The equation of the linear function represented by the table below in slope intercept form is f(x) = 4x - 1.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
General equation of a linear function in slope intercept form is,
y = f(x) = mx + c
Here c is the y intercept and m is the slope.
y intercept is the point on the line when x coordinate equals zero.
Given four points on the line (-1, -5), (1, 3), (3, 11) and (5, 19).
Consider two points (1, 3) and (3, 11).
Slope, m = (11 - 3) / (3 - 1) = 8 / 2 = 4
So the equation is y = 4x + c.
Substitute (1, 3) in the above equation.
3 = (4 × 1) + c
c = 3 - 4
c = -1
So the equation is y = 4x - 1.
Hence the given function can be represented as f(x) = 4x - 1.
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What is the zero in the equation y=2x+8?
Answer:
The zero in the equation y = 2x + 8 is when x = -4. When x = -4, y = 0.
A baseball diamond measures 28 meters along each side. If a batter hit 1 single in a game, how many kilometers did the batter run?
The batter ran a distance of 0.112 kilometers or approximately 112 meters.
What is the distance?A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.
A baseball diamond is made up of four bases, and the distance a batter runs for a single is from home plate to first base, then first base to second base, then second base to third base, and finally third base back to home plate.
So the total distance the batter runs is 4 times the distance from home plate to first base, which is 28 meters.
28 meters x 4 = 112 meters
To convert meters to kilometers, divide by 1000:
112 meters / 1000 = 0.112 kilometers
Thus, the batter ran 0.112 kilometers or approximately 112 meters.
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100 points + answer fast ! thank u very much xoxo
Answer:
Attached below is an image with the answer
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Answer:
1) Given
2) Multiplication Property of Equality
3) 3x + 6 = 24 Distributive Property of Addition
4) 3x = 18 Subtraction Property of Equality
5) x = 6 Division Property of Equality
Step-by-step explanation:
[tex]\begin{array}{|l|l|}\cline{1-2}\vphantom{\dfrac12} \rm Statements & \rm Reasons\\\cline{1-2}\vphantom{\dfrac12}\frac{3(x+2)}{4}=6& \rm Given\\\cline{1-2}\vphantom{\dfrac12}3(x+2)=24&\text{Multiplication Property of Equality}\\\cline{1-2}\vphantom{\dfrac12}3x+6=24&\text{Distributive Property of Addition}\\\cline{1-2}\vphantom{\dfrac12}3x=18&\text{Subtraction Property of Equality}\\\cline{1-2}\vphantom{\dfrac12}x=6&\text{Division Property of Equality}\\\cline{1-2}\end{array}[/tex]
Given:
[tex]\dfrac{3(x+2)}{4}=6[/tex]
Apply the Multiplication Property of Equality by multiplying both sides by 4:
[tex]\implies 3(x+2)=24[/tex]
Apply the Distributive Property of Addition:
[tex]\implies 3 \cdot x + 3 \cdot 2=24[/tex]
[tex]\implies 3x+6=24[/tex]
Apply the Subtraction Property of Equality by subtracting 6 from both sides:
[tex]\implies 3x+6-6=24-6[/tex]
[tex]\implies 3x=18[/tex]
Apply the Division Property of Equality by dividing both sides by 3:
[tex]\implies \dfrac{3x}{3}=\dfrac{18}{3}[/tex]
[tex]\implies x=6[/tex]
--------------------------------------------------------------------------------
Multiplication Property of EqualityFor all numbers, a, b, and c:
If a = b, then a · c = b · cDistributive Property of AdditionMultiplying a number by a group of numbers added together is the same as multiplying each number separately:
a(b + c) = ab + acSubtraction Property of EqualityFor all numbers, a, b, and c:
If a = b, then a - c = b - cDivision Property of EqualityFor all numbers, a, b, and c:
If a = b, and c ≠ 0, then a ÷ c = b ÷ cThe relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: != -0.0127 + 0.0180x The above equation implies that__________
A. each beer consumed increases blood alcohol by 1.27%
B. on average it takes 1.8 beers to increase blood alcohol content by 1%
C. each beer consumed increases blood alcohol by an average of amount of 1.8%
D. each beer consumed increases blood alcohol by exactly 0.018
The correct answer is B. on average it takes 1.8 beers to increase blood alcohol content by 1%.
