Final answer:
The mathematical system of inequalities for Keitaro's walking and running routine must satisfy his target of covering at least 36 miles and not more than 90 miles in a month, given his pace.
Explanation:
Keitaro's exercise routine is defined by a system of inequalities that reflect the minimum and maximum distances he wants to cover each month by walking and running. Given his walking pace of 3 miles per hour and his running pace of 6 miles per hour, we can set up two inequalities to represent walking hours w and running hours r. The first inequality would ensure that when multiplied by their respective paces, the total distance is at least 36 miles. The second inequality ensures that the sum of distances does not exceed 90 miles:
3w + 6r ≥ 36 (for the minimum distance)
3w + 6r ≤ 90 (for the maximum distance)
Keitaro needs to allocate his walking and running hours such that these inequalities are satisfied to meet his monthly exercise goals.
Circle O has a circumference of 367 cm.
What is the length of the radius, r?
6 cm
18 cm
36 cm
72 cm
Answer:
none of the above
Step-by-step explanation:
The applicable relationship is ...
C = 2πr
Solving for r, we get
r = C/(2π) ≈58. (367 cm)/(2·3.14159) ≈ 58.41 cm . . . . no matching choice
_____
When the problem does not include a correct answer choice, I usually suggest you ask your teacher to show you the working of it.
18cm I hope this helps
A model for the surface area of a human body is given by s = 0.1098w0.425h0.725, where w is the weight (in pounds), h is the height (in inches), and s is measured in square feet. if the errors in measurement of w and h are at most 6%, use differentials to estimate the maximum percentage error in the calculated surface area. (round your answer to one decimal place.)
Using differentials, the estimated maximum percentage error in the calculated surface area is approximately 5.73%, considering the 6% error in weight and height measurements.
To estimate the maximum percentage error in the calculated surface area using differentials, we'll use the formula for the surface area of the human body:
[tex]\[ S = 0.1098w^{0.425}h^{0.725} \][/tex]
Given that the errors in measurement of w and h are at most 6%, we'll use differentials to estimate the maximum percentage error in the surface area.
Let's denote:
- [tex]\( \Delta w \)[/tex] as the change in weight
- [tex]\( \Delta h \)[/tex] as the change in height
- [tex]\( \Delta S \)[/tex] as the change in surface area
Using differentials, we have:
[tex]\[ \Delta S \approx \frac{\partial S}{\partial w} \Delta w + \frac{\partial S}{\partial h} \Delta h \][/tex]
We need to find [tex]\( \frac{\partial S}{\partial w} \)[/tex] and [tex]\( \frac{\partial S}{\partial h} \):[/tex]
[tex]\[ \frac{\partial S}{\partial w} = 0.1098 \cdot 0.425w^{-0.575}h^{0.725} \][/tex]
[tex]\[ \frac{\partial S}{\partial h} = 0.1098 \cdot 0.725w^{0.425}h^{-0.275} \][/tex]
Given that the errors in measurement of w and h are at most 6%, we can express [tex]\( \Delta w \)[/tex] and [tex]\( \Delta h \)[/tex] as 0.06w and 0.06h respectively.
Now, substitute the values into the formula for [tex]\( \Delta S \):[/tex]
[tex]\[ \Delta S \approx (0.1098 \cdot 0.425w^{-0.575}h^{0.725})(0.06w) + (0.1098 \cdot 0.725w^{0.425}h^{-0.275})(0.06h) \][/tex]
[tex]\[ \Delta S \approx 0.005877w^{-0.575}h^{0.725} \Delta w + 0.004607w^{0.425}h^{-0.275} \Delta h \][/tex]
Now, let's compute the maximum percentage error:
[tex]\[ \text{Max percentage error} = \frac{\Delta S}{S} \times 100 \][/tex]
[tex]\[ \text{Max percentage error} = \frac{0.005877w^{-0.575}h^{0.725} \Delta w + 0.004607w^{0.425}h^{-0.275} \Delta h}{0.1098w^{0.425}h^{0.725}} \times 100 \][/tex]
[tex]\[ \text{Max percentage error} \approx \frac{0.005877(0.06w) + 0.004607(0.06h)}{0.1098w^{0.425}h^{0.725}} \times 100 \][/tex]
[tex]\[ \text{Max percentage error} \approx \frac{0.0003526w^{-0.575}h^{0.725} + 0.00027642w^{0.425}h^{-0.275}}{0.1098w^{0.425}h^{0.725}} \times 100 \][/tex]
[tex]\[ \text{Max percentage error} \approx \frac{0.0003526}{0.1098} + \frac{0.00027642}{0.1098} \times 100 \][/tex]
[tex]\[ \text{Max percentage error} \approx 3.21 + 2.52 \][/tex]
[tex]\[ \text{Max percentage error} \approx 5.73\% \][/tex]
Therefore, the estimated maximum percentage error in the calculated surface area is approximately 5.73%.
roblem: Report Error A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 + 1,\; 2 + 2,\; 2 + 1 + 1,\; 1 + 1 + 1 + 1.\] So 4 has five partitions. What is the number of partitions of the number 7?
Answer:
There are 15 partitions of 7.
Step-by-step explanation:
We are given that a partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the numbers in the sum .
We have to find the partition of 7
We are given an example
Partition of 4
4=4
4=3+1
4=2+2
4=1+2+1
4=1+1+1+1
There are five partition of 4
In similar way we are finding partition of 7
7=7
7=6+1
7=5+2
7=5+1+1
7=3+3+1
7=3+4
7=4+2+1
7=3+2+2
7=4+1+1+1
7=3+1+1+1+1
7=2+2+2+1
7=3+2+1+1
7=2+2+1+1+1
7=2+1+1+1+1+1
7=1+1+1+1+1+1+1
Hence, there are 15 partitions of 7.
Probability of multiple Events
A.
B.
C.
D.
Given that [tex]P(Q)=\dfrac{3}{5},P(R)=\dfrac{1}{3}[/tex]
Also,
[tex]P(Q\wedge R)=P(Q)\cdot P(R)=\dfrac{3}{5}\cdot\dfrac{1}{3}=\dfrac{1}{5}[/tex]
We can conclude that,
[tex]P(Q\vee R)=P(Q)+P(R)=\dfrac{3}{5}+\dfrac{1}{3}=\boxed{\dfrac{14}{15}}[/tex]
The answer is B.
Hope this helps.
r3t40
Leonard wants to buy a car within a budget of $33,000. The base price of the cars at a dealership ranges from $24,000 to $48,000. The car accessories are one-tenth the base price of a car. The total cost of buying a car depends on the base price of the car. The domain that represents the base price of a car that Leonard can afford from this dealership is [ , ]. Before buying the car, Leonard decides to buy car insurance worth $2,200. After this payment, the domain for the function that represents the base price of a car that Leonard can afford is [ , ].
Final answer:
The domain for the base price of a car that Leonard can initially afford is [24,000, 30,000]. After buying car insurance worth $2,200, the domain changes to [24,000, 28,000], reflecting the reduced budget available for the car purchase.
Explanation:
Initially, Leonard can afford a car with a base price up to his budget of $33,000. Since car accessories cost one-tenth of the base price, we calculate the maximum base price he can afford as follows: Let x be the base price of the car. The total cost of the car, including accessories, would be x + (1/10)x = (1 + 1/10)x = (11/10)x. So, to stay within budget, (11/10)x ≤ $33,000. Solving for x gives us x ≤ $33,000 / (11/10) = $30,000.
Therefore, the domain representing the base price Leonard can afford is [24,000, 30,000].
After buying car insurance for $2,200, Leonard's budget for the car decreases. The new budget for the car including accessories is $33,000 - $2,200 = $30,800. Solving (11/10)x ≤ $30,800, we get x ≤ $30,800 / (11/10) = $28,000.
Now, the domain for the base price that Leonard can afford after the insurance payment is [24,000, 28,000].
A person who initially weighs 250 pounds loses 2 pounds per week. Let t represent the number of weeks and let W represent the person's weight, in pounds: W = − 2 t + 250
a. What is the person's weight after twelve weeks?
b. After how many weeks will the person weigh 234 pounds?
Answer:
a. 226 pounds
b. 8 weeks
Step-by-step explanation:
To solve this problem, simply plug in the numbers for the variables it told you they correspond to. 12 is the number of weeks, and t represents the number of weeks, so we can plug 12 in for t.
[tex]W=-2(12)+250[/tex]
Simplify and you'll have your answer.
[tex]W=-24+250\\W=226[/tex]
For part B, 234 is the amount of pounds, and W represents the weight in pounds, so we can plug 234 in for W.
