Answer:
The car's average 18 number of miles per gallon
Step-by-step explanation:
The car has different efficiencies depending if its used on highway or city streets.
The efficiency on a highway is:
[tex]E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}[/tex]
The efficiency for city driving is:
[tex]E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}[/tex]
We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.
Then, we can calculate how many miles makes the car on average as:
[tex]E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}[/tex]
Please answer this correctly
Answer:
# of pages # of magazines
1-20 7
21-40 4
Step-by-step explanation:
Numbers 1 through 20:
10, 11, 14, 16, 17, 17, 20 (7 numbers)
Numbers 21 through 40:
21, 28, 29, 32 (4 numbers)
x⁴+1/x⁴=47,find the value of x³+1/x³
Answer:
The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5
Step-by-step explanation:
x^4 + 1/x^4 = 47
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5
The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the total
sales after 39 months. A) $102,400 B) $102,370 C) $102,500 D) $102,442
Answer:
A) $102,400
Step-by-step explanation:
For these answers, we must assume the increase is linear.
The two-point form of the equation for a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Filling in the given (x, y) values of (3, 25000) and (23, 68000), we have ...
y = (68000 -25000)/(23 -3)(x -3) +25000
y = 2150x +18,550
Then for x = 39, we find the predicted sales to be ...
y = (2150)(39) +18,550 = 102,400
The predicted sales after 39 months is $102,400.
_____
The graph shows sales in thousands of dollars.
Solve for B. R = x(A + B)
Answer:
B = R/x -A
Step-by-step explanation:
[tex]\text{Divide the equation by x:}\\\\\dfrac{R}{x}=A+B\\\\\text{Subtract A:}\\\\\dfrac{R}{x}-A = B\\\\\text{The solution is ...}\\\\\boxed{B=\dfrac{R}{x}-A}[/tex]
Answer:
[tex] b = \frac{r - ax}{x} \\ [/tex]
Step-by-step explanation:
[tex]r = x(a + b) \\ r = ax + bx \\ r - ax = bx \\ \frac{r - ax}{x} = b[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
Answer:
V ≈ 382 inches ³
Step-by-step explanation:
V = 4/3πr³
V = 4/3(3.14)(4.5)³
V = 1145.11/3
V = 381.7
V ≈ 382 inches ³
What is an equivalent function to f(x)=(x-2)^3
Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
Researchers want to compare the effectiveness of an extract of St. John's Wort with placebo in outpatients with major depression. They recruited 200 adult outpatients diagnosed as having major depression and having a baseline Hamilton Rating Scale for Depression (HAM-D) score of at least 20. Participants were randomly assigned to receive either St. John's Wort extrat, 900 milligrams per day (mg/day) for 4 weeks, increased to 1200 mg/day in the absence of an adequate response thereafter, or a placebo for 8 weeks. The response variable was the change on the HAM-D over the treatment period. After analysis of data, it was concluded that St. John's Wort was not effective for treatment of major depression.
Required:
a. What type of experimental design this is?
b. What is the population that is being studied?
c. What is the response variable in this study?
d. What are the treatments?
e. Identify the experimental units.
f. What is the control group in this study?
Answer:
a) Experimental Design: Randomised Experimental Design
b) Population : All Adult outpatients diagnosed with major depression
c) Responsive Variable : Effectiveness of extracts on depression patients' HAM-D rating
d) Treatments : John Wart extracts or Placebo
e) Experimental units : 200 adult outpatients diagnosed with major depression having HAM-D score > 20
Step-by-step explanation:
a) Randomised Experimental Design is being used : As experimental units are randomly assigned to any of the experimental groups, each receiving different treatments
b) Population refers to the entire group of objects or individuals, to whom the experiment research can be applied. So, all adult outpatients diagnosed with major depression as per HAM-D depression score are population
c) Responsive variable is the dependent variable being affected by independent variables. It is effectiveness of extracts on depression patients, ie change in change on the HAM-D depression rating
d) Treatments are the ways or objects with which experimental units are treated. These are John wart extracts or Placebo
e) Experimental units are the selected sample people or objects for experiment conduct. These are '200' adult outpatients diagnosed with major depression, having a baseline Hamilton Rating Scale for Depression (HAM-D) score > 20
An analysis of 8 used trucks listed for sale in the 48076 zip code finds that the power model ln(\hat{price})=3.748-0.1395ln(miles)ln(price^)=3.748−0.1395ln(miles), for price (in thousands of dollars) and miles driven (in thousands), is an appropriate model of the relationship. If a used truck has been driven for 47,000 miles, which of the following is closest to the predicted price for the truck?(A) $9.46(B) $24.80(C) $3,210.00(D) $9,460.00(E) $24,800.00
Answer:
(E) $24,800.00
Step-by-step explanation:
[tex]ln(\hat{price})=3.748-0.1395ln(miles)[/tex]
If a used truck has been driven for 47,000 miles
Miles=47 (in thousands)
We therefore have:
[tex]ln(\hat{price})=3.748-0.1395ln(47)\\ln(\hat{price})=3.2109\\$Take the exponential of both sides\\e^{ln(\hat{price})}=e^{3.2109}\\Price=e^{3.2109}\\$Price=24.80 \\Since the price is in thousands of dollars\\Price=24.80 X \$1000\\Predicted Price=\$24800.00[/tex]
The correct option is E.
Suppose you buy a CD for $500 that earns 3% APR and is compounded quarterly. The CD matures in 3 years. Assume that if funds are withdrawn before the CD matures, the early withdrawal fee is 3 months' interest. What is the early withdrawal fee on this account?
Answer:
$3.75
Step-by-step explanation:
I = Prt
I = $500·0.03·(3/12) = $3.75
The early-withdrawal fee is $3.75 for the first quarter.
_____
Each quarter after that, the principal amount will be larger, so the interest penalty will be larger. The fee would be the amount of interest that would be credited at the end of the next quarter, or at the end of the quarter currently in progress.
Seven students were surveyed on the number of hours of TV they watch each week. The results are shown below.
8, 12, 13, 15, 16, 17, 17
What is the mode of the data set?
7
14
15
17
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes. How long to finish filling the remaining jugs
Answer:
Step-by-step explanation:
=20
This take 30 minutes to finish filling the remaining jugs.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Now,
Let the time to finish filling the remaining jugs = x
Since, A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.
Hence, By definition of proportion we get;
⇒ 20 / x = 2 / 3
⇒ 20 × 3 / 2 = x
⇒ x = 30
Thus, The time to finish filling the remaining jugs = 30 minutes
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Evaluate the expression 2x-7 for x = -4
Answer:
-15
Step-by-step explanation:
The solution of expression for x = - 4 is,
⇒ - 15
We have to given that,
An expression is,
⇒ 2x - 7
Now, We can simplify the expression for x = - 4 as,
An expression is,
⇒ 2x - 7
Plug x = - 4;
⇒ 2 × - 4 - 7
⇒ - 8 - 7
⇒ - 15
Thus, The solution of expression for x = - 4 is,
⇒ - 15
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Identify the range of the function shown in the graph
Answer:
D Y is all real numbers
Step-by-step explanation:
When looking at the y axis, you can see that if the graph were to be bigger, the line would keep going. This means y will never stop.
A tank contains 180 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answer:
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
Step-by-step explanation:
Given that:
A tank contains 180 liters of fluid in which 50 grams dissolved inside.
Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min
The salt pumped out[tex]= \dfrac{6 L}{180 L} = \dfrac{1}{30}[/tex] of initial amount added salt
At (t = 0) = 50
To determine the number A (t)
[tex]\dfrac{dA}{dt}=Rate_{in} - Rate _{out}[/tex]
[tex]A' = 6 - \dfrac{1}{30}A[/tex]
[tex]A' + \dfrac{1}{30}A = 6[/tex]
Integrating factor [tex]y = e^{\int\limits pdt[/tex]
[tex]y = e^{\int\limits \dfrac{1}{30}dt}[/tex]
[tex]y = e^{\dfrac{t}{30}}[/tex]
[tex](e^{ \frac{t}{30}}A)' =4 e ^{\dfrac{t}{30}}+c[/tex]
Taking integral on the both sides;
[tex]Ae ^{\dfrac{t}{30}}= 6 * 30 e^{\dfrac{t}{30}} + c[/tex]
[tex]A = 180+ ce^ {-\dfrac{t}{30}}[/tex]
At A(t = 0) = 50
50 = 180 + C (assuming C = [tex]ce ^{-\dfrac{t}{30}}[/tex])
C = 50 - 180
C = 130
[tex]\mathbf{A(t) = 180 - 130e ^{-\dfrac{t}{30}}}[/tex]
What are the names for the sides of a triangle?
Answer:
there are none
Step-by-step explanation:
a triangle its is own shape and does not have any name for each side.
Pls help me with this
Answer:
x = 1.5
Step-by-step explanation:
Given
[tex]\frac{x}{2} \geq 0.75[/tex]
[tex]\frac{x}{2} < 2.5[/tex]
Required
Find the value of x.
First, the inequalities need to be rewritten and merged;
if [tex]\frac{x}{2} \geq 0.75[/tex], then
[tex]0.75 \leq \frac{x}{2}[/tex]
Multiply both sides by 2
[tex]2 * 0.75 \leq \frac{x}{2} * 2[/tex]
[tex]1.5 \leq x[/tex]
Similarly;
[tex]\frac{x}{2} < 2.5[/tex]
Multiply both sides by 2
[tex]2 * \frac{x}{2} < 2.5 * 2[/tex]
[tex]x < 5[/tex]
Merging these results together; to give
[tex]1.5 \leq x < 5[/tex]
This means that the range of values of x is from 1.5 to 4.9999....
From the question, x is the smallest rational number; from the range above ([tex]1.5 \leq x < 5[/tex]), the minimum value of x is 1.5 and 1.5 is a rational number;
Hence, x = 1.5
(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume the "worst case" scenario for the value of both sample proportions. We want a 99% confidence level and for the error to be smaller than 0.08.
(b) Again find the sample size required, as in part (a), but with the knowledge that a similar student last year found that the proportion of boys afraid of spiders is 0.7 and the proportion of girls afraid of spiders was 0.69.
Answer:
a) The size of each of the two samples(equal), n = 518
b) Sample size, n = 439
Step-by-step explanation:
For clarity and easiness of expression, the complete solution to this question is handwritten and attached as files. Check the attached files below for the explanations.
Which of the following is the solution to 4 | X+32 8 ?
A. XS-5 or x 2-1
B. X25 or x 2-1
C. $-5 and x-1
D. -1
SUBMIT
Answer:
A
Step-by-step explanation:
x + 3 must be 2 or greater, or -2 or less
So x must be ≥ -1 or ≤ -5
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
idk dont ask me
Step-byi-step explanation:
Answer:
a+b+c=2003
a+b=814
2003-819=189
Step-by-step explanation:
What measures of the cylinder do 12 and 42 describe?
A cylinder with height of 42 millimeters and radius of 12 millimeters.
radius and diameter
radius and height
diameter and height
diameter and area of base
Answer: radius and height
Step-by-step explanation:
Radius is the distance between the center of the circle to its boundary.
Height is the length of the figure from top to bottom.
Given statement : A cylinder with height of 42 millimeters and radius of 12 millimeters.
That clearly means that the cylinder is having radius of 12 millimeters i.e. 12 is representing the measure of the radius of the cylinder.
And Similarly, 42 is representing the measure of the height of the cylinder.
Hence, the 2 and 42 describe the radius and height respectively of the cylinder.
Answer:
radius and height
Step-by-step explanation:
i just took the test edge 2020. rate me 5 stars!
Tori needs to make some house repairs in three years that will cost $9,000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
She needs to have approximately $6950 on that account.
Step-by-step explanation:
Since the account has an interest rate of 9% annually, then it's compounded and the earnings can be found by the following expression:
[tex]M = C*(1 + r)^t[/tex]
Where M is the final amount, C is the initial amount, r is the interest rate and t is the time elapsed in years.
She needs the money in 3 years, therefore t = 3. Applying this to the problem we have:
[tex]9000 = C*(1 + 0.09)^3\\9000 = C*(1.09)^3\\C*1.295 = 9000\\C = \frac{9000}{1.295}\\C = 6949.81[/tex]
She needs to have approximately $6950 on that account.
The box plots represent the birth weights, in pounds, of
babies born full term at a hospital during one week.
Female Birth Weight
Complete the statements to compare the weights of
female babies with the weights of male babies.
The median female birth weight is
the
median male birth weight.
The range of female birth weight is
the
range of male birth weight.
Which birth weight measure is the same for both
genders?
5
6
7
8
9
10
11
Male Birth Weight
Answer:
Step-by-step explanation:
The median female *less than*
The range of female*less than*
Which birth weight:*minimum*
Answer:
The median female birth weight is
✔ less than
the median male birth weight.
The range of female birth weight is
✔ less than
the range of male birth weight.
Which birth weight measure is the same for both genders?
✔ minimum
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass? Possible responses are yes or no,or not sure.
Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
Step-by-step explanation:
a. The sample size for the poll would be at most 10% of the total readers of the tennessean.
b. Categorical data...data collected in groups or categories.
c. Yes it would make more sense to use percentages as this gives a better estimate for proportion.
d. The number of individual that provided this response is 67% of the sample size (which is at most 10% of the total population of readers of the online newspaper).
334% of what number is 33,400
Answer:
10000
Step-by-step explanation:
3.34x=33400
x=10000
The number is x=10000.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
let, the number = x
now, we get,
3.34x=33400
x=10000
Hence, The number is x=10000.
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Sample Space: Tutorial
Activity
In this exercise, you'll use the formula for the probability of the complement of an event.
Another game you've set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points
depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails).
Question 1
Find the total number of possible outcomes in each trial of this game.
Answer:
The number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
Given
Rolling of a 6 sided die followed by tossing of a fair coin
Required
Number of possible outcomes
The first step is to list out the possible outcomes of rolling a die and tossing a coin
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {Head, Tail}
Let Head be represented by H and Tail be represented by T;
So,
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {H, T}
The question states that a roll of a 6 sided die is followed by a toss of a fair coin
This means that each trial is {A roll of die and A toss of coin}
So, the sample space is as follows
Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
Number of outcomes in the sample space is 12.
Hence, the number of possible outcomes in each trial of this game is 12
Answer:
the total number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
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A store has 8 puppies, including 3 poodles, 3 terries, and 2 retrievers. If Rebecca and Jas, in that order, each select one puppy at random without replacement, find the probability that Jas Selects a retriever, given that Rebecca selects a poodle.
Answer:
2/7
Step-by-step explanation:
Since Rebecca is garunteed to pick a poodle, there are 7 puppies left. There are 2 retrievers so the probability is 2/7
Answer:2/7
Step-by-step explanation:
what is the positive solution for the equation
Answer:
x=3
Step-by-step explanation:
4x^2 - 36 = 0
Add 36 to each side
4x^2 -36 +36 = 0+36
4x^2 = 36
Divide each side by 4
4x^2/4 =36/4
x^2 = 9
Take the square root of each sdie
sqrt(x^2) = ±sqrt(3)
x = -3,+3
We want the positive square root
x=3
If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =
Answer:
[tex]x + y = \frac{1000}{9}[/tex]
Step-by-step explanation:
Step 1: Identify the approach:
With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.
Step 2: Analyze:
[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]
Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.
Step 3: Perform manipulation:
[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]
Rearrange:
[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]
Simplify:
[tex]9(x + y) + 0 + 0 = 1000[/tex]
Simplify:
[tex]x + y = \frac{1000}{9}[/tex]
Hope this helps!
:)
Assume that when adults with smartphones are randomly selected, 53% use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that exactly 5 of them use their smartphones in meetings or classes.
Answer:
[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]
Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194
Step-by-step explanation:
Let X the random variable of interest "number of adults with smartphones", on this case we now that:
[tex]X \sim Binom(n=7, p=0.53)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=5)[/tex]
Using the probability mass function we got:
[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]
Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194
Anyone know the answer ?
Answer:
A. SASD. LLStep-by-step explanation:
Two sides and the angle between are marked as congruent. That immediately tells you that the Side-Angle-Side (SAS) theorem of congruence applies.
The angle is a right angle, which makes the adjacent sides be "legs" of the right triangle. Then the Leg-Leg (LL) theorem of congruence for a right triangle also applies.
Appropriate choices are ...
SAS, LL
