = 2/3
Hence the required probability is 2/3.
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a number cube is rolled 24 times.how many times will a number be less than tree be expected to be rolled?
The number of the times cube is rolled for getting less than three is 8.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability of getting less than three = 2 / 6 = 1 / 3
The number of the times cube rolled is,
Pn = ( 1 / 3 ) x 24 = 8
Therefore, the number of the times cube is rolled for getting less than three is 8.
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The formula for glue says to add 55 mL of hardener to each container of resin. How much hardener should be added to 16 containers of resin? Write your answer in liters.
To determine how much hardener is required for 16 containers of resin, multiply 55 mL by 16 to get 880 mL, and then convert this to liters by dividing by 1,000, resulting in 0.88 liters of hardener needed.
Explanation:To determine how much hardener should be added to 16 containers of resin, we must multiply the amount needed for one container by the number of containers. The formula given states that 55 mL of hardener is required for each container of resin. To find the total amount for 16 containers, we perform the following multiplication:
Calculate the total milliliters needed: 55 mL/container × 16 containers = 880 mL.Convert the total milliliters to liters:Therefore, 0.88 liters of hardener should be added to 16 containers of resin.
Final answer:
To determine the amount of hardener needed for 16 containers of resin, multiply 55 mL by 16 to get 880 mL and then convert that to liters, resulting in 0.88 liters of hardener.
Explanation:
To find out how much hardener should be added to 16 containers of resin, where each container requires 55 mL of hardener, you need to do a simple multiplication operation. Multiply the amount of hardener needed for one container by the number of containers:
Multiply 55 mL by 16:Now, convert milliliters to liters. Since there are 1,000 milliliters in a liter:Therefore, you should add 0.88 liters of hardener to the 16 containers of resin.
Jake has a teepee that is cone shaped it has a height of 9 feet and a diameter of 8 feet find the volume of the teepee in terms of Pi.
A car is traveling at a speed of 75 km/h. Identify the correct conversion factor setup required to compute the speed of the car in m/s.
A)
75km
1hr
x
1000m
1km
x
1hr
60min
x
60s
1min
B)
75km
1hr
x
1000m
1km
x
1hr
60min
x
1min
60s
C)
75km
1hr
x
1000m
75km
x
1hr
60min
x
1min
60s
D)
75km
1hr
x
1000m
75km
x
1hr
60min
x
60s
1min
Therefore, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
A car is traveling at a speed of [tex]75[/tex] km/h.
As we know,
[tex]1km=1000m[/tex]
[tex]1h=60s[/tex]
So,
[tex]75[/tex] km/h=[tex]\frac{75(1000)}{3600}[/tex] m/s
[tex]=\frac{75000}{3600}\\\\[/tex]
Hence, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.
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a circle has an area of 81 3.14 units . what is the diameter in terms of 3.14a circle has an area of 81 Pi square units what is the diameter of the circle
Answer:
18 units
Step-by-step explanation:
[tex]\pi r^2=81\pi[/tex]
Solve for [tex]r[/tex]:
[tex]\pi r^2=81\pi \\r^2=81\\r=9[/tex]
Knowing diameter is 2*r, we can apply the formula to find diameter
[tex]d=2*r\\d=2*9\\d=18[/tex]
PLEASE HELP..... I WILL GIVE BRAINLIEST!!
Geometry Circle - Find the Midsing Angle
Hector has a $5 off coupon at Brenda's Bagels. Bagels cost $8.99 per dozen. Write an equation that models the total amount of money (y) Hector owes if he buys (x) dozen bagels.
HELP!!!!!!!!!!!!!!!!
If (tan^3 theta -1) / (tan theta - 1) - sec^2 theta +1 = 0, find cot theta.
a. -1 b.0 c. 1 d. sec theta
Answer:
Option A. [tex]cot\theta = -1[/tex]
Step-by-step explanation:
[tex]\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0[/tex]
we have to the value of [tex]cot\theta[/tex]
We further solve the equation
[tex]\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0[/tex] [a³- b³= (a-b)(a² + b²+ ab)]
[tex]sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0[/tex]
[tex]\frac{1}{cot\theta }=-1[/tex]
[tex]cot\theta = -1[/tex]
Therefore Option A. [tex]cot\theta = -1[/tex] is the answer.
find the nonpermissible replacement for a in this expression 7/6a
A bag contains 45 marbles of various colours. Lena draws 48 times, each time replacing the marble before drawing again. She gets a total of 16 red marbles. Which is the best prediction of how many red marbles are in the bag?
A) 3
B) 13
C) 15
D) 16
PLEASE HELP! @) POINTS
Describe the relationship between the probability of an event and its complement. If the probability of an event is 0.3, what is the probability of its complement?
1. The probability P of an event and its complement P' are mutually exclusive and add up to 1
2. If the probability of an event is 0.3, then the probability of its complement is 0.7. (1 - 0.3 = 0.7)
James filled 4 glasses with milk. Patrick filled 6 glasses with milk. Each glass held 8 ounces of milk. Which method explains a way to calculate the difference in the amount of milk each boy poured? A. Step 1 Multiply: 4 × 8. Step 2 Multiply: 6 × 8. Step 3 Add the products. B. Step 1 Divide: 8 ÷ 4. Step 2 Divide: 8 ÷ 6. Step 3 Add the quotients. C. Step 1 Multiply: 4 × 8. Step 2 Multiply: 6 × 8. Step 3 Subtract the products. D. Step 1 Divide: 8 ÷ 4. Step 2 Divide: 8 ÷ 6. Step 3 Subtract the quotients.
