Answer:
Jamal needs to save $254.17 each month to cover his expenses.
Step-by-step explanation:
We know that there are 12 months in a year, and Jamal already has $1,000 towards college. Jamal still needs to save $3,050 more dollars because: 4,050 - 1,000 = 3,050. Next, we take how much he has yet to pay ($3,050) divided by how many months in 1 year (12), and that gives us 254.17 per month.
For his first year of college expenses, Jamal needs to save $254.17 each month.
Jamal needs to contribute $4,050 towards his first year of college. He has 1 year to save and $1,000 in his savings account already.
Calculate the remaining amount needed: $4,050 - $1,000 = $3,050.
Divide the remaining amount by 12 months:
[tex]\frac{3050}{12} = 254.17[/tex].
Jamal needs to save $254.17 each month to cover his college expenses.
manufacturing company produces digital cameras and claim that their products maybe 3% defective. A video company, when purchasing a batch of 2000 cameras, applies the following sample plan: They randomly select 20 cameras and accept the whole batch if there are more than 17 working cameras. What is the correct probability statement for the company to accept the whole batch
Answer:
P(X>17) = 0.979
Step-by-step explanation:
Probability that a camera is defective, p = 3% = 3/100 = 0.03
20 cameras were randomly selected.i.e sample size, n = 20
Probability that a camera is working, q = 1 - p = 1 - 0.03 = 0.97
Probability that more than 17 cameras are working P ( X > 17)
This is a binomial distribution P(X = r) [tex]nCr q^{r} p^{n-r}[/tex]
[tex]nCr = \frac{n!}{(n-r)!r!}[/tex]
P(X>17) = P(X=18) + P(X=19) + P(X=20)
P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{20-18}[/tex]
P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{2}[/tex]
P(X=18) = 0.0988
P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{20-19}[/tex]
P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{1}[/tex]
P(X=19) = 0.3364
P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{20-20}[/tex]
P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{0}[/tex]
P(X=20) = 0.5438
P(X>17) = 0.0988 + 0.3364 + 0.5438
P(X>17) = 0.979
The probability that there are more than 17 working cameras should be 0.979 for the company to accept the whole batch
HVAC technician average salary = $28/hour with a one-year Tech school certification costing an average of $7,500. What would your pay be for your first year of work? Assume you work a 40 hour week for 50 weeks.
Answer:
56,000
Step-by-step explanation:
In your first year of work, you would make $56,000.
The pay rate is $28 per hour and a work week has 40 hours for the HVAC technician.
In a week, you will make:
= Number of hours in week x Amount per hour
= 40 x 28
= $1,120
In a year, assuming there are 50 weeks, the HVAC technician would make:
= Amount per week x Number of weeks in year
= 1,120 x 50
= $56,000
In conclusion, you would make $56,000 a year as an HVAC technician.
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Which equation represents a proportional relationship that has a constant of proportionality equal to 1/5
Hattie is making fruit baskets, which includes apples and bananas, to send to some of her real estate clients. She wants each basket to have 12 pieces of fruit, but the fruit should weigh no more than 80 ounces total. On average, each apple weighs 5 ounces, and each banana weighs 7 ounces.
Answer:
Step-by-step explanation:
The answer is 10 bananas and 2 apples
The number of apples are 2 and number of bananas is 10.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Hattie is making fruit baskets, which includes apples and bananas, to send to some of her real estate clients.
She wants each basket to have 12 pieces of fruit, but the fruit should weigh no more than 80 ounces total.
On average, each apple weighs 5 ounces, and each banana weighs 7 ounces.
Let Bananas is denoted by B and Apples are represented by A.
A+B=12...(1)
5A+7B<80...(2)
A=12-B
Substitute in equation 2.
5(12-B)+7B=80
60-5B+7B=80
60+2B=80
Subtract 60 on both sides.
2B=80-60
2B=20
Divide both sides by 2.
B=10
A+B=12
A+10=12
A=2
Hence, the number of apples are 2 and number of bananas is 10.
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A trade magazine routinely checks the drive-through service times of fast-food restaurants. Upper A 95% confidence interval that results from examining 745 customers in one fast-food chain's drive-through has a lower bound of 177.6 seconds and an upper bound of 181.0 seconds. What does this mean?
Answer:
-A person can be 95% confident that the mean drive through service time lies between 177.6 seconds and 181.0 seconds.
Step-by-step explanation:
- Confidence level is the degree of certainty we have on a particular statistic.
-The 95% confidence interval means that we are 95% confident that the mean drive through service time is lies between 177.6 seconds and 181.0 minutes.
Solve the system of linear equations using elimination.
−9x − 10y = 17
−10x − 10y = 10
Answer:
you are to subtract the equation
Answer:
(7,-8)
Step-by-step explanation:
given: f(x)= x^2 -x and g(x)= x+2 find f(-1)
.
Write an equation for the line that is parallel to the given line and that passes through the given point. y=−6x+2;(−1,2)
A. y=−8x−8y=-8x-8
B. y=6x−8y=6x-8
C. y=−6x+4y=-6x+4
D. y=−6x−4y=-6x-4
The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?
Answer:
year 2139
Step-by-step explanation:
The population will double when the factor e^(.005t) is 2.
e^(.005t) = 2
.005t = ln(2)
t = ln(2)/0.005 = 138.6
The population will be double its size at t=0 when t=138.6. That is the population will be about 5.2 million in the year 2139.
The population will double by the year 2139 from its value of 2.6 million in year 2000.
Population function :
[tex]P(t) = 2.6 {e}^{0.005t} [/tex]
Population size at t = 0
[tex]P(0) = 2.6 {e}^{0.005(0)} = 2.6(1) = 2.6[/tex]
Population at t = 2.6 million.
For the population to double ;
2.6 × 2 = 5.2 million :
[tex]5.2 = 2.6 {e}^{0.005t} [/tex]
We solve for t
[tex] \frac{5.2}{2.6} = {e}^{0.005t} [/tex]
[tex]2 = {e}^{0.005t} [/tex]
Take the In of both sides
[tex] ln(2) = 0.005t[/tex]
[tex]t \: = ln(2) \div 0.005 = 138.629[/tex]
The population will double after 139 years
Therefore, the population will double by the 2139 (Year 2000 + 139 years) = year 2139.
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In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast. If a person is selected at random, find the probability that the person preferred milk as his or her primary drink.
Answer:
Probability that the person preferred milk as his or her primary drink = 0.3
Step-by-step explanation:
Given -
In a recent survey, 18 people preferred milk, 29 people preferred coffee, and 13 people preferred juice as their primary drink for breakfast .
Total no of people is = 18 + 29 + 13 = 60
If a person is selected at random ,
The probability of person preferred milk = [tex]\frac{18}{60}[/tex]
The probability of person preferred coffee = [tex]\frac{29}{60}[/tex]
The probability of person preferred juice = [tex]\frac{13}{60}[/tex]
Probability that the person preferred milk as his or her primary drink =
P ( milk ) = [tex]\mathbf{\frac{No\;of\;favourable\;outcomes}{total\;no\;of\:outcomes}}[/tex]
= [tex]\frac{18}{60}[/tex] = 0.3
Look at the cahrt below The number of satisfied customers is given below each month on the x axis select an appropriate scale for the y axis of the graph
Answer:
wydjae is męi ze tak
Step-by-step explanation:
The appropriate scale for the y-axis include:
A = 2000
B = 4000
C = 6000
D = 8000
E = 10000
F = 12000
G = 14000
In Mathematics and Euclidean Geometry, a bar chart is a type of graph that is used for the graphical representation of a data set, especially through the use of rectangular bars and vertical columns.
Since the set of axes starts from the origin (0, 0), an appropriate scale for the y-axis (number of satisfied customers) of the graph can be calculated as follows;
1 unit = 250 customers
4 units = (4 × 250) = 2,000 customers.
In this context, the appropriate scale for the y-axis should be completed as follows:
A = 2000
B = 4000
C = 6000
D = 8000
E = 10000
F = 12000
G = 14000
Complete Question;
Look at chart below.
The number of satisfied customers is given below each month on the x-axis.
Select an appropriate scale for the y-axis of the graph.
