Answer:
Yes
Step-by-step explanation:
−4.9t² + 18.24t + 0.8 = −1.43t + 4.26
-4.9t² + 19.67t - 3.46 = 0
4.9t² - 19.67t + 3.46 = 0
Using quadratic formula:
t = [19.67 +/- sqrt(319.0929l)]/9.8
t = (19.67 +/- 17.8631716109)/9.8
t = 3.8299154705, 0.1843702438
Since the two can be at the same height at the same time, the blocker can knock down the punt
Yes, the blocker can block down the punt.
To determine whether the blocker can knock down the punt, compare the heights of the football and the blocker’s hands at the same time t. The equations for the height of the football h(t) and the height of the blocker’s hands g(t) are given as follows:
[tex]h(t)=-4.9t^2+18.24t+0.8[/tex]
[tex]g(t)=-1.43t+4.26[/tex]
For the blocker to knock down the punt, the heights must be equal at some time t. Therefore, solve for t when h(t) = g(t):
[tex]-4.9t^2+18.24t+0.8=-1.43t+4.26[/tex]
First, move all terms to one side of the equation to set it to zero:
[tex]-4.9t^2+18.24t+0.8+1.43t-4.26=0[/tex]
Combine like terms:
[tex]-4.9t^2+19.67t-3.46=0[/tex]
This is a quadratic equation of the form [tex]ax^2+bx+c[/tex], where:
a=−4.9, b=19.67, c=−3.46
We can solve this quadratic equation using the quadratic formula:
[tex]t=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values of a, b, and c:
[tex]t = \frac{-19.67\pm\sqrt{(19.67)^2-4(-4.9)(-3.46)} }{2(-4.9)}=\frac{-19.67 \pm \sqrt{386.909 - 67.816} }{-9.8}=\frac{-19.67\pm\sqrt{319.903} }{-9.8}[/tex]
[tex]t = \frac{-19.67\pm 17.89 }{-9.8}[/tex]
Now solve for both possible values of t:
[tex]t_1 = \frac{-19.67+17.89}{-9.8} = \frac{-1.78}{-9.8} \approx 0.18\ seconds[/tex]
[tex]t_2 = \frac{-19.67-17.89}{-9.8} = \frac{-37.56}{-9.8} \approx 3.83\ seconds[/tex]
Next, check if these times are within the reasonable range for a football to stay in the air. Since 0.186 seconds and 3.83 seconds are within a typical range for a football's hang time, let's proceed to compare the heights at these times.
For t = 0.186 seconds:
[tex]h(0.186)=-4.9(0.18)^2+18.24(0.18)+0.8[/tex]
[tex]h(0.18) = -4.9(0.0324)+3.2832+0.8[/tex]
[tex]h(0.18)= -0.15876+3.2832+0.8 = 3.92444\ meters[/tex]
[tex]g(0.18)=-1.43(0.18)+4.26[/tex]
[tex]g(0.18) = -0.2574+4.26 = 4.0026[/tex]
For t = 3.83 seconds:
[tex]h(3.83)=-4.9(3.83)^2+18.24(3.83)+0.8[/tex]
[tex]h(3.83)=-4.9(14.6689)+69.8592+0.8[/tex]
[tex]h(3.83)=-71.8781+69.8592+0.8 = -2.0189+0.8=-1.2189\ meters[/tex]
[tex]g(3.83)=-1.43(3.83)+4.26[/tex]
[tex]g(3.83)=-5.4769+4.26[/tex]
[tex]g(3.83)=-1.2169\ meters[/tex]
Since at t = 0.186 seconds, the heights h(0.186) and g(0.186) are nearly equal and are positive, the blocker can knock down the punt at t around 0.186 seconds.
Full-price tickets for a concert cost $ 58.50. Students can purchase a discounted ticket for $ 48.50. If a total of 3250 tickets are sold and if the total amount of ticket sales was $ 160,045a) how many full-price tickets were sold? b) how many student tickets were sold?
Answer:
242 Full Tickets were sold; and
3008 Student Tickets were sold.
Step-by-step explanation:
Let the number of full tickets sold=x
Let the number of student tickets sold =y
A total of 3250 tickets were sold, therefore:
x+y=3250Cost of a Full Ticket =$58.50.
Cost of a Discounted Ticket=$48.50
Total Amount =(58.50. X Number of Full Tickets sold)+(58.50 X Number of Student Tickets sold)
Total amount of ticket sales was $ 160,045
Therefore:
58.50x+48.50y=160045We solve the two equations simultaneously to obtain the values of x and y.
From the First Equation, x=3250-y
Substitute x=3250-y into the Second Equation.
58.50x+48.50y=160045
58.50(3250-y)+48.50y=160045
Open the brackets
190125-58.50y+48.50y=160045
-10y=160045-190125
-10y=-30080
Divide both sides by -10
y=3008
Recall: x=3250-y
x=3250-3008
x=242
Therefore:
242 Full Tickets were sold; and
3008 Student Tickets were sold.
Final answer:
To solve for the number of full-price and student tickets sold, a system of two linear equations is set up and solved using the elimination method. The solution shows that 242 full-price tickets and 3008 student tickets were sold.
Explanation:
To solve this problem, we will use a system of linear equations. Let's define x as the number of full-price tickets and y as the number of student tickets. The two equations based on the information provided will be:
x + y = 3250 (the total number of tickets sold)
58.50x + 48.50y = 160,045 (the total revenue from ticket sales)
To find the number of full-price and student tickets sold, we need to solve this system of equations. We can do this using either the substitution or elimination method. I'll demonstrate the elimination method.
Step 1: Multiply the first equation by 48.50 to align the y terms.
48.50x + 48.50y = 157,625
Step 2: Subtract this new equation from the second equation.
58.50x + 48.50y = 160,045
- (48.50x + 48.50y = 157,625)
10x = 2,420
Step 3: Solve for x
x = 242
Step 4: Use the value of x to solve for y in the first equation.
242 + y = 3250
y = 3250 - 242
y = 3008
So, 242 full-price tickets were sold, and 3008 student tickets were sold.
A cylindrical can, open at the top, is to hold cm3 of liquid. Find the height, , and the radius, , that minimize the amount of material needed to manufacture the can. Enter the exact answers.
Answer:
[tex]r=4\ cm,\ h=4\ cm[/tex]
Step-by-step explanation:
Minimization
Optimization is the procedure leading to find the values of some parameters that maximize or minimize a given objective function. The parameters could have equality and inequality restrictions. If only equality restrictions hold, then we can use the derivatives to find the possible maximum or minimum values of the objective function.
The problem states we need to minimize the amount of material needed to manufacture the cylindrical can. The material is the surface area of the can. If the can has height h and radius r on the base, then the surface area is
[tex]A=2\pi rh+\pi r^2[/tex]
Note there is only one lid at the bottom (open at the top), that is why we added only the surface area of one circle.
That is our objective function, but it's expressed in two variables. We must find a relation between them to express the area in one variable. That is why we'll use the given volume (We'll assume the volume to be [tex]64\pi cm^3[/tex] because the question skipped that information).
The volume of a cylinder is
[tex]V=\pi r^2h[/tex]
We can solve it for h and replace the formula into the formula for the area:
[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]
Substituting into the area
[tex]\displaystyle A=2\pi r\cdot \frac{V}{\pi r^2}+\pi r^2[/tex]
Simplifying
[tex]\displaystyle A=\frac{2V}{ r}+\pi r^2[/tex]
Now we take the derivative
[tex]\displaystyle A'=-\frac{2V}{ r^2}+2\pi r[/tex]
Equating to 0
[tex]\displaystyle \frac{-2V+2\pi r^3}{ r^2}=0[/tex]
Since r cannot be 0:
[tex]-2V+2\pi r^3=0[/tex]
[tex]\displaystyle r=\sqrt[3]{\frac{V}{\pi}}[/tex]
Since [tex]V=64\pi[/tex]
[tex]\displaystyle r=\sqrt[3]{\frac{64\pi}{\pi}}=4[/tex]
[tex]r=4\ cm[/tex]
And
[tex]\displaystyle h=\frac{64\pi}{\pi 4^2}=4[/tex]
[tex]h=4\ cm[/tex]
Summarizing:
[tex]\boxed{r=4\ cm,\ h=4\ cm}[/tex]
1. A group of 400 town residents is asked to attend a
town hall meeting. Of the 400 residents asked to
attend, 36 were able to attend. What percentage of the
town residents were able to attend?
