The length of a social media interaction is normally distributed with a mean of 3 minutes and a standard deviation of 0.4 minutes.
What is the probability that an interaction lasts longer than 4 minutes?
1)0.0045254
2)0.043351
3)0.0095254
4)0.006209
Answer: 4) 0.0062097
Step-by-step explanation:
Given : The length of a social media interaction is normally distributed with a mean of [tex]\mu=3[/tex] minutes and a standard deviation of [tex]\sigma=0[/tex] minutes.
Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponding to x=4 will be :-
[tex]z=\dfrac{4-3}{0.4}=2.5[/tex]
Using the standard normal distribution table for z-value , the probability that an interaction lasts longer than 4 minutes will be :-
[tex]P(z>2.5)=1-P(z\leq2.5)=1-0.9937903=0.0062097[/tex]
Hence, the probability that an interaction lasts longer than 4 minutes = 0.0062097
The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.
What does the value 5 represent in this situation?
A. Five quarters are added to the bowl every week.
B. The value of the quarters in the bowl on Week 1 was $5.
C. Quarters were added to the bowl for 5 weeks.
D. There were 5 quarters in the bowl on Week 1.
The statement "Five quarters are added to the bowl every week" is a correct option (A) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.
q(w) = 3 + 5(w−1)
q(w) = 5w - 5 + 3
q(w) = 5w - 2
y = mx + c
m = 5
Here 5 means five quarters are added to the bowl every week.
Thus, the statement "Five quarters are added to the bowl every week" is a correct option (A) is correct.
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Your medical bill is $2345. Your health insurance covers 70% after a $120 deductible. What amount of the bill will you pay?
Answer:
It is $787.50.
What is the standard form equation of the line shown below?
Graph of a line going through negative 1, 1 and 1, 4
−3x + 2y = 5
3x − 2y = −5
y − 4 = three halves(x − 1)
y = three halvesx + five halves
Final answer:
The standard form equation of the line through the points (-1, 1) and (1, 4) is 3x - 2y = -5.
Explanation:
The standard form equation of a line can be represented as Ax + By = C, where A, B, and C are constants. To find the equation of the line through the points (-1, 1) and (1, 4), we can use the point-slope form.
First, find the slope using the formula m = (y2 - y1)/(x2 - x1). In this case, m = (4 - 1)/(1 - (-1)) = 3/2.
Next, choose one of the given points, let's say (-1, 1), and substitute the values into the point-slope formula. y - y1 = m(x - x1). We have y - 1 = (3/2)(x - (-1)).
Simplify the equation by distributing the slope and rearranging the terms. y - 1 = (3/2)x + 3/2.
Finally, convert the equation to standard form by moving all terms to one side and multiplying by a common denominator. 3x - 2y = -5.
Which of the following values is equal to 1 micrometer?
A. 0.000001 meter
B. 0.001 meter
C. 1,000 meter
D. 1,000,000 meter
The drawing of a building, shown below, has a scale of 1 in to 30 ft. what is the actual height, in ft, of the building
The function f(x)=400(1.5)xf(x)=400(1.5)x models an insect population after x months. How does the average rate of change between Months 2 and 4 compare to the average rate of change between Months 0 and 2?
The average rate of change is 2.25 times as fast.
The average rate of change is 2 times as fast.
The average rate of change is 3.125 times as fast.
The average rate of change is 1.5 times as fast.
Answer:
The answer is 2.25 times as fast. I just did this one
Step-by-step explanation:
What is the domain and range for the function below?
1/square root x+4
Divide. Write each quotient in simplest form.
2/3 ÷ 2 = _____ Show step-by-step solution.
You can buy DVDs at a local store for $15.49 each. You can buy them at an online store for $13.99 each plus $6 for shipping. How many DVDs can you buy for the same amount at the two stores?
what is the sum of this infinite geometric series? 2+ 2/5+2/25+2/125+..... ...?
Final answer:
The sum of the infinite geometric series 2 + 2/5 + 2/25 + 2/125 + ... is 2.5, determined by using the formula for the sum of a convergent geometric series, which in this case is S = 2 / (1 - 1/5).
Explanation:
The question you've asked relates to the sum of an infinite geometric series. The series given is 2 + 2/5 + 2/25 + 2/125 + ..., which is a series where each term after the first is found by multiplying the previous term by 1/5. To find the sum of this infinite geometric series, we can use the formula for the sum of a convergent geometric series, which is S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio (the factor we multiply by to get each term in the series).
In this case, the first term 'a' is 2, and the common ratio 'r' is 1/5. So our formula becomes S = 2 / (1 - 1/5), which simplifies to S = 2 / (4/5) or S = 2 * (5/4), which gives us S = 2.5. Therefore, the sum of the infinite geometric series is 2.5.
A line contains the points (−26, −37) and (−32, −61) .
What is the slope of the line in simplified form?
Answer:
the answer should be 4, you left the - off of the 61
Step-by-step explanation:
If f(n) = n^ 2 - n, then f(-4) is _____.
-20
20
12
-12
f(-4) = 20 when evaluated in the given function f(n) = n^2 - n. This result was obtained through substitution in the function followed by simplification.
Explanation:In this problem, you are given a function f(n) = n^2 - n. To find the value of f(-4), you simply need to substitute -4 in place of n in the function and compute.
So,
f(-4) = (-4)^2 - (-4)
= 16 - (-4)
= 16 + 4 = 20
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Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
y = ± square root of x^2 - 5
A. Asymptotes: y = ± x
B. Asymptotes: y = ± 5/3 x
C. Asymptotes: y = ± 5/3 x
D. Asymptotes: y = ± x
Answer:
3rd graph is the correct graph
Step-by-step explanation:
Given is the equation of hyperbola as
[tex]y = ± \sqrt{x^2-5}[/tex]
Square both sides and rearrange to get
[tex]y^2=x^2-5 \\x^2-y^2 =5[/tex]
Vertices are [tex](\sqrt{5} ,0) \\(-\sqrt{5} ,0)[/tex]
Asymptotes would have the same equation as hyperbola except constant term as 0
[tex]x^2-y^2 =0[/tex]
are the asymptotes
Or [tex]y = ± x[/tex] option d is right.
how do you solve this?
f a computer costs $600.00 and the sales tax rate is 7.5 percent, what is the total cost of the computer?
As per linear equation, the total cost of the computer is $645.00.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given, the cost of computer is $600.00.
The sales tax rate is 7.5%.
Therefore, the total cost of the computer is
= $[tex][600.00 + \frac{(7.5)(600.00)}{100}][/tex]
= $[tex][600.00 + 45.00][/tex]
= $[tex]645.00[/tex]
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The weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs. What is the range of actual weights of the object?
Answer:
[tex]144.9\leq x\leq 145.5[/tex]
Step-by-step explanation:
Let x represent actual weight of object.
We have been that the weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs.
[tex]|\text{Actual}-\text{Ideal}|\leq \text{Tolerance}[/tex].
Upon substituting our given values, we will get:
[tex]|x-145.2|\leq 0.3[/tex]
Applying absolute value rule [tex]|u|\leq a=-a\leq u\leq a[/tex], we will get:
[tex]-0.3\leq x-145.2\leq 0.3[/tex]
Add 145.2 on each side:
[tex]-0.3+145.2\leq x-145.2+145.2\leq 0.3+145.2[/tex]
[tex]144.9\leq x\leq 145.5[/tex]
Therefore, our required range will be [tex]144.9\leq x\leq 145.5[/tex].
A triangle with a base of 4 units and a height of 14 units?
Which number is a perfect cube? a.21 b.49 c.343 d.600
Answer:
343
Step-by-step explanation:
7*7*7=343
The factor of the 343 will be 7, 7, and 7. Then the number 343 is a perfect cube of 7.
What is a perfect cube?The integers that are the threefold multiplication with the same number are known as perfect cubes.
To put it another way, a perfect cube is the combination of complex times multiplying a whole integer by itself.
A perfect cube is a quantity that may be stated as the composition of three different numbers.
A. The factor of the 21 will be 3 and 7. It can not be a perfect cube.
B. The factor of the 49 will be 7 and 7. It can not be a perfect cube.
C. The factor of the 343 will be 7, 7, and 7. It is a perfect cube.
D. The factor of the 600 will be 2, 2, 2, 3, 5, and 5. It can not be a perfect cube.
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The ratio of the number of cats to the number of dogs in an animal shelter was 2:3. After 120 cats were adopted, the ratio of the number of cats to the number of dogs became 3:7. Find the total number of cats and dogs in the animal shelter in the end?
how are the variables related on the graph?
A. As speed decreases, height stays constant
B. As speed deceases , height increases
C. As speed increases , height decreases
D. As speed increases , height increases
Answer:
The answer to this question is
As speed increases the height Increases
Step-by-step explanation:
Because increases mean going up so when the speed is going up the height of the speed also increases so that's why when the speed increases also the height increases
I hope this works
YW!
The correct explanation of the graph will be;
''As speed increases, height is decreases.''
Option D is true.
What is an mathematical expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph is shown in figure for the relation of height and speed.
Since, The graph is shows when the speed of any object increase, then its height will also be increase.
Thus,
The correct explanation of the graph will be;
''As speed increases, height is decreases.''
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The solution set for the inequality - 3 (x - 4) > 6(x - 1), includes 3 as an element. True False
The solution set for the inequality - 3 (x - 4) > 6(x - 1) does not include 3 as an element which is inequality is false.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have been given inequality as:
-3(x-4) > 6(x-1)
To determine the solution set for the inequality.
Substitute x = 3 in the given inequality for each value of x with 3 and simplify both sides.
⇒ -3(x-4) > 6(x-1)
⇒ -3(3-4) > 6(3-1)
⇒ -3(-1) > 6(2)
⇒ 3 > 12
Since inequality 3 > 12 is not true,
So, for x = 3, the given inequality is false. Therefore, 3 is not included in the solution set.
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Sheila is ordering pizzas for a party. each plain pizza costs $9.00, and each topping costs $1.50. the delivery charge is $3.00. write a function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings. how much will 5 pizzas cost?
Answer: [tex]c=12x+3[/tex], where c is the total cost of x pizzas.
The cost of 5 pizzas = $63
Step-by-step explanation:
Given : Cost of each pizza = $9.00
Cost of each topping = $1.50
⇒ Cost of 2 toppings = 2 x $1.50 = $3.00
Then, the cost of each pizza having 2 toppings = $9.00+ $3.00= $12.00
Let x be the number of pizzas .
Then , the cost of x pizzas = 12x
Since , Delivery charge = $3.00
Then, the total cost of ordering x pizzas( in dollars) = Cost of x pizzas+ Delivery charge = 12x+3
Function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings : [tex]c=12x+3[/tex] , where c is the total cost.
Put x= 5
[tex]c=12(5)+3=60+3=63[/tex]
Hence, the cost of 5 pizzas = $63
If a line crosses the y-axis at (0, -3) and has a slope of 3, what is the equation of the line?
find a value of the constant k such that the limit exists:
lim (x^2+4x+k)/(x+2) as x goes to -2 ...?
There are total of 84 students in the robotics club and the science club. The science club has 12 more students than the robotics club. How many students are in the science club?
By setting up an equation and solving for the number of students in each club, we find there are 48 students in the science club.
To solve the problem, we can set up an equation based on the information given. Let the number of students in the robotics club be represented by x.
According to the problem, the science club has 12 more students than the robotics club, so the science club has x + 12 students. We also know that there are a total of 84 students in both clubs combined. Therefore, we can set up the following equation:
x + (x + 12) = 84
Combining like terms, we have:
2x + 12 = 84
Subtracting 12 from both sides gives us:
2x = 72
Dividing both sides by 2 gives us:
x = 36
So, there are 36 students in the robotics club. To find the number of students in the science club, we add 12 to the number of students in the robotics club:
36 + 12 = 48
Therefore, there are 48 students in the science club.
The midpoint of a segment is (2,-5) and one of the end points is (3,6). Where is the other endpoint?
find the amount that results from each. $50 invested at 6% compounded monthly after a period of 3 years ...?
Final answer:
Using the compound interest formula, the total amount after three years for $50 invested at 6% compounded monthly is approximately $59.70.
Explanation:
To calculate the future value of $50 invested at 6% compounded monthly after a period of three years, we use the formula for compound interest:
FV = P × (1 + (r/n))³⁼ ×⁴
where:
FV is the future value of the investment,
P is the principal amount ($50),
r is the annual nominal interest rate (6% or 0.06),
n is the number of times the interest is compounded per year (12, for monthly compounding),
t is the time the money is invested for, in years (3 years).
Using these values, we calculate as follows:
FV = $50 × (1 + (0.06/12))³·×´ = $50 × (1 + 0.005)·¹·´
Now we calculate this raised to the power of 36 (3 years times 12 months):
FV = $50 × (1.005)³···¶ = $50 × 1.194052
Thus, FV ≈ $59.70
The total amount after three years would be approximately $59.70, assuming the interest is compounded monthly at a rate of 6%.
Stephen has a dog that weighs 5 times as much as ian’s dog. the total weight of both dogs is 72 pounds. how much does stephen’s dog weigh?
The weight of Stephen's dog such that Stephen has a dog that weighs 5 times as much as Ian's dog will be 60 pounds.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's assume the weight of Stephen's dog is "s" while Ion's dog is "i".
As per the given,
Stephen has a dog that weighs 5 times as much as Ian's dog.
s = 5i
Total weight, s + i = 72
Substitute, i = 72 - s into s = 5i
s = 5(72 - s)
s = 360 - 5s
s + 5s = 360
6s = 360
s = 60 pounds.
Hence "The weight of Stephen's dog such that Stephen has a dog that weighs 5 times as much as Ian's dog will be 60 pounds".
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How many radians is 270°??