The equation implies that for each beer consumed, the blood alcohol content increases by 0.0180, meaning it takes 1.8 beers to increase the blood alcohol content by 1%.
It is important to note that different people metabolize alcohol at different rates, so the number of drinks it takes to reach a 0.08% BAC can vary significantly. Generally, it takes about 1.8 drinks to raise the BAC by 1%. This means that an average person would need to consume 15 drinks in order to reach the legal limit of 0.08%.
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Sweeten Company had no jobs in progress at the beginning of March and no beginning inventories. The company has two manufacturing departments—Molding and Fabrication. It started, completed, and sold only two jobs during March—Job P and Job Q. The following additional information is available for the company as a whole and for Jobs P and Q (all data and questions relate to the month of March):
Molding Fabrication Total
Estimated total machine-hours used 4,200 2,520 6,720
Estimated total fixed manufacturing overhead $ 16,800 $ 25,200 $ 42,000
Estimated variable manufacturing overhead per machine-hour $ 1.40 $ 2.20
Job P Job Q
Direct materials $ 21,840 $ 13,440
Direct labor cost $ 35,280 $ 12,600
Actual machine-hours used:
Molding 2,890 1,340
Fabrication 1,010 1,480
Total 3,900 2,820
Sweeten Company had no underapplied or overapplied manufacturing overhead costs during the month.
4. What was the total manufacturing cost assigned to Job P? (Do not round intermediate calculations.)
The total manufacturing cost assigned to Job P is $84,240.
How to compute the total manufacturing cost:The total manufacturing cost consists of direct material, direct labor, variable overhead, and fixed overhead costs.
The variable manufacturing costs include direct materials, direct labor, and variable overhead while the fixed overhead costs are period costs related to the production process.
Molding Fabrication Total
Machine hours used 4,200 2,520 6,720
Fixed manufacturing overhead $16,800 $25,200 $ 42,000
Fixed manufacturing overhead per hr $4 $10
Variable manufacturing overhead
per machine-hour $ 1.40 $ 2.20
Job P Job Q
Direct materials $ 21,840 $ 13,440
Direct labor cost $ 35,280 $ 12,600
Actual machine hours used:
Molding 2,890 1,340
Fabrication 1,010 1,480
Total 3,900 2,820
Actual Manufacturing Costs (Job P):
Job P
Direct materials $21,840
Direct labor costs $35,280
Overheads:
Variable $5,460 (3,900 x $1.40)
Fixed:
Molding = $11,560 ($4 x 2,890)
Fabrication = $10,100 ($10 x 1,010) $21,660
Total manufacturing costs $84,240
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Select the correct answer. The sum of the digits of a three-digit number is 13. The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits. Which system of equations can be used to find each digit?
Could someone help me understand? im a but confused
Using the system of equations we get the values of 3 digit number as:
238
Given:
The sum of the digits of a three-digit number is 13.
The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.
we are asked to determine each digit of the given number:
we frame the equation as:
tens digit (t) = 1+h
hundreds digit (h) = h
units digit (u) = 3+(t+h)
hence,
h + (1+h) + (3+(t+h)) = 13
open the brackets.
h+1+h+3+(t+h)=13
substitute t value from the above mentioned state.
h+1+h+3+((1+h)+h)=13
h+1+h+3+1+h+h=13
arrange the like terms and add.
4h + 5 = 13
4h = 13-5
4h=8
h = 8/4
h = 2
hence we get the hundreds digit as 2.
now substitute it to get t and u value.
t = 1+h
t = 1+2
t = 3
tens digit = 3
u = 3+(t+h)
u = 3+(3+2)
u = 3+5
u = 8
units digit = 8
A polygon has two pairs of complementary interior angles in three sets of supplementary interior angles. The sum of the remaining interior angles is 1440°. How many sides does a polygon have? Explain 
If X and Y are independent exponential random variables with pdf f(x) = 0.5e-as, x 0, find p(X > 1,Y > 4)
The joint probability distribution function for exponential random variables with pdf f(x) = 0.5e^(-0.5x), x ≥ 0, find P(X > 1,Y > 4) is, e^(-5/2).
The X and Y are independent variables, so probability distribution function of X is same as that of Y.
The joint probability distribution function for independent variables is,
[tex]\int \int f(x)f(y) dx dy[/tex]
where f(x) and (y) are the probability distribution function in x and y respectively.
In this question, X>1 and Y>4, so the limits of integration for X goes from 1 to infinity and for Y it goes from 4 to infinity.
[tex]\int_4^\infty \int_1^\infty 0.5 \times 0.5 \times e^{-0.5x} e^{-0.5y} dx dy\\= 0.25\int_4^\infty e^{-0.5y} dy \int_1^\infty e^{-0.5x} dx\\= 0.25 \times [-2e^{-0.5y}]_4^\infty \times [-2e^{-0.5x}]_1^\infty \\= 0.25 \times \dfrac{2}{{e}^2} \times \dfrac{2}{\sqrt{e}}[/tex]
The integral is, e^(-5/2).
The joint probability distribution function is, e^(-5/2).
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--The complete question is, If X and Y are independent exponential random variables with pdf f(x) = 0.5e^(-0.5x), x ≥ 0, find P(X > 1,Y > 4).--
Question 1
Identify the fragment below:
Can you go to the store for me? I need flour, baking soda, and candles. Milk too. While you are out, please make sure you fill the gas tank. I have to go to work early tomorrow morning.
I need flour, baking soda, and candles.
I have to go to work early tomorrow morning.
Can you go to the store for me?
Milk too.
(b) If the sum of two numbers is 10 and difference is 4. Find the number.
Answer:6
Step-by-step explanation:
The two numbers are 3 and 7.
Let the two numbers be x and y.
Considering the first statement :
x + y = 10 ...........................(1)
Considering the second statement:
x - y = 4 ............................(2)
Adding equations (1) and (2):
x + y + x - y = 10 + 4
2x = 14
x = 7
Substituting the value of x in equation (1):
7 + y = 10
y = 10 - 7
y = 3
Therefore, the value of the two numbers is 3 and 7.
For reference:
https://www.cliffsnotes.com/study-guides/algebra/algebra-i/word-problems/number-problems-with-two-variables
Randall wants to mix 21 lb of nuts worth $2 per lb with some nuts worth $9 per lb to make a mixture worth $8 per lb. How many pounds of $9 nuts must he use?
The number of pounds of $9 nuts he must used, 126
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Randall wants to mix 21 lb of nuts worth $2 per lb,
with some nuts worth $9 per lb
He wants to make a mixture worth $8 per lb
The number of pounds of $9 nuts must he use = ?
Suppose, the number of pounds of $9 = x
Then, According to given condition,
Average price in a mixture = (9x + 21 x 2)/x +21
= 8
(9x + 21 x 2)/x +21 = 8
9x + 42 = 8(x + 21)
9x + 42 = 8x + 168
9x - 8x = 168 - 42
x = 126
Hence, the number of pounds of $9 nuts is 126
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Carmen is starting a small gardening and lawn care business in her neighborhood for the summer. To get the business started she spends some money on advertising. The table shows her weekly profit for the first few weeks of the summer.
Week Profit ($)
1 −44.50
2 −26.25
3 80.50
4 88.75
5 95.50
Based on the average profit per week, how much total profit can she expect to earn over the course of the 12-week summer break?
On average Carmen earned $38.8 per week of profit and for 12 weeks the profit earned is $465.6.
What is average?
In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).
The profit earned by Carmen in her first week = -$44.50
The profit earned by Carmen in her second week = -$26.25
The profit earned by Carmen in her third week = $80.50
The profit earned by Carmen in her fourth week = $88.75
The profit earned by Carmen in her fifth week = $95.50
The average profit earned by Carmen is = sum of profit earned / number of weeks profit earned
Substitute the values into the equation -
Average = [(-44.50) + (-26.25) + 80.50 + 88.75 + 95.50] / 5
Average = 194/5
Average = 38.8
The avearge profit per week is $38.8
To find the profit Earned by Carmen in 12 weeks use the arithmetic operation of multiplication -
Profit Earned = 12 × Average profit per week
Substitute the values in the equation -
Profit Earned = 12 × 38.8
Profit Earned = 465.6
Therefore, the profit earned is $465.6.
