9514 1404 393
Answer:
726 ft²
Step-by-step explanation:
The perimeter of the room is ...
P = 2(L+W) = 2(18 +15) = 66 . . . . ft
Then the gross wall area (including windows) is ...
A = LH = (66 ft)(8 ft) = 528 ft² . . . . gross wall area
The area of the 3 windows is ...
A = 3×LW = 3×(6 ft)(4 ft) = 72 ft² . . . . window area
The area of the ceiling is ...
A = LW = (18 ft)(15 ft) = 270 ft² . . . . ceiling area
__
Then the net area to be painted is ...
gross wall area + ceiling area - window area
= 528 ft² +270 ft² -72 ft² = 726 ft²
The area that Marta will paint is 726 ft².
Please help. I don't understand how to solve for number 17, 19, and 21. Please show how you solved each problem
(17) From the plot, you see that
Pr[$15,500 ≤ x ≤ $18,500] = 99.7%
We can split up the probability on the left at the mean, so that
Pr[$15,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $18,500] = 99.7%
Any normal distribution is symmetric about its mean, so the two probabilities here are the same. The one on the left is what you want to compute. So you have
2 × Pr[$15,500 ≤ x ≤ $17,000] = 99.7%
==> Pr[$15,500 ≤ x ≤ $17,000] = 49.85%
(19) The mean of a normal distribution is also the median, so half the distribution lies to either side of the mean. Mathematically, we write
Pr[x ≥ $17,000] = 50%
The plot shows that
Pr[$16,500 ≤ x ≤ $17,500] = 68%
and by using the same reasoning as in (17), we have
Pr[$16,500 ≤ x ≤ $17,000] + Pr[$17,000 ≤ x ≤ $17,500] = 68%
2 × Pr[$17,000 ≤ x ≤ $17,500] = 68%
Pr[$17,000 ≤ x ≤ $17,500] = 34%
Now
Pr[x ≥ $17,000] = 50%
Pr[$17,000 ≤ x ≤ $17,500] + Pr[x ≥ $17,500] = 50%
34% + Pr[x ≥ $17,500] = 50%
==> Pr[x ≥ $17,500] = 16%
(21) From the plot,
Pr[$16,000 ≤ x ≤ $18,000] = 95%
This means (by definition of complement) that
Pr[x ≤ $16,000 or x ≥ $18,000] = 100% - 95% = 5%
and by symmetry,
Pr[x ≤ $16,000 or x ≥ $18,000] = 5%
Pr[x ≤ $16,000] + Pr[x ≥ $18,000] = 5%
2 × Pr[x ≤ $16,000] = 5%
==> Pr[x ≤ $16,000] = 2.5%
Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for $5dollar each. If she buys 10 raffle tickets, then she would spend a total of $135 at the fundraiser.
The number S of dollars Camille spends at the fundraiser is a function of r, the number of raffle tickets she buys.
Write the function's formula.
Answer:
50r + a = 135
Admission cost was $85
Step-by-step explanation:
We are missing a crucial amount of information here. It is how much she spent on her admission. We can create an equation symbolizing this problem.
5r + a = 135
We know that she purchases 10 tickets so we can substitute that in r and solve for a.
50 + a = 135
a = 85
Best of Luck!
You want to buy a house that has a purchase price of $180,000 you plan to make a down payment of 10% of the purchase price and then while the rest what is the dollar value of the down payment?
Step-by-step explanation:
=10% of $180000
= 10*$180000/100
=$180
The duration of shoppers' time in Browse Wrld's new retail outlets is normally distributed with a mean of 27.8 minutes and a standard deviation of 11.4 minutes. How long must a visit be to put a shopper in the longest 10 percent
Answer:
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
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.
Mean of 27.8 minutes and a standard deviation of 11.4 minutes.
This means that [tex]\mu = 27.8, \sigma = 11.4[/tex]
How long must a visit be to put a shopper in the longest 10 percent?
The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 27.8}{11.4}[/tex]
[tex]X - 27.8 = 1.28*11.4[/tex]
[tex]X = 42.39[/tex]
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
Devaughn is 10 years older than Sydney. The sum of their ages is 104. What is Sydney's age?
I
Answer:
Sydney's age = 42
Step-by-step explanation:
104 divided by 2 = 52
52 - 10 = 42
I am sorry if this is wrong. But this is what I learned at my school.
A cone has a volume of 4000cm3
. Determine the height of the cone if the diameter of the cone
is 30 cm.
