The value of the 47th term of the given arithmetic sequence is -55.7
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.
We are given the explicit rule for an arithmetic sequence as follows -
[tex]a_n[/tex] = 8.7 - 1.4(n-1)
We have to find the value of the 47th term in the series.
So, we have the value of n = 47
The equation will become -
[tex]a_{47}[/tex] = 8.7 - 1.4(47-1)
[tex]a_{47}[/tex] = 8.7 - 1.4(46)
[tex]a_{47}[/tex] = 8.7 - 64.4
[tex]a_{47}[/tex] = -55.7
Thus, the value of the 47th term of the given arithmetic sequence is -55.7
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Arabella wants to buy 42 dresses.
Each dress costs £8.70.
Estimate the cost of Arabella's 42 dresses
Answer:
378 Euros
Step-by-step explanation:
A good way to estimate is to round to the nearest whole number or 10th and then multiply:
8.70 --> 9.00 (since 7 > 5 you round up to the nearest whole number, in this case 9)
then you multiply. A good way to do this in your head is doing:
split 42 into 2 numbers:
40, 2
then multiply by nine:
9 * 4 = 36 (9 * 40 = 360) added a zero since we multiplied by 40, its just easier to multiply by smaller numbers
9 * 2 = 18
then add the two numbers together:
360 + 18 = 378 Euros
The actual answer with a calculator is 365.4 Euros, so for an estimation its fairly close.
Another way you could solve it is to just round 8.70 --> 10 (rounding to the nearest 10th)
then:
10 * 42 = 420 (nice)
I don't recommend it since its way too off from the original value, but could be good for quick estimations.
hope this helped you :)
5/10 the students in Sam's class are girls. Of the girls, of them wear glasses. What
fraction of the student's wear glasses?
As 5/10 are Girls in Class And 1/5 of the girls wear glasses So on overall girls wear glasses is 1/10 in the whole class.
The fraction 5/10 is equal to 1/2 of the total and 1/5 of the girls wear glasses so if you multiply 1/2 and 1/5 you get 1/10, To get a total fraction of girls who wear glasses overall will be by multiplying both the fraction. So,
1/5*1/2 = 1/10
Here the answer is produced by multiplying the numerator with the numerator and similarly denominator with the denominator to get the answer of total friction of girls wearing glasses in the whole class.
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At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
Answer: Because 2 places to the right of the the decimal.
Step-by-step explanation:
A 6 ft. tall man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How high off the ground is the kite?
The kite is 84.8 feet off the ground.
What is an angle of elevation?The angle produced whenever an object if viewed above the horizontal plane is termed the angle of elevation.
To determine how high off the ground is the kite, we have;
let the altitude of the kite from the man's head be represented by s,
Sin θ = opposite/ hypotenuse
Sin 52 = s/ 100
s = Sin 52*100
= 0.7880*100
s = 78.8 feet
The height of the kite off the ground = 78.8 + 6
= 84.8
The height of the kite off the ground is 84.8 feet.
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can someone help me please?
Answer:
Step-by-step explanation:
a) A(11) > M(11)
45 > 40
Go to x axis where t=11 then go straight up to find the y values (temp.) on each line
b) Look for where the lines intersect. This is where t≈47, t≈60
c) M(t) < A(t) where t=2, t=11
Look for where the Minn. line (dashed orange) is BELOW the Aspen line (solid blue)
students who score within 22 points of the number 78 will pass a particular test. write this statement using absolute value notation and use the variable x for the score.
The statement using absolute value notation will be x - 78 ≤ 22.
The student will pass the test which scores 22 points for the number 78
Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.
In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.
Le the score of student be = x
Forming the absolute value notation -
This can be expressed as,
x - 78 ≤ 22.
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Given reflections R₁ and Rk where "h" is a line with equation
x = -3 and "k" is a line with equation x = 2, how can you determine
the distance of the translation resulting from the composition
Rk Rh
The distance of the translation resulting from the composition of the two reflections Rk and Rh is equal to |1 + 2x|
How to determine the distance of the translationTo determine the distance of the translation resulting from the composition of two reflections Rk and Rh, we can calculate the difference in x-coordinates of the pre-image and image points.
