Answer:
Step-by-step explanation:
x2 - 4x - 12 = 0
x2 - 6x + 2x - 12= 0
x(x - 6) + 2(x - 6) = 0
x + 2 = 0
x = - 2
x - 6 = 0
x = 6
The length of a rectangle is (3x − 5) inches, and its width is 2x inches. Find the area of the rectangle.
Hint: Area of a rectangle = length × width.
Answer:
A = 6x² - 10x
General Formulas and Concepts:
Area of a Rectangle: Length × Width
To expand, use FOIL - First, Outside, Inside, Last
Step-by-step explanation:
Step 1: Define variables
l = 3x - 5
w = 2x
Step 2: Find area
Substitute: A = (3x - 5)(2x)Expand (FOIL): A = 6x² - 10xAnswer: A=6x^2-10x ✅
Step-by-step explanation:
Hii, do you need to find the area of the rectangle? Let me help you out! (:
Luckily, there's a formula to find this! (:
AreaTo find the area of a rectangle, multiply its length times its width. This is shown below.
[tex]\LARGE\boldsymbol{A=L W}[/tex]
Here, "A" denotes the area
"L" denotes the length
"W" denotes the width
NB : "L" and "W" are interchangeable
Next, it's just a matter of sticking in the known values...
[tex]\twoheadrightarrow\sf A=2x(3x-5)[/tex]
===> it's perfectly legal to stick in the values the other way around, because they are interchangeable
Alright, the next step is to multiply the values...
[tex]\twoheadrightarrow\sf A=(2x\cdot3x)-(2x\cdot(-5)[/tex]
Then we need to simplify...
[tex]\twoheadrightarrow\sf A=6x^2-10x[/tex]
Voila! There's the area of this rectangle! (:
Cheers! (:_______________Hope I helped! Best wishes.
⚜ Reach far. Aim high. Dream big. ⚜
_______________What is the slope of a line that is perpendicular to the line y = x + 4?
The slope of the line is
Answer:
-1
Step-by-step explanation:
Answer:
- 1/6 is correct
perpendicular refers to the opposite of 1/6 therefor being negative 1/6
Step-by-step explanation:
Compute a 99% confidence interval for the mean weight of toxic substance per gram of mold culture. State the assumption you make about the population.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 99% confidence interval is [tex]2.4309 < \mu < 4.9328[/tex]
Step-by-step explanation:
From the question we are told that
The data is 3, 2,5, 3, 2, 6, 5,4.5, 3, 3, and 4
The sample size is n = 11
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{n}[/tex]
=> [tex]\= x = \frac{3+ 2+5+ \cdots +4 }{11}[/tex]
=> [tex]\= x = 3.6818 [/tex]
Generally the sample standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum [ x_i - \= x ] }{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{[ 3 - 3.6818 ]^2 +[ 2 - 3.6818 ]^2 + \cdots + [ 4 - 3.6818 ]^2 }{11} }[/tex]
=> [tex]\sigma = 1.3091[/tex]
Given that the confidence interval is 99% then the level of significance is mathematically represented as
[tex]\alpha= (100 - 99) \%[/tex]
=> [tex]\alpha= 0.01[/tex]
Given that the sample size is small we will making use of t distribution table
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\frac{\alpha }{2} , 10 } =3.16927267 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = 3.16927267 * \frac{1.3091 }{\sqrt{11} }[/tex]
[tex]E = 1.251[/tex]
Generally 99% confidence interval is mathematically represented as
[tex]3.6818 -1.251 < p < 3.6818 + 1.251 [/tex]
=> [tex]2.4309 < \mu < 4.9328[/tex]
90% of runners in a marathon successfully completed it. 30% of these runners were men. How many total runners began the marathon if 270 men completed it?
Answer:
1000
Step-by-step explanation:
270 is 30% of 900 total who completed.
900 is 90% of 1000
An architect wants to build a scale model of a building that is in the shape of a rectangular prism. The building has a height of 500 ft., a width of 120 ft., and a length of 600 ft.The scale model is 1% of the size of the building based off its length and width, so the length of the scale model is and the height of the scale model is .
Height: 5ft.
Legnth: 6ft.
Width: 1.2 ft.
1% of 500 is 5ft
1% of 600 is 6ft
1% of 120 is 1.2ft
The function that represents the amount of caffeine in milligrams remaining
Answer:
Step-by-step explanation:
The function that represents the amount of caffeine, in milligrams, remaining in a body after drinking two mountain dew sodas is given by f(t) = 110(0.8855)^t, where t is time in hours.
