Answer:
16
Step-by-step explanation:
From the question given above, the following data were obtained:
Sum of N term (Sₙ) = 292
2nd term (T₂) = 8.5
5th term (T₅) = 13
Number of terms (N) =?
Next, we shall determine the first term (a) and the common difference (d) of the series. This can be obtained as follow:
T₂ = a + d
8.5 = a + d ........ 1
T₅ = a + 4d
13 = a + 4d ........ 2
Subtract equation 1 from equation 2 i.e
(2) – (1)
.. 13 = a + 4d
– 8.5 = a + d
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
4.5 = 3d
Divide both side by 3
d = 4.5 / 3
d = 1.5
Substitute the value of d into any of the equation to obtain the value of a. Here, we shall use equation 1.
8.5 = a + d
d = 1.5
8.5 = a + 1.5
Collect like terms
8.5 – 1.5 = a
a = 7
Finally, we shall determine the number of terms as follow:
Sum of N term (Sₙ) = 292
Common difference (d) = 1.5
First term (a) = 7
Number of terms (N) =?
Sₙ = n/2[2a + (n – 1)d]
292 × 2 = n[(2 × 7) + (n – 1)1.5]
584 = n[14 + 1.5n – 1.5]
584 = n[12.5 + 1.5n]
584 = 12.5n + 1.5n²
Rearrange
1.5n² + 12.5n – 584 = 0
Using formula method, the value of n can be obtained as follow:
a = 1.5
b = 12.5
c = –584
n = –b ± √(b² – 4ac) / 2a
n = –12.5 ± √(12.5² – 4 × 1.5 × –584) / 2 × 1.5
n = –12.5 ± √(156.25 + 3504) / 3
n = –12.5 ± √(3660.25) / 3
n = –12.5 ± 60.5 / 3
n = –12.5 + 60.5 / 3 or –12.5 – 60.5 / 3
n = 4 /3 or –73 / 3
n = 16 or –73 / 3
Since the number of terms can not be negative, therefore, the number of term is 16
HELP, I can't figure out the first question
Answer choice for first question
1. linearly
2.quadratically
3.exponentially
Fill in the table using this function rule.
y=5x-1
The table values with the function y = 5x - 1.
x y
-1 -6
0 -1
1 4
2 9
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y = 5x - 1
For x = -1,
y = -5 - 1 = -6
For x = 0,
y = - 1
For x = 1,
y = 5 - 1 = 4
For x = 2,
y = 10 - 1 = 9
Thus,
The table values are given above.
Learn more about functions here:
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A textbook store sold a combined total of 447 sociology and psychology textbooks in a week. The number of psychology textbooks sold were 43 less than the number of sociology textbooks sold. How many textbooks of each type were sold
Answer:
404
Step-by-step explanation:
48 boxes are loaded onto a truck. The still need to load 96% of the boxes onto the truck. What is the total number of boxes being loaded
Answer:
the total number of boxes being loaded is 1,200 trucks
Step-by-step explanation:
Given that
There are 48 boxes that should be loaded onto a truck
And, still it is required to lead 96% of the boxes onto the truck
We need to find out the total number of boxes that should be loaded
So
Since 48 boxes represent the 4% of the boxes that are loaded
So,
The total number of boxes would be
= 48 × 100 ÷ 0.04
= 1,200 trucks
Hence, the total number of boxes being loaded is 1,200 trucks
In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?
Is this an example of a sample proportion OR a sample mean?
Answer:
sample mean
Step-by-step explanation:
Using the normal distribution and the central limit theorem, considering that this is a sample proportion, as we are dealing with percentages, it is found that there is a 0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex].In this problem:
55% of the registered voters are Democrats, hence [tex]p = 0.55[/tex].A sample of size 100 is taken, hence [tex]n = 100[/tex]The mean and the standard deviation of the sampling distribution of sample proportions are given by:
[tex]\mu = p = 0.55[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.55(0.45)}{100}} = 0.04975[/tex]
The probability of getting less than 50% Democrats in a random sample of size 100 is the p-value of Z when X = 0.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.55}{0.04975}[/tex]
[tex]Z = -1.01[/tex]
[tex]Z = -1.01[/tex] has a p-value of 0.1562.
