Answer:
(-1, 3)
Step-by-step explanation:
5x + 3y = 4
2x + y = 1 ⇒ y=1-2x
5x+3(1-2x)=45x+3-6x=4-x=4-3-x=1x=-1y= 1-2(-1)= 1+2=3Based on an indication that mean daily car rental rates may be higher for Boston than for Dallas, a survey of eight car rental companies in Boston is taken and the sample mean car rental rate is $47, with a standard deviation of $3. Further, suppose a survey of nine car rental companies in Dallas results in a sample mean of $44 and a standard deviation of $3. Use alpha = 0.05 to test to determine whether the average daily car rental rates in Boston are significantly higher than those in Dallas. Assume car rental rates are normally distributed and the population variances are equal. The null hypothesis for this problem is ______.
a) μ1 - μ2 < 0
b) μ1 - μ2 > 0
c) μ1 - μ2 = 1
d) μ1 - μ2 ≠ 0
e) μ1 - μ2 = 0
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean daily car rental rates for Boston and μ2 be the mean daily car rental rates for Dallas.
The random variable is μ1 - μ2 = difference in the mean daily car rental rates for Boston and the mean daily car rental rates for Dallas
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
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)
From the information given,
μ1 = 47
μ2 = 44
s1 = 3
s2 = 3
n1 = 8
n2 = 9
t = (47 - 44)/√(3²/8 + 3²/9)
t = 1.41
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 = [3²/8 + 3²/9]²/[(1/8 - 1)(3²/8)² + (1/9 - 1)(3²/9)²] = 4.515625/0.28571428571
df = 16
We would determine the probability value from the t test calculator. It becomes
p value = 0.09
Since alpha, 0.05 < than the p value, 0.09, then we would fail to reject the null hypothesis.
A grocery store sells one dozen ears of white corn for $2.40. What is the unit rate for one ear of corn?
Please include work! :)
Answer:
m = 13.
Step-by-step explanation:
Recall that adding logarithmic equations, (ex: log a + log b) is the same as log (a·b). Therefore:
log 12 + log 5 = log (4m + 8)
log (12·5) = log (4m + 8)
log (60) = log (4m + 8) **Ignore 'Log' to solve for 'm'
60 = 4m + 8 **Subtract both sides by 8
52 = 4m **Divide both sides by 4
m = 13.
Solve these equations. Thanks.
Answer:
1. 3.572 x 10^(-1)
2. 3.108 x 10^(6)
3. 5.31881533 x 10^(-6)
4. 4.18676122 x 10^(-1)
Hope this helps
Please I could really use some help on this (50 points, 5 stars and Brainliest)
Aunt Ga Ga gave you $5,500 to save for college. You deposit the money in a savings account that earns 4% annual interest, compounded quarterly. (Show your work for each question)
a. Write an exponential function to model this situation. Define your variables.
b. What will the value of the account be after 2 years?
c. how long would it take the account to be worth $10,000?
Answer:
(a)[tex]A(n)=5500(1.01)^{4n}[/tex]
(b)$5955.71
(c)15.02 years
Step-by-step explanation:
For an initial principal P deposited in an account at an annual interest r compounded for a number of period k, the amount in the account after n years is given by the model:
[tex]A(n)=P(1+\dfrac{r}{k})^{nk}[/tex]
(a)Aunt Ga Ga gave you $5,500 to save for college.
P=$5,500
Annual Interest, r=4%=0.04
Since interest is compounded quarterly, Number of Periods, k=4
Therefore, an exponential function modeling this situation is:
[tex]A(n)=5500(1+\dfrac{0.04}{4})^{4n}\\A(n)=5500(1+0.01)^{4n}\\$Simplified\\A(n)=5500(1.01)^{4n}[/tex]
(b)After 2 years, i.e. when n=2
[tex]A(2)=5500(1.01)^{4*2}\\=\$5955.71[/tex]
(c)When A(n)=$10000, we have:
[tex]10000=5500(1.01)^{4n}\\$Divide both sides by 5500\\(1.01)^{4n}=\dfrac{10000}{5500} \\$To solve for n, we change to logarithm form\\Log_{1.01}\dfrac{10000}{5500}=4n\\= \dfrac{ Log \dfrac{10000}{5500}}{Log 1.01}=4n\\4n=60.08\\n=60.08 \div 4\\n=15.02\\$Therefore, in 15.02 years, the account would be worth $10,000.[/tex]
What is another way to write the equation StartFraction 7 over 8 EndFraction x + three-fourths = negative 6?
Answer:
1/8 x + 3/4 = -6
Step-by-step explanation:
If you want to solve this as well:
1/8 x = -5 3/4
x = -42
Answer:
B
Step-by-step explanation:
Shianne is looking up at the flag on the top of the sailboat she is sailing on. She is sitting 16 feet from the bottom
of the flag, and her line of sight is 58° from horizontal. Her eyes are 6 feet above the bottom of the sail boat.
To the nearest foot, how high up is the flag from the bottom of the sailboat?
Answer:
height of the flag from the bottom of the boat ≈ 32 ft (nearest foot)
Step-by-step explanation:
She is on her boat and the angle of elevation to the top of the flag is 58°. Her eyes her 6 ft above the bottom of the boat she is sailing on. The height of the flag from the bottom of the boat is the sum of the height of the flag and the remaining height from the horizontal line of sight upward to the flag top.
A right angle triangle was formed Shianne line of sight. The angle from her line of sight is 58° from the horizontal. Therefore,
the adjacent side of the triangle formed is 16 ft which is the distance from the boat to the flag.
adjacent side = 16 ft
opposite angle = ?
using tangential ratio
tan 58° = opposite/adjacent
tan 58° = h/16
cross multiply
h = 16 × 1.60033452904
h = 25.6053524647
height of the flag from the bottom of the boat = 25.6053524647 + 6 = 31.6053524647
height of the flag from the bottom of the boat ≈ 32 ft(nearest foot)
A sheriff is interested in the average speed that people drive on Highway 50. Match the vocabulary word with its corresponding example.
Answer:
1. Statistics
2. Sample
3. Population
4. Variable
5. Data
6. Parameter
Step-by-step explanation:
1. Statistics is the mean of the sample taken - The average speed that the 250 randomly selected drivers drove on Highway 50
2. Sample is the representative part of the population - The 250 randomly selected drivers who were on Highway 50
3. Population is the group of people from which the sample was taken - All people who drive on Highway 50
4. Variable is a quantity that has values which differ - The speed that a driver drives on Highway
5. Data is information obtained used for a specific purpose - The list of the 250 speeds that the drivers studied drove
6. Parameter is the mean of a population - The average speed that all drivers go on Highway 50
Principal Coleman used random samples from student
records to determine how many people live in each
student's household.
What is the mean total household of the 7th-grade
sample to the nearest tenth?
7th-Grade Total Household
What is the mean total household of the 8th-grade
sample to the nearest tenth?
5,4,4,4,4, 7, 3, 4, 2, 3,
4.4, 2, 4, 3, 8, 7, 5, 4,5
8th-Grade Total Household
7,5,5,5, 3, 4, 5, 3, 2, 8,
6,5,6,3,3,4,4,53,4
Done
Answer:
7th-grade: 4.3
8th-grade: 4.5
Step-by-step explanation:
7th-grade and 8th-Grade samples have 20 data points. The mean is obtained adding the values of the data set and dividing this addition by the amount of values.
Mean total household of the 7th-grade sample: (5+4+4+4+4+ 7+ 3+ 4+ 2+ 3+ 4+4+ 2+ 4+ 3+ 8+ 7+ 5+ 4+5)/20 = 4.3
Mean total household of the 8th-grade sample: (7+5+5+5+3+ 4+ 5+ 3+ 2+ 8+ 6+5+6+3+3+4+4+5+3+4)/20 = 4.5
Answer:
7th grade: C
8th grade: B
Step-by-step explanation:
100% true
What’s the correct answer for this question?
Answer:
C.°
Step-by-step explanation:
According to the theorem , "Angles in the same segment are congruent"
So
m<D = 55°
MegaPhone Design Inc. designs megaphones with sport team stickers on opposite sides
of the megaphone. Estimate the percent of the surface area of the megaphone
covered by the stickers. Round to the nearest percent.
*see attachment for the megaphone being referred to here
Answer:
9%
Step-by-step explanation:
==>Given:
Conical megaphone with the following dimensions:
Slant height (s) = 2.25 ft
Diameter (D) = 1.2 ft (radius r = 0.6 ft)
π = 3.1
Area covered by sticker on one side = area of square = 6 in × 6 in = 0.5 ft × 0.5 ft = 0.25 ft²
==>Required
% of the surface of area of the conical megaphone that is covered by the sticker = area covered by the sticker ÷ surface area of megaphone × 100
==>SOLUTION
Area covered by sticker on both sides = 0.25 ft² + 0.25 ft² = 0.5 ft²
Surface area of the megaphone = surface area of a cone = πrs + πr²
S.A of megaphone = (3.14 × 0.6 × 2.25) + (3.14 × 0.6²)
S.A = 4.239 + 1.1304
S.A = 5.3694 ft²
Therefore, % of the surface of area of the conical megaphone that is covered by the sticker = 0.5 ÷ 5.3694 × 100
= 9.31202741
= 9%
Answer:
Statistics show the megaphone was a success in South Carolina.
Step-by-step explanation:
(Geometry) PLZ HELP ASAP
Answer:66.4
Step-by-step explanation:
[tex]A_{semicircle} =\frac{1}{2} \pi r^2=\frac{1}{2} \pi (\frac{13}{2} )^2= 66.36614 \approx66.4[/tex]
Two dataset in descending order (8,x,4,1) and (9,y,5,2). If the median is equal, find (y-x)
Answer:
y-x = -1
Step-by-step explanation:
Given the two dataset;
(8,x,4,1) and (9,y,5,2)
Since they are already arranged in descending order;
The median for the first dataset is;
M1 = (x+4)/2
The median for the second dataset is;
M2 = (y+5)/2
The median is equal;
M1 = M2
(x+4)/2 = (y+5)/2
x+4 = y+5
Collecting the like terms;
4-5 = y-x
y-x = -1
Consider reflection of JKL what line of reflection maps point L to point L at (-2,3)
It’s the y-axis for the first answer and the other one it’s a reflection of JKL what line of reflection maps point L to point L at (-2,3).
What is the line of reflection?When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed-line. The fixed-line is called the line of reflection.
What reflection will produce an image of RST?RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.
Learn more about the line of reflection at
https://brainly.com/question/8496129
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The data below are the monthly average high temperatures for New York City. What is the five-number summary? 40, 40, 48, 61, 72, 78, 84, 84, 76, 65, 54, 42
Select the correct answer below:
A) Sample minimum: 42, Sample maximum: 78
Q1: 45, Median: 63, Q3: 77
B) Sample minimum: 40, Sample maximum: 84
Q1: 45, Median: 63, Q3: 77
C) Sample minimum: 40, Sample maximum: 42
Q1: 54.5, Median: 81, Q3: 70.5
D) Sample minimum: 40, Sample maximum: 84
Q1: 40, Median: 61, Q3: 76
Answer:
B) Sample minimum: 40, Sample maximum: 84
Q1: 45, Median: 63, Q3: 77
Step-by-step explanation:
The first step is to write the temperatures in crescent order:
40, 40, 42, 48, 54, 61, 65, 72, 76, 78, 84, 84,
The sample minimum is the lowest value = 40
The sample maximum is the highest value = 84.
Since there are 12 numbers, the sample median is the average between the 6th and 7th terms:
[tex]M = \frac{61+65}{2}\\ M=63[/tex]
The first quartile is the average between the 3rd and 4th terms:
[tex]Q_1 = \frac{42+48}{2}\\ Q_1=45[/tex]
The third quartile is the average between the 9th and 10th terms:
[tex]Q_3 = \frac{76+78}{2}\\ Q_3=77[/tex]
Therefore, the answer is:
B) Sample minimum: 40, Sample maximum: 84
Q1: 45, Median: 63, Q3: 77
Use the power of ten to complete the question
531 times what equals 5310
WILL MARK BRAINLYEST
Answer:
10 to the 1st power
Step-by-step explanation:
531 x 10 = 5310
In an agricultural study, the average amount of corn yield is normally distributed with a mean of 189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 180 bushels of corn per acre?
