Answer:
45
Step-by-step explanation:
Given the legs of the right triangle.
Then using Pythagoras' identity
The square oh the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is
h² = 36² + 27² = 1296 + 729 = 2025 ( take the square root of both sides )
h = [tex]\sqrt{2025}[/tex] = 45
Answer:
45
Step-by-step explanation:
When you are given the opposite and adjacent sides of a triangle, the easiest way to find the hypotenuse is through the Pythagorean theorem!
The formula is a^2 + b^2= c^2
Plugging in the values, your formula would now look like 36^2 + 27^2= c^2
Once you do square your values and add them up, the result would end up being 2025, but since that is squared, to find the actual value of c you have to take the square root of this number, this will result in 45.
Solve the inequality for y.
y - 9x > 6
please help!!!!!!!
Answer:
y>9x+6
Step-by-step explanation:
y-9x+(9x)>6+(9x)
y>9x+6
sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test
Answer: (upside down fancy u) q5
Step-by-step explanation:
Simply apply the law of conservative (upside down fancy u)
1. The total area within any continuous probability distribution is equal to 1.00.
A. True
B. False
2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed.
A. True
B. False
3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed.
A. True
B. False
Answer:
1. True
2. False.
3. True.
Step-by-step explanation:
1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).
Hence, for continuous probability distribution: probability = area.
2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.
Hence, it cannot be computed.
3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.
Hence, it can be computed.
If the blue radius below is perpendicular to the green chord and the segment
AB is 8.5 units long, what is the length of the chord?
A
A. 8.5 units
8.5
B
O B. 17 units
O C. 34 units
O D. 4.25 units
Answer:
O B. 17 units
Step-by-step explanation:
The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:
[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]
The length of the chord is 17 units.
Answer:
The answer is 17 units :D
Step-by-step explanation:
(OFFERING ALL THE POINTS I HAVE) Word Problem. Please help!! Part 1 of problem: The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number and use 3.14 for Pi. (Use sphere volume formula) Part 2: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? Part 3: Using the information from part 2, answer the following question by filling in the blank: The volume of the actual tank is __% of the mock-up of the tank.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
Answer:
Part 1: 359,007 ft³
Part 2: 216 times smaller
Part 3: 21600%
Step-by-step explanation:
Part 1:
The parameters for the tank are;
The radius of the tank = 70 feet
The volume of a sphere = 4/3·π·r³
Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere
The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3
Plugging in the value for the radius gives
Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.
Part 2:
The dimension of the scale model = 1/6 × Actual dimension
Therefore, we have the radius of the sphere of the scale model = 1/6 × 70
Which gives;
The radius of the sphere of the scale model = 35/3 = 11.67 feet
The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³
The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times
The number of times smaller the scale model is than the actual volume = 216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.
Part 3:
The percentage of the mock-up, x, to the volume of the actual tank is given as follows
x/100 × 1662 = 359,007
∴ x = 216 × 100 = 21600%
The percentage of the mock-up, to the volume of the actual tank is 21600%.
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions ?
Answer:
The width is 23.5 ft and the length is 47 ft
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
141 = 2(l+w)
The length is twice the width
l = 2w
141 = 2 ( 2w+w)
141 = 2( 3w)
141 = 6w
Divide each side by 6
141/6 = 6w/6
23.5 = w
l = 2w = 2(23.5) = 47
The width is 23.5 ft and the length is 47 ft
Answer:
[tex]\boxed{Width = 23.5 \ feet}[/tex]
[tex]\boxed{Length = 47 \ feet}[/tex]
Step-by-step explanation:
Let Length be l and Width be w
Perimeter = 2(Length) + 2(Width)
Condition # 1:
2l+2w = P
=> 2 l + 2 w = 141
Condition # 2:
=> l = 2w
Putting the second equation in the first one
=> 2(2w)+2w = 141
=> 4w + 2w = 141
=> 6w = 141
Dividing both sides by 6
=> Width = 23.5 feet
Given that
=> l = 2w
=> l = 2(23.5)
=> Length = 47 feet
In a class Vidya ranks 7th from the top. Divya
is 7 ranks ahead of Medha and 3 ranks
behind Vidya. Sushma who is 4th from the
bottom is 32 ranks behind Medha. How many
students are there in the class?
Answer:
52 students
Step-by-step explanation:
From the question above, we have the following information:
a) Vidya ranks 7th from the top.
Mathematically,
Vidya = 7th student
b) Divya 3 ranks behind Vidya.
Divya = Vidya + 3
Hence, Mathematically:
Divya = 7 + 3 = 10
Divya = 10th student
c) Also, Divya is 7 ranks ahead of Medha.
Mathematically,
Medha = 10 + 7= 17
Medha= 17th student
d)Sushma is 32 ranks behind Medha
Mathematically,
Sushma = Medha + 32
= 17 + 32 = 49
Sushma is the 49th student
Therefore, since, Sushma is 4th from the bottom, total number of students is:
49 + 3 = 52 students
A standard deck of of 52 playing cards contains 13 cards in each of four suits : diamonds, hearts , clubs and spades. Two cards are chosen from the deck at random.
Answer:
Probability of (one club and one heart) = 0.1275 (Approx)
Step-by-step explanation:
Given:
Total number of cards = 52
Each suits = 13
FInd:
Probability of (one club and one heart)
Computation:
Probability of one club = 13 / 52
Probability of one heart = 13 / 51
Probability of (one club and one heart) = 2 [(13/52)(13/51)]
Probability of (one club and one heart) = 0.1275 (Approx)
Answer:
D. 0.1275
Step-by-step explanation:
Justo took the Pre-Test on Edg (2020-2021)!!
A combination lock has 6 different numbers. If each number can only be used ONCE, how many different combinations are possible?
Answer:
151200 possible combinations
Step-by-step explanation:
There are 10 digits 0 - 9 ( 0,1,2,3,4,5,6,7,8,9)
There are 10 choices for the first digit
10
There are 9 choices for the second digit
9
There are 8 choices for the third digit
8
and so on since we can only use each digit once
10 *9*8 *7 *6*5
151200 possible combinations
38. Convert 85 to a number in base eight.
O 95 (base eight)
O 105 (hase eight)
O 115 (base eight)
O 125 (base eight)
Answer:
divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125
7 - 5x > 3x + 31
A.X2-3 (all numbers greater than or equal to -3 will satisfy the inequality)B.xs-3 (all numbers less than or equal to -3 will satisfy the inequality)
C.X26 (all numbers greater than or equal to 6 will satisfy the inequality)
D.xs 6 (all numbers less than or equal to 6 will satisfy the inequality)
Answer: B. (all numbers less than or equal to -3 will satisfy the inequality)
Step-by-step explanation:
Hi, to answer this question we have to solve the inequality for x:
7 - 5x > 3x + 31
7-31 > 3x +5x
-24 > 8x
-24/8 > x
-3 > x
x < -3
So, the correct option is:
B. (all numbers less than or equal to -3 will satisfy the inequality)
Feel free to ask for more if needed or if you did not understand something.
Need help with these last two questions, tysm if you do :D
Answer:
D.
A. x ≤ 1
Step-by-step explanation:
Well for the first question we need to simplify the inequality.
4x + 3 < x - 6
-x to both sides
3x + 3 < -6
-3 to both sides
3x < -9
Divide 3
x < -3
So if x is less than -3 than it goes to the left starting at -3.
So D. is the answer.
So to solve the floowing inequality we simplify, distribute, and combine like terms.
3(2x - 5) + 3 ≤ -2(x + 2)
6x - 15 + 3 ≤ -2x -4
6x -12 ≤ -2x - 4
8x - 12 ≤ -4
+12
8x ≤ 8
8/8
x ≤ 1
Hence the answer is A. x ≤ 1
Write each of the following expressions without using absolute value.
|a−7|−|a−9|, if a<7
PLEASE HELP!!!! D:
=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
Scarlett Squirrel teaches a hula dancing class to young squirrels. 141414 squirrels showed up to class on Monday, 101010 squirrels on Tuesday, 888 squirrels on Wednesday, 101010 squirrels on Thursday, and 121212 squirrels on Friday. Find the mean number of the squirrels
Answer:
93107
Step-by-step explanation:
add all of the numbers together
divide by 5 since there are 5 numbers
you would get 92106.8
so round that up since you cannot have 1/8 of a squirrel
Hope this helps!!
On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]
[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
Learn more about graph here:
brainly.com/question/16608196
#SPJ5
Solve the equation using the zero-product property. (2x − 8)(7x + 5) = 0 x = –2 or x = 7 x = –4 or x = x = 4 or x = x = 4 or x =
Answer:
x = 4 or x = - [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Given
(2x - 8)(7x + 5) = 0
Equate each factor to zero and solve for x
2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4
7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]
The ratio of Ed's toy cars to Pete's toy cars was initially 5:2. After Ed gave 30 toy cars to Pete, they each had an equal number of cars. How many toy cars did they have altogether?
Answer:
140 toy cars
Step-by-step explanation:
The ratio of Ed's toy car to Pete's toy car is initially given as 5:2
Ed gave Pete a total number of 30 cars
Let x represent the greatest common factor that exists between both number
Number of Ed's car is represented as 5x
Number of Pete car is represented as 2x
Since they each have an equal number of cars which is 30 then we can solve for x as follows
5x-30=2x+30
Collect the like terms
5x-2x= 30+30
3x= 60
Divide both sides by the coefficient of x which is 3
3x/3=60/3
x=20
Ed's car is 5x, we substitute 20 for x
5(20)
= 100 cars
Pete car is 2x,we substitute 20 for x
2(20)
= 40 cars
Therefore, the total number of cars can be calculated as follows
= 100+40
= 140 toy cars
Hence they have 140 toy cars altogether
Answer:
140
Step-by-step explanation:
Determine how many litres of water will fit inside the following container. Round answer and all calculations to the nearest whole number.
