Solve the system of equations.
y = 2x
y = –x + 6
X=
Y=
Answer:
x=2 y=4
Step-by-step explanation:
y = 2x
y = –x + 6
Set the two equations equal to each other
2x = -x+6
Add x to each side
2x+x =-x+x+6
3x = 6
Divide each side by 3
3x/3 = 6/3
x =2
Now find y
y = 2x
y =2(2)
y = 4
For the following case, assume that the population standard deviation is known and decide whether use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answer. The variable under consideration is very close to being normally distributed, and the sample size is 10. Choose the correct answer below. A. It is not reasonable to use the z-interval procedure in this case since it is very likely that with such a small sample size that there will be outliers in the sample. Knowing that the variable under consideration is very close to being normally distributed does not mean the sample is. B. It is reasonable to use the z-interval procedure in this case since both the sample is large (size 10 or greater) and the variable under consideration is very close to being normally distributed. C. It is reasonable to use the z-interval procedure in this case since, although the sample is small (size less than 15), the variable under consideration is very close to being normally distributed. D. It is not reasonable to use the z-interval procedure in this case because the sample is too small (size less than 15).
Answer:
B. It is reasonable to use the? z-interval procedure in this case? since, although the sample is small? (size less than? 15), the variable under consideration is very close to being normally distributed.
Step-by-step explanation:
answer b is considered to be correct because we know that the population is normal and the standard deviation is known, which allows using the interval z, the answer A is not correct because although the option to use the interval z is given, which is correct, the large sample is not favored, the answer C and D are incorrect because they both reject the use of the z interval and in d it is further rejected that although there is a normal distribution the sample is not, which is false
Assuming the population variance is known in this case, and examining it using the z-interval approach to obtain a confidence interval for the mean is fair, which can be defined as follows:
Using the z-interval procedure is appropriate in this case because, despite the small sample size (less than 15), the variable in the examination is almost distributed normally. Conformity is fulfilled because the population is normal, and we may utilize the z-interval because the population standard deviation was known.Therefore the final answer is "Option C".
Learn more about the analysis of variance:
brainly.com/question/14265451
The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to make a profit of $1220.
Did you ever figure this out. I need the answer for a test.
After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles for 10 of his clients and checked online price quotes for their policies. Then, based on paired data on the 10 clients (the price he offered them and the corresponding online quote) and using Excel’s t-test for paired data, he obtained t-statistic = 0.709 p-value = 0.248 Note that the above is based on the difference between his price and online quotes.
What are the null and alternative hypotheses, respectively?
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_d[/tex] = 0
Alternate Hypothesis, [tex]\mu_d\neq[/tex] 0
Step-by-step explanation:
We are given that a local insurance agent randomly selected profiles for 10 of his clients and checked online price quotes for their policies.
Then, based on paired data on the 10 clients (the price he offered them and the corresponding online quote), he obtained t-statistic = 0.709 p-value = 0.248.
Here , we will use the concept of Paired data test statistics because the prices that the local insurance agent offered and the corresponding online quotes are from the same single data. These information has not been taken from the two independent samples.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_d[/tex] = 0
Alternate Hypothesis, [tex]\mu_d\neq[/tex] 0
Here, null hypothesis states that there is no difference between the price he offered them and the corresponding online quote.
On the other hand, alternate hypothesis states that there is difference between the price he offered them and the corresponding online quote.
Hence, this would be the correct null and alternative hypothesis.
A triangle is a parallelogram with all sides the same length.
Answer:
False
Step-by-step explanation:
what is the domain of f/g given f(x) = x+4 and g(x) = x-1
Answer: the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.
Step-by-step explanation:
since f(x) = x + 4 and g(x) = x - 1
then f/g = x + 4/x - 1
the denominator of a function cannot be zero since a fraction with a denominator of zero is undefined.
∴ x - 1 ≠ 0
the value of x when g(x) = 0 is
x - 1 = 0
x = 1
∴ x ≠ 1
Therefore the domain of f/g is every real number except 1 which can be conventionally expressed as {(x,y): x ∈ R, x ≠ 1} OR (-∞ ≤ x < 1) ∩ (1< x ≤ ∞) OR x ∈ R; x ≠ 1.
