The actual distance between the cities is 200 km using multiplication.
The scale of the map is 3 cm : 20 km. This means that for every 3 cm on the map, the actual distance in real life is 20 km.
If two cities are 30 cm apart on the map, we can use the scale to find the actual distance between them. First, we need to determine how many times the scale goes into the distance on the map. To do this, we divide the distance on the map by the length of the scale:
30 cm ÷ 3 cm/20 km = 30 ÷ 3 × 20 = 200 km
Therefore, the actual distance between the two cities is 200 km.
Alternatively, we can use the proportionality between the scale and the actual distance to set up a proportion and solve for the actual distance. Let x be the actual distance between the cities in kilometers:
3 cm / 20 km = 30 cm / x
Cross-multiplying and solving for x, we get:
x = (20 km / 3 cm) × 30 cm = 200 km
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Given the equation, what is the center and radius of the circle?
(X-2) ^2+ (Y+11)^2=100
Answer:
Center: (2, -11)
Radius: 10
Step-by-step explanation:
(x - 2)² + (y + 11)² = 100
(x - h)² + (y - k)² = r²
-------------------------------
x - 2 = 0
+2 +2
x = 2
------------
y + 11 = 0
-11 -11
y = -11
------------------------------
r² = 100
r = √100
r = 10
----------------------------
Center: (h, k)
Radius: r
-------------------------------
Center: (2, -11)
Radius: 10
I hope this helps!
We are given the equation of circle (x - 2)² + (y + 11)² = 100 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;
So, consider the equation of circle ;
[tex]{:\implies \quad \sf (x-2)^{2}+(y+11)^{2}=100}[/tex]
Can be further written as ;
[tex]{:\implies \quad \sf (x-2)^{2}+\{y-(-11)\}^{2}={10}^{2}}[/tex]
On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows
Centre = (2, -11)Radius = 10 unitsHarry is scuba diving off the coast of Australia. When he is ready to come back to the surface, he rises 12 meters at a safe speed. He climbs 15 centimeters every second. How many seconds will it take him to reach the surface?
The radius of a circle is 14 centimeters. What is the circle's circumference?
Hello!
To solve this exercise, we must use the formula below:
[tex]\mathrm{C=2\cdot\pi\cdot r}[/tex]
C = ?π = 3.14r = 14cmKnowing these values, let's replace them in the formula to obtain r:
[tex]\mathrm{C=2\cdot 3.14 \cdot 14}\\\mathrm{C=6.28 \cdot 14}\\\\\boxed{\mathrm{C=87.92}}[/tex]
So, the circle's circumference is 87.92cm.
Hope this helps!
Answer:
[tex]\boxed{\sf{87.92cm}}[/tex]Step-by-step explanation:
To solve this problem, you need to multiply the radius of a circle by the circumference formula.
Circumference formula:
[tex]\sf{C=2\pi r}[/tex]
[tex]\sf{C=2*\pi r}[/tex]
C=?
π= 3.14
r= 14
[tex]\sf{2*3.14*14}[/tex]
Solve.
[tex]\sf{2*3.14=6.28}[/tex]
[tex]\sf{6.28*14=\boxed{\sf{87.92}}[/tex]
Therefore, the correct answer is 87.92cm.I hope this helps you! Let me know if my answer is wrong or not.
please answer correctly thanks
Answer:
Step-by-step explanation:
add all the three.
Answer:
60
Step-by-step explanation:
AD= AB+BC+CD
=22+29+9
=60 cm
Pls help me 20 points
Step-by-step explanation:
a volume is created (calculated) by multiplying 3 dimensions (e.g. length, width and height).
am area is created by multiplying 2 dimensions (e.g. length and width).
but a scale factor applies only to any length in the model (but then separately for every dimension of the model).
so, when we multiply 2 dimensions, we have to multiply the scale factor with every dimension (2 times) in there too.
and for 3 dimensions 3 times.
so,
1.
the scale factor 1/100 or 0.01 says that every side of the model cube is 1/100 the side length of the real cube.
