Answer:
a) 21.58% probability that exactly 3 people are repeat offenders
b) 97.91% probability that at least one person is a repeat offender
c) 3.69
d) 1.83
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders
This means that [tex]p = 0.09[/tex]
41 people arrested for DUI in Illinois are selected at random.
This means that [tex]n = 41[/tex]
a. What is the probability that exactly 3 people are repeat offenders?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158[/tex]
21.58% probability that exactly 3 people are repeat offenders
b. What is the probability that at least one person is a repeat offender?
Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex].
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791[/tex]
97.91% probability that at least one person is a repeat offender
c. What is the mean number of repeat offenders?
[tex]E(X) = np = 41*0.09 = 3.69[/tex]
d. What is the standard deviation of the number of repeat offenders?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83[/tex]
Evaluate the expression. StartFraction 9 factorial Over 3 factorial EndFraction 3 6 60,480 362,874
Answer:
60,480 is the correct answer.
Step-by-step explanation:
First of all, let us have a look at the formula of factorial of a number 'n':
[tex]n! = n \times (n-1) \times (n-2) \times ...... \times 1[/tex]
i.e. multiply n with (n-1) then by (n-2) upto 1.
Keep on subtracting 1 from the number and keep on multiplying until we reach to 1.
So, [tex]9![/tex] can be written as: [tex]9 \times 8 \times 7 \times ...... \times 1[/tex]
Similarly [tex]3![/tex] can be written as: [tex]3 \times 2 \times 1[/tex]
Re-writing [tex]9 ![/tex] :
[tex]9 \times 8 \times 7 \times ...... 3 \times 2 \times 1\\\Rightarrow 9 \times 8 \times 7 \times ...... 3 ![/tex]
Now, the expression to be evaluated:
[tex]\dfrac{9!}{3!} = \dfrac{9 \times 8 \times 7 \times ..... \times 3!}{3!}\\\Rightarrow 9 \times 8 \times 7 \times 6 \times 5 \times 4\\\Rightarrow 60480[/tex]
Answer:
60480
Step-by-step explanation:
WILL GET BRAINLIEST AND 20 POINTS!
Answer:
1) 2(x-1)^2
2) y=2(x-1)^2
Step-by-step explanation:
The 1st one is a statement in the terms of x, and the 2nd on is in the slope intercept(graphing) format
After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S year(t), is modeled by the following function: S year(t)=25,000,000⋅(0.78)t Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places. Every decade, the number of species decays by a factor of
Answer:
Every decade, the number of species decays by a factor of 0.0834.
Step-by-step explanation:
Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:
[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]
Every decade, the number of species decays by a factor of 0.0834.
Answer:
28% subtracted
Step-by-step explanation:
khan
Seventy-five cars sit on a parking lot. Thirty have stereo systems, 30 have air conditioners and 40 have sun roofs. Thirty of the cars have at least two of these three options, and 15 have all three.
Required:
a. How many cars on the lot have at least one of the three options?
b. How many have exactly one?
Answer:
a. 55 cars
b. 25 cars
Step-by-step explanation:
Let's call the number of cars with stereo systems N(ss), with air conditioners N(ac) and with sun roofs N(sr).
So we have that:
N(ss) = 30
N(ac) = 30
N(sr) = 40
N(ss and ac and sr) = 15
N(at least two) = 30
a.
To find how many cars have at least one option (N(at least one) or N(ss or ac or sr)), we have:
N(ss or ac or sr) = N(ss) + N(ac) + N(sr) - N(ss and ac) - N(ss and sr) - N(ac and sr) + N(ss and ac and sr)
N(ss or ac or sr) = 30 + 30 + 40 - (N(at least two) + 2*N(ss and ac and sr)) + 15
N(ss or ac or sr) = 30 + 30 + 40 - (30 + 2*15) + 15 = 55
b.
The number of cars that have only one option is:
N(only one) = N(at least one) - N(at least two)
N(only one) = 55 - 30 = 25
What is the leading coefficient of a cubic polynomial that has a value of −208 when x=1, and has zeros of 5, 5i, and −5i?
