Answer:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
Step-by-step explanation:
We assume that the function of interest is:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
Use the appropriate double-angle formulas to rewrite the numerator and denominator of the expression given below. For the denominator, use the double-angle formula that will produce only one term in the denominator when it is simplified.
1+ Cos2x/ Sin2x = 1+ (____)/____
= _____ / _____
The expression from the previous step then simplifies to cot x using what?
a. Even-Odd Identity
b. Quotient Identity
c. Pythagorean Identity
d. Reciprocal Identity
Answer:
x=1
Step-by-step explanation:
1+1+2x+2x= 6
1+1=2
2x+2x=4x
2+4x=6
x=1
help i will give you brailenst
how do you find the x- and y-intersepts of an equation
Answer:
To find the x-intercept, simply plug in the value y = 0 into your equation and then solve for x. To find the y-intercept, plug in x = 0 and solve for y.
Categorical independent variables are _____. The independent variables must all be categorical (nonmetric) to use ANOVA
Answer:
Categorical independent variables are ___FACTORS__
The independent variables that are categorial should be factors.
What are the factors?In terms of mathematics, factor represents the no of algebraic expression where it split the other number that contains the zero remainder. As the factor of 12 should be 3 and 4. So based on this, the independent variables that are categorical should be considered as the factors.
Therefore, we can conclude that The independent variables that are categorial should be factors.
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what's the answer for this?
Answer:
6.4 miles
Step-by-step explanation:
Use pythogoras theorem here:
? ²= 5² + 4² =
?² = 25 + 16=
?²= 41
?= √41
? = 6.4
You don't need to thank me, I hope this helped
Answer:
Let d represent the distance from home to school
To find d we use the formula for Pythagoras theorem
That's
a² = b² + c²
Where a is the hypotenuse or the longest side
From the question
d is the hypotenuse
So we have
d² = 4² + 5²
d² = 16 + 25
d² = 41
d = √41 miles or 6.403 milesHope this helps you
Which equation describes the line graphed above?
Answer:
D: y = 2/3x + 4
Step-by-step explanation:
hope this helps :)
Given ABCD is a parralelogram choose and label approproate coordinates for A, B, C, and D, and prove that the opposite sides of ABCD are congruent. point A is (0,0) point B is (10,0) point C is (12,7) and point D is (3,7)
Answer:
proved: see explanation below
Step-by-step explanation:
The parallelogram ABCD has cordinates point A is (0,0) point B is (10,0) point C is (12,7) and point D is (3,7).
For the opposite sides of ABCD to be congruent, the slope of the opposite sides would be equal
If AB // CD, BC // AD, it’s a parallelogram.
If slope of AB = CD, BC = AD then it’s a parallelogram.
slope = Δy/Δx
slope AB = (0-0)/(10-0) = 0
slope BC = (7-0)/(12-10) = 7/2
slope CD = (7-7)/(12-3) = 0
slope DA = (0-7)/(0-3) = 7/3
slope DA is supposed to be equal to slope BC
It means the coordinate of D is (2,7)
slope DA becomes= (0-7)/(0-2) = 7/2
Therefore it would be proved that the opposite sides of ABCD are congruent as two pair of slopes are equal
Given the graph of the circle find the equation
Answer:
(x + 4)² + (y + 1)² = 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = )- 4, - 1) and r = 2 , thus
(x - (- 4))² + (y - (- 1))² = 2² , that is
(x + 4)² + (y + 1)² = 4 ← equation of circle
The equation of the circle will be (x + 4)² + (y + 1)² = 4.
What is a circle?The circle is at equidistant of points drawn from the center. The radius of a circle is the distance between the center and the circumference.
A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x – h)² + (y – k)² = r²
From the diagram, the center of the circle is at (-4, -1) and the radius of the circle is 2 units.
Then the equation of the circle will be
(x + 4)² + (y + 1)² = 2²
Simplify the equation, according to the problem.
(x + 4)² + (y + 1)² = 4
The equation of the circle will be (x + 4)² + (y + 1)² = 4.
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A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.65 lb, the mean of all of the weights is x=2.135 lb, and the standard deviation of the weights is s=2.316 lb. a. What is the difference between the weight of 5.65 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.65 lb to a z score. d. If we consider weights that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the weight of 5.65 lb significant?
Answer:
Explained below.
Step-by-step explanation:
Let the random variable X represent the weights (lb) of plastic discarded by households.
It is provided that the mean weight is, [tex]\bar x=2.135\ \text{lb}[/tex] and the standard deviation of the weights is, [tex]s=2.316\ \text{lb}[/tex].
