Answer:
48 square feet
Step-by-step explanation:
Given
Before expansion
[tex]A_1 = \frac{1}{2}bh[/tex] --- area of a triangle
[tex]A_1 = 16ft^2[/tex] --- value of the area
After the base and height were expanded, the area becomes:
[tex]A_2 = \frac{1}{2}BH[/tex]
Where
[tex]B = 2b[/tex]
[tex]H = 2h[/tex]
Substitute 2b for B and 2h for H in [tex]A_2 = \frac{1}{2}BH[/tex]
[tex]A_2 = \frac{1}{2} * 2b * 2h[/tex]
[tex]A_2 = \frac{1}{2} * 2*2*b*h[/tex]
[tex]A_2 = \frac{1}{2} * 4*b*h[/tex]
Rewrite as:
[tex]A_2 = 4 * \frac{1}{2} *b*h[/tex]
[tex]A_2 = 4 * \frac{1}{2}bh[/tex]
Recall that: [tex]A_1 = \frac{1}{2}bh[/tex]
So, we have:
[tex]A_2 = 4 * A_1[/tex]
Substitute 16 for [tex]A_1[/tex]
[tex]A_2 = 4 * 16[/tex]
[tex]A_2 = 64[/tex]
So, the area is [tex]64ft^2[/tex] after the dimensions were expanded
The area increased by:
[tex]Increment = A_2 - A_1[/tex]
[tex]Increment = 64 - 16[/tex]
[tex]Increment = 48[/tex]
It increased by [tex]48ft^2[/tex]
The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.
Required:
Construct a 92% Confidence Interval for the true proportion of girls in the ages 8-12 beginning ice-skating classes at the Ice Chalet.
Answer:
The answer is "(0.73,0.87)".
Step-by-step explanation:
Given:
number of girls[tex]= 64[/tex]
number of boys[tex]= 16[/tex]
Total number of children[tex]= 64+16= 80[/tex]
So,[tex]n=80[/tex]
Calculating the value of the proportion which is given by girls:
[tex]\hat{p}= \frac{\text{number of girls}}{\text{total number of childrens}}[/tex]
[tex]=\frac{64}{80}\\\\=\frac{8}{10}\\\\= 0.8[/tex]
Therefore the confidence interval is:
[tex]\to \hat{p}\pm z_{(1-\frac{\alpha }{2})}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to 0.8 \pm 1.75\sqrt{\frac{0.8(1-0.8)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.8(0.2)}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{\frac{0.16}{80}}\\\\\to 0.8 \pm 1.75 \sqrt{0.002}\\\\\to 0.8 \pm 1.75 (0.04)\\\\\to 0.8 \pm 0.07\\\\\to (0.73,0.87)[/tex]
[tex]\therefore \\\\\text{The lower confidence limit} = 0.73\\\\\text{The upper confidence limit} = 0.87\\[/tex]
HLEP ME PLEASE MY HOMEWORK IS SO HARDDDDDDDD
Answer:
the other side is 4
Step-by-step explanation: its a right triangle
Step-by-step explanation:
this is my answer if u are asking for the adjacent length...sorry if its wrong
Please help me i need it
Answer:
x+4x=5x
5x+x=6x
6x+8x=14x.
Olivia completed a high dive from a platform at a recent competition.
The graph below shows her distance from the pool, in meters, as a
function of time, in seconds.
Answer:
B
Step-by-step explanation:
Answer:
B). It takes Olivia about 3.2 seconds to enter the pool.
In an arithmetic sequence, u1 = 1.3 , u2 = 1.4 and uk = 31.2.
7a. Find the exact value of Sk
what is 2/10 as a decimal number
Answer:
0.2 is the answer .
Hope it helps..
60% of what number is 33?
60 percent (calculated percentage %) of what number equals 33? Answer: 55.
Answer:
55 :)
Step-by-step explanation:
A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices. Of the devices checked, 84% are not defective. What is the probability of an incorrect conclusion? Round your answer to the nearest tenth of a percent.
The probability of an incorrect conclusion is,
In 84 % of inspection, [tex]7.56\%[/tex] of them labeled as not defective but they are actually defective
Probability :It is given that,
A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices.
Of the devices checked, 84% are not defective.
