Answer:
4 mph
Explanation :
Let us call x, the woman speed as she goes uphill
Now, we know that it took the woman 2 hours to go uphill; therefore, the distance covered is
4* (x)
shortly afterwards, when the woman returns she is walking at x + 2 mph; therefore, the distance she covers is
D = 4 (x +2 )
Since the uphill and the downhill distances ar the same, we have
4x = 2 (x +2 )
4x = 2x + 4
x = 2
Hence, going to the hill, the woman speed is 2 miles per goo
For each relation, decide whether or not it is a function.
Relation 1 and Relation 3 are functions while Relation 2 and Relation 4 are not functions.
Function is a relation which maps a set to another set with some criteria.
It includes a property that one element of the domain set should only be related to exactly one element in the range set. That is, same element from the domain cannot be related to different elements in the range. Also all elements in the domain should have images in the range also.
Now we will check all the relations given one-by-one.
In relation 1, the relations are:
Chair ---------> 0
Pencil --------> 0
Paper ---------> 4
Star ------------> 1
Here All the domain elements are mapped only once to one element from the range. So it is a function.
In relation 2, the relations are:
4 ----------------> 5
4 ----------------> 9
0 ----------------> -9
1 -----------------> 4
8 -----------------> -4
Here 4 is mapped to both 5 and 9. So it does not satisfy the definition of a function and hence is not an function.
In relation 3, the relations are:
z -----------------> c
k -----------------> a
a -----------------> k
c ------------------> c
Here also all elements in the domain are mapped only once to an element from the range. So it is a function.
In relation 4, the relations are:
-4 -----------------> m
-4 -----------------> d
-4 -----------------> c
9 -----------------> s
Here, -4 is mapped to m, d and s. So it cannot be a function as it has more than one images.
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A crate of medicine with a density of 2,200 kilograms per cubic meter will be shipped from England to the U.S. What is the crate's density in pounds per cubic foot?
The crate's density in pounds per cubic foot = 137.28 lb/ft³
What is density?Density is defined as the quantity that shows the relationship between the mass and volume of an object which is measured in kilograms per cubic meter or in pounds per cubic foot.
The density of the given crate of medicine = 2,200 kg / m³
To convert to pounds per cubic foot;
1 kg/m³ = 0.0624 lb/ft³
2,200 kg/m³ = X
Make X the subject of formula;
X = 2,200 × 0.0624/1
X = 137.28 lb/ft³
Therefore, when converter to pounds per cubic foot the density of the crate of the medicine= 137.28 lb/ft³.
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Nicholas earned $2,000.00 working over the summer and wants to put the money into a savings account. A savings account at bank A earns 5% simple interest and a savings account at bank B earns 4% interest compounded quarterly. If Nicholas plans to deposit the $2,000.00 and leave it in the account for 4 years, at which bank would he earn more interest? A. The interest earned cannot be calculated from the given information. B. The interest earned at both banks will be the same. C. bank A D. bank B
Answer:
Choice C
==> Bank A
Step-by-step explanation:
Principal P = $2000
Bank A calculation
Simple Interest at 5% for 4 years = Prt = 2000 x 5/100 x 4 = $400
Bank B Calculation
At 4% interest compounded quarterly, the accrued value(Principal + Interest) is given by the formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
where
P = principal
r = annual interest rate as percentage
n = number of compounding per year
t = number of years
We have r = 4/ 100 = 0.04
n = 4 since interest is computed quarterly or 4 times a year
t = 4 years
[tex]A = 2000 ( 1 + 0.04/4)^{(4) \cdot (4)}\\\\A = 2000 (1.01)^{16} = \$2,345.16\\\\\text{Interest } = 2345.16 - 2000 = $345.16[/tex]
Since interest earned at bank A (400) > interest earned at bank B(345.16), the answer would be C. ==> Bank A
Write two expressions that represent the volume of the cube, one with exponents and one without. The side of the cube is the fraction 3/5.
(3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5.
1.) For the first expression with exponents:
(3/5)to the power of 3 can be written as , where the number 3/5 is called the base, and 3 is the power or exponent of the expression. So (3/5) times 3 .
Where, Side of the cube (a) = 3/5
⇒ (3/5)^3
⇒ 0.216 cube.units
2.) For the second expression without exponents:
The formula of volume of the cube is given by volume(side) =a*a*a, where a is the length of its sides or edges.
Cube ⇒ ( 3/5 × 3/5 × 3/5)
Cube ⇒ 0.216 cube.units
Cube of having side (3/5) = 0.216 cube.units
Hence, (3/5)^3 and (3/5 × 3/5 ×3/5) are the two expressions that represent the volume of the cube having side 3/5 .
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Find the value of f(7) y = f(x) 10 6 4 -10 -8 -6 -4. -2 4 10 -4 -6 GO -10 Answer: Submit Answer
Answer:
f(7) = -5
Step-by-step explanation:
To find f(7), we would need to first find on the graph 7 on the x-axis.
We would next need to see where 7 on the x-axis meets with the graph. In this case, we would go down.
Now that we see where 7 on the x-axis meets with the graph, we would now look at the number on the y- axis that spot on the graph matches with.
In this case, we would go left from the graph all the way to the y-axis, where the correspo ding number would be -5.
please helppppppppppppppppppppppppppppppp!
Answer:
(9 x 27) x 5
Step-by-step explanation:
First we have to figure out the powers. 3 To the power of 2 is 9 and 3 to the power of 3 is 27 so we first multiply that and later multiply 5
Solve for x:
3(x+1)-22+13=12
Answer:
x=6
Step-by-step explanation:
3 (x+1) -22 +13=12
3x+3 -22+13=12
3x+3-9=12
3x-6= 12
3x= 12+6
3x= 18
x= 18/3
x= 6
The quotient of 1 and the square of a number. Write it as an expression
Answer:
1 ÷ [tex]\sqrt{n\\}[/tex] = x
Step-by-step explanation:
For the given, "the quotient of 1 and the square of a number", the expression is 1+√n
What is a mathematical expression?
A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, Mathematicians have the ability to multiply, divide, add, and subtract. A mathematical operator, a number or variable, and an expression make up an expression.
The phrase "The quotient of 1 and the square of an integer" is presented.
The dividend and the amount being divided by the divisor are, respectively, referred to as the dividend and the amount being divided by it. The quotient is created by dividing the result.
If n is the number the expression can be written as,
=1+√n
Thus, for the given expression the expression is 1+√n.
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Bill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the compound amount in 6 years
Given:
Initial deposit = $8500
rate of interest = 5% compounded annuallly
time (t) = 6 years
If Ao is invested at an annual interest rate r and compounded semiannually, the amount At after t years is given by the formula:
[tex]A_t\text{ = }A_0(1\text{ + }\frac{r}{2})^{2t}[/tex]The compound amount in 6 years:
[tex]A_t\text{ = 8500 }\times\text{ (1 + }\frac{0.05}{2})^{2\times6}[/tex]Simplifying we have:
[tex]\begin{gathered} A_t\text{ = 8500 }\times1.025^{12} \\ =\text{ 11431.56} \end{gathered}[/tex]Answer:
$11431.56
Research one of the methods listed above or another method of your choice for factoring trinomials of the form ax² + bx + c.State the method you are using and explain the process of factoring a trinomial in words, modeling the process by using examples that contain all the steps to factor the trinomial
The grouping (a · c) method is another method for factoring trinomials of the form ax² + bx + c.
The process of factoring a trinomial using the grouping method is,
First, find a GCF and then factor it out.The coefficient of the leading phrase an is then multiplied by the constant term c. List the elements of this product (a · c) to discover the pair of factors, f1, and f2, that add to b, the middle-term coefficient. When c is positive, the sign of the components of (a · c) is the same - Find the pair of factors that adds to b if the middle-term bx is positive. If the middle-term bx is negative, both factors are negative. When c is negative, the elements of (a · c) have the inverse sign - Find the pair of factors that subtracts to b. The largest of these factors has the same sign as the middle term.Rewrite the middle term bx with the components f1 and f2 from Step 2. The phrase currently has four terms: ax² + bx + c = ax² + f1x + f2x + cThen, as illustrated, group the expression's terms into binomial pairs: (ax² + f1x) + (f2x + c) Then, for each pair, factor out a GCF The terms will have a common binomial factor if the equation can be factored by grouping. To write the factorization, subtract the common binomial factor.Finally, double the result to confirm.Learn more about factoring trinomials at
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In the the diagram to the right, sphere O with radius 5 cm is intersected by a plane 4 cm from center O. Find the radiusof the cross section O A
Since a right triangle is formed, the radius of the cross-section is the missing side of the triangle.
Apply the Pythagorean theorem:
C^2 = a^2 + b^2
Where:
c = hypotenuse = 5
a & b = the other 2 legs of the triangle = 4 and x
Replacing:
5^2 = 4^2 + x^2
solve for x ( radius of the cross-section)
25 = 16 + x^2
25-16 = x^2
9 = x^2
√9 = x
x = 3 cm
Find the percent change. Round to the nearest tenth of a percent when necessary. From 50 to 94.
Percent change of 88%
1) Consider 50 as equivalent to 100% as well as 94 to x.
50 ----------- 100%
94 ------------ x
2) Now we can set the ratios and cross multiply then:
[tex]\begin{gathered} \frac{50}{94}=\frac{100}{x} \\ 50x=94\cdot100 \\ 50x=9400 \\ \frac{50x}{50}=\frac{9400}{50} \\ x=188 \\ \end{gathered}[/tex]So 94 corresponds to 188%. Then we can see that there was an increase. Since 94 >50.
But we need to subtract from 100% to find out the percent change from 50 to 94.
188%-100%= 88%
3) Hence, the answer is an increase of 88%
Write and equation for each of the following problems and solve. (40 points each)3. The length of a rectangle is 5 cm more than three times the width. If the width is 12, what is thelength of the rectangle?
It is given that,
The length of a rectangle is 5 cm more than three times the width.
That is, l=3w+5
Put width, w=12.
Therefore, the length becomes,
l=3(12)+5
l=36+5
l=41 cm.
Hence, the length of the rectangle is 41 cm.
Pick a number 1 through 20. Now do it again.Now do it a third time. I am going to writedown my prediction of what numbers youpicked. Assuming no magic was used, what isthe probability I guessed right? Put youranswer in fraction form. (Note: Numbers CANbe used more than once.)
There are 20 numbers to choose from. Thus, the total sample space is 20.
If you choose one number, the probability of choosing that number is:
[tex]\frac{1}{20}[/tex]Now, if after choosing one number in the first round, you proceed to choose another number in the second round.
The probability of choosing a number for this second round will be:
[tex]\frac{1}{20}[/tex]Note that you are allowed to repeat numbers, so therefore, this is a probability problem with replacement.
For the third round, you choose another number from 1 to 20. The probability is the same as the previous two:
[tex]\frac{1}{20}[/tex]The probability that a person guesses these 3 numbers is the same as the probability of actually choosing the numbers randomly.
Thus the final answer:
[tex]\frac{1}{20}\times\frac{1}{20}\times\frac{1}{20}=\frac{1}{8000}[/tex]Therefore, the final answer is:
[tex]\frac{1}{8000}[/tex]Please help ASAP
Question is attached below
Answer:
√30/4
I Hope that This Helped!
After 12 weeks, how much more will he made in sales of buttered popcorn than the sales of caramel popcorn
We have two functions for the sales of popcorn:
[tex]\begin{gathered} B(w)=8w+9 \\ C(w)=6w-1 \end{gathered}[/tex]being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.
We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.
We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.
Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).
Then, we can calculate the difference in sales as:
[tex]\begin{gathered} D=11\cdot B(12)-11\cdot C(12) \\ D=11\cdot(8\cdot12+9)-11\cdot(6\cdot12-1) \\ D=11\cdot(96+9)-11\cdot(72-1) \\ D=11\cdot105-11\cdot71 \\ D=1155-781 \\ D=374 \end{gathered}[/tex]Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.
A doll’s house has an original price of $x. It is sold for $350 after its original price has been decreased by 5% and then by 10%. Find x.
Answer:
Step-by-step explanation:
0.95x*0.9=0.855
350/0.855=409.35
x=409.35
what is 3 +(-4) on a number line
Hello! Question is in photo please help me out.
