Answer:
6 out of the 20 values are below 2. 6/20 = 30%.
Since 30% of the values are below 2, 2 is located at the 30th percentile.
Step-by-step explanation:
a number has 2,5 and 7 as its prime factors. what are the four smallest values it and take
Answer:
70, 140, 280, 350
Step-by-step explanation:
Obviously, it must have the factors 2, 5, 7 as a minimum, so the smallest value is 2×5×7 = 70.
Any of these primes can be added to the product. In increasing order, the smallest additional factors will be 2, 4, 5, 7, 8, 10, ...
So, the four smallest numbers with prime factors of 2, 5, and 7 are ...
70 = 2·5·7
140 = 2²·5·7
280 = 2³·5·7
350 = 2·5²·7
Which two ratios represent quantities that are proportional? A 25/28 and 5/7 B 22/33 and 14/21 C 16/13 and 13/16 D 48/60 and 35/42
Answer:
Step-by-step explanation:
If $a>0$ and $b>0$, a new operation $\nabla$ is defined as follows:$$a \nabla b = \dfrac{a + b}{1 + ab}.$$For example,$$3 \nabla 6 = \dfrac{3 + 6}{1 + 3 \times 6} = \dfrac{9}{19}.$$For some values of $x$ and $y$, the value of $x \nabla y$ is equal to $\dfrac{x + y}{17}$. How many possible ordered pairs of positive integers $x$ and $y$ are there for which this is true?
This happens when
1 + a b = 17 ==> a b = 16
With a and b both positive integers, and 16 = 2^4, we can have
• a = 1 and b = 16
• a = 2 and b = 8
• a = b = 4
and vice versa. So there are 5 possible ordered pairs.
An Aquarium’s dimensions are 3 1/4 ft x 2 ft x 1 3/4. What is the volume of the Aquarium?
Volume = length x width x height
Volume = 3 1/4 x 2 x 1 3/4 = 11 3/8 cubic feet
Answer:
11 3/8 ft^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 3 1/4 * 2 * 1 3/4
Change the number to improper fractions
V = (4*3+1)/4 *2 * (4*1+3)/4
= 13/4 *2* 7/4
Rewriting
= 13/1 * 2/4 * 7/4
= 13/1 * 1/2 *7/4
= 91/8
Changing back to a mixed number
8 goes into 91 11 times with 3 left over
11 3/8 ft^3
PLEASE HELP ME!!!!!!!!!
The relationship between hours exercised and the score on a memory test is modeled by the following line of best fit: y
= 4.8x + 27. Interpret the slope and intercept of the trend line within the context of the data.
Answer:
Slope: 4.8, x-intercept: -27/4.8, y-intercept: 27
Step-by-step explanation:
To find the slope, use the formula y = mx + b. In this formula, m represents the slope. Since the given equation is based on the above formula, m is 4.8.
To find the x-intercept, set y equal to 0 and solve for x.
y = 4.8x + 27
0 = 4.8x + 27
-27 = 4.8x
-27/4.8 = x
x = -27/4.8
To find the y-intercept, we use the formula y = mx + b again. In this formula, b represents the y-intercept. And, since the equation is based on this formula, b is 27.
(Remember this for future reference: even though the formula says +b, the y-intercept can still be negative).
I hope this helped!
How much water will be in each bottle if the total amount of water is equally divided among the bottles?
Answer:
D
Step-by-step explanation:
add everything up devide by 3
Answer:
C. 1/2 liter
Step-by-step explanation:
First, find the total amount of water by multiplying the amounts of water by the number of bottles, then adding all 3 values together:
1/4(1) = 1/4 liter
1/2(4) = 2 liters
3/4(1) = 3/4 liter
1/4 + 2 + 3/4 = 3 liters
There are 6 bottles in total, if we count the number of dots.
To find how much water would be in each bottle if the water was equally divided, divide the total amount of water by the number of bottles:
3 / 6 = 1/2
= 1/2 liter
prove that (3-4sin^2)(1-3tan^2)=(3-tan^2)(4cos^2-3)
Answer:
Proof in the explanation.
