Answer:
Surface Area of a Cube = 6[tex]a^{2}[/tex]
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
Surface Area of a Sphere = 4 pi r[tex]^{2}[/tex]
Surface Area of a Cylinder = 2( pi [tex]r^{2}[/tex]) + (2 pi r)* h
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a bottle contains 2.360 ml of a liquid. the total mass of the bottle and liquid together is 6.160g. The mass of the empty bottle is 4.850 g. what is the density of the liquid?
A) 2.610 ml
B) 1.802 ml
C) 0.555 ml
D) 2.055 ml
Answer:
C.) 0.555
Step-by-step explanation:
This is annoying because we're dealing with decimals.
So, we need to know how density works. Density works by dividing mass (g) by volume (ml).
Since the empty bottle has a mass of 4,850g and the bottle + the liquid have a total mass of 6.160g, we'll subtract the bottle's mass from the total mass, giving us 1.310g. Again, we divide mass by volume to obtain density (which should be listed as g/ml).
1.310 ÷ 2.360 = ~0.555
Therefore, your answer is 0.555
The density of the liquid in the bottle is calculated by dividing the mass of the liquid (found by subtracting the mass of the empty bottle from the total mass when full) by its volume. The correct answer is C) 0.555 ml.
Explanation:The subject here is density, which is a physical property of a substance that can be calculated by its mass over its volume. In your case, you are being asked to find the density of the liquid inside the bottle. This can be done by first, finding the mass of the liquid alone, then dividing that by the volume of the liquid given in the question.
The mass of the liquid can be found by subtracting the mass of the empty bottle from the total mass of the bottle when full (6.160g - 4.850g = 1.310g). The volume of the liquid is already given as 2.360 ml.
Finally, you compute the density by dividing the mass of the liquid by its volume (1.310g / 2.360 ml = 0.555 g/ml).
So, the correct choice is C) 0.555 ml.
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Kevin's sock drawer contains 6 white socks, 4 black socks, 3 grey socks, and 5 red socks. If Kevin randomly picks two socks, what is the probability that they are both white?
Answer:
5/51
Step-by-step explanation:
The probability of Kevin choosing a white sock on the first pick, there are 6 white socks and 18 socks total so the chances are 6/18. But 6/18 simplified is 1/3. On the second choice he has to pick another sock and there are 5 left out of 17 socks total remaining. So the chances of him picking another sock are 5/17. If you multiply 1/3 by 5/17 you will end up with your answer, 5/51.
Probabilities are used to determine the chances of an event.
The given parameters are:
[tex]\mathbf{White = 6}[/tex]
[tex]\mathbf{Black = 4}[/tex]
[tex]\mathbf{Grey = 3}[/tex]
[tex]\mathbf{Red = 5}[/tex]
So, the total is:
[tex]\mathbf{Total = 6 + 4 + 3 + 5}[/tex]
[tex]\mathbf{Total = 18}[/tex]
The probability that both selections are white socks is:
[tex]\mathbf{Pr = \frac{White}{Total} \times \frac{White - 1}{Total - 1} }[/tex]
1 is subtracted from the fractions of the second factor, because it is a selection without replacement.
So, we have:
[tex]\mathbf{Pr = \frac{6}{18} \times \frac{6 - 1}{18 - 1} }[/tex]
[tex]\mathbf{Pr = \frac{1}{3} \times \frac{5}{17} }[/tex]
So, we have:
[tex]\mathbf{Pr = \frac{5}{51} }[/tex]
Hence, the probability that both selections are white socks is 5/51
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The population of a village has a constant growth of 5% every year. If its present population is 1,04,832, what was the population two years ago?
Answer:
95086
Step-by-step explanation:
We let the population one year ago be x, the relationship between x and the present population is;
(105/100)*x = 104832
This is because the present population exceeds the population one year ago by 5%.
therefore,
1.05*x = 104832
x = 99840
We now let the population two years ago be y, the relationship between y and the population one year ago is;
(105/100)*y = 99840
This is because the population one year ago exceeds the population two years ago by 5%.