Actual not defective is,
[tex]\frac{91*84}{100} = 76.44\%[/tex]
In [tex]84\%[/tex] of inspection,[tex]76.44\%[/tex] are actually not defective
But [tex]84- 76.44 = 7.56\%[/tex] of them labeled as not defective but they are actually defective
Learn more about Probability here:
https://brainly.com/question/24756209
Shonna is reading a 528 page book she reads 22 pages every day how many days will it take Shana to read the entire booK
Find two integers whose sum is -9 and product is 14
*PLEASE HELP QUICK*
Felipe is driving at a constant speed. The distance travelled depends on time.
d= distance in miles
t= time in hours
what is the rate of change of felipes driving speed?
how far will felipe drive in 6hrs?
9514 1404 393
Answer:
0150 milesStep-by-step explanation:
The appropriate relation is ...
distance = speed · time
d = 25t
__
The rate of change of Felipe's driving speed* is zero, since his speed is given as constant.
Felipe will drive 150 mile in 6 hours, as found using the equation:
d = 25(6) = 150
_____
* The question posed here asks for rate of change of driving speed. Perhaps, you want rate of change of distance, which is driving speed: 25 miles per hour.
The bakers at Healthy Bakery can make 310 bagels in 2 hours. How many
bagels can they bake in 20 hours? What was that rate per hour?
Answer:
The number of bagels made in 20 hours is 3100 bagels, at the rate of 155 bagels per hour.
Step-by-step explanation:
Given;
number of bagels in 2 hours = 310 bagels
The rate per hour is calculated as;
[tex]Rate = \frac{310 \ bagels}{2 \ hours}\\\\Rate = 155 \ bagels \ per \ hour[/tex]
In 20 hours, the number of bagels made is calculated as;
Number of bagels = 155 (bagels/hour) x 20 (hour)
= 3100 bagels.
Therefore, the number of bagels made in 20 hours is 3100 bagels, at the rate of 155 bagels per hour.
Find the equation of the given line.
Answer:
y=2/3x+1
Step-by-step explanation:
m= (slope)
b= (y-intercept
Select all of the ratios that are equivalent to 6:16. 2:8 3:8 1218 3080 18 to 48
Answer:
c and d
Step-by-step explanation:
The equivalent ratios to 6 : 16 are, 3 : 8, 30/80 and 18 to 48.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, A ratio 6 : 16 = 3 : 8.
So, One equivalent ratio is 3 : 8.
Now, Going through options,
10×3 : 10×8.
= 30 : 80.
= 30/80.
6×3 : 6×8.
= 18 : 48.
= 18 to 48.
learn more about proportion here :
https://brainly.com/question/7096655
#SPJ2
Part 2: Free Response 11. The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces. Company managers do not want the weight of a chocolate bar to fall below 8 ounces, for fear that consumers will complain. (a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces.
Answer:
0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces.
This means that [tex]\mu = 8.1, \sigma = 0.1[/tex].
(a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces
This is the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.1}{0.1}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.1587 = 15.87% probability that the weight of a randomly selected candy bar is less than 8 ounces.
At a football game, 45% were supporting the visiting team. If 946 people attending supported the home team, what was the total number of people attending the game?
Answer: 1720
Step-by-step explanation:
Factorise fully 3m+12
Answer:
The answer is 3(m+4)
hope it helps..
Answer:
Step-by-step explanation:
3(m+4)
Marshall has 3 bags in each of his 2 toy chests. Each bag has 5 marbles. How many
marbles does he have in all?
A. 10
B. 15
C. 30
D. 35
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Clear Answer
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Answer:
C. 30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
3 bags in each of 2 toy boxes. 3x5=15. That Would be the answer but he has 2 toy boxes go he has 6 bags. 15x2=30 or 15+15=30
The Kelly Students Council sold holiday swags for $10 for a fundraiser.. They spent $90 on materials to make the swags.. If they want to make at least $400,, how many swags do they need to sell? Write and solve the inequality.
Answer:
the answer would be 49
Step-by-step explanation:
they need to sell 49 to get their money back and make the 400 dollar goal
what is the remainder when 849,400 is divided by 216
Answer:
The remainder is 88
Step-by-step explanation:
The Remainder of a Division
We have to find the remainder when we divide 849,400 by 216.
It could be found by doing the long division, but we'll do it with a calculator.
Entering the division in the calculator we get:
849,400/216=3,932.4074...
We take the whole part of the quotient (3,932) and multiply it by the divisor:
3,932*216=849,312
The remainder is obtained by subtracting 849,400-849,312=88
The remainder is 88
Suppose you have $20 in your bank account. You start saving $5 each week. Your friend has $5 in his account and is saving $10 each
week. Assume that neither you nor your friend makes any withdrawals.