Answer:
17cm
Step-by-step explanation:
Given that the Volume of a cone is 4,000 cm³. And we need to determine the height of the cone , if the diameter is 30cm .
Diagram :-
[tex]\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\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)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17.5,1.6){\sf{15cm }}\put(9.5,10){\sf{17\ cm }}\end{picture} [/tex]
Step 1: Using the formula of cone :-
The volume of cone is ,
[tex]\rm\implies Volume_{(cone)}=\dfrac{1}{3}\pi r^2h [/tex]
Step 2: Substitute the respective value :-
[tex]\rm\implies 4000cm^3 =\dfrac{1}{3}(3.14) ( h ) \bigg(\dfrac{30cm}{2}\bigg)^2 [/tex]
As Radius is half of diameter , therefore here r = 30cm/2 = 15cm .
Step 3: Simplify the RHS :-
[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) (15cm)^2\\ [/tex]
[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) 225cm^2\\ [/tex]
Step 4: Move all the constant nos. to one side
[tex]\rm\implies h =\dfrac{ 4000 \times 3}{ (3.14 )(225 )} cm \\[/tex]
[tex]\implies \boxed{\blue{\rm Height_{(cone)}= 16.98 \approx 17 cm }}[/tex]
Hence the height of the cone is 17cm .
ASAP!!!!!! SHOW WORK!!!! Thank you!!!!!!!!!
Its A trapezium
For Calculations Refer to the attachment
Answer:
SquareStep-by-step explanation:
Plot the points.
See the attached.
It is easy to calculate the length of sides and diagonals using the coordinates and the distance formula.
The sides are all equal to [tex]\sqrt{5}[/tex] units and the diagonals are both equal to [tex]\sqrt{10}[/tex] units.
This is a property of a square.
if the r-value, or correlation coefficient, of a data set is 0.941, what is the coefficient of determination
Answer:0.824
Step-by-step explanation:
The coefficient of determination is approximately 0.885 or 88.5%.
What is the correlation coefficient?A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.
The coefficient of determination (R-squared) is equal to the square of the correlation coefficient (r).
Therefore, to find the coefficient of determination with an r-value of 0.941, we can simply square it:
R-squared = r² = 0.941² = 0.885481
Thus, the coefficient of determination is approximately 0.885 or 88.5%.
This means that 88.5% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.
Learn more about the correlation coefficient here:
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which of the following is q point slope equation of a line that passes through the point (5,2)and (-1,-6)
Answer:y - y1 = m(x + x1)
m = (y2 - y1)/(x2 - x1) = (-6 - 2)/(-1 - 5) = -8/(-6) = 4/3
y - 2 = 4/3(x - 5) is a possible answer
y + 6 = 4/3(x + 1) is also a possible answer
Step-by-step explanation:
can i be brainliest
Write a linear equation in point slope form with the given slope of 1/4 and passing through the point (8,-3)
Answer:
The equation is
y=1/4x-3
Answer:
y = 1/4x - 5
Step-by-step explanation:
If gradient or slope (m) equal to 1/4
then y - y¹ = m( x - x¹) ..........(1)
where the line happen to be passing through the point given above
therefore let x¹ be 8.........(2)
and y¹ be -3...............(3)
substitute (3) and (2) into (1)
we have y -(-3) = 1/4 (x - 8)
so 4(y+3)= (x-8)
4y = x - 8 - 12
therefore y = 1/4x - 5
Which ratio represents the tangent of an angle?
a. adjacent/hypotenuse
b. opposite/hypotenuse
c. adjacent/opposite
d. opposite/adjacent
Answer:
option d.opposite / adjacent
Step-by-step explanation:
opposite /adjacent ratio represents the tangent of an angle .
hope it is helpful to you ☺️
Answer:
D.
Step-by-step explanation:
From the trigonometry shortcuts we can use the acronyms:
SOH CAH TOA
for an arbitrary angle Ф, plug in the length of the sides:
sin(Ф) = opposite/hypotenuse
cos(Ф) = adjacent/hypotenuse
tan(Ф) = opposite/adjacent
If you have a right triangle with legs a =6 and b= 8, what is the value of the hypotenuse? show work.
Answer:
10
Step-by-step explanation:
1. [tex]6^{2} + 8^{2} = c^{2}[/tex]
2 [tex]100 = c^{2}[/tex]
3. c = 10
Danielle needs to walk 3 miles. If she wants to reach her destination in 45
minutes ( hour), how fast does she need to walk?