Answer:
[tex]\approx[/tex] 11 litres of water will fit inside the container.
Step-by-step explanation:
As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.
Given:
Height of cylinder, [tex]h_1[/tex] = 15 cm
Diameter of cylinder/ cone, D = 26 cm
Slant height of cone, l = 20 cm
Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]
Here,
[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]
To find the Height of Cylinder, we can use the following formula:
[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]
Now, putting the values to find the volume of container:
[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]
Converting [tex]cm^{3 }[/tex] to litres:
[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]
[tex]\approx[/tex] 11 litres of water will fit inside the container.
if 12 1/2% of a sum of money is $40, what is the TOTAL sum of money?
Answer:
$320
Step-by-step explanation:
Let the total sum of money be $x.
Therefore,
12 1/2% of x = 40
25/2% * x = 40
0.125 * x= 40
x = 40/0.125
x = $320
Thus, total sum of money is $320.
Which expression is equivalent to
-21/4over -2/3
Answer:
[tex]\frac{9}{4}/\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].
[tex]-\frac{2}{3}[/tex] can stay put.
The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.
In addition, when two negatives are put together the answer must always be positive.
Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].
Find the area of the shape shown below.
Answer:
28
Step-by-step explanation:
We divide the shape covenientely, like this, and area 1 is 4*4=16
area 2=4*4/2=8
area 3= 2*4/2=4
Area total = Area 1 + Area 2 + Area 3=16+8+4=28
What is the margin of error for 95% confidence for a sample of size 250 where p = 0.45?
A. 0.0541
B. 0.0775
C. 0.0706
D. 0.0617
Answer:
0.0617
Step-by-step explanation:
so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!
This method applies to any problems with the same basic format. Good luck!
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11)
Answer:
A ( -4, -7)
Step-by-step explanation:
if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )
Answer:
A.
Step-by-step explanation:
Bruhhh I need help dude !!!
Answer:
(B), in which the first two values are 2 and 10.
Step-by-step explanation:
We can tell that this is a proportional relationship because we can examine the numbers in there.
(2,10)
(4,20)
and (6,30).
If you notice, the x value times 5 gets us the y value for every single point there.
Therefore, B is proportional and it's equation is y = 5x.
Hope this helped!
Answer:
B.
Step-by-step explanation:
B. Is the only one that proportional because,
(2,10)
(4,20)
(6,30)
All these x values multiply by 5 to get the y value.
So the equation is y = 5x meaning it is linear and it goes through the origin which makes it proportional.
Thus,
answer choice B is correct.
Hope this helps :)
An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.
The amount of cardboard required to make one box is___square inches.
a)130
b)111
c)109
d)84
Answer:
130
Step-by-step explanation:
just did test on plato/edmentum..it was correct
84 (the answer above) is incorrect
Answer:
Hi sorry for late respond but the answer in 130!!
Step-by-step explanation:
An item is selling for $7,000. This item gets a discount and it is now $4,900. What percentage was the discount?
Answer:
30%Step-by-step explanation:
Discount =$7000-$4900
Discount% =
[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]
Answer the problem below
Answer:
D. 4z^3
Step-by-step explanation:
First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3
Hope this helps, if you want me to explain more, feel free to ask questions.
Have a good day! :)
Answer:
4 z^3
Step-by-step explanation:
( 64 z^9) ^ 1/3
Rewriting 64 as 4^3
( 4^3 z^9) ^ 1/3
We know that ( ab) ^c = a^c * b^c
4^3 ^ 1/3 z^9 ^ 1/3
We know that a^ b^c = a^ ( b*c)
4^(3 * 1/3) z^ (9 * 1/3)
4 ^ ( 1) z^ ( 3)
4 z^3
What is the slope of the line in the graph? A.2 B.1/2 C.-2 D.-1/2
Step-by-step explanation:
bhdjdjsjshhdfhfbtvyvyvjdjshdjfy
The sum of ages Afful and Naomi is 34. In 5 years time , Afful will be 2 times the age on Naomi now. How old are they now.
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.
The sum of their ages is 34. In other words:
[tex]A+N=34[/tex]
In 5 years time, Afful will be two times the age of Naomi now. In other words:
[tex]A+5=2N[/tex]
Solve for the system. Substitute.
[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]
Afful is currently 21 and Noami is currently 13.
Answer:
Naomi=x
Afful=2x
In 5 years time= +5
So Naomi=x+5
and and Afful=2x+5
=x+5+2x+5=34
=3x+10=34
Subtract 10 on both sides
3x=24
Divide 3 on both sides
X=8
Check:
X=8
Naomi=16
In 5 years
=16+5=21
Naomi=8+5=13
13+21=34
Hope this helps
Step-by-step explanation:
If you had a cube with a side length of 4, how can your write the calculations in exponential form? What are 2 other ways to read the exponent verbally?
Answer: 4^3
(Four cubed or Four to the power of 3)
Step-by-step explanation: