Answer:
1) P(258.5-cm < M < 259-cm) = 8.71%.
2) P17 = 125.57cm
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.
Question 1:
Mean of 258.5-cm and a standard deviation of 2.3-cm, which means that [tex]\mu = 258.5, \sigma = 2.3[/tex]
Find the probability that the average length of a randomly selected bundle of steel rods is between 258.5-cm and 259-cm.
This is the pvalue of Z when X = 259 subtracted by the pvalue of Z when X = 258.5.
X = 259
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{259 - 258.5}{2.3}[/tex]
[tex]Z = 0.22[/tex]
[tex]Z = 0.22[/tex] has a pvalue of 0.5871
X = 258.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{258.5 - 258.5}{2.3}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.5871 - 0.5 = 0.0871
0.0871*100% = 8.71%. So
P(258.5-cm < M < 259-cm) = 8.71%.
Question 2:
Mean of 127.1-cm and a standard deviation of 1.6-cm, which means that [tex]\mu = 127.1, \sigma = 1.6[/tex]
Find P17, which is the average length separating the smallest 17% bundles from the largest 83% bundles.
This is the 17th percentile, which is X when Z has a pvalue of 0.17. So X when Z = -0.954.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.954 = \frac{X - 127.1}{1.6}[/tex]
[tex]X - 127.1 = -0.954*1.6[/tex]
[tex]X = 125.57[/tex]
P17 = 125.57cm
prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k
The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k
The equation is given as:
x^2 + (1 - k).x+k-3 = 0
For an equation to have real root, then the following must be true:
[tex]b^2 \ge 4ac[/tex]
In x^2 + (1 - k).x+k-3 = 0, we have:
a = 1
b = 1 - k
c = k - 3
So, we have:
[tex](1 - k)^2 \ge 4 * 1 * (k - 3)[/tex]
Evaluate
[tex]1 - 2k + k^2 \ge 4k - 12[/tex]
Collect like terms
[tex]k^2 - 2k - 4k + 1 + 12 \ge 0[/tex]
[tex]k^2 - 6k + 13 \ge 0[/tex]
Using a graphing calculator, the value of k is all real numbers
Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k
Read more about real values at:
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Which graph shows a proportional relationship between X and y
how do you write 2 divided by 3 as a fraction
Answer: 2/3
Step-by-step explanation:
The sales tax rate is 8.5%. If Helen buys a pillow priced at $18, how much tax will she pay?
Answer:
$1.53 for tax
Step-by-step explanation:
18 times .085 = 1.53
What is the value of f(x) when x=3?
0 -3
0-2
0 1
04
The value of the function when x=3 is approximately 18.83.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The function
Now,
we need to substitute x=3 into the function and simplify it. We get:
3(3)−1+(1+3)2
=8+16
≈2.83+16
=4
Therefore, by the given function answer will be 4.
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Does anyone know how to do this
csc x ( sin x + cos x) = 1 + cot x
9514 1404 393
Explanation:
Use the identities ...
csc(x) = 1/sin(x)
cot(x) = cos(x)/sin(x)
__
[tex]\csc(x)(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{1}{\sin(x)}(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{\sin(x)}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}=1+\cot(x)\\\\1+\cot(x)=1+\cot(x)[/tex]
8. Find the value of
8^x/2^y
if 3x - y = 4,
Matthew kennedy of urbana, ohio is single and has been working as an admissions counselor at a university for five years. mathhew owns a home values at 250,000 on which he owns 135,000. he has a two year old vehicle valued at 32,000 on which he owes 26,000. he has about 20,000 remaining on hisnstudent loans. his rerirment account has grown to 32,000, and he owns some stock valued at 9,000. matthew has no life insurance and is considering buying some. how much should he buy?
Answer:
10,000.
Step-by-step explanation:
The solution is, Total assets is 164754.
What is assets?Assets are resources controlled by the entity as a result of past events and from which future economic benefits are expected to flow to the entity (AAA).
here, we have,
we know,
Mortgage is recorded separated by the home and is treated as liability
Loan & Auto loan are also liabilities of Matthew
Credit cards balances are only his indication of capacity to buy which is if that happens said transaction would result into an obligation of Matthew to pay or simply his liability
we have,
Based on the data given, assets is computed as follows;
Cash (checking account)= 2000
Cash (savings account)= 10000
Home =120000
Investments =12789
Car= 19965
Total assets is = 164754
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complete question:
Matthew currently has $2,000 in his checking account and $10,000 in a savings account. He owns a home worth $120,000 and he owes $75,900 on his mortgage. His investments in a 401(k) are valued at $12,789. He owes $29,526 on his student loans and just bought a new car. The car is currently valued at $19,965. His auto loan balance is $19,156. He is carrying a balance on two credit cards that adds up to $5,234. What is the value of Matthew's total assets? (Do not include the $ sign or commas in your answer).
Will 3in,4in,7in form a triangle.
Will 3in, 4in, 6in form a triangle
Will 1m, 2m, 3m form a triangle
Yes or no
Answer:
No, Yes, No
Step-by-step explanation:
3in by 4in by 5in will not make a triangle.
3in by 4in by 6in will make a triangle.
1m by 2m by 3m will not make a triangle.
The reason two of these triangles cannot be form is because the side lengths do not adhere to the triangle inequality theorem. This theorem states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.
50 POINTS QUICK Given that ab = x, evaluate the following:
1.) [tex]a^{2b}[/tex]
2.)[tex]a^{b+2}[/tex]
Answer:
2)The answer is x*a^2 because the equation is saying a^b*a^2. And if we knew that a^b = x, then the answer is x*a^2
Step-by-step explanation:
1.What is the total interest you will have paid for the scenario below?
The home you purchased was sold for $141,000 with a fixed APR of 1.035% across 40 years. The down payment required was 6.0%.
help what is it
Answer:
la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
8 The length of Adriana's chicken coop is 3x + 12 feet. The length of her garden is
6x – 16 feet. The garden is the length of the chicken coop.
What is the length of the chicken coop? Enter the number of feet only.
What is the length of the garden? Enter the number of feet only.
Answer:
Rounded down to the nearest foot, the length of the garden is nine feet.
Step-by-step explanation:
We're told that the length of the chicken coop, 3x + 12 feet, is equal to the length of the garden, 6x - 16 feet. Let's put them together then and solve for x:
3x + 12 = 6x - 16
First, we'll subtract 6x from both sides
3x - 6x + 12 = 6x - 6x - 16
-3x + 12 = -16
Now we subtract 12 from both sides:
-3x + 12 - 12 = -16 - 12
-3x = -28
Finally divide both sides by -3
-3x / -3 = -28 / -3
x = 28/3
x = 9 and 1/3
As the question asks for the number of feet only (not inches), the answer is nine feet.
A third of a foot though is four inches, so the more exact answer is nine feet and four inches, or 9'4"
what is the answer to y+5<9
Answer:
I think the answer would be y<4
Juan threw a dart onto the board. Which of the following is most likely?
A. Juan scored 0 points.
B. Juan scored at least 2 points.
C. Juan scored at least 4 points.
D. Juan scored at least 8 points.
Answer:
I think the answer should be.
B
Answer:
B
Step-by-step explanation:Edg 2021
Please answer this problem 3x−9<6
Answer:
your answer is five
Step-by-step explanation:
and stay safe and happy
if (-1 ,5 ) satisfies the equation 3x + Ky =7 then k =?
Answer:
k = 2
Step-by-step explanation:
3(-1) + k(5) = 7
-3 + 5k = 7
5k = 10
k = 2
The value of K in the equation 3x + Ky =7 is 2.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Equation 3x + Ky =7.
And we have also given that (-1, 5) satisfies the equation.
That means,
(-1, 5) is a solution of the equation.
To find the value of K;
Substitute the value of x = -1 and y = 5
So,
3x + Ky =7,
3(-1) + K(5) =7
-3 + 5K = 7
5K = 10
K = 2
Therefore, the value of K is 2.
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Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at the constant rate of 2 m/sec.How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point?
Missing information:
How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
Answer:
[tex]Rate = 0.935042^\circ /cm[/tex]
Step-by-step explanation:
Given
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]T(x,y) =x\sin2y[/tex]
[tex]r = 1m[/tex]
[tex]v = 2m/s[/tex]
Express the given point P as a unit tangent vector:
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]u = \frac{\sqrt 3}{2}i - \frac{1}{2}j[/tex]
Next, find the gradient of P and T using: [tex]\triangle T = \nabla T * u[/tex]
Where
[tex]\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j[/tex]
So: the gradient becomes:
[tex]\triangle T = \nabla T * u[/tex]
[tex]\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j][/tex]
By vector multiplication, we have:
[tex]\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}[/tex]
[tex]\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)[/tex]
[tex]\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5[/tex]
[tex]\triangle T = 0.935042[/tex]
Hence, the rate is:
[tex]Rate = \triangle T = 0.935042^\circ /cm[/tex]
need help asap provide explanation
Answer:
B is the correct answer
a map has a scale of 1 cm :15.5 km two cities are 2.3 cm apart on the map. to the nearest tenth of a kilometer,whatis the actual distance corresponding to the map distance
PLEASE HELP QUICKK!!!! TYSM!!!
Answer:
The answer for the question is 3/10
i can’t figure this one out.
Answer:
5
Step-by-step explanation:
3/12=x/20
cross multiply
12x=3(20)
12x=60
x=60/12
x=5
1
-
2 x(x-2x+4
Ayuda
Answer:
Simplified - 2x(-x+4), Solution - -2x(-x+4)
What is the common denominator of 4/12
Answer:
lcm of
Step-by-step explanation:
it is 12and 2.........
How many cubes with the side lengths of 1/4 cm does it take to fill the prism?
9514 1404 393
Answer:
224 cubes
Step-by-step explanation:
In terms of 1/4 cm cubes, the dimensions of the prism are ...
(2 cm)/(1/4 cm/cube) = 8 cubes long
(7/4 cm)/(1/4 cm/cube) = 7 cubes wide
(1 cm)/(1/4 cm/cube) = 4 cubes high
The volume in 1/4-cm cubes is ...
V = LWH = (8)(7)(4) = 224 . . . cubes
224 cubes are required to fill the volume.
please help me with this ASAP
Answer:
32
Step-by-step explanation:
15x+19=2(10x+2)
15x+19=20x+4
19-4=20x-15x
15=5x
x=3
PQ=QN
10x+2=
10(3)+2=
30+2=
32
what is the equation for the graph below?
Answer:
ummmm, i cant see the graph
Step-by-step explanation:
Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.6 feet and a height of 3.4 feet. Use percentage to compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism. Round your final answer to the nearest tenth.
(I will mark the person who gets the answer correct as brainliest)
Answer:
89.7 is the percent
Step-by-step explanation:
38.41/43.7=0.879 (87.9%).
I can’t find the answer pls help!!
Answer:
470 x 1.1 = 517
Step-by-step explanation:
f(x) = -x^2- 4x + 10
in the standard form
f(x) = a(x – h)^2 + k
Answer:
y = - ( x + 2 )² + 14
Step-by-step explanation:
f(x) = ax² + bx + c
f(x) = a(x - h)² + k (where (h, k) are coordinates of the vertex.
h = - [tex]\frac{b}{2a}[/tex]
~~~~~~~~~~~~
f(x) = - x² - 4x + 10
a = - 1, b = - 4, c = 10
h = - [tex]\frac{-4}{2(-1)}[/tex] = - 2
k = - ( - 2)² - 4( - 2) + 10 = 14
(h, k) = ( - 2, 14 )
y = - ( x + 2 )² + 14
what value from the set makes x/6 =18
true?
A.3
B.12
C.54
D.108
Answer:
D
Step-by-step explanation:
Plug it in 108 divide by 6