Line RS is tangent to circle Q at point R.
What is the measure of ∠SQR ?
Enter your answer in the box.
Using the tangent and radius theorem, the measure of ∠SQR is 58°.
What is Circle Geometry??From the question, we are to determine the measure of ∠SQR
In the given diagram, QR is a radius
By the tangent and radius theorem,
If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another
∴ ∠QRS = 90°
∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)
∠SQR + 32° + 90° = 180°
∠SQR + 122° = 180°
∠SQR = 180° - 122°
∠SQR = 58°
Hence, the measure of ∠SQR is 58°.
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What is the standard deviation of the following data set rounded to the nearest tenth? 52.1, 45.5, 51, 48.8, 43.6
Answer:
Standard deviation is 3.2.
Step-by-step explanation:
Given data is,
52.1, 45.5, 51, 48.8, 43.6,
Let x represents the data points,
Now, mean of the data is,
[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]
Population size, N = 5,
Hence, the standard deviation of the following data set is,
[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]
[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]
[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]
[tex]=\sqrt{10.372}[/tex]
[tex]=3.2205589577[/tex]
[tex]\approx 3.2[/tex]
A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12
2=sqrt P solve for P
find the greatest common factor 6x^2a + 6xa^2
Find the surface area of the equilateral triangular pyramid.
Students washed cars to raise funds for their school. they collected $291 by charging $3.00 per car. how many cars did they wash?
Identify a counterexample to disprove 6n>n^2/6,where n is a real number.
A counterexample to disprove the inequality [tex]6n > n^2/6[/tex] is n = 12, because when plugged into the inequality, it results in 72 > 24, which is false.
The question is asking for a counterexample to disprove the inequality [tex]6n > n^2/6[/tex], where n is a real number. To find a counterexample, let's test an arbitrary positive number, such as n = 7, to see if the inequality holds.
Substituting 7 for n, we get:
6 x 7 > 72/6
42 > 49/6
42 > 8.167
This is indeed true, so 7 is not a counterexample. However, we can think of a larger value of n. Let's try n = 12:
6 x 12 > 122/6
72 > 144/6
72 > 24
This is false. Hence, n = 12 serves as a counterexample to disprove the given inequality. So, the inequality does not hold for all real numbers.
_________________ lines are lines that never intersect and are not coplanar. A) Parallel B) Perpendicular C) Skew D) Transversal
What is cos 45? Please HELP !!!
Answer:
A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Step-by-step explanation:
Given : Triangle 90 -45 -45 .
To find : What is cos 45.
Solution : We have given
Triangle 90 -45 -45
Hypotenuse = √2 ,
Adjacent side to 45 degree = 1 .
By the trigonometric ratio : cosine is the ratio of the adjacent side to angle to the hypotenuse .
Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].
Plug the values Hypotenuse = √2 , Adjacent side to 45 degree = 1 .
Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
The cosine of 45° is √2 / 2.
In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.
In this case, we want to find the cosine of 45°.
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.
Using the formula for cosine, we have:
cos 45° = adjacent side / hypotenuse
Substituting the values, we get:
cos 45° = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
cos 45° = (1 / √2) * (√2 / √2) = √2 / 2
Therefore, the cosine of 45° is √2 / 2.
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Need help to write equations for 5, 6 & 7
PLEASE ANSWER ASAP Becky purchased a home entertainment center for $2,254 using an 18-month deferred payment plan with an interest rate of 22.48%. She did not make any payments during the deferment period. What will Becky's monthly payment be if she must pay off the home entertainment center within three years after the deferment period?
$121.01
$87.45
$62.61
$113.72
Answer:
$62.61
Step-by-step explanation:
Data:
The price of home entertainment = $ 2 254
Time to pay = 18 months
interest rate = 22.48 %
monthly payment = $ 2254/ 18
= $ 125. 22
= - 22.48 (2254)/18
= $ 62.61
Hamilton received a 75 on his algebra exam. The professor is allowing students to take a 7-question bonus quiz to improve their algebra exam score. Each question answered correctly on the bonus quiz will add 3 points to the exam score. Hamilton needs to receive at least a 90 on his exam score in order to make an "A" for the semester. If x represents the number of questions answered correctly on the bonus quiz, which of the following inequalities symbolizes this situation?
A. 3x + 75 < 90
B. 7x + 75 > 90
C. 3x + 75 > 90
D. 7x + 75 < 90
Final answer:
The correct inequality should be 3x + 75 ≥ 90 to indicate Hamilton needs at least 90 on his exam. The closest option given, which is not entirely accurate, is C. 3x + 75 > 90.
Explanation:
To determine the inequality that represents Hamilton’s situation, we need to calculate how many points he requires to reach a score of at least an “A”, which is 90. Each correct bonus question adds 3 points to his exam score of 75. We need to find the number of questions, x, Hamilton must answer correctly to achieve a total score of 90 or more. Therefore, the inequality that encompasses this scenario is 3x + 75 ≥ 90 because each correct answer contributes 3 points towards closing the 15-point gap between his current score and the desired score of 90.
However, the options given do not include the correct representation which would be 3x + 75 ≥ 90. Instead, the closest option is C. 3x + 75 > 90, which would imply that Hamilton must score more than 90, which is not a requirement for making an “A” (as “A” can include exactly 90).
An investment of $450 increases at a rate of 6.5% per year. What is the growth factor, b?
O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale.
Assuming that lines that appear to be tangent are tangent, what is the value of x?
The square root of 136 is between which two whole numbers?
A carpenter earns $18 an hour for a regular work week (40) hours. He earns time and a half for overtime. The weekly wage function is W(h)={ 18h 040} where h is the number of hours worked for the week. Find the wage if the carpenter worked 42.5 hours in the week
Final answer:
To find the carpenter's weekly wage after working 42.5 hours, we calculate the regular pay for 40 hours at $18 per hour, which is $720, and then add the earnings from 2.5 hours of overtime at time and a half ($27 per hour), which is $67.5. The total weekly wage is $787.5.
Explanation:
To calculate the weekly wage of the carpenter who worked 42.5 hours, with $18 per hour for the first 40 hours and time and a half for overtime, we will use the wage function provided: W(h) = 18h for hours up to 40, and for hours above 40, it's (18 × 1.5) × (h - 40). Let's apply this to the 42.5 hours worked.
The carpenter's earnings for the regular 40 hours are $720 (which is 40 hours × $18). For the 2.5 hours of overtime, he earns time and a half, which is $27 per hour (18 × 1.5). The overtime earnings are $67.5 (2.5 hours × $27). So, the total wage is:
$720 + $67.5 = $787.5
Therefore, the carpenter's weekly wage for working 42.5 hours at the given rate is $787.5.
If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
Answer:
15
Step-by-step explanation:
x =ky
48 = k16
divide by 16
k = 3
plug k into x=ky
x=3*5
x=15
Sophia and Tyler are running around a 400-meter track. They start running from the same place, at the same time. Sophia runs at a speed of 5 m/s and Tyler runs at a speed of 4 m/s. How long will it take Sophia to lap Tyler?
Answer: 400 seconds
Step-by-step explanation:
5x = 400 + y
4x = y
take 4x and add it to the top so it looks like this:
5x = 400 + 4x
cancel 4x if you don't know how to do it you do it like this you take +4x and instead you do -4x to cancel.
and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400
x = 400
From a point on a circle, two perpendicular chords are drawn. One is 6 cm from the center and the other one is 3 cm from the center. Find the lengths of these chords.
Find the slope of the line on the graph
Simplify the trigonometric expression.
Quadrilateral ABCD has the following vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6). Quadrilateral ABCD is a
A. trapezoid
B. parallelogram
C. square
D. rectangle
the answer is TRAPEZOID
Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?
I understand the steps where I am stuck is how did you get 2/3/
The function f(x) = 12x + 50 gives the amount of money a worker earns for working x hours per week. What is the inverse function?
A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?
Need this geometry answer quick!
PLEASE HELP AS SOON AS POSSIBLE!!!!!!!!!!!!!!!!!! |r+3| ≥7 solve the inequality (please show work and steps )
The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area?