Answer:
P = 0,3749 or P = 37,49 %
Step-by-step explanation:
17 girls play football 10 boys do ⇒ 27 students
24 girls running 3 boys do ⇒ 27 students
then 6 girls play tennis and 12 boys do ⇒ 18 students
Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )
P = P1 + P2
P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running
Probability of girl 47/72 = 0,6528
Probability of running is equal to 24/47 = 0,5106
Then the probability of girl running is equal to
P2 = 0,6528*0,5106 = 0,3333 or 33,33 %
P2 = 0,3333 or P2 = 33,33 %
Now we have 72 students 25 boys, then the probability of choosing a boy is = 25/72 = 0,3472
And the probability of running is 3/25 = 0,12
Then
P1 = 0,3472*0,12
P1 = 0,04166 and
P = P1 + P2
P = 0,04166 + 0,3333
P = 0,3749 or P = 37,49 %
During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1530, 1532, 1495, 1508, 1528, and 1511. (a) Find the mean and the median of the contents. (b) The third value was incorrectly measured and is actually 1515. Find the mean and the median of the contents again. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error?
Answer:
Step-by-step explanation:
Given the values of the actual content of protein powder recorded as shown:
1530, 1532, 1495, 1508, 1528, and 1511
a) We are to find the mean and median of the contents.
Mean is the average sum of the numbers. It is expressed mathematically as xbar = ΣXi/N
Xi are individual values
N is the total number of values present.
N = 6
xbar = (1,530+1,532+1,495 +1,508+1,528+1,511)/6
xbar = 9104/6
xbar = 1517.33
Median of the data is the value at the middle after rearrangement. On rearranging from lowest to highest:
1,495, 1508, 1511, 1528, 1530, 1532
The two values at the centre are 1511 and 1528.
Median = 1511+1528/2
Median = 1519.5
b) If the third value was incorrectly measured and is actually 1515, then our new data will become.
1530, 1532, 1515, 1508, 1528, and 1511
xbar = (1,530+1,532+1,515 +1,508+1,528+1,511)/6
xbar = 9124/6
xbar = 1520.67
For median:
We arrange first
1508, 1511, 1515, 1528, 1530, 1532
The two values at the centre are 1515 and 1528.
Median = 1515+1528/2
Median = 1521.5
c) To know the measure of central tendency that was most affected, we will look at the difference in the values gotten for both mean and median.
∆Mean = 1520.67-1517.33
∆Mean = 3.34
∆Median = 1521.5 - 1519.5
∆Median = 2.0
It can be seen that the measure of central tendency with greater deviation is the mean. Therefore, the mean is more affected by the data entry error.
determining probability of events. please help!
Answer:
23/90
Step-by-step explanation:
55/90 + 12/90 = 67/9090 - 67 = 2323/9023/90 balls are green or white
i hope this helps!
consider the distribution of monthly social security (OASDI) payments. Assume a normal distribution with a standard deviation of $116. if one-fourth of payments are above $1214,87 what is the mean monthly payment?
Answer:
$1137
Step-by-step explanation:
Solution:-
We will define the random variable as follows:
X: Monthly social security (OASDI) payments
The random variable ( X ) is assumed to be normally distributed. This implies that most monthly payments are clustered around the mean value ( μ ) and the spread of payments value is defined by standard deviation ( σ ).
The normal distribution is defined by two parameters mean ( μ ) and standard deviation ( σ ) as follows:
X ~ Norm ( μ , σ^2 )
We will define the normal distribution for (OASDI) payments as follows:
X ~ Norm ( μ , 116^2 )
We are to determine the mean value of the distribution by considering the area under neat the normal distribution curve as the probability of occurrence. We are given that 1/4 th of payments lie above the value of $1214.87. We can express this as:
P ( X > 1214.87 ) = 0.25
We need to standardize the limiting value of x = $1214.87 by determining the Z-score corresponding to ( greater than ) probability of 0.25.
Using standard normal tables, determine the Z-score value corresponding to:
P ( Z > z-score ) = 0.25 OR P ( Z < z-score ) = 0.75
z-score = 0.675
- Now use the standardizing formula as follows:
[tex]z-score = \frac{x - u}{sigma} \\\\1214.87 - u = 0.675*116\\\\u = 1214.87 - 78.3\\\\u = 1136.57[/tex]
Answer: The mean value is $1137
What is the approximate volume of the cone? Use 3.14 for π. radius-16 height-9
Answer:
2411.52
Step-by-step explanation:
1/3(3.14*16*16*9) = 2411.52
Answer:
2411.52 units³Step-by-step explanation:
Given,
Radius ( r ) = 16
Height ( h ) = 9
pi ( π ) = 3.14
Volume of cone = ?
Now, let's find the volume of cone:
[tex]\pi \: {r}^{2} \frac{h}{3} [/tex]
plug the values
[tex]3.14 \times {16}^{2} \times \frac{9}{3} [/tex]
Evaluate the power
[tex]3.14 \times 256 \times \frac{9}{3} [/tex]
Calculate the product
[tex]2411.52 \: {units}^{2} [/tex]
Hope this helps..
Best regards!!
f(n)=4n-3 find the 15th term of the sequence defined by the explicit rule
Answer:
57
Step-by-step explanation:
f(15)=4(15)-3
f(15)=60-3
f(15)=57
Hope that helps, tell me if you need more help
Answer:
57
Step-by-step explanation:
If you plug 15 into the equation, you get f(15)=4(15)-3
60-3
57
:)
the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty one. Find the numbers
Answer:
The numbers are 5 and 4Step-by-step explanation:
Let the first number be x
Let the second number be y
For the first equation
2x + 3y = 22
For the second equation
3x + 4y = 31
Multiply the first one by 3 and the second one by 2
That's
First equation
6x + 9y = 66
Second equation
6x + 8y = 62
Subtract the second equation from the first one
That's
6x - 6x + 9y - 8y = 66 - 62
y = 4Substitute y = 4 into 2x + 3y = 22
That's
2x + 3(4) = 22
2x = 22 - 12
2x = 10
Divide both sides by 2
x = 5Hope this helps you
Use the given categorical data to construct the relative frequency distribution. Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 53, 63, 68, 58, 61, 43, 54. Does it appear that such births occur on the days of the week with equal frequency?
Answer: Yes
Step-by-step explanation:
See explanations in the attached document
If 2/3 of a certain number is subtracted from twice the number, the result is 20. Find the number.
Let x be the number.
Set up an equation:
2x - 2/3x = 20
Simplify:
1 1/3x = 20
Divide both sides by 1 1/3
X = 15
The number is 15
Richard is buying a subscription for video game rentals. The plan he has chosen has an
initial fee of $20 plus $2 per video game rented. This plan can be represented by the
function f(x) = 2x + 20. How much money will Richard pay this month if he rents 5 video
games?
Answer:
Richard will pay $30.
Step-by-step explanation:
Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!
In 2009, a school population was 1,700. By 2017 the population had grown to 2,500. Assume the population is changing linearly. How much did the population grow between 2009 and 2017?
Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.
Answer:
100
Step-by-step explanation:
aaaaa
A new city Mayor would like to determine the proportion of community voters who are ages 18 to 20 years. He has heard it is 10%. To test this prediction, he surveys 1000 random community voters and found that 111 of them are aged 18 to 20. The following is the setup for this hypothesis test: H0:p=0.10 H0:p≠0.10 The p-value for this hypothesis test is 0.04. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer: He should reject the null hypothesis.
Step-by-step explanation: When using P-Values to decide if you accept or not the alternative hypothesis, compare the p-value with the chosen significance level (α).
In the Mayor's survey:
p-value = 0.04
α = 5% or 0.05
If the p-value is less than α, reject the null hypothesis and accept the alternative. If p-value is greater than or equals α, fail to reject the null hypothesis and don't accept the alternative.
