What is the area of the figure below?
To what place vaule is the number rounded 5.319 to 5.3
coat that usually cost $123 is marked 1/3 off what is the sale price of the coat
a car drives 630 miles on 35 gallons of gas. How far can it drive on 12 gallons?
The car can drive 216 miles on 12 gallons.
What is displacement?The rate of change of position is called as displacement.
Now it is given that,
Distance traveled by car = 630 miles
Gas required to travel 630 miles = 35 gallons
Therefore, Distance travel n 1 gallon = Distance traveled by car / Gas required to travel 630 miles
⇒ Distance travel n 1 gallon = 630 / 35 miles
⇒ Distance travel n 1 gallon = 18 miles
Therefore, Distance travel n 12 gallon = 12 * Distance travel n 1 gallon
⇒ Distance travel n 12 gallon = 12 * 18 miles
⇒ Distance travel n 12 gallon = 216 miles.
Thus, the car can drive 216 miles on 12 gallons.
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What is the domain of this relation?
{ (-1,5), (4,1), (8,3), (4,5) }
A spring stretches in relation to the weight hanging from it according to the weight hanging from it according to the equation y = 0.75x + 0.25 where x is the weight in pounds and y is the length of the spring in inches.
How to graph the equation including axis labels
How to interpret the slope and the y-intercept of the line
Answer and Explanation:
Given : A spring stretches in relation to the weight hanging from it according to the equation [tex]y = 0.75x + 0.25[/tex] where x is the weight in pounds and y is the length of the spring in inches.
To find :
1) How to graph the equation including axis labels ?
2) How to interpret the slope and the y-intercept of the line?
Solution :
Linear equation [tex]y = 0.75x + 0.25[/tex]
1) To draw the graph we find the x and y-intercept of the line,
x- intercept i.e. y=0
[tex]0.75x + 0.25=0[/tex]
[tex]0.75x=-0.25[/tex]
[tex]x=-\frac{0.25}{0.75}[/tex]
[tex]x=-0.33[/tex]
y- intercept i.e. x=0
[tex]y=0.75(0) + 0.25[/tex]
[tex]y=0.25[/tex]
Plotting these two points (-0.33,0) and (0,0.25).
Refer the attached figure below.
2) The general form of line is [tex]y=mx+c[/tex]
where, m is the slope and b is the y-intercept of the line.
Comparing with given line [tex]y = 0.75x + 0.25[/tex]
The slope of the line is m=0.75
and the y-intercept of the line is b=0.25.
Express 15/(1 - 3x)2 as a power series by differentiating the equation below. what is the radius of convergence?
what is the solution of the following system? x-y=11
-x+y=-11
The population of a city has increased by 34% since it was last measured. If the current population is 46,900 , what was the previous population?
Joey received a report that he scored in the 97th percentile on a national standardized reading test but in the 72nd percentile on the math portion of the test. Explain to Joey’s grandmother, who knows no statistics, what these numbers mean.
Mark is planning to run in a 10-km race he will have to run 1 4/5 km uphill, 2 7/10 km downhill, and the rest of the race on level ground how many kilometers are level
Write an inequality for each situation fewer than 250 people atend the rally
Determine whether these statements are true or false.
a.∅ ∈ {∅}
b.∅ ∈ {∅,{∅}}
c.{∅} ∈ {∅}
d.{∅} ∈ {{∅}}
e.{∅} ⊂ {∅,{∅}} f ) {{∅}} ⊂ {∅,{∅}} g) {{∅}} ⊂ {{∅},{∅}}
a, b, d, e true: empty set fits in its own container.
c, f false: bigger container doesn't hold smaller container.
Here are the truths and falsehoods of the statements:
a) ∅ ∈ {∅} - True. The empty set is an element of the set containing only the empty set.
b) ∅ ∈ {∅, {∅}} - True. The empty set is also an element of the set containing both the empty set and the set containing the empty set.
c) {∅} ∈ {∅} - False. The set containing the empty set is not an element of the set containing only the empty set.
d) {∅} ∈ {{∅}} - True. The set containing the empty set is an element of the set containing only the set containing the empty set.
e) {∅} ⊂ {∅, {∅}} - True. The set containing the empty set is a subset of the set containing both the empty set and the set containing the empty set.
f) {{∅}} ⊂ {∅, {∅}} - False. The set containing the set containing the empty set is not a subset of the set containing only the empty set and the set containing the empty set.
