Answers
Answer:
(a) 63 cups
(b) 16 cups
Step-by-step explanation:
Given that the volume of the sink = (2000/3)×π in³
(a) For the cup that has diameter = 4 in. and height, h = 8 in.
The radius, r = Diameter/2 = 4/2 = 2 in.
The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×2²×8 = (32/3)×π in.³
The number of cups to scoop = (Volume of the sink)/(Volume of the cup)
The number of cups to scoop = ((2000/3)×π)/((32/3)×π ) = 125/2=62.5 cups
Rounding to the next whole number gives 62.5 cups ≈ 63 cups
(b) For the cup that has diameter = 8 in. and height, h = 8 in.
The radius, r = Diameter/2 = 8/2 = 4 in.
The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×4²×8 = (128/3)×π in.³
The number of cups to scoop = (Volume of the sink)/(Volume of the cup)
The number of cups to scoop = ((2000/3)×π)/((128/3)×π ) = 125/8=15.625 cups
Rounding to the next whole number gives 15.625 cups ≈ 16 cups.
Related Questions
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method.
Construct and interpret the 95% confidence interval. Select the correct choice below and fill in the answer boxes within your choice.
(Round to three decimal places as needed.)
A. The proportion of students who eat cauliflower on Jane's campus is between___ and __ 95% of the time.
B.There is a 95% chance that the proportion of students who eat cauliflower in Jane's sample is between __ and __.
C. There is a 95% chance that the proportion of students who eat cauliflower on Jane's campus is between __ and__.
D. One is 95% confident that the proportion of students who eat cauliflower on Jane's campus is between __ and __.
Answers
Answer:
A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].
Step-by-step explanation:
We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower
n = sample of students
p = population proportion of students who eat cauliflower
Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;
[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]
n = [tex]24 + 1.96^{2}[/tex] = 27.842
[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141
95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]
= [0.012, 0.270]
Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].
The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.
Lucy is tiling her bathroom. She buys white and blue tiles in the
ratio 13:2.Blue tiles cost £2.80 while white tiles cost £2.35.If she
buys 16 blue tiles how much does Lucy spend on tiles in total?
Answers
Answer:
£289.20
Step-by-step explanation:
13:2 = x:16 or 13/2 = x/16
cross multiply: 208 = 2x
simplify: x = 104
16 blue tiles x £2.80 each = £44.80
104 white tiles x £2.35 each = £244.40
44.80 + 244.40 = £289.20
plzzzz answer right away will mark BRAINLIST AND FIVE STARS PLUS The table below shows the possible outcomes of rolling a six-sided number cube and flipping a coin. A 7-column table with 2 rows. Column 1 has entries H, T. Column 2 is labeled 1 with entries H 1, T 1. Column 3 is labeled 2 with entries H 2, T 2. Column 4 is labeled 3 with entries H 3, T 3. Column 5 is labeled 4 with entries H 4, T 4. Column 6 is labeled 5 with entries H 5, T 5. Column 7 is labeled 6 with entries H 6, T 6. What is the probability of getting a number less than 3 and a tails? StartFraction 1 over 12 EndFraction StartFraction 1 over 6 EndFraction One-fourth One-third
Answers
Answer:
P((1 or 2) and Tail) = 1/6 = StartFraction 1 over 6
Step-by-step explanation:
A six-sided die and a coin.
Probability of getting <3 and tail.
P((1 or 2) and Tail)
= 2/6 * 1/2
= 1/6
Answer:
1/6
Step-by-step explanation:
A magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. Describe what is meant by the statement that "the margin of error was given as percentage points.
Which one would be a true statement?
A. The statement indicates that the study is 100%−3%=97% confident that the true population percentage of people that prefer chocolate pie is 11%
B. The statement indicates that the interval 11%+3% is likely to contain the true population percentage of people that prefer chocolate pie.
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11%±3%.
D. The statement indicates that the study is only 3% confident that the true population percentage of people that prefer chocolate pie is exactly 11%.