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Answer:465.6
Step-by-step explanation:
Using the information below, work out the length t.
Give your answer to the nearest integer.
The length t of the triangle side is 44 mm
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
according to law of cosines,
t² = 41² +54² - 2 (41)(54) cos x
t² = 41² +54² - 2 (41)(54) ( 3/5)
t² = 1681 + 2916 - (13284/5)
t² = 1681 + 2916 - (13284/5)
t² = 4597 - 2656.8 =1940.2
t = ±√1940.2 = ±44 mm
length is positive
The length t of the triangle side is 44 mm
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consider randomly selecting a student who is among the 14,000 registered for the current semester in a college. let be the number of courses the selected student is taking, and suppose that has the following probability distribution: X 1 2 3 4 5 6 7 F(x) 0.02 0.01 0.20 0.17 0.39 0.20 0.01 find the 30th percentile of this distribution.
So,the value of the 30th percentile of the given data will be =P30=4
The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.
Using the Cumulative Distribution Function to Calculate Probabilities
F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:
To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):
First, we will determine the value of the cumulative probability P(X<=x):
x f(x) P(X<=x)
1 0.02 0.02
2 0.01 0.03
3 0.2 0.23
4 0.17 0.4
5 0.39 0.79
6 0.2 0.99
7 0.01 1
30th percentile will be the x value,
below which less than or equal to 30% of the data falls.
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fraction numerator d y over denominator d x end fraction plus 5 space y squared equals sin space x comma space y left parenthesis 0.3 right parenthesis equals 5 and using a step size of h equals 0.3, the value of y left parenthesis 0.9 right parenthesis using Euler's method is most nearly
Select one:
A. None of the above
B. -669.05
C. -658.91
D. -35.318
E. -36.458
y(0.9) ≈ -658.91 using Euler's method with the ODE [tex]dy/dx + 5y^2 = sin x[/tex], initial condition y(0.3) = 5, and step size h = 0.3.
Given that ODE:
[tex]dy/dx + 5y^2 = sin x[/tex]
with the initial condition:
y(0.3) = 5
and step size h = 0.3, the value of y(0.9) using Euler's method can be approximated as follows:
Starting with the initial condition y0 = 5, use the formula:
[tex]y(x + h) = y(x) + hf(x, y(x))[/tex]
where [tex]f(x, y) = (sin x - 5y^2)/(dy/dx) + 5y[/tex] is the right-hand side of the ODE, and h = 0.3.
After two iterations, the approximate value of y(0.9) is y2 ≈ -658.91.
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Solve three and two fifths plus three and four sixths
Group of answer choices
six and six thirtieths
seven and two thirtieths
seven and six elevenths
nine and two thirtieths
Answer:
3 2/5 = 17/5
3 4/6 = 22 / 6 = 11 / 3
17/5 + 11 / 3 need to find and 15 is the least common denominator
51 / 15 + 55 / 15 = 106 / 15
106 / 15 = 7 1 / 15 lowest terms
Note 7 1/15 = 7 2/30 second of 4 answers
need help will reward
The factor by which g([tex]x[/tex]) grows over the interval from 14 to 16 is 1.1429.
Whar is factor?The factor is a number that can be divided evenly into another number. For example, 2, 3, 5 and 10 are all factors of 10. When two or more numbers are multiplied together, each number is a factor of the product.
The factor by which g(x) grows over the interval from 14 to 16 can be determined by calculating the ratio of the values of g(x) at the endpoints of the interval.
At x = 14, g(x) = 4(14) = 56
At x = 16, g(x) = 4(16) = 64
The factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.
This means that g(x) grows by a factor of 1.1429 over the interval from 14 to 16.
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Help! I have to go to the park and park in the park and park on the park
Answer:
Please type or attach a math question to be answered.
Answer:
About extravagance philosophy
Determine the sample type.
A student is researching if people like to study at the city library. The student stands by the door of the city library and surveys people walking in.
Student use simple random sampling method.
What is a population and sample?There are two types of data sets are collected for the research. They are population and sample. Population includes all the elements from the data set. Sample is a part of population.
A student is researching if people like to study at the city library.
The student stands by the door of the city library and surveys people walking in.
It is type of simple random sampling.
In this simple random sampling every member of an population has an equal chance of being selected.