and so, while the volume of the real cube is
side × side × side = 3,401,244 ft³,
the volume of the model cube is
side × 1/100 × side × 1/100 × side × 1/100 =
= side × side × side × (1/100)³ =
= real volume × 1/1,000,000 =
= 3,401,244 / 1,000,000 = 3.401244 ft³
2.
the scale factor is 3/4.
that means that it applies to length as well as to width of the floor.
so, the area of the first floor is
length × width = 1,260 ft²
and the area of the second floor is then
length × 3/4 × width × 3/4 =
= length × width × (3/4)² =
= area first floor × 9/16 = 1,260 × 9/16 = 708.75 ft²
In a math competition, every question that is answered correctly gets a score of 4. Wrong gets a score of -2. and not answered gets a score of -1. Ali got a score of 106 with 4 questions answered incorrectly and 6 questions not being answered. Many questions were answered correctly by........
please explain it
Answer:
Step-by-step explanation:
First we need to find the score of the incorrect answers and the questions that were not answered.
Score for the incorrect answers = 4*(-2) = -8
Score for the questions not answered = 6*(-1) = -6
Score for the questions answered correctly = 106 - [ (-8) + (-6) ]
= 106 -[-14]
= 106 + 14
= 120
Number of questions answered correctly = total score for questions that were answered correctly ÷ score of 1 correct answer
= 120 ÷ 4
= 30
30 questions were answered correctly.
Can someone help me out? I can't understand this shape. (Explanation also please). I'll mark brainliest
The surface area of the rectangular prism is 46m²
How to find surface area of a rectangular prism?length = 4mwidth = 2.5mheight = 2mSurface area of a rectangular prism = 2(width×length + height×length + height×width)
SA = 2(wl + hl + hw)
= 2(2.5×4 + 2×4 + 2×2.5)
= 2(10 + 8 + 5)
= 2(23)
= 46m²
Therefore, the surface area of a rectangular prism is 46m²
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what is the volume of a oblique cylinder with the height of 6 cm and a 4 cm as the radius of its base
Answer :
301.44 cm³⠀
Explanation :
We know,
[tex]{ \longrightarrow \qquad\pmb {\boldsymbol{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}[/tex]
Where,
r is the radius of the cylinder. Here, the radius is 4 cmh is the height of the cylinder. Here, height is 6 cmHere, we will take the value of π as 3.14 approximately .⠀
Substituting the values in the formula :
⠀
[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times ({4})^{2} \times 6 \: }}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times 16\times 6 \: }}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times 96 \: }}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \ { \it{ \pmb{ Volume_{(cylinder)} {= 301.44 \: }}}}}}[/tex]
⠀
Therefore,
The volume of the cylinder is 301.44 cm³ approximately.Which expression is equivalent to the following complex fraction?
Consider the fraction first ;
[tex]{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}[/tex]
Hence, Option B) is required answer
I need help with Biased vs Unbiased
Answer:
13 a) 12% prefer pumpkin pie
b) 6.4% prefer pumpkin pie
c) 80% did NOT prefer raspberry pie
d) 235 people would be expected to say that their favorite pie is apple
or blueberry.
14 a) 20% prefer Marlin
b) 12% prefer Dolphins
c) 48.33% prefer seahawks or sharks as their mascot.
d) 116 students would be expected to say that their favorite mascot is a
Penguin.
15 a) 20% prefer Science fiction
b) 46 people would be expected to report mystery as their favorite
genre.
c) 810 people would be expected to report drama, history, or romance
as their favorite genre.
Step-by-step explanation:
13. *There are a total of 125 participants or customers.*
35 people prefer apple pie15 people prefer pumpkin pie.8 people prefer pecan pie.28 people prefer cherry pie.25 people prefer raspberry pie.14 people prefer blueberry pie.a) 15/125 = 0.12 = 12%
12% prefer pumpkin pie
b) 8/125 = 0.064 = 6.4%
6.4% prefer pumpkin pie
c) Since 25 people preferred raspberry pie. 125-25= 100 people did NOT prefer raspberry pie.
100/125 = 0.8 = 80%
80% did NOT prefer raspberry pie
d) Out of 600 people, how many would you expect to say their favorite pie is apple or blueberry?
Apple: 35/125 = 0.28 = 28%
Blueberry: 14/125 = 0.112 = 11.2%
If there were 600 people:
Apple: 600*0.28 = 168
Blueberry: 600 * 0.112 = 67.2 (there can't be a 0.2 of a
person, so it's rounded to 67)
168 + 67 = 235
235 people would be expected to say that their favorite pie is apple or blueberry.
14. *There are a total of 60 students.*
5 people prefer Penguins.12 people prefer Marlins.9 people prefer Seahawks.14 people prefer Dolphins.20 people prefer Sharks.a) 12/60 = 0.2 = 20%
20% prefer Marlin
b) 14/60 = 0.12 = 12%
12% prefer Dolphins
c) Seahawks: 9/60 = 0.15 = 15%
Sharks: 20/60 = 0.33 = 33.33%%
15% + 33.33% = 48.33% prefer seahawks or sharks as their mascot.
d) If there are 1,400 students in the school, how many would you expect to choose the Penguins as their favorite mascots.
Penguins: 5/60 = 0.083 = 8.33%
If there were 1,400 students:
Penguins: 1,400*0.083 = 116.2 (there can't be a 0.2 of a
person, so it's rounded to 116)
116 students would be expected to say that their favorite mascot is a Penguin.
15. *There are a total of 75 people.*
8 people prefer Action.4 people prefer Comedy.16 people prefer Drama.7 people prefer Mystery.10 people prefer Romance6 people prefer Science fiction3 people prefer Biography12 people prefer History9 people prefer Othera) 6/75 = 0.2 = 20%
20% prefer Science fiction
b) Out of 500 people, how many would you expect to report mystery as their favorite genre?
Mystery: 7/75 = 0.093 = 9.3%
If there were 500 people:
Mystery: 500*0.093 = 46.5 (there can't be a 0.5 of a
person, so it's rounded to 46)
46 people would be expected to report mystery as their favorite genre.
c) If there are 1,600 people, how many would you expect to report drama, history, or romance as their favorite genre?
Drama: 16/75 = 0.2133= 21.33%
History: 12/75 = 0.16 = 16%
Romance: 10/75 = 0.1333 = 13.33%
If there were 1,600 students:
Penguins: 1,400*0.083 = 116.2 (there can't be a 0.2 percent of a
person, so it's rounded to 116)
Drama: 1,600*0.2133 = 341.28 (there can't be a 0.28 of a
person, so it's rounded to 341)
History: 1,600*0.16 = 256
Romance: 1,600*0.1333 = 213.28(there can't be a 0.28 percent of a
person, so it's rounded to 213)
341 + 256 + 213 = 810
810 people would be expected to report drama, history, or romance as their favorite genre.
Hope this helps!
The daily sleep duration among college students is normally distributed with a mean of 8.13 and standard deviation of 1.87. You want to use a sample size such that 95% of the averages fall within +/- 15 minutes (.25 of an hour) of the true mean of 8.13. Determine the smallest number of students you need to sample.
Using the z-distribution, as we have the standard deviation for the population, it is found that 215 students must be sampled.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The margin of error is of M = 0.25, with a population standard deviation of [tex]\sigma = 1.87[/tex], hence we solve for n to find the minimum sample size.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 1.96\frac{1.87}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 1.96(1.87)[/tex]
[tex]\sqrt{n} = \frac{1.96(1.87)}{0.25}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96(1.87)}{0.25}\right)^2[/tex]
[tex]n = 214.9[/tex]
Rounding up, 215 students must be sampled.
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The perimeter of the surface
of a workbook is 36 inches. The
area is 80 square inches. What
are the dimensions of the
workbook?
Answer:
10 inches by 8 inches
The length and with would be half the perimeter: 36/2 = 18
find 2 numbers when added together equal 18 and when multiplied together equal 80.