The value of x for the given similar triangle will be 5 units.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
From the similarity concept, the value of x will be calculated as:-
( 10 / x ) = ( 6 / 3 )
10 = 2x
x = 10 / 2
x = 5
Therefore, the value of x for the given similar triangle will be 5 units.
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Which graph best represents 16≤x²+y²≤25
The most appropriate choice for annular region will be given by
This graph represents an annular region shown in the figure
What is annular region?
Annular region represents the space between two concentric circles of different radii.
Equation of annular region centered at (0, 0) is
[tex]a^2 \leq x^2+y^2\leq b^2[/tex]
Here,
[tex]x^2 + y^2\geq 16\\x^2 + y^2 \geq 4^2\\[/tex]
It denotes the outside of a circle of radius 4 centered at (0, 0)
[tex]x^2 + y^2\leq 25\\x^2 + y^2 \leq 5^2\\[/tex]
It denotes the inside of a circle of radius 5 centered at (0, 0)
So the complete graph is being attached here.
This region is known as annular region
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yes I am having problems learning about equations
If we have a function [Equation] it would look something like this:
3x+y=4
In order to solve for both values and graph it [If that's what you are trying to do], you solve for y and then replace values [Of your own choosing, or they are given to be studyed] in x, after we replace the values in x, we are going to have the respective value of y.
From our previous example, it would be:
y = -3x+4
So, when we start replacing the values of X, we will get the respective values for Y, let's try doing it from -3 to 3.
x = -3 => y = -3(-3)+4 => y = 13
x = -2 => y = -3(-2)+4 => y = 10
x = -1 => y = -3(-1)+4 ) => y = 7
x = 0 => y = -3(0)+4 => y = 4
x = 1 => y = -3(1)+4 => y = 1
x = 2 => y = -3(2)+4 => y = -2
x = 2 => y = -3(3)+4 => y = -5
From this, we would end up with the following points:
(-3, 13)
(-2, 10)
(-1, 7)
(0, 4)
(1, 1)
(2,
A sequence is defined by the recursive formula f(n + 1) = 1.56(0). Which sequence could be generated using the formula? 0 -12 -18, -27 ! EE 0 -20, 30, -45, -18, -16.5, -15, ... 0-16, -17.5, -19, ...
f(n+1) is
[tex]f(n+1)=\frac{3}{2}^nf(n-(n-1)[/tex]Therefore, substitutig, we get, option c.
A combined total of 598 hamburgers and cheeseburgers were sold. There were 52 fewer cheeseburgers sold in hamburgers. How many hamburgers were sold
I need over y-axis, y = x, and y = -x
Given:
(3,2)
Reflection on x axis: (3,-2)
Reflection on y-axis: (-3,2)
Reflection of y=x : (2,3)
Reflection on y=-x : (-2,-3)
Solve for X picture include
The sum of angles of a triangle is equal to 180 degree.
Determine the value of x, by using angle sum for the triangle.
[tex]\begin{gathered} 2x-4+3x-4+3x-4=180 \\ 8x=180+12 \\ x=\frac{192}{8} \\ =24 \end{gathered}[/tex]The value of x is 24
Pythagorean Theorem• Create a real-world problem involving threelengths that form a right triangle• Give the measurement of the "legs", then solvefor the missing side
SOLUTION
Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.
The problem can be modeled using the figure below
Notice that the triangle formed is a right triangle:
Therefore using Pythagorean theorem it follows:
[tex]x^2+150^2=170^2[/tex]Solve for x
[tex]\begin{gathered} x^2=170^2-150^2 \\ x^2=6400 \\ x=80 \end{gathered}[/tex]Therefore the other leg no miss
I NEED HELP ON TRIG PROOFS, SOMEONE PLEASE HELP!!!! URGENT!!!!
Step-by-step explanation:
:)))))))))))))))))))))
The five number summary of a dataset is given as
0, 4, 8, 12, 17
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
An observation is considered an outlier if it is below -16.75
An observation is considered an outlier if it is above 33.25
Extremely low or high values in a data set are considered outliers. Outliers are a product of statistical observational errors and variability. They frequently produce significant statistical issues, hence they are frequently left out of the study.
We must think about if it meets the following criteria in order to identify an outlier:
Q₁ - 1.5 (IQQ) ⇒ for lower value
Q₃ + 1.5 (IQR) ⇒ for higher value
Q₁ stands for the lower quantile, Q₃ for the higher quantile, and IQR for the inter-quantile range. Using the previous data,
Q₁ and Q₃ come from:
Q₁ = (0 + 4) / 2 = 4 / 2 = 2
Q₃ = (12 + 17) / 2 = 29 / 2 = 14.5
IQR = Q₃ - Q₁ = 14.5 - 2 = 12.5
(a) An observation is considered an outlier if it is below:
Q₁ - 1.5 (IQR) = 2 - 1.5 (12.5) = 2 - 18.75 = -16.75
An outlier is a number that is less than -16.75
(b) An observation is considered an outlier if it is above:
Q₃ + 1.5 (IQR) = 14.5 + 1.5 (12.5) = 14.5 + 18.75 = 33.25
An outlier is a number that is greater than 33.25
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A) list roots and multiplicity.B) domain and range C) degree : 4 D) equation (show work by solving for a)
ANSWER :
A. (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain : (-∞, ∞)
C. Range : (-16, ∞)
D. Degree : 4
E. f(x) = (x + 3)(x + 1)(x - 1)(x - 3)
EXPLANATION :
From the problem, we have a graph in the illustration.
A. Roots are the points in which the graph intersects the x-axis.
Multiplicity means how many times the graph intersects at the specific point.
Roots :
The graph intersects at (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain and Range.
Domain is the set of x-values in the graph.
Range is the set of y-values in the graph.
From the graph,
Domain :
x values are all real numbers. (-∞, ∞)
Range :
y values are from y = -16 to the positive infinity. That will be (-16, ∞)
C. Degree : 4
D. The equation of a function with a degree of 4 is given by :
[tex]f(x)=a(x-b)(x-c)(x-d)(x-e)[/tex]where a = coefficient
b, c, d and e are the roots of the function.
Since we already solved for the roots, that will be :
b = -3, c = -1, d = 1 and e = 3
The equation will be :
[tex]f(x)=a(x+3)(x+1)(x-1)(x-3)[/tex]Plug in the given point (0, 9) then solve for the value of "a"
[tex]\begin{gathered} 9=a(0+3)(0+1)(0-1)(0-3) \\ 9=a(3)(1)(-1)(-3) \\ 9=9a \\ a=\frac{9}{9} \\ a=1 \end{gathered}[/tex]The equation will be :
[tex]f(x)=(x+3)(x+1)(x-1)(x-3)[/tex]HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
[tex]\textsf{Let $\boxed{x}=\boxed{\textsf{The total dollar amount of all phone sales}}$}\:.[/tex]
[tex]\textsf{Let $\boxed{y}=\boxed{\textsf{The total dollar amount of all computer sales}}$}\:.[/tex]
System of Equations
[tex]\boxed{x + y = 3600}[/tex]
[tex]\boxed{0.04x + 0.06y = 178}[/tex]
Step-by-step explanation:
Given information:
4% commission on the total dollar amount of all phone sales.6% commission on all computer sales.Total sales = $3600Total commission = $178Define the variables:
Let x = The total dollar amount of all phone sales.Let y = The total dollar amount of all computer sales.Convert the percentages into decimal form:
[tex]\implies \sf 4\%=\dfrac{4}{100}=0.04[/tex]
[tex]\implies \sf 6\%=\dfrac{6}{100}=0.06[/tex]
Therefore, the system of equations that could be used to determine the dollar amount of phone sales and computer sales is:
[tex]\begin{cases}x + y = 3600\\0.04x + 0.06y = 178\end{cases}[/tex]
Solving the system of equations
Rewrite the first equation to isolate y:
[tex]\implies x=3600-y[/tex]
Substitute the expression for x into the second equation and solve for y:
[tex]\implies 0.04(3600-y)+0.06y=178[/tex]
[tex]\implies 144-0.04y+0.06y=178[/tex]
[tex]\implies 144+0.02y=178[/tex]
[tex]\implies 0.02y=34[/tex]
[tex]\implies y=1700[/tex]
Therefore, Cameron made $1,700 of computer sales.
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x+1700=3600[/tex]
[tex]\implies x=1900[/tex]
Therefore, Cameron made $1,900 of phone sales.