Answer:
D. 130
Step-by-step explanation:
The lines are tangent to the circle therefore 90º which makes 65º + 25º. The small triangle with C is iso so the angle of C would be 130 and equivalent to x
Answer:
[tex]D.\ \ 130[/tex]
Step-by-step explanation:
1. Approach
Refer to the attached diagram of the figure for further explanation. In this problem, one is asked to solve for the degree measure of arc (x). The easiest method to do so is to use the triangle (CAB). One can solve for the measure of angle (<CBA) by using the tangent to radius theorem. Then one can solve for the measure of angle (CAB) by using the base angles theorem. Then one can use the sum of angles in a triangle theorem to solve for angle (<BCA). Finally, one can use the central angles theorem to solve for the arc (x).
2. Find the measure of angles in the triangle
A. Find the measure of angle (<CBE)
As per the given image, lines (BE) and (AE) are tangent. This means that they intersect the circle at exactly one point. A radius is the distance from the center of a circle to the circumference or outer edge of a circle. All radii in a single circle are congruent. The radius of tangent theorem states that, when a tangent intersects a circle at a point of tangency, and a radius also intersects the point of tangency, the angle between the radius and the tangent is a right angle. One can apply this here by stating the following:
[tex]m<CBE = 90[/tex]
Express angle (<CBE) as the sum of two other angles:
[tex]m<CBE = m<CBA + m<ABE[/tex]
Substitute with the given and found information:
[tex]m<CBE = m<CBA + m<ABE[/tex]
[tex]90 = m<CBA + 65[/tex]
Inverse operations,
[tex]90 = m<CBA + 65[/tex]
[tex]25= m<CBA[/tex]
B. FInd the measure of angle (<CAB)
As stated above all radii in a single circle are congruent. This means that lines (CB) and (CA) are equal. Therefore, the triangle (CAB) is an isosceles triangle. One property of an isosceles triangle is the base angles theorem, this theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. Applying this theorem to the given problem, one can state the following:
[tex]m<CBA = m<CAB = 25[/tex]
C. Find the measure of angle (<ACB)
The sum of angles in any triangle is (180) degrees. One can apply this theorem here to the given triangle by adding up all of the angles and setting the result equal to (180) degrees. This is shown in the following equation:
[tex]m<CAB + m<CBA + m<ACB = 180[/tex]
Substitute,
[tex]m<CAB + m<CBA + m<ACB = 180[/tex]
[tex]25 + 25 + m<ACB = 180[/tex]
Simplify,
[tex]25 + 25 + m<ACB = 180[/tex]
[tex]50 + m<ACB = 180[/tex]
Inverse operations,
[tex]50 + m<ACB = 180[/tex]
[tex]m<ACB = 130[/tex]
3. Find the measure of arc (x)
The central angles theorem states that when an angle has its vertex on the center of the circle, its angle measure is equivalent to the measure of the surrounding arc. Thus, one apply this theorem here by stating the following:
[tex]m<ACB = (x)\\130 = x[/tex]
The price of a certain item is P dollars. The sales tax on the item is 7%. Which expressions represent the total cost of the item, in dollars, after the tax has been applied? Select EACH correct anwser
0.07P 1.07P P+0.07P 1+0.07P (1+0.07)P
Step-by-step explanation:
P = $ Dollars
Item = 7%
Answer
item 7/100 = 0.07/1 item
(1+0.07) P
Initial amount problem help
Answer:
3000
growth
2.2%
Step-by-step explanation:
he following chart reports the number of cell phones sold at a big-box retail store for the last 26 days. a. What are the maximum and the minimum numbers of cell phones sold in a day? b. Using the median, what is the typical number of cell phones sold?
Answer:
Maximum = 19
Minimum = 4
Median = 12
Step-by-step explanation:
The maximum number of phone sold per day is the value to the right of the horizontal axis as the values are arranged in ascending order ; Hence, the maximum number of phones sold per day is 19
Also, the minimum number of phones sold per day is the value to the left of the plot, Hence, minimum number of phones sold per day is 14.
The Median value : 4, 9, 14, 19
The median = 1/2(n+1)th term
1/2(5)th term = 2.5 th term
Median (9 + 14) /2 = 13 /2 = 11.5 = 12 phones
Find the value of x rounded to the nearest tenth.