Answers
Answer:
C. The statement indicates that the true population percentage of people that prefer chocolate pie is in the interval 11%±3%.
Step-by-step explanation:
Data provided in the questions
Number of respondents = 1,000
Choose chocolate pie = 11%
margin of error = ±3 percentage points
Based on the above information,
The lower limit is
= 0.11 - 0.03
= 0.08
And, the upper limit is
= 0.11 + 0.03
= 0.14
So based on the above computation, the option c is correct as it represents the true population percentage of people with respect to the chocolate pie preference
What is the method of comparing Coefficient
Answers
Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.
.
27. The area of a square plot is 0.0324 hectares. It was fenced using 3
strands of wire. What was the total length of wire used?
O A 72
O 8.144 m
O com
O 0.216
Answers
Answer: 0.216 km .
Step-by-step explanation:
Given, The area of a square plot is 0.0324 hectares.
Since , 1 hectare =10,000 meters
Then, the area of a square plot = 10,000 x 0.0324
= 324 meters
Area of square = side²
[tex]\Rightarrow\ (\text{side})^2=324\\\\\Rightarrow\ \text{side}=\sqrt{324}=18\ m[/tex]
Perimeter = 4(side) = 4 x 18 = 72 m
Since it was fenced using 3 strands of wire.
So, Total length of wire used = 3 (Perimeter) = 3 (72)m
= 216 m
Hence, the total length of wire used 216 m.
In km , 216 m = 0.216 km [ 1 m = 0.001 km]
Hence, the correct option is 0.216 km .
Please answer this in two minutes
Answers
Answer:
tan(X) = 1.05
Step-by-step explanation:
The triangles WXY and VTU are similar using the case AA (angle-angle).
The angle X is equal the angle T, therefore they have the same tangent value.
The tangent value is given by the opposite side to the angle divided by the adjacent side to the angle, so we have that:
[tex]tan(T) = UV / UT[/tex]
[tex]tan(T) = 21 / 20 = 1.05[/tex]
[tex]tan(X) = tan(T) = 1.05[/tex]
Please answer this now two minutes
Answers
Answer:
s = 8 degrees
Step-by-step explanation:
12s + 42 + 42 = 180
12s + 84 = 180
12s = 96
s = 8 degrees
PLEASEEEEE I don't understand this question.
Answers
Answer:
262°
Step-by-step explanation:
The relationship between the angle at B (82°) and the arcs of the circle, CGF and CDF, is that the angle is half the difference of those arcs. Of course the sum of those arcs is 360°, since together they make a full circle. So. we have ...
CGF +CDF = 360
(CGF -CDF)/2 = 82
We need to solve this system of equations to find CGF.
__
Multiplying the second equation by 2 and adding the first, we get ...
2((CGF -CDF)/2) +(CGF +CDF) = 2(82) +(360)
2CGF = 524 . . . . . simplify
CGF = 262 . . . . . . divide by 2
The measure of arc CGF is 262°.
_____
Alternate solution
Here's another way to get there. Arc CDF is the supplement to angle B, so is ...
CDF = 180° -∠CBF
Of course, arc CGF is 360° minus arc CDF, so ...
CGF = 360° -(180° -∠CBF)
CGF = 180° +∠CBF . . . . . simplify . . . please note this is a general solution
Then ...
arc CGF = 180° +82° = 262°.
The polygon below is a regular pentagon.
Calculate the size of the angle
X
Y
Z
Answers
x = 108
y = 36
z = 72
=============================================================
Explanation:
Check out the diagram below. I have added letters of x, y and z in places to help find the values of y and z. Note the triangle on top is isosceles (since a regular polygon has all sides equal; therefore the triangle on top has the top diagonal sides equal).
Before we find either y or z, let's find x.
For any regular polygon, the interior angles are all the same measure. They sum to 180(n-2). In this case, n = 5, so the angles sum to 180(5-2) = 540. Each individual interior angle is 540/n = 540/5 = 108 degrees
x = 108
Another way to find this interior angle is to first find the exterior angle. For any convex polygon (regular or not), the exterior angles always add to 360. When we talk about regular polygons, each individual exterior angle is 360/n. So in this case, we have 360/5 = 72 as one exterior angle. The adjacent interior angle is therefore x = 180-72 = 108. So there are two ways to find the measure of an interior angle.
--------
Referring to the diagram, specifically the isosceles triangle on top, we can see that it has angles of x, y and y. They add to x+y+y = x+2y. Set this equal to 180, plug in x = 108 and solve for y
x+2y = 180
108+2y = 180
2y = 180-108
2y = 72
y = 72/2
y = 36
--------
The bottom most triangle is a congruent copy of the triangle on top. We have another isosceles triangle with the same side lengths as before. This triangle also has x, y and y as mentioned above.
Notice the adjacent angles of y and z in the bottom left corner. They must add to 108 as this was the measure of the interior angle of a regular pentagon. So,
y+z = x
36+z = 108
z = 108-36
z = 72
find the rules for these sequence
Answers
Answer:
start with -29, multiply each term by 4
start with 60, multiply each term by 0.1
start with 97 and multiply each term by 0.5
3.03 cells
Step-by-step explanation:
1. The first sequence begins with -29. -116 ÷ -29 = 4, -464 ÷ -116 = 4, etc. Each value is multiplied by 4 to get the next value.
2. The second sequence begins with 60. 6 ÷ 60 = 0.1, 0.6 ÷ 6 = 0.1, etc. Each value is multiplied by 0.1 to get the next value.
3. The colony starts with 97 cells. Splitting into two is the same as multiplying by 0.5.
4. Multiply 97 by 0.5, 5 times for 5 minutes.
97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03
how to do this question plz
Answers
Answer:
148 cm ^2
Step-by-step explanation:
Hey there!
Well is the area of the base is 30 then we can conclude that the side lengths are 5 and 6.
Then if the volume is 120 we can do,
120 ÷ 30 = 4
So the height is 4 cm.
Now we already have the area of the base we just need to find the area of the rest of the rectangles.
If the bottom base is 30 then the top base is also 30.
30 + 30 = 60cm^2
Now we can do the two rectangles on the side that have side lengths of 5 and 4.
5*4 = 20
20+20 = 40 cm^2
Now we can do the two final rectangles that have side lengths of 6 and 4.
6*4=24
24 + 24 = 48 cm^2
Now we can add all the areas up,
48 + 40 + 60
= 148 cm^2
Hope this helps :)
please help i really don't understand
Answers
Answer:
80 square units
Step-by-step explanation:
The area formula refers to a generic triangle ABC in which side lengths 'a' and 'b' are known and angle C is between those sides.
In the given figure, we have known side lengths of 12 and 14, and the angle between them is 72°.
Putting these numbers into the formula, we find the area to be ...
A = (1/2)(12)(14)sin(72°) ≈ 79.9 ≈ 80 . . . . square units
The area of the triangle is about 80 square units.
a supermarket sells 4 brands of detergents a,b,c and d on a particular day 15% of the total boxes sold was brand a and 45% was brand c.Find the ratio of number of boxes of brand a sold to the number of boxes sold. Give your answser in a fraction Search Results Web results
Answers
Answer:
The ratio of number of boxes of brand a sold to the number of boxes sold is 3/20
Step-by-step explanation:
A supermarket sells 4 brands of detergents a, b, c, d.
On this particular day, 15% of the total boxes sold was brand a and 45% was brand c.
ratio of number of boxes of brand a sold to the number of boxes sold = ?
15% of the boxes sold is box a
Total number of boxes sold is 100%,
therefore,
ratio of box a sold to the whole boxes sold will be
15/100 = 3/20 in fraction
A soft drink machine can be regulated so that it discharges an average of Mu ounces per cup. If the ounces of fill are Normally distributed with a standard deviation of 0.4 ounces, what value should Mu be set at so that 6-ounce cups will overflow only 2% of the time
Answers
Answer: 5.0693 ounces
Step-by-step explanation:
For a 6 ounce cup to overflow, then the cup content is beyond 6 ounce, at 2%
P(x > 6) = 2% = 0.02; similarly
P(x<6) = 1 - P(x > 6)'.
