The value of x from the given figure is 7.
From the given figure, the measure of two angles are given 118° and (8x+6)°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Here,
(8x+6)°=m∠4 (Interior alternate angles are congruent)
⇒ 118°+m∠4=180° (Adjacent angles adds up to 180°)
⇒ m∠4=180°-118°
⇒ m∠4=62°
Thus, (8x+6)°=62°
⇒ 8x=62-6
⇒ 8x=56
⇒ x=7
Therefore, the value of x from the given figure is 7.
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If you know 2 sides of a right triangle what method can you use to find the third side?
Answer:
Pythagorean theorem
Step-by-step explanation:
You can use the Pythagorean theorem to find the third side of a triangle.
A^2 + B^2 = C^2.
An arithmetic sequence has a 2nd term equal to 3 and 10th term equal to -13.
Find the term of the sequence that has value -93?
Answer:
n = 50
Step-by-step explanation:
Let a be the first term and d be the common difference.
An arithmetic sequence has a 2nd term equal to 3 and 10th term equal to -13.
\(a_n=a+(n-1)d\)
According to the given condition,
\(a_2=3\\\\a_{10}=-13\)
or
\(a+(2-1)d=3\\\\a+d=3\ ...(1)\\\\a+(10-1)d=-13\\\\a+9d=-13\ ...(2)\)
Subtract equation (1) from (2).
a+9d-(a+d) = -13-3
8d = -16
d = -2
Put the value of d in equation (1).
a+(-2) = 3
a = 3+2
a = 5
Now,
\(a+(n-1)d = -93\\\\5+(n-1)(-2)=-93\\\\5-2n+2=-93\\\\7+93=2n\\\\2n=100\\\\n=50\)
So, 50th term has the value of -93.
find the length of the circumference of the circles under the following condition, take pie =3.14
pls show me explanation question no 1,
radius =20 cm
Answer:
The answer is 125.66 cmStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius
From the question
r = 20 cm
We have
C = 2(20)π
= 40π
= 125.663706143592...
We have the final answer as
125.66 cmHope this helps you
the composite method for determining the location of the center of gravity of a composite body requires . a) integration b) differentiation c) simple arithmetic d) all of the above
The composite method for determining the location of the center of gravity of a composite body requires integration.
So, the answer is A.
What is the center of gravity?The center of gravity is the point at which the entire weight of a body appears to act when the body is in equilibrium.
The concept of a center of gravity is used to calculate the behavior of a body when subjected to external forces. The composite method for determining the location of the center of gravity of a composite body involves integration.
The center of gravity is found by dividing the sum of the products of individual masses with their corresponding distance from an arbitrary reference line by the total mass of the system. When there is more than one weight distribution involved, the composite method is employed.
Hence, the answer of the question is A.
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Does nobody understand this? I really really really really need help Here!
Using translations, it is found that:
12. The representations are:
Coordinate: (x,y) -> (x + 4, y + 3).Vector: (4,3).13. The representations are:
Coordinate: (x,y) -> (x + 1, y - 7).Vector: (1, -7).14. The coordinates are K(-5,0).
15. The coordinates are P(9,0).
What is a translation?A translation is when the graph of a function is moved either left, right, up or down.
The function keeps it congruence, orientation and inclination, the only change is in the position.
For item 12, we have that each vertex was moved:
4 units right.3 units up.Hence the coordinate rule is:
(x,y) -> (x + 4, y + 3).
The vector rule is:
(4,3).
For item 13, we have that each vertex was moved:
1 unit right.7 units down.Hence the coordinate rule is:
(x,y) -> (x + 1, y - 7).
The vector rule is:
(1,-7).
For item 14, the rule is:
(x,y) -> (x - 3, y + 6).
After the translation, we have that K'(-8,6). Hence, applying the inverse translation, the original coordinates are as follows:
K(-8 + 3, 6 - 6) = K(-5,0).
For item 15, the rule is:
(x,y) -> (x - 8, y). -> due to the vector rule
After the translation, we have that P'(1,-2). Hence, applying the inverse translation, the original coordinates are as follows:
P(1 + 8, -2 + 0) = P(9,0).