Answer:
2
Step-by-step explanation:
We already have the zeros, so we can write the cubic polynomial in this general form:
[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]
Where:
[tex]x_1 = 5[/tex]
[tex]x_2 = 5i[/tex]
[tex]x_3 = -5i[/tex]
So we have that:
[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]
[tex]y = a(x -5)(x^2 + 25)[/tex]
To find the value of the leading coefficient 'a', we can use the point (1, -208) given:
[tex]-208 = a(1 -5)(1 + 25)[/tex]
[tex]-208 = a(-4)(26)[/tex]
[tex]a = -208 / (-104) = 2[/tex]
So the leading coefficient is 2.
please answer thank you
Answer:
Option A
Step-by-step explanation:
Given function is,
f(x) = x² + 3x + 5
We have to find the value of f(a + h) so we will substitute (a + h) in place of x, and simplify the expression.
f(a + h) = (a + h)² + 3(a + h) + 5
= a² + 2ah + h² + 3(a + h) + 5 [(a + b)² = a² + 2ab + b²]
= a² + 2ah + h² + 3a + 3h + 5
Therefore, Option A will be the answer.
Which expression has a positive value?
A - Negative 4 + (negative 5) (negative 6) divided by (negative 3)
B - 8 Left-bracket 10 divided by (2) (negative 2) Right-bracket
C - 3 (negative 64 divided by 8) + 25
D - Negative 2 (negative 5) (negative 3) divided by 10
Answer:
C - 3 (negative 64 divided by 8) + 25 =1
Step-by-step explanation:
Answer:
C is correct answer
Step-by-step explanation:
Single discount rate equavalent to a series of discounts 20% and 25% is
Answer:
The single discount rate equavalent is a discount of 40%.
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
Discount of 20%:
20% decrease:
1 - (20/100) = 1 - 0.2 = 0.8
Discount of 25%:
1 - (25/100) = 1 - 0.25 = 0.75
Series of discounts(20% and 25%):
0.8*0.75 = 0.6
1 - 0.6 = 0.4
The single discount rate equavalent is a discount of 40%.
The angle that is a
corresponding
angle with angle 1
is angle [?]
Answer:
2
Step-by-step explanation:
A corresponding angle is in the same position on another parallel line
1 and 2 are both above the parallel line and to the left of the transversal
1 and 2 are corresponding angles
Answer: Angle 2
Step-by-step explanation:
Corresponding Angles are angles that take up the same spot at independent vertices, with the same transversal. Both angle 1 and 2 are the top left angles of their vertex.
Hope it helps <3
The Mehta family's living room is shown in the scale drawing. Mrs. Mehta wants to carpet the room.
Which of the following could you use to find the
area?
This is a Multiple Response question. There is more than one correct answer. Choose all correct answers (and no incorrect answers) to receive
credit.
Answer:
Step-by-step explanation:
the second and last oneThe function g(x) is a transformation of the parent function f(x). Decide how f(x) was transformed to make (gx). Table f(x) x= -2, -1, 2, 3, 4 y= 1/9, 1/3, 9, 27, 81 Table g(x) x= -2, -1, 2, 3, 4 y= -17/9, -5/3, 7, 25, 79
I need answers this in 5min pls help!!
Answer:
f(x) translate 2 units down to get the function g(x).
Step-by-step explanation:
From the given tables it is clear that the x-values for both tables are -2,-1,2,3,4.
Difference between y-values of both functions are:
[tex]\dfrac{-17}{9}-\dfrac{1}{9}=-2[/tex]
[tex]\dfrac{-5}{3}-\dfrac{1}{3}=-2[/tex]
[tex]7-9=-2[/tex]
[tex]25-27=-2[/tex]
[tex]79-81=-2[/tex]
So, difference between y-values of both functions is constant, i.e., -2.
Now, we get
[tex]g(x)=f(x)-2[/tex]
It means function f(x) shifts 2 units down to get the function g(x).
Therefore, f(x) translate 2 units down to get the function g(x).
Answer: horizontal or vertical stretch
helppppppp pleassssseeeeee
Answer:
First blank is 4, second blank is 0
Step-by-step explanation:
divide it :)
Answer:
Yellow box #1=0
Yellow box #1=4
Step-by-step explanation:
find the product of (a + b + c) and (a + b)
Answer:
a² + 2ab + b² + ac + bc
Step-by-step explanation:
(a + b + c) * (a + b) = aa + ab + ac + ba + bb + bc
= a² + 2ab + b² + ac + bc
The trick you use here is called the distributive property.
