Your friend is looking at laptops for college, and is comparing the different
screen sizes. Use the diagram and formula below to find the height of the
laptop screen. Round your answer to the tenths place.
d - VW
d= 72.7mn
h
W 026
Answer:
B. h = 7.4 inches
Step-by-step explanation:
height of the laptop screen = h
d = 12.1 in.
w = 9.6 in.
We are given the formula,
d = √(w² + h²)
Plug in the values and solve for h
12.1 = √(9.6² + h²)
Square both sides
12.1² = 9.6² + h²
146.41 = 92.16 + h²
146.41 - 92.16 = h²
54.25 = h²
√54.25 = h
7.4 = h (nearest tenth)
h = 7.4 inches
100 POINTS!!!!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Given answer the questions that follow.
a. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x ≥ 0. Is your friend correct? Explain your reasoning.
b. How are the 2 functions different?
Answer:
a. The friend is incorrect.
2(x) is the same as x(2). PEMDAS does not apply to the same order of operation under normal conditions and both are directly proportional functions.
b. The parentheses are the only thing making the functions different. After you simplify from the parentheses, both values have the same priority.
Step-by-step explanation:
Suppose that E and F are points on the number line. If EF=20 and E lies at 4, where could F be located?
Answer:
F lies at 24Step-by-step explanation:
Since EF = 20 and E is at 4
F is at:
4 + 20 = 243x+4 number of terms
9514 1404 393
Answer:
2
Step-by-step explanation:
In this expression, the terms are the parts of the sum. They are 3x and 4. There are 2 terms.
Two statements are logically equivalent when:
A. The two statements are true in virtue of their logical structure alone, i.e. the two statement are always true.
B. The first statement implies the second, i.e. if the first statement is true, so is the second.
C. The two statements agree in point of truth or falsehood in virtue of their logical structure alone, i.e. the two statement are true or false in exactly the same conditions.
D. The two statements are false in virtue of their logical structure alone, i.e. the two statement are always false.
C. The two statements agree in point of truth or falsehood in virtue of their logical structure alone, i.e. the two statement are true or false in exactly the same conditions.
Step-by-step explanation:For two statements to be logically equivalent, their truth values (true or false) must be the same for every variation of their constituent variables. In other words, if the truth tables of both statements are the same for every possible value of their variables, then they are logically equivalent.
For example;
The two statements P ∩ (Q U R) and (P ∩ Q) ∪ (P ∩ R) are logically equivalent.
If P, Q and R are all true, then;
P ∩ (Q U R) = true
(P ∩ Q) ∪ (P ∩ R) = true
If P, Q and R are all true, then;
P ∩ (Q U R) = false
(P ∩ Q) ∪ (P ∩ R) = false
If P = false, Q = true and R = true, then;
P ∩ (Q U R) = false
(P ∩ Q) ∪ (P ∩ R) = false
Checking for all other possible combinations of truth values of P, Q and R will always give the same results for the two statements, therefore, they are logically equivalent.
An electronic system contains three cooling components that operate independently. The probability of each component's failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.
Answer:
[tex]Pr= 0.00725[/tex]
Step-by-step explanation:
Given
[tex]p = 0.05[/tex] ---- probability that each component fails
[tex]n = 3[/tex]
Required
[tex]P(System\ Overheats)[/tex]
We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z
The events that the system will overheat are: xyz', xy'z, x'yz and xyz
Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)
So, we have:
[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]
[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]
[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]
[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]
So, the required probability is:
[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]
[tex]Pr= 0.00725[/tex]
My daughter had a quiz today and the 3 questions did not make sense to me. Can anyone decifer how you would solve for the variable on these? I am stumped!!
1) In 10 years, Sara will be 81 older than she is now. How old is Sara now?
2) In 8 years, Sara will be 49 years older than she is now. How old is Sara now?
3) In 11 years, Bob will be 100 years than he is now. How old is Bob now?
Answer:
1 71years
Step-by-step explanation:
x+10=81
x=71
2. x+8=49
x=41
3. x+11=100
x=99
If f(x)=5x and g(x)=2x-1, what is the composition f(g(x))?
Answer:
10x-5
Step-by-step explanation:
f(x)=5x
g(x)=2x-1
To create a composite function, replace x in f(x) with g(x)
f(g(x)) = 5(g(x) = 5(2x-1) = 10x-5
What is the correct line graph for y=3x+5?
Answer:
The equation y=−3x+5 is in slope intercept form, and represents a straight line in which -3 is the slope, and 5 is the y -intercept.
The following formula gives the area A of a trapezoid with base lengths b1 and b2, and height h.
A=12(b1+b2)h
Find the area of a trapezoid with base lengths 3 and 6 and a height of 8.
The expansion of (x-2)(x+2) is …..
Answer:
x2-4
Step-by-step explanation:
Answer:
(x+2)(x-2)(x²-2²)(x²-4)hope it helps
stay safe healthy and happy...Samantha acored 15 points in her laat
basketball game. She made 3 free throwa
that are worth 1 point each. The rest of
her pointa came on 2 point field goala,
Write an equation that can be used to find
the number of 2 point field goals that
Samantha made
(uae p as your variable)
Help fasttt
Answer:
15=2p+3
Step-by-step explanation:
The function f(x) is shown below.
х
-6
-3
f(x)
1
2
5
3
Coon
0
If g(x) is the inverse of f(x), what is the value of f(g(2))?
-6
оооо
5
Answer:
[tex]f(g(2)) = 2[/tex]
Step-by-step explanation:
Given
[tex]x \to f(x)[/tex]
[tex]-6 \to 1[/tex]
[tex]-3 \to 2[/tex]
[tex]g(x) = f^{-1}(x)[/tex] --- inverse
Required
[tex]f(g(2))[/tex]
For two functions f(x) and g(x) where f(x) and g(x)are inverse;
[tex]f(g(x)) = x[/tex]
So, by comparison:
[tex]f(g(2)) = 2[/tex]
by what number should 2/9 be divided to obtain 8/3
Answer:
[tex] \frac{1}{12} [/tex]
Step-by-step explanation:
[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]
So, if you divide 2/9 by 1/12, you'll get 8/3
Answered by GAUTHMATH
ANSWER ASAP IM BEING TIMED
IF I GET AN A ON THIS I WILL DO ANOTHER POINT FREE DROP, PLEASE SHOW YOUR WORK
The side of a square measures (4x − 7) units.
Part A: What is the expression that represents the area of the square? Show your work to receive full credit. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
(10 points)
Step-by-step explanation:
Area of a square = s x s
(4x-7)x(4x-7)
Open brackets
4x(4x-7)-7(4x-7)
16x^2-28-28x+49
16x^2-28x+21
Marty's barber shop has one barber. Customers arrive at a rate of 2.2 per hour and haircuts are given at a rate of 5 customers per hour. Assume a Poisson arrival rate and an Exponential service time distribution.
Required:
a. What is the probability that one customer is receiving a haircut and one customer is waiting?
b. What is the probability that one customer is receiving a haircut and two customers are waiting?
c. What is the probability that more than two customers are waiting?
Answer:
Step-by-step explanation:
Arrival rate = ∧ = 2.2 customers per hour
Service rate = u = 5 customers per hour
1. Probability that one customer is receiving a haircut and one customer is waiting
P(2 customers)=(∧/u)^2 * (1-∧/u)=(2.2/5)^2 * (1-2.2/5)=0.1936*0.56= 0.108416
2. Probability that one customer is receiving a haircut and two customers are waiting
P(3 customers)= (∧/u)^3 * (1-∧/u)=(2.2/5)^3 * (1-2.2/5)= 0.085184
* 0.56= 0.04770304
3. Probability that more than two customers are waiting
P(more than 3 customers)=1- P(less than 3 customers) =
1- [P(0)+P(1)+P(2)+P(3)]=
= 1- [(1-2.2/5) +2.2/5*(1- 2.2/5) + 0.108416+0.04770304]=1-0.9625=0.0375
Suppose z varies directly with x and inversely with the square of y. If z = 16 when x = 4 and y = 1 , what is z when x = 8 and y = 9 ?
Answer:
z = 3.6
Step-by-step explanation:
Given that,
z varies directly with x and inversely with the square of y. We can write it as :
[tex]z\propto \dfrac{x}{y}\\\\z=\dfrac{kx}{y}[/tex]
Where
k is constant
Put z = 16 when x = 4 and y = 1
[tex]16=\dfrac{k\times 4}{1}\\\\k=4[/tex]
Now put k = 4, x = 8 and y = 9
[tex]z=\dfrac{4\times 8}{9}\\\\z=3.6[/tex]
So, the value of z is equal to 3.6.
The value of Tonya's car is $21,000. The car's value depreciates at a rate of 15% per year.
Which function represents the value of the car after t years?
f(t)=0.85(21,000)t
f(t)=1.15(21,000)t
f(t)=21,000(0.85)t
f(t)=21,000(1.15)t
9514 1404 393
Answer:
(c) f(t)=21,000(0.85)^t
Step-by-step explanation:
Each year, the value is multiplied by 1-15% = 85% = 0.85. This is correctly shown in the function ...
f(t)=21,000(0.85)^t
A teacher is paid an annual salary of $37.165. What is her gross monthly salary.
Answer:
3.01
Step-by-step explanation:
To Find :-
Monthly salary .SOLUTION :-
=> Monthly salary = $ 37.165/12= $ 3.01
please help please help
Answer:
1. number line or 3
2. D
3. E and K
4. B
5. A
Brainliest please~
June, Gavyn and Alex share some sweets in the ratio 5:5:3. June gets 22 more sweets than Alex. How many sweets are there altogether?
Answer:
Let June's sweets be 5x.
Then Gavyn's sweets will be 5x.
And Alex's sweets will be 3x.
5x = 3x + 22
2x = 22
x = 11
So June has 5 x 11 = 55 sweets
Gavyn has 5 x 11 = 55 sweets
And Alex have 3 x 11 = 33 sweets
Total
= 55 + 55 + 33
= 143 sweets
870,640 rounded to the nearest ten thousand
Answer: 870,000
Step-by-step explanation: First find the digit in the rounding place
which in this case is the 7 in the ten thousands place.
Next, we look at the digit to the right of the 7, which is 0.
According to the rules of rounding, if the digit to the right
of the rounding place is less than 5, we round down.
So the 7 in the rounding place stays the same
and all digits to the right of the become 0.
So 870,640 rounded to the nearest ten thousand is 870,000.
-2,6,-18,54, what is the common ratio of the sequence
Answer:
2
Step-by-step explanation:
Answer:
Common Ratio=-3
Step-by-step explanation:
To find any common ratio in a sequence, always take the second number in the sequence and divide it by the first number. However, you must be careful because the common ratio should only be negative if the values in the sequence are alternating between negative and positive. Therefore, if the sequence of numbers is simply decreasing in value, this does not mean that the common ratio is negative. The common ratio would still be positive. If the sequence is decreasing in value, this means that the common ratio would be a fraction or a decimal less than one.
In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home. Give the value of the standard error for the point estimate.
Answer:
The value of the standard error for the point estimate is of 0.0392.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.
This means that [tex]n = 100, p = \frac{81}{100} = 0.81[/tex]
Give the value of the standard error for the point estimate.
This is s. So
[tex]s = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]
The value of the standard error for the point estimate is of 0.0392.
A gym at a school is being painted. The four walls and the ceiling are to be painted (but not the floor). The gym measures 100 ft x 65 ft x 25 ft. A 5 gallon can of paint costs $151.99 and covers 1750 ft. How many cans should be purchased? What will it cost to paint two coats for this gym (include HST)?
9514 1404 393
Answer:
17 cans$2,971.40Step-by-step explanation:
We assume ...
the 25' dimension is the wall heightthe HST rate is 15% (the paint is not purchased in Ontario)only full cans of paint can be purchasedThe wall area is the wall height times the perimeter of the room.
wall area = (25')(2(100' +65')) = 8250 ft²
The ceiling area is the product of length and width.
ceiling area = (100')(65') = 6500 ft²
Then the area to be painted with each coat is ...
painted area = wall area + ceiling area = (8250 +6500) ft² = 14750 ft²
Then two coats of paint will require sufficient paint to cover ...
(2 coats)×(14750 ft²/coat) = 29,500 ft²
__
If each can of paint covers 1750 ft², the number of cans required is ...
(29,500 ft²)/(1750 ft²/can) = 16.86 cans
17 cans must be purchased
__
The cost of 17 cans of paint with sales tax will be ...
(17 cans)($151.99/can)(1 +15%) = $2971.40
Sam takes a job with a starting salary of $50,000 for the first year. He earns a 4% increase each year. Which expression gives the partial sum, S3, (in thousands)?
A sample of students was asked what political party do they belong. which of the following types of graphical display would be appropriate for the sample?
A. Stemplot.
B. Pie chart.
C. Scatterplot.
D. All of the above.
Answer:
B. Pie chart.
Step-by-step explanation:
In this question, the students are asked what political party they belong. The best display format would be one in which the graph can be divided into parts, or percents, according to the percentage of students belonging to each political party. The graph that best describes this, distributing a group into parts, is a pie chart, and thus, the correct answer is given by option b.
Scatterplot is used when two variables correlate together, that is, there is a relationship between them, which we don't have between the number, or proportion of students belonging to each political party. Stemplot are used when there is a high number of quantitative data, which we do not have here.
Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned
Answer:
The warranty period should be of 30 months.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months.
This means that [tex]\mu = 37, \sigma = 5[/tex]
What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned?
The warranty period should be the 7th percentile, which is X when Z has a p-value if 0.07, so X when Z = -1.475.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.475 = \frac{X - 37}{5}[/tex]
[tex]X - 37 = -1.475*5[/tex]
[tex]X = 29.6[/tex]
Rounding to the nearest whole number, 30.
The warranty period should be of 30 months.
what is nine and three hundred twenty-one thousandths in decimal notation?
Answer:
Step-by-step explanation:
find the x-intercepts y=2x^2 + 5x + 2/x^2-4x+3
Answer:
[tex]{ \tt{y = \frac{2 {x}^{2} + 5x + 2}{ {x}^{2} - 4x + 3 } }} \\ x - intercept : y = 0 \\ { \tt{ \frac{2 {x}^{2} + 5x + 2 }{ {x}^{2} - 4x + 3 } = 0 }} \\ \\ { \tt{2 {x}^{2} + 5x + 2 = 0}} \\ x = \frac{1}{2} \: \: and \: \: x = - 2[/tex]
