The solution is, 6x + 4 cm is the perimeter of the rectangle.
Given:
The length of rectangle(l) = (x+3) cm
and a width of rectangle (w) = 2x-1 cm
we know that,
Perimeter of rectangle is to add the lengths of all the four sides.
so,
Perimeter of rectangle (P) is given by;
P=2(l+w)
Substituting the value,
l = (x+3) cm and w =2x-1 cm
then,
P = 2 ( x+ 3 + 2x -1 )
=2 (3x + 2)
= 6x + 4
Hence, 6x + 4 cm is the perimeter of the rectangle.
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Find the minimum value of f=8x-3y in the feasible region shown below
The minimum possible value of the objective function is -36
Finding the minimum possible value of the objective functionFrom the question, we have the following parameters that can be used in our computation:
Objective function, F = 8x - 3y
The coordinates of the feasible region are
(5, 5), (0, 8). (0, 12), (10, 0) and (15, 0)
Substitute (5, 5), (0, 8). (0, 12), (10, 0) and (15, 0) in the above equation, so, we have the following representation
F(5, 5) = 8(5) - 3(5) = 25
F(0, 8) = 8(0) - 3(8) = -24
F(0, 12) = 8(0) - 3(12) = -36
F(10, 0) = 8(10) - 3(0) = 80
F(15, 0) = 8(15) - 3(0) = 120
The minimum value above is -36 at (0, 12)
Hence, the minimum possible value of the objective function is -36
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ask your two questions in each of the two cells below, and provide the entire operation using probability statement(s) needed to calculate the answer to the question you've come up with. for example, if you ask what is the probability that (using the example from hw9) a basketball player makes a 2-point shot when defended, you would find:
The probability that a randomly selected light bulb will last for more than 900 hours is approximately 0.0228 or 2.28%. The probability that a randomly selected box of this cereal weighs less than 15 ounces is approximately 0.0228 or 2.28%.
Solution 1 :-
We can use the standard normal distribution to answer this question by finding the z-score for a lifespan of 900 hours and then finding the corresponding probability.
z = (x - μ) / σ
where:
x = lifespan we want to find the probability for = 900 hours
μ = mean lifespan = 800 hours
σ = standard deviation = 50 hours
Plugging in the values, we get:
[tex]z = (900 - 800) / 50 = 2[/tex]
We discover that the probability associated with a z-score of 2 is around 0.0228 using a conventional normal distribution table or calculator.
Solution 2:
We can use the standard normal distribution to answer this question by finding the z-score for a weight of 15 ounces and then finding the corresponding probability.
z = (x - μ) / σ
where:
x = weight we want to find the probability for = 15 ounces
μ = mean weight = 16 ounces
σ = standard deviation = 0.5 ounces
Plugging in the values, we get:
[tex]z = (15 - 16) / 0.5 = -2[/tex]
We discover that the probability associated with a z-score of -2 is around 0.0228 using a basic normal distribution table or calculator.
The study of the possibility or chance of an event occurring is the focus of the mathematic branch known as probability. It is a measure of how likely it is for an event to occur, ranging from 0 to 1, with 0 indicating that the event will never occur and 1 denotes that the event will always take place.
Probability can be expressed in different ways, such as fractions, decimals, or percentages. It is often used in various fields such as science, economics, and finance, to make predictions and informed decisions based on the available data. Probability is essential in statistical analysis, where it is used to calculate the likelihood of certain outcomes, test hypotheses, and make predictions.
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Complete Question:-
Ask your two questions in each of the two cells below, and provide the entire operation using probability statement(s) needed to calculate the answer to the question you've come up with. for example, if you ask what is the probability that (using the example from hw9) a basketball player makes a 2-point shot when defended, you would find:
Question 1: A company produces light bulbs and claims that they have a mean lifespan of 800 hours with a standard deviation of 50 hours. What is the probability that a randomly selected light bulb will last for more than 900 hours?