The appropriate scale for the y-axis is:
A =
B =
C =
D =
E =
F =
G =
A ticketholder on the merry-go-round is riding a horse that is at a radius of 12 feet. How far does she travel after the merry-go-round rotates 3π5 radians? Give approximate answer. Round decimal to the tenth space.
The correct value of the angle of rotation is 3π/5
Answer:
Distance travelled ≈ 22.6 ft
Step-by-step explanation:
We are given;
Radius;r = 12 ft
Angle of rotation; θ = 3π/5
The formula for calculating distance travelled is;
Distance travelled = rθ
So, plugging in the relevant values;
Distance travelled = 12 x 3π/5
Distance travelled ≈ 22.6 ft
Which statements are correct? Check all that apply.
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
If a quadratic function has two real roots, then both roots must be rational.
A quadratic function can have three zeros.
All quadratic functions touch or cross the x-axis at least once.
Answer:
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
Step-by-step explanation:
A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
What is quadratic function?A quadratic function is a polynomial function with one or more in which highest exponent of variable is two.
According to the question,
A quadratic function can have two irrational roots.
example: [tex]x^{2} -2x -2 =0[/tex]
This equation have two irrational roots 1+√3 and 1 - √3.
A quadratic function can have no real number solutions
Hence, A quadratic function can have two irrational roots.
A quadratic equation can have no real number solutions.
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Graph y=4x-9 ill give brainliest for first one that is correct
Answer:
I hope this helps
A rectangular bin is going to be made with a volume of 646 cm^3. The base of the bin will be a square and the top will be open. The cost of the material for the base is 0.5 cents per square centimeter, and the cost of the material for the sides is 0.3 cents per square centimeter. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost?
Answer:
The base is a square of side 9.19 cm and the height is 7.66 cm
[tex]C_m=126.58\ cents[/tex]
Step-by-step explanation:
Optimization
We'll use simple techniques to find the optimum values that minimize the cost function given in the problem. Since the restriction is an equality, the derivative will come handy to find the critical points and then we'll prove they are a minimum.
First, we consider the shape of the rectangular bin has a square base and no top. Let x be the side of the base, thus the Area of the base is
[tex]A_b=x^2[/tex]
Let y be the height of the box, thus each one of the four lateral sides of the box is a rectangle with sides x and y and the total lateral area is
[tex]A_s=4xy[/tex]
The cost of the material used to manufacture the box is 0.5 cents per square centimeter of the base and 0.3 cents per square centimeter of the sides, thus the total cost to produce one box is
[tex]C(x,y)=0.5x^2+0.3\cdot 4xy[/tex]
[tex]C(x,y)=0.5x^2+1.2xy[/tex]
Note the cost is a two-variable function. We need to have it expressed as a single variable function. To achieve that, we use the volume provided as [tex]646 cm^3[/tex]. The volume of the box is the base times the height
[tex]V=x^2y[/tex]
Using the value of the volume we have
[tex]x^2y=646[/tex]
Solving for y
[tex]\displaystyle y=\frac{646}{x^2}[/tex]
Replacing into the cost function, it only depends on one variable
[tex]\displaystyle C(x)=0.5x^2+1.2x\cdot \frac{646}{x^2}[/tex]
Operating
[tex]\displaystyle C(x)=0.5x^2+ \frac{775.2}{x}[/tex]
Taking the first derivative
[tex]\displaystyle C'(x)=x-\frac{775.2}{x^2}[/tex]
Equating to 0
[tex]\displaystyle x-\frac{775.2}{x^2}=0[/tex]
Solving
[tex]\displaystyle x=\sqrt[3]{775.2}[/tex]
[tex]x=9.19\ cm[/tex]
Now find the height
[tex]\displaystyle y=\frac{646}{9.19^2}[/tex]
[tex]y=7.66\ cm[/tex]
Find the second derivative
[tex]\displaystyle C''(x)=1+\frac{1550.4}{x^3}[/tex]
Since this value is positive, for all x positive, the function has a minimum at the critical point.
Thus, the minimum cost is
[tex]\displaystyle C_m=0.5\cdot 9.19^2+ \frac{775.2}{9.19}[/tex]
[tex]\boxed{C_m=126.58\ cents}[/tex]
Answer:
126.58 cents or $1.27
Step-by-step explanation:
the math from above is correct they just want the answers in dollars
Lucia hit a golf ball 240 feet. How many yards did she hit the ball?