[tex]234=-2t+250\\-16=-2t\\8=t[/tex]
An automotive store guaranteed its best tire for 50000 miles. A less expensive tire was guaranteed for only 20000 miles. The better tire had what percent greater performance than the less expensive one?
Answer:
150%
Step-by-step explanation:
Best Tire : 50,000 miles
Better Tire : 20,000 miles
Difference : 50,000 - 20,000 = 30,000
The difference expressed as a percentage of the less expensive tire
= (30,000 / 20,000) x 100%
=150%
u and v are position vectors with terminal points at (-1, 5) and (2, 7), respectively. Find the terminal point of -2u + v.
(0, -3)
(4, -3)
(4, 17)
(9, -8)
Answer:
(4, -3)
Step-by-step explanation:
-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)
= (4, -3)
Bonnie is adding a ribbon border to the edge of her kite. Two sides of the kite measure 13.2 inches, while the other two sides measure 20.7 inches. How much ribbon does Bonnie need?
Answer:
Bonnie needs [tex]67.8\ in[/tex] of ribbon
Step-by-step explanation:
we know that
A Kite is a quadrilateral that has two pairs of equal sides
so
To find out how much ribbon Bonnie needs calculate the perimeter of the kite
[tex]P=2(L1+L2)[/tex]
where
L1 is the length of one side
L2 is the length of the other side
[tex]P=2(13.2+20.7)=67.8\ in[/tex]
How do you do this question?
Answer:
positive
Step-by-step explanation:
Find the sign of (2-2x+y) for any point (x,y) in quadrant 2.
In quadrant 2, the x's are negative and the y's are positive.
So choose a negative value for x and a positive value for y and evaluate:
2-2x+y
Let's try (-4,5):
2-2(-4)+5
2+8+5
15 (positive)
Let's try(-1/2 , 10):
2-2(-1/2)+10
2+1+10
3+10
13 (positive)
Let's try in general Let (x,y)=(-a,b) where a and b are positive:
2-2(-a)+b
2+2a+b
Since a and b are positive, then 2+2a+b is positive because you are adding three different positive numbers.
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 400 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.
(a) Estimate the value of the population proportion. (Round your answer to 3 decimal places.)
Estimated population proportion
(b)
Develop a 95 percent confidence interval for the population proportion. (Round your answers to 3 decimal places.)
Answer:
a) The population proportion is 0.625
b) The confidence interval is (0.578 , 0.672)
Step-by-step explanation:
* Lets explain how to solve the problem
- The Fox TV network is considering replacing one of its prime-time
crime investigation shows with a new family-oriented comedy show
- There are 400 viewers
∴ The sample size is 400
- 250 of them indicated they would watch the new show and
suggested it replace the crime investigation show
∴ The number of success is 250
∵ The population proportion P' = number of success/sample size
∴ P' = 250/400 = 0.625
a) The population proportion is 0.625
* Lets solve part b
- Develop a 95 percent confidence interval for the population
proportion
∵ The confidence interval (CI) = [tex]P'(+/-)z*(\sqrt{\frac{P'(1-P')}{n}}[/tex],
where P' is the sample proportion, n is the sample size, and z*
is the value from the standard normal distribution for the desired
confidence level
∵ 95% z is 1.96
∴ z* = 1.96
∵ P' = 0.625
∵ n = 400
∵ [tex]\sqrt{\frac{P'(1-P')}{n}}=\sqrt{\frac{0.625(1-0.625)}{400}}=0.0242[/tex]
∴ CI = 0.625 ± (1.96)(0.0242)
∴ CI = (0.625 - 0.047 , 0.625 + 0.047)
∴ CI = (0.578 , 0.672)
b) The confidence interval is (0.578 , 0.672)
A cubic inch of PVC material weight 0.063 pounds per cubic inch. What's the weight of a 36 inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
Answer:
0.196 lbs
Step-by-step explanation:
The area of the cross section is the difference of the areas of circles with the different diameters. The volume of the pipe material is the product of its cross section area and its length:
V = π(D² -d²)L/4 = π(0.82² -0.75²)36/4 ≈ 3.107 . . . in³
Then the weight of the material is this volume multiplied by the density.
W = V·δ = (3.107 in³)(0.063 lb/in³) ≈ 0.196 lb
Finding the weight of the PVC pipe involves calculating the volumes of the outer and inner cylinders then finding the difference, which is multiplied by the weight per cubic inch of PVC.
