Answer:
it can be times a number tjatgoes into 8
A ball, thrown vertically upwards, from the ground, has its height h (in meters) expressed as a function of time t (in seconds), elapsed after the launch, by the law h(t) = 20t - 5t2. According to this information, determine the height at which the ball is 3 seconds after the throw and the maximum height reached by the ball.
Answer:
a. 15 meters.
b. 20 meters.
Step-by-step explanation:
a. The height of the ball at 3 seconds. 20 * 3 - 5 * (3)^2 = 60 - 5 * 9 = 60 - 45 = 15.
The ball will be 15 meters high.
b. The maximum height reached by the ball.
To get that, we need to find the vertex of the parabola. We do so by doing -b/2a to find the x-coordinate of the vertex.
In this case, a = -5 and b = 20.
-20 / 2(-5) = -20 / -10 = 20 / 10 = 2.
Then, we find the y-coordinate by putting 2 where it says "t".
h(2) = 20(2) - 5(2)^2 = (40) - 5(4) = 40 - 20 = 20 meters.
Hope this helps!
Answer:
pen
Step-by-step explanation:
Write the equation of the line perpendicular to 2x - 6y = 12 that passes through the point (-3,0).
slope intercept: y = 1/3x - 2
Answer:
y = -3x -9
Step-by-step explanation:
slope = 1/3
perpendicular slope = -3
y = mx + b
0 = -3(-3) + b
-9 = b
y = -3x -9
Answer:
y = -3x-9
Step-by-step explanation:
2x - 6y = 12
Solving for y we get
-6y = -2x+12
y = 1/3x -2
The slope is 1/3
Perpendicular lines have slopes that multiply to -1
m * 1/3 = -1
Multiply each side by 3
m * 1/3 * 3 = -1 *3
m = -3
The perpendicular line has a slope of -3
Using the slope intercept form
y = mx+b
y = -3x +b
And the point (-3,0) is substituted into the equation
0 = -3(-3) +b
0 = 9+b
B = -9
y = -3x-9
PLEASE HELP ASAP don’t have much time.
Answer: 4
Step-by-step explanation:
numerator - denominator
Numerator: w¹³ Denominator: w⁸ · w¹
13 - (8 + 1)
13 - 9 = 4
The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Which statement about the radius of the sphere is true
Answer:
Radius of sphere is 3 units.
Step-by-step explanation:
Volume of sphere is given by [tex]4/3 \pi r^3[/tex]
surface area of sphere is given by [tex]4 \pi r^2[/tex]
where r is the radius of the sphere.
Given that
The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.
we equate formula of Volume of sphere and surface area of sphere
assuming r as the radius.
thus,
[tex]4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3[/tex]
Thus, radius of sphere is 3 units.
Can somebody please help me!!
Step-by-step explanation:
Simply you replace X and Y by their values
Given: x=-1 y=-4
10 - (-X)^3 + y^2
=10 + X^3 + Y^2
Now replace X and Y
=10 + (-1)^3 + (-4)^2
=10 - 1 + 16
= 25
What do you guys think?
Two numbers are in the ratio 3: 7. If 1 is added to the smaller number and 7 is added to the larger, they will be in the ratio 1: 3. Find the numbers.
Answer:
6 and 14
Step-by-step explanation:
The numbers are in the ratio 3 : 7 = 3x : 7x (x is a multiplier )
adding 1 to smaller number is 3x + 1 and 7 to the larger is 7x + 7, then
3x + 1 : 7x + 7 = 1 : 3
Expressing the ratio in fractional form
[tex]\frac{3x+1}{7x+7}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
3(3x + 1) = 7x + 7
9x + 3 = 7x + 7 ( subtract 7x from both sides )
2x + 3 = 7 ( subtract 3 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Thus the numbers are
3x = 3(2) = 6
7x = 7(2) = 14
Forty cards are placed into a box, each bearing a number 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, with each number entered on four cards. Four cards are drawn from the box at random and without replacement. Let $p$ be the probability that all four cards bear the same number. Let $q$ be the probability that three of the cards bear a number $a$ and the other bears a number $b$ that is not equal to $a$. What is the value of $q/p$?
