Answer:
0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.
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.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
The width of a casing for a door is normally distributed with a mean of 24 in and a standard deviation of 0.14 in.
This means that [tex]\mu_{C} = 24, \sigma_{C} = 0.14[/tex]
The width of a door is normally distributed with a mean of 23.87 in and a standard deviation of 0.08 in.
This means that [tex]\mu_{D} = 23.87, \sigma_{D} = 0.08[/tex].
Find the probability that the width of the casing exceeds the width of the door by more than 0.25 in?
This is P(C - D > 0.25).
Distribution C - D:
The mean is:
[tex]\mu = \mu_{C} - \mu_{D} = 24 - 23.87 = 0.13[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\sigma_{C}^2+\sigma_{D}^2} = \sqrt{0.14^2+0.08^2} = 0.1612[/tex]
Probability:
This probability is 1 subtracted by the pvalue of Z when X = 0.25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.25 - 0.13}{0.1612}[/tex]
[tex]Z = 0.74[/tex]
[tex]Z = 0.74[/tex] has a pvalue of 0.7704
1 - 0.7704 = 0.2296
0.2296 = 22.96% probability that the width of the casing exceeds the width of the door by more than 0.25 in.
find an ordered pair (x, y) that is a solution to the equation 4x-y=5
Answer:
An ordered pair that is a solution to the equation is (2,3).
Step-by-step explanation:
To find an ordered pair that is a solution to the equation, we attribute a value to one of the variables(x or y), and find the other.
4x-y=5
Using y = 3
4x - 3 = 5
4x = 8
x = 8/4 = 2
An ordered pair that is a solution to the equation is (2,3).
What is the value of the y-intercept of the graph of f(x) = 29(5.2)* ?
Answer:
(0,29)
Step-by-step explanation:
To find the y-intercept, substitute in
0 for x and solve for y OR use a graphing calculator.
A 13-foot ladder leaning against a building meets the side of the building exactly 12 feet above the ground. How far from the building is the base of the ladder rounded to the nearest hundredth foot?
Answer:
At the moment in question, we have a 5-12-13 right triangle.
x^2 + y^2 = 13^2
2x dx/dt + 2y dy/dt = 0
2(5)(2/3) + 2(12) dy/dt = 0
dy/dt = -5/18 ft/s
the area is 1/2 xy, so
da/dt = 1/2 y dx/dt + 1/2 x dy/dt
= (1/2)((12)(2/3) + (5)(-5/18))
= 119/36
Step-by-step explanation:
HELPPPPPP
Order the following numbers from least to greatest.
10 square number 5
10square number -99
10 square number -17
10 square number 14
10 square number -5
10 square number 30
Answer:
10^-99
10^-17
10^-5
10⁵
10¹⁴
10³⁰
A Carpenter has a board that measures 6 feet x 4 feet. a small rectangle measuring 1 foot x 1 foot is cut out of the middle how much area is left?
if the circumference of a circle is 52 cm, what is the radius? round to the nearest tenth. PLESE HELP I DONT HAVE THAT MUCH TIME :(
Answer:
8.3
Step-by-step explanation:
Given,
Circumference of the circle = 52 cm
Therefore ,
By the problem,
[tex] = > 2\pi r = 52[/tex]
[tex] = > 2 \times 3.14 \times r = 52[/tex]
[tex] = > r = \frac{52}{3.14 \times 2} [/tex]
=> r = 8.2802547771
Rounded to nearest tenth,
=> r = 8.3 (Ans)
The thickness of the backfat in pigs is used in evaluating the quality of their flesh for consumption. To compare the backfat thickness of pigs raised on two different diets, an animal researcher randomly sampled a group of pigs raised on Diet 1 and another group raised on Diet 2:
Sample Mean Sample SD Sample Size
Diet 1 3.63 cm 0.29 cm 18
Diet 2 3.37 cm 0.25 cm 18
POOLED SE 0.09
A) After confirming all relevant assumptions, you want to test if the mean backfat thicknesses of the pigs raised on these two diets differs. What is the absolute value of the test statistic?
B) If the critical value for this test is 2.032 (confirm that it is), what would be an appropriate conclusion for this test?
A. An conclusion is not warranted for this test
B. This data provides evidence that mean backfat thickness of pigs on Diet 1 is different from pigs on Diet 2 (p<.05)
C. This data provides no evidence that mean backfat thickness of pigs on Diet 1 is different from pigs on Diet 2 (p<.05)
D. This data provides evidence that diet is independent of backfat thickness (p<.05)
E. There is no evidence that diet is independent of backfat thickness (p>.05)
Answer:
A) The test statistic is approximately 7.5056
B) E. There is no evidence that diet is independent of backfat thickness
Step-by-step explanation:
The given data are;
The sample mean for pigs raised on Diet 1, [tex]\overline x_1[/tex] = 3.63 cm
The sample SD for pigs raised on Diet 1, s₁ = 0.29 cm
The number of pigs in the sample for pigs raised on Diet 1, n₁ = 18
The sample mean for pigs raised on Diet 2, [tex]\overline x_2[/tex] = 3.37 m
The sample SD for pigs raised on Diet 2, s₂ = 0.25 cm
The number of pigs in the sample for pigs raised on Diet 2, n₂ = 18
The pooled SE = 0.09
A) The test statistic is given by the following formula;
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(3.63-3.37)}{\sqrt{\dfrac{0.29^{2} }{18}-\dfrac{0.25^{2}}{18}}} \approx 7.5056[/tex]
The test statistic, t ≈ 7.5056
B) The degrees of freedom, df = n₁ - 1 = 18 - 1 = 17
At a confidence level of 95%, the critical value is 2.11
Given that the value of the test statistics tic if larger than the critical value, the null hypothesis is rejected and there is a difference in the backfat of the pigs on different diet
Therefore, there is no evidence that diet is independent of backfat thickness
a person invests 6500 dollars in a bank. the bank pays 6.75% interest compounded semi-annually. to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 15700 dollars?
A = P(1+r/n)^nt
Answer:
t=13.28382 ≈ 13.3 years
It takes 13.3 years to amount $15700 from the principal $6500.
Given that, a person invests 6500 dollars in a bank. the bank pays 6.75% interest compounded semi-annually.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = A = P(1+r/n)^nt
Now, 15700 =6500(1+6.75/2×100)^2t
⇒ 15700/6500=(1+6.75/200)^2t
⇒ 15700/6500=1.03375^2t
⇒ 2.415=1.03375^2t
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
t=ln(2.415)/2ln(1.03375)
Decimal Form:
t=13.28141707
≈ 13.3 years
Therefore, it takes 13.3 years to amount $15700 from the principal $6500.
To learn more about the compound interest visit:
https://brainly.com/question/14295570.
#SPJ2
PLEASE HELP DEW IN 1 hour
Answer: B
Step-by-step explanation:
2(—2) + 10 = 6.
2(0) + 6 = 6.
2(2) + 2 = 6.
2(4) + (—2) = 6
what is 1 plus 1 2+2 sara has this much how can she divide it to her 1 friend and her?
Answer: 7.5 each
Step-by-step explanation:
15/2
What 2 things put an expression in simplest form?
Answer:
Step-by-step explanation:
All you need to simplify most expressions is basic arithmetic -- addition, subtraction, multiplication, and division -- and the order of operations.
427 to the nearest hundred
Answer:
400
Step-by-step explanation:
The two is less than 5 so it becomes 0 and so does the 7
Whoever responds first will get marked Best!please look at the picture!Which scenario has the same area as the given figure?
A:A triangle with a base of 6 ft and a height of 10 ft.
B:A rectangle with a base of 9 ft and a height of 10 ft.
C:A parallelogram with a base of 10ft and a height of 16 ft.
D:A triangle with a base of 7 ft and a height of 24 ft.
