CLASS 8 SPOT TEST
1. WHAT IS THE PROBABILITY THAT AN INTEGER CHOSEN AT RANDOM BETWEEN 1 TO 10 INCLUSIVE IS EVEN?
2. A BAG CONTAINS 5 WHITE, 4 BLACK AND 1 BLUE BALLS. ONE BALL IS CHOSEN AT RANDOM. WHAT IS THE PROBABILITY THAT IT IS BLACK?
3. FIND THE PROBABILITY OF GETTING AN ODD NUMBER IN A SINGLE TOSS OF A FAIR DIE?
4. A FAIR DIE IS THROWN 900 TIMES. FIND THE NUMBER OF TIMES YOU WOULD EXPECT TO GET A 6.
5. THE PROBABILITY THAT IT WILL BE CLOUDY TOMORROW IS 0.45. WHAT IS THE PROBABILITY THAT IT WILL NOT BE CLOUDY TOMORROW?
Step-by-step explanation:
1. Of the following 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Only these 5 are even: 2, 4, 6, 8, 10.
The probability on an even number is 5 / 10 = 0.5 = 50%
2. The total number of balls is 10.
5 WHITE, 4 BLACK AND 1 BLUE
The probability on a black ball is 4 / 10 = 0.4 = 40%
3. A fair die can show the following 6 numbers 1, 2, 3, 4, 5, 6.
Only these 3 are odd: 1, 3, 5.
The probability on an odd number is 3 / 6 = 0.5 = 50%
4. The probability of a six is 1 / 6. If the die is cast for 900 times you can expect it to be 900 * 1 / 6= 900/6 = 150. The number of times you would expect a 6 would be 150.
5. If the probability on a cloudy tomorrow is 0.45, then in mathematics, that defines the propability for an non cloudy tomorrow as 1 - 0.45 = 0.55, which is 55%.
(The total should always add up to 100%).
Calculate the width of a 70" TV if the TV has an aspect ratio of 16:9.
Answer:
The TV has a length of 61.01" and a height of 34.32"
Step-by-step explanation:
The size of a TV is given by the length of it's diagonal, in this case the diagonal of the TV is 70". The ratio of the screen is 16:9, which means that for every 16 units on the length of the tv there are 9 inches on its height. The diagonal of the screen forms a right angle with the length and the width, therefore we can apply Pythagora's theorem as shown below:
[tex]diagonal^2 = height^2 + length^2\\\\height^2 + length^2 = (70)^2\\\\height^2 + length^2 = 4900[/tex]
Since the ratio is 16:9, we have:
[tex]9*length = 16*height[/tex]
[tex]length = \frac{16}{9}*height[/tex]
Applying this on the first equation, we have:
[tex]height^2 + (\frac{16}{9}*height)^2 = 4900\\\\height^2 + \frac{256}{81}*height^2 = 4900\\\\\frac{337}{81}*height^2 = 4900\\\\height^2 = \frac{4900*81}{337}\\\\height^2 = \frac{396900}{337}\\\\height^2 = 1177.744\\\\height = \sqrt{1177.744}\\\\height = 34.32[/tex]
[tex]length = \frac{16}{9}*34.32\\\\length = 61.01[/tex]
The TV has a length of 61.01" and a height of 34.32"
Approximate the value of positive square root 5 to the nearest hundredth
Answer:
2.2
Step-by-step explanation:
The maximum point on the graph of the equation
y = f(x) is (2,-3). What is the maximum point on
the graph of the equation y=f(x-4)?
Answer:
(6, - 3 )
Step-by-step explanation:
Given f(x) then f( x + c) represents a horizontal translation of f(x)
• If c > 0 then a shift to the left of c units
• If c < 0 then a shift to the right of c units, thus
y = f(x - 4) represents a shift to the right of 4 units, so
(2, - 3 ) → (2 + 4, - 3 ) → (6, - 3 )
The maximum point on the graph after translation y = f( x -4) is (6 , -3)
What is translation of a graph?Translation of a graph is the movement of the graph either in horizontal direction or vertical direction .