Question 2: A grocery store sells a certain brand of cereal and claims that the weights of the boxes follow a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounces. If a customer selects a box at random, what is the probability that it weighs less than 15 ounces?
if we increase a number by 15 percent, we get 356.5
The number which we increase by 15 percent gives 356.5 is the number
Given that,
if we increase a number by 15 percent, we get 356.5
Let x be the unknown number.
Then the given statement can be numerically written as,
x + (15% of x) = 356.5
x + (15/100) of x = 356.5
x + 0.15x = 356.5
1.15x = 356.5
Dividing both sides by 1.15, we get,
x = 356.5 / 1.15 = 310
Hence the unknown number is 310.
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Please I need help what is the area of the shapes
The solution is, 28.5cm^2 is the area of shape B.
A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition polyhedral of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus. Sought a general definition of surface area.
(3×7)+(1.5×5)
21+7.5
28.5cm^2
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Naomi was watching a game show where a contestant had 20 points and then had 5 turns where he scored -10 points on each turn. Then she stopped watching. What was the contestant's score when Naomi stopped watching the show?
A. -50
B. -30
C. 50
D. 70
Answer: the answer is b, -30.
The total cost of attending a state university is $22,700 for the first year.
A student's parents will pay half of this cost.
. Academic scholarships will pay another $8,300.
• The student will need to save money to pay for the remaining cost.
Use this information to complete the following statements.
The students parents will pay _____. The student needs to save a total of ____ to pay the remaining cost. If the student plans to save the needed amount in 12 months, then he/she should save _____ each month
Answer:
Total cost of attending university per year: $22,700
Parent's will pay half of it: ?
To know half of the number, we divide it by 2.
= $22,700 ÷ 2 = $11,350
Parents will pay: $11,350
Academic scholarship will pay: $8,300
= $11,350 - $8,300 = $3,050
So, The student have to save a total of $3,050.
To know how much she would need ro save every month, we would divide $3,050 by 12.
= $3,050 ÷ 12 = $254.15
The student Parents will pay $11,350. The student needs to save a total of $3,050 to pay the remaining cost. If the student chose to pay the needed amount in 12 months, then he/she would save $254.15 every month.
Which graph represents a function with an initial value of One-half?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.08), (0, 0.4), (1, 2).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.1), (0, 0.5), (1, 2.5).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.4), (0, 0.2), (1, 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.12), (0, 0.6), (1, 3).
The correct option is the second one, because it contins the point (0, 0.5), thus, the initial value is 0.5
Which graph represents a function with an initial value of One-half?For any function.
y = f(x)
We define the initial value as the value that y takes when we evaluate it in x = 0.
y = f(0) is the initial value, and it is represented by the pointy (0, y).
So a function will have an initial value of one-half if it contains the point (0, 0.5)
From the given options, the only one that conatins it is the second option "On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.1), (0, 0.5), (1, 2.5)."
So that is the correct one.
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I NEED HELP ON THIS ASAP!!!
The table should be completed by writing each part of the exponential function as follows;
Geometric sequence Exponential function Mathematical meaning
gₙ f(x) dependent variable
g₁/r a coefficient of power
r b base of power
n x independent variable (exponent)
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio or constant ratio.a₁ represents the first term of a geometric sequence.What is an exponential function?In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.By comparison, we have:
gₙ = f(x) (dependent variable)
g₁/r = a (coefficient of power)
r = b (base of power).
n = x (independent variable or exponent).
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How do I solve this? (with work)
Answer: 5400
Step-by-step explanation:
For a cube V=lwh
Volume for the larger box = 4.5 x 5 x 3.75 =84.375 or 675/8
Volume for smaller box =.25 x .25 x .25 = .015625 or 1/64
divide the larger by smaller.
84.375/.015625=5400
or
[tex]\frac{675}{8} /\frac{1}{64}[/tex] keep change flip = [tex]\frac{675}{8} * \frac{64}{1}[/tex] = 5400
An office manager orders one calculator or one calendar for each of the office's 60 employees. Each calculator costs $12, and each calendar costs $10. The entire order totaled $700. Part A: Write the system of equations that models this scenario. (5 points) Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps. (5 points)
Answer:
50 calculators and 10 calendars.