Answer:
If you are referring to a logarithmic function with a continuous rate of decrease(as implied by remaining), then here is your answer:
A(t) = c×e^(dt)
where c is the starting amount of caffeine in miligrams, e is euler's number (base of a natural logarithm), and d is continuous rate of logarithmic change(as a percentage decay(negative)) per t(time) in standard unit of time(i.e hours)
I.e(for instance): if you are given a cup of coffee with an initial 190 mg of caffeine, leaving the body at a rate of 36% every hour.
This relationship solving for the remaining miligrams can be given by:
A(t) = 190 mg × e ^ (-.36t)
Where t is the amount of hours.
Assuming the butterflies traveled 3000 miles to reach their winter home, they averaged 60 miles per day and flew for an average of 8 hours per day.
What is there average speed per hour?
How many days would it take for them to reach their destination?
Answer:
1. 7.5 mph
2. 400
Step-by-step explanation:
1. You would just do 60/8 to find the answer.
2. You would take the answer you got from the previous question and do 3000/7.5
Hope I helped!! :)
Which two numbers both round to 1,500 when rounded to the nearest hundred?
Answer:
C
Step-by-step explanation:
Just take it lol
The two numbers where both round to 1,500 when rounded to the nearest hundred is option c. 1457 and 1547.
What is Rounded number?
The rounded number should be that where the number should be rounded to the nearest tenth, hundred or thousand
Since the number is 1500
So for hundred the number should be likely 1457 and 1547.
hence, the option c is correct.
learn more about number here: https://brainly.com/question/21474983
A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below. Age (in years) Height (inches) 7 47.3 8 48.8 5 41.3 8 50.4 8 51 7 47.1 7 46.9 7 48 9 51.2 8 51.2 5 40.3 8 48.9 6 45.2 5 41.9 8 49.6 How much of the variation in the sample values of height does the model estimate
Answer:
0.940
Step-by-step explanation:
Given the data:
Age in years(X) _____Height(Y)
7 _________ 47.3
8 _________48.8
5 __________41.3
8 _________ 50.4
8 ___________51
7 __________47.1
7 __________46.9
7 ___________48
9 __________51.2
8 __________51.2
5 __________40.3
8 __________48.9
6 __________45.2
5 __________41.9
8 __________49.6
The proportion of Variation explained by the line of best fit in a regression model can be determined by calculating the Coefficient of determination (R²) of the model.
Using the online R² calculator, the variation in the sample values of height which is estimated by the model is 0.9696² = 0.94012416.
Hence about 0.94 or 94% variation in sample values of height is estimated by the model while (1 - 0.94 = 0.06 or 6%) is explained by other factors.
maria has 15 fewer apps on her phone than orlando. if the total number of apps on both phones is 29, how many apps are on each phone
This is impossible because 15 fewer than 29 is 14 and then she would have to have negative apps.
Step-by-step explanation:
Orlando's number of apps = 22
Maria's number of apps = 7
Given,
Maria has 15 fewer apps on her phone than Orlando.
The total number of apps on both phones is 29.
We need to find out how many apps are on each phone.
What does the term mean?- M fewer than N by 2
This means if N = P then M = P - 2
- M more than N by 2
This means if N = P then M = P + 2
We have,
Total number of apps = 29 _____(1)
Maria has 15 fewer apps on her phone than Orlando.
We can write this as:
Orlando's number of apps = O.
Now,
Maria's number of apps = O - 15
Now,
From (1)
Orlando's number of apps + Maria's number of apps = 29
O + O - 15 = 29
2O - 15 = 29
2O = 29 + 15
20 = 44
O = 44/2
0 = 22
Orlando's number of apps = 22
Maria's number of apps = 22 - 15 = 7
Thus,
Orlando's number of apps = 22
Maria's number of apps = 7
Learn more about how to find the number of apps for each person here:
https://brainly.com/question/13502950
#SPJ2
Each of 7 students reported the number of movies they saw in the past year. Here is what they reported.
13, 8, 18, 19, 13, 14, 12
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.
Answer:
13.9
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms
In the picture, what is the ratio of the number of circles to the number of squares? Select your answers from the drop-down list.
Answer:
3/6 ♀️
Step-by-step explanation:
the ratio of ten more than three times a number to the square of the same number is equal to ... Write an expression for the number of circles in the Nth figure.
Answer:
7 circles and 6 squares
Step-by-step explanation:
7 to 6
4.) Ariel makes her own jewelry to sell at the Street Fair. She can make 12 bracelets in 4 hours. If she works for 5 hours every Thursday for 4 Thursdays, how many bracelets will she make?