Answer:
The value of q/p = 144
Step-by-step explanation:
Number of cards in the box = 40
Each bearing a number: 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10
Each number appears 4 times cards in total
p = the probability that all four cards bear the same number.
q = the probability that three of the cards bear a number 'a' and the other bears a number 'b' that is not equal to 'a'.
The cards were chosen without replacement.
For Probability without replacement, the total number of items decrease after each pick. When considering same items, the number of the same item also decrease after each pick.
a) In this question, the order of the 4 cards picked is irrelevant.
Pr (4 same cards) = p = 4/40 × 3/39 × 2/38 × 1/37
p = 24/2193360 = 1/91390
Pr (3same cards and 1 different card) = q
Probability of picking 'a' card = 4/40
Probability of picking other cards aside 'a' = Probability of not picking 'a' card
= 36/40
Since we were not told what the particular number of the other number is, it would be any of the remaining 36 numbers.
b) In this question, we would consider the order of the 4 cards picked.
q = Pr(baaa) + Pr(abaa) + Pr(aaba) + Pr(aaab)
Without replacement
q = (36/40 × 4/39 × 3/38 × 2/37) + (4/40 × 36/39 × 3/38 × 2/37) + (4/40 × 3/39 × 36/38 × 2/37) + (4/40 × 3/39 × 2/38 × 36/37)
q = 4[(36×24)/2193360]
q= 144(24)/2193360 = 144(24/2193360)
q= 144(1/91390) = 144/91390
The value of q/p = (144/91390)/(1/91390)
The value of q/p = (144/91390) × (91390/1)
The value of q/p = 144
1 a.
7 + 10
(4 + 3)
this is the last question I'm going for today
Answer:
7 + 10 = 17
7 * 7 * 7 = 343
17 / 343 = 0.04956268221
What is the quadratic regression equation that fits these data? WILL GIVE BRAINLIEST.
Answer:
D
Step-by-step explanation:
Just take x and replace it by 0 to see if you get 12
you will get 11.93 wich is close to 12
A regression can either be linear, nonlinear or no relationship at all
The equation of the quadratic regression is [tex]y = -0.89x^2 +3.24x +11.93[/tex]
To determine the equation of the quadratic regression, we make use of a graphing calculator.
From the graphing calculator, we have the following calculator summary
a = -0.89 b = 3.24 c = 11.93A quadratic regression equation is represented as
[tex]y = ax^2 + bx + c[/tex]
So, we have:
[tex]y = -0.89x^2 +3.24x +11.93[/tex]
Hence, the equation of the quadratic regression is [tex]y = -0.89x^2 +3.24x +11.93[/tex]
Read more about regression equations at:
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You purchase a $100,000 life insurance policy for a $300 premium each year. If the probability of living is 0.999, find the expected value for the insurance company.
Answer:
The expected value for the insurance company is $200
Step-by-step explanation:
In order to calculate the expected value for the insurance company we would have to make the following calculation:
expected value for the insurance company=expected value live+expected value die
expected value live=Net gain*probability of living
expected value live=$300*0.999=$299.70
expected value die=Net gain*probability of die
expected value die=(-$100,000 + $300)*0.001
expected value die=$-99.70
Therefore, expected value for the insurance company=$299.70-$99.70
expected value for the insurance company=$200
The expected value for the insurance company is $200
What do I do please help
Answer:
The answer is y=1x+2
Step-by-step explanation:
Simply count up on both sides. Then take the number of increases between each y value and place it on top of the increase of the x value. Divide. To find the y-intercept, or "b", take the constant of the y and count back until the x is zero. For example, since the chart is consistently going up by 1s on each side, take the first "y" value, 3, and count one back to zero on the x. It is two.
Answer:
y=1x+2
Explanation:
You use the equation y=mx+b.
