Answers
Answer:
∠ I = 60°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan I = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{HJ}{IJ}[/tex] = [tex]\frac{3\sqrt{30} }{3\sqrt{10} }[/tex] = [tex]\frac{\sqrt{30} }{\sqrt{10} }[/tex] = [tex]\sqrt{\frac{30}{10} }[/tex] = [tex]\sqrt{3}[/tex] , then
∠ I = [tex]tan^{-1}[/tex] ([tex]\sqrt{3}[/tex] ) = 60°
Answer:
60°
Step-by-step explanation:
You want the measure of angle I in right triangle HIJ, given that the side opposite is 3√30 and the side adjacent is 3√10.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
In this triangle, ...
tan(I) = (3√30)/(3√10) = √(30/10) = √3
Then the angle is ...
I = arctan(√3) = 60°
The measure of angle I is 60°.
__
Additional comment
The trig functions of 30° and 45° and their relationships to each other are based on the side relationships of the two "special" right triangles:
30°-60°-90° triangle has side ratios 1 : √3 : 2
45°-45°-90° triangle has side ratios 1 : 1 : √2
Of course, side lengths are in the same order as their opposite angles.
The mnemonic SOH CAH TOA can help you remember the necessary relationships:
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/Adjacent
Related Questions
Lines and Angles
10) In the figure below BD is the perpendicular bisector of AC. Find the value of x.
3(2x-8)
4425
Enter your answer in the box.
x=
Answers
Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.
Solving for x, we have:
3(2x - 8) = 4425
6x - 24 = 4425
6x = 4451
x = 741.83
Rounding to the nearest whole number, we have x = 742.
Therefore, x = 742.
The mean monthly salary of female employees of a company is 3750 Birr, while the mean monthly salary of male employees is 4500 Birr. It is known that the mean monthly salary of male and female employees combined is 4000 Birr. a) What is the ratio of the number of female employees to male employees? b) What percentage of employees are females?
Answers
a) We can use the information given to set up the following equation:
(3750f + 4500m)/(f + m) = 4000
Multiplying both sides by f + m, we get:
3750f + 4500m = 4000(f + m)
Expanding and simplifying, we get:
250f = 500m
Dividing both sides by 250, we get:
f/m = 2/1
Therefore, the ratio of the number of female employees to male employees is 2:1.
b) The total number of employees is f + m. To find the percentage of employees that are female, we can use the ratio we found in part a) to write:
f/(f + m) = 2/(2+1) = 2/3
Multiplying by 100%, we get:
females as a percentage = (2/3) x 100% = 66.67%
Therefore, approximately 66.67% of the employees are females.
A map shows the vertices of a campsite are (25,10), (25,-5), (-5,-5), and (-5,10). The vertices of your tent are (0,-3), (0,6), (10,6), and (10,-3). The coordinates are measured in feet. What percent of the campsite is not covered by your tent?
Answers
The percent of the area that is not covered is 80 percent
How to calculate the area that is not coveredIn mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².
area of tent
= (10 - 0) * (6 - (-3))
= 90
The area of the campsite would be:
(25 - (-5) x (10 - (-5))
= 450
Then the area would be 450 - 90
= 360
the percentage that is not covered by tent = 360 / 450 x 100
= 80 percent
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Trundle wheels are used to measure distances along the ground.
The radius of the trundle wheel is 30 cm.
Jim wants to work out the distance between two junctions on a road.
He rolls the trundle wheel between the two junctions.
The trundle wheel rotates exactly 48 times.
Work out the distance between the two junctions.
Give your answer in metres correct to the nearest metre.
Answers
The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.
:: Radius of trundle wheel = 30 cm = 0.3 meter (as 100 cm = 1 m)
:: No. of rotations = 48
:: Circumference of a circle = ( 2 x π x r )
where, r is radius of the circle
So, as,
Distance between junctions = [ (circumference of trundle wheel) x (no. of rotations) ]
Therefore,
Distance = (2 x π x 0.3) x (48)
Distance = 2 x (3.14) x 0.3 x 48
Distance = 90.432 meters
When rounded off to the nearest meter,
Distance = 90 meters.
So, The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.