Answer:
D) 96 is closest
Step-by-step explanation:
12x7=84
1/2(8)(4)=16
84+16=100
A = 30
B = 45
C = 160
D = 96
Which of the following sets of data does NOT represent a function? Set A x y 6 3 8 4 5 7 9 2 Set B x y 0 3 1 8 2 8 3 -7 Set C x y 10 7 20 11 30 9 40 7 Set D x y 3 9 2 2 8 -3 2 1 a. Set A b. Set B c. Set C d. Set D
Answer:
Set D
Step-by-step explanation:
There's 2 different y-values for the x value, 2 in Set D
5x + (1x+6)= 78
BARDZO POTRZEBUJĘ
Answer: x = 12
Step-by-step explanation:
1. add 5x + 1x which will equal 6x so now your equation is: 6x + 6 = 78
2. subtract 6 from 78 to get 72: 6x = 72
3. divide 72 by 6x to get your answer 12
Answer:
x = 12
Step-by-step explanation:
6x + 6 = 78
6x = 78 - 6
6x = 72
x = 72 / 6
x = 12
Mam nadzieję, że to pomoże!
Is it a right triangle please help!
Answer:
no
Step-by-step explanation:
Hello There!
We can figure out if the given side lengths form a right triangle using the Pythagorean Theorem
The Pythagorean Theorem states that the hypotenuse (longest side) squared equal to sum of the two legs squared
so if it is a right triangle then
[tex]74^2=71^+24^2[/tex]
[tex]74^2=5476\\71^2=5041\\24^2=576\\5041+576=5617\\5476\neq 5617[/tex]
5617 is not equal to 5476 therefore the given side lengths do not form a right triangle
~TheMathWIz
Kelly has some savings. After mowing lawns Saturday, she added $70 to her savings. How much money has Kelly saved?
Answer:
70
Step-by-step explanation:
saveings +70 the money she added to the money he or she saved
A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed random variables with parameter 2 for component A, and parameter 3 for component B. The system fails at the first component failure.
(a) - Read section 1.5.2 in the textbook.
(b) - What is the mean time to failure for component A and for component B
Answer:
[tex]E(x) = \frac{1}{2}[/tex] -- Component A
[tex]E(x) = \frac{1}{3}[/tex] -- Component B
Step-by-step explanation:
Given
Distribution = Exponential
[tex]\lambda = 2[/tex] --- Component A
[tex]\lambda = 3[/tex] --- Component B
Solving (a): The mean time of A
The mean of an exponential distribution is:
[tex]E(x) = \frac{1}{\lambda}[/tex]
We have:
[tex]\lambda = 2[/tex] --- Component A
[tex]E(x) = \frac{1}{2}[/tex]
Solving (b): The mean time of B
The mean of an exponential distribution is:
[tex]E(x) = \frac{1}{\lambda}[/tex]
We have:
[tex]\lambda = 3[/tex] --- Component B
[tex]E(x) = \frac{1}{3}[/tex]
which of the following phrases describes the expression 2 - 2x
Answer:c
Step-by-step explanation:cccccc
Someone Help Me Please
Answer:
y=-4x-5
Step-by-step explanation:
as considering (x,y) as(-2,3)this shows the perpendicularity
The expression (x^3) (x12) is equivalent to x^n. What is the value of n?
3 and n are exponents
Answer:
Step-by-step explanation:
(x^3) (12x)
(x^4)(12)
12x^4
We can really find the exponent without knowing what x is equal to but I hope this helps
What is the value of the expression
3+(2+8)^2+4*(1/2)^4
Answer:
Use photo math, it will explain it all
First here's the expression written out a little clearer
[tex]3+(2+8)^2+4*(\frac{1}{2} )^4[/tex]
Parentheses: (2+8) = (10).
Exponents: 10^2 is 100, and [tex](\frac{1}{2} )^4[/tex] is [tex]\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot\frac{1}{2} =[/tex] [tex]\frac{1}{16}[/tex]
Multiplication and division: 4 * 1/16 is [tex]\frac{4}{16}[/tex] or [tex]\frac{1}{4}[/tex] simplified
Addition and subtraction: Go left to right. 3 + 100 + [tex]\frac{1}{4}[/tex] = 103.25 (final answer)
Given f(x)= 3|2x-4|-8
find f(-3)=
Hi there!
[tex]\large\boxed{f(-3) =22 }}[/tex]
Find f(-3) by substituting in -3 for x:
f(x) = 3|2x - 4| - 8
f(-3) = 3|2(-3) - 4| - 8
Simplify:
f(-3) = 3|-6 - 4| - 8
f(-3) = 3|-10| - 8
f(-3) = 3(10) - 8 = 22
what is this figure ?