Here is how I got my answer
step 1: Find the slope by finding the change in y values and x values
x y
1 3
2 4
3 5
4 6
5 7
X=+1
Y=+1 you do the change of y over the change of x and get 1/1=1
So far in the equation now you have y=1x+b
Step 2:Solve for the b value by substituting the y and x variable with a value from the table
x y y=1x+b
1 3 3=1(1)+b-->3=1+b-->3-1=b+1-1-->2=b
2 4
3 5
4 6
5 7
Step 3: Plug in all the numbers you got into the equation y=mx+b
y=1x+2
What is the interquartile range of the data set? {33, 38, 45, 56, 57, 63, 72, 91}
Answer:
[tex] IQR =Q_3 -Q_1[/tex]
We have for this case n= 8 values. In order to find the Q1 we can select the first 4 values {33, 38, 45, 56 and the Q1 would be:
[tex] Q_1 = \frac{38+45}{2}= 41.5[/tex]
And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:
[tex] Q_3= \frac{63+72}{2}= 67.5[/tex]
And then the interquartile range would be:
[tex] IQR =Q_3 -Q_1 = 67.5-41.5 = 26[/tex]
Step-by-step explanation:
For this problem we have the following dataset ordered:
{33, 38, 45, 56, 57, 63, 72, 91}
And we want to find the interquartile range defined as:
[tex] IQR =Q_3 -Q_1[/tex]
We have for this case n= 8 values. In order to find the Q1 we can select the first 4 values {33, 38, 45, 56 and the Q1 would be:
[tex] Q_1 = \frac{38+45}{2}= 41.5[/tex]
And for the Q3 we can select the last 4 values 57, 63, 72, 91 and for Q3 we got:
[tex] Q_3= \frac{63+72}{2}= 67.5[/tex]
And then the interquartile range would be:
[tex] IQR =Q_3 -Q_1 = 67.5-41.5 = 26[/tex]
The correct answer is:
26
I took the test, hope this helps!
ABC and ADC are triangles The area of ADC is 52m^2 Work out the length of AB Give your answer to 1 decimal place
Answer:
Length of side AB = 10.2m
Step-by-step explanation:
Given:
The given area of triangle ADC = 52m²
Side AD = 12m,
Given angle D = 102°
Then we can calculate the area of triangle ADC using below formula
Area= ½ × a × b × sin(C)
52m² = ½ × 12 × CD × sin102
But sin102= 0.9781
52 = 6 × CD *(0.9781)
CD = 52/(6× 0.9781)
CD = 52/5.8686
Therefore, the length of side CD= 8.86m= 8.9m If we approximate
If we will need to find sides AC by applying Cosine rule as follows
d² = a² + c² -2ad ×(cosD)
d² = 8.9² + 12² - 2*8.9*12× Cos102
Cos102 = -0.2079
d² = 267.61744
d = √267.61744
Therefore, sides AC = 16.4m
We can apply sine rule to ∆ABC as
xsinX = y/sinBY
AB/sin46) = AC/(sin120)
AB/0.7193 = 16.4/(0.866)
AB = (14.2023) ×0.7193
Therefore, side AB = 10.2m
Can someone solve the hypotenuse for me?
Thank you!
Answer:
Side a = 88.67626
Side b = 57
Side c = 67.92995
Angle ∠A = 90° = 1.5708 rad = π/2
Angle ∠B = 40° = 0.69813 rad = 2/9π
Angle ∠C = 50° = 0.87266 rad = 5/18π
Area = 1,936.00371
Perimeter p = 213.60621
Semiperimeter s = 106.80311
Height ha = 43.66453
Height hb = 67.92995
Height hc = 57
Median ma = 44.33813
Median mb = 73.66633
Median mc = 66.35224
Inradius r = 18.12685
Circumradius R = 44.33813
Vertex coordinates: A[0, 0] B[67.92995, 0] C[0, 57]
Centroid: [22.64332, 19]
Inscribed Circle Center: [18.12685, 18.12685]
Circumscribed Circle Center: [33.96498, 28.5]
The perimeter of a rectangle is 70 cm. The ratio of length to width is 2:5. Find the length and width of the rectangle.
Answer:
length = 10 cm; width = 25 cm
Step-by-step explanation:
Let's call the length 2x and the width 5x. Since perimeter can be calculated by multiplying the sum of the length and width by 2 we can write:
2 * (2x + 5x) = 70
2 * (7x) = 70
7x = 35
x = 5 which means the length is 2 * 5 = 10 and the width is 5 * 5 = 25.
