A flat screen television measures diagonally 40 inches and 24 inches in length. What is the width of the television?
Answers
Answer:
The width of the Television is 32 inches.
Step-by-step explanation:
It seems as if the hypotenuse of the triangle is 40 inches, and one of the side lengths of it is 24 inches.
a2+b2=c2
So if we square 40 we get 1600, which is c2
If we square 24, we get 576, which is a2.
Then you solve, 576+b2=1600
you get b2=1600
Then you get the square root of both sides which in turn gives you the answer
b=32, which is the width of the television.
Step-by-step explanation:
use the pythagorean theorem c^2 = a^2 + b^2 diagonal is the hypotenuse...
40^2 = 24^2 + b^2
b^2 = 40^2 - 24^2
b =
\( b = \sqrt{40 {}^{2} - 24 {}^{2} } \)
Related Questions
the are of the circle below is 28.26 ft. squared. What is the diameter
Answers
Answer: 8.06 Inches
The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.
Among all pairs of numbers whose sum is 24, find a pair whose product is as large as possible. Show the work(the steps)! Write an equation of the corresponding quadratic function. How parabola opens? What is the maximum product? Does this function has a maximum value or the minimum value? Explain. Graph the function and upload the image.
Answers
The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.
To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.
Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.
To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:
P(x) = x(24 - x)
This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.
The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.
To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.
Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.
So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.
Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.
To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]
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Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
Answers
The dimensions of the length and width are 25 meters and 12. 5 meters respectively.
How to determine the valuesArea of a rectangle
area of rectangle = l × w
where
l = length
w = width
Note that,
Perimeter = 2w+ l
50 = 2w + l
l = 50 - 2w
Hence,
area = w(50 - 2w)
288 = 50w - 2w²
-2w² + 50w - 288 = 0
-w² + 25w - 144 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 25
w = - 25 / 2 × -1
w = 12.5 meters
Then, we have that
l = 50 - 2w
Substitute the value of w
l = 50 - 2(12.5)
l = 50 - 25
I = 25 meters
Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.
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Help! :)
Find the average.
a) 23.6, 15.78, 12.4
b) 1116 mm, 1289 mm, 1218 mm (in metres)
Answers
B) 1.21 meters
Sarah begins the week with $21.55. A school lunch costs $2.75. How many
school lunches can she buy and still have at least $10 left at the end of the
week? Write and solve an inequality that Sarah can use to determine the
number of lunches n that she can buy. Don’t add links.I need the answer
Answers
Answer:
so you do 21.55 - 10.00 to get 11.55 now divide 11.55 by 2.75
you get 4.2 or 4 meals
the inequality is
X is the number of meals
x = 11.55 divided by sybmol 2.75 = 4.2
or 21.55 - 10 = 11.55 divided by 2.75 = 4.2
Step-by-step explanation:
The diagram shows a prism. Draw the front and side elevation of the prism on the grid. Use the scale 2 squares to 1m.
I know that the side elevation is correct but I can't get the front. Please help!
Answers
The sketch of the front elevation and the side elevation of the prism are added as an attachment
How to draw the front elevation and the side elevation of the prismFrom the question, we have the following parameters that can be used in our computation:
The prism
Using the figure as a guide, we understand that:
The front elevation is a rectangle of 2m by 0.5m
While the side elevation is a rectangle merged with a trapezoid
Next, we draw the elevations (see attachment)
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At Best Buy, all Samsung Galaxy cell phones are on sale for a discount of 25%. Which statement best represents the functional relationship between the sale price of a cell phone and the original price? * . the original price is dependent on the sale price b. the sale price and the original price are both dependent on each other c. There is not enough information to determine the relationship d. the sale price is dependent on the original price
Answers
Answer: The correct answer is:
d. The sale price is dependent on the original price.