After how many weeks will you and your friend have the same amount of money in your accounts? How much money will each of you
have?
Answer:
The answer is after 3 weeks you will have the same amount of money
Step-by-step explanation:
5x + 20 = 10x +5
5x - 10x = 5 -20
-5x = -15
x = -15/-5
x = 3
what fraction does each get if six people share one whole pizza
Answer:
Does it say how many peices the pizza has? (if not then 1/6 ^^)
b - 1/8= 3 1/2
what’s b equal
Simplify the expression.
- 2.6f +0.2f - 15 - 3
i need help with this, anyone?
Answer: -2.4f-18
Step-by-step explanation:
Add 0.2f to -2.6f then subtract 3 from -15
Suppose that the functions g and f are defined as follows.
g(x)=-3+2x^2
f(x)=9-6x
a. Find (g/f)(2)
b. Find all values that are NOT in the domain of g/f
If there is more than one value, separate them with commas.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Given:
[tex]\to g(x)= -3+2x^2 \\\\\to f(x)=9-6x[/tex]
Calculating the value of [tex](\frac{g}{f})(2)[/tex]:
[tex]\to (\frac{g}{f}) (2)= (\frac{g(x)}{f(x)}) \times (2)[/tex]
[tex]=\frac{2x^2-3}{9-6x} \times 2\\\\=\frac{2\cdot 2^2-3}{3(3-2\cdot 2)} \\\\=\frac{2\cdot 4-3}{3(-1)}\\\\ =\frac{8-3}{-3}\\\\ =\frac{5}{-3}\\\\ = - \frac{5}{3}\\\\[/tex]
x=[tex]- \frac{\sqrt{3}}{2}[/tex] and x=[tex]\frac{\sqrt{3}}{2}[/tex] are not in the domain.
Domain: [tex]x \belong (- \infty, -\frac{\sqrt{3}}{2})\cup (- \frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2} )\cup (\frac{\sqrt{3}}{2}, \infty)[/tex]
3 4/5 • 3 1/2 divide reduce to the lowest term
Answer:
133/10
Step-by-step explanation:
first turn into proper fraction
19/5 * 7/2 = 133/10
every computer that a business owner purchases will lose most of its value after 5 years of use. the owner plans to purchase a computer for $2.100 and replace it after 4 years.
The business owner bought a computer that cost $2,400 instead of $2,100. the owner plans to replace the computer after 3 years instead of 4 years. Comparing both methods, which statement is true about the remaining value of this computer after 3 years of use ?
Answer:
Step-by-step explanation:
a) Data and Calculations:
Estimated useful life of a computer = 5 years
Cost of a computer purchased = $2,400
Annual depreciation expense = $480 ($2,400/5)
This means that the business owner chooses to spread (expense) the cost of the computer over 5 years at a rate of $480.
After 3 years, the cost already expensed = $1,440 ($480 * 3)
The Remaining value of this computer after 3 years of use will be $960 ($2,400 - $1,440).
b) Depreciation is an accounting method for spreading (or expensing) the cost of a long-term asset over its useful life.
Simply (2^3)-2
0 - 1/64
0 1/64
0 2
0 64
The correct answer is,
[tex] \frac{1}{64} [/tex]
Answer:
1/64
Step-by-step explanation:
when exponents are separated by parentheses, multiply them
so (2³)^-2 = 2^-6
whenever an exponent is negative, change into fraction form with one as the numerator and the other term goes into the denominator and the exponent now becomes positive
2^-6 = [tex]\frac{1}{2^6}[/tex] = [tex]\frac{1}{64}[/tex]
find the height of the cylinder whose volume is 1.54 cubic m and radius of the base is 70 cm
need full solution or I'll report
find the height of the cylinder whose volume is 1.54 cubic m and radius of the base is 70 cm
Required diagram :
[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{ 70 \: cm}}\put(9,17.5){\sf{h}}\end{picture}[/tex]
Solution :For a cylinder having a radius r and a height h ;
Volume Of Cylinder :
π r² .Here , the radius of the cylinder is given as 70 cm and the volume is 1.54 m³ .
Converting ;
1 m³ = 1 × 10⁶ cm³ .> 1.54 × 10⁶ cm³ .> 1540000 cm ³.> π r² h = 1540000> 22/7 × 70 × 70 × h = 1540000> 22 × 10 × 70 h = 1540000> 15400 h = 1540000> h = 100 cm = 1 m.The height of the cylinder is 100cm.=1m.
if somone can help.
Answer:
c cause it says length = 5x