Answer:
P (blue) = 23 / 82
Step-by-step explanation:
There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls
or,
23 / 82
So, the probability of a blue ball being chosen is 23/82
(or a 28% chance [rounded])
2x + 4y = 15
6x +12y = 45
What would the solution to the system of equations be?
Answer:
They both have an infinite number of solutions.
Step-by-step explanation:
Given system of equations:
a) 2x + 4y = 15
b) 6x + 12y = 45
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Rewrite both equations into slope-intercept form:
a) 2x + 4y = 15
⇒ 2x + 4y = 15 [subtract 2x from both sides]
⇒ 2x - 2x + 4y = 15 - 2x
⇒ 4y = - 2x + 15 [divide both sides by 4]
⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
b) 6x + 12y = 45
⇒ 6x + 12y = 45 [subtract 6x from both sides]
⇒ 6x - 6x + 12y = 45 - 6x
⇒ 12y = - 6x + 45 [divide both sides by 12]
⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
New equations:
[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.
System of equations can have the following:
No Solution: the same slope (both lines will be parallel)
One Solution: different slopes and different y-intercepts
Infinitely Many Solutions: the same slope and y-intercept
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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.
Slope-Intercept Form ⇒ [tex]y = mx + b[/tex]m = slopeb = y-interceptEquation #1
Subtract 2x from both sides
[tex]2x + 4y = 15[/tex][tex]2x - 2x + 4y = 15 - 2x[/tex][tex]4y = -2x + 15[/tex]Divide both sides by 4
[tex]\frac{4y}{4} = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = -0.5x + 3.75[/tex]Equation #2
Subtract 6x from both sides
[tex]6x + 12y = 45[/tex][tex]6x - 6x + 12y = 45 - 6x[/tex][tex]12y = -6x + 45[/tex]Divide both sides by 12
[tex]\frac{12y}{12} = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = -0.5x + 3.75[/tex]Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other. Therefore, there are infinite solutions as they will always continue on top of each other.
Points ABC forms a right triangle.
A: (-2,4) B: (5,0) C: (2,6)
The sum of the squares of the lengths of the legs of the triangle is?
The square of the length of the hypotenuse of the triangle is?
The sum of squares of the lengths of the triangle is 130 and the square of the length of the hypotenuse is 65
What is a right-angled triangle?This is a triangle with 3 sides and one side is called the hypotenuse which faces one of the angles 90°
Analysis:
distance between two points = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
distance AB with coordinates A(-2,4) B(5,0) = [tex]\sqrt{(5 - -2)^{2} + (0 - 4)^{2} }[/tex] = [tex]\sqrt{65}[/tex]
distance AC with coordinates A ( -2,4) C(2,6) = [tex]\sqrt{(2--2)^{2} + (6-4)^{2} }[/tex] = [tex]\sqrt{20}[/tex]
distance BC with coordinates B(5,0) C(2,6) = [tex]\sqrt{(2-5)^{2} + (6-0)^{2} }[/tex] = [tex]\sqrt{45}[/tex]
sum of squares of the lengths = [tex](\sqrt{45} )^{2}[/tex] + [tex](\sqrt{65}) ^{2}[/tex] + [tex](\sqrt{20}) ^{2}[/tex] = 65 + 45 + 20 = 130
the square of the length of the hypotenuse = 65
In conclusion, the sum of the squares of the three length is 130 and the square of the hypotenuse is 65
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Select the correct answer.
Over which interval of the domain is function h decreasing?
25?
Answer:
the function is only increasing.
Step-by-step explanation:
Which one is the right conversion?
Answer:
1, 4, 5, 6
Step-by-step explanation:
to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).
you can also double check by plugging both into a calculator and see if they equal the same number.
HELP ASAP!!!!! The graph compares temperatures and numbers of cyclists. The equation of the trend line for the scatterplot is y = 4x + 10. Predict the number of cyclists when the temperature is 12°C.
So
Put x ax 12°CHence
y=4(12)+10y=48+10y=58Option A
Answer:
Option A
Step-by-step explanation:
y=4x+10
So
Put x ax 12°C
Hence
y=4(12)+10
y=48+10
y=58
Solve for x to the nearest tenth of centimetre
Answer:
Step-by-step explanation:
Can someone pls help quickly?
From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.
What is a ratio?A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.
What is the explanation for the solution above?Step 1 - Indicate your assumptionsLet X be the width of one of the rectangles and let its height be Y.
It is clear from the image that:
4X = 3Y
Hence
(4/3)X = Y
Therefore,
Lenght (L) = 3Y
= 3 (4/3)X
= 4X
Width (W) = Y + 2X
= (4/3)X + 2X
= (10/3)X
Therefore,
L : W = 4X: 10/3X
= 4:10/3
To remove the fraction, multiply both sides of the ratio by 3
= 12 : 10, furhter simplify by halving each value, and we have
= 6:5
Hence, the ratio L: W in simplified form is 6 : 5.
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41 is a prime number found in the middle of a list of 7 consecutive numbers. find the 7 consecutive numbers
Answer: 29, 31, 37, 41, 43, 47, 53.
Step-by-step explanation:
Solve for x: -24 = 6x
1/4
-4
4
- 1/4
Answer:
-4
Step-by-step explanation:
[tex]~~~~~-24 = 6x\\\\\\\implies -\dfrac{24} 6 = \dfrac{6x}6\\\\\\\implies x = -4[/tex]
8 3/8 + 3 3/8 + 2 3/8 + 3/8
what is the answer of this ?
The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have an expression:
[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]
After simplification:
[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]
[tex]= \dfrac{67+27+19+3}{8}[/tex]
= 116/8
= 29/2
[tex]= 14\dfrac{1}{2}[/tex]
Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
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Answer:
i dont understand your question
Step-by-step explanation:
a camp charges $40 per student for a full-day camp and the camp only runs if 5 students enroll but the enrollment limit is 16 students. the amount of revenue that the camp collects is a function of the number of students that enrolled defined by this equation: [tex]R(n)=40n[/tex]
please describe the set of all possible outputs of this function
please describe the set of all possible inputs of this function
The set of input of the function are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }
The set of output of the function is a multiple of 40 from 200 to 640
How to find the output and input of a function?The input of the function can be found as follows:
The camp can only run if we have at least 5 students.
The limits of student is 16.
Therefore, the input are {5, 6, 7, 8, 9,10, 11, 12,13, 14, 15, 16 }
The output are the dependent variables or the range. They are gotten when we input the values of the input in the function.
Therefore,
R(n) = 40n
R(5) = 40(5) = 200
R(16) = 40(16) = 640
The output are multiple of 40 from 200 to 640
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Question 6(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -5x² + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
O The value of f(1) cannot be compared to the value of f(2).
O The value of f(2) is larger than the value of f(1).
O The value of f(2) is smaller than the value of f(1).
O The value of f(1) is the same as the value of f(2). help
Answer:
O The value of f(2) is smaller than the value of f(1).
Step-by-step explanation:
First, let's solve for both. When the problem says f(1) or f(2), this just means that the x value is equal to that. So:
f(1) = -5(1)^2 + 2(1) + 9 = 6
f(2) = -5(2)^2 + 2(2) + 9 = -7
Since f(1) = 6 and f(2) = -7, we know that f(1) is greater than f(2). Therefore, the value of f(2) is smaller than the value of f(1)
Which of the following points is not coplanar with points C, D and E?
The point R is the point which is not coplanar with points C, D and E.
We need to find the point which is not coplanar with points C, D and E.
What are coplanar points?The points that lie on the same plane are called coplanar points.
In the given figure there are five planes which are as follows:
BCUD, BRAE, BRAC, BTDE, ACUDE
Now, points C,D and E lie in plane ACUDE.
In the plane ACUDE points A, C, U, D, E and S lies.
From the options point, R is not lining in the same plane as C, D and E lies.
Therefore, the point R is the point which is not coplanar with points C, D and E.
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If one student is chosen at random, Find the probability that the student was NOT a female that got a "C"
--------- A // B // C // Total
Male: 10 // 8 // 15 // 33
Female: 7 // 9 // 17 // 33
Total: 17 // 17 // 32 //66
The probability that the student was NOT a female that got a "C" is 15 / 32.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C = 15 / 32.
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Simplify the quotient 3-¹ ÷34
Answer:
[tex]\frac{1}{102}[/tex]
Step-by-step explanation:
1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].
[tex]\frac{1}{3}\div 34[/tex]
2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].
[tex]\frac{1}{3}\times \frac{1}{34}[/tex]
3) Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].
[tex]\frac{1\times 1}{3\times 34}[/tex]
4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].
[tex]\frac{1}{3\times 34}[/tex]
5) Simplify [tex]3\times 34[/tex] to [tex]102[/tex] .
[tex]\frac{1}{102}[/tex]
the diagram shows a right angled triangle. 9cm 15cm x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
Answer:
31°
Step-by-step explanation:
As the opposing side and adjacent side of the angle x are given, we need to take the tan ratio of the angle.
=============================================================
Solving :
⇒ tan x° = 9/15
⇒ tan x° = 3/5
⇒ x = tan⁻¹ (0.6)
⇒ x = 31°
The size of the unknown angle "x"
Solution:We'll have to check which is the appropriate one from SOHCAHTOA.
In this question we'll have to use tan because opposite and adjacent is given.
[tex]\large\boxed{Formula: tan(A)= \frac{opp}{adj}}[/tex]
Substitute according to the formula.
[tex]tan \: x= \frac{9}{15}[/tex]
We'll have to use tan inverse.
[tex]x={tan}^{-1}(\frac{9}{15})[/tex]
[tex]x=30.96375653[/tex]
[tex]\large\boxed{x=31° }[/tex]
Hence, the size of the unknown angle "x" is 31°
If the probability that a person over 40-year-old is diabetic, is 0.55
and the probability that a person has hypertension is 0.62. If a person
is selected randomly, find the probability that he is diabetic and and has hypertension
Answer:
0.341
Step-by-step explanation:
Multiply the probabilities: 0.55 * 0.62 = 0.341
You roll a number cube. What is the probability it will land on a number greater than 5?