Answer:
9%
Step-by-step explanation:
36/400=9/100=9%
A fence on a hill uses vertical posts L and M to hold parallel rails N and P. ∠10 and ∠14 are alternate interior angles. What is the transversal?
A. M
B. N
C. P
D. L
Line P exists the common transversal of parallel lines L and M.
What is the transversal?Let, L and M exists vertical posts,
⇒ L and M exists parallel to one another,
Given: ∠10 and ∠14 are alternative interior angles of the parallel lines L and M.
Since, the alternative interior angles on the parallel line exists created by a common transversal.
Consider to the diagram,
Line P creates the angles 10 and 16 on the parallel lines L and M.
Line P exists the common transversal of parallel lines L and M.
Therefore, the correct answer is option C. P.
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Step by step
Help ?
Given:
The given figure consists of a triangle, a rectangle and a half circle.
The base of the triangle is 2 mi.
The height of the triangle is 4 mi.
The length of the rectangle is 9 mi.
The diameter of the half circle is 4 mi.
The radius of the half circle is 2 mi.
We need to determine the area of the enclosed figure.
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]A=\frac{1}{2}bh[/tex]
where b is the base and h is the height
Substituting b = 2 and h = 4, we get;
[tex]A=\frac{1}{2}(2\times 4)[/tex]
[tex]A=4 \ mi^2[/tex]
Thus, the area of the triangle is 4 mi²
Area of the rectangle:
The area of the rectangle can be determined using the formula,
[tex]A=length \times width[/tex]
Substituting length = 9 mi and width = 4 mi, we get;
[tex]A=9 \times 4[/tex]
[tex]A=36 \ mi^2[/tex]
Thus, the area of the rectangle is 36 mi²
Area of the half circle:
The area of the half circle can be determined using the formula,
[tex]A=\frac{\pi r^2}{2}[/tex]
Substituting r = 2, we get;
[tex]A=\frac{(3.14)(2)^2}{2}[/tex]
[tex]A=\frac{(3.14)(4)}{2}[/tex]
[tex]A=\frac{12.56}{2}[/tex]
[tex]A=6.28[/tex]
Thus, the area of the half circle is 6.28 mi²
Area of the enclosed figure:
The area of the entire figure can be determined by adding the area of the triangle, area of rectangle and area of the half circle.
Thus, we have;
Area = Area of triangle + Area of rectangle + Area of half circle
Substituting the values, we get;
[tex]Area=4+36+6.28[/tex]
[tex]Area = 46.28 \ mi^2[/tex]
Thus, the area of the enclosed figure is 46.28 mi²
What is the volume of a hemisphere with a diameter of 52.9 inch, rounded to the nearest tenth of a cubic inch ?
Answer:
38755.7
Step-by-step explanation:
The volume of the hemisphere is 55495.5 cubic inches.
Explanation:To find the volume of a hemisphere, we can use the formula for the volume of a sphere and divide it by 2.
The volume of a sphere can be calculated using the formula:
V = (4/3)πr³
Given that the diameter of the hemisphere is 52.9 inches, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 52.9 inches / 2 = 26.45 inches
Now we can calculate the volume of the hemisphere:
Volume = (4/3)π(26.45 inches)³ / 2
Using the value of π as approximately 3.14159, we can substitute the values into the formula:
Volume ≈ (4/3) × 3.14159 × (26.45 inches)³ / 2
Simplifying the calculation:
Volume ≈ 55495.5314 cubic inches
Rounding to the nearest tenth of a cubic inch, the volume of the hemisphere is approximately 55495.5 cubic inches.
amy wants to frame a poster that has a wdith of 8 inches and a lenghth of 1 foot. What is the permiter of the poster?
To find the perimeter of Amy's poster, convert all measurements to inches, resulting in a length of 12 inches and a width of 8 inches. Then use the formula for the perimeter of a rectangle, which is 40 inches in this case.
To calculate the perimeter of a poster, we must first have all dimensions in the same units. Amy's poster has a width of 8 inches and a length of 1 foot. Since there are 12 inches in a foot, the length is 12 inches. The perimeter of a rectangle is calculated by adding together the lengths of all the sides, or using the formula 2 * (length + width).
Using Amy's measurements, the perimeter of her poster would be:
2 * (12 inches + 8 inches) = 2 * 20 inches = 40 inches.
Therefore, the poster has a perimeter of 40 inches.
Which of the following explains how ΔAEI could be proven similar to ΔDEH using the AA similarity postulate?
Quadrilateral ABDC, in which point F is between points A and C, point G is between points B and D, point I is between points A and B, and point H is between points C and D. A segment connects points A and D, a segment connects points B and C, a segment connects points I and H, and a segment connects points F and G. Segments AD, BC, FG, and IH all intersect at point E.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then dilate ΔHED to confirm segment ED ≅ segment EA.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then dilate ΔHED to confirm segment ED ≅ segment EI.
Answer:
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
Step-by-step explanation:
tbh im not suuper sure but my educated guess is that by looking at it. Good Luck!
Two triangles are said to be similar by AA if two angles of both triangles are equal. The explanation that proves the similarity of [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] by AA is option (a)
Given that: [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex]
To prove that [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] are similar by AA, it means that two corresponding angles of both triangles must be congruent. So, the following must be true:
The angle at point E in both triangles must be equal. i.e. [tex]\angle AEI \cong \angle DEH[/tex]. This is so because the angle at E is a vertical angle to both triangles, and vertical angles are congruent.The angle at A and D of both triangles must be equal, i.e. [tex]\angle IAE \cong HDE[/tex]. This is so because a 180 degrees rotation of [tex]\triangle DEH[/tex] around the center E will give a similar (but larger) triangle to [tex]\triangle AEI[/tex]. Point D can then be shifted to A.Hence, (a) is true
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In the figure below, BD and EC are diameters of circle P.
What is the arc measure of AE in degrees?
Answer:
27°Step-by-step explanation:
We know by given
[tex]m \angle APB = 90\°[/tex]
[tex]m \angle DPE=63\°[/tex]
According to the given circle,
[tex]m\angle DPE + m\angle EPA + m\angle APB=180\°[/tex], by supplementary angles.
Replacing each value, we have
[tex]63\° + m\angle EPA + 90\° = 180\°\\m \angle EPA = 180\° - 153\°\\m \angle EPA = 27\°[/tex]
Now, the angle EPA subtends the arc AE, and this angle is a central angle. So, according to its defintion, the arc AE is equal to its central angle.
[tex]arc(AE)= m\angle EPA = 27\°[/tex]
Therefore, the answer is 27°
How many solutions does the system have? \begin{cases} 3y =- 6x+9 \\\\ y =-6x+9 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 3y=−6x+9 y=−6x+9
Answer:
Exactly one answer
Step-by-step explanation:
The equations show that 3y = y and the only number that could make it equal is 0, therefore there is only one solution.
Answer:
only one
Step-by-step explanation:
A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, the distance to the cat appears to be A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, the distance to the cat appears to be Equal to the actual distance. Less than the actual distance. More than the actual distance.
Answer:
Hence A fish in an aquarium see the cat more than actual distance.
Step-by-step explanation:
Given:
A fish in aquarium with flat silde looks out to cat .
To find :
Appearance of fish to the cat.
Solution:
Now this problem is related to the refractive index of 2 mediums
So cat is in air medium and a fish in water i.e. aquarium
R.I of water =1.33
R.I of air =1.00
We know the incident ray ,reflected ray,refracted ray and normal .
When a incident ray enter in denser medium it bends towards normal.
But it diverges outward direction and goes beyond the actual object.
(Refer the Attachment).
Hence A fish in an aquarium see the cat more than actual distance.
Please Help, Will give Brainliest!