If T={x:X is an integer between 1 and 4} (A) List down the elements of set T in set notation. B write down the number of elements in set T . C list down all the subsets of set T.D separate the proper and improper subsets of T.
Answer:
The answer is given below
Step-by-step explanation:
A) Integers are whole numbers (without fraction) that are either positive or negative. If T={x:X is an integer between 1 and 4}, therefore the elements in set T = {2, 3}
B) Since the elements in set T = {2, 3}, then the number of elements in set T = 2
C) The subsets of set T are {}, {2}, {3} and {2,3}
D) Proper subset of set T are subsets of T that is not equal to T. The proper subsets of T are {2} and {3}
An improper subset of set T contains all the element of set T and a null element. The improper subset of set T are {2,3} and {}
Find the center and radius of the circle x2 + y2 –6y – 16 = 0
Answer:
centre=(0,3) radius =5
Step-by-step explanation:
A sector of a circle has an arc length of 8 pi inches and a central angle of 20 degrees, as shown. What is the circumference of the circle? Express the answer in terms of Pi.
Answer:
Step-by-step explanation:
Arc length has a formula of
[tex]AL=\frac{\theta}{360}*2\pi r[/tex] and we have all the info we need to solve for the radius, which we will then use in the circumference formula:
[tex]8\pi=\frac{20}{360}*2\pi r[/tex] and simplifying a bit,
[tex]8\pi=\frac{2}{36}*2\pi r[/tex] and a bit more,
[tex]8\pi=\frac{4\pi r}{9}[/tex]. Multiply both sides by 9:
72π = πr . Divide both sides by π to get that
r = 72.
Now we will sub that into the circumference formula to find the circumference. Recall that C = 2πr.
C = 2π(72) so
C = 144π
Answer:it’s c (144 inches)
Step-by-step explanation:
Which ordered pair is a solution if the equation? 2x + 3y = 10
Answer:
See below.
Step-by-step explanation:
Try each ordered pair in the equation. Each ordered pair is of the form (x, y). Replace x and y in the equation by values of x and y, respectively, in each ordered pair. Whichever ordered pair makes the equation a true statement is the answer.
For example:
Try (2, 3):
2x + 3y = 10
2(2) + 3(3) = 10
4 + 9 = 10
13 = 10
Since 13 = 10 is a false statement, (2, 3) is not a solution.
Try (2, 2):
2x + 3y = 10
2(2) + 3(2) = 10
4 + 6 = 10
10 = 10
Since 10 = 10 is a true statement, (2, 2) is a solution.
Someone answer quick please for brainliest !
Find the equation of the line that passes through (1,2) and is perpendicular to y=2x +3
Leave your answer in the form y=mx +c
Answer:
The equation of the line is
[tex]y = - \frac{1}{2} x + \frac{5}{2} [/tex]
Step-by-step explanation:
Equation of a line is
[tex]y = mx + c[/tex]
Where m is the slope
c is the y intercept
y = 2x + 3
Comparing with the above formula
m is 2
Since the lines are perpendicular the slope of the other line is the negative inverse of the original line .
That's
m = - 1/2
Equation of the line using point (1,2) and slope - 1/2 is
y - 2 = -1/2(x - 1)
y - 2 = -1/2x + 1/2
y = -1/2x + 1/2 + 2
The final answer is
[tex]y = - \frac{1}{2} x + \frac{5}{2} [/tex]
Hope this helps you.
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Simplify [Q - R] + [S - T].
10m - 7n - 14
10m + 5n - 24
10m - 5n + 24
10m + 7n - 14
Answer:
The answer is 10m + 7n - 14
Step-by-step explanation:
Q = 7m + 3n
R = 11 - 2m
S = n + 5
T = -m - 3n + 8
[Q - R] + [S - T] is
[ 7m + 3n - (11 - 2m) ] + [ n + 5 - ( - m - 3n+8)]
Solve the terms in the bracket first
That's
( 7m + 3n - 11 + 2m ) + ( n + 5 + m + 3n - 8)
( 9m + 3n - 11 ) + ( m + 4n - 3)
Remove the brackets
That's
9m + 3n - 11 + m + 4n - 3
Group like terms
9m + m + 3n + 4n - 11 - 3
The final answer is
10m + 7n - 14Hope this helps you
The slope of the graph is –1. Which statement describes how the slope is related to the burning of a candle? candle height increases 1 cm per hour candle height decreases 9 cm per hour candle is 1 cm tall candle burns down 1 cm per hour
Answer:
candle burns down 1 cm per hour
Step-by-step explanation:
I believe that since the slope is -1, the steepness would be going downward. This means the candle would burn down.