Answer:
About 786 would be expected to yield more than 180 bushels of corn per acre
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 189.3, \sigma = 23.5[/tex]
Proportion of acres with more than 180 bushels of corn per acre:
This is 1 subtracted by the pvalue of Z when X = 180. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 189.3}{23.5}[/tex]
[tex]Z = -0.4[/tex]
[tex]Z = -0.4[/tex] has a pvalue of 0.3446.
1 - 0.3446 = 0.6554
Out of 1200:
0.6554*1200 = 786.48
About 786 would be expected to yield more than 180 bushels of corn per acre
The table shows the blood pressures of 16 clinic patients. What is the interquartile range of the data?
Answer:
i need a the data
Step-by-step explanation:
Find the value of x.
Answer:
x=4
Step-by-step explanation:
Answer:
√21 or 4.58
Step-by-step explanation:
area of triangle can be found in different ways, and they are equal as:
1/2*x*(7+3)= 1/2*√(x²+3³)*√(x²+7²)
(10x)²= (x²+3³)*(x²+7²)
x²= y
100y= (y+9)(y+49)y²+58y+9*49-100y=0y²-42y +441=0y=21x²=21
x=√21 = 4.58
A county is in the shape of a rectangle that is 60 miles by 70 miles and has a population of 50,000. What is the average number of people living on each square mile of the county? Round your answer to the nearest whole number.
192
10
14
12
Answer:
The correct answer is:
12
Step-by-step explanation:
Length of county = 70 miles
breadth of county = 60 miles
area of county (rectangle) = Length × Breadth = 60 × 70 = 4,200 sqaure miles
population of county = 50,000
Therefore, to find the average number of people living on each square mile of the county, we will assume that the whole population is equally distributed in the county, hence the population per square mile is calculated thus:
Total area = 4,200 square miles
total population = 50,000
This means that:
4,200 square miles contains 50,000 people
4,200 sq. miles = 50,000 people
∴ 1 sq. mile = 50,000 ÷ 4,200 = 11.9 = 12 people (to the nearest whole number)
therefore number of people living per square mile = 12
Answer:
12
Step-by-step explanation:
Got it right on the test! <3
The driver of a car traveling along a straight, flat road applies the brakes, which produce a constant acceleration ofspace a (t )thin space equals space minus 20 space f t divided by s e c squared. If the car is traveling at 80 feet per second when the driver applies the brakes, how far does the car travel between the time the brakes are applied and the time the car comes to a stop
Answer:
x = 160 ft
Step-by-step explanation:
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is given by:
[tex] v_{f}^{2} = v_{0}^{2} + 2ax [/tex]
Where:
[tex]v_{f}[/tex]: is the final speed of the car = 0 (since it stops)
[tex]v_{0}[/tex]: is the initial speed of the car = 80 ft/s
a: is the acceleration of the car = -20 ft/s²
x: is the distance recorred by the car
The distance traveled by the car between the time the brakes are applied and the time the car comes to a stop is:
[tex] x = \frac{v_{f}^{2} - v_{0}^{2}}{2a} = \frac{0 - (80 ft/s)^{2}}{2*(-20 ft/s^{2})} = 160 ft [/tex]
Therefore, the car travels 160 ft between the time the brakes are applied and the time the car comes to a stop.
I hope it helps you!
Explain your answer choice with sentences or record your explanation.
Which expression is equivalent to n + n - 0.18n?
A. 1.18n
B. 1.82n
C. n – 0.18
D. 2n – 0.82
Answer:
B. 1.82n
Step-by-step explanation:
Expression given: n + n - 0.18n
Adding n+n gives '2n'
then subtracting 0.18n from 2n gives= 1.82 n
Therefore,
n + n - 0.18n=0.18n
A line passes through the point (-8,-5) and has a slope of 3/4. Write an equation in point slope form for this line.
Answer:
y+5 = 3/4(x+8)
Step-by-step explanation:
The point slope form of the equation of a line is
y - y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line
The slope is 3/4 and the point is (-8,-5)
y - -5= 3/4( x - -8)
y+5 = 3/4(x+8)
The telephone company charges $1.35 fir the first 3 minutes of a phone call and $0.35 for each additional minute. i talk on the phone from 4:17 pm till 4:31 pm. what will the phone call cost?
