Answer:
Let's try (x+5) first. According to the Remainder Theorem, if (x+5) is a factor of the polynomial, the remainder is zero.
when x+5=0, x=-5
use synthetic division:
-5 I 1 7 11 5
I -5 -10 -5
----------------------
1 2 1 0
the remainder is 0, so (x+5) is a factor:
the result is (x+5)(x²+2x+1)
factor again: (x+5)(x+1)(x+1) is the final answer.
An object of mass 2kg is attached to a spring. A force of 5nt is applied to move the object 0.5m from its equilibrium position. The damping force of the object sliding on the table is int when the velocity is 0.25m/second. The object is pulled to the left until the spring is stretched lm and then released with the initial velocity of 2m/second to the right.
Set up an I.V.P. to describe the motion of the object and solve it, then state the amplitude function of the motion.
Answer:
[tex]\mathbf{x(t) = \dfrac{ \sqrt 5}{2}e^{-t} }[/tex]
Step-by-step explanation:
Given that:
mass of the object = 2 kg
A force of 5nt is applied to move the object 0.5m from its equilibrium position.
i.e
Force = 5 newton
Stretchin (x) =0.5 m
Damping force = 1 newton
Velocity = 0.25 m/second
The object is pulled to the left until the spring is stretched lm and then released with the initial velocity of 2m/second to the right
SOLUTION:
If F = kx
Then :
5 N = k(0.5 m)
where ;
k = spring constant.
k = 5 N/0.5 m
k = 10 N/m
the damping force of the object sliding on the table is 1 newton when the velocity is 0.25m/second.
SO;
[tex]C \dfrac{dx}{dt}= F_d[/tex]
[tex]C* 0.25 = 1[/tex]
C = [tex]\dfrac{1 \ N }{0.25 \ m/s}[/tex]
C = 4 Ns/m
NOW;
[tex]m \dfrac{d^2x}{dt^2}+ C \dfrac{dx}{dt}+ kx = 0[/tex]
Divide through by m; we have;
[tex]\dfrac{m}{m}\dfrac{d^2x}{dt^2}+ \dfrac{C}{m} \dfrac{dx}{dt}+ \dfrac{k}{m} x= 0[/tex]
[tex]\dfrac{d^2x}{dt^2}+ \dfrac{C}{m} \dfrac{dx}{dt}+\dfrac{k}{m}x= 0[/tex]
[tex]\dfrac{d^2x}{dt^2}+ \dfrac{4}{2} \dfrac{dx}{dt}+\dfrac{10}{2}x= 0[/tex]
[tex]\dfrac{d^2x}{dt^2}+ 2 \dfrac{dx}{dt}+5x= 0[/tex]
we all know that:
[tex]x(t) = Ae^{(\alpha \ t)}[/tex] ------ (1)
SO;
[tex]\alpha ^2 + 2\alpha + 5 = 0[/tex]
[tex]\alpha = \dfrac{-2 \pm \sqrt{(4)-(4*5)}}{2}[/tex]
[tex]\alpha = -1 \pm 2i[/tex]
Thus ;
[tex]x(t) = e^{-t}[A \sin (2t)+ B cos (2t)][/tex] ------------ (1)
However;
[tex]\dfrac{dx}{dt} = e^{-t}[A \sin (2t)+ B cos (2t)]+ 2e ^{-t} [A \cos (2t)- B \ Sin (2t)][/tex] ------- (2)
From the question ; we are being told that;
The object is pulled to the left until the spring is stretched 1 m and then released with the initial velocity of 2m/second to the right.