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Determine the area, in square units, of the triangle below. Round your answer to one decimal place.
1.53
26°
1.22
Answer:
Area =0.41 units^2
Step-by-step explanation:
sin 26 degrees=height/1.53
height=.438371 x 1.53=0.67
Area =(1/2)(0.67)(1.22)=0.41 units^2
Suppose you qualify for a credit card with a limit of $1500, with an annual interest rate of 19.99%. Let’s pretend that you maxed out the credit card, and your minimum required monthly payment is $50 per month. How long would it take you to pay the card off only paying the minimum?
a 30 months
b 41.92 months
c 35.99 months
Let's say you are approved for a credit card with a $1500 limit and a 19.99% annual interest rate. Assume that your credit card was maxed out and that your minimum monthly payment is $50. The answer is (b) 41.92 months.
To calculate the time it takes to pay off a credit card with only the minimum payment, we can use the following formula:
\(\begin{equation}Number\ of\ months = \frac{Total\ balance}{Minimum\ payment} \div \frac{1 - (1 + Interest\ rate)^{-(Number\ of\ months)}}{1}\end{equation}\)
In this case, the total balance is $1500, the minimum payment is $50, and the interest rate is 19.99%. Plugging these values into the formula, we get:
\(\begin{equation}Number\ of\ months = \frac{1500}{50} \div \frac{1 - (1 + 0.1999)^{-(Number\ of\ months)}}{1}\end{equation}\)
Solving for the number of months, we get:
Number of months = 41.92 months
Therefore, it would take 41.92 months to pay off the credit card with only the minimum payment.
If you only make the minimum payment, you will pay a lot of interest over time. In this example, you will pay $1278.98 in interest. If you can afford to pay more than the minimum payment, you will save money on interest and pay off your debt faster.
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how do you calculate the circumference and area of a circle?
Answer:
The circumference of a circle can be calculated using two formulas: C = 2πr or C = πd, where π is a mathematical constant roughly equal to 3.14, r is equal to the radius, and d is equal to the diameter.
The area of a circle can be determined using either the diameter or the radius using two alternative formulas: A = πr^2 or A = π(d/2)^2, where π is a mathematical constant roughly equal to 3.14, r is the radius, and d is the diameter.
Step-by-step explanation:
Hi, I need help, am struggling with this. Question is in image below.
Answer:
I believe that would be -24/16, -√2, 21/51, and then 0.42
Step-by-step explanation:
This is according to math app
Select the values of x that make the inequality true: choose three
Answer:
C,D,B
Step-by-step explanation:
Four integers are consecutive terms of an arithmetic sequence. The sum of these four numbers is 24 and the product is 945.Find the largest of these four integers.
When common difference, \(d=\sqrt{39}\) then the largest term of these four terms will be \(6+3\sqrt{39}\)
Let four consecutive terms of AP is,
\(a-3d, a-d, a+d, a+3d\)
Since, sum of all four terms is 24
So, \(a-3d+a-d+a+d+a+3d=24\\\\a=6\)
And product is 945
So, \((a-3d)(a+3d)(a-d)(a+d)=945\\\\9d^4-360d^2+351=0\\\\d^4-40d^2+39=0\\\\(d^2-1)(d^2-39)=0\\\\d=1,-1\\d=\sqrt{39}, -\sqrt{39}\)
When d= 1, -1 then largest term is 9
When \(d=\sqrt{39}, -\sqrt{39}\) then largest term is \(6+3\sqrt{39}\)
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Simply
7p2 x 3p
14p4
Answer:
\({ \tt{ = \frac{7 {p}^{2} \times 3p}{14 {p}^{4} } }} \\ = { \tt{ \frac{21 {p}^{3} }{14 {p}^{4} } }} \\ = { \tt{1.5 {p}^{ - 1} }}\)
Question 10 solve for me please
Answer: D.
Step-by-step explanation:
x + 3 > 2 Original equation
x > -1 Subtract 3 on both sides
Number line that has an open circle and on -1 that goes right = D.
Find an equation for the line tangent to the graph of the given function at the indicated point. 8 3) f(x): () = at at (4,2) X 1 4) f(x)=x2-x at (4, 12)
(a) tangent line to the graph of f(x) = x^3 at the point (4,2).
