Step-by-step explanation:
Given - In selecting a sulfur concrete for roadway construction in regions that experience heavy frost, it is important that the chosen concrete has a low value of thermal conductivity in order to minimize subsequent damage due to changing temperatures. Suppose two types of concrete, a graded aggregate and a no-fines aggregate, are being considered for a certain road. The table below summarizes data on thermal conductivity from an experiment carried out to compare the two types of concrete.
Type ni xi si
Graded 42 0.486 0.187
No-fines 42 0.359 0.158
To find - a. Formulate the above in terms of a hypothesis testing problem.
b. Give the test statistic and its reference distribution (under the null hypothesis).
c. Report the p-value of the test statistic and use it to assess the evidence that this sample provides on the scientific question of difference in mean conductivity of the two materials at the 5% level of significance.
Proof -
a.)
Hypothesis testing problem :
H0 : There is significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
H1 : There is no significant difference between mean conductivity for the graded concrete and mean conductivity for the no fines concrete.
b)
Test statistic :
[tex]Z = \frac{x_{1} - x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1}} + \frac{s_{2}^{2} }{n_{2}} } }[/tex]
[tex]Z = \frac{0.486 - 0.359 }{\sqrt{\frac{0.03496 }{42} + \frac{0.02496 }{42} } }[/tex]
[tex]Z = \frac{0.127 }{\sqrt{0.001468}}[/tex]
[tex]Z = \frac{0.127 }{0.0377}[/tex]
⇒Z(cal) = 3.3687
Z(tab) = 1.96
As Z (cal) > Z(tab)
So, we reject H0 at 5% Level of significance
p-value = 0.99962
Hence
There is significant difference in mean conductivity at the two materials.
Solve (z + 6)2 = 5
{−6±5‾√}
{6±5‾√}
{5‾√±−6}
{−6+5‾√,6−5‾√}
9514 1404 393
Answer:
(a) -6±√5
Step-by-step explanation:
(z +6)^2 = 5 . . . . . given
z +6 = ±√5 . . . . . take the square root
z = -6 ±√5 . . . . . . subtract 6
solve the equation -3 + 1/2n = 1/2 (-n + 14) in two different ways.
Answer:
Step-by-step explanation:
-3 + 1/2n = 1/2 (-n + 14)
distribute
-3 + 1/2n = -1/2n + 7
-1/2n
cancel out -1/2n
-3 = n + 7
-10 = n
subtract 7
n = -10
Find the surface area of a cylinder with the following dimensions. Use 3. 14 for $. Round your answer to the nearest
tenth
d = 11.4 cm, h = 4.4 cm
a. 5172 sq. cm
723.6 sq. cm
b. 361.5 sq. cm
d. 294.5 sq.cm
C.
Please select the best answer from the choices provided
Ο Α
ОВ
ОС
OD
Answer:
b
Step-by-step explanation:
r=d/2=11.4/2=5.7
slant surface area=2πr*h=11.4×3.14×4.4=157.5024 cm^2
area of base and top=2(πr²)=2×3.14×(5.7)²=204.0372 cm²
total surface area=157.5024+204.0372=361.5396=361.5 sq. cm
PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
Answer:
124
Step-by-step explanation:
Elm St. and Oak St. are parallel lines.
Cedar St. is a transversal to the other two streets.
When parallel lines are cut by a transversal, corresponding angles are congruent.
The angles with measures 9x + 61 and 3x + 103 are corresponding angles, so they are congruent and have the same measure.
9x + 61 = 3x + 103
Subtract 3x from both sides.
6x + 61 = 103
Subtract 61 from both sides.
6x = 42
Divide both sides by 6.
x = 7
9x + 61 = 9(7) + 61 = 63 + 61 = 124
3x + 103 = 3(7) + 103 = 21 + 103 = 124
NO FILES I WILL MARK YOU IF RIGHT I ASKED THIS FIVE TIMES ALL I GET IS SCAM FILES!!!!!!!!!!!!! PLZZZZZZ HELP
Answer:
90 degree angle i think
Step-by-step explanation:
Hope this helps you
9514 1404 393
Answer:
b = 90°
Step-by-step explanation:
Angles a, b, c total 180°, and angles a and c are complementary, meaning they total 90°. The measure of angle b is ...
b = 180° -90°
b = 90°
__
All of the angle measures are ...
a = 90° -c = 90° -56° = 34°
b = 180° -90° = 90°
c = given = 56°
d = given = 124°
e = c = 56°
This is an isosceles trapezoid.
R.
S
75
N
Х
Y У
T
U
z =
[?]
Enter the number that belongs in
the green box.
Enter
Answer:
75
Step-by-step explanation:
it would be the same as it opposite side S because they are the same
Please help meeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation:
h = 4.2 in
Volume = 3.6 cubic inches
[tex]\frac{1}{3}\pi r^{2}h = 3.6\\\\\frac{1}{3}*3.14*r^{2}*4.2 = 3.6\\\\r^{2}= \frac{3.6*3}{3.14*4.2}\\\\ = 0.81\\r=\sqrt{0.81}\\\\[/tex]
r = 0.9 in
Answer:
.... ..................
please help i have an F right now
Answer:
4
Step-by-step explanation:
If you add up all of those, you get 24. Then you divide by 6. 24/6 = 4.
Find the volume of the figure. Use 3.14 for pi a cone sphere has a diameter of 10 and a sphere has a height of 12 cm asking for a friend they need help asap will mark brainliest
Answer:
576 cm³
Step-by-step explanation:
cone = 1/3x3.14x5x5x12=314
1/2 sphere = 1/2x4/3x3.14x5x5x5=262
314+262=576
Please give me the correct answer.Only answer if you're very good at math.Please use the Pythagorean Theorem formula which is a^2 + b ^2 = c^2.
Answer:
8.7 in
Step-by-step explanation:
a = 7.3
b = 4.8
c^2 = 7.3^2 + 4.8^2 = 76.33
c = sqrt(76.33) which is around 8.7
Which is bigger 1/4 or 3/5
Answer:
3/5
Step-by-step explanation:
Let {u1,u2,u3} be an orthonormal basis for an inner product space V. If
v=au1+bu2+cu3
is so that ∥v∥=42, v is orthogonal to u3, and ⟨v,u2⟩=−42, find the possible values for a, b, and c.
• ||v|| = 42, which is to say
||v||² = 〈v, v 〉
… = 〈a u₁ + b u₂ + c u₃, a u₁ + b u₂ + c u₃〉
… = a ² 〈u₁, u₁〉 + b ² 〈u₂, u₂〉 + c ² 〈u₃, u₃〉 + 2(ab 〈u₁, u₂〉 + ac 〈u₁, u₃〉 + bc 〈u₂, u₃〉)
… = a ² ||u₁||² + b ² ||u₂||² + c ² ||u₃||²
[since each vector in the basis for V is orthogonal to any other vector in the basis, and 〈x, x〉 = ||x||² for any vector x ]
42² = a ² + b ² + c ²
[since each vector in the basis has unit length]
42 = √(a ² + b ² + c ²)
• v is orthogonal to u₃, so 〈v, u₃〉 = 0. Expanding v gives the relation
〈v, u₃〉 = 〈a u₁ + b u₂ + c u₃, u₃〉
… = a 〈u₁, u₃〉 + b 〈u₂, u₃〉 + c 〈u₃, u₃〉
… = c ||u₃||²
… = c
which gives c = 0, and so
42 = √(a ² + b ²)
• Lastly, 〈v, u₂〉 = -42, which means
〈v, u₂〉 = 〈a u₁ + b u₂ + c u₃, u₂〉
… = a 〈u₁, u₂〉 + b 〈u₂, u₂〉 + c 〈u₃, u₂〉
… = b ||u₂||²
… = b
so that b = -42. Then
42 = √(a ² + (-42)²) → a = 0
So we have a = 0, b = -42, and c = 0.