Lisa has 1 set of 12 cars and she gives her sister 3cars. What fraction of Lisa's set did she give her sister
Find the unknown. 531 = ( × 6) + 21
Evaluate the expression. If necessary, round to the nearest hundredth.
log 2.8
Mrs.Nellon’s class sold 18 rolls of wrapping paper.In all, the school sold 82 rolls. About what percent of the sales came from Mrs.Nellon’s class?
how farare 27and -54 apart on the number line
How far are 27 and -54 apart on the number line?
Solution:
If we see on the number line , 27 is 27 units apart from 0 and it is 27 units to the right of 0
And, -54 is 54 units apart from 0 and it is 54 units to the left of 0. So, -54 is in opposite direction with respect to 27.
So, To find how far is 27 from -54 we must add 27 and 54
As, 27+54=81
So, -54 and 27 are 81 units away from each other.
Answer:81 units
Please see the number line attached.
On which of the following lines does the point (7, 1) lie?
A.) y= 5x + 4
B.) y= -x + 8
C.) y= x- 10
D.) y= -4x + 3
Write an Inequality for the following situation
No more than 8 books are in your bag
It says "No more than 8 books are in your bag". Here "Not more than" a specific number would be a set of all values that are "less than or equal" to given number.
So let's consider 'n' represents the number of books in the bag and we know this number can not be a negative value i.e. n is "greater than or equal" to 0.
Also n is "less than or equal" to 8 as given in the question.
Hence, the inequality would be 0 ≤ n ≤ 8.
which of the following represents the formula that could be used to find the height of the cone
lliana’s math grade increased from 65 to 86. Fiona’s math grade increased from 70 to 80. What is the difference, rounded to the nearest whole number, between the approximate percent increases?
The line plots shows the number of hours two different age groups of teenagers spent online the previous week.
Select from the drop-down menus to complete each statement.
The range is? is the same for both
is greater for data set 1
is greater for data set 2
The mean? is the same for both
is greater for data set 1
is greater for data set 2
Answer:
is greater for data set 2 ; is greater for data set 2
Step-by-step explanation:
The range is found by subtracting the highest and lowest value. The range of the first plot would be
34-21 = 13.
The range of the second plot would be
36-12 = 24.
The mean is found by adding together all of the data points and dividing by the number of data points. For the first plot, the sum of the data is 274 and there are 10 data points; this makes the mean 274/10 = 27.4.
For the second plot, the sum of the data is 280.5 and there are 10 data points; this makes the mean 280.5/10 = 28.05.
The range is greater for data set 2.
Then mean is greater for data set 2.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Consider the data plot for 13 to 15 years olds.
Mean = Average of the values
= (21 + 24 + 26 + 27 + 27 + 28 + 28 + 28 + 31 + 34) / 10
= 27.4
Range = Maximum value - Minimum value
= 34 - 21
= 13
Consider the data plot for 16 to 18 years olds.
Mean = Average of the values
= (12 + 21 + 28 + 28 + 28 + 28 + 30.5 + 34 + 35 + 36) / 10
= 28.05
Range = Maximum value - Minimum value
= 36 - 12
= 24
Hence the range and mean are greater for data set 2.
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an equation of the horizontal line that passes through the point (-2,5)
y = 5 is the equation of the horizontal line that passes through the point (-2,5).
Mathematically, an equation is a statement that two expressions are equal. The expressions on either hand of the equals sign are termed the left-hand side and the right-hand side of the equation. The equals sign is perused as" is equal to" or" equals".
An equation comprises variables, numbers and comparison sign.
As the ordinate of the given point is 5 then y = 5 is the horizontal line that passes through (-2,5).
Thus, the equation that passes through the point (-2,5) and is the horizontal line is y = 5.
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What is the area of the figure?
While bowling with friends, Brandy rolls a strike in 5 out of 10 frames. What is the experimental probability that Brandy will roll a strike in the first frame of the next game? Enter your answer as a simplified fraction.
The experimental probability of Brandy rolling a strike in the first frame of the next game is 1/2.
Explanation:To find the experimental probability that Brandy will roll a strike in the first frame of the next game, we need to divide the number of times Brandy rolled a strike in the first frame by the total number of frames. In this case, Brandy rolled a strike in 5 out of 10 frames, so the experimental probability is 5/10, which simplifies to 1/2.
Can someone please explain number 11?
factorise 36n(squared) divide by 25 minus 1
Answer:
[tex]( \frac{36n^{2} }{25} - 1) [/tex] factors to become [tex]( \frac{6}{5}n - 1)( \frac{6}{5}n + 1) [/tex]
Explanation:
The binomial [tex]( \frac{36n^{2} }{25} - 1) [/tex] is what is called a difference of two squares which can be identified by the equation being in the form (a² - b²) where both terms can be square-rooted.
Because the equation is a difference of two squares, its factors will be in the form: (a - b)(a + b).
With a² = [tex]\frac{36n^2}{25}[/tex] and b² = 1, we can find the square root of both and plug them into the above factor form.
√(36n² / 25) = 6n/5
√1 = 1
So the factors are [tex](\frac{6}{5}n -1)(\frac{6}{5}n +1)[/tex]