Answer:
140
Step-by-step explanation:
The arithmetic series is 5, 7, 9, 11, ........., 23.
First u have to determine the no. of terms that can be done by using
Tₙ = [a + (n - 1)d]
Tₙ-------nth term
a---------first term
n---------no.of terms in the series
d---------common difference
here a = 5,d = 2.
let it contain n terms Tₙ= [a + (n-1)d]
Substitute Tₙ, a, and d in the equation
23 = 5 + (n - 1)2
Subtract 5 from each side.
18 = (n-1)2
Divide each side by 2
(n - 1) = 9
Add 1 to each side
n = 9 + 1 = 10
The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]
Substitute Sₙ, a, n and d in the equation
Sₙ= (10/2)[2(5) + (10-1)2]
Sₙ= (5)[10 + (9)2]
Sₙ= 5[10 + 18]
Sₙ= 5[28] = 140
Therefore the sum of the arithmetic sequence is 140.
The sum of the arithmetic sequence 5, 7, 9, 11,...,23 is calculated by first finding the number of terms (10 in this case), then applying the formula for the sum of an arithmetic sequence. The sum is 140.
Explanation:The question is asking to find the sum of an arithmetic sequence consisting of the numbers between 5 and 23, increasing by 2 each time. An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. This is the common difference. In this case, the common difference is 2.
Instead of adding each individual term, we use the formula for the sum of an arithmetic sequence. The formula is S_n = n/2 ( a + l ) where n is the number of terms, a is the first term, and l is the last term.
First, we need to find the number of terms (n). This can be found with the formula n = ( l - a ) / d + 1 where d is the common difference, a is the first term, and l is the last term. In this case, n = (23 - 5) / 2 + 1 = 10.
Therefore, the sum of this sequence is S_10 = 10/2 * (5 + 23) = 140.
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NEED HELP ANSWERING THIS QUESTION
Answer:
B. [tex]\frac{x\sqrt{2}}{2y}[/tex]
Step-by-step explanation:
We want to divide [tex]\sqrt{9x^2}[/tex] by[tex]\sqrt{18y^2}[/tex].
This becomes:
[tex]\frac{\sqrt{9x^2}}{\sqrt{18y^2}}[/tex]
[tex]\frac{\sqrt{(3x)^2}}{\sqrt{2(3y)^2}}[/tex]
We remove the perfect squares to obtain
[tex]\frac{3x}{3y\sqrt{2}}[/tex]
Cancel out the common factors to get;
[tex]\frac{x}{y\sqrt{2}}[/tex]
Rationalize the denominator to get:
[tex]\frac{x}{y\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\frac{x\sqrt{2}}{2y}[/tex]
The correct answer is B
Answer:
[tex]\large\boxed{B.\ \dfrac{x\sqrt2}{2y}}[/tex]
Step-by-step explanation:
[tex]\sqrt{9x^2}:\sqrt{18y^2}=\dfrac{\sqrt{9x^2}}{\sqrt{18y^2}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{\sqrt9\cdot\sqrt{x^2}}{\sqrt{18}\cdot\sqrt{y^2}}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{3\cdot x}{\sqrt{9\cdot2}\cdot y}=\dfrac{3x}{\sqrt9\cdot\sqrt2\cdot y}=\dfrac{3x}{3y\sqrt2}\qquad\text{cancel 3}\\\\=\dfrac{x}{y\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\qquad\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\\\\=\dfrac{x\sqrt2}{2y}[/tex]
Please help me with this
B. The graph that best represents the equation y = |x| - 1 is the option B.
To solve this problem we have to try with some values, the symbol |x| is the absolute value which means any number either positive or negative always is positive |-5| = 5 and |5| = 5.
Let's take x = -3, -2, -1, 0, 1, 2, 3.
For x = -3
y = |-3| - 1 = 3 - 1
y = 2
For x = -2
y = |−2| - 1 = 2 - 1
y = 1
For x = -1
y = |−1| - 1 = 1 - 1
y = 0
For x = 0
y = |0| - 1 = 0 - 1
y = -1
For x = 1
y = |1| - 1 = 1 - 1
y = 0
For x = 2
y = |2| - 1 = 2 - 1
y = 1
For x = 3
y = |3| - 1 = 3 - 1
y = 2
y ║ x
2 -3
1 -2
0 -1
-1 0
0 1
1 2
2 3
If we graph the points obtain in the table above, the result is a graph with the characteristics of the option B.
Find the area bounded by the curves y2 = 2x + 6 and x = y + 1. Your work must include an integral in one variable.
Answer:
18.
Step-by-step explanation:
y^2 = 2x + 6
2x = y^2 - 6
x = 1/2(y^2 - 6)
The points of intersection of the curves are calculated:
y + 1 = 1/2( y^2 - 6)
2y + 2 = y^2 - 6
y^2 - 2y - 8 = 0
( y - 4)(y + 2) = 0
y = 4, -2
when y = 4, x = 5 and when y = -2 x = -1.
Integrating between y = 4 and y = -2
4
INT [ ( y + 1 + 1/2 (6 - y^2) ]dy
-2
= 4
{ y^2 / 2 + y + 3y - y^3/6 }
-2
= 13 1/3 - (-4 2/3)
13 1/3 + 4 2/3
= 18 answer.
The area bounded by the two given curves which are y² = 2x + 6 and x = y + 1 is; 18
How To solve Boundary Integrals?We want to find the area bounded by the curves;
y² = 2x + 6 and x = y + 1
Put y + 1 for x in first equation to get;
y² = 2(y + 1) + 6
y² - 2y - 8 = 0
Using quadratic equation calculator gives;
y = -2, 4
Now, we can rewrite the first two equations like this;
x = (y²/2) - 3 and x = y + 1
Thus, the area is;
A = [tex]\int\limits^4_{-2}[/tex] [y + 1 - (¹/₂y² - 3)]dy
Integrating this gives us;
A = [4y + ¹/₂y² - ¹/₆y³]⁴₋₂
Solving by plugging in the boundary values gives;
A = 18
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You are on the high school basketball team. The ball you use has a diameter of 9 inches. What is the volume of the ball? Use 3.14 to approximate pi. Round your answer to the nearest tenth.
Answer:
381.5 cubic inches
Step-by-step explanation:
Please answer this multiple choice question for 30 points and brainliest!!
Subtract 6 from both sides
-x > -1 - 6
Simplify -1 - 6 to -7
-x > -7
Multiply both sides by -1
= A. x < 7
Answer:
a. x<7 is the correct choice.
Step-by-step explanation:
The question is telling that the equation 6-x is larger than 1, so the last three choices are eliminated.
When the definition of a function involves a fraction, the function is undefined at any value that would make the denominator of the function ______?
Answer:
zero
Step-by-step explanation:
Given a rational function then the denominator cannot be zero as this would make the function undefined.
Answer:
zero
Step-by-step explanation:
We have to fill the correct word in the blank space.
Suppose
[tex]f(x)=\frac{1}{x}[/tex]
Substitute x=0 then we get
[tex]f(x)=\frac{1}{0}=\infty[/tex]
The function is not defined at x=0
Because the denominator of the function at x=0 is zero which makes the function not define.
When the definition of a function involves a fraction , the function is undefined at any value that would make the denominator of the function zero.
Please help me with this
Answer:
4.4 in
Step-by-step explanation:
If a radius is perpendicular to a chord, it bisects that chord. You can use Pythagorean theorem here
[tex] {3.7}^{2} + {2.4}^{2} = {x}^{2} [/tex]
Once solved you'll find x to be roughly 4.4 in
Answer:
x = 4.4 in
Step-by-step explanation:
The segment from the centre of the circle to the chord is a perpendicular bisector, hence
7.4 ÷ 2 = 3.7
Consider the right triangle with legs 3.7 and 2.4 and hypotenuse x
Using Pythagoras' identity in the right triangle, then
x² = 2.4² + 3.7² = 5.76 + 13.69 = 19.45
Take the square root of both sides
x = [tex]\sqrt{19.45}[/tex] ≈ 4.4 in
What sine function represents an amplitude of 4, a period of pi over 2, no horizontal shift, and a vertical shift of −3?
Answer:
The sine function is y = 4 sin (4 x) - 3
Step-by-step explanation:
The explanation in the attached file
What is the value of
–4.00
–0.25
1.51
2.41
For this case we must resolve the following expression:[tex]log_ {0.5} (16)[/tex]
We have to:
[tex]log_ {a} (x) = \frac {log_ {b} (x)} {log_ {b} (a)}[/tex]
The base change rule can be used if a and b are greater than 1 and are not equal to x.
We substitute the values in the base change formula, using [tex]b = 10[/tex]
[tex]\frac {log (16)} {log (0.5)} = - 4[/tex]
Answer:
-4
Option A
Two cars started moving from San Jose to San Diego. The speed of the faster car was 12 mph less than twice the speed of the other one. In 6 hours the faster car got to San Diego, and by that time the slower one still was 168 miles away from the destination. Find their speeds. Please help, all the other answers were incorrect.
Answer:
40 mph and 68 mph
Step-by-step explanation:
Let x mph be the speed of the slower car, then 2x-12 mph is the speed of the faster car.
In 6 hours the faster car got to San Diego, so it travels the distance
[tex]6\cdot (2x-12)=12x-72\ miles.[/tex]
By that time the slower car was 168 miles away from the destination, so the slower car travels the distance
[tex]12x-72-168=2x-240\ miles[/tex]
It takes the slower car 6 hours to travel 12x-240 miles, so
[tex]6x=12x-240\\ \\6x-12x=-240\\ \\-6x=-240\\ \\6x=240\\ \\x=40\ mph.[/tex]
Now,
[tex]2x-12=2\cdot 40-12=80-12=68\ mph[/tex]
13. Simplify this expression: 19-(-8) - (-14) = ?
Answer:
19-(-8)-(-14) = 41
Step-by-step explanation:
First, we have to solve what is in parentheses
by law of signs ( - . - = +)
19 + 8 + 14 = ?
Then, we only have to sum the number to obtain the result
19 + 8 + 14 = 41
Answer:
41
Step-by-step explanation:
We must do multiplication before addition or subtraction here.
-(-8) = +8 and -(-14) = +14, and therefore:
19 - (-8) - (-14) becomes 19 + 8 + 14, or 19 + 22, or 41.
Use the grouping method to factor this polynomial completely. 2x 3 + 6x 2 + 5x + 15
your answer choices are
A. (2x^2+ 5)(x + 3)
B. (2x^2+ 5)(x + 5)
C. (2x^2+ 3)(x + 5)
D. (2x^2 + 3)(x + 3)
Answer:
A
Step-by-step explanation:
Group the 4 terms into groups of 2 without changing their order. That looks like this:
[tex](2x^3+6x^2)+(5x+15)[/tex]
Now within each group pull out what's common:
[tex]2x^2(x+3)+5(x+3)[/tex]
Now we have (x + 3) common between the 2 terms, so let's pull that out. With grouping, you know that it "works" if what's in the parenthesis are both exactly the same term. Ours are both (x + 3). What's "left over" are the things we originally pulled out, so group those together and you're done!
[tex](x+3)(2x^2+5)[/tex]
Greg wants to move out of his dormitory and into an apartment near his college. His parents agreed, on the condition that the rent is no more than 25% of the cost of dorm living. To get an idea of rent amounts for one-bedroom apartments, Greg looks at listings in a local newspaper and on an Internet site.
Which answer best describes the sample and population?
A. Sample: all available apartments near the college
Population: listings in a local newspaper and on an Internet site
B. Sample: all available apartments near the college
Population: all available dormitories near the college
C. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college
D. Sample: all available dormitories near the college
Population: all available apartments near the college
Step-by-step explanation:
The population is all possible apartments that Greg could rent. The sample is the ones he finds listed in newspapers and online.
So the answer is the third one.
The sample represents a part of the population from which data is actually taken. In this scenario, the apartments listed in the newspaper and Internet site are the sample, and all the apartments near the college form the population. Therefore, the correct answer is C.
Explanation:In this question, Greg is trying to estimate the cost of living in an apartment. The population refers to the entire group of entities from which he might theoretically collect data. In this case, the population would be all available apartments near the college. That's because these apartments represent the full scope of possible information Greg would need for his research.
On the other hand, the sample is a subset of this population that Greg is actually reviewing for data. In this case, it would be the listings in a local newspaper and on an Internet site since these listings are the specific data points that Greg is examining.
So, the correct answer is C: 'Sample: listings in a local newspaper and on an Internet site; Population: all available apartments near the college'
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In a survey at a local university 32% of students say they get less than the recommended eight hours of sleep per night. In a group of 3330 students how many would you expect to get 8 or more hours?
Answer:
2264 students
Step-by-step explanation:
3330/100=33.3
100-32=68
33.3 x 68=2264.4
Hope This Helps! :D
Answer:
2264 students get 8 or more hours of sleep.
Step-by-step explanation:
We are given that 32% of students say they get less than the recommended eight hours of sleep per night.
We are to find the number of students who get 8 or more hours of sleep.
Percentage of students who get 8+ hours of sleep = 100 - 32 = 68%
Number of students who get 8 or more hours = 68/100 - 3330 = 2264
Tim answered all queston on is math test but got 10 answers wrong. He received 4 points for every corect answer, and there was no penalty for wrong answers. His score was 76 points Write an equation to determine the total number of question (q) on Tim math test. Find the total number of question on his math test
Answer:
See below in Bold.
Step-by-step explanation:
If he scored 76 points he must have answered 76/4 = 19 questions correctly.
If the total number of questions is q then our equation is q = 10 + 76/4
= 10 + 19 = 29 questions.
Please help me answer this and learn how to find the equation for line of best fit
Answer:
y=-12/5x+62
Step-by-step explanation:
to solve this i turned two point form, 5,50 and 17 1/2,20, into slope intercept form by using the formula y-y1=(y2-y1/x2-x1)(x-x1), which when input with the data becomes y-50=(20-50/17 1/2-5)(x-5) which then becomes y-50=-12/5(x-5), then y-50=-12/5x+12, and finally y=-12/5x+62
Please please help me
Answer:
y = 105°
Step-by-step explanation:
In an isosceles trapezoid
• Any lower base angle is supplementary to any upper base angle
• The lower base angles are congruent
75 and x are supplementary, thus
x = 180° - 75° = 105°
x and y are lower base angles and congruent, so
y = x = 105°
Gina is a tour boat operator and she wants to know the mean age of all the people in her tour group.
She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34.
What is the best estimate of the mean age of all the people in the tour group?
Round to the nearest whole number.
Enter your answer in the box.
___ years
Answer:
30
Step-by-step explanation:
The population mean can be estimated with the sample average, so add up all the ages and divide by how many there are.
(19 + 27 + 25 + 21 + 44 + 22 + 45 + 34) / 8
29.625
Rounded to the nearest whole number, the average age is 30.
A Digital Media Player is marked "Reduced 20%, Now Only $149." Find the original
price of the media player.
Answer: $186.25
Step-by-step explanation:
To find the original price of the Digital Media Player before the 20% reduction, you can follow these steps:
1. Understand the discount:
A 20% reduction means the item is sold for 80% of its original price (100% - 20% = 80%).
2. Set up the equation to represent this situation:
Let the original price be \( P \). If the player is marked down by 20%, then it is now being sold for 80% of its original price. So we can write the following equation:
\[ 0.80 \cdot P = 149 \]
3. Solve for \( P \) (the original price):
To find the original price, divide the reduced price by 0.80 (which represents the 80% it is now being sold for).
\[ P = \frac{149}{0.80} \]
4. Calculate the result:
\[ P = \frac{149}{0.80} \]
\[ P = 186.25 \]
So the original price of the Digital Media Player was $186.25.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A new car depreciates at a rate of 15% per year. What is the expected value of a $25,000 car after 5 years (rounded to nearest whole dollar)?
Answer:
$18.750
Step-by-step explanation:
Answer: B) $11,093
Step-by-step explanation:
[tex]\text{The formula for depreciation is: }\\EV=P(1-r)^t\\\\\bullet EV=expected\ value\\\bullet P=principal\ \text{(original value)}\\\bullet r=rate\ of\ depreciation\\\bullet t=time\ \text{(in years)}\\\\\\\text{The given values are: }\\\bullet P=\$25,000\\\bullet r=15\%\quad (0.15)\\\bullet t=5\\\\\\EV=25,5000(1-0.15)^5\\.\quad =25,000(0.85)^5\\.\quad =25,000(0.443705)\\.\quad =\large\boxed{11,092.63}[/tex]
Ted's debt is 14 less than half of Mike's debt. If we let w represent Mike's debt, write an algebraic expression for Ted's debt.
Ted's debt can be expressed as 2w - 28
Data;
Mike debt = wTed's debt = xAlgebraic ExpressionThis is a mathematical expression written to represent word problems.
Given that Ted's debt is 14 less than half of Mike's debt and Mike's debt is represented as w.
Let x represent Ted's debt
[tex]x = \frac{w}{2} - 14\\ x = 2w -28[/tex]
The expression can be written as 2w - 28
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Please please help me
Answer:
Linear
Step-by-step explanation:
It is not quadratic or exponential since the term to term sequence is +2.
- 5 ⇔ -3
( Adding 2 )
- 3 ⇔ -1
( Adding 2 )
- 1 ⇔ 1
( Adding 2 )
The manager of a warehouse would like to know how many errors are made when a product’s serial number is read by a bar-code reader. Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.
What is the mean and standard deviation for these six samples?
Mean: 20.5
Standard Deviation: 11.5
The mean is the total of the numbers divided by the amount of numbers. So, add 36 + 14 + 21 + 39 + 11 + 2 to get 123. Now, divide 123 by 6 to find that the mean is 20.5.
The standard deviation is the mean of the distances from the numbers to the mean. So, find the distance from the mean for each number. You get 15.5, 6.5, 0.5, 18.5, 9.5, and 18.5. Find the mean of these distances. Start by adding them together to get 69, then divide that by 6 to get a standard deviation of 11.5.
Answer with Step-by-step explanation:
Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors
Mean=(Sum of all observations)/(Total number of observations)
=(36+14+21+39+11+2)/6
= 123/6
= 20.5
Standard deviation is the square root of mean of squares of deviation around mean
Deviation around mean:
36-20.5, 14-20.5, 21-20.5, 39-20.5, 11-20.5, and 2-20.5
15.5,-6.5,0.5,18.5,-9.5 and -18.5
Square of deviations:
240.25,42.25,0.25,342.25,90.25 and 342.25
Mean of square of deviations
=(240.25+42.25+0.25+342.25+90.25+342.25)/6
=176.25
square root of mean of deviations= [tex]\sqrt{176.25}=13.28[/tex]
Hence, Standard deviation=13.28
and Mean=20.5
If f(x)=2x+9, then f(-1)= _____
Answer:
f(-1) = 7
Step-by-step explanation:
Put -1 where x is and do the arithmetic.
f(-1) = 2(-1) +9 = 7
What is the y-value of the vertex of 4x2 + 8x - 8?
Answer:
-12
Step-by-step explanation:
To put the equation into vertex form, you can factor out the leading coefficient, then add and subtract a value equal to the square of half the x-coefficient (inside parentheses).
= 4(x^2 +2x) -8
= 4(x^2 +2x +1) -8 -4
= 4(x +1)^2 -12
The y-value of the vertex is -12.
The answer would be -12
how many solutions are there to the equation below?
8 (x-3) = 8x-24
Answer:
infinite number of solutions
Step-by-step explanation:
Given
8(x - 3) = 8x - 24 ← distribute left side
8x - 24 = 8x - 24
The expressions on both sides are equal
Hence any real value of x is a solution
That is there are an infinite number of solutions
Petey calculated |5+13i|
Answer:
[tex]|5+13i|=\sqrt{194}[/tex]
Step-by-step explanation:
The given expression is [tex]|5+13i|[/tex].
This is a complex number expression.
The absolute value of the complex number means the magnitude of the complex number.
Recall that;
[tex]|a+bi|=\sqrt{a^2+b^2}[/tex]
This implies that:
[tex]|5+13i|=\sqrt{5^2+13^2}[/tex]
[tex]|5+13i|=\sqrt{25+169}[/tex]
[tex]|5+13i|=\sqrt{194}[/tex]
Write an inequality to represent the amount of money charged per lawn, the cost of the lawnmower and the profit.
Thelma and Laura start a lawn-mowing business and buy a lawnmower for $225. They plan to charge $15 to mow one lawn. They would like to earn a profit of at least $750
Answer:
50
Step-by-step explanation:
Divided $225 divided by $15 which equal $15 then divided $750 divided by 15 which equal $50.
Thelma and Laura need to mow at least 65 lawns to make a profit of $750 after accounting for the $225 cost of the lawnmower. They must charge $15 per lawn to meet this goal.
Explanation:Let's define x as the number of lawns mowed. Thelma and Laura charge $15 per lawn mowed, so the total money they make through mowing lawns is $15x. They initially spent $225 for a lawnmower, and they want to make a profit of at least $750. Profit is calculated as revenue (money made) minus costs, so we have the inequality $15x - $225 >= $750. Simplify this inequality to get x >= 65. Therefore, they need to mow at least 65 lawns in order to make their desired profit.
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Please help me out please
if your teacher allows the pi symbol then your answer is 2513. if your teacher requires you to use 3.14 for pi then your answer is 2512. basically you use the Pythagorean theorem to find the height, and then plug the height (24) and the radius which is half the diameter (10) into the equation to find the volume of the cone. if you have any other questions about it please ask! hope this helps:)
Please help me out :)
Answer:
[tex]\frac{\sqrt{17} }{7}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
sinx = [tex]\sqrt{1-cos^2x}[/tex]
Note that ([tex]\frac{4\sqrt{2} }{7}[/tex])² = [tex]\frac{32}{49}[/tex]
sinΘ = [tex]\sqrt{1-(32/49)}[/tex]
= [tex]\sqrt{\frac{17}{49} }[/tex] = [tex]\frac{\sqrt{17} }{7}[/tex]