The number of times that the value of the digit 1 in the population of Cleveland in this value is 10.
How to illustrate the information?Based on the information, it should be noted 7 is in ten thousand place for Memphis. This means that it represents 70000.
It should be noted the 1 in Denver is in the same place. It represents 10000. On Cleveland, this is 1000.
Therefore, the number of times will be:
= 10000 / 1000
= 10
Therefore, the correct option is 10.
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Cleveland population 431,369 Denver population 610,345
Memphis population 676,640 What is the value of the digit 7 in the population of Memphis? What is the value of the digit 1 in the population of Denve?How many times as great the value of the digit 1 in the population of Cleveland is this value?
- 4 - (-10) Find the difference.
Reason:
-4 - (-10) = -4 + 10 = 6
The two negatives cancel to form a positive.
Here's how to visualize what's going on: Draw a number line. Plot a marker at -4. Then move 10 units to the right and you should arrive at 6. This visually indicates -4+10 = 6
Another way to visualize: Imagine you are on basement level 4 of a tall building. If you move up 10 floors, then you'll arrive at the 6th floor. We treat the ground floor as floor 0. It might help to draw a vertical number line.
15. You have a part-time job after school. You work three hours after
school on Monday, Wednesday, and Friday. On Saturday you babysit and
earn an additional fifteen dollars and are given your weekly allowance of
twenty dollars on Sunday. You made a total of $100.25 this week, how
much money are you paid per hour at your part-time job?
Answer:
$100.25 total
100.25-15-20= $65.25 total for three days
For three Dayan three hours so 3*3 = 9 hrs total
65.25/9=7.25
Hence per hour $7.25
Step-by-step explanation:
I’m so confused can anyone help me?
Answer:
Following is the answer for your question your question can be done in this manner.
fraction equivalent to 4/6 with 3 as denominator
Answer:
2/3
Step-by-step explanation:
6 divided by 3 is 2, so you have to divided 4 by 2, which is 2.
Answer:
⅔
Step-by-step explanation:
4 divide by 2 = 2
6 3
therefor 2/3 is equvelet too 4/6.
Hope this helped
One number is a lot more than another one.
Both numbers are greater than 100.
What could the two numbers be?
Write the equation of a quadratic with the vertex at (2,-3) and passing through the point (6,4)
[tex]\displaystyle\\Answer:\ y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]
Step-by-step explanation:
The vertex is also the symmetry point of the parabola. The formula for finding the x-coordinate of the parabola: x = -b/2a (2,-3)
Hence,
[tex]\displaystyle\\2=\frac{-b}{2a} \\[/tex]
Multiply both parts of the equation by -2a:
[tex]\displaystyle\\-4a=b\ \ \ \ \ (1)[/tex]
[tex]y=ax^2+bx+c\ \ \ \ \ -\ \ \ \ \ the\ quadratic\ equation\\\\Thus,[/tex]
You can make a system of equations on two points belonging to the quadratic equation:
[tex]-3=a(2)^2+b(2)+c\\4=a(6)^2+b(6)+c\\\\-3=4a+2b+c\ \ \ \ (2)\\4=36a+6b+c\ \ \ \ (3)\\\\[/tex]
Substitute (1) into equations (2) and (3):
[tex]-3=4a+2(-4a)+c\\4=36a+6(-4a)+c\\\\-3=4a-8a+c\\4=36a-24a+c\\\\-3=-4a+c\ \ \ \ (4)\\4=12a+c \ \ \ \ (5)\\\\\\[/tex]
Subtract equation (4) from equation (5):
[tex]7=16a[/tex]
Divide both parts of the equation by 16:
[tex]\displaystyle\\\frac{7}{16} =a\ \ \ \ (6)[/tex]
Substitute (6) into equations (1):
[tex]\displaystyle\\-4(\frac{7}{16} )=b\\\\-\frac{4*7}{4*4}=b\\\\-\frac{7}{4}=b[/tex]
Substitute values a and b into equation (2):
[tex]\displaystyle-3=4(\frac{7}{16})+2(-\frac{7}{4})+c\\\\ -3=\frac{7}{4} -\frac{14}{4}+c\\\\ -3=-\frac{7}{4}+c \\\\-3+\frac{7}{4}=-\frac{7}{4}+c+\frac{7}{4} \\\\ \frac{-3*4+7}{4} =c\\\\\frac{-12+7}{4}=c\\\\ -\frac{5}{4}=c[/tex]
Thus,
[tex]\displaystyle\\y=\frac{7}{16}x^2 -\frac{7}{4}x-\frac{5}{4}[/tex]
statistical power is influenced by all of the following except . a. significance error b. critical value level
Statistical power is influenced by all of the following except observed test value.
What is statistical power?
If there is a real effect present to detect, the statistical power of a hypothesis test is the likelihood of finding it. When an experiment is complete, power may be calculated and presented to make comments about how confident one could be in the conclusions taken from the study's results. It may also be employed as a tool to calculate the sample size or the number of observations needed to detect an effect in an experiment. You will learn the significance of a hypothesis test's statistical power in this lesson, and you'll learn how to compute power analyses and power curves as part of an experimental design.
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Please Perform The Operation.
Add:
1.) A - 5
+ 2a - 3
2.) 5t² - 6st + 8t - 3
+ 7t² + 8st - 2t + 9
3t² + 2st + 5t + 5
Subtract:
1.) 10m - 2n - 1
- 5m - 2n + 2
2.) -5x³ + 3x² +6x
- 3x³ + 9x² + 4x
:)
The resulting polynomials are listed below:
3 · a - 8 15 · t² + 4 · s · t + 11 · t + 11 5 · m - 3 - 8 · x³ + 12 · x² + 10 · xWhat are the resulting expression by adding and subtracting polynomials?Herein we find two cases of addition of polynomials and the two cases of subtraction of polynomials. Each operation must be done by taking algebra properties into account. Complete procedures are shown below:
Addition - Case 1
(a - 5) + (2 · a - 3) Given
(a + 2 · a) + [- 5 + (- 3)] Associative and commutative properties
3 · a - 8 Distributive property / Definitions of addition and subtraction
Addition - Case 2
(5 · t² - 6 · s · t + 8 · t - 3) + (7 · t² + 8 · s · t - 2 · t + 9) + (3 · t² + 2 · s · t + 5 · t + 5) Given
(5 · t² + 7 · t² + 3 · t²) + (- 6 · s · t + 8 · s · t + 2 · s · t) + (8 · t - 2 · t + 5 · t) + (- 3 + 9 + 5) Associative and commutative properties
15 · t² + 4 · s · t + 11 · t + 11 Distributive properties / Definitions of addition and subtraction / Result
Subtraction - Case 1
(10 · m - 2 · n - 1) - (5 · m - 2 · n + 2) Given
(10 · m - 5 · m) + (- 2 · n + 2 · n) + (- 1 - 2) Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b
5 · m - 3 Distributive property / Cancellative property / Definition of addition and subtraction / Modulative property / Result
Subtraction - Case 2
(- 5 · x³ + 3 · x² + 6 · x) - (3 · x³ + 9 · x² + 4 · x) Given
(- 5 · x³ - 3 · x³) + (3 · x² + 9 · x²) + ( 6 · x + 4 · x) Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b
- 8 · x³ + 12 · x² + 10 · x Distributive property / Definition of addition and subtraction / Result
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flip 98 fair coins and 1 hh coin and 1 tt coin. given that you see an h, what is the probability that it was the hh coin? explain in layman’s terms.
The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]
Conditional Probability P(B/A) is defined as probability of occurrence of B given that A has already occurred .
Baye's Theorem describes the probability of an event based on conditions that might be related to event .
P(A/B)={P(B/A)*P(A)}/P(B)
Total number of coins =100
Total number of HH coins = 1
P(HH) =Probability of getting HH=1/100
P(H/HH)=Probability of H knowing that HH has already occurred=1
Next to find Probability Of H
We need to find two thing
(i) Probability H appears and is a fair coin= [tex]\frac{1}{2} *\frac{98}{100} =\frac{98}{200}[/tex]
(ii)Probability H appears and is a HH coin = [tex]\frac{1}{100}[/tex]
P(H)= (i)+(ii) =100/200=1/2
BY Baye's Theorem
P(HH|H)={P(H|HH)∗P(HH)}/P(H)
[tex]=\frac{1*\frac{1}{100} }{\frac{100}{200} }[/tex]
[tex]=\frac{2}{100}[/tex]
[tex]=\frac{1}{50}[/tex]
Therefore , The probability that it was an HH coin is [tex]\frac{1}{50}[/tex]
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A t-shirt vendor sells yellow shirts and blue shirts at a ratio of 1:4 what percent of the shirts are yellow?
Answer: 25%
Step-by-step explanation:
according to a report on sleep deprivation by the centers for disease control and prevention, the proportion of california residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for oregon residents. these data are based on simple random samples of 11,545 california and 4,691 oregon residents.
[tex]Let$p_1$ - true proportion of California residents who reported insufficient rest or sleep during the preceding 30 days$p_2$ - true proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days$\hat{p}_1$ - sample proportion of California residents who reported insufficient rest or sleep during the preceding 30 days $=0.08$$\hat{q}_1=1-\hat{p}_1=1-0.08=0.92$$n_1$ - sample size of CA residents $=11,545$[/tex][tex]$\hat{p}_2$ - sample proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days $=0.088$$\hat{q}_2=1-\hat{p}_2=1-0.088=0.912$$n_2$ - sample size of OR residents $=4,691$The $95 \%$ Confidence Interval for $\left(p_1-p_2\right)$ is given by,$$[/tex][tex]\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{p_1 q_1}{n_1}+\frac{p_2 q_2}{n_2}}$$if $p_1$ and $p_2$ are unknown we use$$\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}}$$where $Z^*=Z_{\frac{\alpha}{2}}=Z_{0.0250}$[/tex][tex]Plugging in, we get$$\begin{aligned}\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}} \\(0.08-0.088) & \pm 1.96 \sqrt{\frac{0.08(0.92)}{11545}+\frac{0.088(0.912)}{4691}} \\&-0.008 \pm 0.009498026 \\&(-0.017498026,0.001498026) \\& \approx(-0.0175,0.0015)\end{aligned}$$[/tex][tex]a) For the Hypothesis Test we have,- i) State the hypotheses.$$\begin{aligned}&H_0: p_1-p_2=0 \\&H_1: p_1-p_2 \neq 0\end{aligned}$$[/tex]
What is hypothesis?A hypothesis test examines a suggested mathematical model to see if a sample of data contains enough evidence to disprove the null hypothesis.
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Mary will rent a car for the weekend she can choose one or two plans the first plane has it in initial fee of $55 and cost an additional $0.12 per mile driven the second plan has an initial fee of $50 in cost an additional $0.17 per mile driven
By using the concept of linear equations, amount of driving when two of these plans cost the same will be at x = 100.
The cost when two plans cost the same is $67.
What is Linear Equation in one variable?The linear equation in one variable is written as ax + b = 0, where a and b are two integers and x is a variable. This equation has only one solution.
Given data:
First plan has it in initial fee of $55 and cost an additional $0.12 per mile.
Second plan has an initial fee of $50 in cost an additional $0.17 per mile.
Linear Equation for first plan: f(x) = 55+0.12x
Linear Equation for second plan: s(x) = 50+0.17x
Here, x is a variable.
To find out the distance when the two plans cost the same, we'll need to solve:
55 + 0.12x = 50 + 0.17x
55 - 50 = 0.17x- 0.12x
5 = 0.05x
x = 5/0.05
x = 100
The cost when the two plans cost the same :
f(100) = 55 + 0.12(100)
f(100) = $67
s(100) = 50 + 0.17(100)
s(100) = $67
Hence, two of the plans will cost the same at x=100 and cost will be $67.
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{(2,-4),(3,-4),(4,-4),(5,-4),(6,-4)}
Selena says that this relation represents a function. Jose says that it is not a function who do you agree with
Selena is right. This relation represents a function.
The set of points given is {(2,-4),(3,-4),(4,-4),(5,-4),(6,-4)}.
We can consider 2, 3, 4, 5, 6 as x-values and -4 as the y-value.
Here, the values 2, 3, 4, 5, 6 are related to -4.
This relation represents a function.
Because no two same x-values are related to different y-values. In other words, different x-values can be mapped to same y-value. But two same x-values should not be related to different y-values for the map to be a function.
So here all the x-values are related to the y-value -4. So this is a many-to-one function.
Function is a relation which maps a particular set of points(Domain) to another set of values(Codomain) through which one domain value has exactly one image in the co-domain.
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Given the equation -12x+4y=12
a) solve for y if x=1
b) solve for y in general
Answer:
a) y = 6
b) y = 3x + 3
Step-by-step explanation:
a.)
plug 1 into x in the equation:
[tex]-12+4y=12[/tex]
add 12 to both sides to isolate 4y:
[tex]4y=24[/tex]
divide both sides by 4 to simplify x:
[tex]y=6[/tex] [24/4=6]
b.)
add 12x to both sides to isolate 4y:
[tex]4y=12x+12[/tex]
divide both sides by 4x to simplify x:
[tex]y=3x+3[/tex]
Reduce completely
[tex]1*2*3*4*5*6\\--------\\6*7*8*9*10[/tex]
33-2[3(3+12)-(5x2)3]
Answer:
3
Step-by-step explanation:
33 - 2[3(3 + 12) - (5 x 2)3] =
= 33 - 2[3(15) - (10)3]
= 33 - 2[45 - 30]
= 33 - 2[15]
= 33 - 30
= 3
need help asap!
What will be the location of the x value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( 24, -13)
Point R' is located at (28, -20)
=========================================================
Reason:
The translation rule is [tex](\text{x},\text{y})\to (\text{x}+4,\text{y}-7)[/tex]
It says to add 4 to the x coordinate, and subtract 7 from the y coordinate.
If we apply the rule to point R(24, -13), then we have...
[tex](\text{x},\text{y})\to (\text{x}+4,\text{y}-7)\\\\(24,-13)\to (24+4,-13-7)\\\\(24,-13)\to (28,-20)\\\\[/tex]
This rule shifts the point 4 units to the right and 7 units down.
f(x) = x; vertical stretch by a factor of 2 followed by a translation 1 unit up
Answer:
f(x)=2x+1
Step-by-step explanation:
Use formula:
f(x)=a(x-h)+k
a=shrinking/stretching
h= horizontal translation
left (+)
right (-)
k= vertical translation
left (-)
right (+)
what is this equation 6+4÷2
Answer:
Step-by-step explanation:
6+4=10
10/2
answer =5
8x + 5 (2x+3) = 195 find x
Answer:
x = 10
Step-by-step explanation:
We are given the following equation:
[tex]8x + 5(2x+3) = 195[/tex],
and told to find [tex]x[/tex].
In order to calculate the value of [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] the subject:
[tex]8x + 5(2x+3) = 195[/tex]
⇒ [tex]8x + (5 \times 2x) + (5 \times 3) = 195[/tex] [Distributing 5 into the brackets]
⇒ [tex]8x + 10x + 15 = 195[/tex]
⇒ [tex]18x + 15 = 195[/tex]
⇒ [tex]18x + 15 - 15 = 195 - 15[/tex] [Subtracting 15 from both sides of equation]
⇒ [tex]18x = 180[/tex]
⇒ [tex]\frac{18}{18}x = \frac{180}{18}[/tex] [Dividing both sides of equation by 18]
⇒ [tex]x = \bf 10[/tex]
Therefore, the value of x is 10.
The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11. a) find y b) find CD
The value of y = 5 and CD = 4 cm in the segment.
What is a segment ?The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11.
CD = (1/2) CF
3y - 11 = (1/2) (2y -2) (multiply both sides by 2)
6y - 22 = 2y - 2
6y - 2y = -2 + 22
4y = 20
y = 5
Substitute with the value of y in the equation of CD, you get:
CD = 3y-11 = 3(5) - 11 = 15 - 11 = 4 cm
In geometric terms, a line segment is a section of a straight line that is bordered by two clearly defined end points and contains all of the points on the line that lie inside that segment. The Euclidean distance between two endpoints of a line segment provides the length of the segment.
Between two points of a line or curve. a portion of a plane or solid figure that is eliminated due to the intersection of a line, plane, or planes, particularly one that occurs between a chord and a circle's arc.
A line segment in geometry is bordered by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points.
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You have 16 digs for your current volleyball season. There are 3 games left in the season. You want to break your previous record of 20 digs in a
season. Write and solve an inequality that represents the number 2 of digs you must get in the remaining 3 games to break your record
Answer: 16+d>20
d>4
Step-by-step explanation:
d=digs
16+d>20
16-16+d>20-16
d>4
All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 2% of students brought their lunch. 50 students brought their lunch. How many students in total are in Ridgewood Junior High School? Multiply/scale up to solve.
The total number of students in Ridgewood Junior High School is 2500 students
It is given that all students in Ridgewood Junior High School either get lunch in the school cafeteria or brought it from home on Tuesday.
No. of students who brought their lunch on Tuesday= 2% = 50 students
Let x be the total number of students in the Ridgewood Junior High School, therefore formulating the equation we get:
2% of x = 50
2/100*x = 50
x = 2500
Total number of students in the school = 2500
Hence, the total number of students in Ridgewood Junior High School is 2500 students
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Select the correct answer.
An insurance data scientist is researching a certain stretch of a rural highway where drivers are never pulled over. The mile markers in the solution of the following inequality determines the conclusion of his research.
Solve and interpret the compound inequality, where x represents the mile marker along the highway.
2x − 18 ≥ 122 or 5x + 15 < 250
Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.
Drivers located between mile marker 46 and mile marker 71 never get pulled over.
Drivers located below mile marker 46 or at mile marker 71 or above never get pulled over.
Drivers located between mile marker 47 and mile marker 70 never get pulled over.
The correct interpretation regarding the solution of the compound inequality is given as follows:
Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.
How to solve a compound inequality involving the or operation?To solve a compound inequality involving the or operation, we solve each inequality, then apply the union operation to their solutions.
In this problem, the following inequalities help us find the miles x in which the drivers are never pulled over.
2x - 18 ≥ 122.5x + 15 < 250.The solutions are found as follows:
2x - 18 ≥ 122
2x ≥ 140
x ≥ 140/2
x ≥ 70.
5x + 15 < 250.
5x < 235
x < 235/5
x < 47.
Hence the correct option is given by:
Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.
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send help guys thanks
The solutions associated with each case are listed below:
3 · x + 22 - x2 · x² + 4 · x1 / 2 + 1 / x2 · x + 22 · x + 4x + 44 · x- 82How to use operations between functions and evaluate resulting expressionsAccording to the statement, we find that the two functions are f(x) = x + 2 and g(x) = 2 · x and we are asked to perform on the functions to obtain all resulting expressions and, if possible, to evaluate on each case:
Case 1
(f + g) (x) = f (x) + g (x) = (x + 2) + 2 · x = 3 · x + 2
Case 2
(f - g) (x) = f (x) - g (x) = (x + 2) - 2 · x = 2 - x
Case 3
(f · g) (x) = f (x) · g (x) = (x + 2) · (2 · x) = 2 · x² + 4 · x
Case 4
(f / g) (x) = f (x) / g (x) = (x + 2) / (2 · x) = 1 / 2 + 1 / x
Case 5
(f ° g) (x) = f [g (x)] = 2 · x + 2
Case 6
(g ° f) (x) = g [f (x)] = 2 · (x + 2) = 2 · x + 4
Case 7
(f ° f) (x) = f [f (x)] = (x + 2) + 2 = x + 4
Case 8
(g ° g) (x) = g [g (x)] = 2 · (2 · x) = 4 · x
Case 9
(g ° g) (- 2) = 4 · (- 2) = - 8
Case 10
(f ° f) (- 2) = - 2 + 4 = 2
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jackie has a checking account. For each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day. Her current balance in the account is –$12.50. If she does not make any deposits or withdrawals, what will be the new balance in her account after 2 days? Show your work.
The new balance in Jackie's account after 2 days will be -$27.50.
How to illustrate the expression?It should be noted that for each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day.
Since her current balance in the account is –$12.50, the new balance after 2 days will be:
= -12.50 + (-7.50 × 2)
= -12.50 + -15
= -27.50
The balance is -27.50
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5 plus 5 equals what?
Answer: 10
Step-by-step explanation: 1 1 1 1 1+ 1 1 1 1 1= 1 1 1 1 1 1 1 1 1 1 or 10
What is the correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x
a StartFraction A Over x squared + StartFraction B Over 9 x EndFraction
b StartFraction A Over x EndFraction + StartFraction B Over x + 9 EndFraction
c StartFraction A x + B Over x squared EndFraction + StartFraction C Over 9 x EndFraction
d StartFraction A x + B Over x EndFraction + StartFraction C Over x + 9 EndFraction
The correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)
The correct answer is an option(B)
In this question, we have been given an expression x² + 9x = x (x + 9),
We need to write the correct form of the partial fraction decomposition for given expression.
Suppose, (7x + 18) / (x² + 9x) = A/x + B/(x + 9)
where A and B are some constants.
To find them, multiply both sides by x² + 9x :
7x + 18 = A (x + 9) + Bx
and then we solve for A and B.
Therefore, the correct form of the partial fraction decomposition for given expression 7x+18/x^2+9x is A/x + B/(x + 9)
The correct answer is an option(B)
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Answer:
The correct answer is option B
Step-by-step explanation:
Thomas has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For each part below, if the marble selected is replaced before the next marble is drawn, find the probability for the given draw. Write your answer as a simplified fraction.
A.What is the probability of getting a red marble?
B.What is the probability of getting a red or a green marble?
C.What is the probability of getting an orange marble?
Using it's concept, the probabilities are given as follows:
A. 1/4.
B. 11/16.
C. 0.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, the number of marbles is given by:
7 + 5 + 4 = 16.
Then:
For item a, 4 are red, hence the probability is 4/16 = 1/4.For item b, 4 are red and 7 are green, hence the probability is 11/16.For item c, there are no orange marbles, hence the probability is of 0.More can be learned about probabilities at https://brainly.com/question/14398287
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Select the correct answer.
A diagram of angles 1, 2, and 3 Is shown.
Given: Angles 1 and 2 are complementary
m/1=36°
21 and 22 are
complementary
given
m21-36
given
36⁰+ m2 = 90°
definition of
complementary
angles
22 and 23 are
a linear pair
m22+ m23 = 180°
given
linear pairs theorem
What is most likely being shown by the proof?
OA m/1 + m/3 = 90°
OB. m/3 144°
OC m/1 + m/3= 180°
OD. m/3= 126°
m22=54"
subtraction
property of
equality
54+ m23=180"
substitution
property of
equality
Analyzing the given data, it cab be concluded that Option D, that is, mL3 = 126° is most likely being shown by the proof.
It can be observed from the given diagram, angle 1 and angle 2 are complementary. By the definition of complementary angles, we get the sum of angle 1 and angle 2 equal to 90°.
=> mL1 + mL2 = 90°
The value of angle 1 is given as 36.
=> mL1 = 36⁰
Using the first observed condition and the value of angle 1, we can obtain the value of angle 2.
=> 36⁰ + mL2 = 90°
=> mL2 = 90 - 36 = 54°
Therefore, the value of angle 2 is obtained as 54°.
From the diagram given in the question, it can also be inferred that angle 2 and angle 3 form a linear pair. Using the linear pair theorem, we get the sum of angle 2 and angle 3 as 180°.
=> mL2 + mL3 = 180°
Previously, we have obtained the value of angle 2 as 54°.
Hence, by substituting the value of angle 2 in the above equation, we get,
54° + mL3 = 180°
=> mL3 = 180 - 54 = 126°
Therefore, By researching all the data and the results, we can conclude that all other options are discarded and the correct option is option D.
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