Answer:
60bracelets
Step-by-step explanation:
To solve this problem, we need to find her rate. This is the number of jewelries she makes per unit of time;
Rate = [tex]\frac{number of jewelries}{time taken }[/tex]
Number of jewelries = 12 bracelets
time = 4hrs
Input the parameters:
Rate = [tex]\frac{12}{4}[/tex] = 3bracelets/hr
She works 5hrs for 4 Thursdays;
Number of hours worked = 5 x 4 = 20hrs
Now, working at a rate of 3bracelets/hr for 20hrs, the number of bracelets she will produce is given as;
Number of bracelets = number of hours x rate
= 20 x 3
= 60bracelets
jessie worked four more hours than Ben. They worked a total of 25 hours. How many hours did each boy workz?
Answer:
jessie: 14.5
ben: 10.5
Select two ratios that are equivalent to 27:927:927, colon, 9. Choose 2 answers: Choose 2 answers: (Choice A) A 3:13:13, colon, 1 (Choice B) B 9:39:39, colon, 3 (Choice C) C 6:36:36, colon, 3 (Choice D) D 9:69:69, colon, 6 (Choice E) E 12:312:3
Answer:
A. [tex]Ratio = 3:1[/tex]
B. [tex]Ratio= 9:3[/tex]
Step-by-step explanation:
Given
[tex]Ratio= 27:9[/tex]
Required
Determine equivalent ratios:
[tex]Ratio= 27:9[/tex]
First, we simplify the ratio to the least possible
[tex]Ratio = 27/9:9/9[/tex]
[tex]Ratio = 3:1[/tex]
By comparison with the given options, we have A and B as answer.
See Proof Below
Proof: A
Compare this to the simplified ratio (given), we have:
[tex]Ratio = 3:1[/tex] = [tex]Ratio = 3:1[/tex]
Proof B
[tex]Ratio= 9:3[/tex]
Simplify the ratio to the least possible
[tex]Ratio= 9/3:3/3[/tex]
[tex]Ratio= 3:1[/tex]
Compare this to the simplified ratio (given), we have:
[tex]Ratio = 3:1[/tex] = [tex]Ratio = 3:1[/tex]
Answer:
9:3 and 3:1
Step-by-step explanation:
I just did this lesson
Y = x Squared - 2x - 15
Answer:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y. x-intercept(s): (5,0),(−3,0)y-intercept(s): (0,−15)
A product's demand per period follows a normal distribution with mean of 60 and standard deviation of 10. The lead time is 3 periods. What order-up-to level should be used to achieve at least a 90% in-stock probability?
Answer:
209
Step-by-step explanation:
Since the lead time is 2 periods at the time of order, the stocks should last for 3 periods with the 90% probability.
The z-value of 90$ in stock probability = 1.7
Mean of the demand over is (1 + 1 + 1 ) or (2+1 which is 3)
= 60 x 3 = 180
Now the standard deviation of demand over the three periods = 17.3
Therefore, the order up level would be = 180 + ( 1.7 x 17.3 )
= 209
Which of the following is a binomial?
Answer:
B
Step-by-step explanation:
Kari is building a rectangular garden bed. The length is 6 feet. She has 20 feet of boards to make the sides. Write and solve an inequality to find the possible width of her garden bed.
Answer:
ahe using 12 feet of boards and threre 8 ft of board left so i guess the with will be 4.
Step-by-step explanation:
6+6 =12 for the lenghth
4+4=8= for the with
What is the slope of a line that is perpendicular to the line y =-1/5
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 0 0 . All lines that are parallel to y=−15 y = - 1 5 have the same slope of 0 .
Find f’(2) for f(x)=5e^-xln(x^2+5x)
9514 1404 393
Answer:
f'(2) ≈ −1.3508
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 5(-e^-x·ln(x^2 +5x) +e^-x·(2x +5)/(x^2 +5x))
Then ...
f'(2) = 5e^(-2)(-ln(14) +9/14) ≈ -1.3508
Which of the expressions below will have a 8 in the thousandths place of the quotient? Select all that apply.
A) 765.812 ÷ 100
B) 98.14 ÷ 1,000
C) 18.723 ÷ 100
D) 22.38 ÷ 10
Answer:
A
Step-by-step explanation:
3. Write the inequality that best represents the relationship shown on this number line:
The probabilities that stock A will rise in price is 0.42 and that stock B will rise in price is 0.58. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.14. a. What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.)
Answer:
0.92
Step-by-step explanation:
a. What is the probability that at least one of the stocks will rise in price? (Round your answer to 2 decimal places.)
P(A) = 0.42
P(B) = 0.58
P(A|B) = 0.14
Step 1
P(A|B) × P(B) = 0.14 × 0.58
= 0.0812
The probability that at least one of the stocks will rise in price
P(A) + P(B) - 0.0812
0.42 + 0.58 - 0.0812
= 1 - 0.0812
= 0.9188
Approximately to 2 decimal place = 0.92
7. A crew of electricians can wire 6 houses in 243 hours. How many hours will it take them to wire
13 houses?
esearchers studying anthropometry collected body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender, for 507 physically active individuals. The histogram below shows the sample distribution of heights in centimeters (Heinz, 2003). Min 147.2 Q1 163.8 Median 170.3 Mean 171.1 SD 9.4 Q3 177.8 Max 198.1 a) What is the point estimate for the average height of active individuals
hello
the question is incomplete, but based on directives from brainly i did an online search and i was able to get the complete question.
Researchers studying anthropometry collected body girth measurements
and skeletal diameter measurements, as well as age, weight, height and gender, for 507 physically
active individuals. The histogram below shows the sample distribution of heights in centimeters(a) What is the point estimate for the average height of active individuals? What about the median?
(b) What is the point estimate for the standard deviation of the heights of active individuals?
What about the IQR?
(c) Is a person who is 1m 80cm (180 cm) tall considered unusually tall? And is a person who is 1m 55cm (155cm) considered unusually short? Explain your reasoning.
(d) The researchers take another random sample of physically active individuals. Would you
expect the mean and the standard deviation of this new sample to be the ones given above.
Explain your reasoning.
(e) The samples means obtained are point estimates for the mean height of all active individuals,
if the sample of individuals is equivalent to a simple random sample. What measure do we use to quantify the variability of such an estimate? Compute this quantity using the data from the original sample under the condition that the data are a simple random sample
Step-by-step explanation:
1. the point estimate for the average height is the mean = 171.1
the median of active individuals is 170.3
2. point estimate of sd = 9.4
to get IQR
[tex]Q3-Q1[/tex]
= 177.8 -163.8
= 14
3. mean +- SD
171.1 +-2(9.4)
171.1+18.8 = 189.9
171.1-18.8 = 152.3
[189.9, 152.3]
180CM is within the limits of 2SD. so a height of 180cm is not unusually tall
155 cm is within the 2sd limit so this height is not unusually short
4.
mean and sd are not same. a great probability exists that a different sample would have similar but different results if the same sample size is 507.
5.
[tex]9.4/sqrt507[/tex]
= 0.417
≈ 0.42
Simplify using order of
operations.
7(6 + 3) – 4 x 5
P
E
MD
AS
Answer:
[tex]43[/tex]
Step-by-step explanation:
If you dont know what PEMDAS means
P= Parenthesis
E= Exponents
M= Multiplication
D= Division
A= Addition
S= Subtraction
[tex]7(6 + 3) - 4 \times5[/tex]
[tex]6 + 3 = 9[/tex]
[tex]7(9) - 4 \times 5[/tex]
No exponents but there is multiplication
[tex]7 \times 9 = 63[/tex]
[tex]63 - 4 \times 5[/tex]
[tex] - 4 \times 5 = - 20[/tex]
[tex]63 - 20 = 43[/tex]
[tex]43[/tex]
Interest earned on 5000 with a rate of 6.4% for 4 years
Answer:
1280
Step-by-step explanation:
I = p x r x t
I = 5000 x 6.4/ 100 x 4
I = 5000 x 0.064 x 4
I =1280
is 3/4 less than,greater than,or equal to -1/2 ?
Answer: Greater than
3/4 greater than -1/2
3/4 > -1/2
Any positive number is always larger than any negative number
On a number line, stuff on the right side is always larger than stuff on the left side.
Answer:
it"s greater then
How do you find the whole in percent problems
Answer:
So essentially, you are trying to find what the overall whole is based off of a number that is the percent of the number. In order to do this, you must turn your percentage into a fraction over 100. You are going to then create the number that is a percentage of another number into a fraction over "x". Cross multiply the two fractions. Since there is an "x", count is as a zero. Now, create a fraction with the numerator as the number you just got from multiplying, and the denominator as the number you have to refer to as the percent of the whole. Since fraction is division, divide the two numbers and you get your answer. Sorry if this is so complex I tried to simplify it as best as I could
Step-by-step explanation:
Example: 8 is 80% of what number?
80% to 80/100
8 to 8/x
*cross multiply*
80x/80 = 800/80
800 divided by 80 is 10.
so, 8 is 80% percent of 10.