Mike leaves the house traveling 2 miles per hour. Kim leaves 6 hours later to catch up traveling 8 miles per hour. It will take Kim Blank 1 hours to catch Mike.
any answers ?
Answer:
2 hours
Step-by-step explanation:
Mike has a six hour head start so he is 6 x 2 = 12 miles ahead
their 'closing speed' is 8-2 = 6 m/hr
it will take Kim 12 / 6 = two hours to catch Mike
Solve the following inequality algebraically:
-2 less-than x/3 + 1 less than 5
a.
Negative 9 greater-than x greater-than 12
b.
Negative 9 less-than x less-than 12
c.
Negative 2 less-than x less-than 5
d.
Negative 2 greater-than x greater-than 5
Answer:
d
Step-by-step explanation:
In a P.7 class, 20% of the boys were absent for the Mock Examinations, of the remainder of the boys were present Find the fraction of the girls in the class.
What is 5 over 8 expressed as a percent?
Answer: 62.5%
Step-by-step explanation:
5/8 = 0.625
0.625 x 100 = 62.5
Chandler wants to buy a bike
that costs $345. He has a job that
pays an hourly wage of $6. He
needs to pay back $35 that he
borrowed from his mom. How
many hours does Chandler need to
work to have enough money to
purchase the bike?
Convert the degree measure to radian measure. Round to three decimal places.
75°
radians
The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.
What is conversion?Conversion means to convert the same thing into different units.
Convert the degree measure to the radian measure.
⇒ 75°
We know the conversion is given as
180° = π radian
1° = π/180°
Then we have
75° = 75° x π/180° radian
75° = 1.30899 radian
75° ≅ 1.31 radian
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Find the circumference of a circle that has a diameter of 2 ft. Use 3.14 for pi.
5.14 ft
6.28 ft
12.56 ft
7.14 ft
Answer:
6.28 ft
Step-by-step explanation:
using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer
Please help I am so confused
The phone company Ringular has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 480 minutes, the monthly cost will be $277. If the customer uses 990 minutes, the monthly cost will be $532.
A) Find an equation in the form
y=mx+b, where x is the number of monthly minutes used and
y is the total monthly cost of the Ringular plan.
Answer:
y=
B) Use your equation to find the total monthly cost if 881 minutes are used.
Answer: If 881 minutes are used, the total cost will be
The total cost when 881 minutes is used is $477.50.
What are the equation that model the question?a + 480b = 277 equation 1
a + 990b = 532 equation 2
Where:
a = flat fee b = variable fee What is the flat fee and the variable fee?Subtract equation 1 from equation 2
510b = 255
b = 255 / 510
b = $0.50
In order to determine the flat fee, substitute for b in equation 1
a + 480(0.5) = 277
a + 240 = 277
a = 277 - 240
a = $37
What is the total cost when 881 minutes is used?
Total cost = flat fee + (variable cost x number of minutes spoken)
$37 + (881 x 0.5) = $477.50
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If f(x) = 3x +3, which of the following is the inverse of f(x)?
O
A. f-1(x) = 3(x-3)
5
OB. f-1(x) = 3(x+3)
5
O C. f-1(x) = 5(x+3)
3
O D. f-1(x) = 5(x-3)
3
The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
How to determine the inverse?The equation is given as:
f(x) = 3x + 3
Express f(x) as y
y = 3x + 3
Swap the positions of y and x
x = 3y + 3
Make y the subject
3y = x - 3
Divide by 3
y = 1/3x - 1
Replace y with the inverse function
f-1(x) = 1/3x - 1
Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
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What is the volume, in cubic meters, if the prism below?
=================================================================
Explanation:
Imagine rotating the figure so that the triangular face is flat on the ground. This makes the triangular faces to be the floor and ceiling of this room.
The floor is a triangle with base 24 meters and height 7 meters. The floor area is base*height/2 = 24*7/2 = 84 square meters.
Multiply this floor area with the height of the room (22 m) to get the volume of the room.
volume = (floor area)*(height) = 84*22 = 1848 cubic meters
9x10^2 which sentence matches the question assigned
The computation of the index shows that the value of 9 × 10² will be 900.
How to calculate the indices?From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:
= 9 × 10²
Note that 10² simply means that you've to multiply 10 twice. This will be:
= 10 × 10 = 100
Therefore, 9 × 10² will be:
= 9 × 100
= 900
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can someone help me find the missing ones
Answer:
The answer is in Step.
Step-by-step explanation:
Domain: (- inf, + inf)
Range: (- inf, 3]
Increasing: (- inf , 0)
Decreasing: (0 , + inf)
Positive: (- 1 , 1 )
Negative: (- inf , -1) , (1 , + inf)
Maximum: (0,3) or just 3.
Minimum: None.
x-int: -1, 1
y-int: 3