Answer:
Question 1 = D) Acute
Question 2 = C)3 feet
Question 3 = D) Obtuse
Question 4 = C)27.73 ft.
Step-by-step explanation:
Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths
5 = a, 6 = b and c = 7
a² + b² = c²
5² + 6² = 7²
25 + 36 = 49
61 = 49
61 ≠ 49, Hence 61 > 49
Therefore, this is an Acute Triangle
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
This is question that deals with proportion.
The formula to solve for this:
Height of the statue/ Length of the shadow of the person = Height of the person/ Length of the shadow of the person
Height of the statue = 15 feet
Length of the shadow of the person = 20 feet
Height of the person = unknown
Length of the shadow of the person = 4
15/ 20 = Height of the person/4
Cross Multiply
15 × 4 = 20 × Height of the person
Height of the person = 15 × 4/20
= 60/20
Height of the person = 3 feet
Therefore, the person is 3 feet tall.
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths 17, 12, 9
9 = a, 12 = b and c = 17
a² + b² = c²
9² + 12² = 17²
81 + 144 = 289
225 = 289
225 ≠ 289
225 < 289
Hence, This is an Obtuse Triangle.
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
To calculate how far apart the two friends are we use the formula
Distance = √ ( Length² + Breadth²)
We are given dimensions: 12ft by 25ft
Length = 12ft
Breadth = 25ft
Distance = √(12ft)² + (25ft)²
Distance = √144ft²+ 625ft²
Distance = √769ft²
Distance = 27.730849248ft
Approximately ≈27.73ft
Therefore, the friends are 27.73ft apart.
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
Factor this trinomial completely. -6x^2 +26x+20
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
2000 people attended a baseball game. 1300 of the people attending supported the home team, while 700 supported the visiting team. What percentage of people attending supported the home team?
Answer:
Percentage of home team supporters =65%
Percentage of visiting team supporters =35%
Step-by-step explanation:
Total attendees=2,000 people
Home team supporters=1,300
Visiting team supporters=700
What percentage of people attending supported the home team?
Percentage of people attending who supported the home team = home team supporters / total attendees × 100
=1,300/2,000 × 100
=0.65 × 100
=65%
Visiting team supporters = visiting team supporters / total attendees
× 100
=700/2000 × 100
=0.35 × 100
=35%
Alternatively,
Visiting team supporters = percentage of total attendees - percentage of home team supporters
=100% - 65%
=35%
What number is the opposite of -3?
Explain your reasoning
Nan lives 13 miles from the airport. Felipe lives 6 miles from the airport.
How many more miles does Nan live from the airport than Felipe?
Answer:
7
Step-by-step explanation:
it's simply 13 - 6
7 it the answer, that was easy
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
The graph of y = −4x2 + 13x + 12 is shown below. What are the zeros of the function (as exact values), the y-intercept, and the maximum or minimum value of the function?
Answer:
zeros: -3/4, 4y-intercept: 12maximum: 22 9/16Step-by-step explanation:
The graph tells you the zeros of the function are x=-3/4 and x=4.
The y-intercept is the constant in the function: 12.
The maximum is 22.5625 at x = 1.625.
For
90° < 0 < 270°
, which of the primary trigonometric functions may have positive values?
Answer:
sine and tangent
will be positive.
You work for a pharmacy and monthly sales of asthma inhalers in your pharmacy follows a normal distribution with a mean of 191 inhalers per month and a standard deviation of 21 due to a storm the next shipment of inhalers did not arrive. The pharmacy only has 163 inhalers currently in stock and available to sell for the current month. What is the z score corresponding to selling 163 inhalers?
Answer: -1.33 .
Step-by-step explanation:
Formula to find the Z-score :
[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]
Given: Mean = 191 and Standard deviation = 21
Then , the z-score corresponding to the expected value of 163 will be :
[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]
Hence, the z score corresponding to selling 163 inhalers is -1.33 .
A researcher would like to test the claim that the mean lung capacity of middle-aged smokers is less than the mean lung capacity of senior citizen nonsmokers. Independent random samples of 34 middle-aged smokers and 34 senior citizen nonsmokers will be used in a hypothesis test of this claim, and it is believed that the standard deviations of the lung capacities in the populations of middle-aged smokers and senior citizen nonsmokers are the same. Which test statistic formula should be used for this test
Answer:
The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]
Cheers.
Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
What is composite functionThe composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.
In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.
Solving a composite function means finding the composition of two functions.
Function p(t)The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:
s(t)= q[p(t)]
4t -21= 4[p(t)]³ – 1
Solving:
4t -21 +1= 4[p(t)]³
4t -20 = 4[p(t)]³
(4t -20)÷ 4 = [p(t)]³
4t÷4 -20÷ 4 = [p(t)]³
t -5 = [p(t)]³
[tex]\sqrt[3]{t-5}=p(t)[/tex]
Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
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Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.
Answer:
The Variable has a coefficient.
Step-by-step explanation:
Find the value of x.
A. 22
B. 7.3
C. 3.6
D. 5.5
Answer:
x= 5.5
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
x*4 = 11*2
4x = 22
Divide each side by 4
4x/4 = 22/4
x =5.5
This test statistic leads to a decision to...
reject the null
accept the null
fail to reject the null
As such, the final conclusion is that...
There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.
There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 88.9.
The sample data support the claim that the population mean is not equal to 88.9.
There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.
Answer:
There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.
Step-by-step explanation:
We are given the following hypothesis below;
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 88.9 {means that the population mean is equal to 88.9}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 88.9 {means that the population mean is different from 88.9}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 81.3
s = sample standard deviation = 13.4
n = sample size = 7
So, the test statistics = [tex]\frac{81.3-88.9}{\frac{13.4}{\sqrt{7} } }[/tex] ~ [tex]t_6[/tex]
= -1.501
The value of t-test statistics is -1.501.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_6[/tex] < -1.501) = 0.094
Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that the population mean is equal to 88.9.
What is the area, in square meters, of the shaded part of the rectangle shown below?
Answer:
C) 100 cm²
Step-by-step explanation:
(14*6)/2*10
20/2*10
10*10
100
The area of the given shaded part of the rectangle is 100 square meters as shown.
What is the area of a triangle?The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.
The fundamental formula for calculating the area of a triangle is A = 1/2 b h.
The area of the shaded part = area of the rectangle - area of the triangle
The area of the shaded part = 14 × 10 - (1/2) × 8 × 10
The area of the shaded part = 140 - 80/2
The area of the shaded part = 140 - 40
Apply the subtraction operation, and we get
The area of the shaded part = 100 meters²
Thus, the area of the given shaded part of the rectangle is 100 square meters.
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What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
Write a variable expression for a number w increased by 4 (A) 4 ÷ w (B) w + 5 (C) w + 4
Answer:
C) w+4
Step-by-step explanation:
w=the variable
+4= increased by 4
HOPE THIS HELPS!!!!!! :)
<33333333333
Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.Solve for x (x+4)/3 = 2.
a. x = -2
b. x=2
c. x = 2/3
d. x= -10/3
Answer:
The answer is option BStep-by-step explanation:
[tex] \frac{x + 4}{3} = 2[/tex]
To solve it first of all cross multiply
That's
x + 4 = 6
Move 4 to the right side of the equation
The sign changes to negative
That's
x = 6 - 4
We have the final answer as
x = 2Hope this helps you
Ajar contains 4 red marbles numbered 1 to 4 and 10 blue marbles numbered 1 to 10. A marble is
drawn at random from the jar. Find the probability of the given event.
(a) The marble is red
Your answer is:
(b) The marble is odd-numbered
Your answer is:
(C) The marble is red or odd-numbered
Your answer is:
(d) The marble is blue or even-numbered
Your answer is:
Question Help M Message instructor
Answer:
a)2/7
b)1/2
c)9/14
d)6/7
Step-by-step explanation:
The jar contains 4 red marbles, numbered 1 to 4 which means
Red marbles = (R1) , (R2) , (R3) , (R4)
It also contains 10 blue marbles numbered 1 to 10 which means
Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .
We can calculate total marbles = 4red +10 blues
=14marbled
Therefore, total marbles= 14
The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7
Total number of Blue marbles = 10
Blue and even marbles = 5
(a) The marble is red
P(The marble is red)=total number of red marbles/Total number of marbles
=4/14
=2/7
(b) The marble is odd-numbered
Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,
Red marbles with odd number = (R1) , (R3)
Number of odd numbered =(5+2)=7
P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles
P(marble is odd-numbered )=7/14
=1/2
(C) The marble is red or odd-numbered?
Total number of red marbles = 14
Number of red and odd marbles = 2
The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7
n(red or even )= n(red) + n(odd)- n(red and odd)
=4+7-2
=9
P(red or odd numbered)= (number of red or odd)/(total number of the marble)
= 9/14
(d) The marble is blue or even-numbered?
Number of Blue and even marbles = 5
Total number of Blue marbles = 10
Number of blue that are even= 5
The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)
=7
n(Blue or even )= n(Blue) + n(even)- n(Blue and even)
= 10+7-5 =12
Now , the probability the marble is blue or even numbered can be calculated as
P(blue or even numbered)= (number of Blue or even)/(total number of the marble)
= 12/14
= 6/7
Which expression is equivalent to 2(5)^4
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
While walking from the car into your dormitory you dropped your engagement ring somewhere in the snow. The path is 30 feet long. You are distraught because the density of its location seems to be constant along this 30-foot route. a) What is the probability that the ring is within 12 feet of your car
Answer:
0.4
Step-by-step explanation:
we are required to find the probability that the ring is within 12 meters from nthe car.
we start by defining a random variable x to be the distance from the car. the car is the starting point.
x follows a normal distribution (0,30)
[tex]f(x)=\frac{1}{30}[/tex]
[tex]0<x<30[/tex]
probabilty of x ≤ 12
= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]
a = 12
b = 0
[tex]\frac{1}{30} *(12-0)[/tex]
[tex]\frac{12}{30} = 0.4[/tex]
therefore 0.4 is the probability that the ring is within 12 feet of your car.
Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600
Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
================================================
Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
-----------
Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
The equation before the problem is
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²
X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²
The right side of the equation now has a common denominator
The next step is to factorize the left side of the equation.
(X+b/2a)²= ( b²-4ac)/4a²
Squaring both sides
X+b/2a= √(b²-4ac)/√4a²
Final equation
X=( -b+√(b²-4ac))/2a
Or
X=( -b-√(b²-4ac))/2a
Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25
x y
1 5
2 20
3 45
4 80
5 125
x y
1 5
2 25
3 125
4 625
5 3125
x y
1 2
2 4
3 7
4 16
5 32
Answer:
The first table on the list:
x 1 2 3 4 5
y 5 10 15 20 25
Step-by-step explanation:
A linear equation is when the slope is the exact same between each point. The way we find slope is by finding the change in "y" over the change in "x".
x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5
x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5
x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5
x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5
The slope for each change in points is 5, which means that this table represents a linear function.
The only table that represents a linear function is; Table 1
Linear functionA linear function is one that has the same slope for every coordinate point.
Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;
At x = 1, y = 5 and;Slope = 5/1 = 5
At x = 2; y = 10 and;Slope = 10/2 = 5
At x = 3, y = 15 and;Slope = 15/3 = 5
At x = 4, y = 20 and;Slope = 20/4 = 5
At x = 5, y = 25 and;slope = 25/5 = 5
In conclusion, only table 1 represents a linear function.
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Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
Find and interpret a 95% confidence interval to estimate the average number of bolts per box for all boxes in the population. Round to 3 decimal places.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]49.85 < \mu < 54.15[/tex]
This means that there is 95% chance that the true population mean is within this interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 52[/tex]
The population standard deviation is [tex]\sigma = 6[/tex]
Given that the confidence level is 95% then the level of confidence is evaluate as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]
[tex]E = 2.147[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]52 - 2.147 < \mu < 52 + 2.147[/tex]
[tex]49.85 < \mu < 54.15[/tex]
Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 13 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
Answer:
$1344.9Step-by-step explanation:
This problem can be solved using the compound interest formula
[tex]A= P(1+r)^t[/tex]
Given data
A, final amount =?
P, principal = $586
rate, r= 6.6% = 0.066
Time, t= 13 years
Substituting our values into the expression we have
[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]
To the nearest cent the in 13 years the CD will be worth $1344.9