Step-by-step explanation:
I expanded both sides as a first step. (You may use foil here if you wish and if you use that term.)
This means we want to show the following:
[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
[tex]=12\cos^2(\theta)-9-4\cos^2(\theta)\tan^2(\theta)+3\tan^2(\theta)[/tex].
After this I played with only the left hand side to get it to match the right hand side.
One of the first things I notice we had sine squared's on left side and no sine squared's on the other. I wanted this out. I see there were cosine squared's on the right. Thus, I began with Pythagorean Theorem here.
[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
[tex]3-9\tan^2(\theta)-4(1-\cos^2(\theta))+12\sin^2(\theta)\tan^2(\theta)[tex]
Distribute:
[tex]3-9\tan^2(\theta)-4+4\cos^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]
Combine like terms and reorder left side to organize it based on right side:
[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
After doing this, I since that on the left we had products of sine squared and tangent squared but on the right we had products of cosine squared and tangent squared. This problem could easily be fixed with Pythagorean Theorem again.
[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+12(1-\cos^2(\theta))\tan^2(\theta)-9\tan^2(\theta)[/tex]
Distribute:
[tex]4\cos^2(\theta)-1+12\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
Combined like terms while keeping the same organization as the right:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
We do not have the same amount of the mentioned products in the previous step on both sides. So I rewrote this term as a sum. I did this as follows:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
Here, I decide to use the following identity [tex]\cos\theta)\tan(\theta)=\sin(\theta)[/tex]. The reason for this is because I certainly didn't need those extra products of cosine squared and tangent squared as I didn't have them on the right side.
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]
We are again back at having sine squared's on this side and only cosine squared's on the other. We will use Pythagorean Theorem again here.
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8(1-\cos^2(\theta))-9\tan^2(\theta)[/tex]
Distribute:
[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8+8\cos^2(\theta)-9\tan^2(\theta)[/tex]
Combine like terms:
[tex]12\cos^2(\theta)-9+3tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)[/tex]
Reorder again to fit right side:
[tex]12\cos^2(\theta)-9+4\cos^2(\theta)\tan(\theta)+3\tan^2(\theta)[/tex]
This does match the other side.
The proof is done.
Note: Reordering was done by commutative property.
Hello!! Please help me solve the question, could you please also tell me which calculator we can use? Thank you
You can use any calculator in Maths.
Louis bought 16 cookies at the bakery. He had a
coupon for $7 off his entire purchase. He ended up
paying $13.32. Write an equation to find how much
each cookie originally cost.
Answer:
16x -7 =$13.32
Step-by-step explanation:
$13.32 + $7 = $20.32
$20.32 divided by 16 = $1.27
each cookie cost $1.27
I really hope this help
Answer:- 16x - 7 = 13.32
Also cost of each cookie = $1.27
Explanation:
Let the cost of each cookies be x
ATQ
16x -7 = 13.32
We will mutiply x with 16 because he purchased 16 cookies.
Also he had coupon of $7 which means $7 off which is why -7
And 13.32 is the amount he paid
Now lets solve it
16x - 7 = 13.32
16x = 13.32 + 7
16x = 20.32
x = 20.32/16
x = 1.27
Therefore cost of each cookie is $1.27
please click thanks and mark brainliest if you like :)
Solve for a
5+14a=9a-5 a=
Answer:
-2
Step-by-step explanation:
5+14a=9a-5
+5 +5
10+14a=9a
-9a -9a
10+5a=0
-5a -5a
10= -5a
÷5 ÷5
2= -a
*-1 *-1
-2=a
Shawn wanted to model the number 13,450 using 13,450 using base-ten blocks how many large cubes, flats, and longs does he need to model the number
Answer:
See attached
Step-by-step explanation:
13450 = 13000 + 400 + 50
13*1000 = 13 large cubes4*100 = 4 flats5*10 = 5 longswhat is the graph of the following function??
PLEASE HELP!!
Answer:
umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...
Step-by-step explanation:
Which of the following statements is true about odd
and/or even numbers?
F. The sum of any 2 even numbers is odd.
G. The sum of any 2 odd numbers is ood.
H. The quotient of any 2 even numbers is odd.
J. The quotient of any 2 even numbers is even.
K. The product of any 2 odd numbers is odd.
Answer:
k) the product of ant 2 odd numbers is odd
I don't know.
Let's check um out.
For each choice, I'll try to find an example to show that it's false.
F. The sum of any 2 even numbers is odd.
2+2=4. 4 is even. This one is false.
G. The sum of any 2 odd numbers is ood.
3+3=6. 6 is even. This one is false.
H. The quotient of any 2 even numbers is odd.
8÷4=2. 2 is even. 10÷4=2.5. 2.5 is neither odd nor even. This one is false.
J. The quotient of any 2 even numbers is even.
10÷2=5. 5 is odd. This one is false.
K. The product of any 2 odd numbers is odd.
I can't find an example where this is false.
So I'm gonna say that this is the true one.
in this figure ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90cm^2. Find PT:TR please help me
Answer: The required ratio is PT:TR = 1:2.
Step-by-step explanation:
Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².
To find : PT:TR
.i.e. Ratio of PT to TR.
Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]
[tex]=\dfrac{4\ cm}{8\ cm}[/tex]
Divide numerator and denominator by 4 , we get
[tex]\dfrac{1}{2}[/tex]
Therefore, the required ratio is PT:TR = 1:2.
20. A pool holds 1440 CUBIC feet of water, the aty
charges $). 15 per cubic meter of water
used now, much will it cost to fill the pool?
Complete question :
A pool holds 1440 cubic feet of water, the city charges $1.75 per cubic meter of water used.
How much will it cost to fill the pool?
Answer:
$71.36
Step-by-step explanation:
Amount charged per cubic meter = $1. 75
Total volume of pool = 1440 ft^3
Using the conversion unit chart :
1 cubic meter = 35.3147 cubic foot
Then we can express the capacity of water held by the pool in cubic metre.
If 1 cubic meter = 35.3147 cubic foot
Then ;
y cubic meter = 1440 cubic foot
y = 1440/35.3147
y = 40.776220 cubic meter
Thus;
Cost of filling the pool will be;
$1.75 × 40.776220
= $71.358386
= $71.36
the third term and the fifth term of a geometric progression are 2 and 1/8 respectively. If all terms are positive, find the sum to the infinity of the progression
Answer:
42 + 2/3
Step-by-step explanation:
First, to calculate the sum of an infinite geometric series, our formula is
a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.
To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have
2 * r * r = a₅
2 * r² = 1/8
divide both sides by 2 to isolate the r²
r² = 1/16
square root both sides to isolate r
r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5
Therefore, r = 1/4 .
To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2
a₁ * 1/16 = 2
divide both sides by 1/16 to isolate a₁
a₁ = 2 * 1/ (1/16)
= 2 * 16
= 32
Plugging a₁ and r into our infinite geometric series formula, we have
a₁/(1-r)
= 32 / (1-1/4)
= 32/ (3/4)
= 32/ 0.75
= 42 + 2/3
Type the correct answer in each box
the value of x is ____ and the value of y is ____ . HELP ME PLEASE
Here,
x+50°+70°= 180° [°.°Angle sum of triangle]
↪x= 180°-120°
↪x=60°
.°. x = 60°
Now,
Let z be the unknown angle of the second triangle
z+60°+50°=180° [°.° Angle sum of triangle ]
↪z=180°-110°
↪z=70°
. ° . z=70°
Then,
z+x+y= 180°
↪70°+60°+y=180°
↪y=180°-130°
↪y=50°
.°.y = 50°
Answer:
x = 60°, y = 50°
Step-by-step explanation
We know: the angles measures in a triangle add up to 180°.
(look at the picture)
z + 50 + 60 = 180
z + 110 = 180 subtract 110 from both sides
z = 70°
x + 50 + 70 = 180
x + 120 = 180 subtract 120 from both sides
x = 60°
Angles x, y, and z are on one side of a straight line. Therefore they add to 180°.
x + y + z = 180
60 + y + 70 = 180
y + 130 = 180 subtract 130 from both sides
y = 50°
Examine the table of input (x) and output (y) values below. What is the relationship between the input and output values? Write an equation for this relationship. input (x) –1 0 1 2 3 4 5 output (y) –4 –1 2 5 8 11 14 What do you notice about the relationship between the x and y values?
Answer:
Relationship: As the input increases by 1, the output increases by 3.
Equation: y=3x-1
~Hope this helps~
Can i please get some help im pretty desperate and will give brainiest to first answer with some steps, just try your best please
Answer:
To calculate the vertex you can use the vertex form ( i searched about the vertex and found it) but i don't know how to use it so i used another method.
The vertex is where the function inverts (y values) so it is going to be or a maximum or a minimum of the function. To calculate the min/max you derivate the function and then equal it to zero.
1) y = -3x^2 -12x -10
the derivative of y is y' = -6x -12 = -6(x+2)
y'=0 <=> -6(x+2) = 0 <=> x+2=0 <=> x=-2
y(-2) = -3(-2)^2 -12*(-2) -10 = 2
So the vertex is the point (-2,2) .
Because the slope of the equation is negative that means that the vertex is going to be the maximum , so the maximum is (-2,2) .
To find another 4 points you just have to pick values of x and replace them in the equation y = -3x^2 -12x -10 to find y.
2) y = -2x^2 -12x -16
Do the same thing we did in point 1
y'= -4x-12 = -4(x+3)
y'=0 <=> -4(x+3) = 0 <=> x+3=0 <=> x=-3
y(-3) = -2(-3)^2 -12*(-3) -16 = 2
So the vertex is the point (-3,2) .
The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1
Intersection point of graph of function is known as solution of the function.
Graph is attached below, in which solution is shown.
1. Here, given that [tex]3x^2-3x+2=2[/tex]
It can be written as, [tex]y=3x^2-3x+2\\\\y=2[/tex]
Intersection point of graph of above two equation will be the solution of given function,
Solutions are (1, 2) and (0, 2)
2. Given that , [tex]3x^2-3x-1=x+1[/tex]
It can be written as
[tex]y=3x^2-3x-1\\\\y=x+1[/tex]
Intersection of graph of above two equation will be the solution of given equation.
Solutions are (1.721, 2.721) and (- 0.387, 0.613)
Both graph attached below,
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rational or irrational? and why
Answer:
rational, simplified number is -0.5
Step-by-step explanation:
(see screenshot)
 Which table below matches the scatter plot?
x 3 4 6 1 7 8 1 2
y 5 9 3 2 7 6 4 5
x 2 1 8 6 7 1 4 3
y 5 9 3 2 7 6 4 5
x 3 4 6 1 7 8 1 2
y 1 2 3 4 5 6 7 8
x 3 4 6 1 7 8 1 2
y 2 1 7 1 3 5 6 4
Answer:
The first table
x 3 4 6 1 7 8 1 2
y 5 9 3 2 7 6 4 5
When a boy pulls his sled with a rope, the rope makes an angle of 70° with the horizontal. If a pull of 20 pounds on the rope is needed to move the sled, what is the horizontal component force?
7 lb
19 lb
20 lb
24 lb
Answer:
The answer to your question is 7 lbs.
Step-by-step explanation:
Data
angle = 70°
force = 20 lb
horizontal component
Process
To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.
1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.
cos Ф = adjacent side / hypotenuse
- Solve for the adjacent side
adjacent side = hypotenuse x cosФ
- Substitution
adjacent side = 20 x cos 70
- Simplification
adjacent side = 20 x 0.342
- Result
adjacent side = 6.84 ≈ 7 lb
Bob has a pyramid with a volume of 14. He'd like to create a second pyramid with a volume of 28. Which would guarantee he gets the desired
result?
O Double each side of the base of the pyramid.
O Double one side of the base of the pyramid.
O Double the slant height.
• Double the height.
Answer:
D
Step-by-step explanation:
Doubling the height will guarantee that the volume gets twice since V=(1/3)*B*h
If Bob wants to create a pyramid of volume 28 then he needs to double the height of the pyramid.
What is a pyramid?Design or construction with a base that is a polygon and sides that are three or more triangles that come together at the top.
A pyramid is a 3D shape where 3 triangle comes and meet in such a way that the base side creates a triangle.
The volume of a pyramid is given by
Volume = (1/3)base²×height.
Let say
Base width is = w
Height is = h
Volume V = w²h/3
Given
14 = w²h/3
For volume to be 28
28 = w²(2h)/3
So it is clear that he needs to double the height.
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Forgot how to do this please help, thank you.
3m + 2x=-3, solve for x
Answer:
[tex]\boxed{x =\frac{-3m-3}{2}}[/tex]
Step-by-step explanation:
[tex]3m + 2x=-3[/tex]
[tex]\sf Subtract \ 3m \ from \ both \ sides.[/tex]
[tex]3m + 2x-3m=-3-3m[/tex]
[tex]2x=-3-3m[/tex]
[tex]\sf Divide \ both \ sides \ by \ 2.[/tex]
[tex]\displaystyle \frac{2x}{2} =\frac{-3-3m}{2}[/tex]
[tex]\displaystyle x =\frac{-3m-3}{2}[/tex]
Answer:
x=\frac{-3-3m}{2}
Step-by-step explanation:
1st step: Subtract 3m from both sides. 3m+2x-3m=-3-3m
2nd step: Simplify. 2x=-3-3m
3rd step: Divide both sides by 2. \frac{2x}{2}=-\frac{3}{2}-\frac{3m}{2}
Final step: Simplify. x=\frac{-3-3m}{2}
if three less than one half a number is equal to one-third of the same number, find the number
Answer: The number would be 18
Step-by-step explanation:
18/2=9 9-3=6 6*3=18
The equation be (x/2) - 3 = x/3 then, the number of x = 18.
How to estimate the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Let x be the number
From the given information, we get
(x/2) - 3 = x/3
The set all the fractions on one side and constants on another side
(x/2) - (x/3) = 3
Multiply by LCM
3x - 18 = 2x
Add 18 to both sides
3x - 18 + 18 = 2x + 18
simplify
3x = 2x + 18
Subtract 2x from both sides
3x - 2x = 2x + 18 - 2x
x =18.
Therefore, the number is x = 18.
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How do u find the area of a rectangle?
Answer:
6x-21
Step-by-step explanation:
Area of a rectangle is length times width.
3*(2x-7)-
6x-21
Answer:
6x - 21
Step-by-step explanation:
Since area = L x W (Length x Width)
--> 3(2x - 7)
6x - 21
Jack bought a car for $50,000. He spent $5000 on repairs. He sold the car at a profit of $5000. At what price did he sell the car.
Answer:$60,000
Step-by-step explanation:
If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because
60,000 - 55,000 = 5,000
a submarine is 50 meters below sea level. It goes up 15 meters and down 40 meters. What is the submarines new position relative to sea level
Answer:
-75 m
Step-by-step explanation:
Use sea level as the reference point.
Initially the position is -50 m.
If the submarine goes up 15 m, then its new position is (-50 + 15) m, or -35 m.
If the sub now descends 40 m, its new position is (-35 - 40) m, or -75 m
the area of a square poster is 27 in.2. Find the length of one side of the poster to the nearest tenth of an inc
Answer:
5.2 inches
Step-by-step explanation:
Let a be the side of the square poster.
The area of it is:
● A = a^2
● 27 = a^2
● a = √27
● a = √(9×3)
● a = 3√3
● a = 5.19
Round it to the nearest tenth
● a = 5.2 inches
The length of one side of the poster is approximately 5 inches rounded to nearest tenth.
What is rounding of numbers ?We round numbers because they are easy to deal with and they also retain their value to that place they have been rounded.
According to the given question the area of a square poster is 27inch².
We have to determine the length of one side of the poster.
We know area of a square is (side)².
∴ (side)² = 27.
side = [tex]\sqrt{27}[/tex].
We know [tex]\sqrt{25}[/tex] is 5 and [tex]\sqrt{36}[/tex] is 6 so [tex]\sqrt{27}[/tex] will lie between 5 and 8 and much closer to 5.
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