Step-by-step explanation: The discount of 25% is applied to the original price to calculate the sale price. Therefore, the sale price is determined by the original price.
there is a jar of 25 marbles. 9 of the marbles have a blue and black pattern. 6 of the marbles are purple. 10 of the marbles are green. one marble is chosen at random. what is the probability of picking to blue and black patterned marbles?
Answers
Answer:
Probability = 9/25
This is 36%
Step-by-step explanation:
To find the probability take the total number of possibilities (25 marbles--all of them) put that number on the bottom of a fraction. Then put the number of ways that outcome can happen (9 blue and black) and put that on top of the fraction.
Probability(event)
= specific/total
Probability(blu&blk)
= 9/25
If the fraction can be simplified, do that. 9/25 cannot be simplified.
If you need a percent for your answer, divide then multiply by 100.
A fraction bar is a division symbol.
9/25 means 9÷25.
9/25 = .36
Percent means "per hundred" To convert a decimal to a percent, multiply by 100
.36×100 is 36%
5. Determine the maximum number of real zeros.f
(x)=(x-1/3)^2(x-1)^3
Answers
Answer:
The maximum number of real zeros of the function is 5.
Step-by-step explanation:
Zeros of a polynomial
Any polynomial of positive order can have a maximum number of zeros equal to its order. For example, a quadratic function can have as many as two zeros.
The given polynomial is:
\(f(x)=(x-1/3)^2(x-1)^3\)
The order of this polynomial is 5 since it's factored as a quadratic polynomial by a cubic polynomial. The order is 2+3=5.
Thus, the maximum number of real zeros of the function is 5.
What can teachers do to alleviate statistics anxiety in their students? To explore this question, statistics anxiety for students in two classes was compared. In one class, the instructor lectured in a formal manner, including dressing formally. In the other, the instructor was less formal, dressed informally, was more personal, used humor, and called on students by their first names. Anxiety was measured using a questionnaire. Higher scores indicate a greater level of anxiety. The mean anxiety score for students in the formal lecture class was 25.40 . In the informal class, the mean was 20.41 . Classify 25.40 and 20.41 as parameters or statistics.
Answers
Answer: Statistic
Step-by-step explanation: The difference between a parameter and statistic lies in the set of observation from which either quantity is derived. The parameter represents numerical values which are derived by examining or considering an entire population while the statistic is used to define numerical quantities derived from subset of the population called the sample. In the scenario described above, the population of interest would be the entire population of student and hence statistical derivations made would be called parameters. However, the scenario only experimented using student from two different classes which is a subset of the entire population of student. Hence, the obtained mean values of 25.40 and 20.41 for students in the formal and informal classes are categorized as statistic.
PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️
Answers
Answer:
1st one is 6.9 X 10^6
2nd one is 2 x 10^5
Step-by-step explanation:
Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation.
Bank A (single line) Bank B (individual lines)
6.5 4.0
6.6 5.4
6.7 5.9
6.7 6.2
7.1 6.8
7.4 7.7
7.5 7.7
7.7 8.5
7.7 9.4
7.7 9.8
A) The coefficient of variation for the waiting times at Bank A is
(Round to one decimal place as needed.)
B) The coefficient of variation for the waiting times at Bank B is
(Round to one decimal place as needed.)
C)Is there a difference in variation between the two data sets?
Answers
The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%.
To find the coefficient of variation for each set of data, we need to calculate the mean and standard deviation for each set. The coefficient of variation is then calculated by dividing the standard deviation by the mean and multiplying by 100.
Let's calculate the coefficient of variation for each set of data:
Bank A (single line):
Mean: Calculate the mean of the data set.
Mean = (6.5 + 6.6 + 6.7 + 6.7 + 7.1 + 7.4 + 7.5 + 7.7 + 7.7 + 7.7) / 10 = 7.03 minutes
Standard deviation: Calculate the standard deviation of the data set.
Standard deviation = √[(6.5 - 7.03)² + (6.6 - 7.03)² + ... + (7.7 - 7.03)²] / 10 ≈ 0.565 minutes
Coefficient of variation:
Coefficient of variation = (0.565 / 7.03) * 100 ≈ 8.04%
Bank B (individual lines):
Mean: Calculate the mean of the data set.
Mean = (4.0 + 5.4 + 5.9 + 6.2 + 6.8 + 7.7 + 7.7 + 8.5 + 9.4 + 9.8) / 10 = 7.5 minutes
Standard deviation: Calculate the standard deviation of the data set.
Standard deviation = √[(4.0 - 7.5)² + (5.4 - 7.5)² + ... + (9.8 - 7.5)²] / 10 ≈ 1.916 minutes
Coefficient of variation:
Coefficient of variation = (1.916 / 7.5) * 100 ≈ 25.55%
Comparing the variation:
The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%. Since the coefficient of variation measures the relative variability of the data, we can conclude that the waiting times at Bank B (individual lines) have a higher variation compared to Bank A (single line).
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Maria, Kevin, and Dan have a total of 96$ in their wallets. Dan has 6$ less than Maria. Kevin has 3 times what Dan has. How much do they have in their wallets?
Answers
Answer:
Hi Keke,
Let Amy have x dollars. Then Jose has x - 8 dollars and Milan has 4(x - 8) dollars.
x + (x-8) + 4(x-8) = 152
6x - 40 = 152
6x = 192
x = 32
Amy has $32
Jose has 32 - 8 = $24
Milan has 4*24 = $96
calculate the unemployment rate based on the following data for a country: population: 200, employed workers: 140, labor force: 160, discouraged workers: 10.
Answers
The unemployment rate for the given country is 12.5%. This is calculated by subtracting the number of employed workers from the labor force and expressing the result as a percentage.
To calculate the unemployment rate, we need to use the rainly.com/question/24600056:
Unemployment Rate = (Number of Unemployed Workers / Labor Force) x 100%
We can calculate the number of unemployed workers by subtracting the number of employed workers from the labor force:
Number of Unemployed Workers = Labor Force - Employed Workers
Number of Unemployed Workers = 160 - 140 = 20
Now we can use the formula to calculate the unemployment rate:
Unemployment Rate = (20 / 160) x 100% = 12.5%
Therefore, the unemployment rate for this country is 12.5%.
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consider the sum of cubes identity
a^3 +b^3 =(a+b)(a^2 -ab+b^2) for the polynomial 8x^3 +27, a= and b=
Answers
Answer:
a = 2x
b = 3
Step-by-step explanation:
Consider the sum of cubes identity
a³ + b³ =(a + b)(a² -ab +b²)
for the polynomial 8x³ +27, we factorise
8x³ + 27
∛8 = 2
∛8 = x
∛27 = 3
Therefore, we can say that :
8x³ + 27 = (2x)³ + 3³
Using this: a³ + b³ =(a + b)(a² -ab +b²)
We can say that
a = 2x
b = 3
To confirm that: a = 2x and b = 3 we factorise 8x³ + 27
= (2x)³ + 3³
= (2x + 3)((2x)²− 2x × 3 + 3²)
= (2x + 3)(4x² - 6x + 9)
= 8x³ - 12x² +18x + 12x² - 18x + 27
= 8x³ + 27
Therefore, a = 2x and b = 3 is correct.
=
Why do we square the residuals when using the least-squares line method to find the line of best fit? a.) Squaring the residuals makes it easier to identify smaller residuals. b.) It amplifies the effect of having negative and positive residuals. c.) It cancels out the effect of having negative and positive residuals. d.) We don't square the residuals when using the least-square method.
Answers
Answer:
It cancels out the effect of having negative and positive residuals
Step-by-step explanation: Pay attention to the answer and the multiple guess 'letter' - it changes between testing
ANSWER QUICKLY!!!!!!!!
Answers
Answer:
40°
Step-by-step explanation:
angle FIH =360°-152°-127°=360°-280°=80°
angle FGH = angleFIH ÷2 =40°
I need help with this question
Answers
Can I get Brainly
Mr. Duval paid $2,730 to rent a home for 6 months. Ms. Phee paid $5,496 to rent a home for 1 year. Which of the following is true?
Α. Ms. Phee paid $3 less per month than Mr. Duval.
B. Ms. Phee paid $3 more per month than Mr. Duval.
C. Mr. Duval paid $460 per month to rent the home.
D. Ms. Phee paid $455 per month to rent the home.
Answers
Answer:
B
$2.730 divided by 6 equals 455
$5,496 divided by 12 equals 458
458-455=3 so the answer is B
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars went a combined total of 1375 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week?
Answers
Answer:
Step-by-step explanation:
Let's call the number of gallons of gas consumed by the first car "x" and the number of gallons of gas consumed by the second car "y". We can set up a system of two equations to represent the information given in the problem:
x + y = 45 (equation 1: total gas consumption is 45 gallons)
35x + 25y = 1375 (equation 2: total distance traveled is 1375 miles)
To solve for x and y, we can use the first equation to solve for one variable in terms of the other. For example, we can solve for y as:
y = 45 - x
We can then substitute this expression for y into the second equation, and simplify:
35x + 25(45 - x) = 1375
35x + 1125 - 25x = 1375
10x = 250
x = 25
So the first car consumed 25 gallons of gas that week. We can substitute this value into equation 1 to find the number of gallons consumed by the second car:
25 + y = 45
y = 20
Therefore, the second car consumed 20 gallons of gas that week.
Can someone please help me with this!!!
Answers
Answer: D
Step-by-step explanation:
We know the midline is at y=40, so eliminate A and B.
The period is 160, so \(\frac{2\pi}{b}=160\\\2pi =160b\\b=\frac{\pi}{80}\)
This eliminates option C, leaving us with D.
determine what type of model bets fits the given situation: A $500 raise in salary each year
Answers
The type of model that best fits the situation of a $500 raise in salary each year is a linear model.
In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.
In the given case, the dependent variable is the salary and the independent variable is the year.
You may build a table to show that for increments of 1 year the increments of the salary is $500:
Year Salary Change in year Change in salary
2010 A - -
2011 A + 500 2011 - 2010 = 1 A + 500 - 500 = 500
2012 A + 1,000 2012 - 2011 = 1 A + 1,000 - (A + 500) = 500
So, you can see that every year the salary increases the same amount ($500).
In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).
In this case, m = $500 and b is the starting salary: y = 500x + b.
A rubber ball is bounced from a height of 9 meters and bounces continuously .Each successive bounce reaches a height that is a thrid of the previous height. If the ball continues to bounce in this way, what height will the ball reach during the sixth bounce?
Answers
Answer:
1/81 meters
Step-by-step explanation:
Since it reaches a height of 1/3 the previous height after each bounce, we can set up an equation for "y", the balls height, after x bounces:
\(y=9*(\frac{1}{3})^x\)
Therefore, to find the ball's height after 6 bounces we just plug-in 6 for x in the equation above to get 1/81.
Hope this helps :)
Madison's family traveled 2/7 of the distance to her uncle’s house on Saturday. They traveled 2/5 of the remaining distance on Sunday. What fraction of the total distance to her uncle’s house was traveled on Sunday?
Answers
Answer:
2/7
Step-by-step explanation:
They traveled 2/5 of the remaining distance which is 5/7. So you need 2/5 of 5/7.
When you see the word 'of' just know that it generally means multiply. To know what 2/5 of 5/7 is, you need to multiply them together, which results in 2/7.
This makes sense because if I told you to calulate 2/3 of a meter, you would divide a meter into 3 to find one thirds of a meter, then you would multiply that by 2 since you need two thirds. Same thing here. divide 5/7 by 5 to get 1/7. Multiply that by 2 since you need 2 fifths, to get 2/7.
Consider the probability statements regarding events A and
B below.
P(A or B) = 0.3
P(A and B) = 0.2
P(AB) =0.8
What is P(B)?
A) 0.1
B) 0.375
C) 0.25
D) 0.667
Answers
The calculated value of the probability of B is (c) 0.25
How to calculate the probability of BFrom the question, we have the following parameters that can be used in our computation:
P(A or B) = 0.3
P(A and B) = 0.2
P(A/B) =0.8
First, we have
P(A/B) = P(A and B)/P(B)
Substitute the known values in the above equation, so, we have the following representation
0.2/P(B) = 0.8
So, we have
P(B) = 0.2/0.8
Evaluate
P(B) = 0.25
Hence, the probability of B is 0.25
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Megan's text messaging plan costs $5 for the first 700 messages and 30¢ for each additional text message. If she owes $63.20 for text messaging in the month of January, how many text messages did she send that month?
Answers
Answer:
Fixed cost $14 -350 messages
variable $ 0.25 each message i think
Step-by-step explanation:
58.20/.30=194
So she sent 700+194 for a total of 894 texts
3. Express the following algebraic expressions in standard form.
4. (x + 7)(x - 2) = 0
5. 2x(x + 1) = 12
Answers
Answer:
x^2+5x-14=0
Step-by-step explanation:
(x+7)(x-2)=0
x (x-2)+7 (x-2)=0
x^2-2x+7x-14=0
x^2+5x-14=0
Ana has a rectangular garden with a width of 2.3 meters and a length of 2.8 meters. She makes the model below to help her determine the area of her garden. What is the area of Ana's garden?
Answers
Answer:
6.44 m2
Step-by-step explanation:
A local mattress manufacturer wants to know if its manufacturing process is in or out of control and has hired you, a statistics expert in the field, to analyze its process. Specifically, the business has run 20 random samples of size 5 over the past month and has determined the mean of each sample.
Sample Mean of Sample
1 95.72
2 95.44
3 95.4
4 95.5
5 95.56
6 95.72
7 95.6
8 95.24
9 95.46
10 95.44
11 95.8
12 95.2
13 94.82
14 95.78
15 95.18
16 95.32
17 95.08
18 95.22
19 95.04
20 95.48
Required:
a. Determine the estimate of the mean when the process is in control.
b. Assuming the process standard deviation is 0.50 and the mean of the process is the estimate calculated in part a , determine the Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process.
c. Explain the results to the vice-president of the mattress manufacturer focusing on whether, based on the results, the process is in or out of control.
Answers
Answer:
a. 95.4
b. UCL = 96.07
LCL = 94.73
c. Process is in control
Step-by-step explanation:
a. The computation of estimate mean is shown below:-
\(Estimate\ mean = \frac{\Sigma X}{N} \\\\ = \frac{1908.000}{20}\)
= 95.4
b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-
\(UCL = Mean + \frac{3\times \sigma }{\sqrt{Sample\ size} }\)
\(UCL = 95.4 + \frac{3\times (0.5)}{\sqrt{0.5} }\)
= 95.4 + 0.67082
= 96.07
\(UCL = Mean - \frac{3\times \sigma }{\sqrt{Sample\ size} }\)
\(UCL = 95.4 - \frac{3\times (0.5)}{\sqrt{0.5} }\)
= 95.4 - 0.67082
= 94.73
c. The explanation is shown below:-
From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,
The Process is in control
A number rounded to the nearest hundred thousand is 400,000. The same number is rounded to the nearest ten thousand is 350,000. What could be the number.
Answers
Answer:
354,000
Step-by-step explanation:
The number has to be able to get to 400,000 so the number in the ten thousand spot needs to be 5 or up. It also needs to be a small enough number to be able to be 350,000.