Answers
divide the base by the sin of the opposite angle
base = 2
opposite angle = 30 degrees
2/sin(30) = 4
x = 4
Related Questions
What is the slope of a line that is perpendicular to the line whose equation is 0.5x−5y=9
Answers
0.5x-5y=9
-5y=-0.5x+9
y=0.1x-9/5
The slope is 0.1
To find a perpendicular slope, find the negative reciprocal.
The reciprocal of 0.1 is 10
The negative of 10 is -10
Final answer: -10
To find the slope of a line perpendicular to the line defined by the equation 0.5x−5y=9, first convert the equation into slope-intercept form to determine the slope of the original line. The slope of the line perpendicular to this is its negative reciprocal. For this specific problem, the slope of the line perpendicular to the given line is -10.
Explanation:Firstly, rearrange the given equation, 0.5x−5y=9, into the slope-intercept format, i.e. y=mx+b. Here, 'm' is the slope of the line. To illustrate this rearrangement: 5y = 0.5x - 9, then divide through by 5 to get y = 0.1x - 1.8. Thus, the slope of the given line is 0.1.
Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. In this case, the slope of the given line is 0.1, so the negative reciprocal (which represents the slope of the line perpendicular to this line) is -1/0.1, which equals -10. This is the slope of the line perpendicular to the given line.
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A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?
Answers
From here, we can tell that father's age= son's age+30. We can now create the system of equations as follows.
f= s+30
f=4s
Because both define f, put the two equations together.
4s=s+30
3s=30
s=10
Final answer: The boy was 10 (and his father was 40).
the sum of two numbers is 70. the larger number is five less than twice the smaller number . what are the two numbers
Answers
x=2y-5
x=larger number
y=smaller number
now plug in the value of x to only have one variable in the equation...
Way to solve for y:
(2y-5)+y=70
3y-5=70
add 5 on both sides...
3y=75
divide by 3 on both sides
y=25
1st way to solve for x:
now plug in y in the original equation...
x+25=70
subtract 25 on both sides...
x=45
2nd way to solve for x:
plug in y for the second equation...
x=25(2)-5
x=50-5
x=45
answer: the two numbers are 45 and 25.
Final answer:
To find the two numbers, we created a system of equations with the sum being 70 and the larger number as five less than twice the smaller number. Solving the equations, we found that the smaller number is 25 and the larger number is 45.
Explanation:
The question asks us to find two numbers where the sum is 70, and the larger number is five less than twice the smaller number. To solve this, we'll set up a system of equations with two variables, which we'll call x and y. The first equation would be x + y = 70, since their sum is 70. The second equation is derived from the statement that the larger number is five less than twice the smaller number, which can be expressed as y = 2x - 5. Now we substitute the second equation into the first to solve for x. We get x + (2x - 5) = 70. Simplifying, we have 3x - 5 = 70, thus 3x = 75, and therefore x = 25. With the smaller number found, we can determine the larger number using the second equation y = 2(25) - 5, resulting in y = 45. Hence, the two numbers are 25 and 45.
Find the x and y intercepts of 10x-15y=30
Answers
So the coordinate of that point is (x, 0) , that is, y must be 0 since the point is on the x-axis.
letting y=0, we find:
10x-15y=30
10x=30
x=3
With the same logic, letting x=0, we find the y-intercept:
10x-15y=30
-15y=30
y=-2
Answer:
x- intercept : 3 [point (3, 0)]
y- intercept : -2 [point (0, -2)]
A new car dealer offered to sell her demonstrator model for 90% of the retail price. If the sale price was $9,750, what was the retail price?
Answers
90% = 9,750
9750/90 = 1%
1% = 108.3
100% = 10,833.3
original retail price = $10,833.30
Where would we find the point (–10,0)? A. Quadrant III B. y-axis C. Quadrant II D. x-axis
Answers
Elaine's jewelry box has a volume of 36 cubic centimeters. Which of the following could be the dimensions of Elaine's jewelry box? Choose all answers that apply: A 12 cm long, 12 cm wide, 12 cm high B. 4cm long, 4 cm wide, 2 cm high C 3 cm long, 4 cm wide, 3 cm high
Answers
A. 12*12*12=1728 cm^3
B. 4*4*2=32 cm^3
C. 3*4*3=36 cm^3
Only C is correct
Answer:
Option C is the correct answer.
