The sum of the 3rd and 7th terms of an A.P. is 38, and the 9th term is 37. Find the A.P?
Let a be the first term in the arithmetic progression. Then each successive term differs from a by a fixed number c, so that
• first term = a
• second term = a + c
• third term = (a + c) + c = a + 2c
• fourth term = (a + 2c) + c = a + 3c
and so on. In general, the n-th term in the AP is a + (n - 1) c.
The sum of the 3rd and 7th terms is 38, so that
(a + 2c) + (a + 6c) = 38
==> 2a + 8c = 38
==> a + 4c = 19 … … … [1]
The 9th term is 37, so
a + 8c = 37 … … … [2]
Subtracting [1] from [2] eliminates a and lets you solve for c :
(a + 8c) - (a + 4c) = 37 - 19
4c = 18
c = 18/4 = 9/2
Solve for a using either equations [1] or [2] :
a + 8 (9/2) = 37
a + 36 = 37
a = 1
Then the n-th term in the AP is 1 + 9/2 (n - 1) or 9/2 n - 7/2, where n ≥ 1.
Which of the following is equivalent to the expression - 1/4-(2/5 + 3/7)?
Given:
The expression is:
[tex]-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)[/tex]
To find:
The expression that is equivalent to the given expression.
Solution:
We have,
[tex]-\dfrac{1}{4}-\left(\dfrac{2}{5}+\dfrac{3}{7}\right)[/tex]
Using the distributive property, we get
[tex]=-\dfrac{1}{4}-\dfrac{2}{5}-\dfrac{3}{7}[/tex]
Taking LCM, we get
[tex]=\dfrac{-35-56-60}{140}[/tex]
[tex]=\dfrac{-151}{140}[/tex]
Therefore, the expression [tex]-\dfrac{151}{140}[/tex] is equivalent to the given expression expression.
Note: There are more than one equivalent expressions.
PLEASE HELPPP!!!! WILL GIVE BRAINLIEST!!!!!!!!!!
I also need help anyone can help
The average time to serve a customer at a fast-food restaurant is 4.35 minutes. The standard deviation of the service time is 2.5 minutes. What is the coefficient of variation of the service time
Answer: 0.5747
Step-by-step explanation:
Given: Average time to serve a customer[tex](\mu)=4.35[/tex] minutes
standard deviation of the service time [tex](\sigma)=[/tex] 2.5 minutes
coefficient of variation = [tex]\frac{\sigma}{\mu}[/tex]
[tex]=\dfrac{2.5}{4.35}\\\\=\dfrac{250}{435}\\\\=0.5747[/tex]
Hence, the required coefficient of variation= 0.5747
What percentage is
£7 of £20?
28kg of 40kg?
plz answer both questions
[tex]\huge❥︎\underbrace\mathfrak\red {SoLuTiOn}✈︎[/tex]
1)
[tex] £7 \: of \: £20 \\ \\ \fbox{considering as x} \\ \\ x\%of \: 20 = 7 \\ \\ x\% = \frac{7}{20} \times 100 \\ \\ x\% = \frac{7}{ \cancel{20}} \times \cancel{ 100} \\ \\ x\% = 7 \times 5 \\ \\ x\% = 35\%[/tex]
2)
[tex]28 \: kg \: of \: 40 \: kg \\ \\ \fbox{considering as x} \\ \\ x\% 40 = 28 \\ \\ x\% = \frac{28}{40} \times 100 \\ \\ x\% = \cancel \frac{28}{4 \cancel0} \times 10 \cancel0 \\ \\ x\% = 7 \times 10 \\ \\ x\% = 70\%[/tex]
Hope This Helps You ❤️Find mBAF help ASAP.
Answer:
I think
c. 164
Step-by-step explanation:
m<BAC=m<FAE = 25
m< CAD=m< DAE= 57
m<BAF= 25+25+57+57=164
4 The equation of a curve is y= (3-20)^3 + 24.
(a) Find an expression for dy/dx.
g tau .......................
Look at the figure below: an image of a right triangle is shown with an angle labeled y degrees If sin y° = s divided by 8 and tan y° = s divided by t, what is the value of cos y°?
cos y° = 8s
cos y° = 8t
cos y°= t / 8
cos y°=8 / t
Answer:
Cos y = t / 8
Step-by-step explanation:
Using the hints given in the question, the omitted tribagke will look like the triangle attached on the picture ;
From trigonometry :
Sin y = opposite / hypotenus
Sin y = s / 8
Opposite side = s ; hypotenus = 8
Tan y = opposite / Adjacent
Tan y = s / t
Adjacent side = t
Then ;
Cos y = Adjacent / hypotenus
Hence,
Cos y = t / 8
Answer:
the answer is :
cos y°= t / 8
Step-by-step explanation:
I promise! I got this right, and.....you are welcome.
Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?
∠P
∠Q
∠T
∠U
Answer:
[tex]\angle P[/tex]
Step-by-step explanation:
Given
[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]
[tex]PQ = 20[/tex] [tex]QR = 16[/tex] [tex]PR = 12[/tex]
[tex]ST = 30[/tex] [tex]TU = 34[/tex] [tex]SU = 16[/tex]
See attachment
Required
Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]
Considering [tex]\triangle PQR[/tex]
We have:
[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse
So, we have:
[tex]\sin(P) = \frac{16}{20}[/tex]
Divide by 4
[tex]\sin(P) = \frac{4}{5}[/tex]
Hence:
[tex]\angle P[/tex] is correct
Answer:
A or <P
Step-by-step explanation:
on edge 2021
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. HL Postulate
Answer:
TU ≅ CB
Step-by-step explanation:
HL Postulates that when a leg and the hypotenuse of a right triangle are congruent to a corresponding leg and hypotenuse of another, then both right triangles are congruent.
Both right triangles shown in the diagram above is indicated to possess corresponding lengths of a leg, that is side UV ≅ side BA
We need an additional information that shows that the hypotenuse, TU, of ∆TUV is congruent to the hypotenuse, CB of ∆CBA.
Therefore, additional information needed is TU ≅ CB
2. Express the number 1750 as a product of prime factors of the form:
p * qr * s
9514 1404 393
Answer:
1750 = 2 · 5³ · 7
Step-by-step explanation:
It is often helpful to start with divisibility rules when finding prime factors of a small composite number.
The least-significant digit is even, so we know 2 is a factor.
1750/2 = 875
The least significant digit is 5, so we know 5 is a factor.
875/5 = 175
175/5 = 35
35/5 = 7
7 is a prime number, so we're done.
The factorization is ...
1750 = 2 · 5³ · 7
6. 2(h-8)- h= h - 16
a.8
b. -8
c. infinitely many solutions
d. no solution
i need the answer and a explanation of how to get my answer i need soon pls hurry
Answer:
c. infinitely many solutions
General Formulas and Concepts:
Pre-Algebra
Distributive Properties
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
2(h - 8) - h = h - 16
Step 2: Solve for h
[Distributive Property] Distribute 2: 2h - 16 - h = h - 16Combine like terms: h - 16 = h - 16[Addition Property of Equality] Add 16 on both sides: h = hHello from MrBillDoesMath!
Answer: c (infinitely many solutions)
Steps:
1) Simplify the original equation
2(h-8)- h= h - 16
2.As 2 (h-8) = 2h- 16, the equation in 1) is equivalent to
(2h-16) -h = h - 16
or
(2h-h) - 16 = h - 16
or
h - 16 = h -16
which is true for all values of h.
Regards, MrB
convert 2m 50cm 15mm in cm
Answer:
251.5 cm
Step-by-step explanation:
1 m = 100 cm
1 cm = 10 mm
2 m + 50 cm + 15 mm =
= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)
= 200 cm + 50 cm + 1.5 cm
= 251.5 cm
find all the missing measurement
Given:
[tex]\Delta CAP\sim \Delta DAY[/tex]
To find:
The value of FD.
Solution:
We have, [tex]\Delta CAP\sim \Delta DAY[/tex]. So, the corresponding angles are congruent.
[tex]\angle CAP\cong \angle DAY[/tex]
[tex]\angle ACL\cong \angle AD F[/tex] (Given in the figure)
Two angles are congruent. So,
[tex]\Delta CAL\sim \Delta DA F[/tex]
Corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{CA}{DA}=\dfrac{LC}{FD}[/tex]
Substituting the given values from the figure, we get
[tex]\dfrac{35}{21}=\dfrac{25}{FD}[/tex]
[tex]\dfrac{5}{3}=\dfrac{25}{FD}[/tex]
On cross multiplication, we get
[tex]5\times FD=3\times 25[/tex]
[tex]5FD=75[/tex]
Divide both sides by 5.
[tex]FD=\dfrac{75}{5}[/tex]
[tex]FD=15[/tex]
Therefore, the measure of FD is 15 units.
I’ll mark you as a brain list please help
Answer:
just ignore this whole thing
Answer: There is a pattern if you look closely :)
So yhe required answer would be 7^-1
Step-by-step explanation:
Find the numerical value of the area under the normal curve given the following information:
NOT between -0.79 and 0.99 standard deviations
enter your answer as a decimal (NOT percentage) and lead with a zero...for example: 0.1234
Answer:
0.37585
once again just look up the numbers on the Z table..
in this case you want the values to the LEFT of z=-.79 and to the RIGHT of z=.99
Step-by-step explanation:
-0.79 (L)0.21476
0.99 (R)0.16109
0.37585
The numerical value of the area under the normal curve is 0.3759 if the standard deviation value is NOT between -0.79 and 0.99.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have given:
The standard deviation value = NOT between -0.79 and 0.99
= P(not between - 0.79 and 0.99)
= P( x < -0.79) + P(x > 0.99)
= 1 - P( x < 0.79) + 1 - P(x < 0.99)
From the Z-table:
P( x < 0.79) = 0.7852
P(x < 0.99) = 0.8389
= 2 - 0.7852 - 0.8389
= 2 - 1.6241
= 0.3759
Thus, the numerical value of the area under the normal curve is 0.3759 if the standard deviation value is NOT between -0.79 and 0.99.
Learn more about the normal distribution here:
brainly.com/question/12421652
#SPJ5
16. Jorge plans to paint a bedroom wall that is shaped like a trapezoid. The bottom edge of the wall is 22.5 feet long, and the top edge of the wall is 9.5 feet long. If the wall is 8 feet tall, what is the area of the wall? Round your answer to the nearest hundredth if necessary.
Answer:
128 square feet
Step-by-step explanation:
length of the bottom edge of the wall (a) = 22.5 feet
length of the top edge of the wall (b) = 9.5 feet
height of the wall (h) = 8 feet
then
area of the wall = [(a + b)/2] * h
= [ (22.5 + 9.5)/2] * 8 square feet
= (32/2) * 8 square feet
= 16 * 8 square feet
= 128 square feet
7/18 - 1/3 , 1/2 - 1/5 - 1/10 and 3 1/2 - 2 5/9 please help thank you
To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First Equation: 5x − 4y = 28
Second equation: 3x - 9y = 30
The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 3 and the second equation by −5.
The first equation should be multiplied by 9 and the second equation by 4.
The first equation should be multiplied by 9 and the second equation by −4
Answer:
The first equation should be multiplied by 9 and the second equation by −4
Step-by-step explanation:
Given the simultaneous equation
First Equation: 5x − 4y = 28
Second equation: 3x - 9y = 30
In order to eliminate y, we must make the coefficient of x in both expression to be equal.
To do that the first equation should be multiplied by 9 (negative value of the coefficient of y in equation 2)and the second equation by -4( (coefficient of y in equation 1)
A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 3000 bacteria in the initial polulation and the number doubled after the first 60 minutes, how many bacteria will be present after 2 hours
Answer:
12000 bacteria
Step-by-step explanation:
Recall that
60 minutes = 1 hour
Given that the rate of growth of the bacterial population is proportional to the number present.
If there were 3000 bacteria in the initial population and the number doubled after the first 60 minutes
Then after 60 minutes, the number of bacteria present would be
= 3000 * 2
= 6000
In another 60 minutes, the number would have doubled again, thus the number present then would be
= 6000 * 2
= 12000
Hence after 120 minutes, the number of bacteria present is 12000. 120 minutes is same as 2 hours
3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(X) is shown on the provided graph.
Graph the result of the following transformation on fx).
f(x)+6
which number can be added to the data so that the range of the data will be 50?
Answer: C
Step-by-step explanation:
First, rearrange the data from least to greatest: 45, 47, 54, 59, 81, 90
The range = greatest value(max) - smallest value(min).The current range = 90 - 45Substitute in each of the answer choices, subtract the minimum value from the maximum value, and find one that result in 50.
A. 90 - 44 = 46B. 130 - 45 = 85C. 90 - 40 = 50D. 90 - 6 = 84find all the missing measurement
Answer: h = 18
Step-by-step explanation: At the top we can see that △ICE ~ △AGE meaning that the triangles are "similar"
The way I got my answer was taking 33/22 and getting the scale of 1.5
So with that we can tell that △AGE is 1.5 times larger than △ICE
You can multiply 22 by 1.5 and get an answer of 18.
order the group of quadratic functions from widest to narrowest graph
Answer:
"The coefficient with the largest absolute value is the most narrow graph."
y = ⅓x² → widest
y = -½x²
y = -9x² → narrowest
A number increased by a% and decreased by 80% is 400. What is the number?
will give brainliest
Answer:
If we have a given number N, and we increase it by x%, then the new number is:
N + (x%/100%)*N
While if we decrease it by x%, the new number will be:
N - (x%/100%)*N
Now, we know that:
"A number increased by a% and decreased by 80% is 400. What is the number?"
First, we can not solve the problem, because we have two unknown values, the original number and the "a%", which I guess is a typo.
So, to be general with my answer, let's assume that the actual question is:
"A number increased by 50% and decreased by 80% is 400. What is the number?"
Then, if our original number is N and we increase it by 50%, the new number will be:
N + N*(50%/100%)
N + N*0.5
N*(1 + 0.5)
N*(1.5)
Now we decrease it by 80%, and that will be equal to 400, then:
N*1.5 - N*(1.5)*(80%/100%) = 400
N*1.5 - N*1.5*0.8 = 400
N*(1.5 - 1.5*0.8) = 400
N*(0.3) = 400
N = 400/0.3 = 1,333.33...
Remember that this is a kinda general solution, so you can understand how to solve this type of problem.
Which number produces an irrational number when added to 0.4
Answer:
0.31311311131111....
Step-by-step explanation:
We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,
Rational number :- The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .
Irrational number :- Non terminating and non repeating decimals are called irrational number .
Recall the property that :-
Property :- Sum of a Rational Number and a Irrational number is Irrational .
So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,
[tex] \rm\implies Irrational\ Number = 0.31311311131111... [/tex]
So when we add this to 0.4 , the result will be Irrational . That is ,
[tex] \rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 .. [/tex]
Find the value of x to the nearest tenth!
Answer:
5.7
Step-by-step explanation:
sine cosine tangent
soh cah toa
sine = opposite/hypotenuse
so sin(35)= x/10
you can multiply 10 to both sides to get rid of the 10 denominator on the right leaving you with 10sin(35)=x
be sure your calculator is in degrees.
put that into a calculator leaving you with 5.7
a new extended-life light bulb has an average service life of 700 hours, with a standard deviation of 50 hours. if the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours
Answer:
Hence the distribution will be between 600 hours and 900 hours is 74.9%.
Step-by-step explanation:
I don’t know what this is I took a picture of it here.
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed.
a.) State the random variable.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
f.) What blood pressure do 90% of all people in China have less than?
Answer:
a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.
b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.
d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg
This means that [tex]\mu = 128, \sigma = 23[/tex]
a.) State the random variable.
Mean blood pressure for people in China, which has mean 128 and standard deviation 23.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
This is 1 subtracted by the p-value of Z when X = 135, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 128}{23}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a p-value of 0.6179.
1 - 0.6179 = 0.3821
0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
This is the p-value of Z when X = 141, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{141 - 128}{23}[/tex]
[tex]Z = 0.565[/tex]
[tex]Z = 0.565[/tex] has a p-value of 0.7140.
0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 128}{23}[/tex]
[tex]Z = -0.13[/tex]
[tex]Z = -0.13[/tex] has a p-value of 0.4483.
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 128}{23}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a p-value of 0.3632.
0.4483 - 0.3632 = 0.0851
0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
From item b, when X = 135, Z = 0.3.
Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f.) What blood pressure do 90% of all people in China have less than?
The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 128}{23}[/tex]
[tex]X - 128 = 1.28*23[/tex]
[tex]X = 157.44[/tex]
90% of all people in China have a blood pressure of less than 157.44 mmHg.