The box plot shows all four quartiles of the data set. Each quartile represents 25 percent of the observed data.
Note that the rectangle between 0.5 and 1 second represents the 2nd and 3rd quartiles. That means, the 2nd 25 percent and the tird 25 percent of the mice population in this experiment.
Therefore, the rectangle represents 50 percent of 100 mice, that is 50 mice.
A new cell phone costs $108.99 in the store. What would your total cost be if the sale tax is 7.5% ? Round your answer to the nearest cent, if necessary.
to calculate the tax we need to multiply the % by the price of the cellphone
7.5%=0.075
108.99*0.075=8.17
and the total cost is:
$108.99 + $8.17= 117.16
So the answer is: $
A circular arc has measure of 4 cm and is intercepted by a central angle of 73°. Find the radius r of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.r= __ cm
The arc lenghr is given by:
[tex]s=r\theta[/tex]where s is the arc lenght, r is tha raidus and theta is the angle measure in radians. Since in our problem the angle is given in degrees we have to convert it to radians, to do this we have to multiply the angle by the factor:
[tex]\frac{\pi}{180}[/tex]Then:
[tex]\theta=(73)(\frac{\pi}{180})[/tex]Plugging the value of the arc lenght and the angle in the first formula, and solving for r we have:
[tex]\begin{gathered} 4=r(73)(\frac{\pi}{180}) \\ r=\frac{4\cdot180}{73\cdot\pi} \\ r=3.1 \end{gathered}[/tex]Therefore, the radius of the circle is 3.1 cm.
If Martha is x years old and her mother is 5 times older and the sum of their age is 88, how old is Martha?
Let Martha age = x years old
Since her mother's age is 5 times her age, then
Her mother = 5(x) = 5x years old
Since the sum of their ages is 84, then
Add x and 5x, then equate the sum by 84
[tex]\begin{gathered} x+5x=84 \\ 6x=84 \end{gathered}[/tex]Divide both sides by 6 to find x
[tex]\begin{gathered} \frac{6x}{6}=\frac{84}{6} \\ x=14 \end{gathered}[/tex]Martha is 14 years old
In △GHI, m∠G = (9x - 2), m∠H = (3x - 19), and m∠I = (3x + 6)". Find m∠G.
Answer:
m∠G = 115 degrees
Explanation:
The sum of the angles in a triangle is 180 degrees.
In triangle GHI:
[tex]\begin{gathered} m\angle G+m\angle H+m\angle I=180\degree \\ \implies9x-2+3x-19+3x+6=180\degree \end{gathered}[/tex]First, solve for x:
[tex]\begin{gathered} 9x+3x+3x-2-19+6=180\degree \\ 15x-15=180\degree \\ 15x=180+15 \\ 15x=195 \\ x=\frac{195}{15} \\ x=13 \end{gathered}[/tex]Therefore, the measure of angle G is:
[tex]\begin{gathered} m\angle G=9x-2 \\ =9(13)-2 \\ =117-2 \\ m\angle G=115\degree \end{gathered}[/tex]The measure of angle G is 115 degrees.
A(0,3) B(1,6) C(4,6) D(5,3) rotate it around the origin 270 degrees clockwise
Please answer with the coordinates.
♥
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so i guess A?
♥
Multiple the binomials (simplify) (y-4)(y-8)
Given
[tex](y-4)(y-8)[/tex]Simplify as shown below
[tex]\begin{gathered} (y-4)(y-8)=y(y-8)-4(y-8)=y^2-8y-4y+(-4)(-8)=y^2-12y+32 \\ \Rightarrow(y-4)(y-8)=y^2-12y+32 \end{gathered}[/tex]The answer is y^2-12y+32
If ∠2 = 50° and lines a and b are parallel, which of the following angles cannot be determined? *-∠1-∠3-∠4-∠8-None of the above
If you have the angle 2, you can deduce its the supplement,which is the angle 4. In this case the supplement is equal to 130°.
Angle 2 and angle 6 are corresponding angles, so they have the same measure.
Angle 4 and angle 8 are corresponding, so they have the same measure.
Angle 2 and angle 1 are vertically opposite angles, so they have the same measure.
Angle 5 and angle 6 are vertically opposite angles, so they have the same measure.
Angle 7 and angle 8 are vertically opposite angles, so they have the same measure.
Angle 4 and angle 3 are vertically opposite angles, so they have the same measure.
Therefore the answer is None of the above.
Translate into proportion 16.4 is 45% of what number ?
Given:
16.4 is 45%
[tex]\begin{gathered} 16.4\times\frac{45}{100}=\frac{b}{1} \\ \frac{16.4}{b}=\frac{100}{45} \end{gathered}[/tex]Hence, the required option is D.
what are the similarities between rate and ratio
A rate is a specific type of ratio. A rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
For example, in a bowl, there are 12 fruits: 8 oranges and 4 apples. This means the ratio of oranges to apples is 8:4.
If we simplify the ratio, we can see that the ratio of oranges to apples is 2:1, because:
[tex]\frac{8}{4}=\frac{4\cdot2}{4\cdot1}=\frac{2}{1}=\frac{2}{1}[/tex]Then, there are 2 oranges in the bowl for every apple.
On the other hand, suppose we want to distribute the fruits to 3 people. We can use a rate to find out how many fruits correspond to each person because we have 2 different units:
[tex]\begin{gathered} \frac{12\text{ fruits}}{3\text{ people}}=\frac{x}{1\text{ person}} \\ \text{ Apply cross product} \\ 12\text{ fruits}\cdot1\text{ person}=x\cdot3\text{ people} \\ \text{ Divide by 3 people from both sides} \\ \frac{12\text{ fruits}\cdot1\text{ person}}{3\text{ people}}=\frac{x\cdot3\text{ people}}{3\text{ people}} \\ \frac{12\text{ fruits}}{3}=x \\ 4\text{ fruits }=x \end{gathered}[/tex]Now, we know that each person corresponds to 4 fruits, in other words, the rate is 4 fruits/person.
Therefore, we can see the similarities between rate and ratio are:
• Both are a comparison of two numbers.
,• Both can be written as fractions.
,• Both reduce to the lowest form.
What number is 75% of 96?
Answer
The number is 72
Explanation
75% of 96 is
[tex]\begin{gathered} =\frac{75}{100}\times\frac{96}{1} \\ =\frac{7200}{100} \\ =72 \end{gathered}[/tex]Section 5.2-12. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).3x-3y = -6-x+2y = 8
the Given the simultaneous equations
[tex]\begin{gathered} 3x-3y=-6\text{ ------(1)} \\ -x+2y=8\text{ -------(2)} \end{gathered}[/tex]Solving the above equations by substitution method:
Step 1:
From equation 2, make x the subject of the formula
[tex]\begin{gathered} -x+2y=8 \\ \text{making x the subject of formula, we have} \\ x=2y-8\text{ -------(3)} \end{gathered}[/tex]Step 2:
Substitute equation 3 into equation 1
[tex]\begin{gathered} \text{From equation,} \\ 3x-3y=-6 \\ \text{Thus, we have} \\ 3(2y-8)-3y=-6 \\ \text{opening the brackets, we have} \\ 6y-24-3y=-6 \\ \text{collecting like terms, we have} \\ 6y-3y=-6+24 \\ 3y=18 \\ \text{divide both sides by the coefficient of y.} \\ \text{The coefficient of y is 3. Thus,} \\ y=\frac{18}{3}=6 \end{gathered}[/tex]Step 3:
Substitute the value of y in either equation 1 or 2.
[tex]\begin{gathered} \text{From equation 2,} \\ -x+2y=8 \\ \text{Thus,} \\ -x+2(6)=8 \\ -x+12=8 \\ \text{collecting like terms, we have} \\ -x=8-12 \\ -x=-4 \\ x=4 \end{gathered}[/tex]Thus, the values of (x, y) are (4, 6)
help me please asap!!!
The slope of the function is 1/2 and the y - intercept is 2
The standard form of slope-intercept form of line is y = mx + b
where , m is slope of line
and b is y-intercept.
Observing the graph ,
we can say Linear function also passes through two points
At (4,0) on x-axis and at (0,2) on y-axis and
also , the graph is making right angles triangle at (0,0)
Slope of the function = m = Tan∅
Tan∅ = Perpendicular of right triangle / base of triangle
Perpendicular of triangle = 2 unit
and base = 4 unit
Tan∅ = 2/4 = 1/2
Therefore , slope of line = 1/2
equation of line : y = 1/2 x + b
This line is passing through (0,2)
2 = 1/2(0) + b
b = 2
Therefore , the y-intercept = 2
Hence , the equation of line = y = 1/2 x + 2
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What is the value of x?
