The smallest number of terms of the AP that will make the sum of terms positive is 73.
Since we need to know the number for the sum of terms, we find the sum of terms of the AP
Sum of terms of an APThe sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where
n = number of terms, a = first term and d = common differenceSince we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.
The common difference, d = a₂ - a
= -52.5 - (-54)
= -52.5 + 54
= 1.5
Number of terms for the Sum of terms to be positive
Since we require the sum of terms , S to be positive for a given number of terms, n.
So, S ≥ 0
n/2[2a + (n - 1)d] ≥ 0
So, substituting the values of the variables into the equation, we have
n/2[2(-54) + (n - 1) × 1.5] ≥ 0
n/2[-108 + 1.5n - 1.5] ≥ 0
n/2[1.5n - 109.5] ≥ 0
n[1.5n - 109.5] ≥ 0
So, n ≥ 0 or 1.5n - 109.5 ≥ 0
n ≥ 0 or 1.5n ≥ 109.5
n ≥ 0 or n ≥ 109.5/1.5
n ≥ 0 or n ≥ 73
Since n > 0, the minimum value of n is 73.
So, the smallest number of terms of the AP that will make the sum of terms positive is 73.
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An awards dinner costs $225 plus $5 for each person making reservations the total bill is $735 how many people attended the dinner
The number of people attended dinner is 102.
What is an Equation ?An equation is a mathematical statement when two algebraic expressions are equated by an equal sign.
It is given in the question that
An awards dinner costs $225 plus $5 for each person making reservations
the total bill is $735
people attended the dinner = ?
Let x number of people attended the dinner
$225 + $5 * x = $735
5x = 735-225
5x = 510
x = 102
Therefore , 102 people attended the dinner.
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4 divided by 5/7 in its mixed form and simplest form
[tex]4\div\cfrac{5}{7}\implies \cfrac{4}{1}\div\cfrac{5}{7}\implies \cfrac{4}{1}\cdot \cfrac{7}{5}\implies \cfrac{28}{5}\implies 5\frac{3}{5}[/tex]
Q
7/0
The mean weight of 8 girls in a group is 35 kg. The individual weights of seven of then
are 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg. Find the weight of the 8th girl.
The weight of the 8th girl in the class is 43 kg
How to determine the weight of the 8th girl?The given parameters are:
Mean weight = 35 kg
Weight of 7 girls = 35kg, 28kg, 43kg, 25kg, 33kg, 51kg, and 22kg
Let the weight of the 8th girl be x.
Mean is calculated using:
Mean = Sum/Count
So, we have:
(35+ 28+43+25+33+51+22 + x)/8 = 35
Evaluate the sum
(237 + x)/8 = 35
Multiply both sides by 8
237 + x = 280
Subtract 237 from both sides
x = 43
Hence, the weight of the 8th girl is 43 kg
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y² + 2y - 48 ( factor the polynomial )
Answer:
(y - 6)(y + 8)
Step-by-step explanation:
Find two numbers that add to 2 and multiply to -48. Then put them in the form above. Afterwards, use FOIL (First, Outside, Inside, Last) to check the factoring and you get: y² + 2y - 48
Have a great day! :)
Answer:
−8, 6
Step-by-step explanation:
Write the factored form using these integers. (y−8) (y+6)
PLEASE ANSWER ASAP!!!!!!!!!!!! MUCH APPRECIATED!!
The equation that's illustrated simply depicts an investment as it shows the principal, and interest rate.
What is an investment?It should be noted that an investment simply means a dedication of an asset in order to increase the value over a period of time.
In this case, the equation that's illustrated simply depicts an investment as it shows the principal, and interest rate. To calculate the investment, the time, amount and rate will be considered.
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PLEASE HELP ASAP ILL MAKE YOU THE BRAINIEST
Write the ratio for sin A
Answer:
Step-by-step explanation:
Formula
The sin(A) = opposite / hypotenuse
Givens
Opposite = CB = 11
Hypotenuse = AB = 61
Solution
Sin(A) = 11/61
Sin(A) = 0.1803
Answer
Sin(A) = 11/61
Sin(A) = 0.1803
Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?
4 units to the left
4 units to the right
8 units to the left
8 units to the right
The translation of the function y = 2(x - 15)² to y = 2(x - 11)² + 3 is; 4 units to the left.
How to Interpret Graph Translations?
We are given the graph function;
y = 2(x - 15)²
Now, the function above was translated to get;
y = 2(x - 11)² + 3
Now, when we translate a graph to the right, we subtract from the x-value, but if we move the graph to the left, we subtract from the x-value. Thus;
The translation was 4 units to the left.
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5x + 3 - 2x = 5. What is the value of x?
Answer:
x = 2/3
Step-by-step explanation:
5x + 3 - 2x = 5
3x = 5-3
3x = 2
x = 2/3
give brainliest please!
hope this helps :)
awnser this pls im in a bad mood
Answer:
I think its 1/6 and if I'm wrong I'm very sorry but I think its 1/6
Step-by-step explanation:
Answer:
it's [tex]7* \frac{1}{6} =\frac{7}{6}[/tex]
Step-by-step explanation:
Yeah same, have a great day I guess i don't know I'm not in the mood
Sam opened a stationery store in his neighborhood. His annual profit grew by $5,000 per year in the first 2 years. Then for 2 years, his annual profit was constant at $10,000 each year. Then his annual profit grew by $10,000 per year for the next 3 years.
Which graph models the piecewise function for the given situation?
Please find attached the image of the graph that models the function.
What is a graph?A graph is a pictorial representation of data. A graph is made up of the x-axis and the y-axis. On this graph, the number of years is on the y-axis and the profit is on the x-axis.
Profit in year 1 = $500 Profit in year 2 = $5000 + $5000 = $10,000Profit in year 3 and 4 = 10,000Profit in year 5 = 10,000 + 10,000 = $20,000Profit in year 6 = 20,000 + 10,000 = $30,000Profit in year 7 = 30,000 + 10,000 = $40,000To learn more about graphs, please check: https://brainly.com/question/21527145
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Answer: other dude is correct
Step-by-step explanation:
Amelie solves the following system of equations.
Which values of x and y satisfy this system of equations?
The values of x and y that satisfy this system of equations are 10 and 5 respectively
Simultaneous equationGiven the system of equations
x + y = 20
3x - 3y = 30
_____________________
x + y = 20
x - y = 10
Add the equations
2x = 20 + 10
2x = 30
x = 30/2
x = 15
Substitute
x -y = 10
15 - y = 10
y = 5
Hence the values of x and y that satisfy this system of equations are 10 and 5 respectively
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ΔXYZ has angles with the following measurements:
m∠X=(10x-33)°
m∠Y=(4x-19)°
m∠Z=(100-2x)°
What are the measures of the three angles?
Answer:
Below in bold.
Step-by-step explanation:
The 3 angles add up to 180 degrees as they are in a triangle.
So 10x - 33 + 4x - 19 + 100 - 2x = 180
12x = 180 + 33 + 19 - 100
12x = 132
x = 11.
So the 3 angles are
10(11) - 33 = 110 - 33 = 77 degrees
4(11) - 19 = 25 degrees
100 - 2(11) = 78 degrees
Describe the trend in the scatterplot
Answer:
negative correlation
Step-by-step explanation:
If you were to draw a line of best fit (a line that best expresses the relationship between a group of points), it would have a negative slope.
Agree or disagree.most supervisors accept that i cannot always be on time for work.
Answer:
The answer is your opinion.
Step-by-step explanation:
80 Points, please help!
If using the method of completing the square to solve the quadratic equation x^2-11x-14=0, which number would have to be added to "complete the square"?
Answer:
±√177/2+11/2
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square. Exact Form:x=±√177/2+11/2
x=12.15206734…,−1.15206734…
Answer:
30.25
Explanation:
Quadratic Equation: x² - 11x - 14 = 0
Number added = (b/2)² = (-11/2)² = 30.25
Solving Steps:
x² - 11x = 14[add both sides by 30.25]
x² - 11x + 30.25 = 14 + 30.25[complete square]
(x - 5.5)² = 44.25[exchange sides]
(x - 5.5)² - 44.25 = 0IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
Out of a randomly selected 2200 people from the population, how many of them
would have an IQ less than 115, to the nearest whole number?
Using the normal distribution, it is found that 1851 people would have an IQ less than 115.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 100, \sigma = 15[/tex]
The proportion of IQ scores less than 115 is the p-value of Z when X = 115, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{15}[/tex]
Z = 1
Z = 1 has a p-value of 0.8413.
Out of 2200 people:
0.8413 x 2200 = 1851.
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Answer:
1851
Step-by-step explanation:
if its a whole number than its 1851
Tom and Kathy want to borrow $35,000 in order to build an addition to their home. Their bank will lend them the money for 12 years at an interest rate of 5 3/8%. How much will they pay in interest to the bank over the life of the loan?
The full question.the full question you were asking for
Answer:
I'm getting stuck by
[tex] = lim \: \: \: \: \: \: \frac{ {h}^{ \frac{1}{5} } }{h} \\ h > 0[/tex]
Sorry I can't help you out, if you find the answer through FP lmk
37, 42, 48, 51, 52, 53, 54, 54, 55
What is the probability you spin something larger than 10
The probability you spin something larger than 10 will be 1 / 2.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The given data is:-
There are 8 numbers in the spinner.We need to find the probability of a number greater than 10.The probability will be calculated as:-
Total numbers = 8
Numbers greater then 10 are = 13 , 16 , 22 , 42 = 4
Probability = 4 / 8 = 1 / 2
Therefore the probability you spin something larger than 10 will be 1 / 2.
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solve for x
9x - 5
6x + 4
7x + 7
Answer:
this can not be solved by X cause the equation is not equal to anything
Step-by-step explanation:
Can someone help please?
Answer:
its the first one
Step-by-step explanation:
In a quadratic function, the second differences are the same.
In the first table, the first differences are:
3-6 = -3;
2-3 = -1;
3-2 = 1;
6-3 = 3
The second differences are then:
-1--3 = 2;
1--1 = 2;
3-1 = 2
The second differences are the same, so this is a quadratic function.
Which angle is vertical to ∠EID?
Answer:
C
Step-by-step explanation: It's vertical to the angle, together it makes 368 degrees
Answer:
C) Angle HIA
Step-by-step explanation:
Vertical Angles are the angles directly across from each other in a transversal. In this case, angled EID and HIA are vertical to each other (which also makes them congruent).
Hope it helps!
What is the volume of the right rectangular prism?
15 mm
Î
Area of base = 49 sq. mm
O 64 mm³
3
O 128 mm³
O 735 mm³
O 1,470 mm³
Answer:
735mm³
Step-by-step explanation:
V=A of base×h
=49×15
=735mm³
BRAINLIEST (9th grade mathematics)
Half of the road the boy walked at a speed of 6 m / min, the other half - at a speed of 4 m / min. Calculate the average walking speed of a boy.
Answer:
5 m/min
Step-by-step explanation:
Initial speed = 6 m/ min
Final speedd = 4 m/ min
[tex]Average\:speed\:=\:\dfrac{total\:speed}{2}[/tex]
Average speed = [tex]\dfrac{ 6 + 4}{2}[/tex]
Avg. Speed = 5 m / min.
The dimensions of a right rectangular prism are 1.5 cm,0.5 cm and 2. 25 cm.
What is the volume of the prism?
Find the measures of a right triangle where one of the acute angles is 3.5 times the other
Answer:
the other two angles are 70° and 20°
Step-by-step explanation:
The measures of a right triangle where one of the acute angles is 3.5 times the other angle, the angles are respectively, 20°, 70°, 90°
What are the sum of interior angles of triangle ?The sum of all the interior angles of a triangle is 180°
Given that,
A right angle triangle,
In which one of the acute angle is 3.5 times the other triangle
Suppose, one of the acute angle = x
then the other triangle = 3.5x
The sum of the triangle = 180°
x + 3.5x + 90° =180°
4.5x = 180 - 90
= 90
x = 90/4.5
= 20
The one acute angle = 20
The another triangle = 3.5 x 20
= 70
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A school sold all but 5 of ta school sold all but 5 of their old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally old computers for r1200 each the school received r18000 from the sale. how many comps did the school originally have
Answer:
20
Step-by-step explanation:
The proceeds from the sale can be described by an equation involving the original number of computers.
__
setupLet n represent the number of computers the school originally had. Then n-5 is "all but 5" and is the number sold. Each is sold for ₹1200, and the value of the sale is ₹18000. This can be expressed by the equation ...
(n -5)×1200 = 18000
__
solutionThis 2-step linear equation can be solved by dividing by the coefficient, and adding the opposite of the constant.
n -5 = 18000/1200 = 15 . . . . . divide by 1200
n = 15 +5 = 20 . . . . . . . . . . add the opposite of -5
The school originally had 20 computers.
What figure is a dilation of Figure A by a factor of 12?
A quadrilateral labeled figure A. The sides are labeled 2 inches, 4 inches, 1 inch, and 5 inches, clockwise about the figure.
Note that the images are not necessarily drawn to scale.
A.A quadrilateral. The sides are labeled 1 inch, 3 inches, 0.5 inch, and 4 inches, clockwise about the figure.
B.A quadrilateral. The sides are labeled 4 inches, 8 inches, 2 inches, and 10 inches, clockwise about the figure.
C.A quadrilateral. The sides are labeled 3 inches, 5 inches, 2 inches, and 6 inches, clockwise about the figure.
D.A quadrilateral. The sides are labeled 1 inch, 2 inches, 0.5 inch, and 2.5 inches, clockwise about the figure.
The dilation factor for the question should be 1/2 as per options
So
dilated lengths are
2(1/2)=1in4/2=2in1/2=0.5in5/2=2.5inOption D
Answer:
D
Step-by-step explanation:
Figure A is dilated by a scale factor of 1/2.
Hence, new dimensions will be :
⇒ 1/2 × 2 = 1 inch
⇒ 1/2 × 4 = 2 inches
⇒ 1/2 × 1 = 0.5 inch
⇒ 1/2 × 5 = 2.5 inches
Option D has the right dimensions
15 points, I have 0 idea how to solve this, please explain your answer