The probable question can be: Determine whether these statements are true or false.
a) ∅ ∈ {∅}
b) ∅ ∈ {∅, {∅}}
c) {∅} ∈ {∅}
d) {∅} ∈ {{∅}}
e) {∅} ⊂ {∅, {∅}}
f) {{∅}} ⊂ {∅, {∅}}
Which of the following expressions could be used to represent "the difference between -17 and -8"?
-8 - (-17)
-17 - 8
-17 - (-8)
-8 + (-17)
The expression that represents "the difference between -17 and -8" is the second option:
-17 - (-8)
This expression translates to "negative seventeen minus negative eight," which yields the difference between the two numbers.
Expression: -8 - (-17):This expression represents "negative eight minus negative seventeen." When you subtract a negative number, it's equivalent to adding its positive counterpart. So, this expression can be simplified to:
-8 + 17 = 9
However, this result does not represent the difference between -17 and -8; it gives the difference between 17 and 8.
Expression: -17 - 8:This expression represents "negative seventeen minus eight." This directly calculates the difference between -17 and -8. It simplifies to:
-17 - 8 = -25
This indeed represents the difference between -17 and -8.
Expression: -17 - (-8):This expression represents "negative seventeen minus negative eight." Similar to the first expression, subtracting a negative number is the same as adding its positive counterpart. So, this simplifies to:
-17 + 8 = -9
This result does not represent the difference between -17 and -8; it gives the difference between -17 and 8.
Expression: -8 + (-17):This expression represents "negative eight plus negative seventeen." It simplifies to -25, which again represents the difference between -17 and -8.
Among these expressions, only the second expression, -17 - 8, correctly represents the difference between -17 and -8.
What is the value of 4x to the 3rd degree + 4x when x=4
What is the percent increase of 36 and 63
What makes the statement true? 7^-2=
The joint probability distribution of variables x and y is shown in the table below. rebecca and rachel are car salespeople. let x denote the number of cars that rebecca will sell in a month, and let y denote the number of cars rachel will sell in a month. what is the probability that rachel and rebecca will combine to sell 3 cars in one month?
a. The unconditional mean of X = 1.75 cars.
b. Conditional Mean of X Given Y=1 is 1.38 cars.
c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3 is 1.07.
d. The covariance COV (X,Y) is 0.23. COV(X,Y) ≠ 0, X,Y not independent.
e. The correlation coefficient is 0.52, The strength is (0.3-0.5) and the direction is positive correlation.
f. The expectation and variance of Z are 10.25 cars and 6.66 cars².
Step-by-Step Joint Probability Distribution of Cars Sold:
a. Unconditional Mean of X:
1. Calculate marginal probabilities of X:
P(X=1) = 0.57, P(X=2) = 0.29, P(X=3) = 0.14
Calculate expected value of X:
E(X) = Σ(xi × P(xi)) = (1 × 0.57) + (2 × 0.29) + (3 × 0.14) = 1.75 cars
b. Conditional Mean of X Given Y=1:
1. Calculate conditional probability:
P(X=1|Y=1) = 0.40 / 0.52
2.Calculate conditional mean:
E(X|Y=1) = (1 × 0.806) + (2 × 0.194) = 1.38 cars
c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3:
1. Calculate conditional probability:
P(Y=1|X=3) = 0.15 / 0.14 = 1.07 (impossible, probabilities must be between 0 and 1)
d. Covariance and Independence:
1. Calculate joint expected values:
[tex]E(XY) = \sum (x_i \times y_i \times P(x_i,y_i)) = 2.74[/tex]
2. Calculate individual variances:
Var(X) = 0.74, Var(Y) = 0.24
3. Calculate covariance:
COV(X,Y) = E(XY) - E(X)E(Y) = 2.74 - (1.75 × 0.88) = 0.23
Since COV(X,Y) ≠ 0, X and Y are not independent.
e. Correlation Coefficient:
1. Calculate correlation coefficient:
ρ(X,Y) = COV(X,Y) / (σ(X) × σ(Y)) = 0.23 / (√0.74 × √0.24) ≈ 0.52
2. Strength: weak positive correlation (0.3-0.5)
3. Direction: positive correlation (positive coefficient)
f. Expectation and Variance of Z:
1. Use properties of mean:
E(Z) = E(3X+5) = 3E(X) + 5 = 3 × 1.75 + 5 = 10.25 cars
2. Use properties of variance:
Var(Z) = 9Var(X) = 9 × 0.74 = 6.66 cars²
Complete and correct question:
The joint probability distribution of variables X and Y is shown in the table below. Rebecca and Rachel are car salespeople. Let X denote the number of cars that Rebecca will sell in a month, and let Y denote the number of cars Rachel will sell in a month.
x=1 x=2 x=3
Y=1 0.40 0.18 0.15
Y=2 0.12 0.11 0.04
a. Find the unconditional mean of X.
b. Find the conditional mean number of cars that Rebecca will sell in a month given Rachel sells 1 car in a month.
