I NEED HELP!!
Identify all vertical asymptotes, horizontal asymptotes, and holes.
Thx
Answers
(a) The vertical asymptotes of the function f(x) occur at x = -2 and x = -3.
(b) There are no horizontal asymptotes.
(c) There are no holes.
What are the vertical asymptotes, horizontal asymptotes?
The vertical asymptotes, horizontal asymptotes, and holes of the given function f(x) = (x - 5) / (x² + 5x + 6), is calculated as follows;
Vertical asymptotes occur when the denominator of the function approaches zero, resulting in an undefined value.
x² + 5x + 6 = 0
(x + 2)(x + 3) = 0
x + 2 = 0 or x + 3 = 0
x = -2, -3
Horizontal asymptotes occur when the function approaches a constant value as x approaches positive or negative infinity.
The degree of the numerator is 1 (since it's a linear function) and the degree of the denominator is 2 (since it's a quadratic function).
Since the degree of the denominator is greater than the degree of the numerator, there are no horizontal asymptotes.
Holes occur when both the numerator and denominator of the function have common factors that can be canceled out.
In the given function f(x) = (x - 5) / (x² + 5x + 6), there are no common factors between the numerator and the denominator that can be canceled out.
Therefore, there are no holes in the function.
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Related Questions
Which situation could be represented by 5x > 15? Jakiera makes $5 per hour working at her father's repair shop. She needs to make more than $15 to buy the calendar that she wants for next year. How many hours can she work to achieve this goal? Thomas brought 5 cans for the campus food drive. How many more cans does he need to have at least 15 cans for the food drive? Clarice collects comic books. Her brother, Samuel, has 15 comic books. How many comic books does Clarice need to have more comics than Samuel? Elizabeth is five times older than her grandchild, who is 15. How old is Elizabeth?
Answers
Answer:
First situation
More than 3 hours
At least 10
15
75
Step-by-step explanation:
Let x be the number of hours
The equation will be
\(5x>15\\\Rightarrow x>\dfrac{15}{5}\\\Rightarrow x>3\)
So, she needs to work more than 3 hours in order to make more than $15.
The situation that represents \(5x>15\) is the first one.
Let x be the additional number of cans
The inequality will be
\(x+5\geq15\\\Rightarrow x\geq 15-5\\\Rightarrow x\geq 10\)
So, the additional number of cans to be bought is at least 10.
Let x be the number of comic books Clarice has.
\(x>15\)
So, Clarice needs to have more than 15 comic books.
Let x be age of Elizabeth
The equation will be
\(x=5\times 15\\\Rightarrow x=75\)
So, Elizabeth is 75 years old.
Select all of the numbers that are correctly written in scientific notation. 10.8\times10^{-3}10.8×10 −3 0.54\times10^60.54×10 6 1\times10^{-4}1×10 −4 7.6\times10^{2.5}7.6×10 2.5 9.8\times10^59.8×10 5
Answers
Answer:
1×10⁻⁴ and 9.8×10⁵Step-by-step explanation:
The standard form of writing a scientific notation is expressed as \(a.b*10^n\) where a, b and n are integers. Note that a, b and n cannot be a fraction. When writing in scientific notation, the value of 'a' must not be equal to zero and it must not be a 'two digits values' but just 'a digit value'.
Based on the above conclusion, the following numbers are correctly written in scientific notation.
1×10⁻⁴ and 9.8×10⁵
- The expression 10.8×10 −3 is not correctly written because the value of a on comparison is a two digits number i.e 10.
- Also, 0.54×10^6 is not correctly written because a is zero on comparison
- 7.6×10 2.5 is not correctly written because the power is a decimal number i.e 2.5. We must only have an integer as the degree.
The probability distribution for the number of defective items in a random sample is as follows: x: 0 1 2 3 4 p(x) : 1 0.15 13 07 0.55
calculate:
expected value of X = ____
Answers
From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.
To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.
The expected value of X, denoted as E(X) or μ, is calculated using the formula:
E(X) = ∑ (x * p(x))
where x represents each possible value of X and p(x) represents the corresponding probability.
In this case, the probability distribution for X is given as follows:
x: 0 1 2 3 4
p(x): 0.1 0.15 0.13 0.07 0.55
To calculate the expected value, we perform the following calculations:
E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)
E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2
E(X) = 2.82
The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.