Law Of Cosines.
Answer:
B) a = 6.7, B = 36°, C = 49°
Step-by-step explanation:
Fill in the numbers in the Law of Cosines formula to find the value of "a".
a² = b² + c² -2bc·cos(A)
a² = 4² +5² -2(4)(5)cos(95°) ≈ 44.4862
a ≈ √44.4862 ≈ 6.66980
Now, the law of sines is used to find one of the remaining angles. The larger angle will be found from ...
sin(C)/c = sin(A)/a
sin(C) = (c/a)sin(A)
C = arcsin(5/6.6698×sin(95°)) ≈ 48.31°
The third angle is ...
B = 180° -A -C = 180° -95° -48.31° = 36.69°
The closest match to a = 6.7, B = 37°, C = 48° is answer choice B.
Create a list in steps, in order, that will solve the following equation. 3(x+1^2)=108
Answer: x=35
Step-by-step explanation:
1. Divide both by 3
2. Simplify-x+1=36
3. Subtract 1 form both sides
You answer will be x=35
Answer:
Divide Both Sides by 3
Take the Square Root of Both Sides
Subtract 1 from Both Sides
Step-by-step explanation:
Pray!
Mr. Jackson had $110 to purchase school supplies for his class. He bought 32 boxes of colored pencils and 32 dry erase markers. Each box of colored pencils cost $2.40, and each dry erase marker cost $0.79. How much money did Mr. Jackson have left after these purchases?
Answer:
$7.92
Step-by-step explanation:
110 - ((32 x 2.40) + (32 x 0.79)) = $7.92
Answer:
$7.92 dollars left over
Step-by-step explanation:
32* 2.40= 76.8
32*0.79= 25.28
25.28+ 76.8= 102.08
110-102.08
===========7.92
Location is known to affect the number, of a particular item, sold by an automobile dealer. Two different locations, A and B, are selected on an experimental basis. Location A was observed for 18 days and location B was observed for 13 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 49 of these items with a sample standard deviation of 4. Does the data provide sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.01 level of significance? Select the [Alternative Hypothesis, Value of the Test Statistic].
Final answer:
The question involves hypothesis testing for the difference in mean sales between two car dealership locations, using a t-test at the 0.01 level of significance. We would compare the p-value to 0.01 and if the p-value is less, we can conclude there's evidence supporting fewer mean sales at location A.
Explanation:
The student is asking whether the data from the two car dealership locations provide sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.01 level of significance. This question pertains to hypothesis testing, specifically testing the difference between two means.
To test the hypothesis, we would set up the null hypothesis (H0): μA ≥ μB (mean sales at A are greater than or equal to those at B) and the alternative hypothesis (H1): μA < μB (mean sales at A are less than those at B). We can use a t-test for the difference in means since the population standard deviations are not known and the sample sizes are small.
The test statistic is calculated using the sample means, sample standard deviations, and sample sizes from both locations. Since we are performing a hypothesis test at a 0.01 significance level, we would compare the p-value of our test statistic to 0.01 to determine whether to reject the null hypothesis. If the calculated p-value is less than 0.01, we can conclude that there is sufficient evidence at the 1% significance level to support the claim that location A has fewer mean sales than location B.
Problem 2. (4 points) Suppose A is a matrix of size 4 by 4. Which of the following statements must be TRUE? (I) If the rank of A is 4, then the matrix A must be invertible. (II) If the matrix A is invertible, then the rank of A is 4. (III) If A is invertible, then the nullity of A is 0. (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III
Answer:
(E) I, II, and III
Step-by-step explanation:
Suppose the matrix A has rank 4.
A has 4 linearly independent columns.
As the matrix A is 4 by 4 matrix so all columns of A are linearly independent.
=> det(A) ≠ 0.
=> A must be invertible.
Suppose A is invertible.
Columns of A are linearly independent.
As A has 4 columns and all columns of A are linearly independent so A has 4 linearly independent columns.
As Rank of A = Number of linearly independent columns of A.
=> Rank of A = 4.
Suppose A is invertible.
=> Rank of A = 4.
By rank nullity theorem,
Rank of A + Nullity of A= 4
=> 4 + Nullity of A= 4
=> Nullity of A= 0.
Hence the nullity of A is 0.
simplest form 8/10 - 2/10 =
Answer:
3/5, 0.6
Step-by-step explanation:
8/10 - 2/10 = 6/10
6/10/2= 3/5
PLEASE MARK AS BRAINLIEST
Step-by-step explanation:
8/10-2/10
it will be 6/10 both numbers arre divisible by 2 so 3/5
Final ANSWER
3/5
PLEASE HELP WILL MARK BRAINLIEST!
For the function below, is the discriminant positive, negative, zero
y=x^2 + 4x + 4
A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Salesperson Years of Experience Annual Sales ($1000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136(a) Write an alternative hypothesis.(b). Develop an estimated regression equation that can be used to predict annual sales given the years of experience.(c) Use the estimated regression equation to predict annual sales tor a salesperson with 9 years of experience.
Answer:
A. See diagram
B.y=80+4x
C.110000
Refer below.
Step-by-step explanation:
Refer to the pictures for complete illustration.
The alternative hypothesis suggests a significant relationship between years of experience and annual sales. The estimated regression equation, derived from the given data, can be used to predict the annual sales based on years of service. For instance, a salesperson with 9 years of experience is predicted to make annual sales of $120.5k.
To begin, let's identify the variables of interest. The years of experience is the independent variable (x) and the annual sales is the dependent variable (y).
(a) Alternative Hypothesis: There is a significant linear relationship between the years of experience and the annual sales. It suggests that as the years of experience increase, the annual sales also increase.
(b) Estimated Regression Equation: To create the estimated regression equation, we first need to calculate the slope and y-intercept of the line that best fits the data. For example, using statistical software or a calculator, you might find the slope (B1) and y-intercept (B0) to be around 4.5 and 79 respectively (these numbers are hypothetical and for illustration purposes), resulting in the equation: Annual Sales = 4.5*(Years of Experience) + 79.
(c) Predicting Annual Sales: With 9 years of experience, you would plug the value 9 into the sample regression equation to predict the annual sales: Annual Sales = 4.5*(9) + 79 = $120.5 (in $1000s).
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The point Z(3,−3) is rotated 180°counterclockwise around the origin. What are the coordinates of the resulting point, Z'?
The coordinates of point Z(3, -3) after a 180° counterclockwise rotation around the origin are Z'(-3, 3).
The student has asked about the result of a 180° counterclockwise rotation around the origin for a point with given coordinates. When a point (x, y) is rotated 180° around the origin, both the x-coordinate and y-coordinate flip signs, which is a standard transformation in coordinate geometry.
For the point Z(3,−3), performing this rotation results in the point Z' having the coordinates (-3, 3).
This transformation follows the rule that (x, y) becomes (-x, -y) upon a 180° rotation about the origin.
Which behavior was observed when one and of the earthworm was placed on a wet paper towel while the other end was placed on a dry paper towel
Answer:
the awnser is c
Answer:
C
Step-by-step explanation:
its on egunity ik u hate it im here for u
Assume that the profit generated by a product is given by where x is the number of units sold. If the profit keeps changing at a rate of per month, then how fast are the sales changing when the number of units sold is 1100? (Round your answer to the nearest dollar per month.) $30/month $132,665/month $16,583/month $33,166/month
Answer:
P'(1100)=0.06
(see explanation below)
Step-by-step explanation:
The answer is incomplete. The profit function is missing, but another function will be used as an example (the answer will not match with the options).
The profit generated by a product is given by [tex]P=4\sqrt{x}[/tex].
The changing rate of sales can be mathematically expressed as the derivative of the profit function.
Then, we have to calculate the derivative in function of x:
[tex]\dfrac{dP}{dx}=\dfrac{d[4x^{0.5}]}{dx}=4(0.5)x^{0.5-1}=2x^{-0.5}=\dfrac{2}{\sqrt{x}}[/tex]
We now have to evaluate this function for x=1100 to know the rate of change of the sales at this vlaue of x.
[tex]P'(1100)=\frac{2}{\sqrt{1100} } =\frac{2}{33.16} =0.06[/tex]
Evaluate \dfrac {15}k
k
15
start fraction, 15, divided by, k, end fraction when k=3k=3k, equals, 3.
Answer:
5
Step-by-step explanation:
We desire to evaluate the fraction: [tex]\dfrac{15}{k}[/tex] when k=3.
This is a simple substitution, so what is required is
Replace k with the given numberSimplify the resulting expressionTherefore, when k=3
[tex]\dfrac{15}{k}=\dfrac{15}{3}=5[/tex]
You can try the same for any value of k.
The question requires to evaluate the mathematical expression 15/k when k=3. Substituting k with 3, we get 15/3 which equals to 5.
In the subject of Mathematics, the expression 15/k represents a simple division. The value of this expression changes depending on the value assigned to k. In the case where k = 3, we simply substitute 3 in place of k in the expression. This gives us: 15/3 which equals 5. So, 15/3 = 5. So when k = 3, 15/k equals 5.
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The National Center for Health Statistics interviewed 5409 adults smokers in 2015, and 2636 of them said they had tried to quit smoking during the past year. Consider this to be a random sample. a) Find a 95% confidence interval for the proportion of smokers who have tried to quit within the past year.
Answer:
0.4740<p<0.5006
Step-by-step explanation:
-Given [tex]n=5409, \ x=2636 , \ CI=0.95[/tex]
#we calculate the proportion of trial quitters;
[tex]\hat p=\frac{2636}{5409}\\\\=0.4873[/tex]
For a confidence level of 95%:
[tex]z_{\alpha/2}=z_{0.025}\\\\=1.96[/tex]
The confidence interval is calculated as follows:
[tex]Interval= \hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\\\=0.4873\pm 1.96\times\sqrt{\frac{0.4873(1-0.4873)}{5409}}\\\\\\\\=0.4873\pm0.0133\\\\\\=[0.4740,0.5006][/tex]
Hence, the 95% confidence interval is 0.4740<p<0.5006
The 95% confidence interval for the proportion of smokers who have tried to quit within the past year is (0.4738, 0.5004), calculated using the sample proportion and the z-score for the 95% confidence level.
Explanation:To find the 95% confidence interval for the proportion of smokers who have tried to quit within the past year, we use the formula for a confidence interval for a population proportion:
CI = p± z*(√p(1-p)/n)
Where:
CI = Confidence Interval
p = Sample proportion (successes/sample size)
z = z-score associated with the confidence level
n = Sample size
Given:
p = 2636/5409
n = 5409
And for a 95% confidence level, the z-score is typically about 1.96.
Step 1: Calculate the sample proportion (p):
2636/5409 = 0.4871
Step 2: Calculate the standard error (SE):
SE = √[0.4871*(1-0.4871)/5409] = 0.0068
Step 3: Calculate the margin of error (ME):
ME = z * SE = 1.96 * 0.0068 = 0.0133
Step 4: Calculate the confidence interval:
Lower bound = p - ME = 0.4871 - 0.0133 = 0.4738
Upper bound = p + ME = 0.4871 + 0.0133 = 0.5004
So, the confidence interval is (0.4738, 0.5004).
Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = te9t ℒ{f(t)} = (s > 9)
Answer:
e^-s/s + e^-s/s^2
Step-by-step explanation:
See the attachment please
The question asks for the Laplace transform of f(t) = te^9t using the given definition of the Laplace Transform. This can be calculated using the integral ℒ{f(t)} = ∫ (from 0 to ∞) e^{-st} te^9t dt and likely requires the technique of integration by parts for evaluation.
Explanation:The question is asking for the Laplace transform of the function f(t) = te9t, using the definition of the Laplace transform. The Laplace Transform is a method that can be used to solve differential equations. In general, the Laplace Transform of a function f(t) is defined as ℒ{f(t)} = ∫ (from 0 to ∞) e-st f(t) dt, provided that the integral converges.
In this case, f(t) is equal to te9t so the integral becomes ℒ{f(t)} = ∫ (from 0 to ∞) e-st te9t dt. To find the integral, you would generally need to use integration by parts, which is a method of integration that is typically taught in a calculus course. Note that the given condition (s > 9) will affect the convergence of the integral.
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The ratio of Jane's age to her daughter's age is 9:2.
The sum of their ages is 44. How old is Jane?
A. 22
B. 33
C. 35
D. 36
E. 40
Jane is of 36. Hence the option D. 36 is correct.
The ratio of Jane's age to her daughter's age is 9:2.
The sum of their ages is 44.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
The ratio of age is 9:2
now total = 11
jane age can be given as = 44 x9/11
jane age = 36
Thus, the required age of jane is 36.
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A circle with radius 5 has a sector with a central angle of 9/10 pi radians
Answer: 4.5 pi to this question
Multiply 5 2/5 x 9 2/10 show your work.
Answer: [tex]49\frac{7}{10}[/tex]
Turn 5 2/5 into an Improper Fraction
Multiply 5*5 and get 25. Now add 2 and get 27.
5 2/5=27/5
Turn 9 2/10 into an Improper Fraction
Multiply 9*10 and get 90. Now add 2 and get 92.
9 2/10=92/10
New problem: 27/5×92/10
Multiply
[tex]27/5*92/10=2484/50[/tex]
Divide
[tex]2485/50=49.7[/tex]
Turn 49.7 into a Mixed Number
[tex]49.7=49\frac{7}{10}[/tex]
Answer:
[tex] = 49.68[/tex]
Step-by-step explanation:
[tex]5 \frac{2}{5} \times 9 \frac{2}{10} \\ \frac{27}{5} \times \frac{92}{10} \\ \frac{2484}{50} \\ = 49.68[/tex]
A researcher is studying the effect of ten different variables on a critical measure of business performance. In selecting the best set of independent variables to predict the dependent variable, a forward selection method is used. How are variables selected for inclusion in the model?
A. Smallest p-value
B. Highest increase in the multiple r-squared
C. smallest coefficient
D. Largest p-value
Answer:
D. Largest p-value
Step-by-step explanation:
P-value assists statistician to know the importance of their result. It assists them in determining the strength of their evidence.
A large P-value which is less than 0.05 depicts that an evidence is week against null hypothesis, therefore the null hypothesis must be accepted.
A small P-value <0.05 depicts a strong evidence against null hypothesis, so the null hypothesis must be rejected.
Answer:
B. Highest increase in the multiple r-squared
Step-by-step explanation:
Forward selection is a type of stepwise regression which begins with an empty model and adds in variables one by one. In each forward step, you add the one variable that gives the single best improvement to your model.
We know that when more variables are added, r-squared values typically increase with probability 1. Based on this and the above definition, we select the candidate variable that increases r-Squared the most and stop adding variables when none of the remaining variables are significant.
Certain car manufacturers install a gauge that tells the driver how many miles they can drive until they will run out of gas. A study was conducted to test the accuracy of these gauges. Each driver was assigned a certain gauge reading until empty to watch for. When their car announced it had that many miles remaining until empty, they began to measure their distance traveled. After they ran out of gas, they reported the distance they were able to drive (in miles) as well as the gauge reading they were assigned (in miles). Here is computer output showing the regression analysis: Regression Analysis: Distance versus Gauge Reading Predictor Coef SE Coet Constant -0.7928 3.2114 -0.2469 0.8060 Gauge 1.1889 0.0457 26.0310 0.0000 B = 7.0032 R-39 = 0.9326 2-3q(adj) = 0.9312 Identify and interpret the slope of the regression line used for predicting the actual distance that can be driven based on the gauge reading.
Answer:
that a hard question
Step-by-step explanation:
i tried to use a calculator and graphs to solve it but I couldn't
Answer:
Slope = 1.1889. The predicted distance the drivers were able to drive increases by 1.1889 miles for each additional mile reported by the gauge.
Step-by-step explanation:
The slope is the second value under the “Coef” column. The interpretation of slope must include a non-deterministic description (“predicted”) about how much the response variable (actual number of miles driven) changes for each 1-unit increment of change in the explanatory variable (the gauge reading) in context.