Step-by-step explanation:
Part A: Let x be the number of calculators and y be the number of calendars ordered. Then we have the following system of equations:
x + y = 60 (the total number of items ordered is 60)
12x + 10y = 700 (the total cost of the order is $700)
Part B: To solve this system by substitution, we can isolate x from the first equation and substitute it into the second equation. This gives us:
x = 60 - y
12(60 - y) + 10y = 700
Simplifying and solving for y, we get:
720 - 12y + 10y = 700
-2y = -20
y = 10
Therefore, the number of calendars ordered is 10. To find the number of calculators ordered, we can plug in y = 10 into the first equation and get:
x + 10 = 60
x = 50
Therefore, the number of calculators ordered is 50.
I need help with all of this will give you brain thing
Could you possibly repost your question with a clear image?
The details on this image are unreadable and, therefore, make it difficult to help.
Will bookmark this question so I can find your new post if posted again.
The quality manager at newvis pharmaceutical company is certifying a new process that must produce 90 percent (or better) good product before certification can be completed. a sample of 49 containers from the process line is tested, and 87 percent are found to be good. formulate the appropriate hypotheses and test them using an alpha
If there is enough evidence to reject the null hypothesis and conclude that the new process produces less than 90% good product.
The appropriate hypotheses for this scenario would be:
Null hypothesis (H0): The true proportion of good product produced by the new process is equal to or less than 0.9.
Alternative hypothesis (Ha): The true proportion of good product produced by the new process is greater than 0.9.
To test these hypotheses, we can use a one-sample proportion test. The test statistic for this test is calculated using the formula:
z = (p - P0) / sqrt(P0 * (1 - P0) / n)
where:
- p is the proportion of good product in the sample (0.87 in this case)
- P0 is the hypothesized proportion of good product (0.9)
- n is the sample size (49)
Using an alpha level of 0.05, we can find the critical z-value from a standard normal distribution table. For a one-tailed test (since our alternative hypothesis is one-sided), the critical z-value is 1.645.
Calculating the test statistic using the formula above, we get:
z = (0.87 - 0.9) / sqrt(0.9 * 0.1 / 49) = -1.17
Since the calculated z-value (-1.17) is less than the critical z-value (1.645), we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true proportion of good product produced by the new process is greater than 0.9. The quality manager should investigate the process further to improve the proportion of good product before certifying it.
Let's formulate the appropriate hypotheses and test them using an alpha:
The quality manager at Newvis Pharmaceutical Company wants to ensure that the new process produces at least 90% good product. We can define the null hypothesis (H0) and the alternative hypothesis (H1) as follows:
H0: p ≥ 0.90 (The process produces 90% or more good product)
H1: p < 0.90 (The process produces less than 90% good product)
Now, let's test these hypotheses using an alpha (significance level), which is typically set at 0.05.
1. Calculate the test statistic using the sample proportion (p-hat) and sample size (n):
p-hat = 0.87 (87% of the 49 containers were good)
n = 49
2. Find the standard error of the sample proportion:
SE = √(p * (1-p) / n)
3. Calculate the z-score:
z = (p-hat - p) / SE
4. Compare the z-score to the critical value from the z-table corresponding to the chosen alpha level. If the z-score is less than the critical value, reject the null hypothesis in favor of the alternative hypothesis.
If you complete these steps, you can determine if there is enough evidence to reject the null hypothesis and conclude that the new process produces less than 90% good product.
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What is the volume for this shape thingy- also this needs to be answered by today so
Answer:
60m^3
Step-by-step explanation:
In order to find the volume of this shape, you must solve the volume of the 2 different portions separately. You can do this by considering both of them to be rectangular prisms.
The smaller portion has a length of 1, a height of 2, and a depth(? im not sure if its called depth) of 3, you can get the 3 from the depth(?) of the larger one.
Since the volume of a rectangular prism is length x width x depth(?), the smaller figure has an volume of 6 m cubed, or 6m^3
The larger figure has a length of 6, a height of 3, and a depth(?) of 3, meaning you can multiply 3 x 3 x 6, which gives 54, which means the larger figure's volume is 54m^3
Now, you add the volumes of both figures, which gives a volume of 60m^3.
Darlene and Maggie leave a bookstore at the same time, riding bicycles.
• The number of miles, d, Darlene rides in t minutes are shown in the table.
t (minutes)
1.5
2
3.5
d (miles)
0.345
0.46
0.805
The number of miles, d, Maggie rides in t minutes are represented by the equation d = 0.16t.
Darlene and Maggie take the same route to a park which is 6 miles away.
Based on the given information, which statement is true?
OA. Maggie rides at a faster rate.
O B. It takes Maggie about 60 minutes to arrive at the park.
OC. Darlene rides her bicycle at a rate of 0.115 mile per minute.
O D. Darlene arrives at the park about 12 minutes ahead of Maggie.
there are fourteen juniors and thirteen seniors in the service club. the club is to send four representatives to the state conference. if the members of the club decide to send two juniors and two seniors, how many different groupings are possible?
There are 7098 possible ways of grouping 4 students, where there will be 2 juniors and 2 seniors, by using combinations.
There are 14 juniors and 13 senior in the service club and the club is to send four representatives to the state conference.
The members of the club decide to send 2 juniors and 2 seniors of the club for the state conference. There is no specified order of how to form the groups.
Thus we apply the formula of combinations to calculate the total number of different groupings of 4 students that is possible since order does not matter in combinations = nCr
where, n is the total number of students and r is the required number of students from the total.
Applying formula of combinations,
Total number of possible groupings = (14C2)*(13C2)
Here, 14C2 calculates the number of ways juniors can form groups and 13C2 calculates the number of ways seniors can form groups.
⇒ Total number of possible groupings = [ 14!/{(14-2)!*2!}]* [ 13!/{(13-2)!* 2!}]
= 7098
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20 POINTS!
A math class has 3 girls and 5 boys in the seventh grade and 9 girls and 3 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys? Write your answer as a fraction in the simplest form
The probability that the students teacher selects are both boys is equal to 5/32 (fraction in the simplest form).
Number of girls in Math's class of 7th grade = 3
Number of boys in Math's class of 7th grade = 5
Number of girls in Math's class of 8th grade = 9
Number of boys in Math's class of 8th grade = 3
There are a total of 8 students in the seventh grade
And 12 students in the eighth grade,
For a total of 20 students in the class.
The probability of selecting a boy from the seventh grade is 5/8,
since there are 5 boys out of a total of 8 students in the seventh grade.
The probability of selecting a boy from the eighth grade is 3/12,
since there are 3 boys out of a total of 12 students in the eighth grade.
To find the probability of selecting a boy from both grades, we multiply the two probabilities,
= (5/8) x (3/12)
= 15/96
= 5/32 (fraction in the simplest form)
Therefore, the probability of selecting a boy from the seventh grade and a boy from the eighth grade is 5/32.
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The question is in the picture
Kelly has 64 balloons and 48 flowers to decorate tables for a party.
• She wants to have the same number of balloons on each table.
• She also wants to have the same number of flowers on each table.
What is the greatest number of tables Kelly will be able to decorate for the party?
Answer:
24
Step-by-step explanation:
you dived the number for flowers
Answer:
16 tables
Step-by-step explanation:
Basically this is a question involving the Greatest Common Factor(GCF) also sometimes referred to as Greatest Common Divisor(GCD)
The greatest common factor (GCF or GCD ) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.
To find the GCF, find the factors of each number and then find the largest common factor
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 64 are: 1, 2, 4, 8, 16, 32, 64
16 is the largest common factor and therefore GCF(48, 64) = 16
This means that the greatest number of tables for decoration is 16
With 16 tables there will be 64/16 = 4 balloons per table and 48/16 = 3 flowers per table
Can some help simplify this question, with positive exponents
Answer:
4[tex]a^{9}[/tex][tex]b^{8}[/tex]
Step-by-step explanation:
[tex]\frac{8a^{6}b^{12} x 4a b^{3} }{8x^{-2}b^{7} }[/tex]
[tex]\frac{32a^{7} b^{15} }{8a^{-2} b^{7} }[/tex]
4[tex]a^{9}[/tex][tex]b^{8}[/tex]
Helping in the name of Jesus.
1.2(- 1.3) + 4
-3.5 - 1.4 + (2*2.5)
List the operations that you see and the follow order of operations:
For the first expression, the order of operation is multiplication followed by subtraction and addition, -5.56.For the second expression, the order of operations is multiplication followed by addition, -0.9.
What is addition?The addition is a mathematical operation that involves combining two or more numbers or quantities to find their total or sum. It is typically represented by the plus sign (+) and is one of the fundamental arithmetic operations. Addition is commutative, meaning that the order of the numbers being added does not affect the result.
According to the given information:For the first expression:
Operations:
Multiplication: 1.2 x (-1.3)
Subtraction: 1.2 x (-1.3)
Addition: 1.2 x (-1.3) + 4
Order of operations:
Multiplication: 1.2 x (-1.3) = -1.56
Subtraction: -1.56 - 4 = -5.56
For the second expression:
Operations:
Multiplication: 2 x 2.5
Addition: -3.5 - 1.4 + (2 x 2.5)
Order of operations:
Multiplication: 2 x 2.5 = 5
Addition: -3.5 - 1.4 + 5 = -0.9
Therefore, For the first expression, the order of operation is multiplication followed by subtraction and addition, -5.56.For the second expression, the order of operations is multiplication followed by addition, -0.9.
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What is the value of the expression 2z + 2w when z=7 and w=5
Answer:
The solution is 24
Step-by-step explanation:
z = 7
w = 5
2z + 2w
we enter the numbers
2(7) + 2(5)
= 14 + 10
= 24
The perimeter of the rectangle is at least 50 centimeters. The length is one more than three times the width of the rectangle. What are the minimum dimensions?
The minimum dimensions of the rectangle are 6cm and 19 cm
How to determine the value of the dimensionsThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l + w)
Such that the parameters of the formula are;
P is the perimeter of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Perimeter of the rectangle is = 50 centimeters
length of the rectangle = 3w - 1
Substitute the values
50 = 2(3w + 1 + w)
expand the bracket
50 = 2(4w + 1)
50 = 8w + 2
collect like terms
8w = 548
w = 6 centimeters
Length = 19 centimeters
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The first derivative of the function h is given by h'(x)= x^4 - x^3 + x. On which of the following intervals is the graph of h concave down?
The first derivative of the function h is given by [tex]h'(x)= x^4 - x^3 + x[/tex]. The graph of h is concave down at (−∞,−0.455). Therefore the correct answer is option D.
Given, the first derivative of the function,
[tex]h'(x)=x^{4} -x^{3} +x[/tex]
The second derivative of the function,
[tex]h''(x)=4x^{3} -3x^{2} +1[/tex]
When h''(x)<0, then the function is said to be concave down.
h′′(x)<0
=> [tex]4x^{3} -3x^{2} +1 < 0[/tex]
Finding the root of the equation,
[tex]f(x)=4x^{3} -3x^{2} +1=0[/tex]
This equation has only one real solution,
At x = -0.5, f(−0.5)<0
f(-0.5)<0
At x = -0.4, f(−0.4)>0
f(-0.4)>0
So according to the intermediate value theorem, there is a root in (-0.5, -0.4)
From the option, that root can be x = -0.455
So if the function concave down h''(x) < 0
Interval : (−∞,−0.455)
Therefore, the graph of h is concave down at (−∞,−0.455).
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Consider the graph of the function f (2)
y
-2
L.
2-
-1-
。
-N
in
OA The domain ier &
= log z.
K
-4
Which is a feature of function g if(2)=-4 log(
-10
5
-
8
X
Answer: c
Step-by-step explanation: I'm pretty sure this is right
Please help!!!
What is 5^2?
5^2 is equal to 25.
lol its kinda easy
Answer:
25.
Step-by-step explanation:
The symbol "^" representa exponents.
The exponet (second number) means how many times you mutiply 5 by itself. In this case, it's 2.
2. 5 x 5 = 25
help please!!! tysm :)
The equation of transforming the function h(x) to y = h(x - 3) is h(x - 3) = -1/2(x - 3)² + -1/2(x - 3) + 4
Transforming the function h(x) to y = h(x - 3)The graph h(x) is a quadratic function
A quadratic function is represented as
y = ax² + bx + c
Where c = y when x = 0
So, we have
y = ax² + bx + 4
Using the other points, we have
a + b + 4 = 3
4a + 2b + 4 = 1
So, we have
a + b = -1
4a + 2b = -3
When solved, we have
a = -1/2 and b = -1/2
So, the equation is
y = -1/2x² + -1/2x + 4
Rewrite as
h(x) = -1/2x² + -1/2x + 4
When translated to h(x - 3), we have
h(x - 3) = -1/2(x - 3)² + -1/2(x - 3) + 4
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alice changes size several times. the ratio of her original height to her second height is 24 to 5. the ratio of her second height to her third height is 1 to 12. the ratio of her original height to her fourth height is 16 to 1. the tallest of these four heights is 10 feet. what is her shortest height?
Alice's shortest height is 1.25 feet.
To determine Alice's shortest height, we need to examine the ratios given.
The ratio of her original height to her second height is 24:5, her second height to her third height is 1:12, and her original height to her fourth height is 16:1. We are told that the tallest height is 10 feet.
Since the tallest height is 10 feet, and the ratio of her original height to her fourth height is 16:1, we can find her original height: (10 feet / 1) * 16 = 160 feet. Now that we have her original height, we can find her second and third heights using the other given ratios:
Second height: (160 feet / 24) * 5 = 33.33 feet
Third height: 33.33 feet * 12 = 400 feet
Summary: Among the four heights (160 feet, 33.33 feet, 400 feet, and 10 feet), the shortest height is 10 feet (fourth height). However, since the question asks for her shortest height not mentioned as the tallest, it would be her second height, which is 33.33 feet. After reevaluating the ratios, Alice's original height should be 30 feet, making her second height 1.25 feet (30 / 24 * 5), which is the correct shortest height.
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please help due in 30 minutes if you get it right ill mark you brainilest pls help
The system of linear equations represented by the graph are y=2x-1 and y= -x+2.
A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that,
The coordinates on the blue line are (2, 3) and (0, -1)
The coordinates on the red line are (2, 0) and (0, 2)
Equation of a line with (2, 3) and (0, -1)
Now, m=(y₂-y₁)/(x₂-x₁)
= (-1-3)/(0-2)
= 2
Substitute m=2 and (x, y)=(2, 3) in y=mx+c, we get
3=2(2)+c
c=-1
Substitute m=2 and c=-1 in y=mx+c, we get
y=2x-1
Equation of a line with (2, 0) and (0, 2)
Now, m=(y₂-y₁)/(x₂-x₁)
= (2-0)/(0-2)
= -1
Substitute m=-1 and (x, y)=(2, 0) in y=mx+c, we get
0= -1(2)+c
c=2
Substitute m=-1 and c=2 in y=mx+c, we get
y= -x+2
Therefore, the system of linear equations represented by the graph are y=2x-1 and y= -x+2.
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20 ping pong balls are numbered 1-20, with no repetition of any of the numbers. what is the probability of selecting one ball that is either odd or a number 4 ball?
The probability of selecting one ball that is either odd or a number 4 ball is 11/20.
To find the probability of selecting one ball that is either odd or a number 4 ball, you should first identify the number of odd balls and then add the number 4 ball if it is not already included.
Here are the steps to calculate the probability:
Count the odd balls: There are 10 odd balls (1, 3, 5, 7, 9, 11, 13, 15, 17, 19).Add the number 4 ball if it is not already included: The number 4 ball is not an odd number, so we need to add it. Now we have 11 favorable outcomes (1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 4).Calculate the total number of balls: There are 20 ping pong balls.Find the probability: The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, it is 11/20.For more information about probability, visit:
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which part is a solution to the system of linear equations?
y= -x + 4
x- 3y = 12
A. 0,3
B. 1,2
C. 6,-2
D 4,-4
Answer:
Step-by-step explanation:
0.3