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Write the equation of the line to the following information
Answers
Answer:
y=2x-3
Step-by-step explanation:
Equation of a line is y=mx+b, where m is the slope and b is the y-intercept.
Here, m=2, b=-3
Equation is,
y = 2x-3
How do you solve SSS theorem?
Answers
A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.
Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.
Proof: Given, AB = DE, BC = EF, AC = DF.
To prove: ΔABC ≅ ΔDEF.
We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.
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The vertices of A ABC are A(1, - 2) , B(4, 0) and C(- 3, 3) . What are the coordinates of the vertices after it is reflected across the y - axis ? Plzzz help
Answers
Answer:
A (-1,-2), B (-4,0), C (3,3)
Step-by-step explanation:
Does anyone know the answer? For this problem
Answers
Answer:
136/7
Step-by-step explanation:
similar triangles. so sides have to be proportional
pn/sq = po/sr
4/x = 7/34
x = 4*34/(7)
= 136/7
To raise funds for uniforms and travel expenses, the soccer team is holding a car wash in a part of
town with a lot of car and truck traffic. The team spent $90 on supplies like sponges and soap.
They plan to charge $10 per car and $20 per truck. Their goal is to raise $460.
How many cars do they have to wash if they washed the following numbers of trucks?
1.4 trucks
2. 15 trucks
3.21 trucks
4. 27 trucks
5. t trucks
Answers
Answer:1.38 3.16 3.9 4.0
Step-by-step explanation:
Step 1: Take number of truck multiply $20, get answer(s).
Step 2: subtract answer #1 subtract from $460
Step 3. Divide answer step 2 by $10 car
4: your answer
A patient who weighs 170 lb has an order for an IVPB to infuse at the rate of 0.05 mg/kg/min. The medication is to be added to 100 mL NS and infuse over 30 minutes. How many grams of the drug will the patient receive?
Answers
The patient will receive approximately 0.11568 grams of the drug. This is calculated by converting the patient's weight to kilograms, multiplying it by the infusion rate, and then multiplying the dosage per minute by the infusion duration in minutes.
To determine the grams of the drug the patient will receive, we need to do the follows:
1: Convert the patient's weight from pounds to kilograms.
170 lb ÷ 2.2046 (conversion factor lb to kg) = 77.112 kg (rounded to three decimal places).
2: Calculate the total dosage of the drug in milligrams (mg) by multiplying the patient's weight in kilograms by the infusion rate.
Total dosage = 77.112 kg × 0.05 mg/kg/min = 3.856 mg/min.
3: Convert the dosage from milligrams to grams.
3.856 mg ÷ 1000 (conversion factor mg to g) = 0.003856 g.
4: Determine the total amount of the drug the patient will receive by multiplying the dosage per minute by the infusion duration in minutes.
Total amount of drug = 0.003856 g/min × 30 min = 0.11568 g.
Therefore, the patient will receive approximately 0.11568 grams of the drug.
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In ΔOPQ, m ∠ � = ( 2 � − 5 ) ∘ m∠O=(2x−5) ∘ , m ∠ � = ( 3 � − 8 ) ∘ m∠P=(3x−8) ∘ , and m ∠ � = ( 10 � − 17 ) ∘ m∠Q=(10x−17) ∘ . What is the value of � ? x?
Answers
Answer: Since the angles in a triangle sum up to 180 degrees, we can write:
m∠O + m∠P + m∠Q = 180
Substituting the given angle measures, we get:
(2x - 5) + (3x - 8) + (10x - 17) = 180
Simplifying and solving for x, we have:
15x - 30 = 180
15x = 210
x = 14
Now that we know x = 14, we can find the value of angle θ by substituting x into one of the angle measures:
m∠O = 2x - 5 = 2(14) - 5 = 23 degrees
Therefore, the value of angle θ is 23 degrees and the value of x is 14.
Step-by-step explanation: hope this helps (:
The value of ∠� is 23 degrees, and the value of x is 14.
Step-by-step explanation:
Since ∠O, ∠P, and ∠Q are angles of triangle OPQ, their sum must be 180 degrees. Therefore, we can set up the following equation:
m∠O + m∠P + m∠Q = 180
Substituting the given expressions, we get:
(2x - 5) + (3x - 8) + (10x - 17) = 180
Simplifying the left side, we get:
15x - 30 = 180
Adding 30 to both sides, we get:
15x = 210
Dividing both sides by 15, we get:
x = 14
Now we can find the value of ∠� by substituting x = 14 into the expression for m∠O:
m∠O = 2x - 5 = 2(14) - 5 = 23
Therefore, the value of ∠� is 23 degrees, and the value of x is 14.