Answer:
$5.20
Step-by-step explanation:
Talked on the phone for 14 minutes .
14 - 3 = 11
11 x .35 = 3.85
3.85 + 1.35 = 5.2
Answer:
The answer is $5.20
Step-by-step explanation:
HOPE THIS HELPSSSSSS:)))))
Alicia drove at a constant speed and traveled 182.4 miles in 3 hours. How many miles
would Alicia travel in 11 hours at the same speed?
Answer:
[tex] V = \frac{182.4 mi}{3 hr}= 60.8 \frac{mi}{hr}[/tex]
And then we can find the distance travelled in 11 hours with this formula:
[tex] D = Vt[/tex]
And replacing we got:
[tex] D = 60.8 \frac{mi}{hr} *11 hr =668.8 mi[/tex]
So then after 11 hours she will travel 668.8 mi
Step-by-step explanation:
For this case w eknow that Alicia drove at a constant speed 182.4 mi in 3 hours. We can find the speed with this formula:
[tex] V= \frac{D}{t}[/tex]
Where V is the velocity, D the distance and t the time if we replace we got:
[tex] V = \frac{182.4 mi}{3 hr}= 60.8 \frac{mi}{hr}[/tex]
And then we can find the distance travelled in 11 hours with this formula:
[tex] D = Vt[/tex]
And replacing we got:
[tex] D = 60.8 \frac{mi}{hr} *11 hr =668.8 mi[/tex]
So then after 11 hours she will travel 668.8 mi
If the statement 4 > 3 is true, which of the following are true about the relationship between –4 and –3? Check all that apply.
–4 < –3
The inequality changes from greater than to less than because -4 is less than -3.
–4 > –3
The greater than inequality holds true even when the opposites of 4 and 3 are used.
–4 = –3
Answer:
A AND B
Step-by-step explanation:
TRUST MEEEEE FRENZ:)
If 4 > 3 then - 4 < -3 is true because when additive opposites of numbers are used inequality get reversed.
What is an inequality?Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Given inequality,
4 > 3
If we multiply with -1 on both sides inequality get reversed
-1 × 4 > -1 × 3
-4 < -3.
Hence, the inequality changes from greater than to less than when opposites of 4 and 3 are used.
Learn more about inequality here:
https://brainly.com/question/30231190.
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How many terms are in the expression below?
3x + 4x - 3
In the expression, there are 3 terms.
3x and 4x are like terms because the variables are identical.
Also, we have a constant term which is -3.
The value of 49% of 86 should be just a little over 43.
True
- False
Answer:
False
Step-by-step explanation:
50% of 86 would be 43, 49% would be a bit lower then that.
Answer:
False, Its 42.14
Step-by-step explanation:
What is 49 percent of 86: 49 percent *86 = (49:100)*86 = (49*86):100 = 4214:100 = 42.14. Now we have: 49 percent of 86 = 42.14
Individuals in a group may gain protection from I predators because of the dilution effect: when o predator stocks', the larger the number of prey individuals in the group, me smaller the chance that any particular member of the group will be the victim. Foster and Treherne" tested whether the dilution effect occurred when o predatory fish attacked groups of a marine insect, ine ocean skater. A subset of their data is presented in the table, which shows the number of predator attacks (per 5 minutes) on ocean skater groups differing in size. Calculate the average number of attacks (per 5 minutes! for each group size. Do the fish predators show a clear preference for attacking small groups over large groups [or vice versa)? Explain. For each group size, convert the average that you calculated for question 1 into the average number of attacks per individual (per 5 minutes) Is there a consistent relationship between the overage number of per individual (per 5 minutes) and group size? Explain. Are these results consistent with the dilution effect?
Answer:
ffhn
Step-by-step explanation:
Will mark BRAINLIEST thank you!
Answer:
The above mentioned answer is wrong
Correct answer is option b)14000
Step-by-step explanation:
By the rule of front-end estimation
719 is estimated as 700
And 26 is estimated as 20 .
The product of 719 and 26 is estimated by multiplying 700 and 20.
The product of 700 and 20 is 14000
Hence the correct answer is option b) 14000
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