C. What is the probability that Rachel will sell 1 car in a month given that Rebecca sold 3?
d. Find covariance COV (X, Y). Are X and Y independent? Explain why.
e. Find the correlation coefficient between X and Y. Discuss the strength and the direction of its relationship.
f. Chris, another salesperson, sells a car better than Rebecca. Let Z denote the number of cars that Rebecca will sell in a month, where Z = 3X +5. Get the expectation and variance of Z using the properties of the mean and the variance.
On a map of Texas, one inch represents 25 miles. If Dallas and San Antonio are 6.4 inches apart, how many miles apart are they? A) 1,600 B) 160 C) 256 D) 390.6
I believe your answer is B)160. But i'm not 100%. <3
What is the solution to the following system of equations? 3x-4y=35 and 3x+4y=5
The solution to the system of equations is [tex]\(x = \frac{20}{3}\)[/tex] and [tex]\(y = -\frac{15}{4}\).[/tex]
To solve the system of equations (3x - 4y = 35) and (3x + 4y = 5), we'll use the method of elimination.
Add the two equations together to eliminate the variable (y).
(3x - 4y) + (3x + 4y) = 35 + 5
3x - 4y + 3x + 4y = 40
6x = 40
[tex]\[ x = \frac{40}{6} \][/tex]
[tex]\[ x = \frac{20}{3} \][/tex]
Substitute [tex]\(x = \frac{20}{3}\)[/tex] into one of the original equations. Let's use the first equation:
[tex]\[ 3\left(\frac{20}{3}\right) - 4y = 35 \][/tex]
20 - 4y = 35
-4y = 35 - 20
-4y = 15
[tex]\[ y = \frac{15}{-4} \][/tex]
[tex]\[ y = -\frac{15}{4} \][/tex]
So, the solution to the system of equations is [tex]\(x = \frac{20}{3}\)[/tex] and [tex]\(y = -\frac{15}{4}\).[/tex]
Steve puts only dimes and quarters into his piggy bank. Right now he has five more dimes than quarters there, and they make $74.35. How many quarters and how many dimes are there in Steve’s piggy bank?
There are 211 quarters and 216 dimes in Steve's piggy bank.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
Let Steve has x quarters,
Therefore, Steve will have x + 5 dimes,
Given that,
Steve has total $74.35.
To solve, use equation format,
0.1(x+5)+0.25x=74.35
0.35x+0.5=74.35
0.35x=73.85
x=211
So the number of quarters x= 211
And number of dimes (x+5) =216
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Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (−1, 2) to (1, 2) (a) find a function f such that f = ∇f. f(x, y) = x3 3+ y3 3 correct: your answer is correct. (b) use part (a) to evaluate c ∇f · dr along the given curve
c.
In this exercise we have to perform the parameterization of the given function and we will have:
[tex]\int\limits_C {f} \, dr = f(1, 2)-f(-1, 2)= 2/3[/tex]
In there is some scalar function [tex]f(x, y)[/tex] such that:
[tex]\nabla f(x,y) = f(x, y) = x^2i+y^2j[/tex]
Then we want to find [tex]f[/tex] such that:
[tex]f'(x)= x^2= f(x,y) = \frac{x^3}{3} + g(y)\\f'(y)= y^2= f(x,y)= \frac{y^3}{3} + C\\f(x, y)= \frac{x^3}{3} +\frac{y^3}{3} + C[/tex]
So the vector filed [tex]f(x, y)[/tex] is conservative, which means the fundamental theorem applies; the line integral of [tex]f[/tex] along any path [tex]C[/tex] parameterized by some vector-valued function [tex]r(t)[/tex] over [tex]a\leq t\leq b[/tex] is given by:
[tex]\int\limits_C {f} \, dr\\\int\limits^t=a_t=b {f(r(t))} \, dt= f(r(b))-f(r(a))[/tex]
In the case:
[tex]\int\limits_C {f} \, dr = f(1, 2)-f(-1, 2)= 2/3[/tex]
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This problem requires calculation in multivariable calculus. Function f = ∇f when f(x, y) = x³/3 + y³/3. To calculate the line integral of ∇f · dr over the curve c, take the difference between the end and start points of the scalar function.