(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).
(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.
(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.
In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.
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heeeeeeeellllllllllllpppppppppppppp
Write the function in slope-intercept form
4y=-8x-10
WILL MARK BRAINLIEST
Answer:
Y=2x- 5
-----
2
Step-by-step explanation:
Image transcription text1. In January 2019, you started a study to identify risk factors for developing coronary heart
disease (CHD). You enrolled 2,000 men and women living in the greater Boston area. Each
month, you assessed whether they were diagnosed with CHD. At the start of your study on
January 1, 2019 you screened all members of the cohort and found that 119 had a history of
CHD. On April 31", 20 additional individuals were diagnosed with CHD. On May 31%, 12
of the participants who had CHD on January 1 died from complications of their disease. On
June 31", 25 people free of CHD moved out of the Boston area and withdrew from the study.
On August 31", 5 more individuals were diagnosed with CHD. On November 1*, 20
individuals who had moved to Boston joined the study. Of these 20 new participants, 2
already had CHD when they enrolled in the study. On December 1, an additional 10 healthy
members of the cohort moved away and were lost to follow-up. The study ended on
December 31, 2019. Assume that once a person has CHD, he or she has it for the remainder
of the study. When answering the questions below, be sure to include the relevant units, as
appropriate.
a. What was the prevalence of CHD on January 1, 2019?
b. What was the prevalence of CHD on October 15, 2019?
C.
What was the 4-month cumulative incidence of CHD from January 1, 2019 to April 31,
20197
d. What was the incidence rate of CHD during the entire year?
2. Given a population with a stable age distribution over time, how can you explain that the
prevalence of a disease may increase while the incidence rate of the disease decreases?... Show moreImage transcription text3. Assuming a constant incidence rate, the exact relationship between t-year cumulative
incidence (CQ) and incidence rate (1) is given by C = 1 - e . A reasonably good
approximation, under certain circumstances, is: C = 1 * t.
a. For each of the incidence rates in the table below, (A) calculate the rates in units
of# events per 1 person-year. Then, for time intervals (B) t=1 and (C) t=10 years,
calculate the cumulative incidence that would be expected given these rates, using
the exact formula and the approximate formula. HINT: This will be much more
efficient if the calculations are performed in a spreadsheet or other software.
Incidence
Incidence
Ist
I*t
Cumulative Incidence
Cumulative Incidence
rate
rate
when
when
(C)
(CD)
(#events/
(#events/
t=1 year
t=10
G=It
1000 P-Y)
1 P-Y)
year
(approximation)
(A)
t=1 year
t=10 year
t=1 year
t=10 year
(B)
(B)
+
5
125
50
75
100
125
150
200
+
b. Under what circumstances would you feel comfortable using the approximation?... Show moreBrief and precise answer for all required in words will do like immediately.Thanks
1. CHD prevalence: Jan 1, 2019 - 5.95%, Oct 15, 2019 - 6.8%. Cumulative incidence: Jan to Apr 2019 - 1%. Incidence rate for the year: 2.25%.
2. Prevalence is current cases, incidence rate is new cases over time. Stable age distribution with decreasing incidence increases prevalence. Population size affects prevalence, not incidence.
3. Cumulative incidence using exact and approximate formulas. Approximation accurate for low rates, less for high rates. Good for rates ≤ 100 per 1000 person-years.
1.
a. The prevalence of CHD on January 1, 2019 was 119/2000 = 0.0595 = 5.95%
b. The prevalence of CHD on October 15, 2019 was 136/2000 = 0.068 = 6.8%
c. The 4-month cumulative incidence of CHD from January 1, 2019 to April 31, 2019 was 20/2000 = 0.01 = 1%
d. The incidence rate of CHD during the entire year was (20 + 5) / 2000 = 0.0225 = 2.25%
2.
The prevalence of a disease is the number of people who have the disease at a given point in time. The incidence rate of a disease is the number of new cases of the disease that occur in a given population over a specific period of time.
A population with a stable age distribution over time means that the proportion of people in each age group stays the same. This means that the number of people who are at risk of developing a disease also stays the same.
If the incidence rate of a disease decreases, but the population size remains the same, then the prevalence of the disease will increase. This is because there are fewer new cases of the disease occurring, but the same number of people are at risk of developing the disease.
For example, if a population has 100,000 people and the incidence rate of a disease is 1%, then there will be 1,000 new cases of the disease in a year. If the incidence rate decreases to 0.5%, then there will only be 500 new cases of the disease in a year. However, the prevalence of the disease will still be 1%, because the population size has not changed.
3.
a. The table below shows the calculated cumulative incidence for each of the incidence rates, using both the exact formula and the approximate formula.
Incidence Rate Exact Formula Approximate Formula
5 per 1000 person-years 0.0500 0.0500
12.5 per 1000 person-years 0.1250 0.1250
75 per 1000 person-years 0.7500 0.7500
100 per 1000 person-years 1.0000 1.0000
125 per 1000 person-years 1.2500 1.2500
150 per 1000 person-years 1.5000 1.5000
200 per 1000 person-years 2.0000 2.0000
b. The approximate formula is a good approximation of the exact formula when the incidence rate is relatively low. For example, when the incidence rate is 5 per 1000 person-years, the approximate formula is within 0.01% of the exact formula. However, the approximate formula becomes less accurate as the incidence rate increases. For example, when the incidence rate is 200 per 1000 person-years, the approximate formula is about 10% greater than the exact formula.
In general, the approximate formula is a good approximation of the exact formula when the incidence rate is less than or equal to 100 per 1000 person-years.
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Right answer please.
Answer:
\(32 + 8 \sqrt{10} \)
Step-by-step explanation:
Segment XM= 24
d=
\( \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } \)
\(d = \sqrt{(24 - 0) ^{2} + ( - 3 + ( - 3)) {2}^{?} } \)
\(d = \sqrt{24 ^{2} + 0 ^{2} } \)
\(d = 24\)
Segment XK=8
\(d = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } \)
\(d = \sqrt{(0 - 0) ^{2} + (5 - ( - 3))^{2} } \)
\(d = \sqrt{(0 )^{2} + 8^{2} } \)
\(d = \sqrt{64} \)
\(d = 8\)
Segment KM=
\(d = \sqrt{ {(0 - 24)}^{2} + {(5 - ( - 3))}^{2} } \)
\(d = \sqrt{ { - 24}^{2} + {8}^{2} } \)
\(d = \sqrt{576 + 64} \)
\(d = \sqrt{640} \)
\(d = 8 \sqrt{10} \)
Perimeter = the length of all 3 segments.
\(p = 8 + 24 + 8 \sqrt{10} \)
\(p = 32 + 8 \sqrt{10} \)
4 1/2 plus 1 3/5 equal
Answer:
6 1/10
Step-by-step explanation:
Complete the table.
starting elevation
(feet) change
(feet) final elevation
(feet)
A +200 75 up
B +200 75 down
C +200 200 down
D +200 +25
Write an addition equation and draw a number line diagram for B. Include the starting elevation, change, and final elevation in your diagram.
Answer:
Step-by-step explanation:
Starting elevation of B = +200 feet
Change in elevation for B = 75 feet down
Final elevation of B = +200 - 75 = +125 feet
The addition equation for B can be written as:
Starting elevation + Change = Final elevation
+200 - 75 = +125
The number line diagram for B is as follows:
+------------------------+------------------------+------------------------+
A B C D
+200 +125 +225
<----- 75 ft ----->
(change in elevation)
Brainliest if correct
Answer:
−10x^2−10x+3
Step-by-step explanation:
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 445 gram setting it is beleved that the machine is underfilling the bags. A34 bag sample had a mean of 438 grams. Assume the population variance is known to be 576 . A level of significance of 0.05 will be used.
The null hypothesis for this problem is given as follows:
\(H_0: \mu = 445\)
The alternative hypothesis for this problem is given as follows:
\(H_1: \mu < 445\)
How to identify the null and the alternative hypothesis?The claim for this problem is given as follows:
"It is believed that the machine is underfilling the bags".
At the null hypothesis we test if there is no evidence that the bags are being under filled, that is, no evidence that the mean is less than 445 grams, hence:
\(H_0: \mu = 445\)
At the alternative hypothesis, we test if there is enough evidence that the mean is less than 445 grams, hence:
\(H_1: \mu < 445\)
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There are 12 marbles in a bag. There are 4 blue, 5 red, 1 green, and 2 black.
12 Marbles totall
What is the probability of a red or a green from the bag?
이
5
12
12
Answer:
1/2
Step-by-step explanation:
There are 6 marbles that are either red or green out of 12 total marbles, so you have:
6/12 = 1/2
Answer:
1/2
Step-by-step explanation:
To find the probability, you need to put the number of what you want to know the probability of over the total. In this case, we want to know what the probability of red and green over the total is. So, hence the equation:
\(\frac{5+1}{12}\) or \(\frac{6}{12}\) which can be simplified to \(\frac{1}{2}\).
In a scale drawing of a painting, 2 centimeters represent 9 inches.
The height of the real painting is 26 inches. What is the height of the painting in the scale drawing? If necessary, round your answer to the nearest tenth.
Type your numerical answer (without units) below.
The height of the painting in the scale drawing is approximately 5.8 centimeters (rounded to the nearest tenth).
To find the height of the painting in the scale drawing, we can set up a proportion using the given scale.
Given:
Scale: 2 centimeters represent 9 inches
Real height of the painting: 26 inches
Height in the scale drawing: ?
Let's set up the proportion:
2 centimeters / 9 inches = x centimeters / 26 inches
To solve for x (the height in the scale drawing), we can cross-multiply and then divide:
2 centimeters * 26 inches = 9 inches * x centimeters
52 centimeters = 9x
Dividing both sides by 9:
x = 52 centimeters / 9
x ≈ 5.8 centimeters
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Use the figure to write and solve an equation for x.
a) x and y are two numbers taken from the list below.
5
6
7
8
9
10
(i) What values of x and y will make 3x - 2y equal zero?
(ii) Work out the greatest possible value of 3x - 2y.
(iii) Work out the least possible value of 3x – 2y.
b) Find the value of 5(a – 4b) when a = -7 and b = 1
Answer:
a) i) The equation is satisfies of the values x = 6 and y=9
ii) The greatest possible value of 3x-2y is 20
iii) The least possible value of 3x – 2y is 2 and '0'
b)
The value of 5(a – 4b) = -55
Step-by-step explanation:
Given x and y are two numbers taken from the list below
5 6 7 8 9 10
i)
I will choose x = 6 and y = 9
3x - 2y = 3 (6) - 2(9) = 18 - 18 = 0
The equation is satisfies of the values x = 6 and y=9
ii)
we will choose x =10 and y = 5
3x - 2y = 3(10) - 2(5) = 30 -10 =20
The greatest possible value = 20
iii)
we will choose x =6 and y =8
3x - 2y = 3(6) -2(8) = 18-16 =2
we will choose x =6 and y =9
3x - 2y = 3 (6) - 2(9) = 18 - 18 = 0
b)
Given value of 5(a – 4b)
substitute a = -7 and b = 1
5(a – 4b) = 5(-7-4(1)) = 5 (-11) = -55
Use the Distributive Property to expand the expression 3(3x + 6). Then simplify the expression.
Answer:
After expansion and simplifying the expression gives;
\(9x+18\)Explanation:
Given the expression;
\(3(3x+6)\)Expanding using Distributive Property;
\(\begin{gathered} 3(3x+6) \\ 3(3x)+3(6) \end{gathered}\)simplifying;
\(9x+18\)Therefore after expansion and simplifying the expression gives;
\(9x+18\)Find the value of x so that the function has the given value.
t(x)=-4x-5
t(x)=3
Answer:
x = 8 since 3 × 8 = 24
can you guys help me!!!
I cant see the question, id help if i could
state if each pair of ratios forms a proportion 4/3 and 8/6 yes or no??
We have: \(\frac{4}{3}=\frac{4.2}{3.2}= \frac{8}{6}\)
Answer: Yes
Ok done. Thank to me :>