Horizontal translation to the left is given by f (x+ c) ,c >0
: (x, y) → (x- c , y)
Horizontal translation to the right is given by f (x- c) ,c >0
: (x, y) → (x+ c , y)
Given that the maximum point on the graph of the equation
y = f(x) is (2,-3)
To find the maximum point on the graph of the equation y = f(x-4)
f(x -4) is Horizontal Translation to the right with 4 units , c= 4
then (x, y) → (x+ c , y)
Thus the maximum point (2,-3) is moved to ( 2 +c , -3)
⇒ (2+ c , -3) = (2+4 , -3) = ( 6 , -3)
Therefore, the maximum point of the graph of the equation y = f(x-4) becomes (6,-3)
Also, Learn more abut translation of graphs from the link below:
https://brainly.com/question/11805053
#SPJ5
PLEASE SOMEONE HELP ME ON 4,5, AND 6 ASAP.
Answer:
see below
Step-by-step explanation:
4. If ∠AYX = 25.5° that means that ∠XYZ = 25.5 * 2 = 51° because YA is the angle bisector.
5. If ∠XYZ = 64°, ∠AYZ = 64 / 2 = 32°.
6. You can construct ∠P and PQ by using a protractor. I'm not sure how to attach an image so I'll just tell you the answer I got for c which is about 3 cm.
A water balloon is thrown from the top of a house. The path of the balloon is modelled by the relation, h = -4.9t2 – 14.7t + 19.6,
where h is the balloon's height, in meters, above ground, and wheret is the time, in seconds.
a.
How tall is the house? (1 mark)
b. How long does it take for the balloon to hit the ground? (3 marks)
What is the maximum height that the balloon reaches? marks)
C.
Answer:
(a)19.6 meters
(b) 1 seconds
(c)30.625 meters
Step-by-step explanation:
The height of the balloon is modeled by the equation:
[tex]h = -4.9t^2- 14.7t + 19.6[/tex]
(a)Since the balloon is thrown from the top of the house, the height of the house is at t=0
When t=0
[tex]h(0) = -4.9(0)^2- 14.7(0) + 19.6\\h=19.6$ meters[/tex]
The height of the house is 19.6 meters.
(b)When the balloon hits the ground
Its height, h(t)=0
Therefore, we solve h(t)=0 for values of t.
[tex]h = -4.9t^2- 14.7t + 19.6=0[/tex]
[tex]-49t^2-147t+196=0\\-49(t^2+3t-4)=0\\t^2+4t-t-4=0\\t(t+4)-1(t+4)=0\\(t+4)(t-1)=0\\t+4=0$ or $t-1=0\\t=-4$ or t=1[/tex]
Therefore, the ball hits the ground after 1 seconds.
(c)To determine the maximum height, we take the derivative of the function and solve it for its critical point.
[tex]If$ h = -4.9t^2- 14.7t + 19.6\\h'(t)=-9.8t-14.7\\$Setting the derivative equal to zero$\\-9.8t-14.7=0\\-9.8t=14.7\\t=-1.5\\$Therefore, the maximum height, h(t) is:\\h(1.5) = -4.9(-1.5)^2- 14.7(-1.5) + 19.6\\=30.625$ meters[/tex]
Which data set is least Likely to resemble a normal distribution?
Look at picture
Answer: B) The heights of girls who live on a certain street in the city of Buffalo
Every answer choice starts with "the heights of all 14-year-old girls who", so we can ignore that part. Choice A describes the largest population while choice B describes the smallest population. In other words, choice A is very general and broad, while choice B is very specific and narrow. The more specific you get and the smaller the population is, the less likely its going to be normally distributed.
two dice are thrown together find the probability of getting
a.) two 5s
b.) a total of 8
c.) two perfect square
d.) two even numbers
nine business associates share $736800 from the sale of their company calculate to the nearest count how much they each receive
Step-by-step explanation:
1 business = 736800 ÷ 9 = 81866.66
Each business associates 81866.66
Please help! Correct answer only, please! I need to finish this assignment this week. Find the product AB, if possible. Explain if it is not possible. A. B. C. D.
Answer:
C
Step-by-step explanation:
The matrices are conformable for multiplication.
Multiply and sum the product of corresponding elements in row 1 of matrix A with elements in column of matrix B.