P(x<6) = 1 - 0.02 = 0.98
The z-score for 0.98 = 2.326
The z - formular for a normally distributed goes thus :
Zscore =(observed score - mean) / standard deviation
Substituting the vamus :
2.326 = (6 - mean) / 0.4
2.326 × 0 4 = 6 - mean
0.9304 = 6 - mean
Mean = 6 - 0.9304
Mean = 5.0693
Select all the sentences that can be represented by the equation 25+p=38 A.25 is more than 38 is p B.25 times as much as p is 38 C.38 is p more than 25
Answers
Answer:
Option C: 38 is p more than 25
Step-by-step explanation:
the equation 25 + p = 38
can be read as 38 is 25 plus p units, or similarly ;
38 is p units more than 25.
Therefore from the three sentences you are showing, only the last one (option C) is the correct one.
Please answer this in two minutes
Answers
Answer:
I answered it
Step-by-step explanation:
I answered it
Answer:
∠ V ≈ 33.6°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos V = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{5}{6}[/tex] , thus
∠ V = [tex]cos^{-1}[/tex] ([tex]\frac{5}{6}[/tex] ) ≈ 33.6° ( to the nearest tenth )
I need your help with this question please explain why and show work.
Answers
Answer:
1
Step-by-step explanation:
y=2x+3, 2x represents the slope of the line and 3 represents the y-intercept
You make a scale drawing of a garden plot using the scale 2 in. = 17
ft. If the length of a row of vegetables on the drawing is 3 in., how
long is the actual row?
42.5 ft
25.5 ft
17 ft
34 ft
Answers
Answer 158Step-by-step explanation: you have to multiply the fraction by the numerator and divided by itsself and the subtract everything thren get myy642565780
En el mercado del satisfactor X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 – Px y 1,000 productores idénticos del satisfactor X, cada uno con una función de oferta dada por Qsx = 20 Px
Answers
Answer:
Px = $4
Step-by-step explanation:
Given that:
En el mercado de satisfacción X hay 10,000 individuos idénticos, cada uno con una función de demanda definida por Qdx = 12 - Px y 1,000 productores idénticos de X satisfactorio, cada uno con una función de oferta dada por Qsx = 20 Px
El precio de equilibrio y la cantidad de equilibrio se pueden determinar de la siguiente manera;
Qdx = 10000(12-Px)
Qdx = 120000 - 10000Px
Qsx = 1000(20 Px)
Qsx = 20000 Px
El punto de equilibrio para completar el enunciado, cuando Qdx = Qsx es:
Qdx = Qsx
120000 - 10000 Px = 20000 Px
120000 = 20000 Px + 10000 Px
120000 = 30000 Px
Px = [tex]\mathbf{ \dfrac{120000}{30000}}[/tex]
Px = $4
Find arc length. (NEED ASAP)
Answers
5.23 m
in cm 523 cm
nearest tenth 520cm
Step-by-step explanation:
60 / 360 × 2 ×22/7 × 5
110/ 21
5.23m
Answer:
5,2(3) meters
Step-by-step explanation:
Find arc lengthFormula
arc length = 2π·r (x°/360°)
= 2π·5m(60°/360°)
= 2·3,14·5m·1/6
= 31,4m/6
= 5,2(3) meters
solve the equation INCLUDE THE FORMULA x - 5 = 3 - 5x + 3x + 4
Answers
Answer:
x = 4
Step-by-step explanation:
x-5 = 3-5x+3x+4 x = 3-5x+3x+4+5 x = 3-5x+3x+9x = -5x+3x+12x+5x =3x+12 6x =3x+126x-3x = 12 3x = 12x = 12/3x = 4which of the following product? assume y>0 3 square root(y^2 square root 4+ square root 8y)
Answers
Answer:
[tex]6y^2\sqrt{10}+12\sqrt{5y}[/tex]
Step-by-step explanation:
Use the distributive property and the rules for forming and simplifying square roots.
(√a)(√b) = √(ab)
√(a²b) = a√b
__
[tex]3\sqrt{10}\cdot(y^2\sqrt{4}+\sqrt{8y})=(3\sqrt{10})(2y^2) +(3\sqrt{10})(\sqrt{8y})\\\\=6y^2\sqrt{10}+3\sqrt{80y}\\\\=6y^2\sqrt{10}+3\sqrt{(4^2)(5y)}\\\\=\boxed{6y^2\sqrt{10}+12\sqrt{5y}}\qquad\text{matches the first choice}[/tex]
Answer:
a
Step-by-step explanation:
1.
How can you count following distance?
Answers
At a MINIMUM, during dry weather conditions, you should have at least 2 seconds of space between you and the vehicle in front of you (3 seconds is better). Do this by using a fixed object such as a bridge, tree, or even a crack or shadow in the roadway.
Calculate the gap between you and the car in front of you by selecting an inanimate object along the lane. If the other car goes past the target, then "1000 one, 1000 two ..." count. You are three seconds behind this car when you get to "one thousand three" before you go through the piece.
------------------------------------
Hope this helps!
Brainliest would be great!
------------------------------------
With all care,
Forbidden
Please answer this in two minutes
Answers
Answer:
Hey there!
S would be 2 times 7, or 14.
Hope this helps :)
Answer:
14
Step-by-step explanation:
This is a 30-60-90 triangle, so the sides corresponding are x, 2x, and xsqrt3. the side, s, that we want is the 2x, and the x is 7. So, s is 14.
Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2
Answers
Answer: Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
We must work with linear equations, remember that the general shape is:
y = a*x + b
where a is the slope and b is the y-intercept.
Ok, first we want to find the rate of change (or the slope) of the graphed line:
We know that for a line that passes through the points (x1, y1) and (x2, y2)
The slope is:
a = (y2 - y1)/(x2 - x1)
Then for the graphed function, we can see that it passes through the points:
(0, -2) and (4, 0)
Then the slope is:
a = (0 -(-2))/(4 - 0) = 2/4 = 1/2
Now, the slope of the second line is 15/4.
Let's calculate the difference between the slopes:
15/4 - 1/2 = 15/4 - 2/4 = 13/4
(notice that we are calculating slope2 - slope1)
Then the correct option is:
Function 2 has a greater rate of change by 13/4
Answer:
B) Function 2 has a greater rate of change by 13/4
Step-by-step explanation:
what does the variable k represent in the following equation : k/2 +1/2=3
Answers
Pls solve this question. (If its right will give brainliest) X is 1 SOLVE FOR Y 210=60x+50y
Answers
Answer:
Step-by-step explanation:
I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me....
Answer:
3
Step-by-step explanation:
210=60(1)+50y
210=60+50y
-60 -60
150=50y
divide
y=3
PLEASE help me with this question ASAP!!!!
Answers
Step-by-step explanation:
I believe the answer is
The fuction roughly matches the data
Answer:
The function fits very well
Step-by-step explanation:
The equation for the stats is
y=-0.039866x²+3.99375x-0.4785714
A ladder placed against a vertical wall subtends an angle of 45 degree with the wall. The distance between the foot of the ladder and the wall is 15m, calculate the length of the ladder, correct to the nearest whole number.
Answers
Answer:
we can calculate it by applying trigonometric ratios
Step-by-step explanation:
tan 45 = length of wall/distance between ladder and wall
1 = length of wall/15
length of wall = 15m
(length of wall[tex])^{2}[/tex] + (distance between ladder and wall[tex])^{2}[/tex] = (length of ladder[tex])^{2}[/tex]
length of ladder = [tex]\sqrt{15^{2} + 15^{2} }[/tex]
= [tex]\sqrt{450}[/tex]
= 21.21 m