The trigonometric function that can be used to find the value of x is 12 / tan ( 25 ) . The correct values of a and b will be 12 and 25 resp . .
Given :
A right angle triangle , one angle = 25 ° and side opposite given angle = 12 units .
Trigonometric Formula for Tan θ
tan θ = perpendicular / base , tan θ = ( sin θ / cos θ ) , tan θ = ( 1 / cot θ ) .
where θ = 25 , perpendicular = 12 , base = x .
Substituting values in above first formula ,
tan 25 = 12 / x
Therefore , x = 12 / tan ( 25 ) .
Hence , a = 12 and b = 25 .
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A cartoon of 2 dozen eggs includes 3 with cracks. how many eggs without cracks can be expected in 6 dozen eggs?
If a cartoon of 2 dozen eggs includes 3 with cracks, then the number of eggs without cracks in 6 dozen eggs can be expected to be 63.
A dozen abbreviated as doz is a batch of 12. So in this situation, one dozen refers to 12 eggs. Therefore the number of eggs in 2 dozen will be equal to,
1 dozen = 12 eggs
2 dozen = 12x2= 24 eggs.
Therefore, a cartoon of 24 eggs includes 3 with cracks.
Similarly, 6 dozen is equal to,
1 dozen = 12 eggs
6 dozen = 12 x 6 = 72 eggs
We can determine the number of eggs with cracks by using an algebraic expression,
24 eggs include 3 eggs with cracks
72 eggs include: x eggs with cracks
x = 72×3 ÷ 24
x = 216 ÷ 24 = 9 eggs with cracks.
Therefore the number of eggs without cracks can be calculated by the subtraction of total eggs from the eggs with cracks.
Eggs without cracks= 72 - 9 = 63 eggs.
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the length of a rectangle is 2 feet less than the three times length express the area of the rectangle as a function of its width, using correct function notation
The area of the rectangle as a function of its width is a=3b-2.
[tex]s=(3b-2)b\\=3b^{2}-2b[/tex]
[tex]a=3b-2[/tex]
What is the advantages of area ?
Area is significant in contemporary mathematics. Aside from its obvious significance in geometry and calculus, area is also a fundamental characteristic of surfaces in differential geometry and is connected to the definition of determinants in linear algebra. The amount of space within a form is measured by its area.
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The use of electricity in the US in 1902 was 6.03 x 10^9 kilowatt-hours.
The use of electricity in the US in 1950 was 4.3 x 10^11 kilowatt-hours.
How many times more was the electricity used in 1950 than 1902? Express your answer in Scientific Notation.
a. 7.131 x 10
b. 10.33 x 10^20
c. 1.73 x 10^2
d. 2.6 x 10^20
Using scientific notation , the electricity used in 1950 was 7.131 × 10¹ times more than that used in 1902 .
Values that are either too huge or too little to be conveniently expressed in decimal form can be expressed using scientific notation (typically would result in a long string of digits). It is also referred to as scientific form, standard index form, and standard form in the UK. This base ten notation is often used by scientists, mathematicians, and engineers because it can make various mathematical procedures easier.
One can represent exceedingly large or extremely small quantities using scientific notation. In scientific notation, the result of multiplying an integer between 1 and 10 by a power of 10 is written. For instance, in scientific notation, 35,000,000 can be written as 3.5× 10⁷.
Given that the use of electricity in the US in 1902 was 6.03 x 10⁹kilowatt-hours and the use of electricity in the US in 1950 was 4.3 x 10¹¹ kilowatt-hours.
These are both represented in scientific notation.
Now we have to divide to find the number of times more electricity is used.
(4.3 x 10¹¹) ÷ (6.03 x 10⁹)
= 71.31011...
≈ 7.131 × 10¹
Hence the scientific representation is given by 7.131 × 10¹ times.
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What is the result of adding these two equations can you please answer
Help, I've been stuck on these questions for an hour!
Explanations would be helpful, please!
Answer:
A. 3005
B. 3110
C. 1016.67
Step-by-step explanation:
A. Inital means occuring at the beginning. So the month they got the account, the value is around 3005. Every tick mark on the y-axis represents 30.
B. Like I said, every tick mark represents 30, so on the x-axis, the line between 6 and 8 is 7. go up towards where the line is, and that equals 3110.
C. I really haven't learned about rate of interest yet, but I tried my best to figure it out. I found out that for every month, you get 1016.67 value of interest.
The volume of a prism is given by the formula V=lwh , where l is the length, w is the width, and h is the height of the prism.
a. Solve the formula for h .
Answer:
[tex] \sf \large \: h = \frac{v}{lw} [/tex]
Step-by-step explanation:
Let's solve for h.
v=lwh
Step 1: Flip the equation.
hlw=v
Step 2: Divide both sides by lw.
hlw/lw = v/lw
h= v/lw
The distribution of random variable r has mean 10 and standard deviation 4. The distribution of random variable s has mean 7 and standard deviation 3. If r and s are independent, what are the mean and standard deviation of the distribution of r−s ?.
If [tex]X,Y[/tex] are independent, we have the properties for expectation and variance,
[tex]\Bbb E[aX + bY] = a\,\Bbb E[X] + b\,\Bbb E[Y][/tex]
[tex]\Bbb V[aX + bY] = a^2\,\Bbb V[X] + b^2\,\Bbb V[Y][/tex]
where [tex]a,b\in\Bbb R[/tex] are fixed.
Then
[tex]\Bbb E[R - S] = \Bbb E[R] - \Bbb E[S] = 10 - 7 = \boxed{3}[/tex]
and
[tex]\Bbb V[R - S] = \Bbb V[R] + (-1)^2\, \Bbb V[S] = 4^2 + 3^2 = \boxed{5}\,{}^2 = 25[/tex]
(recall that standard deviation = √(variance))
in the month of januray, i were able to sell 1,200 desserts. In februaryc, your dessert sales increased to 1,500. What is the percent of change
The increment in the percentage of dessert sales will be 25%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
I was able to sell 1,200 desserts throughout the month of January. Your dessert sales jumped to 1,500 in February.
Then the increment in the percentage will be given as,
P = [(1500 - 1200) / 1200] x 100
P = (300 / 1200) x 100
P = 0.25 x 100
P = 25%
The increment in the percentage of dessert sales will be 25%.
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i need help
sum body help
Answer:
p = independent
t = dependent
The amount of hired truckers will depend on the amount of produce that has to be shipped from California to New York.
Hope this helps :)
(Total 3 marks)
5. Dave and Tanvir each think of a number, where Dave's number is larger,
The difference between their numbers is $. Dave's number plus twice Tanvir's number is 26
By forming simultaneous equations, determine each bloke's number.
Dave and Tanvir each think of a number, where Dave's number is larger,
The difference between their numbers is 5. Dave's number plus twice Tanvir's number is 26. By forming simultaneous equations, determine each bloke's number. The numbers are 12 and 7.
The number of Dave is 12 and the number of Tanvir is 7.
Given that
Dave and Tanvir each think of a number, where Dave's number is larger.
The difference between their numbers is 5.
Dave's number plus twice Tanvir's number is 26.
To find
By forming simultaneous equations, determine each bloke's number.
So, according to the question
Let's assume that numbers are x and y.
So, we can say that
x - y = 5 ------------(1) and
x + 2y = 26 ------------(2)
We have to solve that equations by using forming simultaneous equations.
For forming simultaneous equations, we have multiply equation(1) by 2, then add eq(2) with result.
So, we will get
2x - 2y = 10
(+) x + 2y = 26
---------------------------
3x +0 = 36
3x = 36
x = 36/3
x = 12
Putting the value of x in equation (1),
We will get,
x - y = 5 ------------(1)
12 - y = 5
- y = 5 - 12
- y = -7
y = 7
The numbers are 12 and 7.
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Identify all the possible proper subset relationships that
occur among the following sets.
the subsets in this case are:
C ⊆ BC ⊆ AB ⊆ AHow to identify the subsets?Remember that for two sets A and B, we say that A is a subset of B if and only if all the elements of A also are elements of B.
In this case, we have 3 sets:
A = {3n| n ∈ N}B = {6n| n ∈ N}C = {12n| n ∈ N}We can rewrite these ones as:
A = {3n| n ∈ N} = {3, 6, 9, 12, 15, 18, ...}B = {6n| n ∈ N} = {6, 12, 18, ...}C = {12n| n ∈ N} = {12, 24, 36, ...}Here we can see that all the elements in C also belong in B and also belong in A, and all the elements in B also belong to A, then the subsets are:
C ⊆ B
C ⊆ A
B ⊆ A
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Ben bowled 128 and 206 in his first two games. What must he bowl in his third game to have an average of at least 190?
Ben must bowl at least
least 190.
in his third game in order to have an average of at
Answer:
236
See the picture below for the work.
Step-by-step explanation:
the meteorologist made a forecast that a cold front was coming through and the temperature would steadily drop 24.8 degrees over the next six and one fourth hours. how much did the temperature drop each hour? 39.68 degrees 3.968 degrees 31.05 degrees 18.55 degrees
The temperature drop is B. 3.968 degrees each hour.
What is the temperature drop calculated?The temperature drop per hour can be computed by dividing the total temperature drop by the number of hours over which the temperature dropped.
Data and Calculations:The total steady drop in temperature = 24.8 degrees
Total number of hours for the temperature drop = 6¹/₄ hours
6¹/₄ hours = 6.25 hours
Temperature drop per hour = total drop/total hours of drop
= 2(4.8 ÷ 6¹/₄ hours)
= 3.968 degrees
Thus, the temperature drop is B. 3.968 degrees each hour.
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Last week, Pablo drove 115 miles. This week, he drove k miles. Using k, write an expression for the total number of miles he drove in the two weeks. 2-Step Equation find me an answer or sum, and givve me 5 stars.
The expression for the total number of miles Pablo drove in the two weeks is (115+k) miles.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that Last week, Pablo drove 115 miles. This week, he drove k miles. Therefore, the total number of miles for which Pablo drove can be written as,
Total number of miles = Number of miles last week + Number of miles this week
= 115 miles + k miles
= (115 + k) miles
Hence, the expression for the total number of miles Pablo drove in the two weeks is (115+k) miles.
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Which system of linear inequalities is represented by the graph?
y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x +
The system of linear inequalities is represented by the graph is y > x – 2 and y < x + 1.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
The given options are,
y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x + 1
Since,
The linear equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis.
The formula for slope of line with points (x1,y1) and (x2,y2) can be expressed as,
m = (y2 - y1) / (x2 - x1)
Now from y > x – 2 and y < x + 1
the first line passes through (0, 1) and (0, -1)
So,slope m = (0 - 1) / (0 - 1)
⇒ m = 1
Now the line intercept y-axis at (1, 1)
So, c = 1
So,equation of line is given as,
y < x + 1
the second line passes through (0, 2) and (0, -2)
So,slope m = (0 - 2) / (0 - 2)
⇒ m = 1
Now the line intercept y-axis at (-2, 0)
So, c = -2
So,equation of line is given as,
y < x - 2
So, we get y > x – 2 and y < x + 1.
Thus, the system of linear inequalities is represented by the graph is y > x – 2 and y < x + 1.
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The missing graph of the question is attached.
In a proportional relationship when x=6 we know that y=14
Answer:
Given that y varies proportionally with x , with a constant of proportionality k=13 , find y when x=12 .
Write the equation of the proportional relationship.
The variable x varies proportionally with y with a constant of proportionality equal to 13
So,
Substitute the given x value.
Step-by-step explanation:
Which expression is equivalent to
3√50 x √22
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
lets solve ~
[tex]\qquad \sf \dashrightarrow \: 3 \sqrt{50} \times \sqrt{22} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \sqrt{2 \times 5 \times 5} \times \sqrt{2 \times 11} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \sqrt{2 \times 2 \times 5 \times 5 \times 11} [/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times 2 \times 5 \times \sqrt{11} [/tex]
[tex]\qquad \sf \dashrightarrow \: 30 \sqrt{11} [/tex]
find the length s of the arc that subtends a central angle of measure 6 rad in a circle of radius 4 cm.