What are the Slope and Y-intercept of y>-2x+3
Answers
Answer:
The y-intercept would be y > 3
The slope would be -2
Step-by-step explanation:
Slope is very simple to find, as it is just the value next to x.
The y-intercept would be 3 as it is outside the ax.
A manufacturing company buys a new stamping machine for $28,000. The maker of the machine informs the company’s CEO that on average, it depreciates in value according to the schedule shown in the table. Answer the questions that follow.
Months
Value
0
$28,000
6
$24,500
12
$21,000
18
$17,500
24
$14,000
Answer the following questions
1) If the depreciation continues at the same rate, how long will it take until the machine has no value?
2) Based on the pattern you see in the table, how do you know that the graph will be a straight line?
3) Enter the values in the table above in an Excel spreadsheet and use Excel to create a line graph. Label the axes and title the graph. Then copy the graph from your Excel spreadsheet and paste it below.
4) Find the slope of the graph and explain what it means.
5) Find the intercepts of the graph, and describe what each intercept means.
6) If we use the letter x to represent the variable number of months, write an expression that represents the value of the machine.
7) Use your expression from Question 6 to find when the machine has no value, and compare it to the answer you have in Question 1. Do you get the same/different answers? Explain.
Answers
1.The machine will have no value after 48 months. 2.The graph of the machine's value over time will be a straight line. 3.The slope of the graph represents the rate of depreciation per month. 4.The intercepts of the graph indicate the initial value and zero value. 5.The expression V = -750x + 28,000 represents the value of the machine. 6.The machine has no value when x = 37 according to the expression. 7.The answer obtained using the expression differs from the answer in 8.question 1 due to possible rounding errors or calculation variations.
To determine when the machine has no value, we observe the pattern of depreciation. Based on the given data, the machine depreciates by $3,500 every 6 months. Therefore, it will take 48 months (8 cycles of 6 months) for the machine to have no value.
The table shows a consistent decrease in value over time with equal intervals of 6 months. This indicates a linear relationship between the number of months and the value. A linear relationship is represented by a straight line on a graph.
The slope of the graph can be determined by calculating the change in value divided by the change in time. In this case, the slope is (-750), meaning the value decreases by $750 per month. It represents the rate of depreciation per month.
The intercepts of the graph are obtained by determining the value of the machine at the start (initial value intercept) and when it reaches zero (zero value intercept). The initial value intercept is $28,000, which represents the starting value of the machine. The zero value intercept occurs when the machine has no value.
The expression V = -750x + 28,000 represents the value of the machine. The coefficient of x (-750) represents the rate of depreciation per month, while the constant term (28,000) represents the initial value.
Using the expression, when x = 37, the machine has no value. This differs from the answer in question 1 (48 months). The discrepancy could be due to rounding errors or variations in the method used to calculate the exact point at which the value reaches zero.
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As part of the Pew Internet and American Life Project, researchers surveyed a random sample of 800 teens and a separate random sample of 400 young adults. For the teens, 79% said that they own an iPod or MP3 player. For the young adults, this figure was 67%. Do the data give convincing evidence of a difference in the proportions of all teens and young adults who would say that they own an iPod or MP3 player? State appropriate hypotheses for a test to answer this question. Define any parameters you use.
Answers
the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3
To determine if there is convincing evidence of a difference in the proportions of all teens and young adults who own an iPod or MP3 player, we can perform a hypothesis test.
Let's define the following parameters:
- p₁: Proportion of all teens who own an iPod or MP3 player.
- p₂: Proportion of all young adults who own an iPod or MP3 player.
The null hypothesis (H₀) assumes that there is no difference between the proportions:
H₀: p₁ = p₂
The alternative hypothesis (H₁) assumes that there is a difference between the proportions:
H₁: p₁ ≠ p₂
To test this hypothesis, we can use a two-proportion z-test. We calculate the test statistic using the formula:
z = ((p₁ - p₂) - 0) / √((\(\hat{p}_1\) * (1 - \(\hat{p}_1\)) / n₁) + (\(\hat{p}_2\) * (1 - \(\hat{p}_2\)) / n₂))
Where:
- \(\hat{p}_1\): Sample proportion of teens who own an iPod or MP3 player (79% or 0.79)
- \(\hat{p}_2\): Sample proportion of young adults who own an iPod or MP3 player (67% or 0.67)
- n₁: Sample size of teens (800)
- n₂: Sample size of young adults (400)
Using the given values, we can calculate the test statistic:
z = ((0.79 - 0.67) - 0) / √((0.79 * (1 - 0.79) / 800) + (0.67 * (1 - 0.67) / 400))
Calculating this yields the test statistic z = 5.525.
Next, we can determine the critical value or p-value associated with this test statistic using a significance level (α). Assuming a significance level of 0.05, for a two-tailed test, the critical values are approximately -1.96 and 1.96.
Since the calculated test statistic (5.525) is beyond the critical values of -1.96 and 1.96, we can reject the null hypothesis. There is convincing evidence to suggest that there is a difference in the proportions of all teens and young adults who own an iPod or MP3 player.
In conclusion, the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3 player.
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The appropriate hypotheses for testing the difference in proportions of all teens and young adults who own an iPod or MP3 player are:
Null Hypothesis (H0): The proportion of teens who own an iPod or MP3 player is equal to the proportion of young adults who own an iPod or MP3 player.
Alternative Hypothesis (Ha): The proportion of teens who own an iPod or MP3 player is not equal to the proportion of young adults who own an iPod or MP3 player.
To test if there is a significant difference in the proportions of all teens and young adults who own an iPod or MP3 player, we need to set up appropriate hypotheses. Let's denote the proportion of teens who own an iPod or MP3 player as p1 and the proportion of young adults who own an iPod or MP3 player as p2.
The null hypothesis (H0) assumes that there is no difference between the proportions, so we can state it as:
H0: p1 = p2
The alternative hypothesis (Ha) assumes that there is a difference between the proportions, so we can state it as:
Ha: p1 ≠ p2
Here, p1 represents the true proportion of teens who own an iPod or MP3 player, and p2 represents the true proportion of young adults who own an iPod or MP3 player.
To test these hypotheses, we can use a significance level (α) of 0.05, which is a common choice in hypothesis testing. If the p-value (the probability of observing a test statistic as extreme as the one calculated) is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportions.
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SECTION A (20 MARKS) QUESTION 1 (a)Identify the relevant population for the below foci, and suggest the appropriate sampling design to investigate the issues, explaining why they are appropriate. Wherever necessary identify the sampling frame as well. 10 marks A public relations research department wants to investigate the initial reactions of heavy soft- drink users to a new all-natural soft drink'. (b) What type of sampling design is cluster sampling? What are the advantages and disadvantages of cluster sampling? Describe a situation where you would consider the use of cluster sampling. 10 marks
Answers
a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is stratified random sampling. The list of all heavy soft-drink users is the sampling frame.
b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.
The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.
a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.
Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.
Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.
b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.
The advantages of cluster sampling are:
Cluster sampling is an efficient method of sampling large populations. It is much cheaper than other types of sampling methods.Cluster sampling is relatively easy to perform compared to other methods of sampling, such as simple random sampling.Cluster sampling can be used when the population is widely dispersed, and it would be difficult to cover the entire population.The disadvantages of cluster sampling are:
Cluster sampling introduces sampling errors that could lead to biased results.Cluster sampling has a lower level of precision and accuracy compared to other types of sampling methods.Cluster sampling increases the standard error of the estimate, making it difficult to achieve the desired level of statistical significance.A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.
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PLEASE HELP! Will mark Brainliest!
V(t) = P(1 + r)t
In this function, if the value of r were to increase, would the value represented by P also increase or stay the same? Why? Explain your answer using terms such as "rate of growth" and "initial value" in the context of the coin problem.
Base: (1+r)
Constant: P
Exponent: t
THANK YOUUU!!!
Answers
Given the function V(t) = P(1+r)^t, if r or t increases, P remain the same, the variable that changes if r or t changes is V(t).
The given function is:
V(t) = P(1+r)^t
This is an exponential growth function, where:
P = initial value
r = growth rate
t = time in exponent
In a function, there are independent variables, constants, and dependent variables. Independent variables are the inputs, whereas dependent variables are the output.
It is called dependent variable because its values depends on the input. Usually, the dependent variable is written along with the independent variables that affect it.
Example:
f(x) = 2x + 1 <--- here, f(x) is the dependent variable of which its value depends on the value of x, the independent variables.
In the given function, the dependent variable is V(t) and it is a function of t.
P is a constant and not a function of t or r.
Hence, if r or t increases, P remain the same, the variable that changes if r or t changes is V(t).
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with a reserve requirement of 5% and an initial deposit of $400, what is the maximum total amount of money that will be in the money supply? assume that all currency is deposited in a bank 7 banks hold no excess reserves (rr=.05)
Answers
The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.
How to find maximum money?To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.
The money multiplier is given by the formula: MM = 1 / reserve requirement.
Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.
The initial deposit is $400.
To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:
Maximum Money Supply = Initial Deposit * Money Multiplier
= $400 * 20
= $8,000.
Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.
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A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula P t = P o 2 t d , where P o is the original number of bacteria cells, P t is the number after t hours, and d is the time taken to double the number.
Answers
Answer:
Step-by-step explanation:
Explanation:
I would write the growth function as:
y
=
100
e
k
t
So that at
t
=
0
we get:
y
=
100
e
0.02
⋅
0
=
100
bacteria.
At
t
=
5
hours we will get:
y
=
100
e
5
⋅
0.02
=
110
bacteria.
To double the initial number we need to solve:
200
=
100
e
0.02
t
e
0.02
t
=
2
Apply natural logs to both sides:
ln
(
e
0.02
t
)
=
ln
(
2
)
0.02
t
=
ln
(
2
)
t
=
ln
(
2
)
0.02
=
34.65
≈
34.6
34
hours and 36 minutes approx.
Which table represents a linear function?
Answers
Answer:
My laptop doesn't make me see images, but its the one where you subtract the x coordinates and it has the same answer and when you subtract the y coordinates, it has the same answer
Step-by-step explanation:
Imagine: x = 2, 4, 6, 8, 10 and y = 4, 8, 12, 16, 20
For the x,
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
10 - 8 = 2
Notice how the answers are all equal to 2
And for the y,
8 - 4 = 4
12 - 8 = 4
16 - 12 = 4
20 - 16 = 4
Notice how the answers are all equal to 4
Good luck!
PLESE ANSWER NUMBER 8 ASAP !!!!!
Answers
Answer:
the first one
Step-by-step explanation:
1. Find )!xn(!x !n − if n = 8 and x = 3.
2. Find )!xn(!x !n − if n = 8 and x = 1.
3. Find )!xn(!x !n − if n = 8 and x = 0.
4. Find )!xn(!x !n − if n = 52 and x = 2.
Answers
The values are:
C(8, 3) = 56
C(8, 1) = 56
C(8, 0) = 1
C(52, 2) = 1,326
To clarify, I assume you are referring to the binomial coefficient notation (n choose x), where n is the total number of items and x is the number of items chosen. The binomial coefficient is also denoted as C(n, x) or Cnx.
Using the binomial coefficient formula, we can calculate the values you provided:
C(8, 3) = 8! / (3!(8 - 3)!) = 8! / (3!5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
C(8, 1) = 8! / (1!(8 - 1)!) = 8! / (1!7!) = (8 * 7) / 1 = 56
C(8, 0) = 8! / (0!(8 - 0)!) = 8! / (0!8!) = 1
C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2!50!) = (52 * 51) / (2 * 1) = 1,326
Therefore, the values are:
C(8, 3) = 56
C(8, 1) = 56
C(8, 0) = 1
C(52, 2) = 1,326
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which expression is equal to 6 (3x+4) ?
Answers
Answer: 18x+24
Step-by-step explanation:
An IVPB bag has a strength of 100 mg of a drug in 200 mL of NS. The dosage rate is 0.5 mg/min. Find the flow rate in ml/h.
Answers
The flow rate of the IVPB bag is 12,000 mL/h.
To find the flow rate in mL/h (milliliters per hour), we need to convert the dosage rate from mg/min (milligrams per minute) to mL/h.
Given:Strength of the drug in the IVPB bag: 100 mg in 200 mL
Dosage rate: 0.5 mg/min
First, let's find the time it takes to administer the entire contents of the IVPB bag:
Dosage rate = Amount of drug / Time
Time = Amount of drug / Dosage rate
= 100 mg / 0.5 mg/min
= 200 min
Since the bag contains 200 mL of fluid and it takes 200 minutes to administer, the flow rate can be calculated as follows:
Flow rate = Volume of fluid / Time
Flow rate = 200 mL / 200 min
Now, to convert the flow rate to mL/h:
Flow rate = (200 mL / 200 min) * (60 min / 1 h)
= (200 * 60) mL/h
= 12,000 mL/h
Therefore, the flow rate of the IVPB bag is 12,000 mL/h.
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How do I find the angle x if the supplement of the angle is 8 times the angle?
Answers
Answer:
20°
Step-by-step explanation:
According to the question, pair of supplementary angles are x and 8x
since they are supplementary, their sum is equal to 180°
x+ 8x = 180°
9x= 180°
x= 180°/9
x= 20°
a data set consists of 145 observations that range from 56 to 490. what size class interval would you recommend? (round up to the next whole number.)
Answers
The size class interval recommend is 30.
Assume that the observations are more or less evenly distributed across the range, and you should get about 5 observations per class.
It also presumes that your interest in the observations is uniform: you are equally interested in values close to 60 as you are in values close to 480. If you were only interested in values above 450, you could group all values from 56 to 449 into one large class and divide the rest into smaller classes.
It is also necessary to check to see if the distribution is uniform. If it is skewed in either direction, it makes more sense to have smaller classes where the observations are dense and larger classes where they are sparse.
Therefore, the size class interval recommend is 30.
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what is the value of 9 in 56.279
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(2,3), m = -4
I need to write it in standard form
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Answer:
4x +y = 11
Step-by-step explanation:
\(y - y_{1}=m(x-x_{1}\))
y - 3 = -4(x - 2)
y - 3 = -4x + 8
4x + y -3 = 8
4x + y = 8+3
4x + y = 11
=========================================================
Explanation:
The point slope form is
\(y-y_1 = m(x-x_1)\\\\\)
where m is the slope and \((x_1,y_1)\) is a point on the line
We have this given info
\(m = -4\)
\(x_1 = 2\)
\(y_1 = 3\)
Which means....
\(y-y_1 = m(x-x_1)\\\\y-3 = -4(x-2)\\\\y-3 = -4x+8\\\\y = -4x+8+3\\\\y = -4x+11\\\\\)
That last equation is in slope intercept form y = mx+b
Standard form is Ax+By = C. Let's add 4x to both sides
\(y = -4x+11\\\\y+4x = 11\\\\4x+y = 11\)
This equation is in standard form Ax+By = C
A = 4
B = 1
C = 11
What is the constant of proportionality for the relationship shown in this table? PLEAAASE I WILL MAKE U BRAINLIEST
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Answer: 3
Step-by-step explanation:
Divide the x numbers by 3 to then get the y numbers
Example: 3 divided by 1 is 3, 6 divided by 2 is 3, and it goes on!
once again the final answer is 3
hope this helps!
The mean weight of a domestic house cat is 8.9 pounds with a standard deviation of 1.1 pounds. The distribution of domestic house cat weights can reasonably be approximated by a normal distribution. What proportion of domestic house cats weigh less than 7 pounds?
Answers
Answer:
0.0421
Step-by-step explanation:
We solve using the z score formula
z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean = μ = 8.9 pounds
σ is the population standard deviation = σ = 1.1 pounds
For x < 7 pounds
z = 7 - 8.9/1.1
= -1.72727
Probability value from Z-Table:
P(x<7) = 0.042059
Therefore, the proportion of domestic house cats weigh less than 7 pounds is
0.042059
Approximately = 0.0421
Let O be an angle in quadrant IV such that sec =
17/8
Find the exact values of cot and sin.
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dr. huang required half of a group of healthy volunteers to study a reading passage for 1 hour. the other half of the participants studied for 15 minutes. dr. huang then administered a test of participants' memory of details from the passage. what was the dependent variable?
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The correct answer is results of the memory test.
Given that,
Dr. Huang asked the healthy volunteers in a group to read a chapter for an hour. The other half of the attendees spent 15 minutes studying. Dr. Huang next asked participants to recall specifics from the paragraph in a test.
To find :what was the dependent variable ?
It is something on which other elements depend. The test score for a instance, may be the dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were.
Therefore, the correct answer is results of the memory test.
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