Explanation:The subject for this calculation is multivariable calculus, dealing with operations such as the gradient (∇) and line integrals.
According to the given function f(x, y) in part (a), it can be seen that f = ∇f for f(x, y) = x³/3 + y³/3. The vector field of this function is conservative since it corresponds to the gradient of a scalar function.
For part (b), you will need to calculate the line integral of ∇f · dr over the curve c, which is y = 2x² from (-1, 2) to (1, 2). The result of this will be the difference between the end and start points of the scalar function: f(1, 2) - f(-1, 2).
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factor -1/4 out of -1/2-5/4y
To factor -1/4 out of -1/2-5/4y, you can use the distributive property and simplify the expression to 1/8 + 5/16y.
Explanation:To factor -1/4 out of -1/2-5/4y, you can use the distributive property. First, rewrite the expression as (-1/2) + (-5/4)y. Then, factor out -1/4: (-1/4)(-1/2) + (-1/4)(-5/4)y. This simplifies to 1/8 + 5/16y.
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An appropriate tip for a waiter at a restaurant is at least 15%. How much money should be left for a tab of $20.00?
Two friends, rachel and joey, enjoy baking bread and making apple pies. rachel takes two hours to bake 1 loaf of bread and one hour to make 1 pie. joey takes four hours to bake 1 loaf of bread and four hours to make 1 pie. what is rachel's opportunity cost of baking 1 loaf of bread?
a. 1 loaf of bread
b. 2 pies
c. 1/2 loaf of bread
d. 1 pie
e. 4 pies
Answer: Option b
Step-by-step explanation:
Rachel needs two hours for a loaf of bread and one hour for one pie.
Joey needs four hours for one loaf of bread and four hours to a pie.
We want to know the opportunity cost of Rachel to make one loaf of bread.
The opportunity cost is the relation between what she wins and what she could'be wined if she chose the other option.
We know that at the same time that she bakes 1 loaf of bread she could make 2 pies, so the opportunity cost of 1 loaf of bread is option b (what she could have wined if she chose to do the pies instead in that time).
Explain how to find the difference -4/5-3/5
The difference between -4/5 and -3/5 is found by changing the subtraction to addition and combining the numerators, resulting in -1/5.
To find the difference between -4/5 and -3/5, you change the subtraction operation to addition by changing the sign of the second fraction. This is similar to the process described by the example, where subtracting a negative number is the same as adding its positive counterpart (e.g., 2 - (-6) = 2 + 6). In the case of fractions, the process is the same.
So, the problem -4/5 - (-3/5) becomes -4/5 + 3/5. Since both fractions have the same denominator, you can combine the numerators directly. The result is the difference of the numerators over the common denominator:
-4 - (+3) = -4 + 3 = -1Therefore, -4/5 + 3/5 = (-4 + 3) / 5 = -1/5.The difference between -4/5 and -3/5 is -1/5.
Last year, Tammy had $20,000 to invest. She invested some of it in an account that paid 7% simple interest per year, and she invested the rest in an account that paid 5% simple interest per year. After one year, she received a total of $1060 in interest. How much did she invest in each account?
Gabriella bought three cantaloupe for seven dollars how many cantaloupes Shanya buy if she has $21
how do you make a equation from slope intersecpt
Please help my son with #3
Answer:
14/15 more pints of strawberries than grapes
Step-by-step explanation:
You want to find the difference between 2 1/3 and 1 2/5. There are several ways to do this. One is to use a common denominator for the fractions. Here, a convenient denominator is 3·5 = 15. This lets us write the problem as ...
2 5/15 - 1 6/15
= (2 -1) + (5/15 -6/15)
= 1 - 1/15 . . . . of course there are 15/15 in 1, so subtracting 1 of them gives...
= 14/15
Kelly uses 14/15 more pints of strawberries than of grapes in her juice.
_____
Comment on solution details
We have rewritten the fraction 1/3 as 5/15. We can do this by multiplying 1/3 by 1, where 1 is in the form 5/5:
(1/3) = (1/3)·1 = (1/3)·(5/5) = (1·5)/(3·5) = 5/15
Similarly, we have rewritten the fraction 2/5 by multiplying it by 3/3:
(2/5) = (2/5)·(3/3) = 6/15
__
Both numbers can be converted to improper fractions:
2 1/3 = (2·3+1)/3 = 7/3
1 2/5 = (1·5+2)/5 = 7/5
Then the difference can be found using the formula ...
a/b - c/d = (ad -bc)/(bd)
7/3 -7/5 = (7·5 -7·3)/(3·5) = (35 -21)/15 = 14/15