Analysing the Mayor's survey:
p-value = 0.04 < α = 0.05
In conclusion, the Mayor should reject the null hypothesis and accept that the proportion of voters who are aged 18 to 20 is not equal to 10%, i.e., accept the alternative hypothesis: [tex]H_{a}[/tex]: p≠0.10
Given the function below, find value (s) of x if f(x)=7
Explanation:
f(x) and y are often used interchangeably. We are asked to find the x value(s) when y = 7.
Circle the rows where 7 shows up in the y column. You should find that x = -1 and x = 1 are circled as well.
So f(x) = 7 leads to x = -1 or x = 1. In other words, f(-1) = 7 and f(1) = 7 also.
For the function given the value of x can be two, one is 1 and the other one is -1 if the f(x)=7
What is a Function?
A function relates an input to an output means it is a kind of relationship between the variable y and x. It is denoted through f(x).
What is a Variable?A variable is defined as a quantity that may assume any one of a set of values.
How to find the value of x in a function?
In the question the function is given as:
Function is denoted through f(x) and f(x) shows the value of x. We know that the value of f(x)=7 which is given in the question. So we will take the value of x in the front of 7 which is written in the y column. We have got two values in this which are 1 and -1. So they both will be the values of x.
Hence the value of x for the function given in the question are -1 and 1
Learn more about functions at https://brainly.com/question/25638609
#SPJ2
expand(x+y2)2 plzzzzzzzzzzzzzzzz
Answer:
[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]
Hope it helps!!❤❤Please mark me as the brainliest!!!Thanks!!!!
Assume that y varies directly with x, then solve.
If y=6 when x= 2/3 find x when y=12.
х: /
2×y = 2×6= 12 so 2×x = 2×23 = 43 = 113
Step-by-step explanation:
Is this what you are looking for?
Find x and round to the nearest tenth.
Answer:
83.0°
Step-by-step explanation:
Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).
For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.
Thus, we would have this following:
[tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]
Where,
C = X = ?
a = 8 ft
b = 16 ft
c = 17 ft
Plug in the stated values into the formula and solve for X
[tex] cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} [/tex]
[tex] cos(X) = \frac{320 - 289}{256} [/tex]
[tex] cos(X) = \frac{31}{256} [/tex]
[tex] cos(X) = 0.1211 [/tex]
[tex] X = cos^{-1}(0.1211) [/tex]
[tex] X = 83.0 [/tex] (to nearest tenth)
Answer:
its actually 83 not 83.0
Step-by-step explanation:
im only saying this bc i know people with type 83.0 in the box
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
Answer:
B'(0,-2)
Step-by-step explanation:
the coordinates of B (-5,0)
the translation is(x+5,y-2)
B' : (-5+5,0-2)
B'(0,-2)
Wholemark is an internet order business that sells one popular New Year greeting card once a year. The cost of the paper on the which the card is printed is $0.05 per card, and the cost of printing is $0.15 per card. The company receives $2.15 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Their customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from the each of the four regions is normally distributed with mean 2,000 and standard deviation of 500. (Assume these four are independent.)
What is the optimal production quality for the card? (Use Excel's NORMSINV{} function to find the Z-score. Round intermediate calculations to four decimal places. Submit your answer to the nearest whole number.)
Answer:
The optimal production quantity is 9,322 cards.
Step-by-step explanation:
The information provided is:
Cost of the paper = $0.05 per card
Cost of printing = $0.15 per card
Selling price = $2.15 per card
Number of region (n) = 4
Mean demand = 2000
Standard deviation = 500
Compute the total cost per card as follows:
Total cost per card = Cost of the paper + Cost of printing
= $0.05 + $0.15
= $0.20
Compute the total demand as follows:
Total demand = Mean × n
= 2000 × 4
= 8000
Compute the standard deviation of total demand as follows:
[tex]SD_{\text{total demand}}=\sqrt{500^{2}\times 4}=1000[/tex]
Compute the profit earned per card as follows:
Profit = Selling Price - Total Cost Price
= $2.15 - $0.20
= $1.95
The loss incurred per card is:
Loss = Total Cost Price = $0.20
Compute the optimal probability as follows:
[tex]\text{Optimal probability}=\frac{\text{Profit}}{\text{Profit+Loss}}[/tex]
[tex]=\frac{1.95}{1.95+0.20}\\\\=\frac{1.95}{2.15}\\\\=0.9069767\\\\\approx 0.907[/tex]
Use Excel's NORMSINV{0.907} function to find the Z-score.
z = 1.322
Compute the optimal production quantity for the card as follows:
[tex]\text{Optimal Production Quantity}=\text{Total Demand}+(z\times SD_{\text{total demand}}) \\[/tex]
[tex]=8000+(1.322\times 1000)\\=8000+1322\\=9322[/tex]
Thus, the optimal production quantity is 9,322 cards.
Which is the value of this expression when p = 3 and q = negative 9? ((p Superscript negative 5 Baseline) (p Superscript negative 4 Baseline) (q cubed)) Superscript 0 Negative one-third Negative StartFraction 1 Over 27 EndFraction StartFraction 1 Over 27 EndFraction One-third Edge 2020
Answer:
I am pretty sure that the answer is D. The value should be 1.
Step-by-step explanation:
Answer:
Answer is D
Step-by-step explanation:
On Edge 2020
What are the trigonometric ratios? Write all six.
Step-by-step explanation:
Check that attachment
Hope it helps :)
Hey! :)
________ ☆ ☆_________________________________________
Answer:
There are six trigonometric ratios, which will be under “Explanation”
Step-by-step explanation:
Trigonometric ratios are a measurements of a right triangle.
Here are the all the six trigonometric ratios.
1. cotangent (cot)
2. cosecant (csc)
3. cosine (cos)
4. secant (sec)
5. sine (sin)
6. tangent (tan)
Hope this helps! :)
_________ ☆ ☆________________________________________
By, BrainlyMember ^-^
Good luck!
Let a and b be real numbers where a=/b=/c=/0 which of the following functions could represent the graph below?
Answer: The second option; y = (x - a)^2*(x-b)^4
Step-by-step explanation:
Ok, we have that a and b are real numbers different than zero.
In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:
y = x*(x - a)^3*(x - b)^3
then when x = 0 we would have:
y = 0*(0-a)^3*(0-b)^3 = 0
But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.
So the remaining options are:
y = (x - a)^2*(x-b)^4
y = (x - a)^5*(x - b)
Now, another thing you can see in the graph is that it is always positive.
Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.
(For example, if x > a and x < b we would have a negative value for y)
Then the only remaining option is y = (x - a)^2*(x-b)^4
Answer:
B.y = (x - a)^2*(x-b)^4
Step-by-step explanation:
EDGE 2020 Brainliest please
Find the value of x.
A. 6
B. 7
C. 4
D. 5
Answer:
A. 6
Step-by-step explanation:
We see that 20 is a diameter that goes through the center of the point. This means that the top half of the black line is 10 and the top half of the blue line is 8. Use the Pythagorean Theorem to find out the length of the shortest side by doing 10^2 - 8^2 = x^2. x^2 = 36; x = 6.
I toss an unfair coin 12 times. This coin is 65% likely to show up heads. Calculate the probability of the following.
a. 11 heads:
b. 2 or more heads:
c. 7 heads:
d. 9 tails:
e. 8 or less heads:
Answer:
a. 0.0368
b. 0.99992131
c. 0.2039
d. 0.0048
e. 0.6533
Step-by-step explanation:
Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35
Since this is a binomial probability, we use a binomial probability.
a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368
b. Probability of 2 or more heads P(x ≥ 2) is
P(x ≥ 2) = 1 - P(x ≤ 1)
Now P(x ≤ 1) = P(0) + P(1)
= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹
= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹
= 0.000003379 + 0.00007531
= 0.0007869
P(x ≥ 2) = 1 - P(x ≤ 1)
= 1 - 0.00007869
= 0.99992131
c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039
d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048
e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴
= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴
= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367
= 0.6533
Use the elimination method to solve the system of equations choose the correct ordered pair x-3y=-23 5x+6y=74
Answer:
( 4, 9 ) is our solution in an ordered pair, as you could also say x = 4, and y = 9
Step-by-step explanation:
So we have the following system of equations at hand ( given directly below ), and want to make it such that each equation is multiplied by a value that makes a common variable, say x, have opposite values of coefficients such that they cancel each other out when the two equations are added, enabling you to solve for the value of the other variable, in this case variable y.
[tex]\begin{bmatrix}x-3y=-23\\ 5x+6y=74\end{bmatrix}[/tex] - Multiply this top equation by -5, so the coefficient of variable x becomes - 5, opposite to the respective x coefficient in the second equation.
[tex]\begin{bmatrix}-5x+15y=115\\ 5x+6y=74\end{bmatrix}[/tex] - Adding the two equations we receive the simplified equation 21y = 189. y = 189 / 21 = 9. If y = 9, x should = - 23 + 3y = - 23 + 3 [tex]*[/tex] 9 = 4. To get this value of x simply isolate the value of x in the first equation given to us, and substitute the known value of y. We have our solution in the form ( 4, 9 ), where x = 4 and y = 9.
Answer:
4,9
Step-by-step explanation:
Out of 600 people sampled, 66 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.
Required:
Use a 90% confidence level, and give your answers as decimals, to three places.
Answer:
11% of the Total the entire voting population
Step-by-step explanation:
Let's bear in mind that the total number of sample candidates is equal to 600.
But out of 600 only 66 preffered candidate A.
The proportion of sampled people to that prefer candidate A to the total number of people is 66/600
= 11/100
In percentage
=11/100 *100/1 =1100/100
=11% of the entire voting population
How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains had the following weights (pounds):
69 103 126 122 60 64
Assume that the population of x values has an approximately normal distribution.
A) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s.
B) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region.
Answer:
Step-by-step explanation:
From the information given:
Mean [tex]\overline x = \dfrac{\sum x_i}{n}[/tex]
Mean [tex]\overline x = \dfrac{69+103+126+122+60+64}{6}[/tex]
Mean [tex]\overline x = \dfrac{544}{6}[/tex]
Mean [tex]\overline x = 90.67[/tex] pounds
Standard deviation [tex]s = \sqrt{\dfrac {\sum (x_i - \overline x) ^2}{n-1}[/tex]
Standard deviation [tex]s = \sqrt{\dfrac {(69 - 90.67)^2+(103 - 90.67)^2+ (126- 90.67) ^2+ ..+ (64 - 90.67)^2}{6-1}}[/tex]
Standard deviation s = 30.011 pounds
B) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region.
At 75% confidence interval ; the level of significance ∝ = 1 - 0.75 = 0.25
[tex]t_{(\alpha/2)}[/tex] = 0.25/2
[tex]t_{(\alpha/2)}[/tex] = 0.125
t(0.125,5)=1.30
Degree of freedom = n - 1
Degree of freedom = 6 - 1
Degree of freedom = 5
Confidence interval = [tex](\overline x - t_{(\alpha/2)(n-1)}(\dfrac{s}{\sqrt{n}})< \mu < (\overline x + t_{(\alpha/2)(n-1)}(\dfrac{s}{\sqrt{n}})[/tex]
Confidence interval = [tex](90.67 - 1.30(\dfrac{30.011}{\sqrt{6}})< \mu < (90.67+ 1.30(\dfrac{30.011}{\sqrt{6}})[/tex]
Confidence interval = [tex](90.67 - 1.30(12.252})< \mu < (90.67+ 1.30(12.252})[/tex]
Confidence interval = [tex](90.67 - 15.9276 < \mu < (90.67+ 15.9276)[/tex]
Confidence interval = [tex](74.7424 < \mu <106.5976)[/tex]
i.e the lower limit = 74.74 pounds
the upper limit = 106.60 pounds
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P B or B = 1 Choose the correct answer below. A. It is impossible that the selected adult has type B blood or does not have type B blood. B. It is certain that the selected adult has type B blood. C. It is certain that the selected adult has type B blood or does not have type B blood. D. It is certain that the selected adult does not have type B blood.