(a)
Compute the difference between the weight of 5.65 lb and the mean of the weights as follows:
[tex]d=5.65 - \bar x\\\\d=5.65-2.135\\\\d=3.515[/tex]
Thus, the difference is 3.515 lb.
(b)
Compute the number of standard deviations as follows:
[tex]\text{Number of Standard Deviation}=\frac{d}{s}=\frac{3.515}{2.316}=1.518[/tex]
Thus, the number of standard deviation is 1.518.
(c)
Compute the z-score for the weight 5.65 lb as follows:
[tex]z=\frac{a-\bar x}{s}=\frac{5.65-2.135}{2.316}=1.517703\approx 1.52[/tex]
Thus, the z-score is 1.52.
(d)
The z-score for the weight 5.65 lb is 1.52.
This z-score lies in the range -2 and 2.
Thus, the weight of 5.65 lb is neither significantly low nor significantly high.
Statistics students in Oxnard College sampled 10 textbooks in the Condor bookstore, and recorded number of pages in each textbook and its cost. The bivariate data is shown below, Number of Pages ( x ) Cost( y ) 526 52.08 625 59 589 56.12 409 25.72 489 34.12 500 53 906 78.48 251 26.08 595 50.6 719 68.52 A student calculates a linear model y = x + . (Please show your answers to two decimal places) Use the model above to estimate the cost when number of pages is 563 Cost = $ (Please show your answer to 2 decimal places.)
Answer:
y = -0.85 + 0.09x; $49.82
Step-by-step explanation:
1. Calculate Σx, Σy, Σxy, and Σx²
The calculation is tedious but not difficult.
[tex]\begin{array}{rrrr}\mathbf{x} & \mathbf{y} & \mathbf{xy} & \mathbf{x^{2}}\\526 & 52.08 & 27394.08 & 276676\\625& 59.00 & 36875.00 &390625\\589 & 56.12 & 33054.68 & 346921\\409 & 25.72 & 10519.48 & 167281\\489 & 34.12& 16684.68 & 293121\\500 & 53.00 & 26500.00 &250000\\906 & 76.48 & 71102.88 & 820836\\251 &26.08 & 6546.08 & 63001\\595 & 50.60 & 30107.00 & 354025\\719 & 68.52 & 49265.88 & 516961\\\mathbf{5609} & \mathbf{503.72} &\mathbf{308049.76} & \mathbf{3425447}\\\end{array}[/tex]
2. Calculate the coefficients in the regression equation
[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{503.7 \times 3425447 - 5609 \times 308049.76}{10 \times 3425447- 5609^{2}}\\\\= \dfrac{1725466163 - 1727851103.84}{34254470 - 31460881} = -\dfrac{2384941}{2793589}= \mathbf{-0.8537}[/tex]
[tex]b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{3080498 - 2825365.48}{2793589} = \dfrac{255132}{2793589} = \mathbf{0.09133}[/tex]
To two decimal places, the regression equation is
y = -0.85 + 0.09x
3. Prediction
If x = 563,
y = -0.85 + 0.09x = -0.85 + 0.09 × 563 = -0.85 + 50.67 = $49.82
(If we don't round the regression equation to two decimal places, the predicted value is $50.56.)
Analyze the diagram below and complete the instructions that follow. find angle wvx
Answer:
60 degrees
Step-by-step explanation:
it has to be.
Answer:
it's D
Step-by-step explanation:
got it right edge 2021
The height of an object dropped from the top of a 144 foot- building is given by h(t)= -16 square +144. How long will it take the object to hit the ground?
Answer:
3 seconds
Step-by-step explanation:
0 = -16x² + 144
-144 = -16x²
9 = x²
3 = x
The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points does the image cross the x-axis?
Answer:
x = -8 and x = 4
Step-by-step explanation:
given
f(x) = (x+8) (x - 4)
recall that at any point on the x-axis, y = 0 [i.e f(x) = 0]
hence to find where the graph crosses the x-axis, we simply substitue f(x) = 0 into the equation and solve for x
f(x) = (x+8) (x - 4)
0 = (x+8) (x - 4)
Hence
either,
(x+8) = 0 ----> x = -8 (first crossing point)
or
(x-4) = 0 ------> x = 4 (second crossing point)
Hence the graph crosses the x-axis at x = -8 and x = 4
Answer:
A (-8, 0) and (4, 0)
Gamal spent $12.50 at the book store. The difference between the amount he spent at the video game store and the amount he spent at the book store was $17. The equation d minus 12.50 = 17 can be used to represent this situation, where d is the amount Gamal spent at the video game store. Which equation is an equivalent equation that can be used to find the amount Gamal spent at the video game store?