Answer:
[tex]a^2+b^2+2ab+ac+bc[/tex]
Step-by-step explanation:
[tex](a+b+c(a+b)=\\a^2+ab+ac+ab+b^2+bc=\\a^2+b^2+ab+ab+ac+bc=\\a^2+b^2+2ab+ac+bc[/tex]
Consider the y-intercepts of the functions. f(x)= 1/5 [x-15] g(x)= (x-2)^2 The y-coordinate of the greatest y-intercept is..
Answer:
4
Step-by-step explanation:
I used Desmos
We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).
How to find the y-intercepts?For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.
So, for the first function:
[tex]f(x) = (1/5)*|x - 15|[/tex]
The y-intercept is:
[tex]f(0) = (1/5)*|0 - 15| = 15/5 = 3[/tex]
For the second function:
[tex]g(x) = (x - 2)^2[/tex]
The y-intercept is:
[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]
Then we can see that g(x) has a greater y-intercept than f(x).
If you want to learn more about y-intercepts:
https://brainly.com/question/1884491
#SPJ2
A survey found that the average daily cost to rent a car in Los Angeles is $102.24 and in Las Vegas is $97.35. The data were collected from two random samples of 40 in each of the two cities and the population standard deviations are $5.98 for Los Angeles and $4.21 for Las Vegas. At the 0.05 level of significance, construct a confidence interval for the difference in the means and then decide if there is a significant difference in the rates between the two cities. Let the sample from Los Angeles be Group 1 and the sample from Las Vegas be Group 2.Confidence Interval (round to 4 decimal places):
< mu1 - mu2 <
Is there a significant difference in the means?
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = average daily cost to rent a car in Los Angeles
x2 = average daily cost to rent a car in Las Vegas
s1 = sample standard deviation for Los Angeles
s2 = sample standard deviation for Las Vegas
n1 = number of sampled cars in Los Angeles
n2 = number of sampled cars in Las Vegas
Degree of freedom = (n1 - ) + (n2 - 1) = (40 - 1) + (40 - 1) = 38
For a 95% confidence interval, the t score from the t distribution table is 2.024
From the information given,
x1 = 102.24
s1 = 5.98
n1 = 40
x2 = 97.35
s2 = 4.21
n2 = 40
x1 - x2 = 102.24 - 97.35 = 4.89
Margin of error = z√(s1²/n1 + s2²/n2) = 2.024√(5.98²/40 + 4.21²/40) = 2.024√1.3371125
= 2.34
The 95% confidence interval is 4.89 ± 2.34
Hypothesis testing
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean average daily cost to rent a car in Los Angeles and μ2 be the the mean average daily cost to rent a car in Las Vegas
The random variable is μ1 - μ2 = difference in the mean average daily cost to rent a car in Los Angeles and the mean average daily cost to rent a car in Las Vegas
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 0
This is a two tailed test
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (102.24 - 97.35)/√(5.98²/40 + 4.21²/40)
t = 4.23
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [5.98²/40 + 4.21²/40]²/[(1/40 - 1)(5.98²/40)² + (1/40 - 1)(4.21²/40)²] = 1.78786983766/0.02552804373
df = 70
We would determine the probability value from the t test calculator. It becomes
p value = 0.00007
Since alpha, 0.05 > than the p value, 0.00007, then we would reject the null hypothesis. Therefore, at 5% significance level, there is sufficient evidence to conclude that there is a significant difference in the rates between the two cities.
Prove that 2x3 + 3x² + x is always divisible by 6 if x is an integer.
PLEASE I NEED THIS ANSWERED ASAP.
USE PROOF BY EXHAUSTION.
Answer: see proof below
Step-by-step explanation:
Proof by exhaustion means to input several numbers that satisfy the claim and if they all prove to be true then you have proven the claim.
Claim: (2x³ + 3x² + x)/(6) ∈ Z (integer)
Let's choose x = {1, 2, 3, 4)
Case 1: x = 1
2(1)³ + 3(1)² + (1) = 12
12/6 = 2
2 ∈ Z [tex]\checkmark[/tex]
Case 2: x = 2
2(2)³ + 3(2)² + (2) = 30
30/6 = 5
5 ∈ Z [tex]\checkmark[/tex]
Case 3: x = 3
2(3)³ + 3(3)² + (3) = 84
84/6 = 14
14 ∈ Z [tex]\checkmark[/tex]
Case 4: x = 4
2(4)³ + 3(4)² + (4) = 180
180/6 = 30
30 ∈ Z [tex]\checkmark[/tex]
Since each case was shown to be true we have proven the claim is true by exhaustion.
Within a school district, students were randomly assigned to one of two Math teachers - Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25 students. At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10: and Mrs. Jones' students had an average test score of 85, with a standard deviation of 15. Using the above information, answer the following question. a. State the null and the alternative hypothesis b. Calculate the degree of freedom for this estimation c. Estimate the value of the test statistic d. Estimate the confidence interval for the difference between the two student populations e. Using the Critical Value approach test the hypothesis that Mrs. Smith and Mrs. Jones are equally effective teachers. Use a 0.10 level of significance
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. Let μ1 be the mean score of Mrs. Smith's students and μ2 be the mean score of Mrs. Jones students.
The random variable is μ1 - μ2 = difference in the mean score of Mrs. Smith's students and the mean score of Mrs. Jones students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
From the information given,
μ1 = 78
μ2 = 85
s1 = 10
s2 = 15
n1 = 30
n2 = 25
df = [10²/30 + 15²/25]²/[(1/30 - 1)(10²/30)² + (1/25 - 1)(15²/25)²] = 152.11/3.37883141762
df = 45
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (78 - 85)/√(10²/30 + 15²/25)
t = - 1.99
d) Confidence interval = μ1 - μ2 ± z√(s1²/n1 + s2²/n2)
Where z is the t test score for the confidence level. Since alpha = 0.1, confidence level = 1 - alpha = 1 - 0.1 = 0.9. From the t distribution table, test score at df of 45 = 1.301
z√(s1²/n1 + s2²/n2) = 1.301√(10²/30 + 15²/25) = 4.57
Confidence interval = (78 - 85) ± 4.57
Confidence interval = - 7 ± 4.57
e) we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.
1 - α/2 = 1 - 0.1/2 = 1 - 0.05 = 0.95
The critical value is 1.679 on the right tail and - 1.679 on the left tail
Since - 1.99 < - 1.679, it is not in the rejection regions. Therefore, we would fail to reject the null hypothesis. Therefore, at 10% significance level, there is insufficient evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.
Add. Answer as a fraction. Do not include spaces in your answer. Do not include spaces in your answer.
Answer: 49/9
Step-by-step explanation: 42/9 + 7/9 = 49/9
Make first fraction into improper fraction with the same common dominator as 7/9 and add them both
Hope this helps:)
Answer:
49/9
Step-by-step explanation:
Which of the following numbers would be used to get the variable by itself in the equation 7x = 12?
Answer:
Divide by 7 or multiply by 1/7
Step-by-step explanation:
7x = 12
Divide each side by 7
7x/7 = 12/7
x = 12/7
We could also multiply each side by 1/7
7x * 1/7 = 12*1/7
x = 12/7
How large a sample should be selected to provide a 95% confidence interval with a margin of error of 4? Assume that the population standard deviation is 40. Round your answer to next whole number.
Answer:
The large sample size 'n' = 384.16
Step-by-step explanation:
Explanation:-
Given Margin of error = 4
Given Population standard deviation(σ) = 40
The margin of error is determined by
[tex]M.E = Z_{0.05} \frac{S.D}{\sqrt{n} }[/tex]
[tex]4 = 1.96 \frac{40}{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = \frac{40 X 1.96}{4}[/tex]
√ n = 19.6
squaring on both sides , we get
n = 384.16
Final answer:-
The large sample size 'n' = 384.16
A dinner at a restaurant was advertised at $60 plus 18% tax. The total bill for this dinner was. Show working plss
Answer:
Total bill = $70.80
Step-by-step explanation:
$60 × 0.18 = $10.80
$60 + $10.80 = $70.80
Hope this helps! :)
Answer:
$70.8
Step-by-step explanation:
Since it is 18 percent tax,we need to find 18% of 60$.In order to do that we need to do 60/1 mutiplied by 18/100 and doing the math 18% of 60 =10.8
Now we have to add 60+10.8=$70.8
Thank you and I hope all you have an amazing day.Hope this helps you.Thank you.
