Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and work-piece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article "Variables Affecting Mist Generation from Metal Removal Fluids" (Lubrication Engr., 2002: 10-17) gave the accompanying data on x = fluid flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than some value:
x: 89 177 189 354 362 442 965
y: .40 .60 .48 .66 .61 .69 .99
a. Make a scatterplot of the data. By R.
b. What is the point estimate of the beta coefficient? (By R.) Interpret it.
c. What is s_e? (By R) Interpret it.
d. Estimate the true average change in mist associated with a 1 cm/sec increase in velocity, and do so in a way that conveys information about precision and reliability.
e. Suppose the fluid velocity is 250 cm/sec. Find the mean of the corresponding y in a way that conveys information about precision and reliability. Use 95% confidence level. Interpret the resulting interval. By hand, as in part d.
f. Suppose the fluid velocity for a specific fluid is 250 cm/sec. Predict the y for that specific fluid in a way that conveys information about precision and reliability. Use 95% prediction level. Interpret the resulting interval. By hand, as in part d.
Answers
Answer:
Step-by-step explanation:
a) image attached
b) Lets do the analysis in R , the complete R snippet is as follows
x<- c(89,177,189,354,362,442,965)
y<- c(.4,.6,.48,.66,.61,.69,.99)
# scatterplot
plot(x,y, col="red",pch=16)
# model
fit <- lm(y~x)
summary(fit)
#equation is
#y = 0.4041 + 0.0006211*X
# beta coeffiecients are
fit$coefficients
coef(summary(fit))[, "Std. Error"]
# confidence interval of slope
confint(fit, 'x', level=0.95)
The results are
> summary(fit)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5 6 7
-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***
x 6.211e-04 7.579e-05 8.195 0.00044 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.05405 on 5 degrees of freedom
Multiple R-squared: 0.9307, Adjusted R-squared: 0.9168 # model is able to capture 93% of the variation of the data
F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403 , p value is less than 0.05 , hence model as a whole is significant
> fit$coefficients
(Intercept) x
0.4041237853 0.0006210758
> coef(summary(fit))[, "Std. Error"]
(Intercept) x
3.458905e-02 7.579156e-05
> confint(fit, 'x', level=0.95)
2.5 % 97.5 %
x 0.0004262474 0.0008159042
c)
> x=c(89,177,189,354,362,442,965)
> y=c(0.40,0.60,0.48,0.66,0.61,0.69,0.99)
>
> ### linear model
> model=lm(y~x)
> summary(model)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5 6 7
-0.05940 0.08595 -0.04151 0.03602 -0.01895 0.01136 -0.01346
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.041e-01 3.459e-02 11.684 8.07e-05 ***
x 6.211e-04 7.579e-05 8.195 0.00044 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.05405 on 5 degrees of freedom
Multiple R-squared: 0.9307, Adjusted R-squared: 0.9168
F-statistic: 67.15 on 1 and 5 DF, p-value: 0.0004403
s_e is the Residual standard error from the model and its estimated value is 0.05405. s_e is the standard deviation of the model.
d) 95% confidence interval
> confint(model, confidence=0.95)
2.5 % 97.5 %
(Intercept) 0.3152097913 0.4930377793
x 0.0004262474 0.0008159042
Comment: The estimated confidence interval of slope of x does not include zero. Hence, x has the significant effect on y at 0.05 level of significance.
e)
> predict(model, newdata=data.frame(x=250), interval="confidence", level=0.95)
fit lwr upr
1 0.5593927 0.5020485 0.616737
f)
> predict.lm(model, newdata=data.frame(x=250), interval="prediction", level=0.95)
fit lwr upr
1 0.5593927 0.4090954 0.7096901
Related Questions
Chrissy currently has a credit card that charges 15% interest. She usually carries a balance of about $500. What will her total annual interest be with her current card?
Answers
Answer:
$900
Step-by-step explanation:
If she holds $500 and she is charged 15%; it means
The interest she pays per month is ;
$500 × 15/100 = $75
Then annually meaning for 12 months, she pays;
$75 × 12 = $900
Her annual interest on her current card is $900.
How to calculate annual interest?The annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. The annual percentage rate (APR) is a percentage that represents the actual annual cost of funds over the life of a loan or the income earned on an investment.Your daily periodic interest is calculated by dividing your annual percentage rate (APR) by the number of days in the year, which is typically 360 or 365 days depending on your credit card issuer. The annual interest rate is the rate that is applied over a one-year period.Therefore,
She will be taxed 15% if she holds $500, which means
The monthly interest she pays is;
$500 × 15/100 = $75
She then pays annually, which is for a full year;
$75 × 12 = $900
Hence, Her annual interest on her current card is $900.
