To get a probability of 3/5, 16 red marbles must be added.
How many additional red marbles must be added?
There are 8 red, 9 yellow, and 7 green marbles, for a total of:
8 + 9 + 7 = 24.
The probability of getting a particular color of marble is given by the quotient between the number of marbles of that color and the total number of marbles.
Here, we want to get a probability of drawing a red marble equal to 3/5.
So, if we add x red marbles, the probability of getting a red marble will be:
P = (8 + x)/(24 + x)
And that must be equal ot 1/5, then we write:
(3/5) = (8 + x)/(24 + x)
If we multiply both sides bt (24 + x), we will get:
3*(24 + x)/5 = 8 + x
Now we can solve that for x.
3*24/5 - 8 = x - x(3/5) = (2/5)*x
x = (3*24/5)*(5/2) - (5/2)*8 = 16
So 16 red marbles must be added, the correct option is b.
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Find the area of each parallelogram below. 4 cm 5 cm 6 cm
Answer:
24 cm²
when finding area, multiply base by height
[tex]4 * 6 = 24[/tex]
Answer:
A = 24 cm^2
Step-by-step explanation:
The formula for the area of a parallelogram is
A = bh where b is the base and h is the height
A = 6 * 4
A = 24 cm^2
Which is equal to ???
Answer:
[tex]csc54[/tex]°
Step-by-step explanation:
[tex]sec36[/tex]° = [tex]\frac{1}{cos36}[/tex]
and; [tex]\frac{1}{cos36} = \frac{1}{sin 90 -54}[/tex] ... (co-functions)
and [tex]\frac{1}{sin90-54} = csc54[/tex] .... (csc in the reciprocal of sin)
15. What is 3% of 4.14 x 10?
A. 1.242
B. 1.380
C.
12,420
D. 13.800
E. 124.200
Answer:
the answer is a and I hope this helps you.
Hey there!
3% of 4.14 * 10
≈ 3% * 4.14 * 10
≈ 3/100 * 4.14 * 10
≈ 0.03 * 4.14 * 10
≈ 0.1242 * 10
≈ 1.242
Therefore, the answer should be:
Option A. 1.242
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What are the next two terms of the following sequence? -2, 4, -8, 16, ...
Answer:
-32 , 64
Step-by-step explanation:
Geometric sequenceThis is a geometric sequaence and each term is obtatained by multiplying the previous number with the common ratio 'r'
[tex]\sf \boxed{r = \dfrac{second \ term }{first \ term}}[/tex]
[tex]\sf r =\dfrac{4}{(-2)}[/tex]
r = -2
The next two terms ,
Fifth term = 16 *(-2) = -32
Sixth term = (-32) * (-2) = 64
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What are the next two terms of the following sequence?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
The next two terms are -32 and 64.
[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]
First of all, let's identify what kind of sequence this is.
The two main types of sequences are:
[tex]\textsf{Arithmetic.}[/tex] This is where we add/subtract the same number to get to the following term.[tex]\textsf{Geometric.}[/tex] This is where we multiply/divide by the same number to get to the next term.In the given sequence, we use multiplication, so we're dealing with a [tex]\textit{geometric sequence}[/tex].
In order to get to the next term, we multiply by -2.
So in order to find the next two terms of the sequence, we take the previous term and multiply it by -2 as follows:
16•(-2)=-32
We've found the 5th term of the geometic sequence.
Now let's find the 6th:
-32•(-2)=64 (the product of a negative and a negative results in a positive)
Summary of Final Answer:-The next two terms in the sequence are -32 and 64.
Good luck.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
X+4/x^2+3x-10 - x-1/x^2+2x-8 Simplify
An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of expression [(x+4)/(x²+3x-10)] - [(x-1)/(x²+2x-8)] is (4x+21)/(x³+7x²+1x-40).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of expression [(x+4)/(x²+3x-10)] - [(x-1)/(x²+2x-8)] can be done in the following manner,
[tex]\dfrac{x+4}{x^2+3x-10} - \dfrac{x-1}{x^2+2x-8}\\\\\\= \dfrac{x+4}{(x-2)(x+5)} - \dfrac{x-1}{(x+4)(x-2)}\\\\\\= \dfrac{(x+4)(x+4)- (x-1)(x+5)}{(x+4)(x-2)(x+5)} \\\\\\= \dfrac{x^2+16+8x-x^2-5x+x+5}{x^3+7x^2+2x-40}\\\\\\=\dfrac{4x+21}{x^3+7x^2+2x-40}[/tex]
Hence, the simplification of expression [(x+4)/(x²+3x-10)] - [(x-1)/(x²+2x-8)] is (4x+21)/(x³+7x²+1x-40).
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Heidi likes to mix her own horse feed. She creates a mix that is 10%
molasses-covered oats using 18% molasses-covered oats. How many pounds
of each does she need to create 50 pounds of the mixture
The first step is to Prepare. Heidi wants to make a 30 pounds of molasses solution. She mixes and solution together. How much mixture does she make?
evaluate the following
a) 4!=
b) 0!=
c) 2! + 3!=
d) 3! x 4!
e) 10! / 7!
Answer:
See below for answers and explanations
Step-by-step explanation:
4! = 4*3*2*1 = 24
0! = 1
2! + 3! = 2*1 + 3*2*1 = 2 + 6 = 8
3! * 4! = 3*2*1 * 4*3*2*1 = 6 * 24 = 144
10! / 7! = 10*9*8*7*6*5*4*3*2*1 / 7*6*5*4*3*2*1 = 10*9*8 / 1 = 720
the ratio 20:40:100 in its simplest form.
Answer:
1 : 2 : 5
Step-by-step explanation:
20 : 40 : 100 ( divide each part of the ratio by 20 , the HCF of 20, 40, 100 )
= 1 : 2 : 5
From -6 f to 2 f is that increasing or decreasing?
Answer:
Increasing, because it's going from a negative number to a positive number
Step-by-step explanation:
how many miles per gallon did mr.crosby's car get if he drove 200 miles on 15 gallons of gas
Answer:
13.33 miles
Step-by-step explanation:
let the miles per gallon = X
from the question,
200miles--------------15gallons
X miles-------------------1 gallon
cross multiplying
X×15 = 200×1
dividing bothsides by 15
X= 200/15
X= 13.33 miles.
The final scores from the last five games of two basketball teams are given. Jumping Jackrabbits: 70, 65, 72, 80, 73 Leaping Lizards: 61, 47, 70, 63, 54 Determine the MAD of each data set. In your work, show the mean and the absolute deviation of each data value in each set. Compare and interpret the MADs in context of the situation.
PLS PLS HELP ME
The mean absolute deviation for the Jumping Jackrabbits was of 3.8, which was lower than the 6.8 for the Leaping Lizards, hence they had more consistent scores.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.For the Jumping Jackrabbits and the Leaping Lizards, the mean and the MAD are given as follows:
M = (70 + 65 + 72 + 80 + 73)/5 = 72
MAD = (|70 - 72| + |65 - 72| + |72 - 72| + |80 - 72| + |73 - 72|)/5 = 3.6.
M = (61 + 47 + 70 + 63 + 54)/5 = 59
MAD = (|61 - 59| + |47 - 59| + |70 - 59| + |63 - 59| + |54 - 59|)/5 = 6.8.
The mean absolute deviation for the Jumping Jackrabbits was of 3.8, which was lower than the 6.8 for the Leaping Lizards, hence they had more consistent scores.
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If a bus driver leaves her first stop by 7:00 a.m., her route will take less than 37 minutes. If she leaves after 7:00 a.m., she estimates that the same route will take no less than 42 minutes. Which inequality represents the time it takes to drive the route, r?
r < 37 or r ≥ 42
r < 37 or r > 42
37 < r ≥ 42
37 > r ≥ 42
Answer:
i believe the third one so this 37 < r ≥ 42 Step-by-step explanation:
Answer:
(a) r < 37 or r ≥ 42
Step-by-step explanation:
Translating the given relations to math symbols, we have ...
"less than 37 minutes" ⇒ r < 37
"no less than 42 minutes" ⇒ r ≥ 42
__
Written as a single statement, this is ...
r < 37 or r ≥ 42
_____
Additional comment
The solution regions are disjoint, so an "or" statement must be used. The form ...
37 > r ≥ 42
cannot be used, because it is false that 37 > 42.
Find the value of x
Answer:
x = 45
Step-by-step explanation:
Solve the entire figure first
First right triangle:
A = 36
B = 48
C = _
Using Pythagoras theorem to find the hypotenuse
a² + b² = c²
Plug in:
36² + 48² = 84²
1,296 + 2,304 = 3,600
Find the square root of √3600
⇒ √3600 = √( 2 × 2) × (2 × 2) × (3 × 3) × (5 × 5)
⇒ = 2 × 2 × 3 × 5
⇒ 60
The hypotenuse of the bottom right triangle is 60.
Now that we have the given value of the missing line separating both right triangles.
A = 60
C (hypotenuse) = 75
To find the missing side,
use this formula:
c² - a² = b² ---> hypotenuse minus the given side value
Plug in:
75² - 60² = 2,025
Find the square root:
⇒ √2025 = √ ( 3 × 3 ) × ( 3 × 3 ) × ( 5 × 5 )
⇒ 3 × 3 × 5
⇒ 45
Therefore, the missing x value on the second right triangle is 45.
What is the slope of the line that
passes through these two points?
(-3, 1)
(3, 3)
slope
=
Remember. given two points.
(x1.yı)
(x2 - y2)
Slope
rise (y2-y1)
run(x2-x1)
Simplify your answer completely.
Answer:
1/3
Step-by-step explanation:
slope = (y2 - y1)/(x2 - x1)
= (3 -1)/ (3 - (-3))
= 2/ 6
= 1/3
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}}[/tex]
What is the slope of the line that
passes through these two points? (-3, 1) ,(3, 3)?
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Use the slope formula:-
[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\bigstar[/tex] Replace the letters with numbers:-
[tex]\sf{\dfrac{3-1}{3-(-3)}}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\sf{\dfrac{2}{3+3}}[/tex]
[tex]\bigstar[/tex] On further simplification,
[tex]\sf{\dfrac{2}{6}}[/tex]
[tex]\bigstar[/tex] Which results in
[tex]\boxed{\mathrm{Slope=\frac{1}{3}}}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
helppppppppppppppppp
Answer:
42 cm²
Explanation:
cut into 2 rectangles
area of rectangle: Length * Width
4 * (3+3+3) + 3 * 24 * 9 + 636 + 642 cm²the total surface of a pyramid with dimension of 5×10 h=6
Answer:
[tex]154.05[/tex]
Goodluck
SOMEONE PLEASE HELPPPP
I need help on 3 and 4
Answer:
Step-by-step explanation:
Parallel lines and transversal:Linear pair: When the uncommon arms of two adjacent angles form a straight line, the adjacent angles are called linear pair and they add upto 180
3) ∠3 + ∠2 = 180
65 + ∠2 = 180
∠2 = 180 - 65
∠2 = 115°When parallel lines are intersected by transversal, alternate exterior angles are congruent.
a // b and d is transversal.
∠5 = ∠11
∠5 = 100°
When parallel lines are intersected by transversal, the alternate interior angles are congruent.
a // b and c is transversal
m∠13 = ∠3
∠13 = 65°
4) ∠3 & ∠14 are co-interior angles. Co-interior angles are supplementary.
∠3 + ∠14 = 180
65 + ∠14 = 180
∠14 = 180 - 65
∠14 = 115°
∠5 + ∠8 = 180 {Linear pair}
100 + ∠8 = 180
∠8 = 180 - 100
∠8= 80
∠9 = ∠11 {vertically opposite angles are congruent}
∠9 = 100
∠ 3 + ∠14 + ∠ 8 + ∠9 = 65 + 115 + 80 + 100
= 360°
The graph show the probability distribution of a random variable.
What is the value of P(0 ≤X ≤4)?
0.40
O 0.45
O 0.50
O 0.55
Answer:
O 0.50
Step-by-step explanation:
when x = 0, the probability is 0
when x = 1, the probability is 0.1
when x = 2, the probability is 0.2
when x = 3, the probability is 0.125
when x = 4, the probability is 0.05
ANSWER ASAP, find the area. Use 3.14 if needed. Round to nearest hundredth
does someone mind helping me with this problem? Thank you!
Answer:
a = 12
Step-by-step explanation:
Pythagoras’ Theorem
a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
From inspection of the triangle:
leg a = aleg b = 9hypotenuse c = 15Substituting these values into the formula and solving for b:
⇒ a² + 9² = 15²
⇒ a² + 81 = 225
Subtract 81 from both sides:
⇒ a² + 81 - 81 = 225 - 81
⇒ a² = 144
Square root both sides:
⇒ √(a²) = √(144)
⇒ a = 12
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's calculate the value of a using Pythagoras theorem ~
[tex]\qquad \sf \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: a {}^{2} = {15}^{2} - {9}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: a= \sqrt{225-81} [/tex]
[tex]\qquad \sf \dashrightarrow \: a= \sqrt{144} [/tex]
[tex]\qquad \sf \dashrightarrow \: a= 12\: units[/tex]
Need some help here IMMEDIATELY!! :(
Use the given scale factor and the side lengths of the scale drawing to
determine the side lengths of the real object.
Answer: C option
Step-by-step explanation:
Since the drawing is 5x more than real object then we have to divide the numbers
a= 35/5 = 7
b= 30/5 = 6
c= 15/3 = 3
The number of nails of a given length is normally distributed with a mean a length of 5 in. and a
standard deviation of 0.03 in. In a bag containing 120 nails, how many nails are between 4.97
in. long and 5.03 in. long?
ut 57 nails
out 60 nails
out 82 nail
Answer:
82 nails
Step-by-step explanation:
4.97 and 5.03 are both one standard deviation from the mean...
z scores . 8413 and .1587
.8413 - .1587 = .6826 or 68.26 % of the nails are in this range
68.26 % * 120 = ~82 nails
Divide. Give the quotient and remainder.
437/7
Find the mean, variance, and standard deviation for the data set.
6, 16,7 ,3 ,10 ,8 ,12 ,5 ,18 ,5
Need help 10 points
Answer:
50.24
Step-by-step explanation:
8 is the radius of the circle, so using A=πr^2, the equation would be A=(3.14*8^2)/4
(Dividing by 4 because we are solving for 1/4 of a circle, and substituting pi for 3.14)
(3.14*8^2)=200.96
200.96/4=50.24
The amount of a sample remaining after t days is given by the equation p(1) - al2where a is the initial amount of
the sample and h is the half-life, in days, of the substance. a sample contains 60% of its original amount of fermium-
257. the half-life of fermium-257 is about 100 days. about how old is the sample?
52 days
60 days
74 days
136 days
The amount of a sample remaining after t days is given by the equation p(1) - al2 is: 74 days.
Sample remaining after t daysUsing this formula
P(t)=A×(1/2)^t/h
Let plug in the formula
0.6x=x ×(1/2)^t/h
0.6=(1/2)^t/100
Hence:
Log0.6=Log(1/2)^t/100
Log 0.6=t/100× log0.5
Log 0.6/Log0.5×100=t
-0.2218487/-0.30102999×100=t
0.736×100=t
t=73.6
t=74 days (Approximately)
The amount of a sample remaining after t days is: 74 days.
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Answer:
74 DAYS
Step-by-step explanation:
I DID IT ON EDGE
Graph the equation y=-1/8x^2+x-4
The box plot below represents some data set. What is the interquartile range (IQR) of
the data?
Answer:
155-50=105
Step-by-step explanation:
hopefully its right because you have to take the maximum and subtracted from the minimum
Yuki collects data on the average number of sunlight hours per month. She determines the regression model
y = -2.8sin(0.65x + 120.2) + 12.2 to represent the data, where x = 1 represents January.
Based on the regression model, what is the best estimate for the average number of sunlight hours she can expect
each day in June?
O9.4
9.9
O 11
O 15
The best estimate for the average number of sunlight hours she can expect each day in June is 9.9 hours
To answer the question, we need to know what a regression model is
What is a regression model?A regression model is an equation or model that shows if there is a relationship between two variables.
Now, given that Yuki uses the regression model y = -2.8sin(0.65x + 120.2) + 12.2 to calculate the average number of sunlight hours per month, where x = 1 represents January.
Since we need to determine the average number of sunlight hours she can expect each day in June. Since June is the sixth month, we substitute x = 6 into the equation.
Average number of sunlight hours in JuneSo, y = -2.8sin(0.65x + 120.2) + 12.2
y = -2.8sin(0.65(6) + 120.2) + 12.2
y = -2.8sin(3.9 + 120.2) + 12.2
y = -2.8sin(124.1) + 12.2
y = -2.8(0.8281) + 12.2
y = -2.32 + 12.2
y = 9.88
y ≅ 9.9
So, the best estimate for the average number of sunlight hours she can expect each day in June is 9.9 hours
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Two forces of 494 newtons and 590 newtons act on a point. The resultant force is 1079 newtons. Find the angle between the two forces.
Answer:
Use Law of Cosines
Step-by-step explanation:
1079²= 590² + 494²- (2)(590)(494) cos θ.