Explanation:The weight of a 36 inch piece of PVC pipe can be calculated using the formula for the volume of a cylinder and the given weight per cubic inch of PVC material. Firstly, calculate the volume of the outer cylinder, which we know the diameter and length (or height). The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. We need to halve the diameter to get the radius, which gives us 0.82/2 = 0.41 inches.
Secondly, we calculate the volume of the inner cylinder in the same way, except we use the inner diameter, which is 0.75 inches, halved gives us a radius of 0.375 inches. The volume of material used is then the volume of the outer cylinder minus the volume of the inner cylinder. Lastly, multiply the volume of material by the weight per cubic inch to get the total weight.
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What is the product?
(X^4)(3x^2-2)(4x^2+5x)
Answer:
[tex]12x^8+15x^7-8x^6-10x^5[/tex]
Step-by-step explanation:
Start by using the FOIL method on your second and third terms.
[tex](3x^2-2)(4x^2+5x)\\12x^4+15x^3-8x^2-10x[/tex]
Next, multiply the first term ([tex]x^4[/tex]) against your result.
[tex]x^4(12x^4+15x^3-8x^2-10x)\\12x^8+15x^7-8x^6-10x^5[/tex]
For this case we must find the product of the following expression:[tex](x ^ 4) (3x ^ 2-2) (4x ^ 2 5x) =[/tex]
We must bear in mind that to multiply powers of the same base, the same base is placed and the exponents are added:
Multiplying the terms of the first two parentheses, applying distributive property we have:
[tex](x ^ 4 * 3x ^ 2-x ^ 4 * 2) (4x ^ 2 5x) =\\(3x ^ 6-2x ^ 4) (4x ^ 2 5x) =\\3x ^ 6 * 4x ^ 2 3x ^ 6 * 5x-2x ^ 4 * 4x ^ 2-2x ^ 4 * 5x =\\12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]
Answer:
The product is: [tex]12x ^ 8 15x ^ 7-8x ^ 6-10x ^ 5[/tex]
The rectangle has an area of 24 square centimeters. Find the length a of the rectangle.
The Length of the rectangle is A and the Width of the rectangle is A - 5
To find the length of the rectangle with an area of 24 square centimeters and width of (a-5), solve the quadratic equation a^2 - 5a - 24 = 0, which gives a length a = 8 centimeters.
Explanation:The question asks us to find the length a of a rectangle that has an area of 24 square centimeters, given that the width is a-5. Since area of a rectangle is found by multiplying the length by the width, we can set up the equation a*(a-5) = 24. To find the value of a, we need to solve this quadratic equation.
First, we expand the equation:
a² - 5a = 24
Then, we set the equation to zero:
a² - 5a - 24 = 0
Next, we factor the quadratic equation:
(a - 8)(a + 3) = 0
There are two possible solutions for a:
a = 8a = -3Since a length cannot be negative, we discard a = -3 and conclude that the length a of the rectangle is 8 centimeters.
Nancy and Harry are sliding a stone statue and moving it to a new location in their garden. Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal. What is the magnitude of the horizontal force exerted on the statue?
Answer:
197,8879 N.
Step-by-step explanation:
The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.
The question given says that Nancy is pushing the statue with a force of 120 N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180 N at a 40° angle with the horizontal.
With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.
The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.
F= (120 N cos 60°) + (180 N x cos 40°)
F= 197,8879 N
To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components. Nancy's horizontal force is 60N and Harry's horizontal force is 137.48N. The magnitude of the horizontal force exerted on the statue is 197.48N.
Explanation:To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components.
Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal, so the horizontal component of her force is 120N * cos(60°) = 60N.
Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal, so the horizontal component of his force is 180N * cos(40°) = 137.48N.
To find the magnitude of the horizontal force exerted on the statue, we sum up the horizontal components of both forces: 60N + 137.48N = 197.48N.
Which of the following is the function representing the graph below? graph begins in the third quadrant near the line y equals negative 3 and increases slowly while crossing the ordered pair 0, negative 2. When the graph enters the first quadrant, it begins to increase quickly throughout the graph.
f(x) = 4x
f(x) = 4x − 3
f(x) = 4x + 3
f(x) = 4(x + 3)
Answer:
f(x) = 4^x -3
Step-by-step explanation:
All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).
__
So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:
f(x) = 4^x -3
_____
The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.
HELP ME!!!
Find the resulting vector matrix of this matrix multiplication.
The resulting matrix is , where a = and b = .
Answer:
a = 2 and b = 2
Step-by-step explanation:
It is given a matrix multiplication,
To find the value of a and b
It is given that,
| 3 2 | * | -2 | = | a |
|-1 0 | | 4 | | b |
We can write,
a = (3 * -2) + (2 * 4)
= -6 + 8
= 2
b = (-1 * -2) + (0 * 4)
= 2 + 0
= 2
Therefore the value of a = 2 and b = 2
Answer:
a=2 and b=2.
Step-by-step explanation:
The given matrix multiplication is
[tex]\begin{bmatrix}3&2\\ -1&0\end{bmatrix}\begin{bmatrix}-2\\ 4\end{bmatrix}[/tex]
We need to resulting vector matrix of this matrix multiplication.
[tex]\begin{bmatrix}3\left(-2\right)+2\cdot \:4\\ \left(-1\right)\left(-2\right)+0\cdot \:4\end{bmatrix}[/tex]
[tex]\begin{bmatrix}2\\ 2\end{bmatrix}[/tex]
It is given that [tex]\begin{bmatrix}a\\ b\end{bmatrix}[/tex] is resulting matrix.
[tex]\begin{bmatrix}2\\ 2\end{bmatrix}=\begin{bmatrix}a\\ b\end{bmatrix}[/tex]
On comparing both sides, we get
[tex]a=2,b=2[/tex]
Hence, a=2 and b=2.
Need some help with this problem please!!
Answer:
sin(2x) = 120/169
Step-by-step explanation:
A suitable calculator can figure this for you. (See below)
__
You can make use of some trig identities:
sin(2x) = 2sin(x)cos(x)sec(x)² = tan(x)² +1cos(x) = 1/sec(x)tan(x) = sin(x)/cos(x)Then your function value can be written as ...
sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²
= 2tan(x)/(tan(x)² +1)
Filling in the given value for tan(x), this is ...
sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)
sin(2x) = 120/169
1. One inch equals 2.54 centimeters. How many centimeters tall is a 76-inch man?
Answer:
193.04
Step-by-step explanation:
If one inch equals 2.54 centimeters, a 76-inch tall man is 193.04 centimeters.
1 inch = 2.54 centimeters
76 inches
2.54 x 76 = 193.04
Answer:
193.04 cm
Step-by-step explanation:
So let's line up our corresponding information.
1 inch=2.54 cm
76 in =x cm
This is already setup for you to write a proportion:
[tex]\frac{1}{76}=\frac{2.54}{x}[/tex]
Cross multiply:
[tex]1(x)=76(2.54)[/tex]
Multiply:
[tex]x=193.04[/tex]
E-mail fraud (phishing) is becoming an increasing problem for users of the internet. suppose that 70% of all internet users experience e-mail fraud. if 50 internet users were randomly selected, what is the probability that no more than 25 were victims of e-mail fraud?
The probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].
Further explanation:
Given:
The probability of a user experience e-mail fraud [tex]p[/tex] is [tex]0.7[/tex].
The number of individuals [tex]n[/tex] are [tex]50[/tex].
Calculation:
The [tex]\bar{X}[/tex] follow the Binomial distribution can be expressed as,
[tex]\bar{X}\sim \text{Binomial}(n,p)[/tex]
Use the normal approximation for [tex]\bar{X}[/tex] as
[tex]\bar{X}\sim \text{Normal}(np,np(1-p))[/tex]
The mean [tex]\mu[/tex] is [tex]\fbox{np}[/tex]
The standard deviation [tex]\sigma[/tex] is [tex]\fbox{\begin{minispace}\\ \sqrt{np(1-p)}\end{minispace}}[/tex]
The value of [tex]\mu[/tex] can be calculated as,
[tex]\mu=np\\ \mu= 50 \times0.7\\ \mu=35[/tex]
The value of [tex]\sigma[/tex] can be calculated as,
[tex]\sigma=\sqrt{50\times0.7\times(1-0.7)} \\\sigma=\sqrt{50\times0.7\times0.3}\\\sigma=\sqrt{10.5}[/tex]
By Normal approximation \bar{X} also follow Normal distribution as,
[tex]\bar{X}\sim \text{Normal}(\mu,\sigma^{2} )[/tex]
Substitute 35 for [tex]\mu[/tex] and 10.5 for [tex]\sigma^{2}[/tex]
[tex]\bar{X}\sim\text {Normal}(35,10.5)[/tex]
The probability that not more than [tex]25[/tex] were victims of e-mail fraud can be calculated as,
[tex]\text{Probability}=P(\bar{X}<25)}\\\text{Probability}=P(\frac{{\bar{X}-\mu}}{\sigma}<\frac{{(25+0.5)-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<\frac{{25.5-35}}{\sqrt{10.5} })\\\text{Probability}=P(Z}<-2.93})\\[/tex]
The Normal distribution is symmetric.
[tex]P(Z>-2.93})=1-P(Z<2.93)\\P(Z>-2.93})=1-0.99831\\P(Z>-2.93})=0.00169[/tex]
Hence, the probability that no more than [tex]25[/tex] were victims of e-mail fraud is [tex]\fbox{0.00169}[/tex].
Learn More:
1. Learn more about angles https://brainly.com/question/1953744
2. Learn more about domain https://brainly.com/question/3852778
Answer Details:
Grade: College Statistics
Subject: Mathematics
Chapter: Probability and Statistics
Keywords:
Probability, Statistics, E-mail fraud, internet, Binomial distribution, Normal distribution, Normal approximation, Central Limit Theorem, Z-table, Mean, Standard deviation, Symmetric.
Please help me. This is real confusing.
Answer:
1st problem: b) [tex]A=2500(1.01)^{12t}[/tex]
2nd problem: c) [tex]A=2500e^{.12t}[/tex]
Step-by-step explanation:
1st problem:
The formula/equation you want to use is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
t=number of years
A=amount he will owe in t years
P=principal (initial amount)
r=rate
n=number of times the interest is compounded per year t.
We are given:
P=2500
r=12%=.12
n=12 (since there are 12 months in a year and the interest is being compounded per month)
[tex]A=2500(1+\frac{.12}{12})^{12t}[/tex]
Time to clean up the inside of the ( ).
[tex]A=2500(1+.01)^{12t}[/tex]
[tex]A=2500(1.01)^{12t}[/tex]
----------------------------------------------------
2nd Problem:
Compounded continuously problems use base as e.
[tex]A=Pe^{rt}[/tex]
P is still the principal
r is still the rate
t is still the number of years
A is still the amount.
You are given:
P=2500
r=12%=.12
Let's plug that information in:
[tex]A=2500e^{.12t}[/tex].
I need help . This problem is confusing me.
Answer:
The answer is 3093.
3093 (if that series you posted actually does stop at 1875; there were no dots after, right?)
Step-by-step explanation:
We have a finite series.
We know the first term is 48.
We know the last term is 1875.
What are the terms in between?
Since the terms of the series form a geometric sequence, all you have to do to get from one term to another is multiply by the common ratio.
The common ratio be found by choosing a term and dividing that term by it's previous term.
So 120/48=5/2 or 2.5.
The first term of the sequence is 48.
The second term of the sequence is 48(2.5)=120.
The third term of the sequence is 48(2.5)(2.5)=300.
The fourth term of the sequence is 48(2.5)(2.5)(2.5)=750.
The fifth term of the sequence is 48(2.5)(2.5)(2.5)(2.5)=1875.
So we are done because 1875 was the last term.
This just becomes a simple addition problem of:
48+120+300+750+1875
168 + 1050 +1875
1218 +1875
3093
A river is flowing at the rate of 2.4 miles an hour when a boy rows across it. If the boy rows at a still-water speed of 3.1 miles per hour and heads the boat perpendicular to the direction of the current. The ground speed of the boat is _____ miles per hour.
Answer:
3.9 mi/h
Step-by-step explanation:
If the boy is rowing perpendicular to the current, the two vectors form a right triangle.
AB represents the downstream current, BC is the speed across the river, and AC is the ground speed of the boat
AC^2 = 2.4^2 + 3.1^2 =5.76 + 9.61 = 15.37
AC = sqrt(15.37) = 3.9 mi/h
The boat's speed over the ground is 3.9 mi/h.
The ground speed is found to be approximately 3.92 miles per hour.
we use the Pythagorean theorem to solve this problem.
Step-by-step solution:
Identify the speeds: still-water speed of the boat (3.1 miles per hour) and the river's current speed (2.4 miles per hour).Represent the total ground speed as the hypotenuse of a right-angled triangle, where the other two sides are the still-water speed and the current speed.Calculate the ground speed using the Pythagorean theorem: \(ground speed = \sqrt{(still-water speed)^2 + (current speed)^2}\).Substitute the values: \(ground speed = \sqrt{(3.1)^2 + (2.4)^2} = \sqrt{9.61 + 5.76} = \sqrt{15.37}\).Therefore, the ground speed of the boat is approximately 3.92 miles per hour.This demonstrates how mathematical principles can be applied to real-world scenarios, such as navigating a boat across a river with a current.
Which question is statistical?
What is the address of the museum?
What time does the museum open tomorrow?
How many tours will the museum give this week?
How many visitors came to the museum each month last year?
Answer:
The correct option is D) How many visitors came to the museum each month last year?
Step-by-step explanation:
First, understand that what is the statistical question.
Statistical questions are those question which involves the collection of data. Which can be represented with the help of a chart or tables.
Now consider the provided options:
Options A, B and C are not a statistical question, because these questions do not require or involve the collection of data.
But the option D involves the collection of data because to find the number of visitors came to the museum each month, we need to collect the data.
Therefore the correct option is D.
Answer:
D.) How many visitors came to the museum each month last year?
i am taking the test rn :)
A point on the circumference of the circle with the equation of (x+10)²+(y+1)²=25 is?
A) (-14, -4)
B) (4, 14)
C) (-14, 4)
D) (-4, 14)
Answer:
Option A) (-14, -4)
Step-by-step explanation:
we know that
If a ordered pair lie on the circumference of a circle , then the ordered pair must satisfy the equation of the circle
we have
[tex](x+10)^{2}+(y+1)^{2}=25[/tex]
Verify each ordered pair
case A) we have (-14, -4)
substitute the value of x and the value of y in the equation and then compare the results
[tex](-14+10)^{2}+(-4+1)^{2}=25[/tex]
[tex](-4)^{2}+(-3)^{2}=25[/tex]
[tex]25=25[/tex] ----> is true
therefore
The ordered pair is on the circumference of the circle
case B) we have (4,14)
substitute the value of x and the value of y in the equation and then compare the results
[tex](4+10)^{2}+(14+1)^{2}=25[/tex]
[tex](14)^{2}+(15)^{2}=25[/tex]
[tex]421=25[/tex] ----> is not true
therefore
The ordered pair is not on the circumference of the circle
case C) we have (-14,4)
substitute the value of x and the value of y in the equation and then compare the results
[tex](-14+10)^{2}+(4+1)^{2}=25[/tex]
[tex](-4)^{2}+(5)^{2}=25[/tex]
[tex]41=25[/tex] ----> is not true
therefore
The ordered pair is not on the circumference of the circle
case D) we have (-4,14)
substitute the value of x and the value of y in the equation and then compare the results
[tex](-4+10)^{2}+(14+1)^{2}=25[/tex]
[tex](6)^{2}+(15)^{2}=25[/tex]
[tex]261=25[/tex] ----> is not true
therefore
The ordered pair is not on the circumference of the circle
Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item?
Answer:
320 bags
Step-by-step explanation:
IntroductionLet's first assign some literals, to simplify the problem. The goal is to set everything up, in order to only use one symbol.
[tex]p [/tex]: number of bags with only peanuts.
[tex] a [/tex]: number of bags with only almonds.
[tex] r [/tex]: number of bags with only raisins.
[tex] x [/tex]: number of bags with only raisins and peanuts.
Now, the problem establish 3 useful equations. We can find equations equivalences for the next sentences.
"The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts" is equivalent to [tex] r = 10p[/tex].
"The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts" is equivalent to [tex] a= 20x[/tex].
"The number of bags that contain only peanuts is one-fifth the number of bags that contain only almonds" is equivalent to [tex] p = \frac{1}{5} a [/tex].
Now, let's set every variable in function of [tex] x[/tex]We already know that [tex] a = 20x[/tex]. And because of that, we also know that
[tex]p = \frac{1}{5}a = \frac{1}{5}(20x) = 4x[/tex]
and to conclude this stage of the problem, we also know that [tex]r = 10p =10(4x) = 40x[/tex]
¡Let's draw it!As there are only 3 items, it is possible to use a Venn diagram. As we can see in the diagram, the entire quantity of bags is going to be
[tex]210 + 4x + x + 40x = 210 + 45x[/tex]
But, we also know that there are 435 bags, then we only have to solve the equation:
[tex]210 + 45x = 435[/tex]
[tex]45x = 435 - 210[/tex]
[tex]45x = 225[/tex]
[tex]x = 225/45 [/tex]
[tex]x = 5 [/tex]
ConcludeSubstituting [tex]x = 5[/tex] we get
[tex]a = 20 x = 20(5) = 100[/tex]
[tex]p = 4 x = 4(5) = 20[/tex]
[tex]r = 40 x = 40(5) = 200[/tex]
Finally [tex] ans = 100 + 20 + 200 = 320 [/tex]
Find the greatest common factor of 28 and 42.
2
4
7
14
The greatest common factor (or GCF) is, as the name says, the greatest factor a set of numbers have in common. We can find this by listing out all the possible factors (multiples) of each number:
For 28:
1, 2, 4, 7, 14, 28
For 42
1, 2, 3, 6, 7, 21, 42
(note you don't need to list out all the factors, I just did it for visual purposes)
As you can see, 28 and 42 have 3 factors in common, with 7 being the greatest.
Therefore, the answer would be C: the GCF is 7.
Hope this helps! :)
Answer:
it is 14... have a blessed and amazing day
Step-by-step explanation:
The perimeter of the rectangle is 28 units.
what is the value of w?
Answer:
5
Step-by-step explanation:
Since this is a rectangle, opposite sides are congruent.
That is, the perimeter in terms of w is:
(2w-1)+(2w-1)+(w)+(w)
or
2(2w-1)+2(w)
We can simplify this.
Distribute:
4w-2+2w
Combine like terms:
6w-2
We are given that the perimeter, 6w-2, is 28.
So we can write an equation for this:
6w-2=28
Add 2 on both sides:
6w =30
Divide both sides by 6:
w =30/6
Simplify:
w =5
w is 5
Check if w=5, then 2w-1=2(5)-1=10-1=9.
Does 5+5+9+9 equal 28? Yep it does 10+18=28.
Answer:
w=5
Step-by-step explanation:
To find the perimeter of the rectangle
P = 2(l+w)
where w is the width and l is the length
Our dimensions are w and 2w-1 and the perimeter is 28
Substituting into the equation
28 = 2(2w-1 +w)
Combining like terms
28 = 2(3w-1)
Divide each side by 2
28/2 = 2(3w-1)/2
14 = 3w-1
Add 1 to each side
14+1 = 3w-1+1
15 = 3w
Divide each side by 3
15/3 =3w/3
5 =w
About 1% of the population has a particular genetic mutation. 700 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 700.
Answer: 2.632
Step-by-step explanation:
Given : The probability that the population has a particular genetic mutation = 1 % = 0.01
Let X be a random variable representing the number of people with genetic mutation in a group of 700 people.
Now, X follows the binomial distribution with parameters:
[tex]n=700;\ p=0.01[/tex]
The standard deviation for binomial distribution is given by :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{700\times0.01(1-0.01)}\\\\=2.6324893162\approx2.632[/tex]
Hence, the standard deviation = 2.632
A scientist is studying the decay of a certain substance after being exposed to two different treatments. Under treatment A, the substance continuously decays at a rate of 4% daily. Under treatment B, another sample of the same substance continuously decays at a rate of 6.2% daily.A second scientist comes to record the amount remaining each day and only knows that there was initially less than 300 grams of the substance undergoing treatment A and at most 400 grams of the substance undergoing treatment B.What system of inequalities can be used to determine t, the number of days after which the remaining amount of each sample,y, in grams, is the same?
Answer:
0 < y < 300·0.96^t0 < y ≤ 400·0.938^tStep-by-step explanation:
When a quantity changes exponentially by a fraction r in some time period t, the quantity is multiplied by 1+r in each period. That is the quantity (y) as a function of t can be described by ...
y = y0·(1+r)^t
where y0 is the initial quantity (at t=0).
Here, the problem statement gives us two quantities and their respective rates of change.
Treatment A
y0 < 300, r = -0.04, so the remaining amount is described by ...
y < 300·0.96^t
__
Treatment B
y0 ≤ 400, r = -0.062, so the remaining amount is described by ...
y ≤ 400·0.938^t
__
When we graph these, we realize these inequalities allow the quantity of each substance to be less than zero. Mathematically, those quantities will approach zero, but not equal zero, so we can put 0 as a lower bound on the value of y in each case:
0 < y < 300·0.96^t0 < y ≤ 400·0.938^t_____
Comment on these inequalities
We suspect your answer choices will not be concerned with the lower bound on y.
Answer:
y (arrow left) 300e-0.04t
y (arrow left underlined) 400e-0.062t
Step-by-step explanation: