The limit of the function [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)] when x tends to 1 is - 3 / 2.
How to find the limit of a function
In this problem we must determine the limit of a function, that is, the value to which the function goes when x tends to 1. This can be done by means of limit properties for polynomial and trigonometric limits.
First, write the limit:
\(\lim_{x \to 1}\) [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)]
Second, use limit properties and algebra properties:
\(\lim_{x \to 1}\) [[3 · cos (2 - 2x) - 3 + 3 - 3 · x] / (2 · x - 2)]
\(\lim_{x \to 1}\) [[3 · cos (2 - 2x) - 3] / (2 · x - 2)] + \(\lim_{x \to 1}\) [(3 - 3 · x) / (2 · x - 2)]
(3 / 2) · \(\lim_{x \to 1}\) [[1 - cos (1 - x)] / (1 - x)] + (3 / 2) · \(\lim_{x \to 1}\) [(1 - x) / (x - 1)]
Third, use polynomial and trigonometric limits:
(3 / 2) · 0 + (3 / 2) · (- 1)
Fourth, simplify the result:
- 3 / 2
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what is the volume of the figure
Step-by-step explanation:
Volume = width × length × height
= (5×8×22) + (5×12×8)
= ....... m³
one way to display formulas is by pressing this key combination. [CTRL][ ]
To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).
What key combination can be used to display formulas?The key combination [Ctrl]+[] is used to display formulas.
This is a useful feature for checking and editing formulas without altering the calculated values.
By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.
This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.
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does anybody know how to do this?
Answer:
KJ = 22
Step-by-step explanation:
(See attachment below)
Data obtained from a number of women clothing stores show that there is a (linear) relationship between sales (y, in dollars) and advertising budget (x, in dollars). The regression equation was found to be
y = 5000+ 7.25x
where y is the predicted sales value (in dollars). If the advertising budgets of two women clothing stores differ by $30,000, what will be the predicted difference in their sales?
Select one:
a. $150,000,000
b. $222,500
c. $5,000
d. $7250
e. $217,500
Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.
Given a regression equation is y = 5000 + 7.25x, where y is the predicted sales value (in dollars) and x is advertising budget (in dollars).To find the predicted difference in sales of two stores which differ by $30,000 in advertising budget. Here, the slope of the line is 7.25. This means that for every dollar increase in advertising budget, sales will increase by $7.25. Therefore, a $30,000 difference in advertising budget will lead to a difference in sales of:7.25 × 30,000 = 217,500Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.
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what is the horonzontial distance between the two points(3,4) and (8,4)
Answer:
Distance = 5.099
Step-by-step explanation:
Consider the graphs of the following lines.
3x - 5y = 2
3x + 5y = -2
Find the slope m of each line.
3x - 5y = 2
m₁ =
3x + 5y = -2
m2 =
8.6A.
4
Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.
What is slope of the line?The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as
Line slope is a measure of the steepness or direction of a line in the coordinate plane.
m = Δy/Δx
where,m is the slope
Given,
equations of the line
3x - 5y = 2
Moving 3x to RHS
-5y = -3x + 2
y = (3/5)x - 2/5
comparing with slope intercept equation of the line y = mx + c
slope m₁ = 3/5
Now, equation
3x + 5y = -2
moving 3x to RHS
5y = -3x - 2
y = (-3/5)x - 2
comparing with slope intercept equation of the line y = mx + c
slope m₂ = -3/5
Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.
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Help plss!!
(20 points!!)
Answer:Its only 10 points :( 206 is the answer i think GL:)
Step-by-step explanation:Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 +S2 + S3)L + bh
scam:/ i want 20:(:(:(
How do you write an equation in function form?
Answer: Writing an equation in function form. You want to remove the x term from the side y is on and move it to the other side of the equal sign. To do this either add or subtract the x term from both sides. Next divide by the coefficient of the y term. Now your equation is in function form.
explanation: like 57 * Y =142500
what is the number for Y if u don't know u could divided 142500 by 57 and it equals? 2500;) hope I helped
decimals from least to greatest please help put in order. 2.2, 2.15, 2.2012, 2.501
Answer: 2.15, 2.2, 2.2012, 2.501
Answer:
the answer is 2.15, 2.2, 2.2012, 2.501.
Step-by-step explanation:
just help please it's 7th grade supposedly very easy
Answer: P(Quarter & Penny): 9/100
p(Two pennies): 9/25
Step-by-step explanation:
There are 20 coins in the bag, so you have a 3/20 chance of getting a quarter, 5/20 chances of getting a dime and 12/20 chance of getting a penny on each draw if the coins are always replaced.
Im this situation, you can simplify the fractions, the
Multiply the chance of each independent event times the chance of the next independent event.
3/20 × 3/5 = 9/100 for the quarter and the penny
3/5 × 3/5 = 9/25 for the two pennies
the term ________ is best described as a stream of equal installments made at equal time intervals.
The term annuity is best described as a stream of equal installments made at equal time intervals.
An annuity is a term used to define a series of payments of equal size at equal intervals. Equal time intervals such as months, quarters, or years, and uniform payments are the two characteristics that make a series of payments an annuity. Therefore, a series of payments can be an annuity however all series of payments are not annuities. If the series of payments is of different values or at different intervals, it is not considered to be an annuity. An annuity that provides for payments for the remainder of a person's lifetime is known as a life annuity.
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For a school project two students shona and miguel record the number of text messgaes each of them sent each day for 60- day period. the box plots summarize the record data
The range of the data for Shona and Miguel will be 35 and 30, while the median of the data will be 40 and 42.5.
What is a boxplot?A boxplot is a visual representation of a data set's dispersion and centers.
The interquartile range and the mean of the data set are two examples of spread measures. The mean, average, and median are examples of center measures.
The data set of the Miguel is;
25,30,35,40,45,50,55
The median of the data is;
\(\rm Median =( \frac{n+1}{2}) ^{th} term \\\\ Median =( \frac{7+1}{2} )^{th} term \\\\ Median = 4 ^{th} term \\\\ Median = 40\)
Shona's data is;
25,30,35,40,45,50,55,60
The median of Miguel's data is;
\(\rm Median_{shona} = \rm \frac{40+45}{2} \\\\ Median_{shona} =42.5\)
The range of Miguel's data is;
⇒ 55-25
⇒ 30
The range of Shona's data is;
⇒60-25
⇒35
Hence, the median of the data for Shona and Miguel will be 40 and 42.5 and the range of the data for Shona and Miguel will be 35 and 30.
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Which function has zeros of -8, 1, and 3? A. y = (x − 3)(x + 8)(x − 1) B. y = (x + 1)(x − 8)(x + 3) C. y = x(x + 8)(x − 3) D. y = x(x + 3)(x − 8)
Answer:
A
Step-by-step explanation:
In each binomial, just flip the sign before the constant, and that number is a zero.
So for example if you have (x+1), a zero would be -1, if you have (x-8), a zero would be 8, etc.
The zeros of a function are the values of x, when the function equals 0.
The function that has zeros of -8, 1 and 3 is: (a) \(\mathbf{ y = (x - 3)(x + 8)(x - 1)}\)
The zeros are given as:
\(\mathbf{Zeros = -8, 1, 3}\)
Rewrite as:
\(\mathbf{x = -8, 1, 3}\)
Equate to 0
\(\mathbf{x +8 = 0,\ x - 1 = 0,\ x - 3 = 0}\)
Multiply the equations
\(\mathbf{(x +8) \times (x - 1) \times (x - 3) = 0\times 0 \times 0}\)
\(\mathbf{(x +8) \times (x - 1) \times (x - 3) = 0}\)
Express as a function
\(\mathbf{y = n(x +8) \times (x - 1) \times (x - 3) }\)
Where:
\(\mathbf{n \ne 0}\)
The above equation represents functions that have zeros of -8, 1, and 3
By comparing the options, we have:
\(\mathbf{ y = (x - 3)(x + 8)(x - 1)}\) is \(\mathbf{y = n(x +8) \times (x - 1) \times (x - 3) }\), where n = 1
Hence, the function that has zeros of -8, 1 and 3 is:
(a) \(\mathbf{ y = (x - 3)(x + 8)(x - 1)}\)
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Find the value of n so that the following points will lie on a line. (3,5), (−1,3), and (7,n)
Answer:
We get value of n=7
Step-by-step explanation:
If points lie on same line, they have same slope.
First we will find slope of points (3,5), (−1,3)
Using formula: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)
We have \(x_1=3, y_1=5, x_2=-1, y_2=3\)
Finding slope
\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{3-5}{-1-3} \\Slope=\frac{-2}{-4} \\Slope=\frac{1}{2}\)
Using slope 1/2 and points (−1,3), and (7,n) we can find value of n
\(Slope=\frac{y_2-y_1}{x_2-x_1}\\\frac{1}{2} =\frac{n-3}{7-(-1)} \\\frac{1}{2} =\frac{n-3}{7+1} \\\frac{1}{2} =\frac{n-3}{8}\\Cross\:Multiply\\1(8)=2(n-3)\\8=2n-6\\2n=8+6\\2n=14\\n=\frac{14}{2}\\n=7\)
So, we get value of n=7
Find the slope between the
following points:
(-3,3), and (5, 10)
Answer:
7/8
Step-by-step explanation:
I got it right
Answer:
7/8
Step-by-step explanation:
cuz
What are the 2 theoretical quantities of ANOVA?
The two theoretical quantities of ANOVA (Analysis of Variance) are:
1. Between-group variance.
2. Within-group variance:
1. Between-group variance.
This is the variance that can be attributed to differences between the group means.
It is calculated by comparing the mean of each group to the overall mean of all the data points.
The larger the between-group variance, the more likely there are significant differences between the groups.
2. Within-group variance:
This is the variance that can be attributed to differences within each group, i.e., the individual differences among the data points in each group.
It is calculated by comparing the individual data points in each group to their respective group mean.
The smaller the within-group variance, the more likely the groups are homogeneous.
In ANOVA, these two quantities are compared using an F-ratio.
If the between-group variance is significantly larger than the within-group variance, it indicates that there are significant differences between the group means, and the null hypothesis can be rejected.
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Which expression can be used to find the total amount in an account after three years, if the initial deposit is $2,000, and the annual simple interest rate is 2%?
A. 2,000 x 0.02 x 3
B. 2,000 x (2,000 x 0.02 x 3)
C. 2,000 x (2,000 x 2 x 3)
D. 2,000(1 x 0.02)^3
Answer:
Below
Step-by-step explanation:
Actually....NONE of those answers would show the total amount after 3 years
the correct option would be 2000 + (2000*.02 *3) a PLUS sign rather than a multiplication sign ....so the answer MIGHT be B if you transcribed it incorrectly
A polynomial f and a factor of f are given. Factor f completely.
f(x) = 3x³ + 13x²+2x-8; x + 4
Answer:
(x+4)(3x-2)(x+1)
Step-by-step explanation:
Walter needs 40 feet of cable to help secure the backyard tree house that he made for
his family. Store A sells the cable for $1.10 per foot. Store B sells the cable for $3.06 per
yard. From which store should Walter buy the cable and how much will he save by
buying it from that store?
Answer:
Store B
$3.20
Step-by-step explanation:
Store A:
$1.10(40)=$44
Store B:
first let's convert yards to feet
3ft=1yard
$3.06/3=$1.02 per foot
$1.02(40)=$40.80
You would save more by shopping at Store B
to find savings: Store A - Store B= $44-$40.80=$3.20
Complete the table and then graph the function
Answer:
(-8,2) ; (-7,3) ; (-6,4) ; (-5,5) ; (-4,6)
Step-by-step explanation:
just subtract x from 10
ex
y=x+10
x=-8
y=-8+10
y=10-8
y=2
x=-8 y=2
(-8,2)
Can someone really help me please
Answer:
45-4=41 square units
Step-by-step explanation:
full shape area = 9x5=45
cut rectangle area = 4x1=4
blue shape area = 45-4=41
can someone help me with this i ready i will give brainlest:)
Answer:
12 ft^2
Step-by-step explanation:
Base is the bottom..... area = 4 x 3 = 12 ft^2
PLEASE HELP WILL GIVE BRAINLIEST IF CORRECT
To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?
Answer:
Option (1)
Step-by-step explanation:
Diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 to 0.2 cm greater than 1.5 cm.
Let the diameter of the bolt = x cm
Then the value of x will be,
(1.5 - 0.2) cm < x < (1.5 + 0.2) cm
When we plot the possible measures of the diameter of the bolt on a number line,
Measures of x will be between 1.3 cm to 1.7 cm
Option (1) will be the answer.
Answer:
A
Step-by-step explanation:
Its pretty self explainatory, it tells you that the line has to be anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm, so if you look at the graphs A is the only one that maches with what the question in asking.
Please help I will mark brainliest- I already know it’s not the last two- please help!
Answer:
Traversable because it has exactly two odd nodes
Step-by-step explanation:
There is a rule that says it is traversable if it has exactly 2 odd nodes. The are other rule where it can be traversable is if has no odd nodes.
Also if we let the starting point be D and the ending point be B we can travel the network in such way that each edge is only traveled once which is the definition that the network is traversable.
So I will do this by starting at D, then travel to A using the outside edge, then travel to back to D using inside edge, then travel to C, then travel to B, then travel to A using outside edge, and then back to B from A using inside edge.
I got stuck at on a problem what is 3x+4+2x+5=34?
Given:
\(3x+2x=34-5-4\)
\(5x=29-4\)
\(5x=25\)
\(x=25\div5\)
Answer:
\(\bold{x=5}\)x = 5
Step-by-step explanation:Given: 3x+4+2x+5=34
first combine similar values,
3x + 2x and 4 + 5
5x + 9 = 34
time for substitution
5x + 9 - 9 = 34 - 9
5x = 25
divide by the value of x in this instance it is 5
5x = 25 / 5
x= 5
now to check we will plug in 5 for x
3(5) +4+2 (5) +5=34
15 + 4 + 10 + 5 = 34
19 + 15 = 34
34 = 34✓
Hope this helps, happy learning =D
the obtained value must be compared against which of the following? a. test value b. critical value c. expected value
d. observed value
The obtained value must be compared against the critical value. Hence, the correct option is b.
In hypothesis testing, the critical value is a threshold or cutoff point that is determined based on the chosen significance level (alpha level) and the distribution of the test statistic. It helps in determining whether to reject or fail to reject the null hypothesis.
After calculating the test statistic (such as z-score or t-statistic) from the observed data, it is compared to the critical value associated with the chosen significance level.
If the test statistic exceeds the critical value, it falls into the critical region, leading to the rejection of the null hypothesis.
If the test statistic is less than or equal to the critical value, it falls into the non-critical region, resulting in a failure to reject the null hypothesis.
Therefore, the obtained value must be compared against the critical value to make a decision in hypothesis testing. Hence, the correct answer is option b.
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Helpful conversions: 1 acre =43,560 square feet 1 hectare =10,000 square meters 1lb=454 grams 1 kg=2.2lbs=1000grams 1. Scouting for cover crop establishment in the field requires conversion of your massbased seeding rate (e.g., lbs/acre) to a population-based establishment rate (e.g., plants/f? ). Let's practice doing that. Convert the following seeding rates: a. Cereal rye - 60 ibs/acre = H seeds/square foot b. Crimson clover −15 kg/ha= H seeds/square meter 2. Convert the following population-based seeding rates to mass-based seeding rates. a. Oats −30 plants/square foot = Ibs seedlacre b. Hairy vetch −20 plants/square meter = kg seedsha 3. Your farm manager wants you to drill crimson clover seed, but the seed hasn't arrived yet and you don't know if it's coated or not. If the seed is not coated, the seeding rate is 20 blacre. Will you need to increase or decrease your seeding rate if the seed is coated?
Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.
To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:
a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.
b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.
To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:
a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.
b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.
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(1 point) For what values of the variable does the series converge? Use the properties of geometric series to find the sum of the series when it converges
Sum=
20+80x^2 + 320x^3 +1280x^4+......
domain=
(Give your domain as an interval or comma separated list of intervals; for example, to enter the region <-1 and 2 << 3, enter (- infinity,-1). (2.3))
The sum of the series is S = 20+80x^2 + 320x^3 +1280x^4+..... rewritten as S = 20 / (1 - 4x⁻¹) converges for he values |x⁻¹| < 1/4
To obtain what values of the variable the series converge and use the properties of the geometric series to find the sum of the series when it converges, we have to first look at the series given: 20 + 80x² + 320x³ + 1280x⁴ + .........Let's take the first three terms of the series: a₁ = 20a₂ = 80x²a₃ = 320x³
To find the ratio r, let's divide the second term by the first and the third term by the second:a₂/a₁ = (80x²)/20 = 4x²a₃/a₂ = (320x³)/(80x²) = 4x We notice that the ratio r is constant and equal to 4x⁻¹.
Now we can determine the conditions for which the series converges. Condition for the convergence of a geometric series:|r| < 1|r| = |4x⁻¹| < 1|r| = 4|x⁻¹| < 1|r| = |x⁻¹| < 1/4 Therefore, the domain of the series is the set of all x for which |x⁻¹| < 1/4. Since x cannot be zero, we exclude x = 0 from the domain. Then, the domain is obtained by taking the reciprocal of the inequality and inverting the sign:|x⁻¹| < 1/4⇔ - 1/4 < x < 1/4⇔ x ∈ (-1/4, 1/4)
Finally, we can use the formula for the sum of a finite geometric series to find the sum of the given series:S = a₁ (1 - rⁿ) / (1 - r)where n is the number of terms in the sum. Since we have an infinite series, we can take the limit as n approaches infinity:S = a₁ / (1 - r) = 20 / (1 - 4x⁻¹) for |x⁻¹| < 1/4Therefore, the sum of the series is S = 20 / (1 - 4x⁻¹) when the series converges for |x⁻¹| < 1/4.
Assuming that an artist has already recovered the money for his or her royalty advance how many songd would an indie artist need to sell on itunes to equal what an artist under a label would make for an album
Assuming that an indie artist has already recovered their royalty advance, the number of songs they need to sell on iTunes to equal the earnings of an artist under a label depends on several factors, such as royalty rates, distribution fees, and album pricing.
Typically, an artist under a label might receive around 15-20% royalties from album sales, while an indie artist may receive about 70% royalties from iTunes. However, the indie artist might also pay a distribution fee, which can be around 10%, leaving them with 60% net royalties.
To calculate the number of songs an indie artist needs to sell to match a labeled artist's earnings, divide the labeled artist's earnings by the indie artist's net royalty rate and multiply by the labeled artist's royalty rate.
For example, if a labeled artist earns $10,000 from an album, an indie artist would need to sell approximately ($10,000 / 60%) x 20% = $3,333.33 worth of songs on iTunes to achieve the same earnings.
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Please help thank you
Answer:
Step-by-step explanation:
Jared wrote the equation as,
k + (k + 1) + (k + 2) = 4k
Solution for k will be,
3k + 3 = 4k
4k - 3k = 3
k = 3
For k = 3, consecutive numbers will be → 3, 4, 5
Jared did not get the correct answer.Solution to this equation is k = 3, giving 3, 4, and 5 as three integers. However, 3 and 5 are not even integers. He should have used the equation k + (k + 2) + (k + 4) = 4k, which gives k = 6 and the correct answer is 6, 8, 10.