Answer:
d - 12.50 = 17
add 12.50 to both sides to get d alone.
d = 12.50 + 17
Answer:
It's B d= 17 + 12.50
Step-by-step explanation:
Got it right on edg
At the start of 2010 karim had rm5000
Step-by-step explanation:
Tell the whole question please
A newsletter publisher believes that 71q% of their readers own a personal computer. Is there sufficient evidence at the 0.010.01 level to refute the publisher's claim.
Required:
State the null and alternative hypotheses for the above scenario.
Answer:
Null - p= 71%
Alternative - p =/ 71%
Step-by-step explanation:
The null hypothesis is always the default statement in an experiment. While the alternative hypothesis is always tested against the null hypothesis.
Null hypothesis: 71% of their readers own a personal computer- p = 71%
Alternative hypothesis: Not 71% of their readers own a personal computer - p =/ 71%
the answer choices are
sec y= b/6
sec y=6a
sec y=6b
sec y= 6/b
Answer:
sec y=6/b yw
Step-by-step explanation:
the price of apples at three different stores is shown below. Store R sells apples for $1.20 per pound. Store S sells 4 pounds of apples for $5.00. Store T sells 3 pounds of apples for $3.48.
which of these is a true statemnt
Store R sells apples at the lowest rate
Store T sells apples at the lowest rate
Store s charges a lower rate than Store T
Store t charges the same rate as Store R
Store T sells apples at the lowest rate
Step-by-step explanation:
1st We need to make every statement in order of 1 pound. Then We will easily find the lowest rate of apple.
i) R sell 1.20 $ per pound.
ii) S sell 4 pounds for 5$
i.e S sell 1 pound for 5/4 = 1.25$
iii) T sell 3 pound for 3.48$
i.e T sell 1 pound for 3.48/3 = 1.16$
Analysing the above data I get,
Store T sells apples at the lowest rate
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases.
a. Central area = 0.95, df = 10
b. Central area = 0.95, df = 20
c. Central area = 0.99, df = 20
d. Central area = 0.99, df = 60
e. Upper-tail area = 0.01, df = 30
f. Lower-tail area = 0.025, df = 5
Answer:
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
Step-by-step explanation:
In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;
We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.
The following are the answers obtained from the table;
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
URGENT !!!!
A greengrocer has 38 lb of carrots when he opens on Monday morning. During the dayhe gets a delivery of 60 lb of carrots and sells 29 lb of the carrots. How many pounds ofcarrots are left when he closes on Monday evening?
He has 69 lb of carrots left when he closes
If $y^2= 36$, what is the greatest possible value of $y^3$?
Answer:
216
Step-by-step explanation:
y = ±√36 = ±6
y³ = (±6)³ = ±216
The largest of these values is 216, the greatest possible value of y.
A survey found that 39% of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of n
Answer:
61% i think
Step-by-step explanation:
if you have 39% and it 10 out of a 100 well you have a 39/100 and then n would be 61/100 so 61%
0.39 is the value of n for the video games on their smartphones. Thus option A is correct.
What is probability?The mathematical discipline known as probability specializes in determining the possibility of an event occurring. Probability, which expresses the probability of a risk, is calculated by dividing the total possible combinations by the frequency of favorable events. Composite reliabilities vary from 0 to 1, with 1 representing certainty and 0 representing hesitation.
In a binomial distribution, p stands for the success probability. It refers to the likelihood that a certain number of experiments will result in favorable results. For all binomial attempts, the probability of winning stays constant.
This suggests that there will be a distribution of 39/100. The result after the calculation will be 0.39. Therefore, option A is the correct option.
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The question is incomplete, the complete question will be :
A survey found that 39 % of all gamers play video games on their smartphones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smartphones. What is the value of n ?
A) 0.39
B) 0.10
C) 10
D) x
A model of a car is 6.3 in. Long The scale of the model is the actual car 1:30 what is the length of the actual car to nearest foot
21ft
12ft
16Ft
19ft
Answer:
16Ft
Step-by-step explanation:
Well the following ration compares the sI’ve of a model car to a normal car,
1:30
We can make the following fractions,
[tex]\frac{1}{30} = \frac{6.3}{x}[/tex]
We cross multiply.
[tex]x = 189[/tex]
To make this into inches we do,
189 / 12 = 15.75,
or 16 to the nearest foot.
Help, no time left; almost !
Answer:
x = 50
Step-by-step explanation:
Since the triangle has 2 congruent sides then it is isosceles, thus the base angles are congruent, that is x and x
The sum of the angles in a triangle = 180°, thus
x + x + 80 = 180
2x + 80 = 180 ( subtract 80 from both sides )
2x = 100 ( divide both sides by 2 )
x = 50
can someone help me with this question?l
Answer:
1. 32x³ - 25x² + 35x2. 6x - 11y + 14z - 7Step-by-step explanation:
1).(4x³ - 5x² + 3x ) - 4(5x² - 7x³ - 8x)
Remove the brackets and simplify.
We have
4x³ - 5x² + 3x - 20x² + 28x³ + 32x
Group like terms and simplify
That's
4x³ + 28x³ - 5x² - 20x² + 3x + 32x
We have the final answer as
32x³ - 25x² + 35x2).- 3 - ( 4x + 3y - 2z ) - 4 + 2( 5x - 4y + 6z)
Remove the brackets and simplify
That's
- 3 - 4x - 3y + 2z - 4 + 10x - 8y + 12z
Group like terms and simplify
- 4x + 10x - 3y - 8y + 2z + 12z - 3 - 4
We have the final answer as
6x - 11y + 14z - 7Hope this helps you
Help thx!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Answer E
Step-by-step explanation:
If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.
Use the given information to find the p-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With Upper H1: p≠0.377, the test statistic is z=3.06.
a. 0.0022; fail to reject the null hypothesis
b. 0.0011; reject the null hypothesis
c. 0.0022; reject the null hypothesis
d. 0.0011; fail to reject the null hypothesis
Answer:
Option c: 0.0022; reject the null hypothesis
Step-by-step explanation:
Using a p value calculator, with a z score of 3.06 at 0.05 level of significance for a two tailed test, the p-value is 0.002213. This value is lower than 0.05 thus the result is significant we will reject the null hypothesis.
To calculate the p value by hand, we do this
The test statistic is 3.06. Since the test possesses a not equal to alternative, we look up the test statistic on the z table find the corresponding probability. Thus we have 3.06 - on the z table - 0.99889
Then we subtract from 1 and double it
1-0.99889 = 0.00111 x 2 = 0.0022.
Find the number of unique permutations of the letters in each word. SIGNATURE RESTAURANT
Answer:
Ok, we have two words:
"Signature"
The letters are: "S I G N A T U R E"
9 different letters.
Now, we can make only words with 9 letters, so we can think on 9 slots, and in each of those slots, we can input a letter of those 9.
For the first slot, we have 9 options.
For the second slot, we have 8 options (because on is already taken)
For the second slot, we have 7 options and so on.
Now, the total number of combinations is equal to the product of the number of options in each selection:
C = 9*8*7*6*5*4*3*2*1 = 362,880.
Now, our second word is Restaurant.
The letters here are " R E S T A U N" such that R, T and A appear two times each, so we have a total of 10 letters and 7 unique letters.
So first we do the same as beffore, 10 slots and we start with 10 options.
The total number of combinations will be:
C = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
A lot of combinations, but we are counting only unique words.
For example, as we have two R, we are counting two times the word:
Restaurant (because we could permutate only the two letters R and get the same word)
So we must divide by two for each letter repeated.
we have 3 letters repeated, we divide 3 times by 2.
C = ( 3,628,800)/(2*2*2) = 453,600
What is the sum of the series? ∑j=152j Enter your answer in the box.
Answer:
Hope this is correct
HAVE A GOOD DAY!
The function y = sin^?1(3x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative. d dx [f(g(x))] = f '(g(x))g'(x) For the given function sin^?1(3x + 1), the "inside" function is 3x + 1 and the "outside" function is f(x) = arcsin(x).
Recall that the derivative of y = sin?1(x) is y' =__________?
Answer:
dy/dx = 3/√1-(3x+1)²
Step-by-step exxplanation:
Given the inverse function y = sin^-1(3x+1), to find the derivative of the expression, we will use the chain rule as shown;
Let u = 3x+1 ...1
y = sin⁻¹u ...2
From equation 1, du/dx = 3
from equation 2;
Taking the sin of both sides;
siny = sin(sin⁻¹u)
siny = u
u = siny
du/dy = cosy
dy/du = 1/cosy
from trig identity, cos y = √1-sin²y
dy/du = 1/√1-sin²y
Ssince u = siny
dy/du = 1/√1-u²
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/√1-u² * 3
dy/dx = 3/√1-u²
Substituting u = 3x+1 into the final equation, we will have;
dy/dx = 3/√1-(3x+1)²