Answer:
15 million
Step-by-step explanation:
This is a one-tailed test with a significance level of 0.025. The test statistic is -1.83, and we reject the null hypothesis. The p-value is approximately 0.0344.
Explanation:This is a one-tailed test because the alternative hypothesis (H1) is specifying a less than condition (<) for the population mean.
The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis (H0) if the test statistic is less than the critical value.
The test statistic is calculated by subtracting the hypothesized population mean from the sample mean and dividing by the standard deviation divided by the square root of the sample size. In this case, the test statistic is [(215 - 220) / (15 / sqrt(64))] = -1.83 (rounded to 3 decimal places).
In order to make a decision regarding H0, we compare the test statistic with the critical value. If the test statistic is less than the critical value, we reject H0. Otherwise, if the test statistic is greater than or equal to the critical value, we fail to reject H0. In this case, -1.83 is less than the critical value, so we reject H0.
The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. To find the p-value, we look up the test statistic in the standard normal distribution table. In this case, the p-value is approximately 0.0344 (rounded to 4 decimal places).
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Look at the sequence given below.
4, 0, -4, -8, ...
If n = 1 represents the first term in the sequence above, which of the following describes the nth term of the sequence?
A. -3n + 4
B. n + 3
C. -4n + 8
D. -4n + 3
Answer:
C. -4n + 8
Step-by-step explanation:
Try the formulas and see which works.
__
The common difference is -4, so the coefficient of n in the explicit formula is -4. Every term is divisible by 4, so there won't be 3 anywhere in the formula.
__
-4·1 +8 = 4
-4·2 +8 = 0
-4·3 +8 = -4
-4·4 +8 = -8
The formula -4n+8 reproduces the sequence exactly.
A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost.
Answer:
The dimensions that will minimize cost are 3.42 cm and 6.84 cm
Step-by-step explanation:
* Lets explain how to solve this problem
- We have a storage box with a square base
- The volume of the box is 80 cm³
* From the information above we can find relation between the two
dimensions of the box
∵ The base of the box is a square with side length L cm
∵ The height of the box is H cm
∵ The volume of the box = area of its base × its height
- The base is a square and area the square = L² cm²
∴ The volume of the box = L² × H
∵ The volume of the box = 80 cm³
∴ L² × H = 80
- Lets find H in terms of L by divide both sides by L²
∴ H = 80/L² ⇒ (1)
- The cost of the top and bottom is $0.20 per cm²
- We can find the cost of top and bottom by multiplying the area of
them by the cost per cm²
∵ The top and the bottom are squares with side length L cm
∴ The area of them = 2 × L² = 2L² cm²
∵ The cost per cm² is $0.20
∴ The cost of top and bottom = 2L² × 0.20 = 0.40L² ⇒ (2)
- Now we can find the cost of the lateral area (area of the 4 side faces)
by multiplying the area of them by the cost per cm²
∵ The lateral area = the perimeter of its base × its height
∵ The base is a square with side length L cm
∴ The perimeter of the base = 4 × L = 4L cm
∵ The height of the box is H cm
∴ The lateral area = 4L × H
- Now lets replace H by L using equation (1)
∴ The lateral area = 4L × 80/L²
- To simplify it : 4 × 80 = 320 and L/L² = 1/L
∴ The lateral area = 320/L cm²
∵ The cost of the sides is $0.10 per cm²
∴ The cost of the lateral area = 320/L × 0.10 = 32/L ⇒ (3)
- Now lets find the total cost of the box by adding (2) and (3)
∴ The total cost (C) = 0.40L² + 32/L
* For the minimize cost we will differentiate the equation of the
cost C with respect to the dimension L (dC/dL) and equate it
by 0 to find the value of L which makes the cost minimum
- In differentiation we multiply the coefficient of L by its power and
subtract 1 from the power
∵ C = 0.40L² + 32/L
- Lets change 32/L to 32L^(-1) ⇒ (we change the sign of the power by
reciprocal it)
∴ C = 0.40L² + 32L^(-1)
- Lets differentiate
∴ dC/dL = (0.40 × 2)L^(2 - 1) + (32 × -1)L^(-1 - 1)
∴ dC/dL = 0.80L - 32L^(-2)
- For the minimum cost put dC/dL = 0
∴ 0.80L - 32L^(-2) = 0 ⇒ add 32L^(-1) to both sides
∴ 0.80L = 32L^(-2)
- Change 32L^(-2) to 32/L² (we change the sign of the power by
reciprocal it)
∴ 0.80L = 32/L² ⇒ use cross multiplication to solve it
∴ L³ = 32/0.80 = 40 ⇒ take ∛ for both sides
∴ L = ∛40 = 3.41995 ≅ 3.42 cm ⇒ to the nearest 2 decimal place
- Substitute this value of L in equation (1) to find H
∵ H = 80/L²
∴ H = 80/(∛40)² = 6.8399 ≅ 6.84 cm ⇒ to the nearest 2 decimal place
* The dimensions that will minimize cost are 3.42 cm and 6.84 cm
A culture started with 1,500 bacteria. After 5 hours it grew to 2,300 bacteria. How many bacteria with be present after 12 hours? PLSSS
Answer:
4185
Step-by-step explanation:
A culture of bacteria grows exponentially according to the following general exponential growth function;
[tex]P_{t}=P_{0}e^{kt}[/tex]
where;
p(t) is the population at any given time t.
p(0) is the initial population
k is the growth constant
From the information given we have;
p(0) = 1500
at t = 5, p(t) = 2300; p(5) = 2300
We shall use this information to determine the value of k;
[tex]2300=1500e^{5k}[/tex]
Divide both sides by 1500;
[tex]\frac{23}{15}=e^{5k}\\\\ln(\frac{23}{15})=5k\\\\k=0.08549[/tex]
Therefore, the population of the bacteria at any time t is given by;
[tex]P_{t}=1500e^{0.08549t}\\\\P(12)=1500e^{0.08549(12)}=4184.3[/tex]
What are the solution(s) to the quadratic equation 50 – x2 = 0?
x = ±2
x = ±6
x = ±5
no real solution
Answer:
No real solution
Step-by-step explanation:
Work is on another question for this. You have asked it multiple times
For this case we must find the solution of the following quadratic equation:
[tex]50-x ^ 2 = 0[/tex]
Subtracting 50 from both sides of the equation:
[tex]-x ^ 2 = -50[/tex]
Multiplying by -1 on both sides of the equation:
[tex]x ^ 2 = 50[/tex]
We apply square root on both sides to eliminate the exponent:
[tex]x = \sqrt {50}\\x = \pm \sqrt {25 * 2}\\x = \pm \sqrt {5 ^ 2 * 2}\\x = \pm5 \sqrt {2}[/tex]
ANswer:
[tex]x = \pm5 \sqrt {2}[/tex]
Which could be the area of one face of the rectangular prism?Check all that apply
Answer: 24, 44, and 66 [tex]cm^{2}[/tex]
Step-by-step explanation:
Check all of the possible combinations of the faces:
6 × 4 = 24
11 × 4 = 44
11 × 6 = 66
So the answers are 24, 44, and 66 [tex]cm^{2}[/tex]
Answer:
option B 24 cm² option C 44 cm² and option E 66 cm² are the correct options
Step-by-step explanation:
A rectangular prism has 6 faces, in which opposite faces are always similar.
So a rectangular prism has 3 different faces
(1) From the figure given
for face (1) Area = 11 × 4
= 44 cm²
For face (2) Area = 4 × 6
= 24 cm²
For face (3) Area = 11 × 6
=66 cm²
Now we can say that option B 24 cm² option C 44 cm² and option E 66 cm² are the correct options
Heeeeeelp
Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.
Answer:
about 2.33
Step-by-step explanation:
The value can be found from a probability table, any of several web sites, your graphing calculator, most spreadsheet programs, or any of several phone or tablet apps.
A web site result is shown below. (I have had trouble in the past reconciling its results with other sources.) One of my phone apps gives the z-value as about ...
2.26347874
which is in agreement with my graphing calculator.
Answer:
[tex]Z = 2.325[/tex].
Step-by-step explanation:
Problems of normally distributed samples can be 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.
Find the z score that corresponds to P99, the 99th percentile of a standard normal distribution curve.
This is the value of Z when X has a pvalue of 0.99. This is between 2.32 and 2.33, so the answer is [tex]Z = 2.325[/tex].
Which function results after applying the sequence of transformations to f(x)=x^5?
. Reflection over the x-axis
. Vertically Stretch by a factor of 2
. Shift down 1 unit
ANSWERS
---------------
A. g(x)=-2x^5-1
B. g(x)=-(2x)^5-1
C. g(x)=-2x^5+1
D. g(x)=-2(x-1)^5
Need this solved urgently! This is for apex. Also please explain how you got the answer, not just the answer itself.
Answer: Option A
Step-by-step explanation:
Given the parent function [tex]f(x)=x^5[/tex], it can be transformated:
If [tex]f(x)=x^5-k[/tex], then the function is shifted k units down.
If [tex]f(x)=a(x^5)[/tex] and [tex]a > 1[/tex] it is vertically stretched it, but if [tex]0 < a < 1[/tex] it is vertically compressesd.
If [tex]f(x)=-(x^5)[/tex], then the function is reflected over the x-axis.
Then, if the function given is reflected over the x-axis, it is vertically streteched by a factor o 2 and it is shifted down 1 units, the function that results after this transformations is:
[tex]g(x)=-2(x^5)-1[/tex]
[tex]g(x)=-2x^5-1[/tex]
The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet. What are the dimensions of the flower bed? A. 2 ft by 12 ft B. 3 ft by 8 ft C. 3 ft by 6 ft D. 4 ft by 6 ft
ANSWER
B. 3 ft by 8 ft
EXPLANATION
The area is given as 24 square feet.
This implies that,
[tex]l \times w = 24[/tex]
The perimeter of the rectangular field is given as 22 feet.
This implies that,
[tex]2(l + w) = 22[/tex]
Or
[tex]l + w = 11[/tex]
We make w the subject in this last equation and put it inside the first equation.
[tex]w = 11 - l[/tex]
When we substitute into the first equation we get;
[tex]l(11 - l) = 24[/tex]
[tex]11l - {l}^{2} = 24[/tex]
This implies that,
[tex] {l}^{2} - 11l + 24 = 0[/tex]
[tex](l - 3)(l - 8) = 24[/tex]
[tex]l = 3 \: or \: 8[/tex]
When l=3, w=24
Therefore the dimension is 3 ft by 8 ft
Answer:
The correct answer is option B. 3 ft by 8 ft
Step-by-step explanation:
Points to remember
Area of rectangle = length * breadth
Perimeter of rectangle = 2(Length + Breadth)
It is given that, The area of a rectangular flower bed is 24 square feet. The perimeter of the same flower bed is 22 feet
To find the correct option
1). Check option A
Area = 2 * 12 = 24
Perimeter = 2( 2 + 12 ) = 28
False
2) Check option B
Area = 3 * 8 = 24
Perimeter = 2(3 + 8 ) = 22
True
3). Check option C
Area = 3 * 6 = 18
Perimeter = 2( 3 + 6 ) = 18
False
4). Check option D
Area = 4 * 6 = 24
Perimeter = 2( 4 +6 ) = 20
False
The correct answer is option B. 3 ft by 8 ft
based on the pattern table what is the value of a?
A. -64
B. -12
C. 1/16
D. 1/64
Based on the pattern table, the value of a is 1/64.
What is the value of a?Given:
[tex]2^{-1} =\frac{1}{2}[/tex][tex]2^{-2} =\frac{1}{4}[/tex][tex]2^{-3} =\frac{1}{8}[/tex][tex]2^{-4} =\frac{1}{16}[/tex][tex]2^{-5} =\frac{1}{32}[/tex]Find:
The value of [tex]2^{-6}[/tex] which is represented by a.Solution:
The negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.
So, [tex]2^{-6} = \frac{1}{2^{6} } = \frac{1}{64}[/tex]
As, [tex]2^{6} = 64[/tex].
So, a = 1/64
Hence, the value of a is 1/64
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The null and alternate hypotheses are: H0: π1 ≤ π2 H1: π1 > π2 A sample of 100 observations from the first population indicated that X1 is 70. A sample of 150 observations from the second population revealed X2 to be 90. Use the .05 significance level to test the hypothesis. a. State the decision rule. (Round your answer to 2 decimal places.) H0 is rejected if z > b. Compute the pooled proportion. (Round your answer to 2 decimal places.) Pooled proportion c. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding the null hypothesis? H0 is
Answer:
365
Step-by-step explanation:
The perimeter of a rectangular field is 328 yards. If the length of the field is 89 yards, what is its width?
Set up an equation based on the information given
[tex]89 + 89 + x + x = 328[/tex]
Combine like terms
[tex]89 + 89 = 178[/tex]
[tex]x + x = 2x[/tex]
[tex]2x + 178 = 328[/tex]
Solve
[tex]2x + 178 = 328[/tex]
[tex]328 - 178 = 150[/tex]
[tex]2x = 150[/tex]
[tex]x = 75[/tex]
Answer
The width of the rectangular field is 75 yards.
By United States cultural standards, it has been determined that 6 people live comfortably in 1500 square feet of living space. Based on this standard, how many people could be comfortably accommodated with 27,000 square feet of living space? Enter the number only.
I'm unsure about this answer, but I got 108 people. I just did a simple proportion of 6/1500 = x/27000 and solved for x.
Answer:
108 people
Step-by-step explanation:
We can write a proportion to solve this problem. Take the number of people over the living space
6 people x people
------------ = ------------------
1500 ft^2 27000 ft^2
Using cross products
6 * 27000 = 1500 x
Divide each side by 1500
6 * 27000/1500 = 1500x/1500
108 = x
108 people can be reasonably accommodated
f(x) = x2 – 3x – 2 is shifted 4 units right. The result is g(x). What is g(x)?
Answer:
g(x) = x^2 - 11x + 26
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 3x - 2
a shift 4 units to the right implies that we shall be subtracting the constant 4 from the x values of the function;
g(x) = f(x-4)
g(x) = (x - 4)^2 - 3(x - 4) -2
g(x) = x^2 - 8x + 16 - 3x + 12 - 2
g(x) = x^2 - 11x + 26
New York City covers an area of 302.6 square miles. There are 8.54 million people living in New York City. Los Angeles has an area of 503 square miles and has a population of 3.98 million people. How many more people, per square mile, live in New York City verses Los Angeles? Round to the nearest person per square mile.
Answer:
20,309 people more people per sq mile.
Step-by-step explanation:
First step is to calculate the population density of both cities, then we'll be able to answer the question.
We're looking for a number of people per sq mile... so we'll divide the population by the area.
New York City: 8.54 million people on 302.6 sq miles
DensityNYC = 8,540,000 / 302.6 = 28,222 persons/sq mile
Los Angeles: 3.98 million people on 503 sq miles
DensityLA = 3,980,000 / 503 = 7,913 persons/sq mile
Then we do the difference... 28,222 - 7,913 = 20,309 people more people per sq mile.
If we were to make the ratio, we'd get 3.57, 3.57 more people in NYC per sq mile compare to LA.
Final answer:
New York City has approximately 20,309 more people per square mile than Los Angeles when rounded to the nearest person, based on their population densities.
Explanation:
To calculate how many more people per square mile live in New York City versus Los Angeles, we need to find the population density for each city and then subtract Los Angeles's density from New York City's density.
New York City's population density: 8.54 million people ÷ 302.6 square miles = approximately 28,220 people per square mile.
Los Angeles's population density: 3.98 million people ÷ 503 square miles = approximately 7,911 people per square mile.
The difference in population density: 28,220 people per square mile (NYC) - 7,911 people per square mile (LA) = approximately 20,309 people per square mile.Therefore, about 20,309 more people per square mile live in New York City than in Los Angeles, when rounded to the nearest person.
If Joe drives 186.83 miles on a business trip, and the reimbursement from his company is $13.08. At what rate is Joe's employer reimbursing travel miles? (round to the nearest cent)
Please show work
Answer:
7 cents/mile
Step-by-step explanation:
You are looking for a unit rate of cents per mile.
Change the dollar amount to cents, and divide by the number of miles.
$13.08 * (100 cents)/$ = 1308 cents
(1308 cents)/(183 miles) = 7.001 cents/mile
Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 16x2 + 9y2 = 144. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
In the [tex]x[/tex]-[tex]y[/tex] plane, the base has equation(s)
[tex]16x^2+9y^2=144\implies y=\pm\dfrac43\sqrt{9-x^2}[/tex]
which is to say, the distance (parallel to the [tex]y[/tex]-axis) between the top and the bottom of the ellipse is
[tex]\dfrac43\sqrt{9-x^2}-\left(-\dfrac43\sqrt{9-x^2}\right)=\dfrac83\sqrt{9-x^2}[/tex]
so that at any given [tex]x[/tex], the cross-section has a hypotenuse whose length is [tex]\dfrac83\sqrt{9-x^2}[/tex].
The cross-section is an isosceles right triangle, which means the legs occur with the hypotenuse in a ratio of 1 to [tex]\sqrt2[/tex], so that the legs have length [tex]\dfrac8{3\sqrt2}\sqrt{9-x^2}[/tex]. Then the area of each cross-section is
[tex]\dfrac12\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)=\dfrac{16}9(9-x^2)[/tex]
Then the volume of this solid is
[tex]\displaystyle\frac{16}9\int_{-3}^39-x^2\,\mathrm dx=\boxed{64}[/tex]
Solid [tex]\( S \)[/tex] has elliptical base[tex]\( 16x^2 + 9y^2 = 144 \)[/tex]. Triangular cross-sections yield volume [tex]\( 128 \)[/tex] cubic units.
let's break it down step by step.
1. Understanding the Solid: The solid [tex]\( S \)[/tex] has a base in the shape of an ellipse given by the equation [tex]\( 16x^2 + 9y^2 = 144 \).[/tex] The cross-sections perpendicular to the x-axis are isosceles right triangles with their hypotenuse lying on the base ellipse.
2. **Equation of the Ellipse**: To understand the shape of the base, let's rearrange the equation of the ellipse to find [tex]\( y \)[/tex] in terms of [tex]\( x \):[/tex]
[tex]\[ 16x^2 + 9y^2 = 144 \] \[ y^2 = \frac{144 - 16x^2}{9} \] \[ y = \pm \frac{4}{3} \sqrt{9 - x^2} \][/tex]
3. Finding the Length of the Hypotenuse: The length of the hypotenuse of each triangle is twice the value of [tex]\( y \)[/tex] at any given point on the ellipse. So, the length [tex]\( h \)[/tex] of the hypotenuse is given by:
[tex]\[ h = \frac{8}{3} \sqrt{9 - x^2} \][/tex]
4. Area of Each Cross-Section Triangle: The area of each cross-section triangle is [tex]\( \frac{1}{2} \times \text{base} \times \text{height} \),[/tex] where the base is the same as the height. So, the area is:
[tex]\[ \text{Area} = \frac{1}{2} \times \frac{8}{3} \sqrt{9 - x^2} \times \frac{8}{3} \sqrt{9 - x^2} = \frac{32}{9} (9 - x^2) \][/tex]
5. Integrating to Find Volume: To find the volume of the solid, we integrate the area function over the interval that covers the base ellipse, which is [tex]\([-3, 3]\)[/tex] in this case.
[tex]\[ V = \int_{-3}^{3} \frac{32}{9} (9 - x^2) \, dx \][/tex]
6. Solving the Integral: Integrating [tex]\( (9 - x^2) \)[/tex] with respect to[tex]\( x \)[/tex] yields:
[tex]\[ = \frac{32}{9} \int_{-3}^{3} (9 - x^2) \, dx \] \[ = \frac{32}{9} \left[ 9x - \frac{x^3}{3} \right]_{-3}^{3} \] \[ = \frac{32}{9} \left[ (27 - 9) - (-27 + 9) \right] \] \[ = \frac{32}{9} \times 36 \] \[ = \frac{1152}{9} \] \[ = 128 \][/tex]
7. Final Result: So, the volume of the solid [tex]\( S \)[/tex] is [tex]\( 128 \)[/tex] cubic units.
Solve (x + 1 < 4) ∩ (x - 8 > -7).
1 < x < 3 because
( x < 3 ) intersecting ( x > 1)
For this case we must find the intersection of the following inequations:
[tex]x + 1 <4\\x-8> -7[/tex]
So:
[tex]x + 1 <4\\x <4-1\\x <3[/tex]
All values of "x" less than 3.
[tex]x-8> -7\\x> -7 + 8\\x> 1[/tex]
All values of "x" greater than 1.
Thus, the intersection of the equations will be given by the values of "x" greater than 1 and less than 3.
[tex](1 <x <3)[/tex]
ANswer:[tex](1 <x <3)[/tex]
Select the correct answer. Find the slope and the y-intercept of the equation y − 3(x − 1) = 0. A. slope = -3 and y-intercept = -3 B. slope = 3 and y-intercept = 3 C. slope = -3 and y-intercept = 3 D. slope = 3 and y-intercept = -3
Answer:
D. slope = 3 and y-intercept = -3
Step-by-step explanation:
The equation can be rearranged by adding the opposite of the term with parentheses:
y = 3(x -1)
Expanding this to slope-intercept form gives ...
y = 3x -3 . . . . . . . . slope = 3, y-intercept = -3
_____
Slope-intercept form is ...
y = mx +b . . . . . . . . slope = m, y-intercept = b
In triangle ABC, how long is side c if A = 103°, C = 17°, and a = 21?
Answer:
c=6.30 units
Step-by-step explanation:
we know that
Applying the law of sines
a/sin(A)=c/sin(C)
Solve for c
c=a*sin(C)/sin(A)
substitute the values
c=21*sin(17°)/sin(103°)=6.30 units
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = cos(θ) + sin(10θ) y = sin(θ) + cos(10θ) θ = 0 y(x) =
The equation of the tangent to the curve at the point corresponding to the given values of the parametric equations given is;
y - 1 = ¹/₁₀(x - 1)
We are given;
x = cos θ + sin(10θ)
y = sin θ + cos(10θ)
Since we want to find equation of tangent, let us first differentiate with respect to θ. Thus;
dx/dθ = -sin θ + 10cos (10θ)
Similarly;
dy/dθ = cos θ - 10sin(10θ)
To get the tangent dy/dx, we will divide dy/dθ by dx/dθ to get;
(dy/dθ)/(dx/dθ) = dy/dx = (cos θ - 10sin(10θ))/(-sin θ + 10cos(10θ))
To get the tangent, we will put the angle to be equal to zero.
Thus, at θ = 0, we have;
dy/dx = (cos 0 - 10sin 0)/(-sin 0 + 10cos 0)
dy/dx = 1/10
Also, at θ = 0, we can get the x-value and y-value of the parametric functions.
Thus;
x = cos 0 + sin 0
x = 1 + 0
x = 1
y = sin 0 + cos 0
y = 0 + 1
y = 1
Thus, the equation of the tangent line to the curve in point slope form gives us;
y - 1 = ¹/₁₀(x - 1)
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Final answer:
To find the tangent line to the curve defined by the parametric equations at θ = 0, we compute the derivatives of both x and y with respect to θ, leading to a slope of 1/10. By evaluating the original parametric equations at θ = 0, we find that the tangent passes through (1, 1), resulting in the equation y - 1 = 1/10(x - 1).
Explanation:
To find an equation of the tangent to the given parametric curve at θ = 0, we first need the parametric equations given by x = cos(θ) + sin(10θ) and y = sin(θ) + cos(10θ). To find the slope of the tangent, we compute the derivatives δy/δx = (δy/δθ)/(δx/δθ) at θ = 0.
Computing the derivatives, δx/δθ = -sin(θ) + 10cos(10θ) and δy/δθ = cos(θ) - 10sin(10θ), and plugging in θ = 0, we get δx/δθ = 10 and δy/δθ = 1. Hence, the slope is 1/10. Evaluating the functions at θ = 0 gives x = 1 and y = 1. Thus, the tangent line equation at θ = 0 is y - y_0 = m(x - x_0), which simplifies to y - 1 = 1/10(x - 1).
Lines a and b are parallel Line cis perpendicular to both line a and line b. Which
statement about lines a, b, and is NOT true?
CLEARCH
Line a and line b have the same slope.
The sum of the slopes of line b and line cis 0.
The product of the slopes of line cand line bis -1.
The product of the slopes of line a and line cis -1.
Answer:
see below
Step-by-step explanation:
The slopes of parallel lines are the same. The slopes of perpendicular lines are negative reciprocals of each other, hence their product is -1.
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For the most part, the concept of adding slopes of lines does not relate to parallel or perpendicular lines in any way.
Answer:
c
Step-by-step explanation:
Assume that you are provided with the score matrix S, detections can only be matched to a single track, and that tracks cannot be assigned more than once. (a) [5 points] What do the variables in this problem represent? How many are there? (b) [10 points] Define the objective for this 0-1 integer linear program. (c) [15 points] Define the entire 0-1 integer linear program, including constraints, in standard form. How many constraints are there in the program, total?
Final answer:
The variables in this problem represent the scores in the score matrix S. The objective for this 0-1 integer linear program is to maximize the overall score. The entire 0-1 integer linear program in standard form includes constraints to ensure that each detection is assigned to a single track and each track is assigned only once, and there are N + M constraints in total.
Explanation:
(a) In this problem, the variables represent the scores in the score matrix S. There are N detections and M tracks, so we have N rows and M columns in the score matrix.
(b) The objective for this 0-1 integer linear program is to maximize the overall score, which is the sum of the selected detections' scores.
(c) The entire 0-1 integer linear program in standard form can be defined as:
Maximize the objective function: maximize ∑i,j xi,j * Si,j, where xi,j is a binary variable representing whether detection i is assigned to track j.Subject to the constraints:There are N + M constraints in total.
Membership to a national running club is shown in the table. Which answer describes the average rate of change from Year 3 to Year 5? Year: 1, 2, 3, 4, 5 Members(thousands): 87.5, 88.3, 96.8, 87.2, 83.6
answers:
Membership decreased by an average of 6,600 people per year from Year 3 to Year 5.
Membership increased by an average of 13,200 people per year from Year 3 to Year 5.
Membership decreased by an average of 13,200 people per year from Year 3 to Year 5.
Membership increased by an average of 6,600 people per year from Year 3 to Year 5.
Answer:
Membership decreased by an average of 6,600 people per year from Year 3 to Year 5
Step-by-step explanation:
The average rate of change from Year 3 to Year 5 will be given by the slope of the line joining the points;
(3, 96.8) and (5, 83.6)
The slope of a line given two points is calculated as;
( change in y)/( change in x)
In this case y is the number of members for a given year x.
average rate of change = (83.6-96.8)/(5-3)
= -6.6
Since the number of members is given in thousands, we have;
-6,600
The negative sign implies a decrease in the number of members. Therefore, membership decreased by an average of 6,600 people per year from Year 3 to Year 5
What is the greatest common factor of 24s3, 12s4, and 18s?
3
6
3s
6s
Answer:
=> 6s
Step-by-step explanation:
Given terms
24s^3 ,12s^4 and 18s
GCF consists of the common factors from all the terms whose GCF has to be found.
In order to find GCF, factors of each term has to be made:
The factors of 24s^3:
24s^3=2*2*2*3*s*s*s
The factors of 12s^4:
12s^4=2*2*3*s*s*s*s
The factors of 18s:
18s=2*3*3*s
The common factors are(written in bold):
GCF=2*3*s
=6s
So the GCF is 6s ..
Answer:
6s
Step-by-step explanation:
a person invest $1,700 in an account that earns 3.97% annual interest. find when the value of the investment reaches $3,200
Answer:
16 1/4 years
Step-by-step explanation:
Assuming interest is compounded annually, the account balance (A) after t years will be ...
A = P(1 +r)^t
3200 = 1700·1.0397^t
log(3200) = log(1700) +t·log(1.0397)
t = (log(3200) -log(1700))/log(1.0397) ≈ 16.247
The account will reach a balance of $3200 after about 16 1/4 years.
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You may be asked to round your answer to the nearest integer or tenth. We leave that exercise to the student.
A cube-shaped tank that measures 4.64.6 meters on each side is full of water. If some water is drained to fill a cone with a height of 66 meters and a radius of 2.52.5 meters, approximately how much water is left in the tank? Use 3.143.14 for ππ and round your answer to the nearest tenth. The amount of water left in the tank is approximately __________ cubic meters.
Answer:
The amount of water left in the tank is approximately 58.1 cubic meters
Step-by-step explanation:
step 1
Find the volume of the a cube shape tank
The volume is equal to
[tex]V=b^{3}[/tex]
we have
[tex]b=4.6\ m[/tex]
substitute
[tex]V=4.6^{3}=97.336\ m^{3}[/tex]
step 2
Find the volume of cone
The volume is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=2.5\ m[/tex]
[tex]h=6\ m[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]V=\frac{1}{3}(3.14)(2.5)^{2}(6)[/tex]
[tex]V=39.25\ m^{3}[/tex]
step 3
Find the difference of the volumes
[tex]97.336\ m^{3}-39.25\ m^{3}=58.1\ m^{3}[/tex]
Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If there was sneezing, barking, and coughing at 3:15 PM, when is the next time that these three sounds will happen simultaneously?
Answer:
3:45 PM
Step-by-step explanation:
The least common multiple of 3, 5, and 6 is 30, so the next occurrence will be 30 minutes after 3:15 PM, at 3:45 PM.
Answer: The next time at which the three sounds will happen simultaneously at 3 : 45 PM.
Step-by-step explanation: Given that Max sneezes every 5 minutes, Lina coughs every 6 minutes and their dog barks every 3 minutes.
We are to find the time at which these three sounds will happen simultaneously if there was sneezing, barking, and coughing at 3:15 PM.
We have
the sneezing, barking and coughing happen simultaneously at an interval that is equal to the L.C.M. of 5, 6 and 3 minutes.
Now,
L.C.M. (5, 6, 3) = 30.
Therefore, the sneezing, barking and coughing happen simultaneously at an interval of 30 minutes.
Since there was sneezing, barking, and coughing at 3:15 PM, so the next time at which the three sounds will happen simultaneously is
3 : 15 PM + 30 min = 3 : 45 PM.
Thus, the next time at which the three sounds will happen simultaneously is 3 : 45 PM.
PLEASE HELP
I marked the ones I'm stuck on
must show work
Use Slide method for some of them, some are perfect squares:
Watch this video and try it a few times, pay attention to the signs when you are seeing which one will be negative when you multiply it out, in picture is me working out all problems requested.
Ask your brother for further help!
1. Draw the image of ABC under the dilation with scale factor 2 and center of dilation (-4,-3). Label the
image A'B'C'.
Answer:
-4
-
21
2
3
4
5
Answer:
see below
Step-by-step explanation:
Each point moves to twice its original distance from (-4, -3). The point (-4, -3) remains unmoved.
Answer: (-4,1) ; (2,-3) ; (-4,-3)
Find the limit of the function algebraically. limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.
Answer:
[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big)[/tex]
Step 2: Evaluate
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = 0^3 + \frac{1}{0^5}[/tex]Simplify: [tex]\displaystyle \lim_{x \to 0} \Big( x^3 + \frac{1}{x^5} \Big) = \text{und} \text{efined}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits