Using unitary method, the actual distance between the two towns is 105 km.
What is unitary method?The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
1 cm = 30 km
3.5 cm = 30 * 3.5 = 105 km
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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.
What is the area of the figure?
Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.
The linear function that represents this graph is given by:
y = 300 - 0.6667x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the graph, when x = 0, y = 300, hence the y-intercept is of b = 300. The amount decays to 0 when the x-intercept is of x = 450, hence the slope is given by:
m = -300/450 = -0.6667.
Which means that the equation is:
y = 300 - 0.6667x.
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A bicycle rider increases his speed from 5 m/s to 15 m/s in 10 seconds
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.
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.
What is the solution of the equation
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?
Can someone please explain number 11?
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
HELP!!!!!!!!!!!!!!!!
It took 25.5 bottles to fill a cooler and each bottle contained 1.8 liters. How many liters are in the cooler
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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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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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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Geometry Circle - Find the Midsing Angle
PLEASE HELP..... I WILL GIVE BRAINLIEST!!
find the nonpermissible replacement for a in this expression 7/6a
x^2-6x=-1 If the quadratic equation has real solutions, what are the solutions? Explain. Estimate irrational solutions to the nearest tenth.
which of the following represents the formula that could be used to find the height of the cone
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.
Evaluate the expression. If necessary, round to the nearest hundredth.
log 2.8
Pleaseee help
If you multiplied a number by 1/2, the result would be
1. Less than 1
2. Half of the original number
3. A fourth of the original number
4. Twice as large as the original number
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
The triangle shown must be a right triangle if x= in
A) 8
B) 12
C) 16
D) 144
Answer:
The value of x is 12 in
Step-by-step explanation:
Given the right angled triangle having sides 5 in , 13 in and x in
We have to find the value of x.
By applying Pythagoras theorem, we get
[tex]Hypotenuse^{2} = Base^{2} + Perpendicular^{2}[/tex]
⇒ [tex]13^{2}=x^{2}+5^{2}[/tex]
⇒ [tex]169=25+x^{2}[/tex]
⇒ [tex]x^{2} = 144[/tex] ⇒ x=12 in
Hence, length of base is x in i.e 12 in
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 unknown. 531 = ( × 6) + 21
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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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?
anyone know how to solve by giving me not only an explanation in words but can show me the equation, to solve the problem below? thanks
3(x+7)=6(x+2)