The value of x =20 when the angles given are 3x° and (x+40)°.
Given that,
There a picture with 2 lines.
The angles given are 3x° and (x+40)°.
We have to find the x value.
We the alternative angles are equal in an intersecting angles.
Angles that are in opposition to a transversal connecting two lines are known as alternate angles.
x +40=3x
Taking 40 to right side.
x= 3x-40
Taking 3x to left side.
x-3x=-40
Subtracting x ad 3x
-2x=-40
Divide by -2.
x=20
Therefore, the value of x =20 when the angles given are 3x° and (x+40)°.
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I will give brainliest if you help me with this problem not joking
Answer: 9+6+-6+-7
Step-by-step explanation:
im not sure thats my guess tho
identify the rate, base and portion.17% of what number is 60?
For the given question which is;
17% of what number is 60?
We shall begin by determining the value of the number. Let us call the number a.
We can now set up the following equation;
[tex]\begin{gathered} 17\text{ \% of a}=60 \\ 0.17\times a=60 \end{gathered}[/tex]We now divide both sides by 0.17;
[tex]\begin{gathered} \frac{0.17a}{0.17}=\frac{60}{0.17} \\ a=352.9411 \\ \text{Rounded to the nearest whole number,} \\ a=353 \end{gathered}[/tex]So we now have;
"17% of 353 is 60."
The rate is the variable that represents part of the whole and that is 17
The base is the whole number itself which is a 100% value and that is 353
The portion is that part of the whole (base) made up of 17% and that is 60."
ANSWER:
Rate is 17%
Base is 353
Portion is 60
Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Find the circumference in terms of . C = _
Solution:
Given the circle with its radius, r;
[tex]r=11cm[/tex]Thus, the circumference, C, of a circle is;
[tex]C=2\pi r[/tex]Then;
[tex]\begin{gathered} C=2\pi(11)cm \\ \\ C=22\pi cm \end{gathered}[/tex]ANSWER:
[tex]C=22.0\pi cm[/tex]Also, the area, A, of the circle is;
[tex]A=\pi r^2[/tex]Then;
[tex]\begin{gathered} A=\pi(11)^2 \\ \\ A=121\pi cm^2 \end{gathered}[/tex]ANSWER:
[tex]A=121.0\pi cm^2[/tex]If the two expressions are equivalent, find value of x
1. Subtract 1/x in both sides of the equation:
[tex]\begin{gathered} \frac{5}{x}-\frac{1}{x}-\frac{1}{3}=\frac{1}{x}-\frac{1}{x} \\ \\ \frac{4}{x}-\frac{1}{3}=0 \end{gathered}[/tex]2. Add 1/3 in both sides of the equation:
[tex]\begin{gathered} \frac{4}{x}-\frac{1}{3}+\frac{1}{3}=0+\frac{1}{3} \\ \\ \frac{4}{x}=\frac{1}{3} \end{gathered}[/tex]3. Multiply both sides of the equation by x:
[tex]\begin{gathered} x\cdot\frac{4}{x}=x\cdot\frac{1}{3} \\ \\ 4=\frac{x}{3} \end{gathered}[/tex]4. Multiply both sides of the equation by 3:
[tex]\begin{gathered} 4\cdot3=\frac{x}{3}\cdot3 \\ \\ 12=x \\ \\ \text{ Rewrite} \\ x=12 \end{gathered}[/tex]Then, the value of x is 12Is this correct? If not can u show me how to do it
Given
[tex]k(x+y)=2x-4[/tex]Notice that it is the equation of a line.
Then, since it crosses (10,-2), set x=10 and y=-2 in the given equation, as shown below
[tex]\begin{gathered} x=10,y=-2 \\ \Rightarrow k(10-2)=2*10-4 \\ \Rightarrow k(8)=20-4 \\ \Rightarrow k=\frac{16}{8}=2 \\ \Rightarrow k=2 \end{gathered}[/tex]Thus, the answer is k=2.
Which transformations can be used to carry ABCD ontoitself? The point of rotation is (3, 2). Check all that apply.yB1 23 4 5 6A. Translation four units to the rightB. Dilation by a factor of 2C. Rotation of 180°D. Reflection across the line x = 3
C. Rotation of 180°
D. Reflection across the line x = 3
Explanation:The point of rotation = (3, 2)
From the diagram:
The center of the rectangle = (3, 2)
Note that:
The point of rotation = The center of the rectangle
Therefore, the rectangle ABCD will be reflected across its center, x =3 and y = 2
Also note that ABCD has two lines of symmetry. Therefore, a rotation by 180 degrees will carry ABCD back to itself
Find the area of the triangle below. Be sure to include the correct unit in your answer. bu
The area of the triangle = 0.5 x base x height
For the given triangle:
Base = 25 ft
The corresponding height to the base = 7 ft
So, the area =
[tex]0.5\cdot25\cdot7=87.5[/tex]So, the area of the triangle = 87.5 ft^2
Please help me solve the following problem:A conic kettle has a cover which height is 30% of its total height. The height is 2 cm less than the diameter of the base, which has an area of 380 squared cm. Which is the volume capacity of the kettle?
If a conical kettles has a solid cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm², then the volume of the kettle is 798.6cm³.
As per the question statement, a conical kettles has a cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm²,
And we are required to calculate the volume capacity of the kettle.
To solve this question, first we need to know the formula to calculate the volume of a cone, which goes as, [Volume (V) = {π * r² * (h/3)}],
Where, "r" is the radius of the base of the cone,
And, "h" is the height of the cone.
Now, the height of our concerned cone is 2 cm less than the radius of it's base, and the area of the base is 380cm². Assuming that the height of the cone be "h" and the radius of it's base be "r", we get that,
[r = (h - 2)]...(i)
And, [(π * r²) = 380]
Or, [{(22/7) * r²} = 380]
Or, [(r²) = {(380 * 7)/22]
Or, [(r²) = 120.9090]
Or, (r = √120.91)
Or, (r = 10.9959)
Or, (r ≈ 11 cm)
Therefore, using the value for "r" in equation (i), we will get,
[h = (11 - 2)cm = 9cm]
And finally substituting these values of "h" and "r" in the above mentioned formula to calculate the volume of a cone,, we get,
[V = {π * (11)² * (9/3)}]
Or, [V = {(22/7) * 121 * 3}]
Or, [V = (7986/7)]
Or, (V = 1140.85714 cm³)
Or, (V ≈ 1140.86 cm³)
Since the cover of the kettle occupies 30% of the volume of the total structure of the conical kettle with it's cover, the volume capacity of the kettle is [(100 - 30)% = 70%] of the volume of the total structure of the conical kettle with it's cover, that is,
[1140.86 * (70/100)]cm³ = (1140.86 * 0.7)cm³ = 798.6cm³
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The coordinates of the midpoint of GH are M(-2,5) and the coordinates of one endpoint are H(-3, 7).
The coordinates of the other endpoint are(
).
Echeck
? Help
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What are the coordinates of the other endpoint
EXPLANATION :
From the problem, we have segment GH and the midpoint is M(-2, 5).
One of the endpoints has coordinates of H(-3, 7)
and we need to find the coordinates of G(x, y)
The midpoint formula is :
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) are the coordinates of G
(x2, y2) = (-3, 7) are the coordinates of H
and (-2, 5) are the coordinates of the midpoint.
Then :
[tex](-2,5)=(\frac{x+(-3)}{2},\frac{y+7}{2})[/tex]We can equate the x coordinate :
[tex]\begin{gathered} -2=\frac{x+(-3)}{2} \\ \\ \text{ cross multiply :} \\ -2(2)=x-3 \\ -4=x-3 \\ -4+3=x \\ -1=x \\ x=-1 \end{gathered}[/tex]then the y coordinate :
[tex]\begin{gathered} 5=\frac{y+7}{2} \\ \\ \text{ cross multiply :} \\ 5(2)=y+7 \\ 10=y+7 \\ 10-7=y \\ 3=y \\ y=3 \end{gathered}[/tex]Now we have the point (-1, 3)
ANSWER :
The coordinates of the other endpoint are G(-1, 3)
Evaluate the expression when x = 32 and y = 2.
x/14 A. 1/16
B.16/21
D.2
C.4
Answer:
I think its 16/21
Step-by-step explanation:
Answer:
2Step-by-step explanation:
Given x = 14, y = 2x/14
Void "y" because it is not in this equation.= x/14
32/14
= 2.2
≈ 2
using the rule of s-14 - (-2) = -12
We will have:
[tex]-14-(-2)=-12\Rightarrow-14+2=-12\Rightarrow-12=-12[/tex]Vance bought 2 packages of large beads
and 1 package of medium beads. He
bought 2 packages of large buttons and 2
packages of medium buttons. How many
more beads than buttons did Vance buy?.
The no. of more buttons than beads that Vance bought is 1 (medium package)
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
How to solve algebraic expressions?A General Rule for Equation Solving
B Remove parenthesis from either side of the equation and combine similar phrases to make it simpler.
C To separate the variable term on one side of the equation, use addition or subtraction.
D To find the variable, use division or multiplication.
Given:- The no: of package of large beads is 2
The no: of the package of medium beads is 1
The no: of the package of large buttons is 2
The no: of the package of medium buttons is 2
Hence large packages
2(buttons)-2(beads)=0
For medium packages
2(buttons)-1(beads)=0
therefore, the no of more buttons than beads is 1 medium package
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turn the expression from radical form to exponential expression in fractional form. No need to evaluate just be out in simplest form
To answer this question, we need to remember the next property of radicals:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]In this case, we have that:
[tex]\sqrt[3x]{5}[/tex]And we can see that the exponent for 5 is m = 1. Therefore, we can rewrite the expression as follows:
[tex]\begin{gathered} \sqrt[3x]{5}=5^{\frac{1}{3x}} \\ \end{gathered}[/tex]In summary, therefore, we can say that the radical form to an exponential in fractional form is:
[tex]undefined[/tex]x-2Question 8 of 15Use the remainder theorem to find P (2) for P (x)=xª − 3x³ +x−9.-(2,01 mismoSpecifically, give the quotient and the remainder for the associated division and the value of P (2)_Quotient =RemainderP (2)=
8)
The remainder theorem states that when a polynomial P(x) is divided by a linear polynomial x-b, the remainder is given by r=P(b).
Thus, in our case,
[tex]P(2)=2^4-3(2)^3+2-9=16-24+2-9=-15[/tex]Then, the Remainder theorem states that if we divide P(x) by x-2, the remainder will be -15.Calculating the quotient of P(x)/(x-2),
Hence, the answers are[tex]\begin{gathered} Q(x)=x^3-x^2-2x-3 \\ Remainder=-15 \\ P(2)=-15 \end{gathered}[/tex]Given f(x)=2x-1 and g(x) =x^2 -2A) f(5)B) f(g(3))C) f(a+1) - f(a)D) g(2f(-1))E) g(x+h) -g(x)/h
2x + h
Explanation:
Given the following functions
f(x) = 2x - 1
g(x) = x^2 - 2
We are to simplify the expressionn:
[tex]\frac{g(x+h)-g(x)}{h}[/tex]Substitute the given functions into the expression and simplify
[tex]\begin{gathered} \frac{\lbrack(x+h)^2-2\rbrack-(x^2-2)}{h} \\ \frac{\lbrack\cancel{x^2}^{}+2xh+h^2-\cancel{2}-\cancel{x^2}^{}+\cancel{2}}{h} \\ \frac{2xh+h^2}{h} \end{gathered}[/tex]Factor out "h" from the numerator to have:
[tex]\begin{gathered} \frac{\cancel{h}(2x+h)}{\cancel{h}} \\ 2x+h \end{gathered}[/tex]Hence the simplified form of the expression is 2x + h
Solve for y and show steps 75-3.5y-4y=4y+6
Solve for y;
[tex]\begin{gathered} 75-3.5y-4y=4y+6 \\ \text{Collect like terms, which means the values with y would be moved to one side} \\ \text{And the values without y would be moved to the other side} \\ 75-6=4y+4y+3.5y \\ \text{Note that when a positive value moves to the other side of the equation} \\ It\text{ becomes a negative value, and vice versa} \\ 69=11.5y \\ \text{Divide both sides by 11.5} \\ \frac{69}{11.5}=\frac{11.5y}{11.5} \\ 6=y \end{gathered}[/tex]The answer is y equals 6
From the diagram below, we can tell that Δ ABC is similar to ____.
From the diagram, we get that
[tex]\measuredangle ABD\cong\measuredangle ADB.[/tex]By the reflexive property of congruence, we know that:
[tex]\measuredangle A\cong\measuredangle A.[/tex]Therefore, by the Angle-Angle criterion:
[tex]\Delta ABC\sim\Delta ADB.[/tex]Answer: [tex]\Delta ADB.[/tex]