To learn more about annual interest refer to:
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Blood types: The blood type o negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person
Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type o negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S.
residents have type o negative blood. Assume that a blood bank has recruited 18 donors. Round the answers to four decimal places
Part 1 of 3
(a) What is the probability that three or more of them have type o negative blood?
The probability that three or more of them have type o negative blood is
х
Part 2 of 3
(b) What is the probability that fewer than five of them have type o negative blood?
The probability that fewer than five of them have type o negative blood is
х
Part 3 of
(©) Would it be unusual f none of the donors had type o negative blood?
be unusual if none of the donors had type o negative blood since the probability is
X
It choose one) Y
would
would not
Answers
Answer:
a) The probability that fewer than five of them have type o negative blood is 0.1275
b) The probability that fewer than five of them have type o negative blood is 0.9933
c) 0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have type o negative blood, or they do not. The probability of a person having type o negative blood is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
7% of U.S. residents have type o negative blood.
This means that [tex]p = 0.07[/tex]
18 donors.
This means that [tex]n = 18[/tex]
(a) What is the probability that three or more of them have type o negative blood?
Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So
[tex]P(X < 3) + P(X \geq 3) = 1[/tex]
We want [tex]P(X \geq 3)[/tex]
So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]
[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2708 + 0.3669 + 0.2348 = 0.8725[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8725 = 0.1275[/tex]
The probability that fewer than five of them have type o negative blood is 0.1275
(b) What is the probability that fewer than five of them have type o negative blood?
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
[tex]P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669[/tex]
[tex]P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348[/tex]
[tex]P(X = 3) = C_{18,3}.(0.07)^{3}.(0.93)^{15} = 0.0942[/tex]
[tex]P(X = 4) = C_{18,4}.(0.07)^{4}.(0.93)^{14} = 0.0266[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.2708 + 0.3669 + 0.2348 + 0.0942 + 0.0266 = 0.9933[/tex]
The probability that fewer than five of them have type o negative blood is 0.9933.
c) Would it be unusual f none of the donors had type o negative blood?
[tex]P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708[/tex]
0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.
Simplify 1 ∙ x -x/1 .
Answers
Answer:
0
Step-by-step explanation:
1x=x
-x/1=-x
x-x=0
Answer:
Brainleist !
Step-by-step explanation:
x - x /1
x - x = nothing or 0
What is the perimeter of the shape below?
Answers
Answer:
I think it is 288.6 ft. Lol hope this helps
Step-by-step explanation:
What translation was used to ABCD to produce A’ B’C’D’
Answers
Angelina read 30% of her book containing 360 pages. How many pages has she read so far
Answers
Answer:
108 pages
Step-by-step explanation:
Angelina read 30% of the book that contains 360 pages.
30% of 360 pages
"of" also means multiply, so we must multiply 30% and 360.
30% * 360
Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.
30/100=0.30
or
30.0---> 3.0---> 0.30
Plug the decimal in for the percent.
0.30*360
Multiply the 2 numbers together
108
Angelina has read 108 pages so far.
What are the terms in the algebraic expression
102 + 10 +
3b
Answers
Answer:
102, 10, and, 3b
Step-by-step explanation:
The diagram shows a rectangle and a square.
Diagram
accuratel
The rectangle is 2 cm long and 6 cm wide.
The perimeter of the rectangle is the same as the perimeter of the square.
Work out the length of one side of the square.
Answers
Answer:
4 cm
Step-by-step explanation:
The side of the square will be the average of the two sides of the rectangle with the same perimeter.
Formulas for the perimeters are ...
P = 2(L+W)
P = 4s
Equating these gives ...
4s = 2(L+W)
s = (L +W)/2 . . . . . divide by 4
For the given side lengths, ...
s = (2 cm +6 cm)/2 = (8/2) cm = 4 cm
The length of one side of the square is 4 cm.
A sample is taken from all college freshman . Right-handed students are excluded.what is this an example of?
Answers
Answer:
All college freshman is called Population and Right handed students are excluded is called sample from Population
Step-by-step explanation:
Explanation:-
Population:- The total of the observations which we are concerned
given data all college freshman is called Population
Sample :-
A sample is a subset of a Population
Given data all college freshman is called Population and Right handed students are excluded is called sample from Population
A car travels 300 miles in 10 hours at a constant rate. If the distance traveled by the car can be represented as a function of
the time spent driving, what is the value of the constant of variation, K?
O 1/30 mph
30 mph
60 mph
3000 mph
Answers
Answer:
30 mph
Step-by-step explanation:
Distance travelled=300 miles
Time travelled=10hours
At a constant rate,k
Let distance travelled=d
Time travelled=t
Then,
d=kt
300=k*10
300=10k
k=300/10
=30
k=30mph
30 miles per hour
30 MPH ............................................................................................................
Homework: Section 1.2 Applications Linear
Score: 0 of 1 pt
8 of 10 (7 complete)
1.2.31
How many quarts of pure antifreeze must be added to 4 quarts of a 10% antifreeze solution to obtain a 20% antifreeze solution?
quart(s) of pure antifreeze must be added.
(Round to the nearest tenth as needed)
Answers
Answer:
q = 0.5 quarts of 100% antifreeze
Step-by-step explanation:
q = quarts of pure antifreeze
Set this up as a weighted combination of the mixtures.
(100%)(q) + (10%)(4) = (20%)(q + 4)
100q + 40 = 20(q + 4)
5q + 2 = q + 4
4q = 2
q = 0.5 quarts of 100% antifreeze
Identify the type of sampling that is used: A list of all registered voters in a state is given to a researcher who would like to determine if a particular candidate is likely to be elected. The researcher has a computer randomly generate several hundred numbers, and those numbers are used to select names from the list to form a sample. a. systematic b. random c. convenience d. stratified
Answers
Answer:
The correct option is (b) random.
Step-by-step explanation:
A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.
Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.
In this case the researcher has a computer randomly generate several hundred numbers, and those numbers are used to select names from the list to form a sample.
The procedure indicates that the researcher used a simple random sampling technique to select the sample.
Thus, the correct option is (b).
Please answer this correctly
Answers
Answer:
Height of this missing bar would be 1
Step-by-step explanation:
Since there is 1 and only 1 quantity between 80-99.
Answer:
1
There is 1 number that is between 80 and 99 which is 99 so there should be 1 bar.
Step-by-step explanation:
expand and simplify (x - 2)^2
these are the options
2 + 4 + 4 2 − 4 2 − 4 + 4 2 + 4
Answers
Answer:
[tex]x^2-4x+4[/tex]
Step-by-step explanation:
[tex](x - 2)^2[/tex]
[tex](x - 2)(x - 2)[/tex]
[tex]x(x-2)-2(x-2)[/tex]
[tex]x^2-2x-2x+4[/tex]
[tex]x^2-4x+4[/tex]
Answer:
[tex]{x}^{2} - 4x + 4 \\ [/tex]
Step-by-step explanation:
[tex] {(x - 2)}^{2} \\ (x - 2)(x - 2) \\ x(x - 2) - 2(x - 2) \\ {x}^{2} - 2x - 2x + 4 \\ {x}^{2} - 4x + 4[/tex]
hope this helps you
NEED HELP ASAP
Solve the equation or inequality for the unknown number. Show your work.
Answers
Answer:
5
Step-by-step explanation:
3(14+x) = 57
42 +3x = 57
3x = 15
x = 5
The volume of a triangular prism is increased by a factor of 8.
By what factor is the surface area of the figure increased?
o 2
o 4
016
o 24
Answers
i believe that is the right answer
Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice? On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5). On a coordinate plane, blue diamonds appear at points (0, 0), (1, 2), (2, 4). On a coordinate plane, a straight line with a positive slope begins at point (negative 2.5, negative 5), crosses the x- and y-axis at point (0, 0), and ends at point (2.5, 5). On a coordinate plane, blue diamonds appear at points (negative 2, negative 4), (negative 1, negative 2), (0, 0), (1, 2), (2, 4). Mark this and return
Answers
Answer:
On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5)
Step-by-step explanation:
The distinction between "straight line" and "blue diamonds" is that the straight line represents the relation for all possible values of x. The blue diamonds show the values of y for very specific values of x.
Since x is the amount of rice from a bulk bin, we assume it can take any non-negative value. Hence, the graphs with negative values or with "blue diamonds" are not appropriate.
The straight-line graph in the first quadrant is the best choice.
Answer:
The answer is graph 1
Step-by-step explanation:
On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).
Please help me with this problem
Answers
Answer:
10
-5
Step-by-step explanation:
5 - -5
Subtracting a negative is like adding
5+5 = 10
-9 - -4
-9+4
-5
Answer:
Step-by-step explanation:
5+5 = 10
-9+4 = -5
Graph the line that represents this equation. 3x - 4y =8
Answers
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
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helpppppppppppppppppppppppppppppppppp
Answers
Answer:
answer is 2/3
Step-by-step explanation:
probability it is an eclair is 1/15=3/(3+2x+6+x)= 1/(x+3)
so x+3=15 and then x = 12
so the probability it is a humbug is (2*12+6)/(3*12+9) = 30/45 = 2/3
Ben bought 4 volleyballs and 5 footballs for $352.65 altogether. If Ben’s brother bought 2 volleyballs and 4 footballs for $249.12 altogether, what was the price of each football?
Answers
Answer:
$48.53
Step-by-step explanation:
The purchases can be written in equation form as ...
4v +5f = 352.65
2v +4f = 249.12
Doubling the second equation and subtracting the first gives ...
2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)
3f = 145.59 . . . . simplify
f = 48.53 . . . . . . divide by 3
The price of each football was $48.53.
A student used multiple regression analysis to study how family spending (y) is influenced by income
(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousands
of dollars. The following results were obtained.
ANOVA
df SS
Regression 3 45.9634
Residual 11 2.6218
Total
Coefficients Standard Error
Intercept 0.0136
x1
0.7992 0.074
x2
0.2280 0.190
x3
-0.5796 0.920
a. Write out the estimated regression equation for the relationship between the variables. (1
mark)
b. Compute coefficient of determination. What can you say about the strength of this
relationship? (3 marks)
c. Carry out a test to determine whether y is significantly related to the independent variables.
Use a 5% level of significance. (3 marks)
d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
Answers
Answer:
Step-by-step explanation:
Hello!
Given the variables
Y: family spending
X₁: income of a family
X₂: family size
X₃: additions to savings of a family
And the regression output (see attachment)
The population model is Y= α + β₁X₁ + β₂X₂ + β₃X₃
a)
To write the estimated regression equation of the relationship between the variables you have to use the information given in the regression output. Under the column "coefficients", the value that corresponds to "intercept" is the estimation of the y-intercept (a), the value under X₁ corresponds to the estimation for the slop for the variable "income of the family" (b₁), under X₂ is the estimation of the slope for the variable "family size" (b₂) and under X₃ is the estimation for the slope corresponding to the variable "additions to savings" (b₃)
The estimated regression equation is:
^Y= a + b₁X₁ + b₂X₂ + b₃X₃
^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃
b)
Using the SS information you can calculate the coefficient of determination as:
SStotal= SSReg+SSError= 45.9634+2.6218= 48.5852
[tex]R^2= \frac{SS_{Reg}}{SS_{Total}} = \frac{45.9634}{(48.5852)} = 0.946[/tex]
R²= 94.6%
This means that 94.6% of the variability of the average family spending is explained jointly by the family income, the family size and the addition to saving under the estimated model ^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃
c)
The hypotheses are:
H₀: β₁= β₂= β₃= 0
H₁: At least one βi≠0 ∀ i=1, 2, 3
α: 0.05
The statistic for the multiple regression is
[tex]F=\frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg};Df_{Error}}[/tex]
[tex]MS_{Reg}= \frac{SS_{reg}}{Df_{Reg}}= \frac{45.9634}{3} = 15.32[/tex]
[tex]MS_{Error}= \frac{SS_{Error}}{Df_{Error}} = \frac{2.6218}{11} = 0.238[/tex]
[tex]F_{H_0}= \frac{MS_{Reg}}{MS_{Error}}= \frac{15.32}{0.238}= 64.37[/tex]
p-value < .00001
At a 5% significance level, there is enough evidence to reject the null hypothesis. This means that the family income, family size and the addition to savings modify jointly the average spending of families.
d.
Individual tests:
There are two possible statistics to test the significance of each independent variable: [tex]t= \frac{b_i-\beta_i }{S_{b_i}} ~~t_{n-3}[/tex] ∀ i= 1, 2, 3, or [tex]F=\frac{MS_{X_i}}{MS_{Error}} ~F_{Df_{X_i}; Df_{Error\\}}[/tex]
Since the output doesn't give us the information of the individual ANOVA, you have to use the t-test (Df: n-3= 12-3= 9) for these hypotheses. Using the p-value approach. the decision rule for the three hypothesis will be:
If p-value ≤ α ⇒ Reject null hypothesis.
If p-value > α ⇒ Do not reject the null hypothesis.
1)
H₀: β₁ = 0
H₁: β₁ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}= \frac{0.7992-0}{0.074}= 10.8[/tex]
p-value < .00001 ⇒ Decision is to reject the null hypothesis.
2)
H₀: β₂ = 0
H₁: β₂ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}= \frac{0.2280-0}{0.190}= 1.2[/tex]
p-value: 0.260773 ⇒ The decision is to not reject the null hypothesis.
3)
H₀: β₃ = 0
H₁: β₃ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}= \frac{-0.5796-0}{0.920}= -0.63[/tex]
p-value: 0.544355 ⇒ The decision is to not reject the null hypothesis.
So, at a 5% significance level, it seems that the three independent variables influence jointly the variation on the average spending of the families, but looking at them separately, only the income of the families seems to affect their spending habits significantly while the family size or their addition to savings don't seem to have major effect over their spending habits.
I hope this helps!
Which of the following is the solution to |x-1|=8
Answers
Answer:
-7,9
Step-by-step explanation:
x-1=-8
x=-7
x-1=8
x=9
Removing which point from the coordinate plane would make the graph a function of x? On a coordinate plane, points are at (negative 2, negative 3), (negative 2, 1), (negative 4, 3), (0, 4), (1, 1), and (2, 3). (–4, 3) (–2, 1) (0, 4) (1, 1)
Answers
Answer:
(-2, 1)
Step-by-step explanation:
For a relation consisting of (x, y) pairs to be a function, all of the x-values must be unique. In the given relation, points (-2, -3) and (-2, 1) have the same x-value. Removing either point will make the relation a function.
Of these, the only one listed among answer choices is (-2, 1).
Answer:
-2 , 1
Step-by-step explanation:
good luck love
2. The sum of the ages of Denise and Earl is 42
years. Earl is 8 years younger than Denise.
How old is each?
Answers
d-Denis
e-Earl
d+e=42
e+8=d
e+8+e=42
2e+8=42
2e=34
e=17
d=17+8=25
Denis is 25 and Earl is 17
Answer
Earl is 17 years old.
Denis is 25 years old.
See? Easy!
Step-by-step explanation:
Michelle purchased a sofa that was on sale for $125 off. The original price of the sofa was $515. What was the sale price of the sofa?
Answers
Answer:
We know that:
The original price was $515
and
It was $125 off
so we need to find the price of the sofa after the discount.
$515 - $125 = $390
The sale price of the sofa after the discount was $390
hope This helps and pls mark me brainliest if it did :)
Is (-3,2) a solution of 7x+9y>-3
Yes or no
Please help :))
Answers
Answer:
(-3,2) is not a solution.
Step-by-step explanation:
The solution of a linear inequality in two variables like [tex]Ax + By > C[/tex] is an ordered pair [tex](x, y)[/tex] that produces a true statement when the values of x and y are substituted into the inequality.
To find if (-3,2) is a solution of [tex]7x+9y>-3[/tex], you must substitute this point into the inequality.
[tex]7\left(-3\right)+9\left(2\right)>-3\\\\-21+18>-3\\\\-3>-3[/tex]
Because -3 is not greater than -3, (-3,2) is not a solution.
Answer:
No
Step-by-step explanation:
Khan academy
I earn $12.00 in 5 hours. At this rate, how many hours will it take to earn $19.20?
Answers
Answer:
8 hours
Step-by-step explanation:
Solve with a proportion
[tex]\frac{12}{5}[/tex] = [tex]\frac{19.20}{x}[/tex]
Multiply 5 by 1.6 to get x
5 x 1.6 = 8
Please help me with this question!!!!
Answers
Answer:
-3i +-12j
Step-by-step explanation:
P2 -P1 = (-1-2, -6-6) = (-3, -12)
In terms of unit vectors i and j, this is -3i -12j.
For 120 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degree.Round your answer to 4 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.Sample size is .Number of samples is .When constructing a x-bar chart:The center line should be .ESD(x-bar) equals .The upper control limit (UCL) should be .The lower control limit (LCL) should be .
Answers
Answer:
Center line = 46
UCL = 46.84852
LCL = 45.15148
Step-by-step explanation:
Given:
Standard deviation = 0.8
Mean, u = 46
Sample size, n= 8
First calculate the estimated standard deviation:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.8}{\sqrt{8}} = 0.282843[/tex]
a) The center line, X', would be the average across all components. Here the average across all 960 bottles is 46
Therefore,
[tex] X' = 46 [/tex]
b) The upper control limit, UCL:
UCL = u + 3s
= 46 + 3(0.28284)
= 46 + 0.84852
= 46.84852
c) The upper control limit, LCL:
LCL = u + 3s
= 46 - 3(0.28284)
= 46 - 0.84853
= 45.15148