In a triangle PQR, right-angled at Q, PR = 37 inches and angle R =
30°. Find: sin R
Answers
The required value of PQ is 18.5 inches in the given triangle PQR.
What is right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
As per the given question, let's call the length of side PR (the hypotenuse). Since we know that PR = 37 inches and angle R = 30°, we can use the sine rule to write the following equation:
sin R = perpendicular/hypotenuse
sin R = PQ/PR
sin 30° = PQ/37
1/2 = PQ/37
PQ = 37/2
Apply the division operation, and we get
PQ = 18.5
Therefore, the required value of PQ is 18.5 inches.
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In a triangle PQR, right-angled at Q, PR = 37 inches and angle R =
30°. Find: PQ
Related Questions
At a school recess, there needs to be a ratio of 2 adults for every 24 children on the playground. The double number line represents the number of adults and children on the playground at recess. How many adults are needed if there are 72 children?.
Answers
A ratio of 2:24 kids (when simplified) is 1 parent for every 12 kids.
Now it’s a matter of simple multiplication. In order to get 72 kids, what times 12 equals 72?
The answer is 6.
excel grear tire company has produced a new tire with an estimated mean lifetime mileage of 33,500 miles. management also believes that the standard deviation is 3,500 miles and that tire mileage is normally distributed. to promote the new tire, grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. specifically, for tires with a lifetime below 30,000 miles, grear will refund a customer $1 per 100 miles short of 30,000. (a) for each tire sold, what is the average cost of the promotion (in $)? (use at least 1,000 trials. round your answer to two decimal places.) $ (b) what is the probability that grear will refund more than $25 for a tire? (use at least 1,000 trials. round your answer to three decimal places.)
Answers
a) The average cost of the promotion is $ 0.01 per liter
b) the probability that Greer will refund more than $25 for a liter is 0.0107.
a.
Mean lifetime mileage : $33,500
Standard deviation of mileage: $3500
Observed miles: 30,000 miles
100 miles failed $1.00
Hence :
= (33,500 – 30,000) / 3500= 1
Cost of production
100 miles = $1.00
= 1* 1 / 100
= $ 0.01 per tire
b.
P (z < 25000 - 36500/5000)
P (z < -11500/5000)
z < -2.3
Hence:
1 - 0.9893
= 0.0107
Therefore, the Probability that gear will refund more than $50.00 per tire is: 0.0107
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Write the equation of the given line in slope-intercept form.
Answers
Answer:
y=7/2x+1
Step-by-step explanation:
Remember this formula
Y=mx+b
m=slope
b=y-intercept
Question 4 pls help!!!!!!!
Answer choices:
A) construct a perpendicular line to a point not on the line
B) copy a segment
C)copy an angle
D) bisect and angle
Answers
Answer:
The answer is b because none of the other answers are reasonable.
Step-by-step explanation:
cuz im smart
please give brainliest
Find the demand function for the marginal revenue function. recall that if no items are sold, the revenue is 0.
R′(x)=0.06x2−0.05x+138
Answers
The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .
Given that,
We have to find for the marginal revenue function, locate the demand function.
Remember that the income is zero if no things are sold:
R'(x) = 0.06x² - 0.05x + 138
p(x) is what.
We know that,
MR = dTR/dx = 0.06x² - 0.05x + 138
Integrating the marginal revenue function , we get total revenue function,
MR = TR
= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x
= (0.06x³)/3 - (0.05x²)/2 + 138 x
TR = 0.02 x³ - 0.025 x² + 138 x
TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x
P = ( 0.02 x³ - 0.025 x² + 138 x)/x
P = 0.02x² -0.025x + 138
Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .
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How many solutions over the complex number system does this polynomial have 7x^5-33x^4-4x^2+3x+52=0.
Answers
The number of solutions over the complex number system to the given polynomial is 5 .
The complex number is fundamentally the mix of a real number and a nonexistent/imaginary number. The complex number is given by a+ib, where a is defined as the real number and ib = imaginary number. Additionally, a,b has a place with real numbers and i = √-1.
Consequently, a complex number is a straightforward portrayal of expansion of two numbers, i.e., real number and a imaginary number. One piece of it is simply genuine and the other part is absolutely nonexistent.
Now, the given polynomial is 7x⁵ - 33x⁴ -4x²+3x+52=0.
We know very well that for complex number, its number of solution is decided by the degree of the polynomial. Degree is defined as the highest exponent of variables present in polynomial. Highest exponent present in polynomial is 5.
Hence, number of solutions are 5.
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answers for number 21 and 24 questions
Answers
22. f(x)=4.5
23. f(x)=1/4x+7/4 or f(x)=1/4x+1.75 or f(x)=1/4x+1 3/4. (Depends on how your teacher wants the y intercept written)
24. f(x)=-3/2x-7/2 or f(x)=-3/2x-3.5 or f(x)=-3/2x-3 1/2
Find the lower quartile for the data. [20, 3, 7, 2, 6, 3, 12, 7. 12. 2}
A. 6
B. 5
C. 3
D. 4
Answers
Answer:
6
Step-by-step explanation:
its 6
outside of johnny's home there is a grassy area about 40' x 100' that he mows regularly. beyond that grassy area is a wooded area and taller grass where his kids play hide and seek. johnny mows around the trees, but less frequently than the rest of the yard, and then he has several outbuildings in the wooded area as well. the whole area that has been described is enclosed by a fence. beyond the fence is an area that he does not maintain, and he keeps his collection of exotic marijuana plants hidden in the tall grass in this area. the curtilage of johnny's home is best identified as
Answers
Therefore, the space inside the fence serves as the best indicator of Johnny's home's perimeter.
What is perimeter?A perimeter is a closed path that surrounds, encircles, or outlines a two-dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is its circumference. Perimeter calculations have many applications in the real world.
Here,
the grassy area = 40' x 100'
He has numerous outbuildings in the forested area as well, and he mows the area surrounding the trees less regularly than the rest of the yard. A fence completely encloses the area that has been described. He maintains his collection of exotic marijuana plants hidden in the long grass in the area outside the fence, which is an area he does not maintain.
Therefore, the space inside the fence serves as the best indicator of Johnny's home's perimeter.
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Solving for proportions
Answers
Answer:
1. c=72/15
2. y=4
3. k=-37/4
4.d=6
Step-by-step explanation:
1. c/6=12/15
Cross multiply. 72=15c.
Dividing by 15, we get C=72/15.
2. 21/7=3. So, 12/y=3. Solving for y, we get y=4.
3. -37/24=k/6
24/6=4. So, -37/k must equal 4.
-37/k=4
-37=4k
k=-37/4
4.
40/8=5. That means that 30/d=5
30=5d
d=6
Done!
Given the function: f(x) = 1/2 (3x+7) What is the output of the function when the input is x = 9?
Answers
Answer:
17
Step-by-step explanation:
1/2(3x+7)
1/2(3(9)+7)
1/2(27+7)
1/2(34)
17
Mrs. Sparks is a 9th grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores.
Answers
The mean of the class is 94.6 and the range of the class is 55.
What is the mean and the range?A dataset's mean is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
The range of a set of numbers is the difference between its highest and lowest values. To find it, subtract the lowest value from the highest in the distribution.
The given data is 45,68,77,90,90,95,100,100,86,90,50,55.
The mean of the data will be calculated as,
Mean = (sum of the data) / ( number of the data)
Mean = ( 45 + 68 + 77 + 90 + 90 + 95 + 100 + 100 + 86 + 90 + 50 + 55)/12
Mean = 94.6
The range of the data will be calculated as,
Range = Highest value - The lowest value
Range = 100 - 45
Range = 55
The mode of the data is 90 because it has three repetitions.
The median of the data is the middlemost value of the data when the data is arranged in increasing order,
(45,50,55,68,77,86,90,90,90,95,100,100)
Median = ( 90 + 90 ) / 2
Median = 45
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Find LN in the image below
Answers
A squared-- so the length of one of the shorter sides squared-- plus the length of the other shorter side squared is going to be equal to the length of the hypotenuse squared.
What is the Pythagorean theorem easy definition?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.we can use the Pythagorean theorem to find the length of PN in triangle OPNIn any right triangle, the area of the square whose side is the hypotenuse (remember this is the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).a²+b²=c²Pythagoras theorem can be used to find the unknown side of a right-angled triangle. For example, if two legs of a right-angled triangle are given as 4 units and 6 units, then the hypotenuse (the third side) can be calculated using the formula, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs.where a and b are legs and c is the hypotenuse
we are given one leg (OP=8) and the hypotenuse (ON=18) so now we can plug in these numbers to find PN
8²+b²=18²
64+b²=324
b²=260
b=√260
b=√4 * √65
b=2√65
now that we have the value of PN, we can get the value of LN by doubling 2√65
2(2√65) = 4√65
so your answer should be:
LN = 4√65
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Dalvin is 1.85 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 31.35 meters. He stands 27.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answers
Answer: d
Step-by-step explanation: got itright
a study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
Answers
The required probability that their hospital stay is from 5 to 6 days is 3.31%.
What is normal distribution?An normal distribution is a sort of ceaseless likelihood dissemination wherein most information guides bunch to the center of the reach, while the rest tighten evenly toward one or the other limit. The center of the reach is otherwise called the mean of the distribution.
According to question:We have,
mean(a) = 7.37, standard deviation(S) = 2
Using formula
[tex]Z = \frac{x-a}{S}[/tex]
Then,
P( hospital stay is from 5 to 6 days)
P(5[tex]\leq[/tex]x[tex]\leq[/tex]6) = P[tex](\frac{5-7.37}{2}\leq z\leq \frac{6-7.37}{2})[/tex] = P(-3.16 ≤ z ≤-1.827 )
⇒P(z≤-1.827) - P(z≤-3.16)
⇒ 0.034 - 0.001 = 0.331 = 3.31%
Theus, probability is 3.31%
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I need help with this problem
Answers
The expression that represents the chart is 2 * x + 2 * 1 1/2 = 3 * (x + 1 1/2)
How to determine the expression that represents the chart?From the question, we have the following parameters that can be used in our computation:
The chart
On the chart, we have the following values
Green = x
Purple = 3
Orange = 1 1/2
In terms of the variable x, we have the following equation
2 * Green + 2 * Orange = Purple * (x + Orange)
Substitute the known values in the above equation, so, we have the following representation
2 * x + 2 * 1 1/2 = 3 * (x + 1 1/2)
The question does not require that the equation be solved
Hence, the required expression is 2 * x + 2 * 1 1/2 = 3 * (x + 1 1/2)
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3. (6 pts) consider three branch prediction scheme: predict not taken, predict taken, and dynamic prediction. assume that they all have zero penalty when they predict correctly and two cycles when they are wrong. assume that the average predict accuracy of the dynamic predictor is 90%. which predictor is the best choice for each of the following branches? justify your answers. a. a branch that is take with 5% frequency. b. a branch that is taken with 95% frequency. c. a branch that is taken with 70% frequency.
Answers
There are three branch prediction scheme: predict not taken, predict taken, and dynamic prediction. assume that they all have zero penalty when they predict correctly and two cycles when they are wrong.
In computer architecture, a branch predictor is a digital circuit that attempts to guess which direction a branch (e.g. an if-then-else construct) is going finally announced. The purpose of the branch predictor is to improve the flow of the instruction pipeline. Branch predictors play a key role in achieving high performance in many modern pipeline microprocessor architectures.
1. If the branch is taken 5% of the time, the branch prediction scheme is ``predicted-taken'' because the process must start fetching and then executing at the target address.
2. If a branch is taken 95% of the time, the branch outcome is known with certainty, so the branch prediction scheme is "unpredictable".
3. If the branch is taken 70% of the time, then the prediction scheme is "dynamic prediction" and the branch prediction can change dynamically during program execution.
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the sales tax rate is 7.25% in California, then how much would you pay in Los
Angeles for a pair of shoes that cost $39.00?
Answers
Answer:
The sales tax in California is 7.25%, which means that for every dollar you spend, you need to pay an additional 7.25 cents in sales tax. So if you buy a pair of shoes that costs $39.00, you would need to pay an additional $2.84 in sales tax (39 x 0.0725 = 2.84). This means that the total cost of the shoes would be $41.84 (39 + 2.84 = 41.84).
Step-by-step explanation:
Answer:
41.83
Step-by-step explanation:
39 x .0725 = 2.83 Tax rounded to the nearest cent
2.83 + 39 = 41.83
Given the function y= x2 + 10x +16=0
What are the x-intercepts of the function?
Answers
Answer:
(0,-8) and (0,-2)
Step-by-step explanation:
Factorize: x² + 10x + 16 = 0
You'll get: (x + 8)(x + 2) = 0
The roots are x = -8 and x = -2
So the curves intercepts the x-axis at (0,-8) and (0,-2)
Answer:
(-2,0) and (-8, 0)
Step-by-step explanation:
Factor the function:
(x + 2)(x+8) = 0
x = -2, -8
x intercepts are when y=0
Coordinates are:
(-2,0) and (-8, 0)
Find the volume of this prism with height of 9 width if 6 length of 12
Answers
Answer:
SA = 124 cm².
V = 72 cm³
Step-by-step explanation:
Expand -4(6a - 5)
Please help!!!!
Answers
Answer:
-24a+20
Step-by-step explanation:
just use distrubitive property
the fox population in a certain region has an annual growth rate of 9% per year. in the year 2012, there were 20,700 foxes counted in the area. what is the fox population predicted to be in the year 2019? round to the nearest fox.
Answers
37,840 is the fox population predicted to be in the year 2019.
What is a growth rate?
The country, territory, or geographic area's yearly average rate of change in population size over a certain time period. It expresses the proportion, usually multiplied by 100, between the annual growth in population size and the total population for that year.
Here, we have
A growth rate of 9% per year means that at the end of each year, the population is 1.09 times what it was at the start of the year.
We keep this up for t years, starting with an initial population of 20,700, and get
P(n) = 20,700 (1.09)ⁿ
n = years since 2012, when the population was 20,700
For the year 2019,
n = 2019 - 2012 = 7
P(7) = 20,700 (1.09)⁷ ≅ 37,840
Hence, 37,840 is the fox population predicted to be in the year 2019.
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PLEASE HELP IM STUCK ON THIS ONE
Answers
Triangle GHJ is congruent to triangle EKI by using ASA congruence theorem.
The given triangle are GHJ and EKI.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Consider ΔGHJ and ΔEKI
∠H = ∠K (Given in figure)JK=HI (Given in figure)∠EIK = ∠GJH (Given in figure)IK=JK+IJ (segment addition postulate JK=HI, add IJ to the equivalents)HJ=HI+IJ (segment addition postulate JK=HI, add IJ to the equivalents)IK=HI+IJ (substitution property)HJ=IK (transitive property)ΔGHJ ≅ ΔEKI (By ASA congruence theorem)Hence, proved triangle GHJ is congruent to triangle EKI by using ASA congruence theorem.
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If the tree grows an additional 10 feet, what is the new angle of elevation from the point 25 feet from the base of the tree to the top of the tree?.
Answers
Angle of elevation for the tree grows an additional 10 feet, what is the new angle of elevation from the point 25 feet is angle of elevation 47.1 degree.
Angle of elevation is the elevation in the height of angles from a given points.
Length of tree = 10 feet
Angle of elevation = 25 degreesEquation for the peak of tree=?Let x constitute the peak.We recognize that tan Phi = Perpendicular / B * asetan = peak of tree/ duration of basetan Phi = x / l=>x=I^ * (tan phi)x=10 ^ * tan(25 deg)Now, setting values:x=10 ^ * tan(25 deg)x =10 ^ * 0.4663x = 14.43feetSo, the equation to discover the peak is: x = 10 * tan(25 deg) and the peak is x = 47. 1 degree.Read more about angle;
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A unicycle wheel has a diameter of 30 inches and a radius of 15 inches. How many inches will the unicycle travel in 6 revolutions?
Answers
The unicycle wheelof diameter 30 inches travels 282.6 inches in 6 revolution.
What is an inch?An inch can be defined as a unit of length in the customary system of measurement.
To calculate the amount of inches the unicycle will travel in 6 revolution, we use the formula below.
Formula:
R = 6πd.................... Equation 1Where:
The amount of inches the unicycle covered in 6 revolutiond = Diameter of the unicycleπ = PieFrom the question,
Given:
d = 15 inchesπ = 3.14Substitute these values into equation 1
R = 6×15×3.14R = 282.6 inchesHence, the unicycle wheel travels 282.6 inches.
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What is the slope of a line parallel to the line y =- 3x 10?
Answers
To find the slope of a line parallel to a given line, we need to find the slope of the given line. The slope of a line parallel to y = -3x + 10 is -3.
To find the slope of a line parallel to a given line, we need to find the slope of the given line. We can do this by taking the coefficient of x in the equation and making it the numerator of a fraction with a denominator of 1.In the equation y = -3x + 10, the coefficient of x is -3.
Therefore, the slope of a line parallel to y = -3x + 10 is -3.
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5. Explain why 0.3 x 0.9=2.7. What is the correct answer?
Answers
Answer: No, it is
0.27
Step-by-step explanation: No, it is incorrect, because .3 x .9 is not greater than 100, so it would be regularly 3 x 9 (which is 27) and since it is less than 100, it would be 0.27. I hoped this answered your question :)
Safia bakes cakes. The dimensions of the oven tray are 600mm x 500mm. A cake tin is 25 cm in diameter.
Answers
Safia can fit 4 cakes on the oven tray at one time
Firstly, We need to change the measurements from mm to cm
600mm x 0.1cm/1mm = 60cm
500mm x 0.1cm/1mm = 50cm
Area of the Tray (rectangular) = 60cm * 50cm = 3,000cm²
Area of the cake tin (circular) = π r²
r = d/2 = 25/2 = 12.5cm
Area of the cake tin = 3.14 * (12.5cm)²
Area of the cake tin = 3.14 * 156.25cm²
Area of the cake tin = 490.625cm²
Area of the tray ÷ Area of the cake tin = number of cake tins that fit
3,000cm² ÷ 490.625cm² = 6.11 or 6 cake tins.
thus, We can conclude that she can fit 6 cakes in the oven at once.
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(complete question)
Safia bakes cakes. The dimensions of the oven tray are 600mm x 500mm. A cake tin is 25 cm in diameter. How many cake tins can Safia fit on the oven tray at one time?
How do you find slope with x1 and y1?
Answers
The slope of the line passes through two points is (y2-y1)/ (x2- x1).
Slope of a line:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Here we have to find the slope of a line that passes through two points.
Data given:
Point 1 = (x1, y1)
Point 2 = (x2, y2)
The general formula to find the slope of a line:
Slope(m) = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are two points on the line.
Therefore the slope is (y2-y1)/ (x2 - x1).
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If using the method of completing the
square to solve the quadratic equation
2²+3x+37= 0, which number would
have to be added to "complete the
square"?
Answers
Answer:
To solve a quadratic equation using the method of completing the square, we need to first write the equation in the form ax² + bx + c = 0, where a, b, and c are constants. In this case, the given equation is 2²+3x+37 = 0, which can be written as 4+3x+37 = 0.
To complete the square, we need to add a number to the constant term (in this case, 37) so that the coefficient of the x² term is a perfect square. In this case, the coefficient of the x² term is 4, which is already a perfect square. Therefore, we do not need to add any number to complete the square.
The correct answer is 0.
Step-by-step explanation: