By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.
For this exercise, the elements of the given data set would be listed in ascending order as follows:
Set = {-4, -3, -3, -1, 0, 1, 2, 2}
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¿Cuántas personas podrán ir sentadas en 5 buses si en cada uno se suben 85 personas y solo van sentados tres quintas partes de esas personas?
The number of people that are seated in the buses is 425
How to calculate the number of people?From the information, there are 5 buses and there are 85 people in each. Therefore, the total number of people will be:
= 85 × 5.
= 425
Since 3/5 of those people are seated, the number of people seated will be:
= Fraction of those seated × Total number of people.
= 3/5 × 425
= 255
Therefore, there are 255 people.
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Need asap! Write the expression as a power and evaluate it. The expression as a power is __. The value is__.
8•2^7 and 16•32
The expression as power is written as 2¹⁰ and 2^9
The values are
2¹⁰= 1024 2^9 = 512How to write expression as a powerpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.
8• 2^7
= 2 * 2 * 2 * 2^7
= 2^10
= 1024
16•32
2^5 = 2 * 2 * 2 * 2 * 2
2^4 = 2 * 2 * 2 * 2
16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
= 2^9
= 512
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(HELP ASAP) ABC Is Isosceles m
Answer:
m∠A = 55°-----------------------------
A and C are congruent angles opposite to congruent sides of the isosceles triangle.
m∠A = m∠C3x + 40 = x + 503x - x = 50 - 402x = 10x = 5Find the measure of ∠A
m∠A = 3×5 + 40 = 15 + 40 = 55Answer:
The angle A is 55°.
Step-by-step explanation:
We know that,
→ <A = <C
Now the value of x will be,
→ 3x + 40 = x + 50
→ 3x - x = 50 - 40
→ 2x = 10
→ x = 10/2
→ [ x = 5 ]
Then the value of m<A is,
→ A = 3x + 40
→ A = 3(5) + 40
→ A = 15 + 40
→ [ A = 55° ]
Hence, the answer is 55°.
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be kilograms.
According to the scatter plot provided, the weight for someone who is 1.5 meters tall is predicted to be 45.45 kilograms.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical and analytical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the weight (in kilogram) would be plotted on the y-axis of the scatter plot while the height (M) would be plotted on the x-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear function for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.5 meters, we have:
Weight, kg = -114.3 + 106.5(1.5)
Weight, kg = -114.3 + 159.75
Weight, kg = 45.45 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be ____ kilograms.
Write the equation of a parabola with the focus at (3, 0) and the directrix at x = –3.
x^2 = –3y
y^2 = –3x
x^2 = 12y
y^2 = 12x
The equation of the parabola whose focus is at (3, 0) and directrix at x = - 3 is y² = 12 · x. (Correct choice: D)
How to derive the equation of the parabola
In this problem we need to determine the equation of a parabola based on the information of the focus and the directrix. The vertex form of the parabola is described below:
4 · p · (x - h) = (y - k)²
Where p is the distance from the vertex to the focus. The coordinates of the vertex is the midpoint of the line segment of the least distance between the directrix and the focus.
First, determine the coordinates of the vertex:
(h, k) = 0.5 · (- 3, 0) + 0.5 · (3, 0)
(h, k) = (0, 0)
Second, calculate the distance from the vertex to the focus:
p = 3 - 0
p = 3
Third, write the vertex form of the parabola:
y² = 12 · x
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Can someone awnser all three questions please.
Answer:
Step-by-step explanation:
87
99
128
Solve the inequality4x + 13 ≥ 27
Work Shown:
4x + 13 ≥ 27
4x + 13-13 ≥ 27-13
4x ≥ 14
4x/4 ≥ 14/4
x ≥ 7/2
The inequality sign stays the same for each step. The inequality sign only flips if we were to multiply both sides by a negative number (or divide both sides by a negative number).
Note: 7/2 = 3.5
Evaluate the power.
