Answers
Answer:
8a. x = 16√3
8b. y = 8√3
Step-by-step explanation:
8a. Determination of the value of x
Adjacent = 24
Hypothenus = x
Angle θ = 30°
The value of x can be obtained by using cosine ratio as illustrated below:
Cos θ = Adjacent /Hypothenus
Cos 30 = 24 / x
√3/2 = 24/x
Cross multiply
x × √3 = 2× 24
x × √3 = 48
Divide both side by √3
x = 48/√3
Rationalise
x = 48/√3 × √3/√3
x = 48√3 / √3 × √3
x = 48√3 / 3
x = 16√3
8b. Determination of the value of y
Opposite = y
Adjacent = 24
Angle θ = 30°
The value of y can be obtained by using Tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 30 = y / 24
1 / √3 = y /24
Cross multiply
y × √3 = 1 × 24
y × √3 = 24
Divide both side by √3
y = 24 /√3
Rationalise
y = 24 /√3 × √3/√3
y = 24 ×√3 / √3 × √3
y = 24√3 / 3
y = 8√3
Related Questions
Mason bought c chocolates. Cameron bought 20 times as many chocolates as Mason. Write an expression that shows how many chocolates Cameron bought.
Answers
Answer:
20c is the expression
The number of cell phone tower sites in the United States was 195,613 in
2006. By 2012, the number of cell phone tower sites had increased by 54.3%.
Find the number of cell phone towers in 2012. Round your answer to the
nearest whole number
Answers
Answer:
Step-by-step explanation:
195613(1+.543)
195613(1.543)
301831
Need ASAP, please help!
Answers
========================================================
Explanation:
Segments DB and DC are the same length. This makes triangle BCD to be isosceles. Recall that the base angles of any isosceles triangle are congruent angles. The base angles are opposite the congruent sides.
So because DB = DC, this makes B = C the congruent base angles in question. Let's say they are x for now.
Also recall that for any triangle, the three angles always add to 180 degrees.
B+C+D = 180
x+x+44 = 180
2x+44 = 180
2x = 180-44
2x = 136
x = 136/2
x = 68
So angles B and C, of triangle BCD, are 68 degrees each.
This leads to angle BCD to be 68 degrees as well.
Now we'll turn to the Tangent-Chord Theorem. This says that the angle made between a chord and a tangent is the same measure as the inscribed angle that is opposite the chord.
In this case,
AB is the tangentDB is the chord we want to focus onangle ABD is the angle between the chord and tangentangle BCD is the angle opposite the chordSo because angle BCD is 68 degrees, so is angle ABD.
Plzzzzz help meeee
Which correctly lists three places that fresh water is found?
rivers, oceans, lakes
oceans, coastal wetlands, seas
ice sheets, water vapor, rivers
water vapor, streams, oceans
Answers
Answer:
ice sheets water vapor, and rivers
Step-by-step explanation:
vote brainiest if this helped
Answer:
c
Step-by-step explanation:
The distance from Leeds to London is 210 miles. The train
travels at an average speed of 90 mph. If I catch the 9.30 am
train in London, at what time should I expect to arrive in
Leeds?
Answers
Distance = speed x time
Rearrange the formula
Time = Distance/speed
D = 210 miles; S = 90
Time = 210/90 = 2.33 hours
First add 2 hr and then add 0.33333 hr
9:30 + 2 hr = 11:30
Converting 0.33333 into min
0.33 x 60 = 20 min
11:30 + 20 min = 11:50 am
How many parts does the net of a cylinder have?
four
three
two
five
Answers
Answer:
the net of a cylinder has 3 parts to it
Answer:
B three
Step-by-step explanation:
The net of a cylinder consists of three parts: One circle gives the base and another circle gives the top. A rectangle gives the curved surface.
-2/3- (-3/4)
Simplify if needed
Brainliest
Also, 5/6+5/12
Answers
Answer:
[tex]-\frac{2}{3} - (-\frac{3}{4}) = \frac{1}{12}[/tex]
[tex]\frac{5}{6} + \frac{5}{12} = \frac{5}{3}[/tex]
Step-by-step explanation:
Given
[tex]-\frac{2}{3} - (-\frac{3}{4})[/tex]
Required
Solve:
[tex]-\frac{2}{3} - (-\frac{3}{4})[/tex]
Open bracket
[tex]-\frac{2}{3} - (-\frac{3}{4}) = -\frac{2}{3} +\frac{3}{4}[/tex]
Take LCM
[tex]-\frac{2}{3} - (-\frac{3}{4}) = \frac{-8+9}{12}[/tex]
[tex]-\frac{2}{3} - (-\frac{3}{4}) = \frac{1}{12}[/tex]
[tex]\frac{5}{6} + \frac{5}{12}[/tex]
Take LCM
[tex]\frac{5}{6} + \frac{5}{12} = \frac{10+5}{12}[/tex]
[tex]\frac{5}{6} + \frac{5}{12} = \frac{15}{12}[/tex]
Divide by 3/3
[tex]\frac{5}{6} + \frac{5}{12} = \frac{5}{3}[/tex]
Is either x=5 or x=3 a solution to 11- x <7
Answers
Answer:
x = 5Explanation:
11 - x < 7
11 minus a number is less than 7Insert 5 into the equation
11 - 5 < 7
Simplify
6 < 7
This is trueInsert 3 into the equation
11 - 3 < 7
Simplify
8 < 7
This is falsex = 5 is a solution to the equation 11 - x < 7- PacificNorthwest
Answer:
x=5 is the correct answer
Step-by-step explanation:
First we start off to see if x=3 could work (put the x value in)
11-3<7
(11-3=8)
8<7 This is false
Now lets try the other one-
11-5<7
(11-5=6)
6<7
The value x=5 is the correct answer
P.S If you don't mind, could I have brainlest? (if you think my answer is the best)
25 = 3x - 5
What does X equal?
Answers
Answer:
The answer is x = 10
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
hoped this helped!
brainly, please?
Answer:
x = 10
Step-by-step explanation:
Step 1: Flip the equation.
3x−5=25
Step 2: Add 5 to both sides.
3x−5+5=25+5
3x=30
Step 3: Divide both sides by 3.
pls help math qucikly
Answers
Answer:
1/3
Step-by-step explanation:
Plzzzzzz helpppppp!!!!!!
Answers
Answer:
h(x) ≤ 5
Step-by-step explanation:
The function and boundaries given are;
h(x) = x + 2, x < 3
And ;
h(x) = -x + 8, x ≥ 3
Now,in the first condition, the maximum value of x will be 2. This means the maximum value of h(x) there is;
h(2) = 2 + 2 = 4
For the second condition, x ≥ 3. Thus, the maximum value of x is 3.
This means that the maximum value of h(x) here is;
h(3) = -3 + 8 = 5
Foe the 2 conditions combined it is clear that the maximum value of h(x) is 5.
Thus,we can say; h(x) ≤ 5
In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 71 and a standard deviation of 7. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D.
Answers
Answer:
The lowest score on the final exam that would qualify a student for an A is 80.
The lowest score on the final exam that would qualify a student for a B is 74.68.
The lowest score on the final exam that would qualify a student for a C is 67.33.
The lowest score on the final exam that would qualify a student for a D is 62.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Mean of 71 and a standard deviation of 7.
This means that [tex]\mu = 71, \sigma = 7[/tex]
Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's.
This means that:
90th percentile and above: A
70th percentile and below 90th: B
30th percentile to the 70th percentile: C
10th percentile to the 30th: D
Lowest score for an A:
Top 10% receive A, which means that the lowest score that would qualify a student for an A is the 100 - 10 = 90th percentile, which is X when Z has a pvalue of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 71}{7}[/tex]
[tex]X - 71 = 7*1.28[/tex]
[tex]X = 80[/tex]
The lowest score on the final exam that would qualify a student for an A is 80.
Lowest score for a B:
70th percentile, which is X when Z has a pvalue of 0.7, so X when Z = 0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 71}{7}[/tex]
[tex]X - 71 = 7*0.525[/tex]
[tex]X = 74.68[/tex]
The lowest score on the final exam that would qualify a student for a B is 74.68.
Lowest score for a C:
30th percentile, which is X when Z has a pvalue of 0.3, so X when Z = -0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.525 = \frac{X - 71}{7}[/tex]
[tex]X - 71 = 7*(-0.525)[/tex]
[tex]X = 67.33[/tex]
The lowest score on the final exam that would qualify a student for a C is 67.33.
Lowest score for a D:
10th percentile, which is X when Z has a pvalue of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 71}{7}[/tex]
[tex]X - 71 = 7*(-1.28)[/tex]
[tex]X = 62[/tex]
The lowest score on the final exam that would qualify a student for a D is 62.
A loan of $20,000 is made at 7% interest, compounded annually. After how many years will the amount due reach $41,000 or more?
Answers
Answer:
Step-by-step explanation:
11 years
Using the compound interest formula. :
Final amount, A = 41000 or more
Rate, r = 7% = 0.07
Loan amount, P = 20,000
Number of compounding times per period = 1
A = P(1 + r/n)^nt
41000 = 20000(1 + 0.07)^t
41000/20000 = 1.07^t
2.05 = 1.07^t
t = log(2.05) / log(1.07)
t = 10.609727
t = 11 years
A restaurant needs to plan seating for a party of 150 people. Large tables seat 10 people and small tables seat 6. Let x represent the number of large tables and y represent the number of small tables. The expression 10A + 6B, which represents the total number of people you can seat using A large tables and B small tables, is called a linear combination. For instance, 150 people could be seated using 6 large tables and 15 small tables. Use that expression to enter an equation in standard form that models all the different combinations of tables the restaurant could use. Then identify at least one possible combination of tables other than (6, 15).
The equation is . Another possible combination is
Answers
Answer:
15
Step-by-step explanation:
CAN SOMEONE PLEASE EXPLAIN WHY THE ANSWER FOR THIS IS 4N+15. THIS IS 10 MINUTES PAST DUE!!! TAKE 20 POINTS
Answers
so here's the breakdown of the sentence:
Daquan has 15 more than (15 +) 4 times as many (4n) walnut trees in his orchard as he has almond trees.
hopefully this makes sense! have a nice day
Figure ABCD is reflected over the y-axis to obtain figure A′B′C′D′ below: A coordinate plane is shown. Figure ABCD has vertices A at 2 comma 5, B at 1 comma 2, C at 3 comma 1, and D at 4 comma 5. Figure A prime B prime C prime D prime has vertices A prime at negative 2 comma 5, B prime at negative 1 comma 2, C prime at negative 3 comma 1, and D prime at negative 4 comma 5. Which statement best describes the relationship between the two figures? Figure ABCD is similar to figure A′B′C′D′. Figure ABCD is bigger than figure A′B′C′D′. The measure of angle D is equal to the measure of angle A′. The measure of angle D is equal to the measure of angle B′.
Answers
Answer:
A. Figure ABCD is similar to figure A′B′C′D′Step-by-step explanation:
Refer to attached graph
Statements
Figure ABCD is similar to figure A′B′C′D′.
True. Similar sides and congruent angles.Figure ABCD is bigger than figure A′B′C′D′.
False. They have same area.The measure of angle D is equal to the measure of angle A′.
False. D is equal to D'The measure of angle D is equal to the measure of angle B′.
False. D is equal to D'.Answer:
A
Step-by-step explanation: The Person AbovE Is 100% Right and I can't explain this question any better.
what is the answer
y-11=25-3y
Answers
Answer:
9
Step-by-step explanation:
y-11=25-3y
y + 3y = 25 + 11
4y = 36
y = 36 / 4
y = 9
Hope it will help :)
anyone know which company charges the greatest rate per window?
Answers
Company B costs most per window
Step by step:
company a = 25x + 50
company b = 40x + 15
company c = 35x + 25
HELP IT EASY PLEASE D::::::
Answers
Answer:
36 inches
Step-by-step explanation:
The area formula for a rectangle is length times width times height
If you fill in the equation with the values given in the picture then your answer is 3
3 times 12 is 36
4 In February, Alec had 1,581 visitors to his website. In March, he had 1,321 visitors to his website. What is the percentage decrease of the number of visitors to Alec's website from February to March? if necessary, round to the nearest tenth of a percent
Answers
Answer:
It is 16.4 %
Step-by-step explanation:
Subtract 1581 and 1321 to get how much it decreased.
It decreased by 260 so find what percent of 1581 is 260.
260/1581 = 0.164 which is 16.4 %
I put a random subject but can u please help with this question
Answers
Answer:
Parasitism
Step-by-step explanation:
What is the coefficient of the term 12p+9q
Answers
Answer:
The answer is 12.
Step-by-step explanation:
12 is the coefficient because it is the number multiplied by the variable p in the equation.
I hope this helps u! :D
1) A ball is dropped from a height of 50 feet. How long after it is dropped will it reach a height of 18 feet?
Answers
Answer: 1.41 seconds
Step-by-step explanation:
The problem gives the initial velocity by saying "dropped." This indicates a velocity of zero. Acceleration can also be found because the object is in free fall. It would experience the acceleration of gravity. We can use the kinematic equation:
[tex](y_f-y_i)=V_it+\frac{1}{2}at^2[/tex]
The velocity term completely cancels because the object was dropped with an initial velocity of 0.
[tex](18-50)=\frac{1}{2} (32.17)t^2\\[/tex]
[tex]-32=-16.085t^2\\t=\sqrt{1.989} =1.41s[/tex]
A bacteria culture grows at a rate of 16% per hour. If there were 25 bacteria present in the culture to start, how many bacteria are present after one day?
Answers
Step-by-step explanation:
me kuch nhi karunga
When a solid directly changes to gaseous state on heating , without changing to the liquid state , the gaseous material so formed is called?Marvin was buying soil for his flower garden. What would be the most reasonable amount of soil he would need to buy for a flower garden? A. 6 grams B. 60 liters C. 60 kilograms D. 6,000 kilograms
Answers
Answer:
60 liters
Step-by-step explanation:
Answer:
C. 60 kilograms
Step-by-step explanation:
The person above me is incorrect because liters is used on liquids
A number is divided into two parts, such that one part is 10 more than the other, if the two parts are in the ratio 5:3, find the number and the two parts.
Answers
Answer:
Step-by-step explanation:
25:15
5x5=25
3x5=15
There are some apples and 8 pears in a basket. Each of them is either green or yellow. There are three more apples than the total number of green fruit. There are 6 yellow pears. How many yellow apples are there in the basket?
Answers
Answer:
5 yellow apples
Step-by-step explanation:
Pears = p ; apples = a
p = 8 ; let Number of apples = x
All fruits are either green or yellow
Total green fruits = x - 3
Number of yellow pears = 6
Green pears = total pears - yellow pears
Green pears = 8 - 6
Green pears = 2
Green fruits = green pears + green apples
x - 3 = 2 + green apples
Green apples = x - 3 - 2
Green apples = x - 5
Apples = green apples + yellow apples
Yellow apples = apples - green apples
Yellow apples = x - (x - 5)
Yellow apples = x - x + 5
Yellow apples = 5
Hence, there are 5 yellow apples
There are 5 yellow apples in the basket.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent green apples, b represent yellow apples, c represent green pears and d represent yellow pears, hence:
There are some apples and 8 pears in a basket:
c + d = 8
There are three more apples than the total number of green fruit:
a + b = a + c + 3
b = c + 3
c = b - 3
There are 6 yellow pears, d = 6. Since:
c + d = 8, hence:
b - 3 + 6 = 8
b = 5
There are 5 yellow apples in the basket.
Find out more on equation at: https://brainly.com/question/2972832
PLEASE HELP ME!!!!!!!!!!!!!!!!!
One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.
Answers
Answer:
1.8 gallons
SEE NOTE BELOW*
Step-by-step explanation:
2x10x16=320
2x20x10=400
400+320=720
720÷400=1.8 gallons
NOTE* This would be painting the four walls. If you include the floor and ceiling:
2x16x20=640
720+640=1360
1360÷400=3.4 gallons
The least amount of paint needed to paint the walls of a room in the shape of a rectangular prism is 1.8 gallons (2 gallons approx).
What is rectangular prism?Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.
The formula to calculate the total surface area of a rectangular prism is given as,
TSA of rectangular prism = 2(lb + bh + lh)
Where, l is length, b is breadth and h is the height of the rectangular prism.
Calculation for the paint required for rectangular prism:
The area of the sides of prism to be painted is
Area A = 2×(length×height) + 2×(breadth×height)
Length = 20 feet
Breadth = 16 feet
Height = 10 feet
A = 2×(20×10) + 2×(16×10)
A = 720 sq. feet
Now, the paint need for painting 400 sq. feet is 1 gallon.
Thus, paint required for 720 sq. feet is,
=> 720 ft² / 400 ft² /gal = 1.8 gal
Therefore, for painting rectangular prism, the amount of paint required is 1.8 gal.
To know more about the prism, here
https://brainly.com/question/16803016
#SPJ2
Solve for y
2(3 + 3y) + y = 11
Answers
2(3 + 3y) + y = 11
First, apply the distributive property:
2(3 + 3y) + y = 11
6 + 6y + y = 11
6 + 7y = 11
Substract 6 from both sides:
6 - 6 + 7y = 11 - 6
7y = 5
Divide both sides by 7:
[tex]\dfrac{7y}{7} = \dfrac{5}{7}[/tex]
[tex]\boxed{y = \dfrac{5}{7}}[/tex]
Answer. The value of y = 5/7.
A turtle is crawling up a hill that rises 6 feet for every horizontal change of 36 feet. Write the slope of the hill as a
fraction in simplest form.
Answers
9514 1404 393
Answer:
1/6
Step-by-step explanation:
The slope is the ratio of rise to run.
slope = rise/run = (6 ft)/(36 ft) = 6/36 = 1/6
The slope of the hill is 1/6.