A) 80 yards
B) 60 yards
C) 120 yards
D) 300 yards
Answer:
a
Step-by-step explanation:
a yard is 3 feet.24/3 equals 8 .then 80!
American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50. What is the probability that the spending is more than $42.35
Answer:
Probability that the spending is more than $42.35 is 0.7271.
Step-by-step explanation:
We are given that American Statistical Association budget is distributed normally with a mean spending of $45.67 and a standard deviation of $5.50.
Let X = American Statistical Association budget
So, X ~ N([tex]\mu=45.67,\sigma^{2} =5.5^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean spending = $45.67
[tex]\sigma[/tex] = standard deviation = $5.50
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, the probability that the spending is more than $42.35 is given by = P(X > $42.35)
P(X > $42.35) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{42.35-45.67}{5.5}[/tex] ) = P(Z > -0.604) = P(Z < 0.604)
= 0.7271
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.604 in the z table which will lie between x = 0.60 and x = 0.70 which has an area of 0.7271.
Hence, the probability that the spending is more than $42.35 is 0.7271.
PLEASE ANSWER!URGENT! The table below shows the approximate height of a ball thrown up in the air after x seconds. Which quadratic model best represents the data?
Answer:
A) f(x) = –16x2 + 99x + 6
Step-by-step explanation:
ed2021 :)
complete the equation of the line whose slope is -2 and y intercept is (0,3)
Answer:
y = -2x+3
Step-by-step explanation:
Answer:
We have to produce the equation y = mx +b
We start by solving for b
b = y - mx
b = 3 - -2*0
b = 3
Let's put b and the slope into this equation
y = mx +b
y = -2*x +3
Step-by-step explanation:
6th grade math) help please
Answer:
C 66 miles
Step-by-step explanation:
88miles/4 gallons = 22 miles/gallon
22 miles/ gallon * 3 gallons = 66 miles
Answer:
66 miles per 3 gallons
Step-by-step explanation:
if you divide 88 by 4 you get 22 which means you get 22 miles to each gallon so for three gallons you would be able to drive 66 miles
Hope I helped:)
a sweater is marked 30% off during an end of the season sale. if the sweater was orginally 56.00, how much was the sweater on sale for
Answer:
39.20000
Step-by-step explanation:
Sweater costs 56.00
To calculate the discounted price of the sweater
56 * (30/100) = 16.8
We used (30/100) to find out the 30 percent of the sweater which will be on discount/reduced.
56-16.8=39.2 is the discounted price
Then we subtract the amount of discount from the original price of sweater to find out the discounted price.
Consider the following linear programming problem: The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function
Answer:
We have,
max 4x+10y
3x+4y<480
4x+2y<360
The feasible corner points are ( 48,84),(0,120),(0,0),(90,0)
Now, our problem is maximum type so put above feasible points in equation max 4x + 10y one by one and select one point at which our value from this equation is maximum,
(48,84) 4*48+10*84 1032
(0,120) 4*0+10*120 1200
(0,0) 4*0+10*0 0
(90,0) 4*90+10*0 360
Here we get maximum value at (0,120) which is 1200.
Correct option is (B)1200
Answer:
Answer is 1200.
Refer below.
Step-by-step explanation:
The maximum possible value for the objective function is 1200.
Toilet Training You are a great friend and are taking your friend's child to the playground to play with two of his friends: Charles and Elizabeth. You overhear the dads of Charles and Elizabeth talking about a recent study regarding toilet training of children. The study found that the mean age for girls to stay dry during the day (successful completion of toilet training) is 32.5 months, and the mean age for boys is 35.0 months. These two groups had reported standard deviations for the age when a child is successfully toilet trained of 6.7 months for girls and 10.1 months for boys based on a sample of 126 girls and a second sample of 141 boys. Charles's dad and Elizabeth's dad are getting into a disagreement about how to interpret these results. Based on your knowledge from Stats 250, can you help settle their disagreement by helping to answer the following questions about the difference between the population mean age for girls to be successfully toilet trained and the population mean age for boys to be successfully toilet trained? Question 5 Subquestions 5.
a TBD points Based on our given information, should you use the unpooled (Welch's) or the pooled approach to calculate the confidence interval? Make sure to include numerical support for your answer. No answer entered. Click above to enter an answer. 5.
b TBD points The reported 95% confidence interval is (0.3927 months. 4.6073 months). Based on this confidence interval, which group was chosen to be group 1? How do you know? What is the probability that our parameter of interest, the true difference in population means of ages of successful toilet training between boys and girls, is included in the interval? No answer entered. Click above to enter an answer. 5.
C TBD points Charles's dad is upset that this result guarantees that his son will be at a disadvantage, since he will be toilet trained later than Elizabeth. Elizabeth's dad starts to correct him, stating that this only means that there is only a 95% probability that Elizabeth will be toilet trained before Charles. Are either of these statements correct? Explain why you made your choice.
Answer:
Step-by-step explanation:
Hello!
According to a study regarding the average age of female and male kids to complete toilet training is:
Females:
Average age 32.5 months
The standard deviation of 6.7 months
n= 126
Males:
Average age 35.0 months
The standard deviation of 10.1 months
n= 141
The parameter of study is the difference between the age of females are successfully toilet trained and the average age that males are successfully toilet trained. μf - μm (f= female and m= male)
a.
Assuming that both variables have a normal distribution to choose whether you'll use an unpooled or pooled-t to calculate the confidence interval you have to conduct an F-test for variance homogeneity.
If the variances are equal, then you can usee the pooled-t, but if the variances are different, you have to uses Wlche's approach:
H₀: δ²f = δ²m
H₁: δ²f ≠ δ²m
Since both items b. and c. ask for a 95% CI I'll use the complementary significance level for this test:
α: 0.05
[tex]F= \frac{S^2_f}{S^2_m} * \frac{xSigma^2_f}{Sigma^2_m} ~~~F_{(n_f-1); (n_m-1)}[/tex]
[tex]F= \frac{(6.7^2)}{(10.1)^2} *1= 0.44[/tex]
Critical values:
[tex]F_{125;140;0.025}= 0.71\\F_{125;140;0.975}= 1.41[/tex]
The calculated F value is less than the lower critical value, 0.77, so the decision is to reject the null hypothesis. In other words, there is no significant evidence to conclude the population variances of the age kids are toilet trained to be equal. You should use Welch's approach to construct the Confidence Intervals.
[tex]Df_w= \frac{(\frac{S^2_f}{n_f} + \frac{S^2_m}{n_m} )^2}{\frac{(\frac{S^2_f}{n_f} )^2}{n_f-1} +\frac{(\frac{S^2_m}{n_m} )^2}{n_m-1} }[/tex]
[tex]Df_w= \frac{(\frac{6.7^2}{126} + \frac{10.1^2_m}{141} )^2}{\frac{(\frac{126^2}{126} )^2}{126-1} +\frac{(\frac{10.1^2}{141} )^2}{141-1} } = 254.32[/tex]
b.
The given interval is:
[0.3627; 4.6073]
Using Welch's approach, the formula for the CI is:
(X[bar]f- X[bar]m) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
or
(X[bar]m- X[bar]f) ± [tex]t_{Df_w;1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_f}{n_f} +\frac{S^2_m}{n_m} }[/tex]
As you can see either way you calculate the interval, it is centered in the difference between the two sample means, so you can clear the value of that difference by:
(Upper bond - Lower bond)/2= (4.6073-0.3627)/2= 2.1223
The average age for females is 32.5 months and for males, it is 35 months.
Since the difference between the sample means is positive, we can say that the boys were considered "group 1" and the girls were considered "group 2"
You have a95% confidence that the parameter of interest is included in the given confidence interval.
c.
None of the statements is correct, the interval gives you information about the difference between the average age the kids are toilet trained, that is between the expected ages for the entire population of male and female babies.
This represents a guideline but is not necessarily true to all individuals of the population since some male babies can be toilet trained before that is expected as some female babies can be toiled trained after the average value.
I hope it helps!
It takes Ernesto 3 minutes to jog a lap around the school track. How many laps can Ernesto complete in 15 minutes?
Answer:
5 laps
Step-by-step explanation:
We can use ratios to solve
3 minutes 15 minutes
----------------- = ------------------------
1 lap x laps
Using cross products
3x = 15
Divide each side by 3
3x/3 = 15/3
x = 5
He can do 5 laps
How can you use a point on the graph off-1(x) =
9X to determine a point on the graph of f(x) =
logox?
Answer: switch the x- and y- coordinates
And the 2nd part is c, e , f
The point on the graph -1(x) =9X to determine a point on the graph of f(x) =logox is (-1, -9).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
-1(x) =9X
Now,
To use a point on the graph of one function to determine a point on the graph of another function, you need to find the corresponding x-value on the first graph. Then, you can use that x-value to find the corresponding y-value on the second graph.
In this case, you have a point on the graph of the function f(x) = 9x. To find the corresponding point on the graph of the function g(x) = log(x), you need to find the x-value that corresponds to -1 on the graph of f(x) = 9x.
To do this, you can set f(x) = 9x equal to -1 and solve for x:
9x = -1 x = -1/9
The point (-1, -9) on the graph of f(x) = 9x corresponds to the point (-1/9, log(-1/9)) on the graph of g(x) = log(x). However, note that the logarithm function is not defined for negative values of x, so the point (-1/9, log(-1/9)) is not a valid point on the graph of g(x) = log(x).
Therefore, by the graph of function the point will be (-1, -9).
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StartRoot 53 EndRoot is between 7.2 and 7.3. Estimate further to the hundredths place. Which two consecutive values does StartRoot 53 EndRoot fall between?
7.26 and 7.27
7.27 and 7.28
7.28 and 7.29
7.29 and 7.30
Answer:
7.28 7.29 c
Step-by-step explanation:
The square root of 53 can be found to lie between the values of 7.28 and 7.29.
What is the square root function?The square root function can only have non negative values. If we take thee square root of a number, we obtain a value that can be multiplied by itself to obtain the number.
The square root of 53 can be found to lie between the values of 7.28 and 7.29.
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identify the horizontal aysmptote of each graph. t(x)=6^x
Answer:Y=0 Y=-3
Step-by-step explanation:
Answer:
First graph y=0
Second graph y=-3
Step-by-step explanation:
Edge 2022
What is the measure of Zc?
so 90-
42
48
90
180
Angle Zc measures 90° as it is supplementary to the given 90° angle. Therefore, Zc = 90°.
To find the measure of angle Zc, we need to use the properties of angles formed by intersecting lines.
Given:
- Angle Zc is supplementary to angle 90°.
- Angle 90° is formed by the intersection of lines, let's denote them as line AB and line CD.
- Angle 90° is bisected by line EF, forming two congruent angles.
Step-by-step explanation:
1. Since angle Zc is supplementary to angle 90°, we subtract the measure of angle 90° from 180° to find the measure of angle Zc.
Measure of angle Zc = 180° - 90°
= 90°
So, angle Zc measures 90°.
In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.
Answer:
1) Increase the sample size
2) Decrease the confidence level
Step-by-step explanation:
The 95% confidence interval built for a sample size of 1100 adult Americans on how much they worked in previous week is:
42.7 to 44.5
We have to provide 2 recommendations on how to decrease the margin of Error. Margin of error is calculated as:
[tex]M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}[/tex]
Here,
[tex]z_{\frac{\alpha}{2} }[/tex] is the critical z-value which depends on the confidence level. Higher the confidence level, higher will be the value of critical z and vice versa.
[tex]\sigma[/tex] is the population standard deviation, which will be a constant term and n is the sample size. Since n is in the denominator, increasing the value of n will decrease the value of Margin of Error.
Therefore, the 2 recommendations to decrease the Margin of error for the given case are:
Increase the sample size and make it more than 1100Decrease the confidence level and make it lesser than 95%.The two recommendations should be that the sample size should be increased and the confidence interval should be reduced.
Suggestions for reducing the margin of error:Since a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5.
We know that margin of error = z value × population / √n
So for reducing the margin of error of the interval, sample size should be increased and the confidence interval should be reduced.
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evaluate tan( – 33pi/4)
Answer:??
Step-by-step explanation:
Answer: dont have an answer
Step-by-step explanation:
sorry