The required values are, [tex]a=0,b=-42 ,c=0[/tex]
Given,
[tex]v=au_1+bu_2+cu_3[/tex]
[tex]\left\| V\right\|=42[/tex]
Computation:
Since, [tex]v[/tex] is orthogonal to [tex]u_3[/tex] then we have,
[tex]\left<v,u_3 \right> =0\\\left< v,u_2\right> =-42[/tex]
Then,
[tex]\left\| V\right\|^2=\left<v,v \right>\\=\left<au_1+bu_2+cu_3,au_1+bu_2+cu_3 \right>\\=a_2\left\|u_1 \right\|^2+b_2\left\|u_2 \right\|^2+c_2\left\|u_3 \right\|^2\\=a^2+b^2+c^2\\=a^2+b^2+c^2=42^2[/tex]
As we know,
[tex]a=\left<v_1u_1 \right>\\b=\left< v_1u_2\right>= -42\\c=\left<v_1u_3 \right> =0[/tex]
[tex]a_2+b_2+c_2=42\\a=0[/tex]
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This equation shows how the money Kensington Middle School spends on workbooks is related to the total number of workbooks they buy.d = 64.6tThe variable t represents the number of workbooks bought by the school, and the variable d represents the total cost of those workbooks. At most how many workbooks can Kensington Middle School buy if it has $64.60 to spend?
Answer:
1 workbook
Step-by-step explanation:
Equation:
d = 64.6t
Given:
d = total cost
t = number of workbooks
Work:
d = 64.6t
64.6 = 64.6t
t = 64.6/64.6
t = 1
Answer: 1 work book t=1
Step-by-step explanation:
The radius of a cylindrical construction pipe is 1.5 ft. If the pipe is 17 ft long, what is the volume?
Use the value 3.14 for π and round your answer to the nearest whole number.
Answer:
The volume of the cylinder is 120.10 square feet.
Step-by-step explanation:
Given that the radius of a cylindrical construction pipe is 1.5 ft, to determine its volume if the pipe is 17 ft long, the following calculation must be performed, knowing that the volume of a cylinder arises from multiplying the number pi by the radius at square of the cylinder, and that result by the height of the same:
3.14 x 1.5 ^ 2 x 17 = X
3.14 x 2.25 x 17 = X
7.065 x 17 = X
120.105 = X
Thus, the volume of the cylinder is 120.10 square feet.
Calculate the volume of a square-based pyramid with a slant height of 5 ft and base edges of 6 ft.
Answer:
Volume is 60ft³
Step-by-step explanation:
b²h/3
b=6
h=5
The volume of a square-based pyramid will be 180 ft³. Option D is correct.
How to find the volume of a prism?If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is the same as its base, then its volume is:
[tex]\rm V = B^2 \times h \\\ V = 6^2 ft \times 5 \ ft \\\ V=180 \ ft^2[/tex]
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John withdrew 1/4 of his savings to use as deposit on a new phone.He had 164.00 in his savings account.How did John withdrew for the deposit on the phone
Answer:
$41
Step-by-step explanation:
Well he withdrew 1/4 of his savings which is basically 1/4 * 164
In Middletown, Main Street and Market Street are parallel to each other. Patrick Street intersects Market Street to form a 76° angle at the northeast corner, as shown in the figure below. What is the measure of the angle formed at the southeast corner of Main Street and Patrick Street? (Note: Each street is straight and has the same uniform width.) 76° 90° 104° 142° 152°
Answer:
152
Step-by-step explanation:
Edge 2020
Aquestion that can be answered by
collecting data that has variability,
You need to give more info
If the Volume of a Cylinder is 25*pi* and the radius is 4, what is the height "h"?
Round your answer to the nearest tenth if needed.
Answer:
The height of the cylinder is 0.497.
Step-by-step explanation:
Given that the Volume of a cylinder is 25 and the radius is 4, to determine what is the height of said figure, the following calculation must be performed, knowing that the volume of a cylinder is calculated using the following formula (3.14 x r^2 x h = X):
3.14 x (4x4) x h = 25
3.14 x 16 x h = 25
50.24 x h = 25
h = 25 / 50.24
h = 0.497
Therefore, the height of the cylinder is 0.497.
A backpack is on sale for $51.00. This is 75% of the original price. What was the original price?