Answer:
B) rhombus
Step-by-step explanation:
the tic marks on the lines indicate that they are congruent, not parallel there is no way of knowing for sure that those lines are parallel therefore it is not a parallelogram even though it looks like it
State if the triangles in each pair of similar. If so, state how you know they are similar and complete the similarity statement.
triangle UTS~ ____
a. similar, AA, UED
b. similar, SSS, UDE
c. similar, SAS, UDE
d. not similar
Answer:
triangle UTS~∆UED by AAA axiom
Fide the volume and round to the nearest tenth . Please help I will give you brainless
Answer:
46
Step-by-step explanation:
Answer:
4.18 inch^3
Step-by-step explanation:
use the sphere volume formula :
V = (4/3)*pi*r^3
the radius of this sphere is 2/2 = 1 ( diameter / 2)
plugging in the values :
V = (4/3)*3.1415*1^3 = 4.18
Kisi samantar shreni me pratham 6 pado ka yog 42 hai iske 10 we pad tatha 30 we pad me anupat 1:3 ka hai is samtar shereni ka pratham tatha 13 pad gyat kare
Answer:
समांतर श्रेणी का प्रथम पद a = 2
[tex] t_{13}= 26[/tex]
Step-by-step explanation:
माना समांतर श्रेणी का प्रथम पद a और सामन्य अन्तर d है.
इसलिए..
[tex] S_6 = 42....(given) [/tex]
[tex]\therefore \frac{6}{2}\{2a + (6-1)d\}= 42 [/tex]
[tex]\therefore 3\{2a + 5d\}= 42 [/tex]
[tex]\therefore \{2a + 5d\}= \frac{42}{3} [/tex]
[tex]\therefore 2a + 5d=14...... (1)[/tex]
[tex] t_{10} : t_{30}= 1 : 3.....(given) [/tex]
[tex] \therefore \frac{t_{10}}{t_{30}} = \frac{1}{3} [/tex]
[tex] \therefore \frac{a +9d}{a+29d} = \frac{1}{3} [/tex]
[tex] 3(a + 9d) = a + 29d[/tex]
[tex] 3a + 27d = a + 29d[/tex]
[tex] 3a - a = 29d - 27d [/tex]
[tex] 2a= 2d [/tex]
[tex] a= d...... (2)[/tex]
समीकरण (1) और (2) से:
[tex]\therefore 2a + 5a=14[/tex]
[tex]\therefore 7a=14[/tex]
[tex]\therefore a=\frac{14}{7}[/tex]
[tex]\therefore a=2[/tex]
समांतर श्रेणी का प्रथम पद a = 2
a = d = 2... (समीकरण 2 से)
[tex] t_{13}= 2 + (13-1)2[/tex]
[tex] t_{13}= 2 + 12\times 2[/tex]
[tex] t_{13}= 2 + 24[/tex]
[tex] t_{13}= 26[/tex]
Enter the volume of the right rectangular prim in cubic inches
Answer:
602 in^2
Step-by-step explanation:
To find volume, multiply length, width, and height. In this case, it is 5, 14, and 8 3/5. I used a calculator, but if not, solve it using regular multiplication. First 5 times 14 since that is easier to get out of the way, then 8 3/5, and it is easiest to treat a fraction as a decimal when multiplying, in this case it would be 0.6. I am not going to explain how I got that since you were asking how to find volume.
Christa and James both walk from their houses to the bus stop every morning. Christa walks 1.9 kilometers further, and together they walk 4.1 kilometers.
If James walks a distance of d kilometers find the value of d.
Answer:
James walks 2.2 kilometers it is because 4.1-1.9=2.2
Step-by-step explanation:
and to check u can add 2.2 in 1.9 ko get 4.1 so james walked 2.2 distance kilometers from his house.
Answer:
Step-by-step explanation:
d + (d+1.9) = 4.1
2d = 2.2
d = 1.1 km
Write the directed line segment ratio as a fraction.
3:4
O [tex]\frac{3}{12}[/tex]
O [tex]\frac{4}{3}[/tex]
O [tex]\frac{3}{7}[/tex]
O [tex]\frac{4}{3}[/tex]