Reflection Rk reflects points over the line x = 2,
So the x-coordinate of a point and its reflection would have a difference of 2 - x, where x is the x-coordinate of the original point.
Reflection Rh reflects points over the line x = -3,
So the x-coordinate of a point and its reflection would have a difference of -3 - x
When we compose the two reflections
The x-coordinate of a point and its image will have a difference of (2 - x) - (-3 - x)
Evaluate
Distance = 5
Hence, the distance is 5 units
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of the 900 students at columbia middle school, there are 324 7th graders. If one student is chosen at random to lead the pledge at a school assembly, what is the probability the person chosen will be a 7th grader? Use prime factorization to reduce the answer.
Answer:
Step-by-step explanation:
im am sorry but i dont understand so i cant answer this question see you later!
15. Use the given degree of confidence and sample data to find a confidence interval for the
population standard deviation c. Assume that the population has a normal distribution.
Round the confidence interval limits to the same number of decimal places as the sample
standard deviation.
College students' annual earnings: 98% confidence; n = 9, x = $3959, s = $886
Confidence interval will be between $831.57 and $1040.67.
To find a confidence interval for the population standard deviation, we can use the formula:
(sample standard deviation / square root of sample size) x t-multiplier
where t-multiplier is based on the degree of confidence and the sample size.
For a 98% confidence interval and a sample size of 9, the t-multiplier is 2.821 (from a t-table or a calculator with a t-distribution function).
So the confidence interval for the population standard deviation is:
(886 / sqrt(9)) x 2.821 = (886 / 3) x 2.821 = 295.33 x 2.821
= 831.57 to 1040.67
Therefore, we can be 98% confident that the population standard deviation of the annual earnings of college students falls between $831.57 and $1040.67.
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Help me please thhhannkkk youuu
Answer:
25 . 3 %
Step-by-step explanation:
it has the circuits of the brain
The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find m∠HEF .
The measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.
Define the term linear pair?A linear pair is just a pair of neighboring angles created by the intersection of two lines. 1 and 2 create a linear pair in the illustration. The same holds true for pairs 1, 2, 3, and 4. A linear pair's two angles are always supplementary, that means that the sum of their measurements is 180 degrees.The given data:
DH=44.5 feet, EF=39 feet, and m∠GHF=128°As, GE is the straight line.
Thus,
m∠EHF = 180 - 128 (sum of all angles of line is 180, linear pair)
= 52°
Now,
m∠HEF = 180 - 52 / 2 (isosceles triangle)
m∠HEF = 64°
Thus, the measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.
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The diagram for the question is attached.
A company produces a range of 5 computers models which bring in high volume
Assuming that the factory works equally to produce models for 9 hours days 7 days per week, which monitor bring in the highest revenue
The model with the highest revenue is model D
How to determine the model with the highest revenueFrom the question, we have the following parameters that can be used in our computation:
Model A Model B Model C Model D Model E
Time to manufacture (mins) (t) 15 18 13 20 17
% Of monitors sold (s) 75% 73% 84% 95% 81%
Cost per monitor (c) $175 $188 $145 $198 $170
The factor works 9 hours for 7 days
So, the total duration per unit time is
D = 9 hours * 7/t
D = 63/t
Convert t to hours
D = 63 * 60/t
D = 3780/t
The total revenue is then calculated as
R = c * D * s
So, we have
Model A = 175 * 3780/15 * 75% = 33075
Model B = 188 * 3780/18 * 73% = 28820
Model C = 145 * 3780/13 * 84% = 35444
Model D = 198 * 3780/20 * 95% = 35551
Model E = 170 * 3780/17 * 81% = 30569
The highest value above is 35551
Hence, the model is model D
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Complete question
Model A Model B Model C Model D Model E
Time to manufacture 15 minutes 18 minutes 13 minutes 20 minutes 17 minutes
% Of monitors sold per total products 75% 73% 84% 95% 81%
Cost per monitor $175 $188 $145 $198 $170
A company manufactures computer monitors. Among the various models are top
products, which bring high revenue.
Assuming the manufacturing lines are running for 9 hours a day for 7 days a week,
which model brings in the highest revenue?
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
The value of x is 5.5
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Given;
The two polygons are similar
So,
x-1/6=16/21
x/6-1/6=16/21
x/6=16/21+1/6
x=5.5
y+1/32=21/24
y/32+1/32=7/8
y=3
Therefore, the value of x in polygon will be 5.5
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A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
Histogram II shows the distribution of the students’ balance-scale readings, so the correct answer is option (b).
It is stated that most students are very good at reading the scale. Thus, most of the students will read the scale accurately around the actual weight (i.e., around 1.6 ounces), and very few will read far below or far above the accurate weight of 1.6 ounces.
As a large portion of the understudy score tremendous and ought to have rough equivalent aptitude; in this manner, the histogram ought to be around symmetrical.
Therefore, histogram II (symmetrical distribution) shows the perfect distribution of the students' balance-scale readings.
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The complete question is:
A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
(a) Histogram I
(b) Histogram II
(c) Histogram III
(d) Histogram IV
Shane invested $3,500 in a savings account that pays 4% interest
semiannually (every 6 months). How much money will he have in his
account in 5 years?
The money in Shane's account after five years will be $4900.
The formula for simple interest is -
S.I. = PRT/100, where P is principal, R is rate of interest, T is time and SI is simple interest. Interest is calculated semi-annually then t will be 5×2 years.
Keep the values in formula -
S.I. = 3500 × 4 × 5 × 2/100
Performing multiplication in numerator on Right Hand Side of the equation
S.I. = 1,40,000/100
Cancelling common zero on Right Hand Side of the equation
S.I. = $1400
Total amount = Principal + Interest
Keep the values in formula -
Total amount = 3500 + 1400
Performing addition
Total amount = $4900
The total money in account will be $4900.
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How many solutions does this system have? x + 4 y = 6. y = 2 x minus 3a. one b. two c. an infinite number d. no solution
According to the graph, the system of equations x + 4y = 6 and y = 2 x -3 has one solution that is (2,1)
In math the term called graph is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we know that the following equation are known:
=> x + 4y = 6
=> y = 2x - 3
And here we need to find the number of solution for the equations.
Here we have to plot the equation on the graph then we get the graph like the following.
While we looking into the graph, we have identified that the intersection point in the graph is (2,1) and there is no other intersecting point.
Therefore, option (a) is correct.
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What is the value of f(150)?
Answer:
Step-by-step explanation:So make sure you learn this in fifth grade so basically whatever your line go to let's say if it lands on 79 I mean 70 and that's like I mean 150 it depends on what you're using
Systems of Equations and Inequalities 2020-2021 / 5 of 18
Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought
2 spirals and 3 pens for $8. 66. Another student bought 4 spirals and 5 pens for $15. 20. Find the unit cost of a spiral.
1
Each notebook is $5 and each thumb drive is $12.
To Locate:
The price per notebook and per flash drive
Explain x and y:
Let's say a notebook costs x dollars.
I'll pay whatever a thumb drive costs.
Form equations:
4x + y = 32 ------------------------ [ 1 ]
3x + 2y = 39 ---------------------- [ 2 ]
Equation [ 1 ] x 2:
8x + 2y = 64 ---------------------- [ 3 ]
[ 3 ] - [ 2 ] :
5x = 25
x = 5
Substitute x = 5 into [ 1 ]:
4(5) + y = 32
20 + y = 32
y = 32 - 20
y = 12
Find the cost of each notebook and each thumb drive:
notebook = x
notebook = $5
thumb-drive = y
thumb-drive = $12
Each notebook is $5 and each thumb drive is $12.
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a number increased by 7 given 20
Answer:
13
Step-by-step explanation:
Please help with this problem!
The maximized value of the objective function is 3
How to maximize the objective functionFrom the question, we have the following parameters that can be used in our computation:
C = x + y
Subject to
y >= 0
x >= 0
4x + 2y <= 8
2x - y <= 0
When the graphs of these inequalities are plotted (see attachment), we have the following feasible regions
(x, y) = (0, 0) and (1, 2)
This means that
C = 0 + 0 = 0
C = 1 + 2 = 3
3 is greater than 0
Hence, the maximized value is 3
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A group of students were asked which club they planned to join.
Club Percent of Students
Garden Club 0.1
Robotics Club 0.2
Technology Club 0.5
Zoology Club 0.2
Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.
The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).
The student will be more likely to join the Garden Club than the Robotics Club because P(Garden) > P(Robotics).
The statement that is most likely to be true in the question that we have here is that : The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). Option 2
What is meant by probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.
In the question the probability of robotics is 0.2 while the probability of zoology club is 0.2 as well.
They have equal probability
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Answer: Answer B
Step-by-step explanation:
a numerical measure of linear association between two variables is the . a. standard deviation b. covariance c. coefficient of variation d. variance
option b is correct - covariance
The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
Covariance
A numerical measure of linear association between two variables.
Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are. It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.
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2x^2-5x-2=0 quadratic formula
Step-by-step explanation:
First add you two numbers in parethese and then subtract thhat and dit =0
You spin a ball of mass 0.18 kg that is attached to a string of length 0.98 m at ω = 5.2 rad/s in a circle. What is the ball’s angular momentum?
The angular momentum of the the ball is 4.16kgrad/sec
What is angular momentum?Angular momentum is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity. This means that the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. It is measure d in kgrad/sec
angular momentum = mass × angular velocity
mass = 0.18kg
angular velocity = 5.2 rad/s
therefore angular momentum = 0.18× 5.2
= 4.16 kg rad/s
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the value of
3(2x+3) when x=5
Answer:
39
Step-by-step explanation:
3(2x + 3) = 6x + 9 = 6(5) + 9 = 39
[tex]3(2x+3)[/tex] when x is 5
Substitute for x with the given value:
[tex]3(2(5)+3)[/tex]
[tex]3(10+3)[/tex]
[tex]3(13)[/tex]
[tex]=\fbox{39}[/tex]
Solve for x. Express your answer in simplest radical form if necessary.
81 = x²
Answer:
Step-by-step explanation:√81 = √x²
9 = square root cancel square = x
9=
x=
what is the product for (2x+1) and (5-x)
The product for (2x+1) and (5-x) is -2x²+9x+5.
What is Fraction?A fraction represents a part of a whole.
We have to find the product of (2x+1)(5-x)
We use distributive property to find the product.
2x(5-x)+1(5-x)
10x-2x²+5-x
-2x²+10x-x+5
Add the like terms
-2x²+9x+5
Hence, the product for (2x+1) and (5-x) is -2x²+9x+5.
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Can someone please help me on this?
A linear function is plotted on the coordinate plane with the following points: (0, 3) and (2, 7). What is the rate of change (slope) and the initial value (y-intercept) for the linear function?
The rate of change for the linear function is 2.
The initial value for the linear function is 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The points on the coordinate plane:
(0, 3) and (2, 7)
Now,
The equation of the line.
y = mx + c
Slope = m
m = (7 - 3) / (2 - 0)
m = 4/2
m = 2
Now,
(0, 3) = (x, y)
3 = 2 x 0 + c
3 = 0 + c
c = 3
The y-intercept is 3.
Thus,
The rate of change is 2.
The initial value is 3.
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help me pls , thanks :)
its about funtions and i rlly need help on this
The given relations are:
1) It is a function.
2) not a function.
3)it is a function.
4) not a function.
Are the relations functions or not?A function is a relation that maps inputs into outputs, such that each output needs to be mapped into a single input.
1) For example, the first relation each input (left row) is mapped into a single output, thus, it is a function.
2) Here theinput 9 is mapped into two different outputs, then it is not a function.
3) The notation used here is (input, output), so we can see that no input is repeated,so it is a functon.
4) The input 9 is mapped into 3 different outputs, then it is not a function.
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What percent of the area under the tandard normal ditribution lie within two tandard deviation of the mean?
Approximately 95.45% of the area under the standard normal distribution lies within two standard deviations of the mean.
Area Under Standard Normal Distribution Within Two Standard Deviations of the MeanThe standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This means that 68.27% of the area under the standard normal distribution lies within 1 standard deviation of the mean, and 95.45% of the area under the standard normal distribution lies within 2 standard deviations of the mean.
This is because the standard deviation is a measure of the spread of the data; the larger the standard deviation, the more spread out the data is.
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