0.1562 = 15.62% probability of getting less than 50% Democrats in a random sample of size 100.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Triangle ABC with vertices A(-3, 4), B(0, 2),
and C(-2, 1) is translated 4 units right and 5
units down. Which quadrant is the image?
A(-3, -1)
B(0, -7)
C(-2, -4)
Therefore, the image is in the III quadrant (bottom left).
What is the value of y when x = 0?
Answer:
0
Step-by-step explanation:
I am not sure you included the full question, but if it is a multiplication problem, the answer is 0.
A clothing manufacturer offers 2 different styles of jeans, relaxed fit and regular fit, in 5 different colours. How many combinations of a style and a colour are possible?
Answer:
10 combinations
Step-by-step explanation:
We can solve the above question using the Fundamental Counting Principle.
This states that:
If an event has x possible outcomes and a other event has y possible outcomes, then there are x and y total possible outcomes for the two events together.
We are told in the above question that:
Styles of jeans = 2
Number of colors = 5
Hence,the number of combinations of a style and a colour that are possible is calculated as:
5 × 2 = 10 combinations
Please help ASAP!!
A turtle and a snail are 360 meters (who counts this again?) apart, and they start to move towards each other at 3 pm. If the turtle is 11 times as fast as the snail, and they met at 3:40 pm, find the speed of each.
Thank you!! :)
Answer:
Turtle = 11 m / min
Snail = 1 m / min
Total approach speed = 12 m/min
360 m / (12 m/min) = 30 min
Separation is 30 min at assumed speed of 1 m/min
But we know the separation is 40 min
So turtle moves at 3/4 * 11 m / min = 33 m/ 4 min
Snail moves at 3/4 * 1 m /min = 3/4 m / mi
Total approach speed = (33 + 3) / 4 = 9 m / min
So in 40 min
9 m / min * 40 min = 360 m
(Leaving out those units, they approach at 12 * unit of speed)
So the unit of speed has to be 360 m / 40 min = 9 m / min
A peanut butter cookie recipe calls for 3 1/2 cups of flour to make 6 dozen cookies. How many cups of flour must be used to make 20
Complete Question
A peanut butter cookie recipe calls for 3 1/2 cups of flour to make 6 dozen cookies. How many cups of flour must be used to make 20 dozen?
Answer:
11 2/3 cups of flour
Step-by-step explanation:
From the above question:
6 dozen = 3 1/2 cups of flour
20 dozen = x
Cross Multiply
6 dozen × x = 20 dozen × 3 1/2 cups of flour
x = 20 dozen × 3 1/2 cups of flour/6 dozen
x = 20 × 7/2 /6
x = 140/2 ÷ 6
x = 140/2 × 1/6
x = 140/12 cups of flour
x = 11 8/12
= 11 2/3 cups of flour
Therefore, 11 2/3 cups of flour must be used to make 20 dozen.
Can anyone help me with #3 and #4 and #6 please I will give brainlist!!
Answer:
3. 15.02
4. 84.05
6. 4,301
Step-by-step explanation:
I'm not too sure how to explain this, but those are the answers.
Evaluate csc(x + pi/2 ) for x = π.
Answer:
-1 if x=π
Step-by-step explanation:
csc(x+π/2)
csc(π+π/2)
csc(3π/2)
1/sin(3π/2)
1/-1
-1
Therefore, your answer is -1
Two cyclists , A and B , are going on a bike ride and are meeting at an orchard . They left home at the same time . Functions A and B give their distance from the orchard , in miles , after riding for x hours . The functions are defined by these equations
Answer:
Cyclist A lives farther from the Orchard
Step-by-step explanation:
Given
[tex]A(x) =48.5 -21x[/tex]
[tex]B(x) =42 -16.8x[/tex]
Required:
Who lives farther from the Orchard.
To do this, we simply calculate the y intercept.
This represents the total distance traveled to get to the Orchard
To calculate y intercept, we set [tex]x = 0[/tex]
So:
[tex]A(x) =48.5 -21x[/tex]
[tex]A(0) = 48.5-21*0 =48.5-0 =48.5[/tex]
[tex]B(x) =42 -16.8x[/tex]
[tex]B(0) = 42 - 16.8*0 =42-0 =42[/tex]
From the above computation:
[tex]A(0) > B(0) \to 48.5 > 42[/tex]
Hence;
Cyclist A lives farther from the Orchard
Based on the statment, below which statement could be used to prove <1=<2?
vertical angles are congruent
supplementary angles are congruent
complementary angles are congruent
two angles that form a linear pair are congruent
Answer:
Vertical angles are congruent
Mary bought a bag of parsnips that weighed 2 1/4 pounds. She also bought a bag of turnips that weighed 3 times as much as the parsnips. How many pounds of turnips did Mary buy?
Step-by-step explanation:
2 1/4 is improper fraction, because it's 21/4. To simplify;
21/4 = 21/4
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
21/4 = 5 1/4
With 21/4 simplified into 5 1/4, you would then do 5 1/4•3 which would be;
15.75
Conlusion/Answer:
Mary bought 15.75 pounds of turnips.
it’s being timed tysm xx
x=-2
have an amazing day <3
Tell me the answer please. Give me a short answer and a step-by-step explanation.
Answer:
C
Step-by-step explanation:
we should set the equations based on what we know using y=mx+b
in the first set, we have m=5 and the +b as 100. This gives y=5x+100
in the second, we m=20 and the +b of 10. This gives y=20x+10
I belive C would match this. Hope this helps!
Answer:
y=10x+20
y=5x+100
Step-by-step explanation:
find the values of the variables
i will give brainliest to anyone who’s right.
can someone solve this for me?
Answer:
A, C, D
Step-by-step explanation:
42 + 14 = 56
38 + 18 = 56
67 + 33 = 100
70 + 30 = 100
93 + 35 = 128
95 + 33 = 128
B)
40 + 22 = 62
32 + 10 = 42
62 ≠ 42
Answer choices:
16/3
40/9
4/9
4/3
Answer:
0.44444444 or 4/9
Step-by-step explanation:
Since we know the value of [tex]x[/tex], we can rewrite the equation replacing the variables.
[tex]\frac{2}{3}^{2} + 3*\frac{2}{3} - 2[/tex]
Now solve. While solving, remember the order of operations.
[tex]\frac{2}{3}^{2} + 3*\frac{2}{3} - 2 = 0.44444444[/tex] or [tex]\frac{4}{9}[/tex]
8. This model of the backboard of a basketball goal is made of a semicircle. Use the ruler provided to measure the dimensions of the model to the nearest half inch. Which measurement is closest to the area of the model of the backboard in square inches? Use 3 for π.
It is c i did it oh khan
(pls branliest)
Find the surface area of the figure.
11.1 m
3.5 m
4 m
4 m
4 m
Answer and Step-by-step explanation:
Work is in picture.
#teamtrees #PAW (Plant And Water)
The temperature at midnight is -5°C and is expected to drop 12°
by sunrise. What is the expected temperature at sunrise?
Answer:
-17 degrees Celsius.
Step-by-step explanation:
If the temperature at midnight is -5, and it is supposed to drop 12 more by sunrise, the 12 degrees are subtracted from the initial temperature.
-5 - 12 = -17 degrees by sunrise.
Anyone knows this? im giving 20 points pls answer , and it doesnt need to be big im just in 9th grade
Answer:
men=24%
women=72%
Step-by-step explanation:
100/250=0.4
0.4*180=72
0.4*60=24
i think this is the answer
Simplify (2-6)(5)(23 . 5)2.
Which graph represents the inequality
X > 15?
this one because x has to be bigger than 15.
The graph with inequality x>15 is (B)
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
x>15
As, x is greater than 15.
So, the graph with x value labelled from the numbers greater than 15 which is represented by graph on right top corner.
Learn more about inequality here:
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The area of the rectangular school garden is 24 square units. The length of the garden is 8 units. What is the length of the fence needed to enclose the entire garden?
Decide if the expression is positive or negative - explain how you know in words
−11×(23)
What’s the domain of this graph?
Answer: ( ∞ , -∞ )
Step-by-step explanation:
what is 15/9 equivalent to
Answer:
1 6/9 or 1 2/3
Step-by-step explanation:
Answer: A lot of fractions
Step-by-step explanation:
Some Examples: 5/3, 10/6, 20/12