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Find the probability that
event A or B takes place.
Answers
The probability that event A or B takes place is P ( A ∪ B ) = 6/17
Given data ,
Let the probability that event A or B takes place is P ( A ∪ B )
Now , the probability of A is P ( A ) = 2/17
And , the probability of B is P ( B ) = 4/17
where P ( A ∩ B ) = 0
On simplifying the equation , we get
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
So , P ( A ∪ B ) = 2/17 + 4/17
P ( A ∪ B ) = 6/17
Hence , the probability is 6/17
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Find the degree of the monomial. 3a^8b^7
Answers
PLEASE HELP ME QUICK!!!
Answers
Answer:
Option D. [tex]g(x)=5(0.8)^{x}+2[/tex]
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
I understand the lower and upper class limits but there are only one number but I don't know what to do
Answers
The class mark of the modal class is: 25
How to solveFrom the given histogram, the following Frequency Distribution is obtained:
Class Interval Mid point Frequency
625-675 650 3
676-726 701 5
727 - 777 752 7
778 - 828 803 8
829 - 879 854 6
880 - 930 905 2
931 - 981 956 0
982 - 1032 1007 1
b. To find the lower class limit of the first class:
First class: 625
c. The upper limit of the first class is:
First class: 676
The class mark of the modal class is:
The modal class is: 803
The class mark is upper limit + lower limit/2
Thus, 828-778/2
=> 50/2
The class mark of the modal class is: 25
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.If $10,000 is deposited in an account earning 5 ¾ % interest compounded monthly. How much money will be in the account in 5 years.
Answers
The total amount in the acount in 5 years is approximately $13,321.76.
What is the accrued amount in the account in 5 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded monthly n = 12Time t = 5 yearsInterest rate r = 5 3/4% = 5.75%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575
Plug the given values into the above formula and solve for A.
[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]
A = $13,321.76
Therefore, the accrued amount is $13,321.76.
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I need help i don't know how to do this please
Answers
The size of matrix cM is given as follows:
9 x 10.
What happens when a matrix is multiplied by a constant?When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.
The parameters for this problem are given as follows:
Constant c.Matrix M of dimensions 9 x 10.Hence the size of matrix cM is given as follows:
9 x 10.
(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).
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Models that represent z+9=14 ASAP
Answers
To represent z+9=14, we can start by subtracting 9 from both sides of the equation:
z + 9 - 9 = 14 - 9
Simplifying the left side of the equation gives:
z = 5
Therefore, the solution to the equation z+9=14 is z=5.
Rosie earns $25 for travel time plus $18 an hour working at her uncle’s shop. Write an expression that can be used to find the amount Rosie will earn for working, 7, hours.
Answers
Answer:
Earned = 25 + 18h
Earned = 151
Step-by-step explanation:
The amount earned is the travel time plus the amount per hour times the hours
Earned = 25 + 18h
She works 7 hours
Earned = 25 + 18*7
Earned = 25 + 126
Earned = 151
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two serving of blueberry pie provides 1290 calories
Answers
The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.
How to determine the caloric contentTo determine the caloric content, we will assign algebraic notations to each of the dessert types.
1 Icecream + 2 Blueberry pie = 790 calories
3 icecream + 2 Blueberry pie = 1290 calories
Now the first equation will be subtracted from the second equation as follows:
2 icecream = 500 calories
So, 1 ice cream is 250 calories.
Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.
Complete question:
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.
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if my circular garden requires 2 cups of water per 10 square feet, how many cups of water do i need when the radius is 3 feet
Answers
A swimming pool holds 450, 000 L
of water and has two drainage
pipes.
Pipe A, by itself, can drain the pool
in 150 minutes. Pipe B, by itself, can
drain the pool in 225 minutes.
If you turned on both pipes at the
same time, how many minutes
would it take to drain the pool?
Answers
Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.
What is a linear equation?A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.
The quantity of water the swimming pool holds = 450,000 liters
The drainage time of Pipe A working alone = 150 minutes
Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)
The drainage time of Pipe B working alone = 225 minutes
Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)
The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)
Let the number of minutes for both pipes to drain the pool = x
Therefore, the linear equation is 5,000x = 450,000
x = 90 minutes (450,000 ÷ 5,000)
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Plsss help meeee quick
Answers
Answer:
B
Step-by-step explanation:
Lateral surface contains B,C and D (because A and E are bases)
A (lateral surface area) = 70 + 70 + 56 = 196 cm^2
A population of rabbits is increasing at a rate of 1.5% per month. If there are 60 rabbits today, how many will there be after 10 months? Round to the nearest whole.
Answers
If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.
To solve this problem, we need to use the formula for exponential growth:
A = P(1 + r)ᵗ
where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.
Plugging these values into the formula, we get:
A = 60(1 + 0.015)¹⁰
A ≈ 71
t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.
Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.
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What is 2 1/4 divided by 1 1/2?
Answers
Answer:
2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.
Step-by-step explanation:
To divide 2 1/4 by 1 1/2, we first need to convert both mixed numbers to improper fractions:
2 1/4 = (2 × 4 + 1) / 4 = 9 / 4
1 1/2 = (1 × 2 + 1) / 2 = 3 / 2
Now we can divide by multiplying by the reciprocal of the second fraction:
(9/4) / (3/2) = (9/4) * (2/3)
We can simplify this multiplication by canceling the common factor of 3 in the numerator of the second fraction and the denominator of the first fraction:
(9/4) * (2/3) = (33/4) * (2/13) = 9/2
So 2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.
[tex]\boxed{\sf \dfrac{3}{2}}.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf \dfrac{2\dfrac{1}{4} }{1\frac{1}{2} }[/tex]
2. Convert the mixed fractions into improper fractions.[tex]\sf 2\dfrac{1}{4}\Longrightarrow\dfrac{4}{4} +\dfrac{4}{4} +\dfrac{1}{4} =\dfrac{4+4+1}{4} =\dfrac{9}{4}[/tex]
[tex]1\dfrac{1}{2} =\dfrac{2}{2} +\dfrac{1}{2} =\dfrac{2+1}{2} =\dfrac{3}{2}[/tex]
3. Rewrite the division.[tex]\sf \dfrac{\dfrac{9}{4} }{\dfrac{3}{2} }[/tex]
4. Rewrite again using the properties of fractions.• Check the attached image.
[tex]\dfrac{9}{4} *\dfrac{2}{3}[/tex]
5. Calculate and simplify.[tex]\dfrac{9*2}{4*3} =\dfrac{18}{12} \\ \\\dfrac{18/2}{12/2} =\dfrac{9/3}{6/3}=\boxed{\sf \dfrac{3}{2}} .[/tex]
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A spinner divided into three equal sections marked A A and Z is spun 570 times approximately how many times will it be expected to land on an A
Answers
If a spinner divided into three equal sections marked A A and Z is spun 570 times . The number of times it will be expected to land on an A is 380 times.
How to find the Expected number of time ?Since the spinner has three equal sections in which two of them are marked A. The probability of landing on an A in a single spin will be 2/3 while the probability of landing on Z will be 1/3.
So,
Expected number of time E(A) =Number of spins x Probability of landing on A
Expected number of time E(A) = 570 x (2/3)
Expected number of time E(A) = 380
Therefore the Expected number of time E(A) is 380 times.
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A company produces two products, A and B. At
least 30 units of product A and at least 10 units of
product B must be produced. The maximum
number of units that can be produced per day is
80. Product A yields a profit of $15 and product B
yields a profit of $8. Let a = the number of units of
product A and b = the number of units of product
B.
What objective function can be used to maximize
the profit?
P=
DONE✔
a+
b
Answers
The objective function that can be used to maximize the profit is Profit = 15a + 8b
Let a is the number of units of product A and b is the number of units of product B.
Profit = 15a + 8b
This function represents the total profit earned by producing a units of product A and b units of product B
Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.
To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function
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Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer: 100.48 cubic feet
Step-by-step explanation:
Consider the line y = -8x + 7.
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 3).
Find the equation of the line that is parallel to this line and passes through the point (-5, 3).
Answers
The equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
What is a line?A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.
Since lines can exist embedded in two, three, or higher dimensions environments, they are one-dimensional objects.
The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
So, the lines with the same slope but a different y-intercept are said to be parallel.
Therefore, we must use the same slope to plug in the point (7, 6) and solve for the y-intercept.
We thus have:
y = 8x + b
6 = 8(7) + b
6 = 56 + b
b + 56 = 6
b + 56 - 56 = 6 - 56
b = -50
The equation is: y = 8x - 50
Therefore, the equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
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Correct question:
Consider the line y = 8x - 4. Find the equation of the line that is parallel to this line and passes through the point (7, 6).
3.4 The rectangular box has the length of 8x² and the breadth of 6x² - 4x 3.4.1 What is the area of the box? 3.4.2 Factorise the area of the box? 3.4.3 If x = 2 what will be the value of the length and the breadth?
Answers
Answer:
3.4.1) (8x^2)(6x^2 - 4x) = 48x^4 - 32x^2
3.4.2) 48x^4 - 32x^2 = (16x^2)(3x^2 - 2)
3.4.3) Length = 16(2^2) = 16(4) = 64
Width = 3(2^2) - 2 = 3(4) - 2
= 12 - 2 = 10
Area = 64(10) = 640
Which number is the greatest? 20 -100 -45 50
Answers
If GI and JL are parellel lines and m
Answers
The measure of angle IHE is 23°.
Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:
mHJF = mGHJ = 134°
We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:
mHJF + mFJI + mIHE = 180°
Substituting the values we know, we get:
134° + mFJI + mIHE = 180°
Simplifying the equation, we get:
mFJI + mIHE = 46°
We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:
mGHJ + mHJF + mFJI = 180°
Substituting the values we know, we get:
134° + mFJI + mFJI = 180°
Simplifying the equation, we get:
2mFJI = 46°
Dividing both sides by 2, we get:
mFJI = 23°
Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:
mFJI + mIHE = 46°
23° + mIHE = 46°
Subtracting 23° from both sides, we get:
mIHE = 23°
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Complete Question:
If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?
A local radio station is running a contest were 35 people have qualified. From these qualifiers, 3 will be randomly selected to win a trip to the Bahamas. How many different possibilities are there for the outcome of this contest?
Answers
Answer:
39270
Step-by-step explanation:
When the first person is picked, there is a 1 in 35 chance that it will be Person 1. If they are selected, that leaves 34 people left in the pool. After Person 2 is selected, there are 33 people left in the pool for Person 3.
35*34*33=39270
Bob has saved $600 each month for the last 3 years
to make a down payment on a house. The account
earned an interest rate of 0.50 percent per month.
How much money is in Bob's account?
Answers
Answer:
300
Step-by-step explanation:
The cost of a pen is $15. Find the cost of 162 pens
Answers
Answer: 15 x 162 = 2430$
162 x $15 = $2,430
The cost of 162 pens is $2,430. (Without tax)
6 yards 2 feet 5 inches equals
Answers
Answer:
245 inches
Step-by-step explanation:
Yards->Inches
1 yard = 36 inches
Therefore, 6 yards = 36 x 6 = 216 inches
Feet->Inches
1 feet = 12 inches
Therefore, 2 feet = 2 x 12 = 24 inches
Adding all inches,
=> 216 + 24 + 5
=> 245 inches
Find the consumers' surplus at a price level of $1 for the price-demand equation
p= D(x) = 20-0.1x
where p is the price and x is the demand. Do not include a dollar sign or any commas in your answer.
Answers
The consumers' surplus at a price level of $1 for the price-demand equation is -1072.5.
Given that price-demand equation p= D(x) = 20-0.1x, we need to find the consumers' surplus at a price level of $1.
So,
From the equation we have,
20-0.1x = 1
0.1x = 19
x = 190
Therefore, the equilibrium point = (190, 1) = (xe, Pe)
Now,
Cs = [tex]\int\limits^{x_e}_0 {D(x)} \ dx\, -Pexe[/tex]
[tex]\int\limits^{190}_0 {20-0.1x} \ dx\, -(190)[/tex]
= 20-0.1{9025}-190
= -1072.5
Hence the consumers' surplus at a price level of $1 for the price-demand equation is -1072.5
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