So ;
[tex]x(0) = -1 \ m[/tex]
[tex]\dfrac{dx}{dt}|_{t=0} = 2 \ m/s[/tex]
x(0) ⇒ B = -1
[tex]\dfrac{dx}{dt}|_{t=0} =- B +2A[/tex]
[tex]=- 1 +2A[/tex]
1 = 2A
A = [tex]\dfrac{1}{2}[/tex]
From (1)
[tex]x(t) = e^{-t}[A \sin (2t)+ B cos (2t)][/tex]
[tex]x(t) = e^{-t}[\dfrac{1}{2} \sin (2t)+ (-1) cos (2t)][/tex]
[tex]x(t) = e^{-t}[\dfrac{1}{2} \sin (2t)-cos (2t)][/tex]
Assuming;
[tex]A cos \ \phi = \dfrac{1}{2}[/tex]
[tex]A sin \ \phi = 1[/tex]
Therefore:
[tex]A = \sqrt{\dfrac{1}{4}+1}[/tex]
[tex]A = \sqrt{\dfrac{1+4}{4}}[/tex]
[tex]A = \sqrt{\dfrac{5}{4}}[/tex]
[tex]A ={ \dfrac{ \sqrt5}{ \sqrt4}}[/tex]
[tex]A ={ \dfrac{ \sqrt5}{ 2}}[/tex]
where;
[tex]\phi = tan ^{-1} (2)[/tex]
Therefore;
[tex]x(t) = \dfrac{\sqrt 5}{2}e^{-t} \ sin (2 t - \phi)[/tex]
From above ; the amplitude is ;
[tex]\mathbf{x(t) = \dfrac{ \sqrt 5}{2}e^{-t} }[/tex]
: Bobby's Burger Palace had its
grand opening on Tuesday,
They had 164 1/2 lb of ground
beef in stock. They had 18 1/4
Ib left at the end of the day.
Each burger requires 1/4 lb of
ground beef. How many
hamburgers did they sell?
Here is the feasible region.
28
А
52 + 8y 120
B
y 5
What are the coordinates of vertex A?
Enter your answer in the boxes
Answer:
A(8, 10)
Step-by-step explanation:
Vertex A is on the vertical line x=8, so we can find the y-coordinate by solving the boundary equation ...
5x +8y = 120
5(8) +8y = 120 . . . use the x-value of the vertical line
5 + y = 15 . . . . . . . divide by 8
y = 10 . . . . . . . . . . subtract 5
Point A is (8, 10).
What is the distance between (−11, −20) and (−11, 5)?
−25 units
−15 units
15 units
25 units
Answer:
IT'S NOT -15 FOR SUREEE
Step-by-step explanation:
I Believe it's 15
The dose of a drug is 0.05 mg for each kg of a patient’s weight.The Drug is available as an oral liquid containing 50 mcg/0.1 ml.Calculate the dose of the oral liquid in ml for a patient who weighs 132 lb
Answer:
6 mL
Step-by-step explanation:
It is a matter of units conversion.
volume = (mass) × (dose/mass) ÷ (dose/volume)
(132 lb)/(2.2 kg/lb) × (0.05 mg/kg) / (0.05 mg/0.1 mL) = 6 mL
A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 10 to year 20.
Answer:
The farmer should expect to LOSE 10 pounds of soybeans per acre per year
Step-by-step explanation:
f(x)=-x^2 + 20x + 100
just find how many soybeans his land will yield (per acre) after 10 and 20 years:
After 10: 200 pounds of soybeans/acre
After 20: 100 pounds of soybeans/acre
Because 10 years have passed and they lost 100 pounds of soybean production per acre, the farmer should expect to lose 10 pounds of soybeans per acre per year (-10 pounds of soybeans per acre/year)
The cost c in $ of producing x items is in the equation c=x/7+1 which of the following choices will find the cost c if x is 35
Answer:
care of it and I will get back to you with a new one for me and support you in whatever way
Step-by-step explanation:
try to get the morning and then we can go from there to the meeting tonight but I can tomorrow
The value of the cost when x is 35 given the equation c=x/7+1 is $6.
How to calculate the cost?From the information given, the cost c in $ of producing x items is in the equation c=x/7+1.
Therefore, the value of the cost when x is 35 will be;
c = x/7 + 1
c = 35/7 + 1
c = 5 + 1
c = 6
Therefore, the cost is $6.
Learn more about cost on:
https://brainly.com/question/25109150
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Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and passes through the point (2, 18).
By "slope" I assume you mean slope of the tangent line to the parabola.
For any given value of x, the slope of the tangent to the parabola is equal to the derivative of y :
[tex]y=ax^2+bx+c\implies y'=2ax+b[/tex]
The slope at x = 1 is 5:
[tex]2a+b=5[/tex]
The slope at x = -1 is -11:
[tex]-2a+b=-11[/tex]
We can already solve for a and b :
[tex]\begin{cases}2a+b=5\\-2a+b=-11\end{cases}\implies 2b=-6\implies b=-3[/tex]
[tex]2a-3=5\implies 2a=8\implies a=4[/tex]
Finally, the parabola passes through the point (2, 18); that is, the quadratic takes on a value of 18 when x = 2:
[tex]4a+2b+c=18\implies2(2a+b)+c=10+c=18\implies c=8[/tex]
So the parabola has equation
[tex]\boxed{y=4x^2-3x+8}[/tex]
Using function concepts, it is found that the parabola is: [tex]y = 4x^2 - 3x + 14[/tex]
----------------------------
The parabola is given by:
[tex]y = ax^2 + bx + c[/tex]
----------------------------
Slope 5 at x = 1 means that [tex]y^{\prime}(1) = 5[/tex], thus:
[tex]y^{\prime}(x) = 2ax + b[/tex]
[tex]y^{\prime}(1) = 2a + b[/tex]
[tex]2a + b = 5[/tex]
----------------------------
Slope -11 at x = -1 means that [tex]y^{\prime}(-1) = -11[/tex], thus:
[tex]-2a + b = -11[/tex]
Adding the two equations:
[tex]2a - 2a + b + b = 5 - 11[/tex]
[tex]2b = -6[/tex]
[tex]b = -\frac{6}{2}[/tex]
[tex]b = -3[/tex]
And
[tex]2a - 3 = 5[/tex]
[tex]2a = 8[/tex]
[tex]a = \frac{8}{2}[/tex]
[tex]a = 4[/tex]
Thus, the parabola is:
[tex]y = 4x^2 - 3x + c[/tex]
----------------------------
It passes through the point (2, 18), which meas that when [tex]x = 2, y = 18[/tex], and we use it to find c.
[tex]y = 4x^2 - 3x + c[/tex]
[tex]18 = 4(2)^2 - 3(4) + c[/tex]
[tex]c + 4 = 18[/tex]
[tex]c = 14[/tex]
Thus:
[tex]y = 4x^2 - 3x + 14[/tex]
A similar problem is given at https://brainly.com/question/22426360
The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.5 and 5.5, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use = .10. State the null and alternative hypotheses.
Answer:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{5.5}{2.5}=2.2[/tex]
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =16-1=15[/tex] and the F statistic have 15 degrees of freedom for the numerator and 15 for the denominator. And the P value is given by:
[tex]p_v =2*P(F_{15,15}>2.2)=0.138[/tex]
For this case the p value is highert than the significance level so we haev enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviations are not significantly different
Step-by-step explanation:
Information given
[tex]n_1 = 16 [/tex] represent the sampe size 1
[tex]n_2 =16[/tex] represent the sample 2
[tex]s^2_1 = 2.5[/tex] represent the sample deviation for 1
[tex]s^2_2 = 5.5[/tex] represent the sample variance for 2
[tex]\alpha=0.10[/tex] represent the significance level provided
The statistic is given by:
[tex]F=\frac{s^2_2}{s^2_1}[/tex]
Hypothesis to test
We want to test if the variations in terms of the variance are equal, so the system of hypothesis are:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic is given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{5.5}{2.5}=2.2[/tex]
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =16-1=15[/tex] and the F statistic have 15 degrees of freedom for the numerator and 15 for the denominator. And the P value is given by:
[tex]p_v =2*P(F_{15,15}>2.2)=0.138[/tex]
For this case the p value is highert than the significance level so we haev enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviations are not significantly different
Find A x B, where A=(5i+j) , B=（i-5j)
Answer:
5i² - 25ij +ji-5j²
Step-by-step explanation:
Use distributive property
Answer:
The answer is 5i² - 24ij - 5j²Step-by-step explanation:
A = (5i+j)
B = (i-5j)
A × B is
( 5i + j) ( i - 5j)
Expand
We have
5i² - 25ij + ij - 5j²
The final answer is
5i² - 24ij - 5j²
Hope this helps you.
The given equation has been solved in the table.
The closest we get is the addition property, which was used in step 2. This is a fairly similar idea because subtraction is effectively adding on a negative number. Example: 5-7 = 5+(-7). Though because your teacher is making a distinction between addition property of equality and subtraction property of equality, it's safe to say that the subtraction property is not used.
Write the following equation into logarithmic form. 5=3x
Answer:
[tex]log_35=x[/tex]
Step-by-step explanation:
I am going to assume you meant [tex]5=3^x[/tex]
When converting exponential equations into logarithmic form, remember this: [tex]y = log_bx[/tex] is equivalent to [tex]x = b^y[/tex]
You weigh six packages and find the weights to be 19, 15, 35, 17, 33, and 31 ounces. If you include a package that weighs 39 ounces, which will increase more, the median or the mean?
Answer:
Step-by-step explanation:
Mean & median of 6 packages:
15, 17, 19, 31, 33 , 35
Median = [tex]\frac{19+31}{2}[/tex]
= [tex]\frac{50}{2}[/tex]
= 25
[tex]Mean = \frac{15+17+19+31+33+35}{6}\\\\=\frac{150}{6}\\=25[/tex]
Mean & median of 7 packages:
15,17,19,31,33,35,39
Median = 31
[tex]Mean=\frac{19+15+35+17+33+31+39}{7}\\\\=\frac{189}{7}\\\\=27[/tex]
After including 39 ounce package, Median will increase more
Ben bought the enormous box of juice shown below. He drinks 450 cubic centimeters of juice each day. How many days does it take Ben to drink the box of juice?
Answer:
Step-by-step explanation:
to find the answer you have to find the vulume and then divide by 450
Answer:
7 days
Step-by-step explanation:
vol = 20*15*10.5
vol = 3150
how many days to drink 3150 cu.cm if Ben drinks 450 cu.cm per day?
3150 cu.cm / 450 cu.cm per day = 7 days
Together two ferries can transport a day's cargo in 7 hours. The larger ferry can transport cargo three times faster than the smaller ferry. How long does it take the larger ferry to transport a day's cargo working alone?
Answer:
9 hours, 20 minutes
Step-by-step explanation:
When two ferries work together, they transport a day's cargo in 7 hours
The speed proportion or ratio of larger ferry to smaller ferry is given as 3 : 1
The sum of the ratio = 4 (3 + 1)
This means that it will take the smaller ferry = 7 x 4 hours to work alone = 28 hours, since the larger ferry is faster by 3.
Therefore, when larger ferry works alone, it will take it (7 x 4)/3 = 9.33 hours.
9.33 hours = 9 hours, 20 minutes.
A sample of 120 creative artists is used to test whether creative artists are equally likely to have been born under any of the twelve astrological signs. Assuming that the twelve astrological signs each contain an equal number of calendar days, the expected frequency for each category equalsa) 5
b) 10
c) 12
d) 120
Answer:
b) 10
Step-by-step explanation:
In this case the frequency would be equal to the quotient between the sample that creative artists tell us (that is to say 120 people) and the amount of sastrological signs that there are (that is to say 12 signs), therefore it would be:
F = 120/12 = 10
Which means that the expected frequency for each category equal to 10.
So the answer is b) 10
How does changing the maximum value affect the range? A. The range is greatly affected by this change. B. The range of a data set depends on the number of data, not the specific values. Therefore, the range does not vary by changing the maximum value. C. The range becomes more accurate when the maximum value is an outlier. D. The change in the range is low and insignificant.
Answer:
The correct option is (A).
Step-by-step explanation:
The range of a data set is a measure of variability of that data set.
The range is the difference between the maximum and minimum value of the set.
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
Since the maximum value is used in the computation of range, changing the maximum value affects the range greatly.
The correct option is (A).
A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring.
Tutoring
Before After
2.4 3.1
2.5 2.8
3.0 3.6
2.9 3.2
2.7 3.5
Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)
t =
Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.)
d =
Answer:
The test statistic value is, t = -5.245.
The effect size using estimated Cohen's d is 2.35.
Step-by-step explanation:
A paired t-test would be used to determine whether the remedial tutoring has been effective for the statistics tutor's five students.
The hypothesis can be defined as follows:
H₀: The remedial tutoring has not been effective, i.e. d = 0.
Hₐ: The remedial tutoring has been effective, i.e. d > 0.
Use Excel to perform the Paired t test.
Go to Data → Data Analysis → t-test: Paired Two Sample Means
A dialog box will open.
Select the values of the variables accordingly.
The Excel output is attached below.
The test statistic value is, t = -5.245.
Compute the effect size using estimated Cohen's d as follows:
[tex]\text{Cohen's d}=\frac{Mean_{d}}{SD_{d}}[/tex]
[tex]=\frac{0.54}{0.23022}\\\\=2.34558\\\\\approx 2.35[/tex]
Thus, the effect size using estimated Cohen's d is 2.35.
P-value test and Ctitical Value test are identical. P-value and Critical value are two different names for the same steps. They can be used interchangeably.
a. true
b. false
Answer:
Option B - False
Step-by-step explanation:
Critical value is a point beyond which we normally reject the null hypothesis. Whereas, P-value is defined as the probability to the right of respective statistic which could either be Z, T or chi. Now, the benefit of using p-value is that it calculates a probability estimate which we will be able to test at any level of significance by comparing the probability directly with the significance level.
For example, let's assume that the Z-value for a particular experiment is 1.67, which will be greater than the critical value at 5% which will be 1.64. Thus, if we want to check for a different significance level of 1%, we will need to calculate a new critical value.
Whereas, if we calculate the p-value for say 1.67, it will give a value of about 0.047. This p-value can be used to reject the hypothesis at 5% significance level since 0.047 < 0.05. But with a significance level of 1%, the hypothesis can be accepted since 0.047 > 0.01.
Thus, it's clear critical values are different from P-values and they can't be used interchangeably.
In 2 years, my sister will be twice as old as she was 2 years ago, and in 3 years my brother will be three times older than he was 3 years ago. Which sibling is older?
Answer:
Sister
Step-by-step explanation:
Let the sister’s age be x.
Let the brother’s age be y.
2 + x = 2x - 2
3 + y = 3y - 3
Solve the first equation.
x - 2x = - 2 - 2
-x = -4
x = 4
Solve the second equation.
y - 3y = -3 - 3
-2y = -6
y = 3
The sister is 4 years old.
The brother is 3 years old.
The sister is older than the brother.
Identify the slope and y-intercept of the line −2x+5y=−30.
Answer:
slope = 2/5 , y-intercept = -30
Step-by-step explanation:
-2x + 5y = -30
5y = 2x - 30
y = 2/5x - 6
we know that the general form is:
y = (slope)*x + (y- intercept)
so, from our equation, we can say that...
slope = 2/5
y- intercept = -30
3. Your friend is solving a system of linear equations and finds the following solution:
0=5
What is the solution of the system? Explain your reasoning.
Answer:
No solution.
Step-by-step explanation:
Because the equations are combined but the final answers are not equal, the equations have no solution. This is because "no matter what value is plugged in for the variable, you will ALWAYS get a contradiction".
Hope this helps!
8716 no es divisible por 4
Answer:
False
Step-by-step explanation:
No esta verdad.
8716/4 = 2179 (divisible por 4)
The surface area of an open-top box with length L, width W, and height H can be found using the
formula:
A = 2LH + 2WH + LW
Find the surface area of an open-top box with length 9 cm, width 6 cm, and height 4 cm.
Answer:
174 square cm
Step-by-step explanation:
2(9×4) + 2(6×4)+ 9×6
2(36) + 2(24) + 54
72 + 48 + 54
120 + 54
174
a bridge in the shape of a parabolic arch is modelled by this function (see pic).
Answer:
(C) 25,35 and 175,35
A square with side lengths of 3 cm is reflected vertically over a horizontal line of reflection that is 2 cm below the bottom edge of the square. What is the distance between the points C and C’? cm What is the perpendicular distance between the point B and the line of reflection? cm What is the distance between the points A and A’? cm
Answer:
a) 4 cm
b) 5 cm
c) 10 cm
Step-by-step explanation:
The side lengths of the reflected square are equal to the original, and the distance from the axis(2) also remains the same. From there, it is just addition.
Hope it helps <3
Answer:
A) 4
B) 5
C) 10
Step-by-step explanation:
edge2020
A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (25.53, 37.87) and (23.59, 39.81). One of these intervals is a 99% CI and the other is a 95% CI. Please match them.
Answer:
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.
In this question:
The narrower C.I. is the 95%, and the wider is the 99%. So
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
How to find the scale factor, ratio of area, & ratio of volume?
Step-by-step explanation:
If the scale factor of two similar solids is a: b:. then
(1) the ratio of corresponding perimeters is a:b
(2) the ratio of the base areas, of the lateral areas, and of the total areas is [tex]a^2: b^2[/tex]
(3) the ratio of the volumes is [tex]a^3:b^3[/tex]
pls help me pls pls
Answer:
B
Step-by-step explanation:
the slope of parallel lines are equal
It was reported that in a survey of 4764 American youngsters aged 6 to 19, 12% were seriously overweight (a body mass index of at least 30; this index is a measure of weight relative to height). Calculate a confidence interval using a 99% confidence level for the proportion of all American youngsters who are seriously overweight. (Round your answers to three decimal places.)
Answer:
Step-by-step explanation:
confidence level for the proportion of all American youngsters who are seriously overweight is (0.137, 0.163)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue
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