What does not contribute to the destruction of the rainforest in Brazil? farming and ranching cutting down trees to sell the wood constructing a highway having heavy rains
Answer:
heavy rains
Step-by-step explanation:
it makes the forest grow!!1!!1!!!!11111!1!!
Eric spends 4/5 of his pocket money to buy lunches. The rest of the money he will save. If the amount he saves is $2, how much does he spend buying lunch?
Answer:
Wait u want me to answer your question or the Jono question? Or both?
Step-by-step explanation:
1. $6/5
Find the surface area of a square pyramid with side length 5 yd and slant height 7 yd.
Step-by-step explanation:
side length(a)=5yd
slant height(l)=7yd
vertical height(h)=?
Now,
h2=(l)2+(a/2)2
h=find it
Then,
T.S.A.=a2+2al
Surface area of square pyramid is 95 square yard.
What is surface area of square pyramid?The word "surface" means " the exterior or outside part of an object or body". So, the total surface area of a square pyramid is the sum of the areas of its lateral faces and its base.
So, the surface area of a square pyramid is the sum of the areas of four of its triangular side faces and the base area which is square.
Given
Length = 5 yd
Slant height = 7 yd
Surface area of square pyramid = 4 (Area of triangle) + area of square
S = [tex]4\frac{1}{2}bh+side^{2}[/tex]
S = [tex]4 . \frac{1}{2} (5)(7)+5.5[/tex]
S = 70 + 25
S = 95 square yard.
Hence, Surface area of square pyramid is 95 square yard.
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Help I need a equation
9514 1404 393
Answer:
a) y = 3x-1
b) y = x+5
Step-by-step explanation:
a) We notice the x-values change by 1, so the change in the y-value is the slope. -4 -(-7) = 3 is the change between the first two y-values.
The y-intercept is shown by the ordered pair (0, -1). So, the slope-intercept equation is ...
y = 3x -1
__
b) We note that the change in x is 2 units, as is the change in y. Then the slope of the function is m = 2/2 = 1. The y-intercept (b) can be found from ...
b = y -mx
b = 7 -1·2 = 5
Then the slope-intercept equation is ...
y = x + 5
help please. will give Brainly.
Answer:
a10 = 15
an = 6n - 45
Step-by-step explanation:
a12 = 27 = a + 11d - eq 1
a14 = 39 = a + 13d - eq 2
eq 2 - eq 1
2d = 12
d = 6
a + 11(6) = 27
a + 66 = 27
a = -39
a10 = a + 9d = -39 + 9(6) = 15
Tn = a + (n-1)d
-39 + 6(n - 1)
-39 + 6n -6
an = 6n - 45
The angle between the lines xy=0 is
(a) 00
(b) 60°
(c) 90°
(d) 120°
Answer:
(c) 90°
Step-by-step explanation:
Given
[tex]xy = 0[/tex]
Required
The angle between the line
First, solve for x and y
[tex]xy = 0[/tex]
[tex]x = 0[/tex] or [tex]y=0[/tex]
This means that: y axis and x axis
The angle between the two axes is 90 degrees
Hence: (c) is correct
HELP ASAP What is the distance between the following points
Answer:
6
Step-by-step explanation:
At a candy store each bag holds 0.75 pounds. A box with 12 pounds of candy is being put into ,b, bags. How many bags of candy is this?
Answer:
17 bags is correct
Step-by-step explanation:
12 / 75 is equal to 17.14
How
many solutions does the equation 4X + 8 = - 2 - 2 + 5x have?
Two
® One
Zero
Infinitely many
Answer:
x = 12
Step-by-step explanation:
by direct solution
otherwise this system many solution
Answer:
one
Step-by-step explanation:
4x+8=-4+5x
or, 5x-4x = 8+4
hence,
x=12
The weekly average earnings of his drivers in a city is $980 with a standard deviation of $47. Assume that we select a random sample of 81 bus drivers. Compute the standard error of the mean
Answer: do the math, and after that know the definition of what the mean is and it will help you, its best to understand something.
Step-by-step explanation: