Answer:
The rectangle is 5 inches long by 19 inches wide.
Step-by-step explanation:
Let's start by listing what we know:
The perimeter of a rectangle is 48 inches.The width of the rectangle is 4 inches more than 3 times the length of the rectangle.Let's represent the width with "w" and length with "l", and make a system of equations based on what we know.
[tex]\left \{ {{2w + 2l = 48} \atop {w = 3l + 4}} \right.[/tex]
Now, let's solve the system of equations using substitution:
[tex]2w + 2l = 48[/tex]
[tex]2 (3l + 4) + 2l = 48[/tex]
[tex]6l + 8 + 2l = 48[/tex]
[tex]8l + 8 = 48[/tex]
[tex]8l = 40[/tex]
[tex]l = 5[/tex]
The length of the rectangle is 5 inches.
Now, let's use this to solve for the width.
[tex]w = 3l + 4[/tex]
[tex]w = 3(5) + 4[/tex]
[tex]w = 15 + 4[/tex]
[tex]w = 19[/tex]
The width of the rectangle is 19 inches.
Let's check our work:
[tex]2w + 2l = 48[/tex]
[tex]2(19) + 2(5) = 48[/tex]
[tex]38 + 10 = 48[/tex]
[tex]48 = 48[/tex]
The results match, so our answer is correct.
The rectangle is 5 inches long by 19 inches wide.
Jacob Lee is a frequent traveler between Los Angeles and San Diego. For the past month, he wrote down the flight times in minutes on three different airlines. The results are:
Goust Jet Red Cloudtran
51 50 52
51 53 55
52 52 60
42 62 64
51 53 61
57 49 49
47 50 49
47 49
50 58
60 54
54 51
49 49
48 49
48 50
Required:
a. Use the α =0.05 significance level and the six-step hypothesis-testing process to check if there is a difference in the mean flight times among the three airlines.
b. Develop a 95% confidence interval for the difference in the means between Goust and Cloudtran
Solution :
We know that
[tex]$H_0: \mu_1 = \mu_2=\mu_3$[/tex]
[tex]$H_1 :$[/tex] At least one mean is different form the others (claim)
We need to find the critical values.
We know k = 3 , N = 35, α = 0.05
d.f.N = k - 1
= 3 - 1 = 2
d.f.D = N - k
= 35 - 3 = 32
SO the critical value is 3.295
The mean and the variance of each sample :
Goust Jet red Cloudtran
[tex]$\overline X_1 =50.5$[/tex] [tex]$\overline X_2 =50.07143$[/tex] [tex]$\overline X_3 =55.71429$[/tex]
[tex]$s_1^2=19.96154$[/tex] [tex]$s_2^2=14.68681$[/tex] [tex]$s_3^2=36.57143$[/tex]
The grand mean or the overall mean is(GM) :
[tex]$\overline X_{GM}=\frac{\sum \overline X}{N}$[/tex]
[tex]$=\frac{51+51+...+49+49}{35}$[/tex]
= 52.1714
The variance between the groups
[tex]$s_B^2=\frac{\sum n_i\left( \overline X_i - \overline X_{GM}\right)^2}{k-1}$[/tex]
[tex]$=\frac{\left[14(50.5-52.1714)^2+14(52.07143-52.1714)^2+7(55.71426-52.1714)^2\right]}{3-1}$[/tex]
[tex]$=\frac{127.1143}{2}$[/tex]
= 63.55714
The Variance within the groups
[tex]$s_W^2=\frac{\sum(n_i-1)s_i^2}{\sum(n_i-1)}$[/tex]
[tex]$=\frac{(14-1)19.96154+(14-1)14.68681+(7-1)36.57143}{(14-1)+(14-1)+(7-1)}$[/tex]
[tex]$=\frac{669.8571}{32}$[/tex]
= 20.93304
The F-test statistics value is :
[tex]$F=\frac{s_B^2}{s_W^2}$[/tex]
[tex]$=\frac{63.55714}{20.93304}$[/tex]
= 3.036212
Now since the 3.036 < 3.295, we do not reject the null hypothesis.
So there is no sufficient evidence to support the claim that there is a difference among the means.
The ANOVA table is :
Source Sum of squares d.f Mean square F
Between 127.1143 2 63.55714 3.036212
Within 669.8571 32 20.93304
Total 796.9714 34
1.) At a pet store, there are 30 aquariums. Of the 30, 20 have fresh water with 15
fish each. The other 10 aquariums have salt water with 6 fish each. Write an
equation that could be used to find f, the total number of fish at the pet store?
(Equations Review)
Your answer
Answer:
f = (20 × 15) + (10 × 6)
Step-by-step explanation:
You are just find how many fish are salt water and how many freshwater and adding them together. The total number of aquariums is irrelevant in this case.
Answer:
20 x 15 = A A= 300
10 x 6 = B B=60
A + B = F F= 360
300 + 60 = F
300 + 60 =360
Step-by-step explanation:
Pleasee marrkk me blainist
What is sin 0 when cot 0 = {?
0
(1,0)
sin e
Rationalize the denominator if necessary.
9514 1404 393
Answer:
(√6)/3
Step-by-step explanation:
The relation between cot(x) and sin(x) is ...
sin(x) = 1/√(cot(x)^2 +1)
Filling in the given value, we have ...
[tex]\displaystyle\sin{\theta}=\frac{1}{\sqrt{\left(\frac{\sqrt{2}}{2}\right)^2+1}}=\sqrt{\frac{2}{3}}\\\\\boxed{\sin{\theta}=\frac{\sqrt{6}}{3}}[/tex]
Step-by-step explanation:
#CarryOnLearning-. For the event of rolling three standard fair 6-sided dice, find the following probabilities. Give all
answers as a simplified fraction.
The probability of rolling a sum of 8 or a sum of 12.
P(Sum is 8 u Sum is 12)
Answer:
23/108
Step-by-step explanation:
Remark
There are 6 * 6 * 6 = 216 ways that you can throw three dice. There are 21 different ways of throwing an 8There are 25 different ways of throwing a 12I'll list the eights. The 12s are done the same way.Ways of making Eight
116125134143152161215224233242251314323332341413422431512521611Answer
P(8) = 21 / 216
P(12) = 25/ 216
P(8 or 12) = 21/216 + 25/216
P(8 or 12) = 46/216 = 23/108
The length of a rectangle is 54cm it's breadth is 8cm what is it's perimeter ? what is it's area?
Answer:
[tex]perimeter = 2(length + breadth) \\ =2 (54 + 8) \\ = 124 \: cm[/tex]
A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. Using the data provided below, calculate the p-value for the following hypothesis test:
H0:μ=131,520
Ha:μ≠131,520
Listeners after change
125,020
139,250
101,590
94,800
83,700
84,380
139,170
89,380
91,410
139,570
138,980
102,710
124,600
144,770
156,920
131,100
140,020
139,250
118,800
128,380
168,370
133,140
106,930
129,630
120,820
125,250
122,860
122,500
135,230
148,870
Answer:
The p value is: 0.0301
Step-by-step explanation:
Given
[tex]\mu = 131520[/tex]
[tex]\bar x = 124247[/tex]
[tex]n = 30[/tex]
Required
Determine the p value
First, calculate the standard deviation of the given data.
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(83700 - 124247)^2 + (84380- 124247)^2 + (89380- 124247)^2 + ..... + (156920- 124247)^2 + (168370- 124247)^2}{30}}[/tex]
[tex]\sigma = \sqrt{\frac{13427820070}{30}}[/tex]
[tex]\sigma = \sqrt{447594002.333}[/tex]
[tex]\sigma = 21156[/tex]
The test statistic is then calculated as:
[tex]t = \frac{\bar x - \mu}{\sigma/\sqrt n}[/tex]
[tex]t = \frac{124247 - 131520}{21156/\sqrt{30}}[/tex]
[tex]t = \frac{-7273}{21156/5.48}[/tex]
[tex]t = \frac{-7273}{3860.58}[/tex]
[tex]t = -1.88[/tex]
The p value is calculated as:
[tex]P(Z > -1.88)[/tex]
[tex]P(Z>-1.88) = 0.030054[/tex]
[tex]P(Z>-1.88) = 0.0301[/tex] --- approximated.
Hence, the p value is: 0.0301
All vectors and subspaces are in RnR n. Mark each statement True or False. Justify each answer.
a. Not every linearly independent set in RnR n is an orthogonal set.
b. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix.
c. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal.
d. A matrix with orthonormal columns is an orthogonal matrix.
e. If L is a line through 0 and if ˆyy^ is the orthogonal projection of y onto L, then ∥ˆy∥∥ y^ ∥ gives the distance from y to L.
Answer:
a. True
b. True
c. False
d. False
e. False
Step-by-step explanation:
The matrix with orthonormal column must be in square for that it forms orthogonal matrix. Every orthonormal set of non zero vector is linearly independent. This statement is correct because there is linear combination of non zero vectors.
Solve (x-3)^2=5 I need help it’s on a p e x
Answer:
x= 3 + or - √5
hope this helps
have a good day :)
Step-by-step explanation:
Simplify.
10/-4 - √3
Answer:
here you go. hope this helps
Answer:
-4.23205080...
Step-by-step explanation:
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answer:
.7880
Step-by-step explanation:
Answer:
pretty sure it's 0.7880 !!! good luck, this stuff is super tough :(
Step-by-step explanation:
rewrite
3/20
and
2/15
so that they have a common denominator.
Answer:
9/60 and 8/60
Step-by-step explanation:
They both have the number 60 in common
Graph triangle JKL and its image after a reflection in the line x=2 J(1,-1), K(3,0), L(0,-4)
Answer:
I need more information to help you on this question.
Step-by-step explanation:
The points after image reflection in the line x = 2 will be k'(1, 0), L'(4, -4) and J'(3, -1).
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question,
Here mirror (x = 2) is vertical, hence only x-coordinate changes vertical distance from x-axis will not change.
For point k(3, 0)
It is one unit right side or x = 2. So, its image point will be one unit left side that is k'(1, 0).
For point L(0, -4)
It is two unit left side, so L' will be 2 unit right side of x = 2, so the point will be L'(4, -4)
Similarly, point J(1, -1) will become J'(3, -1).
To know more about Graph:
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A writer buys a new laptop for $1866. Every year the laptop decreases in value by 20%.
Answer:
the answer is A
A function that represents a $1866 laptop that decreases in value by 20% each year is f(n)=1866(1.2)ⁿ.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that,
$1866 laptop that decreases in value by 20% each year.
Here, f(n)=1866(1+20%)ⁿ, where n is the number of years
f(n)=1866(1+20/100)ⁿ
f(n)=1866(1.2)ⁿ
Therefore, a function that represents a $1866 laptop that decreases in value by 20% each year is f(n)=1866(1.2)ⁿ.
To learn more about the function visit:
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he first date went well. You are still dating the same person and still looking for a great person to spend your life with. You are cautiously moving forward with the relationship and know that if they are a great match, their likelihood of being kind to animals is 0.9 whereas their likelihood of being kind to animals if they are not a great match is 0.7. You see that your prospective spouse is kind to animals. What is the probability that they are a great match now?
Answer:
0.125 = 12.5% probability that they are a great match now.
Step-by-step explanation:
To solve this question, we need the probability of a person being a great match, which i will use 0.1.
This question is solved using conditional probability.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Is kind to animals.
Event B: Is a great match.
Probability of being kind to animals:
0.9 of 0.1(Is a great match).
0.7 of 1 - 0.1 = 0.9(is not a great match). So
[tex]P(A) = 0.9*0.1 + 0.7*0.9 = 0.72[/tex]
Probability of being kind to animals and a great match:
0.9 of 0.1. So
[tex]P(A \cap B) = 0.9*0.1 = 0.09[/tex]
What is the probability that they are a great match now?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09}{0.72} = 0.125[/tex]
0.125 = 12.5% probability that they are a great match now.
What is the range of y = 7x^2 + 14x – 9?
Answer:
-1,-16
Step-by-step explanation:
y=ax^2+box+c
help I'll give brainliest!!!
LMNP is rotated 180° clockwise around the origin. M 3, 4) N54) 2 RE PX90) What are the coordinates of L'? A. L'(1,0) B. L'(-1,0) c. l'(0,1) D. L'(0, -1)
Answer:
It’s (-3, -4)
Step-by-step
I did this program too.
what is the surface area, in square inches, of the container?
Answer:
62 in
Step-by-step explanation:
You can split up the rectangles and find the surface area of each on them add them
Hope this helps!
Write integer to describe each situation. A. Charge of 24$ is debited from a bank account
Answer:
-24
Step-by-step explanation:
To represent a charge of $24 debited from a bank account, this type of transaction being described as a debit means that a sum of $24 was deducted from the account, meaning the total amount in the account will reduce after this transaction takes place. Hence a charge of $24 being debited will take a negative sign as could be represented by the integer - 24
i need help ASEP please help me
Answer:
5
Step-by-step explanation:
it is 5 because you do 1+4=5
Six scatterplots are shown. Suppose regression lines were generated for them, then order their correlation coefficients from least to greatest.
A) C, D, B, A, E, F
B) F, E, D, C, B, A
C) C, B, D, E, A, F
D) A, B, C, D, E, F
Answer:
C) C, B, D, E, A, F
Step-by-step explanation:
The closer the data points are to each other along the line of best fit on a scatter plot, the greater the correlation coefficient and vice versa.
Therefore, the scatter plot that has the least correlation coefficient would be the scatter plot with the data points that are farther apart from each other along the line of best fit which is C, followed by B, D, E, A, and F.
a system of equations is shown x-2y=-5 2x+4y=14
Answer: here you go
Step-by-step explanation:
A) 2x + 4y = 14
B) 4x + y = 20
If you multiply equation A by -2, then when the equations are added, the x will be eliminated.
The solutions are:
X = 4.714285714285714
Y = 1.1428571428571428
What linear expression would you add to -4y+2 to have a sum of y
Answer:
4
Step-by-step explanation:
Help pleaseeeeeeeeeeee
Answer;
Mark traveled at the highest velocity to Charleston
What are the coordinates of point S?
Write your answer as an integer or decimal to the nearest 0.5.
Answer:
(0,1.5)
Step-by-step explanation:
(x,y)
Christine's age is 6 more than Ken's age. Three times Ken's age plus 5 times
Christine's Age is equal to 46. How old is Christine?
Answer:
6x3+5=23
Step-by-step explanation:
Describe and correct the error in finding the distance between the points (−3 −2) and (7 4)
Answer:
[tex]2\sqrt{34}[/tex] ≈ 11.6619
Step-by-step explanation:
Answer: 6 units Step-by-step explanation: Use the distance formula, [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]. Plug the x and y values from the given points into the distance formula:
[tex]\sqrt{(7-[-3])^{2}+(4-[-2])^{2}}[/tex]
Simplify:
[tex]2\sqrt{34}[/tex] ≈ 11.6619
If this is what you wanted, please consider marking my answer as the Brainliest.
Thank you!
The distance between two coordinate points is 11.66 units.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
The given coordinate points are (-3, -2) and (7, 4)
Substitute (x₁, y₁) =(-3, -2) and (x₂, y₂)=(7, 4) in distance formula, we get
Distance = √[(7+3)²+(4+2)²]
= √(100+36)
= √136
= 11.66 units
Therefore, the distance between two coordinate points is 11.66 units.
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HELP!!!!? ASP! PLSSSS #14
The most expensive type of life insurance is
O limited-payment life insurance
O term insurance
O endowment life insurance
O whole-life insurance
Ann's rent increased from $1,200 to $1,350.
By what percent did her rent increase?
Answer: Percentage increase: 12.5%
Step-by-step explanation: (EXAMPLE) percentage increase/decrease = (Vnew - Vold) / Vold × 100%
Example #1
Price percentage increase from old value of $1000 to new value of $1200 is caluclated by:
percentage increase = ($1200 - $1000) / $1000 × 100%
= 0.2 × 100% = 20%
Answer:
12.5%
Step-by-step explanation:
1350 - 1200 / |1200| × 100% =
150 / 1200 × 100 = 12.5%
can someone explain how to solve and graph this step-by-step?