0.5² =
(Type a whole number or a decimal.)
Find the value of the expression:
3x^0 for x=2.6
Answer:
1
Step-by-step explanation:
We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.
A bicycle with 20 -inch diameter wheels is traveling at 13 mi/h. How many revolutions per minute do the wheels make?
The revolution per minute done by the wheel of a bicycle is 16.9 rev/min.
What is Velocity?Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.
In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.
As per the given information in the question,
Diameter of wheel = 20 inch
Radius, r = 10 inch
The velocity of the bicycle, v = 13 mi/h.
Revolution, R = v²/r
R = 13²/10
R = 16.9 rev/min
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Given mn, find the value of x.
(2x+6) (x+9)"
Answer:
(2x+6) = (x+9) ; x = 3
Step-by-step explanation:
-x both sides ; 2x-x = x and -6 both sides which is x = 3
Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.
What property did Bill use?
The addition property used by Bill in finding the actual December temperature is the commutative property of addition.
According to the question,
We have the following information:
Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.
We know that are five properties of addition: closure property, commutative property, associative property, additive identity property of addition and additive inverse property.
The commutative property of addition means that if two numbers are added and their order is inversed then the result of addition will always be the same.
For example, we get -2 by adding -5+3 and 3+(-5). The change in order of digits does not affect the final result.
Hence, the addition property used by Bill in finding the actual December temperature is the commutative property of addition.
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Determine if the line segment YX is tangent to circle Z. 30 points
Answer:
XY is tangent to circle Z
Step-by-step explanation:
You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.
Pythagorean relationIf the triangle XYZ is a right triangle, then we have ...
XY² +XZ² = YZ²
3.6² +2.7² = (1.8 +2.7)²
12.96 +7.29 = 20.25 . . . . . true
Segment XY is a tangent.
Secant relationIf segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...
3.6² = (1.8)(7.2) . . . . . true
This means XY is a tangent.
Screenshot included in this work
The two blanks on the left side of the equation and the solution blank should be completed with the following ratios:
2050 kg/1 m³ × 2.2 lb/1 kg × 1 m³/35.3 ft³ = 127.76 lb/ft³.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Conversion:
2050 kg/1 m³ × 2.2 lb/1 kg = 4,510 lb/1 m³
4,510 lb/1 m³ × 1 m³/35.3 ft³ = 4,510 lb/35.3 ft³
4,510 lb/35.3 ft³ = 127.76 lb/ft³.
Additionally, take note of the following units of conversion:
kg = kilograms.m³ = cubic meter.lb = pounds.ft³ = cubic foot.In conclusion, we can logically deduce that the crate's density is equal to 127.76 pounds per cubic foot.
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Gavin invested $11,000 in a savings account. If the interest rate is 7%, how much will be in the account in 10 years with monthly compounding?
Round your answer to the nearest cent.
Do NOT round until you calculate the final answer
Answer:
$22,106.28
Step-by-step explanation:
[tex]CI=P(1+(\frac{r}{12}) )^{12t}[/tex], where [tex]P[/tex] is the principal, [tex]r[/tex] is the interest rate in decimal form, and [tex]t[/tex] is the time in years.
[tex]CI=\$11000.00(1+(\frac{0.07}{12}) )^{12(10)}[/tex]
[tex]CI=\$22106.28[/tex]
What is the image of (-9,12)(−9,12) after a dilation by a scale factor of \frac{1}{3} 3 1 centered at the origin?
The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
In the given question,
We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.
Since we have to find the image after a dilation.
So we learn about it now,
Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.
So the given point is (-9,12).
Scale factor is 1/3.
So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as
=(-9×1/3,12×1/3)
Simplifying
=(-3,4)
Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
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Ryan is going to spin the spinner 80 times.
(b)
Work out an estimate for the number of times he should expect the spinner to land on 2
The estimate for the number of times Ryan should expect the spinner to land on 2 is 13.
How to calculate the number of times?From the information, the spanner has numbers labeled 1 - 6 and Ryan is going to spin the spinner 80 times.
It should be noted that the fraction for getting a 2 is 1 out of 6. This will be 1/6.
Therefore, when it's spinned 80 times, the expected number will be:
= 1/6 × 80
= 13
The number of times is 13.
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Complete question
A spanner has numbers labeled 1 - 6. Ryan is going to spin the spinner 80 times. Work out an estimate for the number of times he should expect the spinner to land on 2
Find the equation of the line tangent to the curve defined by f(x) = x^2+1 / square root x at the point (1,2). Show all your work.
Answer:
[tex]y=x+1[/tex]
Step-by-step explanation:
I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.
[tex]f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})][/tex]
Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for [tex]x=1[/tex]:
[tex]f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1[/tex]
We're almost done. We got the point, we have the slope, we can rewrite the tangent line as
[tex]y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1[/tex]
I need help with math please help me..!!!
I need help with math please help me..!!!
I need help with math please help me..!!!
Step-by-step explanation:
please remember you middle school and high school classes, homework and exams.
here on college level this is just meant as a quick reminder.
so, what exactly don't you understand, please, so that I can provide specific guidance ?
6
the vertex : the turn-around point, where the parabola curve changes its tendency : (-3, 0.5)
axis of symmetry : since the parabola opens downwards, the axis of symmetry (it is like a mirror for one half of the curve to the other half) is a vertical line going right through the vertex : x = -3
y-intercept is the y-value when x = 0 : (0, -4)
x-intercepts are the x-values when y = 0 :
(-4, 0) and (-2, 0)
max or min : there is only one identifiable extreme value, it is at the vertex, of course, and is clearly a maximum :
at x = -3 the max value of the function is 0.5
the optimal value is the y-coordinate of the vertex (the function value between the 2 x-intercepts) : 0.5
4
y = 0.5x + 6 is linear. why ? because the highest exponent of x is 1. that creates a proportional relationship between x and y meaning y only increases with x in a constant manner.
y = 2x² + 5 is quadratic. why ? because the highest exponent of x is 2. this squares things, in other words, it makes them quadratic.
the graph as third item in the list is neither. the functional value gets exponentially bigger, the closer x gets to 0.
this looks like y = -1/x = x^(-1)
the graph as forth item in the list is a parabola again, and as such it is quadratic.
If the random variable Zhas a standard normal distribution, then P(1.17 S ZS 2.26) is
The value of P(1.17 <= Z <= 2.26 ) is 0.1091
From the question, we have
Z value for 1.17 is 0.8790
Z value for 2.26 is 0.9881
P(1.17 <= Z <= 2.26 ) = 0.9881 - 0.8790 = 0.1091
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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The figure below is made up of a square with height, h units, and
a right triangle with height, h units, and base length, b units.
h
b
The area of this figure is 80 square units.
Write an equation that solves for the height, h, in terms of b.
Answer: $4x4x
Step-by-step explanation:
5. Simplify the complex fraction. a.-2/7
1 1/3
The simplification of the complex fraction is found as 11/14.
Define complex fraction/mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that. Step 1: Multiply the mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given question, the expression is-
-2/7 + 1 1/3
To convert mixed fraction 1 1/3 i improper fraction, multiply 3 with 1 and add 1.
1 1/3 = 1 x 3 + 1 /3
1 1/3 = 4/3 Put in main equation.
-2/7 + 4/3
Simplify the expression.
= -2 x 3 + 4 x 7/ (7 x 4)
= -6 + 28 / 28
= 22/28
Divide both with 2
= 11/14
Thus, the simplification of the complex fraction is found as 11/14.
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The correct question is
Simplify the complex fraction.
-2/7 + 1 1/3
The letter A B C D
represents the location of –1.5 on the number line.
Answer:
B
Step-by-step explanation:
-1/3v = -7 how do i solve this equation?
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
Gabriel has a stack of nickels that is 2 inches tall. The thickness of a nickel is
0.08 inch. How many nickels does Gabriel have?
Show your work.
Answer: Gabriel has
nickels.
Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
As given in the question,
Gabriel has 2 inches tall stack of nickel
Thickness of each nickel = 0.08inch.
Let 'n' be the number of nickels Gabriel has .
Required equation to get the number of nickel is equal to :
0.08 × n = 2
⇒ n = 2 / 0.08
⇒ n = 200/ 8
⇒ n = 25
Therefore, Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
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Answer 0.04
Step-by-step explanation:
because 0.08 divided by two is 0.04
The equation y = 11x represents a proportional relationship. What is the
constant of proportionality?
A.11
B.x
C.1/11
D.0
The constant of proportionality in the equation y = 11x is 11 , the correct option is (a) .
in the question ,
it is given that
the equation is y = 11x
also given that the equation is proportional relationship ,
we need to find constant of proportionality .
we know that the proportional equation is written as y = k*x
where k is the constant of proportionality , on comparing it with the equation y = 11x
, we get k = 11 ,
So , the constant of proportionality is = 11 .
Therefore , The constant of proportionality in the equation y = 11x is 11 .
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ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)
The missing side length of triangle XYZ is 7.
Given,
Triangle ABC and triangle XYZ are similar.
Triangle ABC;Length of AB = 4
Length of BC = 8
Length of AC = x
Triangle XYZ;Length of XY = 24
Length of YZ = 48
Length of XZ = 42
We have to find the missing length x.
Here,
Triangle ABC and triangle XYZ are similar.
So,
AB : XY = BC : YZ = AC : XZ
Then,
Take AB : XY = AC : XZ
= 4 : 24 = x : 42
= 4 × 42 = 24x
x = 4 × 42 / 24
x = 42/6
x = 7
That is,
The missing side length of triangle XYZ is 7.
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Barbara borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is
The actual end-of-year payment or present value of this ordinary annuity is equal to $1,482.
How to calculate the actual end-of-year payment?For the rate of interest, we have:
Rate of interest, r = APR/12
Rate of interest, r = 0.12/12
Rate of interest, r = 0.01
Next, we would calculate the present value of this ordinary annuity by using this formula:
Present value, PV = [P ÷ [1 - (1 + r)^{-n}]/r]
Where:
r is the interest rate.P is the principal.n is the number of times compounded.Substituting the given parameters into the formula, we have;
Present value, PV = 4,500 ÷ ((1 - (1 + 0.12)^(-4))/(0.12))
Present value, PV = 4,500 ÷ ((1 - (1.12)^(-4))/(0.12))
Present value, PV = 4,500 ÷ ((1 - 0.635518078)/(0.12))
Present value, PV = 4,500 ÷ ((0.364481922)/(0.12))
Present value, PV = 4,500/3.0373
Present value, PV = $1,481.58 ≈ $1,482.
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Pls help 3z2-6z for z=5
Answer:
0
Step-by-step explanation:
to me you use the exponent first and then add the variable after, 30-30=0 and if you do the variable first 225-30=195. But my answer would be 0.
Answer: 78
Step-by-step explanation:
3z2-6z for z=5
2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
The weight of Luna is 82 pounds , the correct option is (d) .
In the question ,
it is given that
Kira has three dogs Luna , Cooper and Daisy .
let the weight of cooper be c .
given Cooper weighs 25 pounds less than Daisy
which is c = daisy - 25
So , daisy = c + 25
and Luna weighs 20 pounds less than three times Cooper ,
which is Luna = 3c - 20
Given the combined weight is = 175 pounds
Cooper + Daisy + Luna = 175
c + c + 25 + 3c - 20 = 175
5c + 5 = 175
5c = 175 - 5
5c = 170
c = 170/5
c = 34
So, Luna = 3c - 20 = 102 - 20 = 82 pounds .
Therefore , The weight of Luna is 82 pounds .
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