This is one of the probability sampling methods.
Hence, student use simple random sampling method.
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A seventh-grade teacher asks her students a survey question. Which questions are appropriate for the teacher to ask her population?
The questions that are appropriate for the teacher to ask her population are:
How many hours of sleep do you get per night?
On average, how long does it take you to complete your homework?
What time do you leave for school in the morning?
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The survey is conducted among the seventh grade students so the valid question their teacher would have asked them is:
How many hours of sleep do you get per night?
On average, how long does it take you to complete your homework?
What time do you leave for school in the morning?
while the other two questions are invalid as it the students are young and they are not legal to vote also it is not necessary that they would arrive to school by car.
Hence, the questions that are appropriate for the teacher to ask her population are:
How many hours of sleep do you get per night?
On average, how long does it take you to complete your homework?
What time do you leave for school in the morning?
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What is the critical F value for a sample of six observations in the numerator and four in the denominator? Use a two-tailed test and the .10 significance level., Mark Nagy has averaged 9 rejects, with a standard deviation of 2 rejects per day. Debbie Richmond averaged 8.5 rejects, with a standard deviation of 1.5 rejects, over the same period. At the .05 significance level, can we conclude that there is more variation in the number of rejects per day attributed to Mark?
The critical F value for a sample of 6 and 4 degrees of freedom at a .10 two-tailed significance level can be found using a F-distribution table. The exact value depends on the specific table used.
How do we compare Mark and Debbie?For the comparison between Mark and Debbie, we would need to perform an F-test for equality of variances to determine if there is more variation in Mark's data. The null hypothesis is that the variances are equal, and the alternative hypothesis is that the variance of Mark's data is greater. The test statistic would be the ratio of the larger variance to the smaller variance, with the degrees of freedom being the smaller of the two sample sizes minus 1.
A .05 significance level means that we reject the null hypothesis if the p-value is less than .05. The p-value can be found using an F-distribution table or a statistical software.
The conclusion would depend on whether the p-value is less than .05 or not.
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I'm giving out 50 points for this riddle: if a homeless eats it, he dies, rich people need this, and some people already have this that are poor
Answer:
nothing
Step-by-step explanation:
Answer:
Step-by-step explanation:
nothing
when you refer to the meer-kitty survey feedback tab, you are pleased to find that the available data is aligned to the business objective. however, you do some research about confidence level for this type of survey and learn that you need at least 120 unique responses for the survey results to be useful. therefore, the dataset has two limitations: first, there are only 40 responses; second, a meer-kitty superfan, user 588, completed the survey 11 times. as the survey has too few responses and numerous duplicates that are skewing results, you should remove the duplicates and continue analyzing the remaining 29 responses.
The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.
To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.
It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.
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A city currently has 133 streetlights. As part of an urban renewal program, the city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed.
The city will have (blank) streetlights at the end of 49 weeks.
The city will have 191 streetlights at the end of (blank) weeks.
The solution to the equations are
a) The city will have 231 streetlights at the end of 49 weeks
b) The city will have 191 streetlights at the end of 29 weeks
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The initial number of streetlights in the city = 133 streetlights
The number of streetlights installed per week = 2 streetlights
So , the number of streetlights after 49 weeks = 49 x number of streetlights installed per week
Substituting the values in the equation , we get
The number of streetlights after 49 weeks = 49 x 2 = 98 streetlights
And , the total number of streetlights after 49 weeks = initial number of streetlights in the city + number of streetlights after 49 weeks
Substituting the values in the equation , we get
The total number of streetlights after 49 weeks A = 133 + 98
The total number of streetlights after 49 weeks A = 231 streetlights
Now ,
Let the number of streetlights after n weeks = 191 streetlights
So , the number of weeks n = ( 191 - initial number of streetlights ) / 2
Substituting the values in the equation , we get
The number of weeks n = ( 58 ) / 2
The number of weeks n = 29 weeks
Hence , the equations are solved
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please help i need this ASAP
Answer:
-5
Step-by-step explanation:
First, find the solutions to the quadratic equation.
[tex]3x^2+15x+9=0\\3(x^2+5x+3)=0[/tex]
Since this is not factorable, use the quadratic formula and simplify.
x = (-5±[tex]\sqrt{(5)^2-4(1)(3)}[/tex])÷2(1)
x = (-5±[tex]\sqrt{13}[/tex])÷2
So x1 = (-5+[tex]\sqrt{13}[/tex])÷2 and x2 = (-5-[tex]\sqrt{13}[/tex])÷2
Now just sub it into the equation and simplify:
(-5+[tex]\sqrt{13}[/tex])÷2 + (-5-[tex]\sqrt{13}[/tex])÷2
= [tex]\frac{-5+\sqrt{13} + (-5)-\sqrt{13}}{2}[/tex]
= [tex]\frac{(-5)+(-5)+\sqrt{13}-\sqrt{13} }{2}[/tex]
= [tex]\frac{-10}{2}[/tex]
= -5
please help me will give u extra points :)
• which one do I put by number line?
Answer: x ≤ -6 or x > 5
Step-by-step explanation: There are 2 lines so you will need 2 inequalities to define it.
The first line is going to left means the variable (x) will have to be less than the greatest value of the line (the right most point) which is -6. Therefore, x < 6 with < representing less than. However, we also have to consider the a CLOSED dot at -6 meaning the sign of the inequality is going to be ≤ since we including that point in the inequlity saying x can be equal to or less than 6.
The second line going to the right means x has to be greater than the smallest value of the line which is -5 (the left most point of the line). Therefore, x > 5 (> means greater than). In this case, we do not use ≥ because the point at -5 has a OPEN dot meaning x cannot equal 5 and we can not include that point in our inequality so it would just be x > 5.
So we get x ≤ -6 or x > 5
Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
6 -3 h
-12 6 4
The value of h such that the matrix is the augmented matrix of a consistent linear system is -2
How to determine the value of hFrom the question, we have the following parameters that can be used in our computation:
6 -3 h
-12 6 4
For a consistent system of linear equation, the equations are the equivalent
So, we have
6x - 3y = h
-12x + 6y = 4
Divide the second equation by -2
6x - 3y = -2
By comparing the equations, we have
h = -2
Hence, the solution of h is -2
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Which graph represents the equation y equals one half times x minus 1?
Step-by-step explanation:
The graph would represent a straight line that slopes downwards and passes through the point (2,1).
One base of a trapezoid is 1 in longer than 2 times the other base. find the lengths of the bases if the trapezoid is 4in high and a area of 20in.
The length of the bases for the trapezoid are
shorter base is 3 in and the longer base is 7 in
How to find the length of the basesThe formula for area of trapezoid is
= 1/2 sum of bases * height
base of the trapezoid
20 = 1/2 sum of bases * 4
1/2 sum of bases = 5
sum of bases = 10
The relationship between the bases
longer base = 2 * shorter base + 1
sum of bases = longer base + shorter base
sum of bases = 2 * shorter base + 1 + shorter base
sum of bases = 3 shorter base + 1
substituting will result to
10 = 3 shorter base + 1
10 - 1 = 3 shorter base
9 = 3 shorter base
shorter base = 3 in
longer base = 2 * shorter base + 1
longer base = 2 * 3 + 1
longer base = 7 in
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A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was (0.46,0.52). Based on the confidence interval, which of the following claims is supported?
A. More than 90 percent of the residents support the increase.
B. Fewer than 10 percent of the residents support the increase.
C. More than 40 percent of the residents support the increase.
D. More than 60 percent of the residents support the increase.
E. Fewer than 25 percent of the residents support the increase.
Confidence interval refer a range of estimates for an unknown parameter and here unknown parameter is percentage of residents support the increase. So, the correct answer is option(c), i.e., More than 40 percent of the residents support the increase.
We have, A random sample of residents in city J, about whether they supported raising taxes to increase bus service for the city and sample is based on survey.
Significance level = 95%
Confidence interval = (0.46,0.52)
Confidence interval: A confidence interval, in statistics, defines to the probability that a population parameter will fall between two set values. Therefore, the population parameter i.e., the proportion lies in range of between 0.46 to 0.52. Therefore the actual population proportion of people who support the increase is surely greater than 40%, but always be less than 52%. So, out of five options, option (c) is that satisfied this condition. That is more than 40% of the residents support the increase, implies the option( C) is the correct answer.
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