8 + 10 = 18
8 x 10 = 80
MARK AS BRAINLIEST
Below is the table of values of a function. Write the output when the input is n.
input
1
2
8
n
output
5
6
12
?
Answer:
Step-by-step explanation:
the answer is correct so good job ok
a baby weights 7 pounds at birth. the table shows the birth weight after each month of life, up to six months
Answer:
y = 1x + 7
Step-by-step explanation:
Let's take 2 points, with x being the month and y being the weight as the month is listed first in the graph.
(0, 7) = the 1st point
(1, 8) = the 2nd point
In y=mx+b, m is the slope.
Slope = change in y / change in x = (y₂-y₁) /(x₂-x₁) = (y₁-y₂) / (x₁-x₂) = (8-7)/(1-0) = 1 / 1 = 1 = (7-8)/(0-1) = -1/-1 = 1
Our equation is thus
y = mx + b = y = (1) x + b
Plug one point, such as (1, 8) into this equation to obtain b
8 = (1) (1) + b
8 = 1 + b
subtract 1 from both sides to isolate b
7 = b
our equation is thus
y = (1) x + 7 = 1x + 7
Answer:
w = 1m + 7
Step-by-step explanation:
w = weight
m = months
If we look at the chart, as every month goes by, the baby gains another pound.
Hence, the best way to find the weight is to just add 7 to the months, since in the beginning (at 0 months) the weighs 7 pounds, so if it’s 1 month, the baby would just way 1 more pound.
This is why the formula: w = 1m + 7 works
Because 1 times the value of any month will be the same value, and all you have to do is add 7.
Example:
(x = multiply in this equation)
At 2 months: w = 1 x 2 + 7
Solve:
1 x 2 = 2
2 + 7 = 9
As you can see, all you have to do is fill in the month # in the formula, and you will get your w (weight).
Hope this helps :)
How do you solve this problem?
Answer:
16 triangles I am pretty sure.
Step-by-step explanation:
PLEASE HELP ASAP!!!!!
a lower auto insurance deductible usually means a higher __
a.) maintenance cost
b.) max out of pocket
c.) premium
d.) ticket.
The deductible is the amount one pays towards the auto insurance
The complete statement is: a lower auto insurance deductible usually means a higher premium
What is deductible?When an insured loss or disaster happens, the amount one pay towards the loss is referred to as the deductible
As a general rule, the more the deductible, the lower the premium; and vice versa.
This means that: a lower auto insurance deductible usually means a higher premium
Hence, the text that completes the statement is premium
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what is the volume of a rectangular prism with height of 12 inches and a base with an area of 2 square inches.
Answer:
24 cubic inches
Step-by-step explanation:
Volume is side x side x side. You already have done side x side so it is just side x area.
Mike spins a spinner and flips a coin. What
is the probability of getting E on the spinner
and the coin landing on heads?
(NEED HELP ASAP)An urn contains three red marbles, and six blue marbles. What is the probability of selecting at random, without replacement, two blue marbles?
Answer:
6/9 or 1/3
Step-by-step explanation:
There is a total of 9 marbles of both colors in the bag.
(3 red marbles + 6 blue marble = 9 marbles)
This means the denominator of your probability will be 9. There are 6 blue marbles in the bag so, in conclusion, the probability that you will take a blue marble out of the bag is 6/9. Also, 6/9 when simplified, is 1/3.
Have a great rest of your day
#TheWizzer
If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
The value of x in the direct and indirect varoation is calculated as: x = 2.
What is Direct and Indirect Variation?If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.
With the information stated, we would have the following:
z = kx/y³
Find k, by plugging in the values of x, y, and z:
12 = k(8/2³)
12 = k(8/8)
12 = k
k = 12
Find x when y = 1 and z = 24:
24 = 12(x)/1³
24 = 12x
24/12 = x
x = 2.
Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.
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Trigonometric Equations
Solve the equation over the interval [0°, 360°)
cos(theta) = -1/2
Answer:
[tex]\frac{2\pi }{3};\frac{4\pi }{3}.[/tex]
Step-by-step explanation:
1) cos(θ)=-0.5;
theta=±2π/3+2πn, where n∈Z;
2) if θ∈[0;360], then
[tex]\theta=\frac{2\pi }{3}; \frac{4\pi }{3}.[/tex]
A box has length 3 ft, width 5 ft, and height 2 ft.
What is the volume?
cu ft
Answer:
30 cubic feet
Step-by-step explanation:
The volume of a box is found by multiplying the area of the base by the height. The area of the base is found by multiplying the length by the width. (3 x 5)(2) = 15(2) = 30 cubic feet
Find the value of x
What is the answer
Answer:
35
Step-by-step explanation:
well, you know the angles of a triangle add up to 180 degrees, and you have the other 2 degrees right there, so all you have to do is add both of the other angles 111+34= 145 and then subtract by 180, 180-145=35 so your answer is 35
Three and one fifth of 1 1/2 is what number?
Answer:
3 1/5 = 16 / 5
1 1/2 = 3 / 2
16 / 5 * 3 / 2 = 48 / 10 = 24 / 5
The correct answer is 24 / 5 = 4 4 /5
(You can check on your calculator)
Write the percent as a decimal.
78% =
Answer:
0.78
Step-by-step explanation:
78 / 100
note that 100% = 1
How many inches are in 6 3/4 feet? Enter only a number. Do not include units.
Answer:
81 inches
Step-by-step explanation:
I believe this is it…
The population of birds on an island is estimated to increase by 10% every year.The population of birds on the island is 20000.
Calculate an estimate for the population of birds in three years time.
Pls give working out & Explanation
And also can anyone tell me how to answer someone question in Brainly. I am new here
Answer:
26,620
Step-by-step explanation:
1 year: 20,000 x 0.10 = 2000
2 years: 22,000 x 0.10 = 2200
3 years: 24200 x 0.10 = 2420
2420 + 24200 = 26620
Have an amazing day!!
Please rate and mark brainliest!!!!
Theres a button on the question taht you are wanting to answer. Sometimes it will allow one other times it is 2
The accompanying diagram show a cross-section of a rectangular pyramid. The cross sectional area is 36in and is 3 inches from the vertex of the pyramid. If the height of the pyramid is 5 inches, what is the area of the rectangular base?
The area of the rectangular base is the amount of space on the rectangular base
The area of the rectangular base is 60 square inches
How to determine the area of the rectangular base?The question is incomplete; as the diagram is not given.
So, I will apply the concept of similar shapes to determine the area of the rectangular base
To determine the area of the rectangular base, we make use of the following equivalent ratio:
Ratio = Height : Area
This gives
3 : 36 = 5 : Area
Express as fraction
36/3 = Area/5
Evaluate the quotient
12 = Area/5
Multiply both sides by 5
Area = 60
Hence, the area of the rectangular base is 60 square inches
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what is m
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
Answer:
66 degrees
Step-by-step explanation:
All three angles on any given triangle have a sum of 180 degrees.
We know that the measure of angle B is the the same as angle C.
So 57 +57 = 114
180 - 114 = 66
Hope that helps!
The data set below represents the different costs of a tablet at an electronic store. $298. $196, $248, $379, $319, $276, $198, $349, $319. What is the median?
Answer:median of (298, 196, 248) - 196
median of (379, 319) - 349
median of (276,198, 349) - 198
Step-by-step explanation:
Answer:
298
Step-by-step explanation:
Given:
$298,$196, $248, $379, $319, $276, $198, $349, $319
Solve:
Put in order:
196, 198, 248, 276, 298, 319, 319, 349, 379
Median -
Arrange data values from lowest to highest value
The median is the data value in the middle of the set
If there are 2 data values in the middle the median is the mean of those 2 values.
Solution:
196, 198, 248, 276, 298, 319, 319, 349, 379
196, 198, 248, 276, 298, 319, 319, 349, 379
196, 198, 248, 276, 298, 319, 319, 349, 379
196, 198, 248, 276, 298, 319, 319, 349, 379
Hence, the median is 298.
~lenvy~