Using the weighted mean, it is found that the office should be located 13.85 miles from Bellevue.
What is the weighted mean?The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
For this problem, the observations are given as follows:
Bellevue, at position 0, with a weight of 5.Jonesville, at position 60, with a weight of 3.These observations are the positions of the cities, considering that they are 60 miles apart, and their weights as given in the problem.
The weighted mean between these positions is found as follows:
M = (0 x 5 + 60 x 3)/(5 + 8) = 13.85.
The meaning of the weighted mean is that:
The office should be located 13.85 miles from Bellevue.
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Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
Answer:
2 and 12
Step-by-step explanation:
2x3=6
12 x 6=72
6 and 72 is 78
Answer:
2 and 12
Step-by-step explanation:
write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (−13, −14)
The standard equation of the circle will be (x+5)²+(y+5)²= 145
The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.
formula for the midpoint
= ((x1+x2)/2, (y1+y2)/2)
Given points are - (3, 4), (−13, −14)
The circle's center is at (-5,-5)
Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.
The distance between a point on the circle and the circle's center in order to get the radius.
Therefore, let's calculate the distance between (-5, -5) and (-13,-14)
Radius R = √((-13+5)²+(-14+5)²) using the distance formula.
= 12.04
equation will be -
(x+5)²+(y+5)²= 145
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solving equations: please help:)
-(x+7)-5= -3x-12+2x
Answer:
x = 3
Step-by-step explanation:
Hello!
Solve for x by isolating the variable
Solve for x- (x + 7) - 5 = -3x - 12 + 2x [tex]\rightarrow[/tex] Distribute-x - 7 - 5 = -3x -12 + 2x [tex]\rightarrow[/tex] Simplify-x - 12 = -3x + 2x [tex]\rightarrow[/tex] Add 3x to both sides2x - 12 = 2x [tex]\rightarrow[/tex] Add 2x4x - 12 = 0 [tex]\rightarrow[/tex] Subtract 124x = 12 [tex]\rightarrow[/tex] Divide by 3x = 3The value of x is 3.
an airplne can cruise at 640 mph how far can it fly in 3/5 of an hour
The plane can fly 384 miles in 3/5 hours.
An airplane can cruise at 570 miles per hour.
We have to find the distance travelled by airplane in 4/3 hours.
Distance = Speed x Time
Distance = 640 x 3/5
Distance = 128 x 3
Distance = 384 miles
Hence, The plane can fly 384 miles in 3/5 hours.
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Which of the following intervals is equivalent to -2
A. [-2, 3]
B. [-2, 3)
C. (-2, 3]
D. (-2, 3)
Answer:
the answer is A
how would you express b⃗ b→b vec using unit vectors? express your answers in terms of the unit vectors x^x^x unit and y^y^y unit . use the button under the menu in the answer box to create unit vectors.
The answer is expressed in terms of unit vectors x^ and y^ as B = B (cos θ x ^ + sin θ y ^)
For expressing the magnetic field B in terms of vectors we need to know the magnitude of the magnetic field and the angle between them.
the angle we have is with respect to the positive side of the x-axis, let's use trigonometry.
cos θ = Bₓ / B
sin θ = / B
Bx = B cosθ
By = B sinθ
hence the resulting vector is
B = Bₓ i ^ + [tex]B_{y}[/tex] j^
The unit vectors are
x ^ = i ^
y ^ = j ^
The answer is expressed in terms of unit vectors x^ and y^ as B = B (cos θ x ^ + sin θ y ^)
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For which domain would f(x) = x be discrete?
Select one:
a.
D = {1, 2, 3, ...}
b.
D={x|0
c.
D = {x|x≥2}
d.
D={all real numbers}
c
in an arithmetic expression
Verify whether x = -1/√3 is a zero of the polynomial 3x²-1.
Answer:
Below.
Step-by-step explanation:
3x² - 1 = 0
3x² = 1
x² = 1/3
x = ±√(1/3)
= -1/√3, 1/√3.
So, -1/√3 is a zero of 3x² - 1 .
Yes, x = -1/√3 is a zero of the polynomial 3x² - 1 because substituting the value results in zero, confirming its solution to the equation.
To verify whether x = -1/√3 is a zero of the polynomial 3x² - 1, we need to substitute this value into the polynomial and check if it results in zero.
Given polynomial: 3x² - 1
Now, substitute x = -1/√3 into the polynomial:
3(-1/√3)² - 1
Now, simplify:
3(1/3) - 1
1 - 1
The result is zero. Since the expression evaluates to zero when x = -1/√3, this means that x = -1/√3 is indeed a zero of the polynomial 3x² - 1.
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Triangle LMK has vertices L(-6, 0), M(0, -6), and K(-6, -6) and triangle XYW has vertices X(0, 6), Y(8, 6), and W(4, 2). Using the definition of congruence, decide whether the two triangles are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Using the distance between two points formula to calculate the side lengths, it is found that the figures are not congruent.
What are congruent figures?Congruent figures are figures that have the same outer side lengths.
We are given the vertices for this problem, hence we use the distance between two points formula to calculate the lengths.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.
For Triangle LMK, the side lengths are given as follows:
[tex]LM = \sqrt{(0 - (-6))^2+(-6 - 0)^2} = 6\sqrt{2}[/tex][tex]KM = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex][tex]LK = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex]For Triangle XYW, the side lengths are given as follows:
[tex]XY = \sqrt{(8 - 0)^2+(6 - 6)^2} = 8[/tex][tex]WY = \sqrt{(8 - 4)^2+(6 - 2)^2} = 4\sqrt{2}[/tex][tex]XW= \sqrt{(4 - 0)^2+(6 - 2)^2} = 4\sqrt{2}[/tex]Due to different side lengths, the figures are not congruent, and nothing can be stated about the transformations that were used.
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Simplify
√5 x √12 x √50
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3} \times \sqrt{2 \times {5}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \times 2 \sqrt{5 \times 3 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: 10 \sqrt{30} [/tex]
Solve 6 + a = 3 for a.
Answer:
subtract 6 from 3 and a is -3
Step-by-step explanation:
Answer:
a= -3
Step-by-step explanation:
a=3-6
a=-3
definition of differentiation in mathematics
Answer:
This is also known as "Derivative"." in mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus."! hope this helps!
Juilan divided his savings equally between two charities. If its Julian's savings, evaluate the expression when s=$125
The expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
WE have been given that Juilan divided his savings equally between two charities. then Julian's savings as 's' =$125
First, we will write the expression;
s/2
Second, substitute the value 125 in for the variable s.
Then simplify by dividing 125 and 2.
=$125 / 2
= $62.50
Hence the expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.
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Find the product. Simplify your answer. (3f–1)(4f+1)
please solve this equation for me its algebra
solve
-4b=48
Answer:-12
Step-by-step explanation: -4b=48 b=48/-4 b=-12
hope it helps
a very lucky gambler starts with one dollar and doubles her money on each bet she makes. how much money will she have after five bets?
$32 money will she have after five bets.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." from Wolfram MathWorld .starting amount = $1
she doubles her money on her each bet.
So, when she makes her first bet , her money doubles and keep doubling
on every bet of the previous amount .
Money she makes on her first bet = 2 * 1 = $2
Money she makes on her second bet = 2 * 2 = $4
money on third bet = 2 * 4 = $8
money on fourth bet = 2 * 8 = $16
money on fifth bet = 2 * 16 = $32
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Solve the system of inequalities by graphing.
y < 2x +3
2x y ≤ 5
Step-by-step explanation:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
2a-18 in algebraic form
Answer: 2(a-9)
Step-by-step explanation:
2a-18
then factor
which leads to 2(a-9)
Answer: 2(a-9)
Step-by-step explanation: Factor out 2 from the expression 2(a-9)
Solve: -5(15)
I’m so confused
Answer:
- 75
Step-by-step explanation:
- 5(15) means - 5 × 15 = - 75
how many liters of acid must be added to a 100-liter solution that is 20 percent acid in order to product a solution that is 25 percent acid?
You can make 106.67 L of 25% v/v acid solution by mixing 6.67 L of pure acid with 100 L of 20% v/v acid solution.
What is an acid?Acids are a type of chemical that can either absorb electrons or give off protons or hydrogen ions. An anion and a cation can form in water when a hydrogen atom that is bonded to an acid releases (dissociates). How acidic a substance is and how acidic its solution pH is depends on how many hydrogen ions it produces.
The word acid stems from the Latin words acidus or acere, which suggest "sour," because one of the characteristics of acids in water is a sour taste (e.g., vinegar or lemon juice).
How thoroughly an acid splits into its ions after being dissolved in water indicates whether it is strong or weak. A strong acid, like hydrochloric acid, completely dissociates into its ions in water.
100 liters * (20/100) = 20 liters acid
Let's assume that the number x represents the amount of pure acid you need to add to your initial solution. The volume of acid will increase by x because you are working with pure acid.
V(acid) = 20 +x
V(solution) = 100+ x
As a result, the percent concentration by volume of the target solution will be equal to
{V(acid)/V(solution)} * 100 = 25%
{(20+x)/(100+x)} * 100 = 25%
(20 +x) 100 = 25(100+x)
2000+100x = 2500 + 25x
75 x = 500
x = 6.67 liters
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an isosceles triangle has an angle that measures 40 what measures are possible for the other two angles
The measures are possible for the other two angles are 70 degrees respectively
Isosceles triangleAn isosceles triangle is a triangle that has 2 of its sides and angles to be equal.
Let the measure of the other possible angles be x and y such that x = y
Since the sum of angle in a triangle is 180 degrees, hence;
x+y +40 = 180
x+x+40=180
2x+40=180
2x=180-40
2x = 140
x = 70
x = y = 70 degrees
Hence the measures are possible for the other two angles are 70 degrees respectively
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Which is the graph of g(x) = (two-thirds) Superscript x – 2?
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)
the correct option is:
"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"
Which is the graph of the given function?
Here we have the exponential function:
g(x) = (2/3)^x - 2
Now, remember that for any real number different than zero, we have that:
x^0 = 1
So if we evaluate our function in x= 0 we will get:
g(0) = (2/3)^0 - 2 = 1 - 2 = -1
Then the function passes through the point (0, -1)
With this in mind, we conclude that the correct option is:
"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"
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Answer:
C: The third graph
Step-by-step explanation:
on edge
Name the following polynomial by degree and tell the leading coefficient.
−6x3
A
3rd degree; 6
B
1st degree; −6
C
3rd degree; −6
D
1st degree; 6
The leading term, the degree of the polynomial is −6x3 is 3rd degree and coefficient −6.
Option (C) is correct.
What is a polynomial ?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables .It is is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Given:
The given expression is
−6x3
We have to find the polynomial by degree and tell the leading coefficient.
According to given question we have
The leading term of a polynomial is the term with the highest degree.
The leading coefficient of a polynomial is the coefficient of the leading term.
The degree of a polynomial is the highest degree of its terms.
Hence, the leading term, the degree of the polynomial is −6x3 is 3rd degree and coefficient −6.
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Reflection over the line y=x of the point (7,2)
Answer:
2,7
Step-by-step explanation:
when y=x similary x= y
Y= 1/2x -2
y= 3/4x +3
Anna is going to save pennies each week according to a sequence she learned.
. She has saved 3 Pennie’s to start on week 0.
. Each week after that, she will save twice the total number of Pennie’s she has saved from the previous week, minus 1.
Which recursive formula can be used to determine the number of pennies Anna will save during the nth week?
Whoever answers correctly will get Brainliest!
Answer:
I think that the answer is D.
Step-by-step explanation:
The cost for decorations and the disc jockey for the homecoming dance was $1,800. The class members sold 279 tickets and made a profit of $3,450. If x represents the price of each ticket sold, which equation could be used to find x?.
a tire shop had to fill 3 1/3 tires with.it took a small air compressor 31/4 seconds to fill them up. How long would take to fill 2 tires?
It would take 21 8/ 12 seconds to fill 2 tires
What is proportion?
Proportion can be defined as the comparison between two numbers or elements
It is also an equation with two ratios draw equal to each other.
From the information given,
If 31/ 3 tires (10/ 3 ) tires is filled in 3 1/4 seconds ( 13/ 4)
Then 2 tires = x seconds
cross multiply
x = 13 / 4 × 2 ÷ 10/ 3
x = 26/ 4 × 3/ 10
x = 260/ 12
x = 21 8/ 12 seconds
Thus, it would take 21 8/ 12 seconds to fill
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Her teacher asked her to write the correct equation or inequality that matches the
graph. Laurie wrote the following: y ≤ 2x - 4. Her teacher marked her answer
incorrect. Explain the error that Laurie made and then write the correct solution.
The correct solution of Laurie's inequality expression is y ≥ 2x – 4
Given,
The inequality expression wrote by Laurie = y > 2x - 4
The graph of the inequality expression that completes this question is added as an attachment
From the attached graph, we can see that the line of the inequality is a thick or closed line
Thick and closed line are represented by the inequality signs ≤ and ≥
Since the upper region is shaded, we make use of ≥ inequality sign
Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4
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HELP ME PLEASE I need this now
question 1 first picture is to this question
As x decreases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y = - 4.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 4.
question 2 the second picture to this question
As x decreases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) increases without bound.
Answer:
Question 1:
As x decreases without bound, f(x) increases without bound. TRUEAs x increases without bound, f(x) approaches the line y = - 4. TRUEAs x decreases without bound, f(x) approaches zero. FALSEAs x decreases without bound, f(x) approaches the line y = 4. FALSEQuestion 2:
As x decreases without bound, f(x) approaches the line y = 6. TRUEAs x increases without bound, f(x) approaches the line y = 6. FALSEAs x increases without bound, f(x) increases without bound. TRUEAs x decreases without bound, f(x) increases without bound. FALSEAs x decreases without bound, f(x) approaches the line y = 6.Step-by-step explanation:
Question 1:
options
As x decreases without bound, f(x) increases without bound.As x increases without bound, f(x) approaches the line y = - 4.As x decreases without bound, f(x) approaches zero.As x decreases without bound, f(x) approaches the line y = 4.Solving notes:
As x decreases without bound, f(x) does NOT approach zero.
As x decreases without bound, f(x) does NOT approaches the line y = 4.
_________________________________________________
Question 2:
options
As x decreases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) increases without bound.As x decreases without bound, f(x) increases without bound.Solving notes:
As x increases without bound, f(x) does NOT approach the line y = 6.
As x decreases without bound, f(x) does NOT increase without bound.