Answer: The rule of complements is apprising us that, the person selected will.eithwr have a type B blood or will not have a type B blood
Step-by-step explanations:
Find explanations in the attachment
The length of a rectangle is 7 more than the width. The area is 744 square centimeters. Find the length and width of the rectangle.
Answer:
the width of the rectangle is 24 centimeters and the length is 31 centimeters.
Step-by-step explanation:
We first have to write an equation for this, but let's just recall that the area of a rectangle is equal to the length times the width. A=L×W.
A is the area
L is the length
W is the width.
So, for our equation we can start out by putting that 744= ? times ?.
So, we are given that the length is 7 more than the width. We are going to have to translate that to represent the length.
We need a variable. Let's use the letter "W," the width of the rectangle.
W=W.
The length is 7 more than the width, so it is L=W+7.
Length represents the W+7
Width represents W.
Now, we can complete our equation.
744=W(W+7).
Simplify the expression.
744=[tex]W^{2}[/tex]+7W.
Alright, you may be thinking on how we are going to solve this problem. This equation correlates with quadratic functions.
Let's complete the square.
In a quadratic function, the standard from is y=[tex]ax^{2} +bx+c[/tex].
We need to find the c value.
We can do this by applying a formula. The formula states that c= b/2 and the whole thing squared. In other words, [tex](\frac{b}{2} )^{2}[/tex].
In this case, the b value is 7.
square 7, which is 49 and square 2 which is 4.
Now, the c value is 49/4.
We have now just created a perfect square trinomial.
Not only do we add 49/4 to W squared plus 7W, we also add 49/4 to 744.
744 plus 49/4 is 756/25.
Now, we have [tex]W^{2}+7w+\frac{49}{4} = 756.25[/tex]
Change W squared plus 7w plus 49/4 to a binomial squared.
Just take the square root of the a value, W, and 49/4 for c. the square root of W squared is W. the square root of 49/4 is 7/2.
Those values are to the power of 2.
In other words, [tex](W+\frac{7}{2})^{2} =756.25[/tex]
To isolate for W, take the square root of both sides.The square root of W plus 7/2 squared is just W+7/2. The square root of 756.25 is 27.5
There are two solutions for W because square roots be positive or negative, but we are dealing with positive since negative doesn't make sense with the context of the problem.
We have [tex]W+3.5 or \frac{7}{2}=27.5[/tex]
Isolate for W by subtracting both sides by 3.5 You get to W=24.
Therefore, the width of the rectangle is 24 centimeters.
Alright, we found the width. We now need to find the length. The problem stated that the rectangle was 7 more than the width. So, 24+7=31. Therefore, the length of the rectangle is 31 centimeters.
L=31cm
W=24cm.
I hope this was helpful! I wish you have an amazing day!
A national survey of 1000 adult citizens of a nation found that 25% dreaded Valentine's Day. The margin of error for the survey was 3.6 percentage points with 90% confidence. Explain what this means.
Answer:
There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.
Step-by-step explanation:
The summary of the statistics from the information given is ;
At 90% confidence interval, 25% dreaded Valentine's Day and the margin of error for the survey was 3.6 percentage points
SO;
[tex]C.I = \hat p \pm M.O.E[/tex]
[tex]C.I = 0.25 \pm 0.036[/tex]
C.I = (0.25-0.036 , 0.25+0.036)
C.I = (0.214, 0.286)
The 90% confidence interval for the proportion of the adult citizens of the nation that dreaded Valentine’s day is 0.214 and 0.286.
There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.
What is the slope of the line passing through the points (6,7) and (1,5)
Answer:
2/5
Step-by-step explanation:
(7-5)/(6-1)