From a group of 10 women and 15 men, a researcher wants to randomly select
women and men for a study in how many ways can the study group be selected?
O A 17,876
78,016,400
OG 105, 102,625
OD 00,000,000
WO
Answer:
The total number of ways the researcher can select 5 women and 5 men for a study is 7,56,756.
Step-by-step explanation:
The complete question is:
From a group of 10 women and 15 men, a researcher wants to randomly select 5 women and 5 men for a study in how many ways can the study group be selected?
Solution:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!\cdot (n-k)!}[/tex]
The number of women in the group: [tex]n_{w}=10[/tex].
The number of women the researcher selects for the study, [tex]k_{w}=5[/tex]
Compute the total number of ways to select 5 women from 10 as follows:
[tex]{n_{w}\choose k_{w}}=\frac{n_{w}!}{k_{w}!\cdot (n_{w}-k_{w})!}=\frac{10!}{5!\cdot (10-5)!}=\frac{10!}{5!\times 5!}=252[/tex]
The number of men in the group: [tex]n_{m}=15[/tex].
The number of men the researcher selects for the study, [tex]k_{m}=5[/tex]
Compute the total number of ways to select 5 men from 15 as follows:
[tex]{n_{m}\choose k_{m}}=\frac{n_{m}!}{k_{m}!\cdot (n_{m}-k_{m})!}=\frac{15!}{5!\cdot (15-5)!}=\frac{15!}{5!\times 10!}=3003[/tex]
Compute the total number of ways the researcher can select 5 women and 5 men for a study as follows:
[tex]{n_{w}\choose k_{w}}\times {n_{m}\choose k_{m}}=252\times 3003=756756[/tex]
Thus, the total number of ways the researcher can select 5 women and 5 men for a study is 7,56,756.
The data represents the number of minutes dan spent on his homework each night 30, 35, 35, 45, 46, 52, 55, 57. Which box plot correctly represents the data
Answer:
Option C
Step-by-step explanation:
The datasets is incomplete. Here is the correct question.
The data represents the number of minutes dan spent on his homework each night 30, 35, 35, 45, 46, 46 52, 55, 57. Which box plot correctly represents the data
The question lacks the required option. Find the options in the diagram below:
To get the correct box plot to represent the data, we need to calculate the lower quartile, median and the upper quartile of the data.
Since our data is already in increasing order of magnitude we can go ahead and calculate this parameters.
To get the lower quartile, we will find Q1 first.
Q1 = N+1/4 th value.
This means we have to locate the N+1/4 the value.
N is the total number present in the dataset = 9
Q1 = 9+1/4 = 10/4
Q1 = 2.5th value
This equivalent is the third value in the dataset.
Hence, our lower quartile is 35
Median is the middle value after rearrangement.
Based on the datasets, the value at the middle is 46 by inspection.
For the upper quartile Q3,
Q3 = 3(N+1)/4 th value
Q3 = 3(9+1)/4
Q3 = 30/4
Q3 = 7.5th value
The upper quartile is the 8th value in the dataset i.e 55
Based on the box plots, the only box that correctly plots this values [35, 46 and 55] is the third option.
Answer:
A
Step-by-step explanation:
edg2020
Solve the system by the method of substitution.
1.5x + 0.8y = 2.3
0.3x − 0.2y = 0.1
Answer:
[tex]\boxed{\sf \ \ \ x = 1 \ \ , \ \ y = 1 \ \ \ }[/tex]
Step-by-step explanation:
hello
we can multiply by 10 both parts of the equations so this is equivalent to
(1) 15x + 8y = 23
(2) 3x - 2y = 1
and we are asked to use the method of substitution
from (2) we can write 3x = 2y + 1
and we substitute 3x in (1) as 15x = 5*3x it comes
5*(2y+1) + 8y = 23
<=> 10y + 5 + 8y = 23
<=> 18y + 5 = 23 let's subtract 5
<=> 18y = 23 - 5 = 18 let's divide by 18
<=> y = 1
and finally replace y in 3x = 2y + 1
3x = 2*1 + 1 = 3 <=> x = 1 (divide by 3)
so the solution is x = 1, y = 1
hope this helps
Answer:
(1,1)
Step-by-step explanation:
1.5x + 0.8y = 2.3
0.3x − 0.2y = 0.1
I'm going to multiply both of these equations by 10, so we can work with whole numbers.