AB = [tex]\left[\begin{array}{ccc}5(2)+2(3)\\3(2)-1(3)\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}10+6\\6-3\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}16\\3\\\end{array}\right][/tex] → C
Please give me the answer
Answer:
the median increases by 0
Step-by-step explanation:
simplify √x^2+6x+9 if x≥3
Answer:
simplified expression for √x^2+6x+9 if x≥3
is x+3
Step-by-step explanation:
[tex]\sqrt{x^2+6x+9} \\=>\sqrt{x^2+3x+3x+9} \\=>\sqrt{x(x+3)+3(x+3)} \\=>\sqrt{(x+3)(x+3)} \\=>\sqrt{(x+3)^2}\\=>(x+3) \ or -(x+3)[/tex]
but given that x≥3
then we have to negate solution -(x+3)\
Then simplified expression for √x^2+6x+9 if x≥3
is x+3
An arithmetic sequence has this recursive formula. a1=9 and 1-3 .
The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.
Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example, 1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term) and common differene d = 2- 1 = 1.
Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.
Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Learn more about arithmetic progression here:
https://brainly.com/question/20334860
#SPJ5
If 3/x=5/y, what is the value of y/x?
Answer:
5/3
Step-by-step explanation:
multiply the whole thing by y to get 3y/x=5 and then divide by 3 to get y/x=5/3
Answer:
y/x=5/3
Step-by-step explanation:
3/x=5/y ⇒ y/x=5/3 replacing y with 3
Haley used unit cubes to build a rectangular prism that is 5 units long, 3 units wide, and 4 units tall. Jeremiah used unit cubes to build a rectangular prism that has twice the volume of Haley's prism. Jeremiah's prism is 4 units long and 3 units wide. How tall is Jeremiah's prism?
Answer:
10 units
Step-by-step explanation:
Let us find the volume of Haley's prism and compare it with the volume of Jeremiah's.
The volume of Haley's prism is:
V = 5 * 3 * 4 = 60 cubic units
Jeremiah's prism has twice the volume of Haley's:
V(J) = 2 * 60 = 120 cubic units
This implies that:
120 = 4 * 3 * h
where h = height of prism
=> 120 = 12h
=> h = 120 / 12 = 10 units
Jeremiah's prism is 10 units tall.
With this diagram, what could be the values of c and d?
Math item stem image
CLEAR CHECK
c=4.2,d=−12
c=−5,d=−84
c=−15,d=11
c=7,d=−54
The values of c and d are c = 4.2, d=−12, c = −5, d=−8/4 and c = −1/5, d=11
How to determine the values of c and d?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
d = integers
c = rational numbers
Integers are numbers without decimal and rational numbers can be expressed as fractions
Using the above as a guide, we have the following possible values
c = 4.2, d=−12, c = −5, d=−8/4 and c = −1/5, d=11
Read more about numbers at
https://brainly.com/question/10853762
#SPJ1
Determine the constant of variation for the direct variation given.
2
1
1/2
Answer:
1/2
Step-by-step explanation:
The constant of variation is the same as the slope. From the graph, the slope is 1/2.
Answer:
I believe the answer is 2
I will give you 10B points plus mark someone again for the Brainliest if you get this right.
Answer:
C
Step-by-step explanation:
Option c gives the actual representation of the question
For cones with radius 6 units, the equation =12ℎ V = 12 π h =12ℎ V = 12 π h relates the height ℎ h ℎ h of the cone, in units, and the volume V V of the cone, in cubic units.
Answer:
Step-by-step explanation:
The question is not properly structured. Here is the complete question.
For cones with radius 6 units, the equation V=12\pi h relates the height h of the cone, in units, and the volume V of the cone, in cubic units. Sketch a graph of this equation on the axes.
The formula for calculating the volume of a cone is expressed as shown;
[tex]V = \frac{1}{3} \pi r^{2} h[/tex] where r is the radius and h is the height.
Given radius r = 6units, on substituting;
[tex]V = \frac{1}{3}*\pi *6^{2}*h\\ V = \frac{36\pi h}{3}\\V = 12\pi h... (1)[/tex]
It can be seen from the derived volume of the cone that it is linear in nature. The volume of the cone has a linear relationship with its height. As the volume increases, the height also increases and vice versa.
Generally for a direct variation
[tex]if\ y\ \alpha x \ \\y = kx[/tex]
where k is the constant of proportionality. comparing to equation 1, k = 12π.
Find the graph attached
URGENT I NEED HELPPP
Answer:
Step-by-step explanation:
The only valid expression from the given list is the one that uses the arctangent ([tex]tan^{-1}(0.75)[/tex] ) function.
Recall that the tangent of an acute angle in a right angle triangle is defined as:
[tex]tan(B)=\frac{opposite}{adjacent}[/tex]
therefore in our case we have:
[tex]tan(B)=\frac{opposite}{adjacent} \\tan(B) = \frac{12}{16} \\tan(B)=0.75\\B=arctan(0.75)[/tex]
Given the equation,D=m/v if D=6/7 and =m+3 then m=. A.18 B.-18 C.15
Answer:
m = 3.86
Step-by-step explanation:
D = 6 / 7
D = m + 3
6 / 7 = m + 3
6 / 7 + 3 = m
m = 3.86
On a coordinate plane, a curved line with minimum values of (negative 0.5, negative 7) and (2.5, negative 1), and a maximum value of (1.5, 1), crosses the x-axis at (negative 1, 0), (1, 0), and (3, 0), and crosses the y-axis at (0, negative 6). Which interval for the graphed function contains the local maximum?
Answer:
D Over the interval [4, 7], the local minimum is -7.
Step-by-step explanation:
What is the midpoint of the line segment with endpoints (-5.5,-6.1) and (-0.5,9.1)
Answer:
(-3, 1.5)
Step-by-step explanation:
Take the averages of the x-coordinates and y-coordinates of the 2 points
-5.5 + -0.5 = -6. Divide by 2 to get the average: -6/2 = -3. So, -3 will be the x coordinate of the midpoint.
-6.1 + 9.1 = 3. Divide by 2 to get the average: 3/2 = 1.5. So, 1.5 will be the y coordinate of the midpoint.
The midpoint will be (-3, 1.5)
Part 1= You are shopping for a shirt, and you want to get the best deal. You go to two stores, the first of which is JCPenney. What is the cost of the shirt at JCPenney?
Part 2=The second store you go to is Macy's. What is the cost of the shirt at Macy? *
Part 3=Which store has the better deal? *
A- Macy's
B- JCPenney
Answer:
Macy’s
Step-by-step explanation:
let’s find the cost of each shirt
JCPenny’s: 14.99 x 0.80 = $11.99
11.99 x 1.06 = $12.70
The final cost of the JCPenny shirt is $12.70
Macy’s: 17.99 x 0.65 = $11.69
11.69 x 1.07 = $12.51
The final cost of the Macy’s shirt is $12.51
$12.51 is less than $12.70
So, the Macy’s shirt is the better deal :)
HELPPP PLEASEE l
The gasoline mileage for two cars can be compared by finding the distance each car traveled and the amount of gasoline used. The table shows the distance that car M traveled using x gallons of gasoline.
The graph shows the distance, y, that car P traveled using x gallons of gasoline
Answer:
Car M:
50.4/2 = 25.2
car M uses up 1 gallon every 25.2 miles
Car P:
Just from the graph, you can see that it uses up 1 gallon every 30 miles
The two graphs vary the /miles slightly but it is around their zones of 25.2 and 30. It varies slightly because the cars may be traveling at a fast speed or slower speed thus using up more or less fuel by the time they've reached the recorded distances on the graphs.
which of these statements us true for f(x)=3•(9)^x
Answer:
C
Step-by-step explanation:
The y-intercept is at x=0, y=3.
Heres is an problem please answer
Answer:
2
Step-by-step explanation:
the - means you have to subtract to add. so subtract 3 over 4 and you get 2
Container X contained 1200g of sand.Container Y contained 7.2kg of sand.After an equal amount if sand was removed from each container,Container Y had 7 times as much sand as container X.how much sand was removed from each container?
Simplify: (2x2 − 9x + 3) + (−7x2 + 4x − 2)
Answer:
-5x^2-5x=+1
Step-by-step explanation:
Select correct answer pls^^
It takes 48 hours if 12 people built the same wall.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
3 x 12 x 129
Step-by-step explanation:
You can get your answer
Suppose f(x)=x^2 and g(x)=1/4x^2. Which statement best compares the
graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 4.
B. The graph of g(x) is the graph of f(x) shifted 1/4 units right.
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 4.
Answer:
Step-by-step explanation:
Statement A is closest to being correct. To get the graph of g(x), we compress the graph of f(x) vertically due to multiplying f(x) by (1/4).
Answer:
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
Step-by-step explanation:
a p e x