Step-by-step explanation:
Volume of box = Length x width x height.
Volume of box = 36 cubic centimetres.
Option A:
Length = 12 cm
Width = 12 cm
Height = 12 cm
Volume = 12 x 12 x 12 = 1728 cubic centimetres.
Option A is wrong.
Option B:
Length = 4 cm
Width = 4 cm
Height = 2 cm
Volume = 4 x 4 x 2 = 32 cubic centimetres.
Option B is wrong.
Option C:
Length = 3 cm
Width = 4 cm
Height = 3 cm
Volume = 3 x 4 x 3 = 36 cubic centimetres.
Option C is correct.
Option C is the correct answer.
Greatest common factor of 8 and 14?
Answers
Let x and y represent two real numbers. Write an algebraic expression to denote the quotient obtained when the product of the two numbers is divided by their sum.
Answers
An algebraic expression to denote the quotient obtained when the product of the two numbers is divided by their sum is (xy)/(x+y).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that let x and y represent two real numbers. The expression to denote the quotient obtained when the product of the two numbers is divided by their sum is written as,
E = (xy)/(x+y).
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If Ying Zyiyu covers the first 200 miles of a trip going 50mph. and the last hundred going 40mph, what was his average speed for the entire trip?
Answers
the last 100 miles were done at 40mph, how long did that take? well, 100/40, or 2 hours and a half.
so.. Ying covered 300 miles in 4+2.5 hours or 300/6.5 is his average speed.
Answer:
46.15
Step-by-step explanation:
I do RSM :)
What is the future value of $20 a week for 10 years at 6 percent interest? assume the first payment occurs at the end of this week?
Answers
52 wk x 10yr=520 wks
520x20=10,400x 0.06% interest=624
10,400+624=
$11,024
Canada has a population that is 1/10 as large as the United States. If Canada's population is about 32 million, about how many people live in the United States? Explain the number of zeros in your answer.
Answers
Answer:
Step-by-step explanation:
Let the American Population = x
1/10 x = 32,000,000 Multiply by sides by 10
x = 320,000,000 Thirty two followed by 7 zeros is the population of America.
EASY 5 POINTS!!! This box has the same length, width, and height as the 2 basketballs. Which expression gives the volume of the empty space encircling the basketballs inside the box?
Answers
1. We know it's a difference, therefore we need to subtract the volume of the balls from the volume of the box. B is wrong.
2. The box is 3dimensional so we must have 3 linear measurements multiplied together in it's volume calculation. D is wrong.
3. The sphere volume formula uses radius cubed (not diameter). C is wrong
A is the only one left and must be correct.
To check:
Volume of the box: [tex] V=lwh = 48 \times 24 \times 24 = 48 \times 24^{2}[/tex]
Volume of two balls: [tex] V = 2(\frac{4}{3} \pi r^{3}) = 2(\frac{4}{3} \pi \times 12^{3})[/tex]
Total volume = box - balls: [tex]V_{total}=48 \times 24^{2} - 2(\frac{4}{3} \pi \times 12^{3})[/tex]
This matches A, just as we thought.
the upper left on TTM Trust
The amount In a savings account increased from $300 to $309. What was the percent of increase?
Answers
increase = (309-300)/300 = 9/300 = 3/100 = 0.03 or 3%
2nd Method: 309/300 = 103/100 = 1.03 (increase over 1 is 0.03 = 3%)
Final answer:
The amount in the savings account increased by 3%. This was calculated by determining the amount of the increase ($9), dividing by the original amount ($300), and then multiplying by 100 to get the percent increase.
Explanation:
The question is asking to calculate the percent of increase in the amount of money in a savings account that went from $300 to $309. To determine the percent increase, you subtract the original amount ($300) from the new amount ($309) to find the amount of the increase, which is $9. Then, you divide the increase ($9) by the original amount ($300) and multiply by 100 to get the percentage:
Percent Increase = (Increase ÷ Original Amount) × 100%
Percentage Increase = ($9 ÷ $300) × 100% = 0.03 × 100% = 3%
Therefore, the percent of increase is 3%.
Children of age 3-6 years require 25% less sleep per day than infants, who need 16hours. How much slee do the 3-6 year olds need?
Answers
16 - 0.25(16) = 16 - 4 = 12 hrs <=
16 - 4 = 12
So therefore, 3-6 year old aneed 12 hours of sleep.
Or you could solve it this way:
100 - 0.25 = 0.75
16 × 0.75 = 12
Either of the two ways you would get 12
rewrite y=x^2-6x+2 then state whether the vertex is maximum or minimum and give its coordinates
Answers
y=x^2-6x+2
y=(x^2-6x+9)-9+2
y=(x-3)^2-7
the vertex is at the point (3,-7), hence the minimum or maximum point is at (3,-7)
A rectangle or shaped swimming pool has a perimeter of 104 feet and is 4 feet longer than 3 times its width. Find its dimensions.
Answers
______
| |
| |
| | [tex]x[/tex]
| |
| |
|_____ |
(i'm using meters instead of feet because I'm more used to it)
The perimeter of the rectangle is [tex]2x+2y[/tex]
The perimeter is 104m
∴[tex]2y+2x=104[/tex]
------------------------------------------------------------------------
It's 4 feet longer than 3 times its width.
[tex]3y=x+4[/tex]
[tex]3y-x=4[/tex]
[tex]6y-2x=8[/tex]
[tex]2y+2x=104[/tex]
[tex]6y-2x=8[/tex]
-------------------------
[tex]8y=112[/tex]
∴[tex]y=14[/tex]m
[tex]2y+2x=104 [/tex]
[tex]2(14)+2x=104[/tex]
[tex]28 +2x=104 [/tex]
[tex]2x=76[/tex]
∴[tex]x=38[/tex]m
Evaluate the given integral by making an appropriate change of variables, where r is the rectangle enclosed by the lines x - y = 0, x - y = 7, x + y = 0, and x + y = 6.
Answers
[tex]\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial u}{\partial y}\\\\\dfrac{\partial v}{\partial x}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&-1\\1&1\end{bmatrix}[/tex]
[tex]\implies\det\mathbf J=2[/tex]
The area of the region is then given by
[tex]\displaystyle\iint_R\mathrm dA=\int_{u=0}^{u=7}\int_{v=0}^{v=6}2\,\mathrm dv\,\mathrm du=84[/tex]
1. 8 7/16 - (-2 4/9)
Answers
8 7/16 - (-2 4/9) =
8 7/16 + 2 4/9 =
8 7/16 = 135/16 = 1215/144
2 4/9 = 22/9 = 352/144
1215/144 + 352/144 = 1567/144 =10 127/144
PLEASE HELP ME!!! NOT GOOD AT MATH.
Answers
L = length = 8 mm
W = width = 6 mm
H = height = 4 mm
TSA = 2*(L*W + W*H + L*H)
TSA = 2*(8*6 + 6*4 + 8*4)
TSA = 208
The units are "square millimeters" often written as sq mm or "mm^2"
Answer: 208
--------------------------------
Part B)
From part A, the total surface area (TSA) was 208 square mm. If it costs $3 per square mm, then that means the total cost C is
C = (cost per sq mm)*(total surface area)
C = 3*208
C = 624
The units for the cost are in dollars. This result is assuming that there isn't any waste.
Answer: 624
--------------------------------
Part C)
Volume = Length*Width*Height
V = L*W*H
V = 8*6*4
V = 192
The units are in cubic millimeters. The notation is sometimes "cubic mm" or "mm^3"
Answer: 192
The table shows the values of why are different values of X which equation shows the relationship between X and y
X y
0 0
1 7
2 14
3. 21
Answers
A team of 10 players is to be selected from a class of 6 girls and 7 boys. Match each scenario to its probability. You have to drag the sentences to match probabilities.
Possible probabilities are:
0.07
0.12
0.44
0.49
Options for answers are:
The probability that a randomly chosen team includes all 6 girls in the class.