Simplify. (x+y)/(x^2y)-(x-2y)/(xy^2)
Answer:
[tex]{ \tt{ = \frac{(x + y)}{ {x}^{2}y } - \frac{(x - 2y)}{ {xy}^{2} } }} [/tex]
Find the LCM of denominators: x²y²
[tex]{ \tt{ = \frac{y(x + y) - x(x - 2y)}{ {x}^{2} {y}^{2} } }} \\ \\ = { \tt{ \frac{xy + {y}^{2} - {x}^{2} +2xy }{ {x}^{2} {y}^{2} } }}[/tex]
Simplify further:
[tex] = { \tt{ \frac{(y - x)(y + x) +3xy}{ {(xy)}^{2} } }} \\ \\ = { \tt{ \frac{(y - x)(y + x)}{ {(xy)}^{2} } - \frac{3}{xy} }}[/tex]
solve please 14a⁹b-8a³d÷ 2a³
Answer:
7a^6b-4d
Step-by-step explanation:
[tex]\frac{14a^9b - 8a^3d}{2a^3} \\\frac{2a^3(7a^6b - 4d)}{2a^3} \\\\7a^6b-4d[/tex]
The Tres Difficult race helps raise money for charity. According to the website, of the proceeds from ticket sales go directly to charity.
2/5
Last year they made $8000 from ticket sales. How much was given to charity?
Answer:
3200
Step-by-step explanation:
We need to find 2/5 of the tickets sales
2/5 * 8000
3200
Answer:
3200
Step-by-step explanation:
you need to find what 2/5 is and the you take that away from 8000 and then you have your answer of 3200
equation for perpendicular to the line -7x + 3y = -10j contains the point (-2,-4)
Answer:
y = 7/3x + 2/3
Step-by-step explanation:
-7x + 3y = -10
3y = 7x - 10
y = 7/3x - 10/3
-4 = 7/3(-2) + b
-4 = -14/3 + b
2/3 = b
Estimate the square root between two consecutive whole numbers of sqrt [55]
9514 1404 393
Answer:
7.4 . . . . between 7 and 8
Step-by-step explanation:
55 is between the perfect squares 49 = 7² and 64 = 8². Using linear interpolation, the square root is approximately 7 +(55-49)/(64-49) = 7 6/15 = 7.4
√55 ≈ 7.4 . . . . approximate root by linear interpolation
_____
Additional comment
A way to improve the estimate of the root is to use the "Babylonian method" of iterating the root. Divide the original number (55) by the estimate of the root, and average that result with the estimate:
next best guess = (55/7.4 +7.4)/2 = 7 77/185 ≈ 7.4162_162(repeating)
This matches the actual root when rounded to 4 decimal places. The number of accurate decimal places approximately doubles with each iteration.
__
Another way to improve the estimate is to modify the fractional portion. (The above method converges on a root more quickly.) For this, the iteration of the fractional part of the root is ...
next fractional part = 6/(14 +(fractional part))
where 6/14 is the linear estimate fractional value with 1 subtracted from its denominator.
For one iteration, the new estimate of the fractional part is 6/(14 +6/15) = 5/12, so the root estimate is about 7.4167 compared to the above 7.4162.
During spring, young moose, unfamiliar with roads and traffic, are wandering around at night in a province, causing risk and road accidents. Suppose that the average number of road accidents involving moose was per day. The government increased the number of hunting licenses and cleared brush to improve drivers' visibility. On one day after these measures were implemented, there were road accidents involving moose.
Required:
a. What would be the chance of such accidents or fewer, assuming the government's measures were ineffective?
b. Do you think the government's measures were effective? State your reasons clearly.
Aiden is a spice trader. He sells any amount of cumin seeds from 1 kilogram to 1000 kilograms. He charges $5 for 1 kilogram and $2000 for 1000 kilograms.
p(w) models the price (in dollars) of w kilograms of cumin seeds in Aiden's shop.
Which number is more appropriate for the domain of p?
Choose 1 answer:
A. Integers
B. Real Numbers
What's the appropriate domain?
Choose 1 answer:
A. 5 ≤ w ≤ 1000
B. 5 ≤ w ≤ 2000
C. 1 ≤ w ≤ 1000
D. 1 ≤ w ≤ 2000
Answer:
A and B
Step-by-step explanation:
Domain of P should be Integers and it should vary from 1 to 2000
The number is more appropriate for the domain of 'p' is real numbers.
The appropriate domain can be represented as (1 ≤ w ≤ 1000).
What is the domain of a function?"The domain of a function is the set of inputs accepted by the function."
Given, Aiden sells any amount of cumin seeds from 1 kilogram to 1000 kilograms.
He charges $5 for 1 kilogram and $2000 for 1000 kilograms.
w = the weight of the cumin seeds
Therefore, it can be represented as (1 ≤ w ≤ 1000).
p(w) = the price of w kg cumin seeds.
It can be represented as (5 ≤ p(w) ≤ 2000).
This domain is of real numbers.
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pls help i’m dying i don’t know how to do this
Answer:
the answer that I got is 1
Answer: hi "1" is right, i checked it again ;)
Consider the probability that no more than 76 out of 504 computers will crash in a day. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 75.5
b. Area to the right of 76.5
c. Area to the left of 75.5
d. Area to the left of 76.5
e. Area between 75.5 and 76.5
Answer:
e
Step-by-step explanation:
(A) Over 1000 students organized to celebrate running water and electricity. To count the exact number of students protesting, the chief organizer lined the students up in columns of different length. If the students are arranged in columns of 3, 5, and 7, then 2, 3, and 4 people are left out, respectively. What is the minimum number of students present? Solve it with Chinese Remainder Theorem. (B) Prove that for n> 1, if 935 = 5 x 11 x 17 divides n80 – 1, then 5, 11, and 17 do not divide n.
Solution :
A). x = 2 (mod 3) [tex]$\mu = 3\times 5 \times 7 = 105$[/tex]
x = 3 (mod 5) [tex]$y_1=35^{-1} (\mod 3)$[/tex]
x = 4 (mod 7) [tex]y_1=2[/tex]
[tex]$y_2=21^{-1}(\mod5) = 1$[/tex]
[tex]$y_3=15^{-1}(\mod7) = 1$[/tex]
[tex]$x=2 \times 35 \times 2 + 3\times 21\times 1+4\times 15\times 1$[/tex]
[tex]=140+63+60[/tex]
[tex]=263[/tex]
≡ 53(mod 105)
Hence the solution is 105 k + 53 > 1000 for k = 10
Therefore, the minimum number of students = 1103
B). [tex]$\phi (935) = 640$[/tex]
By Eulu's theory
[tex]$935 | a^{640}_n -1$[/tex] if n and 935 are coprime.
Now, [tex]$935|n^{80}-1$[/tex] and 80 x 8 = 640
[tex]$935|n^{640}-1$[/tex] ⇒ g(n,935) = 1
⇒ 5, 11, 17 do not divide n
If you apply the changes below to the cube root parent function, F(x) = 3/x
what is the equation of the new function?
• Translate 1 unit right.
• Translate 1 unit up.
A. G(x) = 3/x-1+1
B. G(x) = 3/x +1-1
C. G(x) =3/ x - 1-1
D. G(x) = 3/x+1+1
9514 1404 393
Answer:
A. G(x) = ∛(x -1) +1
Step-by-step explanation:
The transformation f(x-h) +k represents a translation (right, up) by (h, k) of the parent function f(x).
Your translation of f(x) = ∛x by (1, 1) will give you the function ...
G(x) = ∛(x -1) +1
Drag each tile to the correct box.
Match each equation with its solution.
n =
= -1
n = -25
n = 1
Equation
Solution
12 + 15 = -10
>
-511 = 1
- 13 = -12
Answer:
n = 1
n = - 1
n = - 1/5
n = - 25
Step-by-step explanation:
We are to obtain the value if n in the given equations :
1.)
n - 13 = - 12
To find, n ;
Add 13 to both sides
n - 13 + 13 = - 12 + 13
n = 1
2.)
n/5 = - 1/5
Multiply both sides by 5
n/5 * 5 = - 1/5 * 5
n = - 1
3.)
-5n = 1
Divide both sides by - 5
-5n/-5 = 1/-5
n = - 1/5
4.)
n + 15 = - 10
Subtract 15 from both sides :
n + 15 - 15 = - 10 - 15
n = - 25
A researcher wants to know if calcium is an effective treatment for lowering blood pressure. He assigns one randomly chosen group of volunteers to take calcium supplements; the other group will get placebo. At the end of the treatment period, he measures the difference in blood pressure. The 50 members of the calcium group had blood pressure lowered by an average of 25 points with a standard deviation of 10 points. The 50 members of the placebo group had blood pressure lowered by an average of 15 points with a standard deviation of 8 points. To analyze this information we will use a
Answer:
Two sample t procedure
Step-by-step explanation:
The two sample t test is used when want to test for equality between two population means. It tests whether the means of the two groups are equal or not equal.
We use this to analyse this information in this question because we do not have data available for the population standard deviation. Also we are to test for the significant difference between the two different groups of participants
dp/dt = t²p − p + t2 − 1.
dp/dt = t ² p - p + t ² - 1
Factorize the right side:
dp/dt = p (t ² - 1) + (t ² - 1)
dp/dt = (p + 1) (t ² - 1)
So the differential equation is separable as
dp/(p + 1) = (t ² - 1) dt
Integrate both sides:
∫ dp/(p + 1) = ∫ (t ² - 1) dt
ln|p + 1| = t ³/3 - t + C
Solve for p :
p + 1 = exp(t ³/3 - t + C )
p + 1 = C exp(t ³/3 - t )
p = C exp(t ³/3 - t ) - 1
PLEASE HELP with proving lines parallel
HELP PLEASE, Function problem
Answer:
-2
-1
-2
Step-by-step explanation:
please forgive me, but again, this is the simplest of the simplest things. how is that a problem ?
this costs so much more time to just put it in here and then copy answers than just doing it. this is literally a matter of seconds.
the functional value is -2 for all x that are not equal to 2.
and the functional value is -1, when x = 2
so, what is the problem ?
please see my other answer for more details on the solution.
please help me!!!!!!!!!!!!
Step-by-step explanation:
24. = 249030/30
=8,301 rs
Answer:
24. 8301, divide 249030 by 30
25. 9989001, but i dont know the property
Step-by-step explanation:
Find the intercepts of the function y = 3x + 9
Step-by-step explanation:
To solve for the x-intercept, set y=0 then solve for x.
y=−3x−9. 0=−3x−9. 3x=−9.
x=−3 when y=0.
To solve for the y-intercept, set x=0 then solve for y.
y=−3x−9. y=−3(0)−9. y=−9 when x=0.
Hi there!
Y-intercept:
Set the x value to 0:
y = 3(0) + 9
y = 9 --> (0, 9)
X-intercept:
Set the y value to 0:
0 = 3x + 9
Solve for x:
-9 = 3x
x = -3 --> (-3, 0)
given a∥b and c∥d, m<4=35. find m<1, m<2, and m<3
its the rsm problem lesson 6 homework geometry
Answer:
<2 = 35degrees
<3 = 55degrees
Step-by-step explanation:
Find the diagram attached:
From the diagram:
<3 + <4 = 90
<3 + 35 = 90
<3 = 90 - 35
<3 = 55degrees
Also m<1 + m<2+ m<3 = 180 (sum of angles in a traingle)
90+<2+55=180
145+<2 = 180
<2 = 180 - 145
<2 = 35degrees
An ecologist finds 220 yellow-flowered plants and 180 white-flowered plants. Use the normal distribution to find the Lower boundary of a 95% confidence interval for the proportion of yellow-flowered plants. Which of the following answers is correct to 2 decimal places?
a. Lower boundary = 0.30
b. Lower boundary = 0.60
c. Lower boundary = 0.50
d. Lower boundary = 0.40
Answer:
c. Lower boundary = 0.50
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
An ecologist finds 220 yellow-flowered plants and 180 white-flowered plants.
220 out of 220 + 180 = 400. So
[tex]n = 400, \pi = \frac{220}{400} = 0.55[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.96\sqrt{\frac{0.55*0.45}{400}} = 0.5[/tex]
Thus the correct answer is given by option c.
2) If licorice cost $6.59 a pound, how much would it cost to buy a quarter pound of licoric
(Hint: Convert the mixed fraction to an improper fraction or decimal and multiply by th
quantity required)
Answer:
$1.65
Step-by-step explanation:
[tex]6.59*.25=1.65[/tex]or
[tex]6.59*\frac{1}{4} =1.65[/tex]Question
Elvira and Aletheia live 3.2 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira 1/2 hour and Aletheia 2/3 hour to walk to the coffee shop. Find both women's walking speeds.
Missing from the question
Aletheia's speed is 0.6 miles per hour slower than Elvira's speed.
Answer:
[tex]s_E = 3.0[/tex]
[tex]s_A = 2.4[/tex]
Step-by-step explanation:
Given
[tex]d = 3.2m[/tex] -- distance
[tex]t_E = 1/2[/tex] --- Elvira time
[tex]t_A = 2/3[/tex] --- Aletheia time
[tex]s_E - s_A = 0.6[/tex] --- the relationship between their speeds
Required
Their walking speed
Distance (d) is calculated as:
[tex]d = speed * time[/tex]
For Elvira, we have:
[tex]d_E = s_E * 1/2[/tex]
For Aletheia, we have:
[tex]d_A = s_A * 2/3[/tex]
So, we have:
[tex]d_E + d_A = d[/tex] --- total distance
This gives:
[tex]s_E * 1/2 + s_A * 2/3 = 3.2[/tex]
Recall that:
[tex]s_E - s_A = 0.6[/tex]
Make sE the subject
[tex]s_E = 0.6+s_A[/tex]
Substitute [tex]s_E = 0.6+s_A[/tex] in [tex]s_E * 1/2 + s_A * 2/3 = 3.2[/tex]
[tex](0.6+s_A)* 1/2 + s_A * 2/3 = 3.2[/tex]
[tex]0.3+1/2s_A + 2/3s_A = 3.2[/tex]
Collect like terms
[tex]1/2s_A + 2/3s_A = 3.2-0.3[/tex]
[tex]1/2s_A + 2/3s_A = 2.9[/tex]
Express all as decimal
[tex]0.5s_A + 0.7s_A= 2.9[/tex]
[tex]1.2s_A= 2.9[/tex]
Divide both sides by 1.2
[tex]s_A = 2.4[/tex]
Recall that:
[tex]s_E = 0.6+s_A[/tex]
So, we have:
[tex]s_E = 0.6+2.4[/tex]
[tex]s_E = 3.0[/tex]
Find the exact values of the six trigonometric functions at “a” given cos(2a) = - 4/5 and a is
in the 2nd quadrant.
If a is in the second quadrant, then cos(a) < 0 and sin(a) > 0.
Recall the double angle identity for cosine:
cos(2a) = 2 cos²(a) - 1 = 1 - 2 sin²(a)
It follows that
2 cos²(a) - 1 = -4/5 ==> cos²(a) = 1/10 ==> cos(a) = -1/√10
1 - 2 sin²(a) = -4/5 ==> sin²(a) = 9/10 ==> sin(a) = 3/√10
Then we find
1/cos(a) = sec(a) = -√10
1/sin(a) = csc(a) = √10/3
sin(a)/cos(a) = tan(a) = -3
1/tan(a) = cot(a) = -1/3
Which of the following is the vertical asymptote for the graph below?
Answer:
C
Step-by-step explanation:
Vertical asymptotes are always in the form x = ?
If you look at the dotted line, it lands on 2. Because it's a vertical line, the asymptote is going to be x = 2
The ratio of yes votes to no votes was 3 to 4. If there where 2721 yes votes how many no votes where there
Answer:
3628
Step-by-step explanation:
Ratio of yes votes:no votes = 3:4
Yes votes = 2721,
Now,
[tex]\frac{2721}{3} = 907[/tex]
so, [tex]907 * 4 = 3628[/tex]
So, there were 3628 no votes.
3628.
Step-by-step explanation:
The ratio of yes votes: to no votes = 3:4
Yes votes = 2721,
Now,
2721/3 = 907
So 907 × 4 = 3628.
So, there were 3628 no votes.
How do I calculate a ratio?
Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.
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Five friends each spent the same amount of money, x, on school supplies. They expected to spend a total of $130, but the actual
amount spent differed from the expected amount by $15.
Which equation represents the situation? What are the possible amounts that each friend spent?
O
13 - 130 = 15
The amount that each friend spent is $115 or $145.
O
151 - 130 = 15
The amount that each friend spent is $23 or $29.
O
151 + 15 = 130
The amount that each friend spent is $31 or $38.
O
(15.3 – 1300 = 5
The amount that each friend spent is $8 or $9.
Answer:
its the second option
Step-by-step explanation:
hope this helps
Answer: 5x-130=15
Step-by-step explanation:
edmentum