A. 135 miles
per hour
B. 2.25 miles per hour
C. 15 miles per hour
D. 4 miles per hour
Answer:
4 miles per hour
Step-by-step explanation:
3 miles
Change the 45 minutes to hours
45 minutes * 1 hour/60 minutes = 3/4 hour
3 miles ÷ 3/4 hour
Copy dot flip
3 * 4/3
4 miles per hour
Does anyone know this?
Answer:
C
Step-by-step explanation:
Rationalize the denominator by multiplying [tex]\frac{\sqrt{5}}{\sqrt{5} }[/tex]. The denominator will become 5, while the numerator will be 3[tex]\sqrt{100}[/tex]. This is equal to 30/5, which is 6.
Hope this helps!
Find the missing length indicatedOk
Answer:
x = 135
Step-by-step explanation:
4.8 yd
6 yd
1
4.5 yd
5 yd
7 yd
Find the volume of the composite solid. Round your answer to the nearest hundredth.
A. 244.36 B. 264.79 C. 304.51 D. 330.84
Answer:
A
Step-by-step explanation:
The composite solid is made up of a cone and a rectangular prism.
Volume of the composite solid = volume of the cone + volume of the rectangular prism
✔️Volume of Cone = ⅓*π*r²*h
Where,
r = 4.8 yd
h = √(6² - 4.8²) = √12.96 = 3.6 yd
Substitute
Volume of cone = ⅓*π*4.8²*3.6
= 86.86 yd²
✔️Volume of rectangular prism = l*b*h
Where,
l = 7 yd
w = 5 yd
h = 4.5 yd
Substitute
Volume of prism = 7*5*4.5 = 157.5 yd²
✔️Volume of composite solid = 86.86 + 157.6 = 244.4 yd² (which is close to 244.36 yd²)
It's camping season! Ernie and Bert set up their tents 15 m from
each other. Ernie has Tent 1 and Bert has Tent 2. The angle
between the line of sight from Bert's tent to the shower and the
line of sight from Bert's tent to Ernie's tent is 78 degrees. If
Ernie's tent is 19m away from the shower, is Bert 's tent closer or
further away from the shower and by how much? In your
calculations, round your angles to the nearest whole degree and
side measurements to the nearest tenth of a metre.
1
2
Answer:
The answer is "21.6".
Step-by-step explanation:
Let A stand for tent 1
Let B stand for tent 2
Let C be a shower
Using cosine formula:
[tex]c= \sqrt{b^2 +a^2 - 2ab\cdot \cos(C)}\\\\[/tex]
[tex]= \sqrt{(19)^2 + (15)^2 - 2\cdot 19 \cdot 15 \cdot \cos(78^{\circ})}\\\\= \sqrt{361 + 225 - 570\cdot \cos(78^{\circ})}\\\\ = \sqrt{586- 570\cdot \cos(78^{\circ})}\\\\= 21.6\\\\[/tex]
Therefore, you need to reduce the similarity from B to C which is the length from tent 2 to shower:
Tent 2 Distance to Dusk = 21.6m
Bert's tent is 21.6m away from the shower
Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.
Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)[/tex]
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1+a}{2}=\dfrac{3}{2}[/tex]
[tex]1+a=3[/tex]
[tex]a=3-1[/tex]
[tex]a=2[/tex]
Similarly,
[tex]\dfrac{2+b}{2}=\dfrac{2}{2}[/tex]
[tex]2+b=2[/tex]
[tex]b=2-2[/tex]
[tex]b=0[/tex]
And,
[tex]\dfrac{1+c}{2}=\dfrac{-1}{2}[/tex]
[tex]1+c=-1[/tex]
[tex]c=-1-1[/tex]
[tex]c=-2[/tex]
Hence, the coordinates of vertex S are (2,0,-2).
PLZZZZZZ HELP WILL GIVE BRAIN THING AND EXTRA POINTS !What is the least common denominator of the rational expressions below?
Answer:
D is the least common denominator
Triangle plz help me find B,b and c
Answer:
B = 55°
b = 17.1 (rounded to the nearest tenth)
c = 20.9 (rounded to the nearest tenth)
pleas help
given parallelogram ABCD find m<ADB
Answer:
∠ ADB = 19°
Step-by-step explanation:
Consecutive angles in a parallelogram are supplementary, sum to 180° , so
∠ CDA = 180° - ∠ DAB = 180° - 138° = 42°
Then
∠ ADB + ∠ CDB = 42° , that is
∠ ADB + 23° = 42° ( subtract 23° from both sides )
∠ ADB = 19°
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? **
60
60/100
60/40
40/100
Answer:
The proportion of red candies is 60/100.
Step-by-step explanation:
Given that sixty out of every 100 pieces of candy is red, to determine which indicates the proportion of red candies, the following calculation must be performed:
60 red candies out of 100 total candies
60/100
Therefore, the ratio of red candies is 60/100.
please help, it’s urgent !
Answer:
f(-10) = 2 times -10 + 1
= -19
f(2) = 2^2
= 4
f(-5) = 2 times -5 + 1
= -9
f(-1) = (-1)^2
= 1
f(8) = 3-8
= -5
Step-by-step explanation:
A roller coaster descended 32.3 ft in one minute. How would you show this using an integer?
A. -32.3
B. +32.3
C. 32.3-
D. 32.3+\
Answer:
Step-by-step explanation:
a
Determine the difference. 3/4 – 5/16 =?
Answer:
[tex]\frac{3}{4} -\frac{5}{16} =\frac{3(4)}{4(4)} =\frac{5}{16} =\frac{12}{16} -\frac{5}{16} =\frac{7}{16}[/tex]
Answer:
7/16
Step-by-step explanation:
3/4 - 5/16
Get a common denominator of 16
3/4 *4/4 -5/16
12/16 - 5/16
7/16
Which expressions are equivalent to -7+3(-4e-3)
Choose all answers that apply:
A. -4(3e+4)
B. 12e
C. None of the above
Answer: A
-4(3e+4)=
-12e-16
Step-by-step explanation:
-7+3(-4e-3)=
-7-12e-9=
-12e-16
A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $11 the average
attendance has been 26000. When the price dropped to $8, the average attendance rose to 30000. Find a
demand function D(q), where q is the quantity/number of the spectators. (Assume D(q) is linear)
D(q)
(For best results, keep answers in fraction form, not decimals)
Answer:
D(q) = -(3)/(4,000)q+19.5
Step-by-step explanation:
Given:
overall capacity = 60000
price in point one = 11
spectators in first point = 26000
second point - price = 8
spectators = 30000
solution:
The demand of a product as a function of its price and other factors such as the prices of the substitutes and complementary goods, income is the expression known as demand function. It is represented by D(q)
we have two points in our line for given ques:
first point of line = (26,000, 11)
second point of line = (30,000, 8)
Slope = (11 - 8)/(26,000 - 30,000)
= (3)/(-4,000)
y = mx + b
here, b = factors influencing demand besides price
m = slope
x = price
10 = (3)/(-4,000) )(26,000) + b
b = 19.5
y = -(3)/(4,000)+19.5
D(q) = -(3)/(4,000)q+19.5
1. One half of a number added to a second
number equals 4. One half of the first
number decreased by the second number
equals zero. Find the two numbers.
Answer:
(4, 2)
Step-by-step explanation:
½x + y = 4
y = 4 - ½x
½x - y = 0
½x - (4 - ½x) = 0
½x - 4 + ½x = 0
x = 4
y = 4 - ½(4)
y = 2
Which of these statements is true for f(x) = 2 · 3x?
Answer:
the statement number D okay!
The y-intercept of the function will be at (0, 2). Then the correct option is A.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
The function is given below.
y = 2·(3)ˣ
The value of y at x = 0, we have
y = 2·3⁰
y = 2·1
y = 2
The y-intercept of the function will be at (0, 2).
Then the correct option is A.
More about the exponent link is given below.
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What is the probability that the sample mean would differ from the true mean by greater than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
Answer:
The correct solution is "0.0226".
Step-by-step explanation:
The given question seems to be incomplete. Please find below the attachment of the complete query.
According to the question,
Mean
= 29
Standard deviation (s),
= 8
For sample size pf 92,
The standard error will be:
[tex]SE=\frac{s}{\sqrt{N} }[/tex]
[tex]=\frac{8}{\sqrt{92} }[/tex]
[tex]=0.834[/tex]
now,
⇒ [tex]1-P(\frac{-1.9}{0.834} < z < \frac{1.9}{0.834} )[/tex] = [tex]1-P(-2.28<z<2.28)[/tex]
or,
= [tex]1-(2\times P(z<2.28)-1)[/tex]
= [tex]2-2\times P(z<2.28)[/tex]
With the help of table, the normal distribution will be:
= [tex]2-2\times 0.9887[/tex]
= [tex]0.0226[/tex]