What is the value of a in the equation below? 2a + 3 = 4a + 5
Please show work :)
Carla Ridley is a high school algebra teacher. Her annual salary is $38,625.00. If she receives a pay check every month of the year, what is her monthly salary?
Answer:
3218.75 a month
Step-by-step explanation:
In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. A researcher wonders if a smaller proportion of students at her university would respond in the same fashion. Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten. What is the value of the standardized test statistic for this significance test? A) – 0.100 B) – 1.250 C) 0.200 D) – 1.091
Answer:
The value of the standardized test statistic for this significance test is -1.25.
Step-by-step explanation:
We are given that in a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten".
The researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten.
Let p = population proportion of students wanting to reduce gluten at the university.
So, Null Hypothesis, [tex]H_0[/tex] : p = 30% {means that the proportion wanting to reduce gluten at the university is the same as for all adults}
Alternate Hypothesis, [tex]H_A[/tex] : p < 30% {means that a smaller proportion of students would say they want to reduce or be free of gluten}
The test statistics that would be used here One-sample z test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students who would say they want to reduce or be free of gluten = [tex]\frac{5}{25}[/tex] = 0.20
n = sample of students taken = 25
So, the test statistics = [tex]\frac{0.20-0.30}{\sqrt\frac{0.20(1-0.20)}{25} {} }[/tex]
= -1.25
The value of standardized z test statistic is -1.25.
Using the z-distribution, it is found that the value of the standardized test statistic for this significance test is:
D) –1.091
At the null hypothesis, we test if the proportion is of 0.3, that is:
[tex]H_0: p = 0.3[/tex]
At the alternative hypothesis, we test if the proportion is of less than 0.3, that is:
[tex]H_1: p < 0.3[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.3, n = 25, \overline{p} = \frac{5}{25} = 0.2[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.2 - 0.3}{\sqrt{\frac{0.3(0.7)}{25}}}[/tex]
[tex]z = -1.091[/tex]
A similar problem is given at https://brainly.com/question/24166849
a semitruck has 18 wheels. the semitruck has 3 times as many wheels than a garbage truck.how many wheels does a garbage truck have? need by 11;00 am
Answer:
The answer is the garbage truck had 6 wheels
Step-by-step explanation:
Since the semitruck has 18 wheels and the semitruck had 3 times more wheels than a garbage truck all you would have to do is divide 18 by 3 and you will get 6 as your answer.
Hope this helps, its my first time answering.
Given the set of integers one through 12 what is the probability choosing an odd number or a number greater than nine
Answer:
1/4
Step-by-step explanation:
the numbers greater than nine are: 10,11,12
1,3,5,7,9
So that is nine numbers
9/12 can be simplified to 3/4 if you divide by 3
if you like my answer please give me the brainliest. I'm trying to boost my rank and I'm really close
Write an exponential model given the two points (6,120) and (7,230)
Answer:
hhhhhhh
Step-by-step explanation:
Answer:
f(x) = 120(23/12)^(x-6)
Step-by-step explanation:
One way to write the model is ...
f(x) = f(x1)·(f(x2)/f(x1))^((x -x1)/(x2-x1))
Filling in the given numbers, this is ...
f(x) = 120·(230/120)^((x-6)/(7-6))
f(x) = 120(23/12)^(x-6)
__
Comment on this model
This could be written in the form ...
f(x) = a·e^(bx)
but the constants "a" and "b" would be approximations to their irrational values. We have elected to write the model with exact values in a form that reproduces the given two points exactly.
You ordered some eatables. If c represents
the cost of one cookie and p is the cost of one
pizza. Write an expression for the total cost
of 14 cookies and 10 pizzas.
I
Answer:
Total Cost = 14c + 10p
Step-by-step explanation:
Answer:
14c+10p= the total cost
Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p 1 be the proportion of customer complaints with the old dough and p 2 be the proportion of customer complaints with the new dough. State the competing hypotheses to determine if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough g
Answer:
[tex]z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)(\frac{1}{385}+\frac{1}{340})}}=-2.469[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(Z<-2.469)= 0.0068[/tex]
Since the p value is a very low value and using any significance level 5% or 10% we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough.
Step-by-step explanation:
Information provided
[tex]X_{1}=6[/tex] represent the complaints with the old dough
[tex]X_{2}=16[/tex] represent the complaints with the new dough
[tex]n_{1}=385[/tex] sample 1 selected
[tex]n_{2}=340[/tex] sample 2 selected
[tex]p_{1}=\frac{6}{385}=0.0156[/tex] represent the proportion of complaints with the old dough
[tex]p_{2}=\frac{16}{340}=0.0471[/tex] represent the proportion of complaints with the new dough
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic
[tex]p_v[/tex] represent the value
Hypothesis to test
We want to verify if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]
The statitsic is given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{6+16}{385+340}=0.0303[/tex]
Replacing the info provided we got:
[tex]z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)(\frac{1}{385}+\frac{1}{340})}}=-2.469[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(Z<-2.469)= 0.0068[/tex]
Since the p value is a very low value and using any significance level 5% or 10% we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough.
x^2 + (y-7)=16 what is the radius and what’s the center
Answer:
Rewrite in standard form to find the center
( h , k ) and radius r .
Center: ( 0 , 2 ) Radius: 4
Step-by-step explanation:
Answer:
Rewrite in standard form to find the center
( h , k ) and radius r .
Center: ( 0 , 2 ) Radius: 4
Lol hope this helps
Step-by-step explanation:
Help!.!.!.!.!.!.!.!.!.!.!.!.!.!!.!.!.!.!.!.!.!.!.!.
Answer:
~ 0.375 centimeters of the snowflake in real life ~
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. Given the information, let us create a proportionality as such:
48 = 1 ⇒ x - centimeters of the snowflake in real life
18 x
2. Now let us cross multiply, and solve through simple algebra for x:
48 * x = 18,
x = 0.375 centimeters of the snowflake in real ife
Th The radius of a circle is 7 feet what is the circles?Use 3.14 for pie?
Please help due in 30 min!!!!!!
100 points
Answer:
43.96
Step-by-step explanation:
ok so you use the formula: A= 3.14•r•2 next you plug in your values a=3.14•7•2 3.14•7= 28.98•2=43.96
Answer:
43.96
im dying on the question before that one it says "What issues are you having when it comes to area and circumference" you typed nothing really and here you are asking us whats the circles area lol
Step-by-step explanation:
is 1 1/12 more than 1 1/3 ?
The diagram shows a logo made from three circles
Answer:
3cm+2cm+5cm=10cm
%=100
10*10=100
2cm*10=20%
Step-by-step explanation:
the shaded area is width of 2 2/10 or 20/100
Answer:
33%
Step-by-step explanation:
for if u want to do it 4cm then
4+3+3=10
100π cm^2
49π cm^2
16π cm^2
49π - 16π = 33π
33/100 =33%
Which ordered pair (x,y) is a solution to the following?
y = 2x + 5
O(-2,1)
O(2,7)
O(1,6)
O(-3,11)
Answer:
(-2,1)
Step-by-step explanation:
A driveway is 25 meters long how long the driveway in centimeters
Answer:
2500
Explanation : a meter is 100 centimeters long so you would multiply 25 by 100 to get 2500
Answer: 2,500 centimeters
Step-by-step-Explanation: To convert 25 meters into centimeters, we use the conversion factor for meters and centimeters
which is 100 centimeters = 1 meter.
Next, notice that we're converting from a larger unit, meters, to a smaller unit, centimeters and when we go from a larger unit to a smaller unit, we multiply by the conversion factor.
So we multiply 25 by the conversion factor, 100 which gives us 2,500.
So 25 meters = 2,500 centimeters.
Mariska was comparing her options for investment. One choice she was looking at showed that her principal of $1,875 over 10 years would
earn $1,125 in interest giving her a total of $3,000 at the end of the investment period. What interest rate is being used to calculate this
Investment?
The amounts of money Gillian earned each week from babysitting are $5, 10, $20, $10, $15, $5, $42, $5. How is the mean of the data set affected when the outlier is removed?
Answer:
The mean will increase, after the outlier is removed.
What is the area of the paraalllegram
Answer:24
Step-by-step explanation:
Height =4
Base=6
Area of parallelogram=base x height
Area of parallelogram=6 x 4
Area of parallelogram=24
What is the area of the rhombus 10in and 5in
Answer:25 in^2
Step-by-step explanation:
d1=10 d2=5
area of rhombus=( d1 x d2)/2
Area of rhombus=(10x5)/2
area of rhombus=50/2
Area of rhombus=25 in^2
Can someone plz help....!.!.!.!.!!.!.!.!.
Answer:
~ x = 12 centimeters of the route on map ~
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. We can see that we have to determine the cm of the route on the map, so let us convert the 1.8 kilometers ⇒ centimeters:
1.8 km = 180,000 cm
2. Given the information, let us create a proportionality as such:
1 = 15,000 ⇒ x - centimeters of the route on the map
x 180,000
3. Now let us cross multiply, and solve through simple algebra for x:
15,000 * x = 180,000,
x = 12 centimeters of the route on map
Avicenna, a major insurance company, offers five-year life insurance policies to -65 year-olds. If the holder of one of these policies dies before the age of 70 , the company must pay out $24,200 to the beneficiary of the policy. Executives at Avicenna are considering offering these policies for $573 each. Suppose that for each holder of a policy there is a 2% chance that they will die before the age of and 70 a 98% chance they will live to the age of 70.
Answer:
The question is about the least amount to charge each policyholder as premium
The least premium is $484
Step-by-step explanation:
The least amount of premium to charge for this policy is the sum of the expected values of outcome of both instances of policyholder dying before the age of 70 and living after the age of 70 years
expected value of dying before 70 years=payout*probability=$24,200*2%=$484
Expected of living after 70=payout*probability=$0*98%=$0
sum of expected values=$484+$0=$484
Note that payout is nil if policyholder lives beyond 70 years
The premium of $573 means that a profit of $89 is recorded
PLEASE HELP SOLVE FOR ‘X’!!!
Answer:
x= 10
Step-by-step explanation:
1/5 x -2/3 = 4/3
Add 2/3 to each side
1/5x -2/3 +2/3 = 4/3 +2/3
1/5x = 6/3
1/5x = 2
Multiply each side by 5
1/5x * 5 = 2*5
x = 10
Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. It is found that 20% of the members in that city prefer swimming on weekends and are female, while 55% of the members in that city prefer swimming on weekdays and are female.
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is_____.
P = Desired outcomes divided by the total outcomesm me
Answer:
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.
Step-by-step explanation:
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: Prefers swimming on weekends.
Event B: Being female.
25% prefer swimming on weekends
This means that [tex]P(A) = 0.25[/tex]
It is found that 20% of the members in that city prefer swimming on weekends and are female
This means that [tex]P(A \cap B) = 0.2[/tex]
So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2}{0.25} = 0.8[/tex]
The probability that a club member picked randomly is female, given that the person prefers swimming on weekends, is 0.8 = 80%.
A tv programme begins at 7:45 and ends 50 minutes later what time does it finish
Answer:
8:35
Step-by-step explanation:
if u see every hour has 60 mins in it, so if u see 7:45 can be said as 7 hours and 49 mins
what u have to do is first add the mins, so add 45 and 50
45+50=95
every hour has 60 mins, so convert the mins to secs
95 mins=1hr35mins
and the 1hr35mins to 7:00
1hr35mins+7hr=8hr35mins or 8:35
A tv program begins at 7:45 and ends 50 minutes later the TV program ends at 8:35.
What is time?In math, time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.
We know that every hour has 60 minutes in it.
In 7:45 it has 7 hours and 45 minutes
The TV program duration is 50 minutes
So, 45+50=95
Now, 95 minutes has 1 hour 35 minutes
Add 1 hour 35 minutes to 7:00
That is, 7 hours + 1 hour 35 minutes
= 8 hours 35 minutes
Therefore, the TV program ends at 8:35.
Learn more about time here:
https://brainly.com/question/15356513.
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