The probability that a randomly chosen team has 3 girls and 7 boys.
The probability that a randomly chosen team has either 4 or 6 boys.
The probability that a randomly chosen team has 5 girls and 5 boys.
Answers
Answer:
0.07 -The probability that a randomly chosen team has 3 girls and 7 boys.
0.12 -The probability that a randomly chosen team includes all 6 girls in the class.
0.44 -The probability that a randomly chosen team has 5 girls and 5 boys.
0.49-The probability that a randomly chosen team has either 4 or 6 boys.
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When a team of 10 players is to be selected from a class of 6 girls and 7 boys the probability of each scenario occurring is:
0.07 = The probability that a randomly chosen team has 3 girls and 7 boys.
0.12 = The probability that a randomly chosen team includes all 6 girls in the class.
0.44 = The probability that a randomly chosen team has 5 girls and 5 boys.
0.49 = The probability that a randomly chosen team has either 4 or 6 boys.
What is probability?
In simple words, it refers to a numerical guess of how likely an event is to occur. Hence, when it comes to probability we believe there is no guarantee the event would occur.
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How do you work out a percentile rank of a score of 57
Answers
For example: Supposing that the mean of these scores were 52 and the standard deviation 3. You'd need to find the "z-score" of 57 in this case.
57 - 52
It is z = ------------ , or z = 5/3, or z = 1.67.
3
Find the area to the left of z = 1.67. Multiply that area by 100% to find the percentile rank of the score 57.
What is the quotient (3x4 – 4x2 + 8x – 1) ÷ (x – 2)?
Answers
Answer:
the quotient of this problem is 3x^3+6x^+8x+24+47/x-2
What is the length of time a loan will last if it has a rate of 0.02, a principal of $500, and it accrued $60 of interest if Interest = Principal * Rate * Time. How would you reduce the time of the loan?
Answers
I=prt
Solve for t
T=I÷pr
T=60÷(500×0.02)
T=6 years
You can reduce the time of the loan by increasing the rate of interest
For example
T=60÷(500×0.05)
T=2.4 years
T=I÷pr
T=60÷(500×0.02)
T=6 years <-- Answer
A photograph has a length that is 6 inches longer than its width, x. So its area is given by the expression x(x+6) square inches. If the area of the photograph is 112 square inches, what is the width of the photograph?
Answers
112 = x^2 + 6x
x^2 + 6x - 112 = 0
(x - 8)(x + 14) = 0
x - 8 = 0
x = 8
x + 14 = 0
x = -14....not this one because it is negative
x = 8 <===width = 8 inches
L = x + 6
L = 8 + 6
L = 14 ....length = 14
The width of the photograph is 8 inches
let
width of the photograph = x
length of the photograph = 6 + x
Area = x(6 + x)
112 = x(6 + x)
112 = 6x + x²
x² + 6x - 112 = 0
x² - 8x + 14x - 112 = 0
x(x - 8) + 14(x - 8) = 0
(x + 14)(x - 8)
x = -14 or 8
x = 8
x cannot be negative so we use only 8.
width of the photograph = 8 inches
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A bridge hand is made up of 13 cards from a deck of 52. find the probability that a hand chosen at random contains at least 3 kings kings.
Answers
In total there are C(52, 13) ways that we can pick a hand, that is [tex] \frac{52!}{13!39!} [/tex]
2.
P(a hand contains at least 3 kings)
=P(a hand contains exactly 3 kings)+P(a hand contains 4 kings)
3.
first let's find P(a hand contains exactly 3 kings):
P(a hand contains exactly 3 kings)
=n(a hand contains exactly 3 kings)/C(52, 13)
n(a hand contains exactly 3 kings)=C(4, 3)*C(48, 10)
where C(4,3) is the total number of ways we can pick 3 out of 4 kings,
C(48, 10) is the number of picking 10 letters to complete a hand, out of the 52-4=48 non-king cards.
so P(a hand contains exactly 3 kings)=[C(4, 3)*C(48, 10)]/C(52, 13)
4. with the same reasoning as in step 3:
P(a hand contains 4 kings)=n(a hand contains 4 kings)/C(52, 13)
= [C(4, 4)*C(48, 9]/C(52, 13)
5.
P(a hand contains at least 3 kings)
=P(a hand contains exactly 3 kings)+P(a hand contains 4 kings)
=[C(4, 3)*C(48, 10)]/C(52, 13)+ [C(4, 4)*C(48, 9)]/C(52, 13)
=[tex] \frac{C(4, 3)*C(48, 10)+C(4, 4)*C(48, 9)}{C(52, 13)} [/tex]
=[tex] \frac{4* \frac{48!}{10!38!} + \frac{48!}{9!39!}}{ \frac{52!}{13!39!} } [/tex]
simplify by 38! in the denominators and 48! in the numerators :
[tex] \frac{4* \frac{1}{10!} + \frac{1}{9!39}}{ \frac{52*51*50*49}{13!39} } [/tex]
now simplify by 9! in all denominators:
[tex] \frac{ \frac{4}{10}+ \frac{1}{39} }{ \frac{52*51*50*49}{13*12*11*10*39}} [/tex]
[tex] \frac{ 0.426 }{ 9.7} =0.044[/tex]
Final answer:
The probability that a bridge hand chosen at random contains at least 3 kings is 0.0000244.
Explanation:
To find the probability that a bridge hand chosen at random contains at least 3 kings, we need to first determine the total number of possible bridge hands and then calculate the number of favorable outcomes.
The total number of bridge hands is calculated using the combination formula: C(52, 13) = 52! / (13! * (52-13)!) = 635,013,559,600.
To calculate the number of favorable outcomes, we count the number of ways we can select 3 kings and then fill the remaining 10 positions with the remaining 39 cards. The number of ways to select 3 kings is C(4, 3) = 4 and the number of ways to fill the remaining 10 positions is C(48, 10) = 17,259,390.
Therefore, the probability is given by: P(At least 3 kings) = favorable outcomes / total outcomes = (4 * 17,259,390) / 635,013,559,600 = 0.0000244.
Write the equation of a circle with a center at (–7, –7) and a radius of 7
Answers
Final answer:
The equation of a circle with a center at (-7, -7) and a radius of 7 is [tex](x + 7)^2 + (y + 7)^2 = 49.[/tex]
Explanation:
The equation of a circle is typically expressed in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with a center at (–7, –7) and a radius of 7, the equation would be (x + 7)² + (y + 7)² = 7². Here, we squared the radius to get 49, which gives us the final equation (x + 7)² + (y + 7)² = 49.
The quotient of 8.4x10^9 and a number n results in 5.6 x 10^27 What is the value of n?
Answers
so 8.4x10^9/5.6 x 10^27=n
n=1.5x10^-18
Answer:
[tex]1.5\times 10^{-18}[/tex]
Step-by-step explanation:
We have been given that the quotient of [tex]8.4\times 10^9[/tex] and a number n results in [tex]5.6\times 10^{27}[/tex]
To find the value of n we will write our given information in an equation as:
[tex]\frac{8.4\times 10^9}{n}=5.6\times 10^{27}[/tex]
[tex]\frac{8.4\times 10^9}{5.6\times 10^{27}}=n[/tex]
Using quotient rule of exponents [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] we will get,
[tex]\frac{8.4\times 10^{9-27}}{5.6}=n[/tex]
[tex]\frac{8.4\times 10^{-18}}{5.6}=n[/tex]
[tex]1.5\times 10^{-18}=n[/tex]
Therefore, the value of n is [tex]1.5\times 10^{-18}[/tex].
A mixture of
12%
disinfectant solution is to be made from
10%
and
17%
disinfectant solution. How much of each solution should be used if
28
gallons of the
12%
solution are needed?
Answers
Gallon equation:
x+y = 28
Solution equation:
10x + 17y = (28)(12)
Solve with substitution:
y = 28-x (From 1st equation)
(Sub into 2nd equation)
10x + 17(28-x) = 336
10x + 476 - 17x = 336
-7x = -140
x = 20
y = 28-20 = 8
Therefore the solution is (20,8)
You need 20 gal of 10% solution mixed with 8 gal of 17% solution to obtain 28 gal of 12% solution.