Answer:
Please, read the answer below.
Step-by-step explanation:
You have the following function:
[tex]f(x)=12x^4-4x^2+5[/tex]
(a) To find the intervals of increase or decrease of f(x) you first calculate the derivative of f(x):
[tex]\frac{df}{dx}=\frac{d}{dx}[12x^4-4x^2+5]\\\\\frac{df}{dx}=12(4)x^3-4(2)x=48x^3-8x[/tex] (2)
Next, you equal the derivative to zero and obtain the roots of the obtained polynomial:
[tex]48x^3-8x=0\\\\6x^3-x=0\\\\x(6x^2-1)=0[/tex]
Then, you have the following roots for x:
[tex]x_1=0\\\\x_{2,3}=\pm \sqrt{\frac{1}{6}}[/tex] = ±0.40
Hence, there are three special points.
Next, you evaluate the derivative (expression (2)) for the x values close to the x1, x2 and x3. The values of the derivative give to us the value of the slope of a tangent line in that point, and so, if the function increases or decreases:
First interval, for a number lower than -0.40
[tex]48(-0.41)^3-8(-0.41)=-0.02<0[/tex]
The function decreases in the interval:
[tex](-\inft,-\frac{1}{\sqrt{6}})[/tex]
It is necessary that after x=-0.40 the function increases until the next special point, that is x=0. Then, the interval in which the function increases is:
[tex](-\frac{1}{\sqrt{6}},0)[/tex]
By symmetry, from the point x=0 until x=0.40 the function decreases.
[tex](0,\frac{1}{\sqrt{6}})[/tex]
Next, you evaluate the expression (2) for a number higher than 0.40:
[tex]48(0.41)^3-8(0.41)=0.02>0[/tex]
Then, the function increases for the following interval:
[tex](\frac{1}{\sqrt{6}},+\infty)[/tex]
(b) Due to the results obtained in the previous step you can conclude that the local minimum are:
[tex]x_{min}=-\frac{1}{\sqrt{6}}\\\\x_{min}=\frac{1}{\sqrt{6}}[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},f(-\frac{1}{\sqrt{6}}))=P_1(-\frac{1}{\sqrt{6}},4.66)\\\\P_2(\frac{1}{\sqrt{6}},f(\frac{1}{\sqrt{6}}))=P_2(\frac{1}{\sqrt{6}},4.66)[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},0)\\\\P_2(\frac{1}{\sqrt{6}},0)[/tex]
(these are the point in which the function change of a decrease to an increase)
The same reason as before. There in one local maximum:
[tex]x_{max}=0[/tex]
[tex]P(0,f(0))=P(0,5)[/tex]
(c) The inflection points are calculated by using the second derivative:
[tex]\frac{d^2f}{dx^2}=144x^2-8=0\\\\x^2=\frac{8}{144}=\frac{1}{18}\\\\x=\pm \frac{1}{\sqrt{18}}[/tex]
Then , there are two inflection points , given by:
[tex]P_1(-\frac{1}{\sqrt{18}},f(-\frac{1}{\sqrt{18}}))=P_1(-\frac{1}{\sqrt{18}},4.82)\\\\P_2(\frac{1}{\sqrt{18}},f(\frac{1}{\sqrt{18}}))=P_2(\frac{1}{\sqrt{18}},4.82)[/tex]
Which unit would be best for measuring the thickness of a coin?
kilometer
()) centimeter
meter
)) milli
Answer:
Since 1 mm = . 03937 inches, mm would seem to be the units appropriate for defining the thickness of a coin measuring 2 units.
Step-by-step explanation:
6th grade math ! Help me please :))
Answer:
120
Step-by-step explanation:
20 ÷2=10 10×12=120
or 20×6=120
change 5 out of 19 to a percentage
Answer:
26.3%
Step-by-step explanation:
5 is divided by 19
That answer is then multiplied by 100.
You may round your answer to the nearest whole number.
Which images below are scalene triangles?
Triangles A and D
Triangles B and D
Triangles A and C
Triangles C and D
Answer: C & D
Step-by-step explanation:
I took the test and got it right (:
Hope this helps
A scalene triangle has NO equal sides A has 3 equal sides and B has 2 equal sides, so that means Triangles C & D are your answer!
Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible.
Contains (3, 3); perpendicular to the line y = 2x - 1
Answer:
y = (-1/2)x + 9/2
Step-by-step explanation:
the equation of a straight line can be written as;
y = mx + c ......1
Where;
m = slope
c = intercept
For two lines to be perpendicular their slope must be opposite reciprocal of each other.
m1 × m2 = -1 .....2
Given;
The equation Contains (3, 3); and perpendicular to the line y = 2x - 1
Slope of the given equation m1 = 2
Slope of the line m2; substituting m1 to equation 2.
2 × m2 = -1
m2 = -1/2
So,
y = (-1/2)x + c
To solve for c, let's substitute the given point on the line; (3,3).
3 = (-1/2)(3) + c
3 = -3/2 + c
c = 3 + 3/2
c = 9/2
Therefore, the equation of the line that has the given properties is;
y = (-1/2)x + 9/2
Giving brainliest to CORRECT answer.
Answer:
A. 2
Step-by-step explanation:
[tex] y = 16x^2 - 8x + 1[/tex] is a quadratic function, hence on solving it will give two zeros, therefore graph of the function will intersect x axis in two points.
3 1/3 CUPS OF FLOUR IS NEEDED TO MAKE A PAN OF MUFFINS. 2 1/3 CUPS OF FLOUR IS NEEDED FOR A LOAF OF BREAD. HOW MUCH MOE FLOUR IS NEEDED FOR THE PAN OF MUFFINS? DRAW A TAPE DIAGRAM?
Answer:
1 cup
Step-by-step explanation:
3 1/3 - 2 1/3 = 1 cup
Whats is the 6+8-16
Answer:
-2
Step-by-step explanation:
6+8 equals 14. 14-16 equals -2
Answer: The importance of learning is that it helps the individual to acquire the necessary skills through learning and knowledge so that he can achieve his set goals. An important fact about learning is that it is a means to improve knowledge and gain skills that will help in reaching specific goals
Step-by-step explanation:
The importance of learning is that it helps the individual to acquire the necessary skills through learning and knowledge so that he can achieve his set goals. An important fact about learning is that it is a means to improve knowledge and gain skills that will help in reaching specific goals
A calzone is divided into 24 equal pieces. Sophie and Glenn each ate one-fourth
of the calzone on Saturday. The next day, Glenn ate one-sixth
of the calzone that was leftover. How many of the pieces of the original calzone remain? Explain your reasoning.
Answer:
10 pieces
Step-by-step explanation:
Total no. of pieces of calzone = 24
No of pieces of calzone eaten by sophie = 1/4 of Total no. of pieces of calzone = 1/4 of 24 = (1/4)*24= 6 pieces.
No of pieces of calzone eaten by Glenn = 1/4 of Total no. of pieces of calzone = 1/4 of 24 = (1/4)*24= 6 pieces.
Total no of pieces eaten by both of them on saturday = 12.
No of pieces of calzone left = 24-12 = 12
_______________________________________________
No of pieces of calzone eaten by Glenn on next day = 1/6 of Total no. of pieces of calzone left= 1/6 of 12 = (1/6)*12= 2 pieces
No of pieces of calzone left now after Glenn ate 2 of them = 12-2 = 10.
Thus 10 pieces of original calzone are left .
Volume of a sphere in terms of π with a radius of 2
Answer:
33.51
Step-by-step explanation:
You need to use the equation [tex]\frac{4}{3} \pi r[/tex]³.
Hope this helps.
Answer:10.7π
Step-by-step explanation:
radius=r=2
volume of sphere=4/3 x π x r x r x r
Volume of sphere=4/3xπx2x2x2
Volume of sphere=(4xπx2x2x2) ➗ 3
Volume of sphere=32π ➗ 3
Volume of sphere=10.7π
if f(x)=-x^2 and g(x) = -x^2+4x+5 what is the product
Answer:
[tex]x^{4}[/tex] - 4x³ - 5x²
Step-by-step explanation:
-x²(-x² + 4x + 5) Distribute
[tex]x^{4}[/tex] - 4x³ - 5x²
If this answer is correct, please make me Brainliest!
Complete A and B for 5-8 points.
Answer:
a) 4 hours
b) 11 am
Step-by-step explanation:
So say the number of hours is x
a) 72 + 6x = 96
6x = 24
x = 4
b) 7am + 4 hours = 11am
130 cars are parked in a parking lot. Each row holds 8 cars. If every row is full except for the last, how many cars are in the last row?
Answer:
2 are in the last row
Lia has a dog and a cat the pets weigh 16 pounds The dog weighs 3 times as much as the cat
Answer:
The weight of the dog is 12 pounds and the weight of the cat is 4 pounds.
Step-by-step explanation:
Let d represent the weight of the dog. Let c represent the weight of the cat.
Let's make a system of equations.
d+c=16
d=3c
We can use subsitution.
3c+c=16
4c=16
c=4
We can subsitute back into one of the two equations to find the weight of the dog.
d=3c
d=3(4)
d=12
The weight of the dog is 12 pounds and the weight of the cat is 4 pounds.
Which expression has the same value as the one below?
22+(-32)
○ 22+(-22)+(-10)
○22+(22)+(-10)
○22+(-22)+(10)
○22+0+32
Answer:
Option A
Step-by-step explanation:
22+(-32) is the same thing as 22-32.
[tex]22-32=-10[/tex]
Let's see if the given options are equal:Option A:
[tex]22+(-22)+(-10) \\22-22-10\leftarrow \text{Distribute -1 into the Parentheses.} \\0-10\\\boxed {-10}[/tex]
Option A's expression has the same value as the expression given.
Option B:
22+(22)+(-10)
[tex]22+22-10\\44-10\\\boxed {34}[/tex]
Option B's expression does not have the same value as the expression given.
Option C:
[tex]22+(-22)+(10)\\22-22+10\\0+10\\\boxed {10}[/tex]
Option C's expression does not have the same value as the expression given.
Option D:
[tex]22+0+32\\22+32\\\boxed{54}[/tex]
Option D's expression does not have the same value as the expression given.
The correct answer should be A: 22+(-22)+(-10).Answer:
the answer is A
hoped this helped
Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. What is the height of the stacked boxes in meters?
A.
19
B.
29
C.
30
D.
31
Answer:
D. 31
Step-by-step explanation:
The edge dimension of a cube is the cube root of the volume. For the two boxes that are 1331 m³, the height is ...
∛(1331 m³) = 11 m
For the box that is 729 m³, the height is ...
∛(729 m³) = 9 m
Then the total height of the stack of boxes is ...
11 m + 11 m + 9 m = 31 m
Answer:
31
Step-by-step explanation:
I took the test on Edmentum, have a good day hope it helps :)
What is an equation of the line that passes through the point (- 5, - 6) and is parallel to the line 4x - 5y = 35
Answer:
4x - 5y = 10
Step-by-step explanation:
Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.
Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:
4(-5) - 5(-6) = C, or
-20 + 30 = C. Thus, C = 10, and the equation of the new line is
4x - 5y = 10
The equation of line is 4x - 5y = 10
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient. On the y-axis, this number c is referred to as the intercept. Key Point y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.
Given the points (-5,-6)
and parallel to line 4x - 5y = 35...…..(1)
the equation of line is (y - y₁) = m( x - x₁)
for parallel line condition the value of m is equal to both equations
converting eq. 1 in the form of y = mx + c
4x - 5y = 35
we get y = 4/5x -7
here m = 4/5 and c = -7
substitute the value of m in equation of line
where y₁ = -6; x₁ = -5
(y - (-6)) = 4/5(x - (-5))
y +6 = 4/5(x+5)
simplify above eq. we get
4x - 5y = 20
Hence the equation of the line that passes through the point (- 5, - 6) is 4x - 5y = 20
Learn more about equation of line
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HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D. Vertx: (3,-16); Intercepts: x = -1, 7
Step-by-step explanation:
I graphed the equation on the graph below.
The diameter of a golf ball is about four centimeters which of these is closest to the volume of a golf ball?
Answer:
33.51
Step-by-step explanation:
Plz answer BRAINLIEST Choose the statement that is true of both triangles.
9514 1404 393
Answer:
A. Side lengths of 4 units and 2 units and a nonincluded angle of 30°
Step-by-step explanation:
Both triangles have sides marked 2 units and 4 units, but the angle is not between them. The angle is opposite the short side in one triangle (which will be a right triangle), and opposite the long side in the other triangle (which will be an obtuse triangle). The sides and angles of the two triangles will not have the same measures, and neither will have an angle of 100°.
The first description is appropriate:
Side lengths of 4 units and 2 units and a nonincluded angle of 30°
Solve (3x+7)=4x for x
Answer:
x=7
Step-by-step explanation:
(3x+7)=4x
Subtract 3x from each side
(3x+7) -3x=4x-3x
7 = x
Which is the simplified form of m ^-8 p^0
Answer:
Step-by-step explanation:
m−^8p^0
=1/m^8
Franco freezes the vegetables he grows in the summer so he can eat them all year long. He packs the vegetables into cube-shaped boxes that each have a volume of one cubic foot. Then, he places the boxes into a freezer that is shaped like a rectangular prism. The bottom of the freezer can be completely covered by a layer of 6 boxes. If the volume of the freezer is 18 cubic feet, what is its height?
Answer:
3 feet
Step-by-step explanation:
If there are 6 boxes in each layer, there are 3 layers to have a total of 18 boxes, each of which is 1 cubic foot.
Three layers of boxes that are 1 ft high will be 3 ft high.
The height of the freezer space is 3 feet.
solve for the coefficient -5=a(0-2)(0-3)(0-5)
Answer:
a = 1/6
Step-by-step explanation:
-5=a(0-2)(0-3)(0-5)
Simplify
-5=a(-2)(-3)(-5)
-5 = a(-30)
Divide each side by -30
-5/-30 = -30a/-30
1/6 =a
Answer:
1/6
Step-by-step explanation:
A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer In one breast have cancer in the other breast. The study participants were 980 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast.
These women had an MRI exam of the other breast, and 131 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 40 of the 131 did in fact have cancer in the other breast, whereas 91 did not. The women were all followed for one year, and two of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect.
Suppose that for women recently diagnosed with cancer In only one breast, the MRI is used to decide between the two "hypotheses.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)
A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
B) There Is a second type of error that is possible In this setting. Describe this error.
A Type II error would be coming to the conclusion that the woman_______cancer in the other breast when in fact she_______cancer in the other breast.
Answer:
Step-by-step explanation:
A type I error occurs when the null hypothesis is rejected in favor of the alternative hypothesis when the null hypothesis is actually true.
A type II error occurs when the researcher fails to reject the null hypothesis when the null is false.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
This error is a type I error as the patient does have cancer which should warrant failing to reject the null but the null was rejected in favour of the alternative.
A Type II error would be coming to the conclusion that the woman does have cancer in the other breast when in fact she does not have cancer in the other breast.
This is a second type of error that can occur and it is a type II error: failing to reject the null when not true.
PLEASE HELP!!! WILL MARK AS BRAINLIEST!!!
A colony of 300 bacteria doubles in size every 22 minutes can be represented by the exponential function y=300(2)x. If you want to know how many bacteria will be present about 66 minutes, what should you plug in for x?
Answer:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) Estimate the percentage of all males who identify themselves as the primary grocery shopper. Use a 98% confidence interval. Check the conditions first. b) A grocery store owner believed that only 43% of men are the primary grocery shopper for their family, and targets his advertising accordingly. He wishes to conduct a hypothesis test to see if the fraction is in fact higher than 43%. What does your confidence interval indicate? Explain. c) What is the level of significance of this test? Explain.
Answer:
a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.
b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.
c) [tex]\alpha =1-0.98=0.02[/tex]
Step-by-step explanation:
If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:
[tex]p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }[/tex]
Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and [tex]z_{\alpha/2}[/tex] is the z-value that let a probability of [tex]\alpha/2[/tex] on the right tail.
Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, [tex]\alpha[/tex] by 0.02 and [tex]z_{\alpha/2}[/tex] by 2.33
Where p' and [tex]\alpha[/tex] are calculated as:
[tex]p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02[/tex]
So, replacing the values we get:
[tex]0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438[/tex]
With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.
The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.
Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence [tex]1-\alpha[/tex] is equal to 98%
It means the the level of significance [tex]\alpha[/tex] is:
[tex]\alpha =1-0.98=0.02[/tex]
The scores on one portion of a standardized test are approximately Normally distributed, N(572, 51). a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores. b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Answer:
a) The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b) The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Step-by-step explanation:
68-95-99.7 rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Z-score:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu = 572[/tex], standard deviation [tex]\sigma = 51[/tex]
a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores.
By the 68-95-99.7 rule, within 2 standard deviations of the mean.
572 - 2*51 = 470
572 + 2*51 = 674
The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Using the z-score formula.
Between these following percentiles:
50 - (90/2) = 5th percentile
50 + (90/2) = 95th percentile.
5th percentile.
X when Z has a pvalue of 0.05. So when X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = -1.645*51[/tex]
[tex]X = 488.1[/tex]
95th percentile.
X when Z has a pvalue of 0.95. So when X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = 1.645*51[/tex]
[tex]X = 655.9[/tex]
The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Which two whole numbers is √20 between?
Answer:4 and 5
Step-by-step explanation:
√(20) is approximately 4.5 so it is between 4 and 5
Six minus a number divided by 3 equals 8. What is the number?
Answer:
-18
Step-by-step explanation:
let n be the number
(6-n)/3 = 8
6-n = 24
6-24 = n
-18 = n
Answer:
The number is 30
Step-by-step explanation:
Six minus a number divided by 3 equals 8
x-6/3 = 8
x-6 = 8*3
x = 24 +6
x = 30