The length of the arc for the given circle is 24cm.
What is the length of an arc of a circle?The Arc length refers to the distance between two points on a section of a curve or a circle.Length of the arc (L) = r Θ, where r = radius of the curve, Θ = angle subtended by the arc at the centre of the curve in radians.Given:
Angle = 6 radians = ΘRadius of circle = 4cm = rTo find: Length of the arc.
Finding:
On substituting the values of r and Θ in the formula of length of the arc, we get:
L = 4(6) = 24 cm.
Hence, the length of the arc for the given circle is 24cm.
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walter, agnes, and holly are making beaded lizards. walter has 476 green beads and 32 red beads. agnes has 104 green beads and 16 red beads. holly has 281 green beads and 80 red beads. they all share their beads so as to make the largest possible number of lizards. if a beaded lizard requires 94 green beads and 16 red beads, what is the number of green beads left over?
The number of green beads left over = 15
Walter:
Number of green beads = 476
Number of red beads = 32
Agnes:
Number of green beads = 104
Number of red beads = 16
Holly:
Number of green beads = 281
Number of red beads = 80
Total number of red beads = 32+16+80 = 128 beads
Number of red beads required for making one lizard = 16
Since 128/16 = 8 , there will be no red beads left after making 8 lizards.
Total number of green beads = 476+104+281 = 861 beads
Number of green beads required for making one lizard = 94
Now 861/94 = [tex]9\frac{15}{94}[/tex]
That is , 15 is the remainder when 861 is divided by 94
So there will be 15 green beads left after making 9 lizards.
Therefore, the number of green beads left over = 15
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Think About the Process At a te-known vacation spot, taxi fares are a bargain. A 12-mile taxi ride takes 18 minutes and costs $7.20. You want to find the cost of a 33-minute taxi ride. What unit price
do you need?
We need to find out unit price per minute and the unit price is $0.4 per minute.
According to the question we have been given that
12 mile taxi rides takes = 18 minutes
cost of 12 mile taxi ride = $7.20
Thus we need to find the mile and the cost covered in 33 minutes which will be find out by unitary method.
Thus,
18 minutes taxi ride will cover = 12 mile
33 minutes taxi ride will cover = 12/18*33
= 22 miles
cost of 12 mile taxi ride = $7.20
then, cost of 22 miles taxi ride = 7.20/12 * 22
= $ 13.2
Now we need to find out the unit price which is unit price per minute.
Thus unit price is = $13.2/33
= $ 0.4
Hence we need to find out unit price per minute and the unit price is $0.4 per minute.
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Helpppp I will give 60 points for this one
Answer:
Step-by-step explanation:
A. L+W= 2 in. x 2 in. = 4 in.
the length is 2 in.the width is 2 in. so you multiply 2 in.x 2 in. which = 4 in.Below are some things to help you with perimeter and area(just type it into whatever browser you use, copy and paste)
https://youtu.be/LoaBd-sPzkU
https://th.bing.com/th/id/OIP.Q5D_8qbK_9XGQLj1s0tpbwHaJ3?w=186&h=248&c=7&r=0&o=5&dpr=1.65&pid=1.7
[tex]9a-ab+5b if a=2 and b =7[/tex]
Answer:
If you want it graphed the answer is
andb=7
The formula wights are
mass of 1 1 mole of 9 a − a b + 5 b i f a = 2 = 0 g
Step-by-step explanation:
image below, what are the domains and ranges?
Answer:
1. domain: -6 ≤ x ≤ 7
range: -6 ≤ y ≤ 4
2. domain: 5 > x
range: -5 < y
Step-by-step explanation:
1. domain: the farthest number left that the line reaches is -6, while the farthest right is 7. due to the line being closed as well as the points being filled in, you use the less than or equal to sign.
range: the farthest number down that the line reaches is -6, while the farthest is goes up is 4. again, since the points are filled in, you use the "or equal to" sign.
2. domain: since the only plotted point is 5, and the point is not filled in, you would say that 5 is greater than x due to the direction that the line moves
range: the lowest part of the line touches -5 and only goes up from there, therefore y is greater than -5
10 ≤ 3x + 4 < 25
How do I solve
Answer: 2 ≤ x < 7
Step-by-step explanation:
10 ≤ 3x + 4 < 25 ==> solve for x, so work to isolate the x variable
10-4 ≤ 3x + 4-4 < 25-4
6 ≤ 3x < 21
6/3 ≤ 3x/3 < 21/3
2 ≤ x < 7
Answer:
I believe it's [2, 7). It has to be solve differently.
An isosceles triangle has at least two congruent sides. The perimeter of a certain isosceles triangle is at
most 12 in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the
remaining side?
x ≤ 2 but must be greater than 0 . triangles are the possible lengths of the remaining side.
How is an isosceles triangle defined?
Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal.The length of one of the congruent side is 5
The total length of two congruent sides is 10
Perimeter at the most is 12 (meaning the maximum length of perimeter is 12)
The third side of the triangle must be 12-10 = 2 at the most
Writing this requirement as inequality we have
x ≤ 2 but must be greater than 0
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17+|-12--5|--6
show how you got the answer
Answer:
I'm assuming the double minus marks meant 5 and 6 were negative. Answer is 30.
Step-by-step explanation:
[tex]17+\abs(-12--5)-(-6)\\17+\abs(-12+5)-(-6)\\17+\abs(-7)-(-6)\\17+7-(-6)\\17+7--6\\24--6\\24+6\\30[/tex]
Answer:The answer would be 28
Step-by-step explanation:17-6 is 11
The absolute value of -12-5 is 17
17+11=28
So therefore the answer would be 28.
Tim (t), isaac (i), and hannah (h) all sell individual insurance policies. isaac sells four times as much as tim, and hannah sells three times as much as isaac. create an equation in terms of tim (t) in order to find the portion he sells.
Using proportions, the equation in terms of Tim is given by:
T(t) = 17t.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have that:
Isaac sells four times as much as Tim, hence I = 4t.Hannah sells three times as much as Isaac, hence H = 3I = 3 x 4t = 12t.Hence the total amount, as a function of Isaac's amount, is given by:
T(t) = I + H + t
T(t) = 4t + 12t + t
T(t) = 17t.
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A cube-shaped planter has a volume of 729 in.³. What is the length of the planter?
Answer:
9 inches
Step-by-step explanation:
To find the volume of a cube, you could cube the side length, simplified as x³.
x³ = 729
x = 9
9 inches
Hope this helps! :)
if you draw two cards from a deck, what is the probability that you will get the ace of diamonds and a black card?
The probability that the ace of diamonds and a black card will come is 1 / 51 .
Case A :
probability of first getting an ace of diamonds = 1 / 52
probability of getting a black card given first card is ace of diamond = 26 / 51
Hence , probability that the ace of diamonds and a black card will come is ( 1 / 52 ) * ( 26 / 51 ) = ( 1 / 102 )
Case B :
probability of first getting a black card = ( 26 / 52 )
probability of getting an ace , given first card is a black card = ( 1 / 51 )
Hence , the probability that the ace of diamonds and a black card will come is ( 26 / 52 ) * ( 1 / 51 ) = ( 1 / 102 )
P ( A ∪ B ) = P ( A ) + P (B ) + P ( A ∩ B )
= ( 1 / 102 ) + ( 1 / 102 )
= 1 / 51 .
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I need help asap!! (Fractions)
Answer:
b 2 2/9
Step-by-step explanation:
As we know
6×2/3 = {6×3+2}/3
=> 20/3
20/3 is the walk for 3 days
by unitary method
Walk of one day should be
20/3×3
20/9 = 2×2/9 miles per day
Answer:
2 2/9 miles per day
Step-by-step explanation:
If she walked 6 2/3 miles in 3 days, then she walked 1/3 of 6 2/3 miles in 1 days.
We need to find 1/3 of 6 2/3 miles.
1/3 of 6 2/3 =
= 1/3 × 6 2/3
= 1/3 × (6 + 2/3)
= 1/3 × 6 + 1/3 × 2/3
= 2 + 2/9
= 2 2/9