Therefore,
1.05*y = 99840
y = 95085.7
Rounding to the nearest whole number;
95086
the sum of the interior angle measures of a convex 130 gon
(N-2)180
(130-2)180
128 x 180
23040
Final answer:
The sum of the interior angles of a convex 130-gon is 23040 degrees, calculated using the formula S = (n - 2) × 180° with n equal to the number of sides.
Explanation:
The sum of the interior angles of any polygon can be calculated by using the formula S = (n - 2) × 180°, where S is the sum of the interior angles and n is the number of sides in the polygon. In the case of a convex 130-gon, with n = 130, the calculation would be S = (130 - 2) × 180°. This simplifies to S = 128 × 180°, which is S = 23040°. Therefore, the sum of the interior angles of a convex 130-gon is 23040 degrees.
The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?
A) 14°
B) 16°
C) 18°
D) 20°
Answer:
Option C.
The measure of the complement angle is [tex]18\°[/tex]
Step-by-step explanation:
Let
x-----> the angle
we know that
The complement of an angle is equal to [tex](90-x)\°[/tex]
The supplement of an angle is equal to [tex](180-x)\°[/tex]
we have
The complement of an angle is one-sixth the measure of the supplement of the angle
[tex](90-x)\°=(1/6)(180-x)\°[/tex]
solve for x
[tex](540-6x)\°=(180-x)\°\\ (6x-x)=(540-180)\°\\ (5x)=(360)\°\\ x=72\°[/tex]
Find the measure of the complement angle
[tex](90-x)\° ----> (90-72)=18\°[/tex]
Answer:
Option C. 18
Step-by-step explanation:
Let x be the given angle. 1 6 (180 − x) = (90 − x) 30 − 1 6 x = 90 − x 5 6 x = 60 x = 72° The supplement angle to 72° is 108°. The complement angle to 72° is 18°.Which two points in the graphed function have an average rate of change of 5?
Answer:
B. points A and B
Step-by-step explanation:
"Rate of change" is just a fancy name for slope.
The question asks for points on the graph having a slope of 5. We know a slope of 5 is a positive (goes up from left to right) and it's quite steep.
By looking at the graph, we see that to have a slope of 5, it has to take place in the first half of the graph.
Let's look at the possible options:
A. Points D and F: From point D to point F, you're going down, so the slope is negative. NO
B. Points A and B: goes up, pretty steep. Let's calculate the slope.
Point A: (2,1), Point B: (3,6)
Slope = (6 - 1) / (3 - 2) = 5 / 1 = 5
We found it!
C. Points B and C: goes up, pretty steep too. Let's calculate the slope:
Point B: (3,6) , Point C: (4,9)
Slope = (9 - 6) / (4 - 3) = 3 / 1 = 3, NO, not the slope we're looking for
D. Points C and E: goes down, NO, not what we want.
how do i factor 6x squared-12x?
Answer:
6x(x - 2)
Step-by-step explanation:
Find the common factors of 6x² - 12x, which is 6x.
To rationalize the denominator 2 sqrt 10/ 3 sqrt 11 you should multiply the expression by which fraction
Answer:
B
Step-by-step explanation:
To rationalise the denominator.
Multiply the numerator/denominator by the radical on the denominator.
The radical on the denominator is [tex]\sqrt{11}[/tex], thus
Multiply the fraction by
[tex]\frac{\sqrt{11} }{\sqrt{11} }[/tex] → B
The expression (√11 /√11 ) needs to be multiplied to rationalize the denominator.
What are Rational Numbers ?Those numbers which can be written in the form p/q such that q > 0 ae called Rational Numbers.
The expression given is
( 2 √10) /( 3 √11 )
To rationalize the denominator , the radical √11 needs to be rationalize
( 2 √10) /( 3 √11 ) * (√11 /√11 )
(2√110) / 33
Therefore (√11 /√11 ) needs to be multiplied to rationalize the denominator.
Option B is the answer.
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The sum of the present ages of George and his father is 60 years. In 6 years his father will be twice as old as George will be. Find their present ages.
Answer:
60+6= 66, 66/3= 22 in 6 years time his father will be 44 years. now his father age will 38 and George age will be 22
The present age of the father is 42 years and George is 18 years.
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.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the sum of the present ages of George and his father is 60 years. In 6 years his father will be twice as old as George will be.
Make the two linear equations and solve them to get the present ages.
G + F = 60
2 ( G + 6 ) = F + 6
2G + 12 = F + 6
2G + 12 = 60 - G + 6
3G = 54
G = 18 years
Father's age will be,
F = 60 - 18
F = 42 years
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MATH :((
how do the chart??
[tex] - x ^{2} - 9 \geqslant 0[/tex]
Answer:
no solutionStep-by-step explanation:
[tex]-x^2-9\geq0\qquad\text{change the signs}\\\\x^2+9\leq0\\\\\text{the parabola}\ x^2\ \text{is op}\text{en up and shifted 9 units up. Therefore is whole}\\\text{over the x-axis (only positive values)}.\\\\\bold{CONCLUSION}:\\\\\bold{no\ solution}[/tex]
super easy points for you guys :) just need an answer
Answer:
3. Additive
4. [tex]x<2[/tex]
5. Graph the linear line. Then, make the line dotted and shade below the line.
Step-by-step explanation:
3. Adding -15 to both sides to isolate the variable.
4.
[tex]-3x+8>2x-2\\5x<10\\x<2[/tex]
A cube has a volume of 216 cubic centimeters. What can be concluded about this cube? Check all that apply.
Recall the formula: Cube V= s^3
The side length, s, can be found using the equation 3s=216
This is a perfect cube.
The side length is 72 centimeters.
The side length is 6 centimeters.
Taking the cube root of the volume will determine the side length.
If you multiply the volume by three, you can determine the side length.
Answer:
Second option: This is a perfect cube.
Fourth option: The side length is 6 centimeters.
Fifth option: Taking the cube root of the volume will determine the side length.
Step-by-step explanation:
You know that the volume of a cube can be calculated with:
[tex]V=s^3[/tex]
Where s is the lenght of any side of the cube.
Since you know the volume of this cube, you can calculate the side lenght by solving for "s". You can make this taking the cube root of the volume.
Therefore, you get that the side lenght of this cube is:
[tex]s=\sqrt[3]{216cm^3}[/tex]
[tex]s=6cm[/tex]
(Since it has exact cube root, it is a perfect cube)
Answer:
B,D,E
Step-by-step explanation:
Which is the graph of the function f f(x)=(x-4)(x+4)?
Answer:
4th bubble
Step-by-step explanation:
First FOIL: f(x) = x² + 3x - 4. Then convert from Standard Form [y = Ax² + Bx + C] to Vertex Form [y = A(X - H)² + K], where (h, k) is the vertex and -h gives the OPPOSITE terms of what they really are. So, you do this by completing the square [½B]²:
2¼ = [½(3)]² [then figure out figure out how much you need to get to -4 (k)]2¼ - 6¼ = -4Your vertex formula is y = (x + 1½)² - 6¼.Remember, -h gives the OPPOSITE terms of what they really are, so your vertex is (-1½, -6¼).
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Ms. Donaldson earns $18.80 per hour for the first 40 hours she works in a week . She earns 1 1/2 times that amount per hour for each hour beyond 40 hours in a week. Last week Ms. Donaldson worked 45.5 hours. How much money did she earn?
Answer: You take $18.80 divide by 2 =$9.40 then $18.80+$9.40=$28.20
$28.20 x's 5.5=$$155.10
$18.80 x's 40=$752.00
then add 752.00+155.10=$907.10
Step-by-step explanation:
In a unit circle, what is the length of an arc that subtends an angle of
π/4 radians?
A unit circle has radius 1, and thus circumference [tex]2\pi[/tex].
Since an angle of [tex]\frac{\pi}{4}[/tex] is one eighth of a whole turn, the length of an arc that subtends an angle of [tex]\frac{\pi}{4}[/tex] radians will be one eighth of the whole circumference:
[tex]l = \dfrac{2\pi}{8} = \frac{\pi}{4}[/tex]
In fact, the radians have the property that, in the unit circle, the length of the arc is exactly the measure of the angle. In general, you have
[tex]l = r\cdot\alpha[/tex]
where l is the length of the arc, r is the radius and [tex]\alpha[/tex] is the angle in radians. So, if [tex]r=1[/tex], you have [tex]l=\alpha[/tex]
The length of an arc in a unit circle that subtends an angle of π/4 radians is simply π/4, because in a unit circle, the length of an arc is the angle (in radians) multiplied by the radius (which is 1).
Explanation:In Mathematics, particularly in the study of a unit circle, an interesting concept to learn is the length of an arc that subtends an angle. Here, the given angle is π/4 radians. In a unit circle, the length of an arc can be calculated by simply multiplying the angle (in radians) by the radius of the circle. In this case, since the radius is 1 (as it's a unit circle), the length of the arc is simply the measurement of the angle in radians, which is π/4.
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In which quadrant is the number –14 – 5i located on the complex plane?
Answer:
3rd Quadrant
Step-by-step explanation:
The "i" in complex numbers behave same as the y in real numbers, so basically this number translated in real would be same as (-14,-5).
To graph this, we have to go -14 units in x direction and -5 units in y direction. Basically, 14 units to the left and then 5 units down. That will place us in 3rd quadrant.
Hence, -14 -5i will fall in the 3rd quadrant of the complex plane.
Answer:
C. III
Step-by-step explanation:
Determine if these three equations are simplified correctly. You will earn 15 points to solve all of them!
1. (3x+7)÷(7)=3x
2.(6x)÷(2x^2)=(6)÷(2x+1)
3. (5+x)÷(5+2x)=(1)÷(x)
Thank you so Much!
Answer:
1. Not simplified correctly. It is (3/7)x + 1
2. Not simplified correctly. It is (3/x)
3. Not Simplified correctly. I believe it is as simplified as it can get
Step-by-step explanation: When a polynomial is over a denominator, ALL elements of the polynomial is affected
What is the ratio for the volumes of two similar Pyramids, given that the ratio of the edge lengths is 8:3?
Answer:
D
Step-by-step explanation:
Given that the ratio of side lengths = 8 : 3, then
ratio of volumes = 8³ : 3³ = 512 : 27 → D
ANSWER
The correct answer is option D.
EXPLANATION
The given pyramids are similar and the side lengths are in the ratio 8:3
Volume is in cubic units, therefore the volume of the two similar pyramids are in the ratio;
[tex] {8}^{3} : {3}^{3} [/tex]
This simplifies to
[tex]512 : 27[/tex]
The correct answer is option D.
The point (4, 3) is reflected across the y-axis. What are the coordinates of the new point?
a) 4,3
b) 4,-3
c)-4, 3
d)-4,-3
helpppppp!!!!!
The answer is (-4,3) so C
Answer:
[tex]\boxed{\text{c) (-4, 3)}}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign: it becomes (-x, y).
Thus, if a point A, say, (4, 3) is reflected across the y-axis, its reflection A' is at
[tex]\boxed{\textbf{(-4, 3)}}[/tex]
a shoe box measures 15 in. by 7 in. by 4 1/2 in. What is the surface area of the box?
Answer:
408 in²
Step-by-step explanation:
Given in the question that,
length of a show box = 15 in
width of a show box = 7 in
height of a show box = 4.5 in
Formula to calculate the surface area of shoe box is as following
2*(L*W + L*H + W*H)Plug values in the formula
2*(15*7 + 15*4.5 + 7*4.5)
2(105 + 67.5 + 31.5)
408 in²
The surface area of the box = 408 in²
What does x^4-7x+10 equal
Answer:
7
Step-by-step explanation:
A car wash cleans 3 cars in 24 min.
How many cars does the car wash clean in 56 min?
168 cars
8 cars
Jong
18 cars
7 cars
I am a little stuck I just don’t really get expressions
Answer:
$66.50
Step-by-step explanation:
lets break this down a bit:
the tickets are $16 each
there is an additional $2.50 added when tickets are bought online, its a one time fee and does not apply to every ticket
n represents the amount of tickets bought
you're on the right track so far, the expression is as follows:
16n +2.50 <---n is placed next to the 16 because we are calculating the amount of tickets bought and their price plus the one time service fee of $2.50
we are then told that 4 tickets were bought
in this expression, n = 4, so we substitute 4 into the equation for n
16(4) + 2.50
16 x 4 = 64
instead of multiplying like you did on the worksheet, you would add since the original expression we wrote plus 2.50, not times 2.50
64 + 2.50 = 66.50
so, the total price for 4 tickets bought online is $66.50
you were on the right track! let me know if you need anything else cleared up about expressions
Give the terms that best describes arc BC
Answer:
Option D. minor arc
Step-by-step explanation:
we know that
In a circle the measure of minor arc plus the measure of major arc is equal to 360 degrees
The measure of minor arc is less than 180 degrees
The measure of major arc is greater than 180 degrees
In this problem
Arc BDC is a major arc
Arc BC is a minor arc
Eudora transferred a balance of $6400 to a new credit card at the beginning
of the year. The card offered an introductory APR of 7.8% for the first 3
months and a standard APR of 26.5% thereafter. If the card compounds
interest monthly, what will Eudora's balance be at the end of the year?
(Assume that Eudora will make no payments or new purchases during the
year, and ignore any possible late payment fees.)
Final answer:
Eudora's balance at the end of the year will be $7,750.03.
Explanation:
To calculate Eudora's balance at the end of the year, we need to calculate the interest for each period separately and then add them together. The credit card offers an introductory APR of 7.8% for the first 3 months, so we will calculate the interest for this period first.
Step 1: Calculate the interest for the introductory period:
Interest = Balance * Introductory APR * (Introductory Period / 12) = $6400 * 0.078 * (3/12) = $156.00
Since the card compounds interest monthly, we need to calculate the interest for each month of the remaining 9 months at the standard APR of 26.5%:
Step 2: Calculate the interest for each month of the remaining 9 months:
Interest for each month = Balance * Standard APR / 12 = $6400 * 0.265 / 12 = $139.67
Step 3: Add up the interest for the introductory period and the remaining 9 months:
Total interest = Interest for the introductory period + (Interest for each month * Number of months) = $156.00 + ($139.67 * 9) = $1,350.03
Step 4: Calculate the final balance at the end of the year:
Final balance = Balance + Total interest = $6400 + $1,350.03 = $7,750.03
Therefore, Eudora's balance at the end of the year will be $7,750.03.
PLEASE HELP A square has an area of 64 square units. Which set of coordinates could be the vertices of the square?
A) (3, –35) and (3, –28)
B) (21, –14) and (21, –22)
C) (32, –42) and (32, –7)
D) (74, 19) and (82, 27)
Answer:
B
Step-by-step explanation:
it is 64 units so 8 units long each
Answer:
B) (21, -14) and (21, -22)
Step-by-step explanation:
Given,
The area of the square = 64 square unit,
Let x be the side of the square,
[tex]\implies x^2 = 64[/tex]
[tex]\implies x = 8[/tex]
Hence, the side of the square = 8 unit,
⇒ The distance between the adjacent vertices in the square = 8 units,
By the distance formula,
The distance between (3, -35) and (3, -28) is,
[tex]\sqrt{(3-3)^2+(-28-(-35))^2[/tex]
[tex]=\sqrt{0+(-28+35)^2}[/tex]
[tex]=\sqrt{7^2}[/tex]
[tex]=7\neq 8[/tex]
Thus, (3, -35) and (3, -28) can not be the vertices of the square.
The distance between (21, -14) and (21, -22) is,
[tex]\sqrt{(21-21)^2+(-22-(-14))^2[/tex]
[tex]=\sqrt{0+(-22+14)^2}[/tex]
[tex]=\sqrt{8^2}[/tex]
[tex]=8[/tex]
Thus, (21, -14) and (21, -22) are the vertices of the square.
The distance between (32, -42) and (32, -7) is,
[tex]\sqrt{(32-32)^2+(-7-(-42))^2[/tex]
[tex]=\sqrt{0+(-7+42)^2}[/tex]
[tex]=\sqrt{35^2}[/tex]
[tex]=35\neq 8[/tex]
Thus, (32, -42) and (32, -7) can not be the vertices of the square.
The distance between (74, 19) and (82, 27) is,
[tex]\sqrt{(82-74)^2+(27-19)^2[/tex]
[tex]=\sqrt{8^2+8^2}[/tex]
[tex]=\sqrt{64+64}[/tex]
[tex]=\sqrt{128}[/tex]
[tex]=8\sqrt{2}\neq 8[/tex]
Thus, (74, 19) and (82, 27) can not be the vertices of the square.
in a cirlce of radius 5 cm, what is the length in cm of an arc subtended by a central angle measuring 2 radians?
Answer:
The length L is 10 cm
Step-by-step explanation:
We need to find the length of the arc subtended by a central angle of 2 radians and the circle has radius of 5cm.
So, the formula used will be:
l = r Θ
Where L= length of arc
r= radius of circle
and Θ is angle
In The given question
L=?
r = 5 cm
Θ = 2 radians
Putting values in formula:
L = r Θ
L = 5 * 2
L = 10 cm
So, the length L is 10 cm
Final answer:
The length of the arc subtended by a central angle of 2 radians in a circle of radius 5 cm is 5 cm.
Explanation:
The length of an arc subtended by a central angle can be found using the formula:
Length of arc = (central angle / 2π) × circumference of the circle
In this case, the central angle is 2 radians and the radius of the circle is 5 cm. The circumference of the circle is given by 2πr, where r is the radius. So, the length of the arc can be calculated as:
Length of arc = (2 / 2π) × (2π × 5) = 5 cm
Now I want to cover the curved area of the vase in paper. I do not want to cover the bases. My vase has a 6” diameter and is 12” tall. How many square inches of paper will I need?
Answer:
[tex]226.08\ in^{2}[/tex] or [tex]72\pi\ in^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of a cylinder ( curved area of the vase) is equal to
[tex]LA=2\pi rh[/tex]
we have
[tex]r=6/2=3\ in[/tex] ------> the radius is half the diameter
[tex]h=12\ in[/tex]
substitute the values
[tex]LA=2\pi (3)(12)=72\pi\ in^{2}[/tex] -----> exact value
assume
[tex]\pi=3.14[/tex]
[tex]72(3.14)=226.08\ in^{2}[/tex] ----> approximate value
8 1/2 + 7 2/3 = Write the answer as a mixed number.
let's firstly convert the mixed fractions to improper fractions, and then add them up.
[tex]\bf \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}}~\hfill \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}+\cfrac{23}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~+~~(2)23}{6}}\implies \cfrac{51+46}{6}\implies \cfrac{97}{6}\implies 16\frac{1}{6}[/tex]
Look at the table of values below.
Which equation is represented by the table?
A.y = 2x + 1
B.
y = 3x + 2
c.
y = 4x - 1
D. y = 5x - 3
Answer:
Your answer will be C. y= 4x-1
Step-by-step explanation:
On the x value side, the numbers represent what to fill in x with, and y should be the output of it.
For example :
4(1) = 4 - 1 = 3
4(2) = 8 - 1 = 7
4(3) = 12 -1 = 11
Hope this helps and was correct
This y = 4x-1, equation is represented by the table
How the equation is represented by the table:On the x value side, the numbers represent what to fill in x with, and y should be the output of it.
For example :
4(1) = 4 - 1 = 3
4(2) = 8 - 1 = 7
4(3) = 12 -1 = 11
The correct answer is option C.
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