Answer:
D.
Step-by-step explanation:
candle burns down 1 cm per hour
Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the measure of angle b in the image below.
Answer:
complementary
b = 45 deg
Step-by-step explanation:
Angles b and 45-deg are complementary since their measures ad to 90 deg.
45 + b = 90
b = 45
Answer:
Complementary
45°
Step-by-step explanation:
b + 45° = 90°
b = 90° - 45°
b = 45°
explain how to do this question plz
Answer: about 17.7%
Step-by-step explanation:
The area of a trapezoid is ((b1+b2)/2)*h
Thus, the area of the trapezoid is 85 meters squared. Thus, because the garden is 480 meters squared, the trapezoid occupies 85/480 of the garden, or about 17.7 percent.
Hope it helps <3
Answer:
17.7% rounded to the nearest tenth
Step-by-step explanation:
Well to find the percent of space the trapezoid takes up we need to find both areas.
To find the area of a Rectangle we do l*w.
So the l is 30 and the w is 16 so,
30*15 = 480m^2
To find the area of a Trapezoid [tex]\frac{b1 + b2}{2}h[/tex].
So b1 is 20 and b2 is 14,
14 + 20 = 34
34/2 = 17
17 * h
17 * (5) = 85m^2
So now we make a fraction of the areas of the trapezoid and rectangle,
[tex]\frac{85}{480}[/tex]
Now we simplify,
85/5 = 17
480/5 = 96
So 17/96 is in its simplest form so now we do 17/96 which is 0.1770833333
So to the following into a percent we move the decimal places 2 places to the right which is about 17.7% rounded to the nearest tenth.
the graph of the function f is shown in the xyplane above the function f is define by f(x)=mx+b,where m and b are constant which of the following could be the graph of the function where g(x)=-mx-b?
Answer:
Option (C)
Step-by-step explanation:
We will apply the rules of transformations in this question.
Parent function of the given line in the graph is,
f(x) = mx
If the function is f'(x) = -mx
Then the line will be inverted of reflected across the x-axis.
If the function is g(x) = -mx - b
Then the line representing function g(x) = -mx will be shifted b units downwards, similar to the graph given in Option (C).
Brian invests £2300 into his bank account.
He receives 10% per year simple interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
2783 pounds
Step-by-step explanation:
He has got 2300. The factor by which that is multiplied is 1,1 (+10%).
The time given is 2 years. We will calculate it by using equation:
[tex]2300*1.1^{2}[/tex]
2783
Geometry help? prove triangle PQR~ triangle TSR
Answer:
Step-by-step explanation:
The third step's reason is given. Then you must make <QRP and <SRT congruent because all right angles are congruent. Then you have two angles in each triangle congruent and can thus prove the triangles congruent by AA.
Can someone help me with this question please.
Answer:
98
Step-by-step explanation:
3 bed house= 33 rooms
4 bed house 40 rooms
4 bed house 25 rooms
each house is worth 2 houses. so u double everything
hope I got it right
What is (14.2a + 9.8b) - (13.1b - 0.2a) - (3.7a + 4.8b) simplified
Step-by-step explanation:
14.2a + 9.8b -13.1b + 0.2a - 3.7a -4.8b
= 14.2a + 0.2a -3.7a + 9.8b -13.1b -4.8b
= .......a + or - ....... b
The simplified form of the given expression is 10.7a-8.1b.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is (14.2a+9.8b)-(13.1b-0.2a)-(3.7a+4.8b).
Now, 14.2a+9.8b-13.1b+0.2a-3.7a-4.8b
Group like terms, that is
(14.2a+0.2a-3.7a)+(9.8b-13.1b-4.8b)
= 10.7a+(-8.1b)
= 10.7a-8.1b
Therefore, the simplified form of the given expression is 10.7a-8.1b.
To learn more about an expression visit;
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