15x+8y=23
3x-2y=1
We can simplify one of the equations to isolate a variable.
I'm going to isolate y in equation 2.
3x-2y=1
Subtract 3x from both sides.
-2y=-3x+1
Divide both sides by -2.
y=1.5x-0.5
Plug 1.5x-0.5 into the first equation for y.
15x+8(1.5x-0.5)=23
Distribute.
15x+12x-4=23
Combine like terms.
27x-4=23
Add 4 to both sides.
27x=27
Divide both sides by 27.
x=1
Plug that back into original equation to find y.
15(1)+8y=23
15+8y=23
Subtract 15 from both sides.
8y=8
Divide both sides by 8.
y=1
The solution to the system is (1,1).
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 4 x , a = −2
Answer:
4x
Step-by-step explanation:
The Taylor series of a function f(x) about a value x = a is given by f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ... where the terms in f prime f'(a) represent the derivatives of x valued at a.
For the given function, f(x) = 4x and a = -2
So, f(a) = f(-2) = 4(-2) = -8
f'(a) = f'(-2) = 4
All the higher derivatives of f(x) evaluated at a are equal to zero. That is f''(a) = f'"(a) =...= 0
Substituting the values of a = -2, f(a) = f(-2) = -8 and f'(-2) = 4 into the Taylor series, we have
f(x) = f(-2) + f'(-2)(x - (-2))/1! + f''(-2)(x - (-2))²/2! + f'''(-2)(x - (-2))³/3! +...
= -8 + 4(x + 2)/1! + (0)(x + 2)²/2! + (0)(x + 2)³/3! +...
= -8 + 4(x + 2) + 0 + 0
= -8 + 4x + 8
= 4x
Tom, who is considering purchasing a new car, is comparing fuel efficiency between models by car-maker C1 and car-maker C2.
Answer: Car-maker C1
Explanation:
The minimum value is visually shown as the tip of the left whisker. For car-maker C1, the min value is 12. For car-maker C2, the min value is 10, which we can see is less than C1's value. So that's why C1 is the answer.
Evaluate 5 + 2(x + 7)2 for x = -4.
O A. 23
O B. 13
O C. 18
O D. 63
Hey there! :)
Answer:
A. 23.
Step-by-step explanation:
Given:
5 + 2(x + 7)² for x = -4
Substitute in -4 for x in the equation:
5 + 2((-4) + 7)²
5 + 2(3)²
5 + 2(9)
5 + 18 = 23.
Therefore, the correct answer is A. 23.
Answer:
23
Step-by-step explanation:
5 + 2(x + 7)^2
Let x =-4
5 + 2 ( -4+7)^2
Parentheses first
5 +2 (3)^2
5+ 2*9
Multiply
5+18
add
23
Provided that the ACT scores are reasonably normally distributed with a mean of 18 and standard deviation of 6, what is the proportion of students with a score of 24 or higher
Answer:
0.158655253931 or 15.8%
Step-by-step explanation:
What is the measure of angle RST? Help!!
Answer:
62
Step-by-step explanation:
Angle Formed by Two Chords = 1/2(sum of Intercepted Arcs)
RST = 1/2 ( 47+77)
= 1/2 (124)
= 62
How can (4x⁵/2x²)³ be solved in 2 different ways
We assume that we need to simplify the expression in two different ways.
Answer:
One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.
Second way: Simplify the terms inside parentheses, and then raise the result to the third power.
The result of both ways is the same: [tex] \\8x^{9}[/tex]
Step-by-step explanation:
One way
Raise both, the numerator and denominator, to the third power, and then simplify the expression:
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]
[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]
[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]
[tex] \\8x^{9}[/tex]
This is the first simplification.
Second way
Simplify the terms inside parentheses, and then raise the result to the third power.
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]
[tex] \\ (2*x^{5-2})^{3}[/tex]
[tex] \\ (2*x^{3})^{3}[/tex]
[tex] \\ (2^{3}*x^{3*3})[/tex]
[tex] \\ (8*x^{9})[/tex]
or [tex] \\ 8x^{9}[/tex].