The Z-score is 2.306 to three decimal places. However, the Z-test statistic value shows that it is greater than the Z-critical value, so we reject the null hypothesis [tex]\mathbf{H_o}[/tex]
What is the Z-score of a test statistic?A z-score is a measurement of how often standard deviations the score obtained from a z-test is beyond or under the mean population.
From the given data information, let us find the mean and the standard deviation.
[tex]\mathbf{Mean (\bar x) = \dfrac{1154+5998+1007+...3987+4187+887}{10}}[/tex]
[tex]\mathbf{Mean (\bar x) = \dfrac{24256}{10}}[/tex]
Mean (x) = 2425.6
The hypothesis testing can be computed as:
[tex]\mathbf{H_o: \mu = 2425.6}[/tex]
[tex]\mathbf{H_1: \mu \ne 2425.6}[/tex]
The standard deviation (σ) is:
[tex]\mathbf{=\mathbf{ \sqrt{\dfrac{(1154-2425.6)^2+....+(887-2425.6)^2}{10-1}}}}[/tex]
[tex]\mathbf{= \sqrt{3199489}}[/tex]
= 1788.71
Now, the Z-test statistic is determined using the formula:
[tex]\mathbf{|Z| = |\dfrac{\bar x - \mu }{\sigma}| }[/tex]
[tex]\mathbf{|Z| = |\dfrac{2425.6 -6550 }{1788.71}| }[/tex]
[tex]\mathbf{|Z| = |-2.3058| }[/tex]
Z ≅ 2.306
Therefore, at a 0.05 level of significance, the Z-critical value is 2.306. However, since the Z-test statistic value shows that it is greater than the Z-critical value, so we reject the null hypothesis [tex]\mathbf{H_o}[/tex]
The complete question is given as:
Using a sequencing method called "RNAseq," a researcher determines the level of FOXP2 expression in 10 different samples of lung tissue, and obtains these data:
1154 5998 1007 2501 1000 988 2547 3987 4187 887Scientist has previously determined that FOXP2 is expressed in brain tissue at a level of 6,550. Calculate the Z-score associated with a test to see if the average expression of FOXP in her lung tissue samples is different from the levels she measured from brain tissue.
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9)Rover the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall. The
other end of the leash is tied to the top of an 8-foot pole. How far can Rover roam from the
pole?
The dog can roam 59.7 feet if the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
We have:
Rover the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall. The other end of the leash is tied to the top of an 8-foot pole.
After drawing a right-angle triangle from the above information.
Applying Pythagoras' theorem:
60² = 6² + x²
After solving:
x = 59.69 ≈ 59.7 foot
Thus, the dog can roam 59.7 feet if the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall.
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a rhombus has perimeter 120 M and one of its diagonal is 50 M find the area of the Rhombus
The area of the rhombus is 829.1562m².
What is the area of the rhombus?A rhombus is a four sides quadrilateral with the four sides equal in length
The area of a rhombus = [tex]\frac{1}{4}d[/tex] ×√(p² - 4d²)
where p is the perimeter and d is the diagonal
1/4(50) x √(120² - 4 x 50²) =829.1562m²
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Which expression is equivalent to the given expression? 4lh x + lh 3 - lh x
A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 90% confident that his estimate is in error by no more than two percentage points
Answer:
The number of computers that must be surveyed is 1681.
Step-by-step explanation:
The formula to find the sample size is given by:-
[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]
where p = prior population proportion,
[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝
E= Margin of error.
As per the given, we have
Confidence level :
1 - ∝ = 0.90
⇒∝= 1 - 0.90= 0.10
Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64
E= 2%=0.02
We assume that nothing is known about the percentage of computers with new operating systems.
Let us take p=0.5 [we take p= 0.5 if the prior estimate of proportion is unknown.]
The required sample size will be:-
[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]
=> [tex]0.25(82)^{2}[/tex]
=> 1681
Hence, the number of the computer must be surveyed = 1681
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Solve for y.
frankly im confusion
a:4.53
b.4
c.7.47
c.8
Answer:
8
Step-by-step explanation:
Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.
Applying this, we'll be obtaining the equation that of:
[tex]116=15y-4[/tex]
We now simply solve for y.
[tex]120=15y\\y=8[/tex]
Therefore, y is equal to 8.
This can be checked by plugging it into the equation:
[tex]15(8)-4[/tex]
[tex]120-4[/tex]
[tex]116[/tex]
And look at that, we got 116 for our answer, exactly the same as the other angle.
Any questions feel free to ask :)
A restaurant offers 7 appetizers and 8 main courses. In how many ways can a person order a two-course meal?
There are ways a person can order a two-course meal.
Answer:
56
Step-by-step explanation:
so 7 appetizers times 8 main courses
I do a easy trick where I multiple so
7×8=56
Identify the value of the variable in the equivalent expressions.
What is the value of n in the simplified expression?
(4k7)3= 4n ·(k7) 3= 64k21
n =
What is the value of m in the simplified expression?
(Negative 3 r Superscript negative 4 Baseline) Superscript negative 4 Baseline = (negative 3) Superscript negative 4 Baseline times (r Superscript negative 4 Baseline) Superscript negative 4 Baseline = StartFraction 1 Over 81 EndFraction r Superscript m
m =
The value of expression is n=3 and r= 16
What is expression?An expression is a set of terms combined using the operations +, – , x or , /.
Given:
[tex](4k^{7})^{3} = 4^{n}* (k^{7})^{3} = 64 k^{21}[/tex]
[tex](64 k^{21}) = 4^{n}* k^{21} = 64 k^{21}[/tex]
[tex]4 ^{3} * k^{21}= 4^{n}* k^{21}[/tex]
On comparing
n=3
Now,
[tex](-3r^{-4})^{-4} = (-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}[/tex]
[tex](-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}\\1/ (-3)^{4} * 1/(r^{-4})^{4} = 1/81* r^{m}\\1/ (-3)^{4} * (r^{16}) = 1/81* r^{m}[/tex]
1/81 * r^16 = 1/81 * r^{m}
On compairing
r = 16.
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Answer:
answer in picture
Step-by-step explanation:
my sis needs help asap SHOW WORK! :)
Step-by-step explanation:
el resultado le puedo ayudar si sabe Spanish
Answer:
see below
Step-by-step explanation:
White = 1 1/3 = 4/3 = 16/12
Color = 3/4 = 9/12
white - color == 16/12 - 9/12 = (16-9) / 12 = 7/12 of a scoop more for the white load
PLEASEEEE PLEASEEEEEEEEE HELPPPPPPPPPP
how do i solve this equation?
Answer:
360
Step-by-step explanation:
using the definition
n [tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]
where n! = n(n - 1)(n - 2)..... × 3 × 2 × 1
then
6[tex]P_{4}[/tex]
= [tex]\frac{6!}{(6-4)!}[/tex]
= [tex]\frac{6!}{2!}[/tex]
= [tex]\frac{6(5)(4)(3(2)(1)}{2(1)}[/tex] ← cancel 2(1) on numerator / denominator
= 6 × 5 × 4 × 3
= 360
A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R; that is, T=P+R. During the 2012 regular football season, the teams total offense was 4559 yards. The teams passing yardage was 3069 yards. How many yards did the team gain by rushing during the season?
The team gain 1490 yards by rushing during the season.
What is football yardage?Football yardage is the number of yards that a team or player manages to move the ball forward toward their opponent's end zone.
According to the question,
A football teams offense T is found by adding the total passing yardage P to the total rushing yardage R,
i.e. T=P+R
In 2012,
The teams total offense was 4559 yards.
The teams passing yardage was 3069 yards.
By using the formula
T=P+R
T = 4559 yards , P = 3069 yards
Put the values in the above equation;
4559 = 3069 - R
4559 - 3069 = R
R = 1490 yards
Therefore , 1490 yards the team gain rushing during the season.
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I opened a grocery account at my bank with $100. Every week thereafter, I withdraw $45 from the account to pay for groceries. If x is the number of weeks I've had the account, then y is the amount in the account. Find an equation of a line in the form y = mx + b that describes my grocery account balance.
Answer:
y=-45x + 100
Step-by-step explanation:
The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept or in other words the initial amount (when x is 0). Since you start off with 100 dollars the y-intercept is going to be 100 since after 0 weeks (when you opened the account) you put 100 dollars in... so you should have 100 dollars. The slope is going to be -45 since you are withdrawing 45 each week so the value is going to be decreasing by 45 every week. If you put that together you get y=-45x+100
Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
[tex]\sqrt{1}[/tex]
Step-by-step explanation:
We know that a rational number cannot have roots. All of the answer choices cannot be simplified except for [tex]\sqrt{1}[/tex], which can become 1. Therefore, our answer is [tex]\sqrt{1}[/tex].
Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase. Which store offered the better discount, and how much is the difference?
The better option will be at DiscountsRUs 40% off on any purchase.
What is the discount?The amount of money which is reduced on any product below its actual selling price is called the discount.
here we have two offers from the two stores Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase.
For a Dominic, the discount is fixed for any purchase that is if you purchase a $50 product or a $1000 product you will be getting only a $15 discount.
Now for the second store, the discount is given as 40% so if you purchase $50 your discount will be $20. If you purchase $1000 so 40% discount will be $400.
Therefore better option will be at DiscountsRUs 40% off on any purchase.
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A condominium is taxed based on its $78,584 value. The tax rate is $3.49 for every $100 of value. If the tax is paid before March 1, 4%
of the normal tax is given as a discount. How much tax is paid if the condominium owner takes advantage of the discount?
The tax paid by the condominium owner is $2,632.88.
What is the tax paid?
Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.
Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.
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what is the value of n in the equation -1/2(2n +4) + 6 = -9 + 4 (2n +1)
Answer:
n=1
Step-by-step explanation:
-n+4=8n-5
9=9n
n=1
hope that helps
The number N of tree of a given species per acre is approximated by the model
N = 68(10)-0.042
above the ground.
Use the model to approximate the average diameter of the trees in a test plot when N = 21.
7,5 ≤ x ≤ 40 where x is the average diameter of the trees (in inches) 3 feet
Answer:
1 answer
The area of triangle with vertices A(0, 9), B(0, 4) and C( - 5, - 9) is
pls someone help me asap
Answer:
Area: 15.53 square inches
Perimeter: 15.71 inches
Step-by-step explanation:
Area:
So the area of the rectangle is pretty easy to find and is just the width * height. In this case it's 4 * 3 which is 12. Now the area of a circle is [tex]\pi r^2[/tex]. But since this is a semi circle it's half of that which is [tex]\frac{\pi r^2}{2}[/tex]. The diameter of the semicircle is 3 as it sits on top of the rectangle. The radius is half of the diameter so the radius is 1.5. Now plug that into the equation and you get [tex]\frac{(3.14) (1.5)^2}{2} = 3.5325[/tex]. Now add that to 12 and you get 15.5325. Round that number to the nearest hundredth and you get 15.53. So that's the area.
Perimeter:
Pi is the ratio of any circle's circumference to the diameter. Or in other words the circumference is equal to the diameter * 3.14. The diameter is 3 which you multiply by 3.14 to get the circumference of a circle. This will get you 9.42 but since it's a semicircle, the circumference is half of this value which is 4.71. The perimeter of the rectangle is just 2 times the width + 2 times the height. This is not completely the case in this shape since one of the sides of the rectangle is not a side of the two shapes joined together. Which is the side that is parallel to the side of length 3 inches. So the perimeter is going to be 2(4) + 3. This gives you 11 which you add to the 4.71 and get 15.71
a. d(7) 6
b. Interpret the meaning of d(7):
OA. In the first 6 seconds, the particle moved a total of 7 feet.
B. The particle was 7 feet away from the starting line 6 seconds since timing started.
OC. The particle was 6 feet away from the starting line 7 seconds since timing started.
D. In the first 7 seconds, the particle moved a total of 6 feet.
c. Solve d(t) = 2 for t. Use commas to separate your answers if there are more than one solution. t =
d. Interpret the meaning of part c's solution(s):
OA. The article was 2 feet from the starting line 9 seconds since timing started.
OB. The article was 2 feet from the starting line 1 seconds since timing started.
C. The article was 2 feet from the starting line 1 seconds since timing started, or 9 seconds since timing started.
D. The article was 2 feet from the starting line 1 seconds since timing started, and again 9 seconds since timing started.
dit on this problem.
Answer:
Step-by-step explanation:
In pqr the measure of r=90 qp=65 rq=33 and pr=56 what ratio represents the sine of q
We can use sine ratio in given right angled triangle.
The sine of ∠Q is represented by ratio 48/73.
Given data:
∠R=90°,
QP = 73,
PR = 48,
RQ = 55
We know that;
The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.
Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.
Thus, we have:
sin Q = PR/PQ
= 48/73
Thus, the sine of ∠Q is represented by ratio,
48/73.
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again with this please
Answer:
a) A dozen= 24
3 dozen= 24 x 3
= 72
b) 1 dozen= 12 bananas
A dozen cost= 24
So, 1 banana cost= 24/12
= 2
So, 6 bananas would be 2 x 6 = 12
c) 1 dozen= 12 bananas
A dozen cost= 24
1 banana cost= 24/12
= 2
d) I need to know how many people are there in your class so please mention that first :)
Mark me brainliest pleaseee
Simplify x^2+2x+1 divided by x+1
The quotient is x+1.
What Long division method?Long division is a method for dividing one large multi digit number into another large multi digit number.
Given:
f(x)= x²+2x+1
g(x)= x+1
The steps to divide the polynomial is :
Divide the leading term of the dividend by the leading term of the divisor: x²/x=x.Multiply it by the divisor: x(x+1)=x²+x.Subtract the dividend from the obtained result: (x²+2x+1)−(x²+x)=x+1.Divide the leading term of the obtained remainder by the leading term of the divisor: x/x=1.Multiply it by the divisor: 1(x+1)=x+1.Subtract the remainder from the obtained result: (x+1)−(x+1)Learn more about long division method here:
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Could someone answer the rest please!
Much appreciated if you do (:
Answer:
shown below
Step-by-step explanation:
4 x 2 = 8
1 x 2 = 2
a⁸b²
(a⁵b²)(a²b⁶)
a⁷a⁵b⁶b²a²b⁸
a¹⁴b¹⁶
8 - 14 = -6
2 - 16 = -14
a^-6 b^-14
next one
25^3x-21
/
25^2x+14
1^x-35
which matrix equation represents the system of equations
Answer:
option B is correct
To write any equations in the form of matrix
first make a matrix of all coefficients of that equations.. here coefficients of first equation is 4 and - 2 and that of second is 0 ( as there is no value of X) and 3
then make second matrix of X and y
last of answer of the equations, here (-7 ) and 5
someone help solve asap for points
Answer:
[tex]\textsf {p(-4) = -134}[/tex]
Step-by-step explanation:
[tex]\textsf {Given :}\\[/tex]
[tex]\mathsf {p(x) = x^{3} - 3x^{2} + 7x + 6}[/tex]
[tex]\textsf {Substitute x = -4 to find p(-4) :}[/tex]
[tex]\mathsf {p(-4) = (-4)^{3} - 3(-4)^{2} + 7(-4) + 6}[/tex]
[tex]\mathsf {p(-4) = -64 - 48 - 28 + 6}[/tex]
[tex]\textsf {p(-4) = 6 - 140}[/tex]
[tex]\textsf {p(-4) = -134}[/tex]
what is the equation of the following line? be sure to scroll down first to see all the answer options
E. y = -3x
I can give you an explanation in the comments if you'd like
Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).
y = e^sin x
Answer:
g(x) = sin(x)
f(x) = e^x
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(x)=e^x\\g(x)=sin~x\\y=f(g(x))=f(sin~x)=e^{sin~x}[/tex]
Evaluate the expression.
-2(12 - 2 (-4))²
What is the value of the expression?
Enter your answer in the box.
Answer:
-2(10(-4))²
-2(-40)²
-2 × 1600
= -3200
Answer: = -3200
Step-by-step explanation:
took the test
PLEASE HELP! SHOW WORK AND/OR EXPLANATION PLEASE.
Find ‘x’ that will make the following statements true.
1. Sin (35) = Cos (x)
2. Cos (79) = Sin (x)
3. Cos (x) = Sin (2x)
4. Sin (x + 4) = Cos (4x – 9)
Answer:
1. x = 55°
2. x = 11°
3. x = 30°
4. x = 19°
Step-by-step explanation:
Trigonometric Identities
[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]
[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]
Question 1
[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]
[tex]\implies x=55^{\circ}[/tex]
Question 2
[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]
[tex]\implies x=11^{\circ}[/tex]
Question 3
[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]
Question 4
[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]
What's the circumference of a
circle with a radius of 7 feet?
Use 3.14 for .
C = [?] feet
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = 2πr
Answer:
43.96ft
Step-by-step explanation:
In the hint, you are given the equation [tex]C = 2\pi r[/tex].
Here, [tex]C[/tex] is the circumference, [tex]r[/tex] is the radius, and [tex]\pi[/tex] is a constant (a value that doesn't change). In this question, you are told to assume the value of [tex]\pi[/tex] is 3.14.
You are told the radius is 7, therefore, [tex]r[/tex] = 7.
Now we have these values, let's substitute them into the equation:
[tex]C = 2 * 3.14 *7[/tex]
For clarification, the stars mean multiplication.
So, the product of those values will give us our circumference, [tex]C[/tex].
In this case, you get an answer of 43.96ft.
Problem 5. Utility Bills The monthly utility bills in a city are normally distributed and
represented by the variable X, with a mean of $100 and a standard deviation of $12. Find the
probability that a randomly selected utility bill is
(a) less than $70,
(b) between $90 and $120,
(c) more than $140.
(2 points)
(2 points)
(2 points)
Hint: Convert the normal distribution X to Standard normal using Z formula Z =
and then look the Z-values from the table and then find the probability.
X-μ
6
The probabilities in the question are
0.00620.74990.000429How to solve for the probabilitiesa. For x < 70
we have
z< 70 - 100/12
= z < -30/12
= -2.5
Such that p (x<70) = 0.0062
Hence the probability that is is less than $70 = 0.0062
b. between $90 and $120,90 - 100/12. 120 - 100/12
= -0.8333 <z< 1.67
p(90<x<120) = 0.95224 - 0.20234
= 0.7499
0.7499 is the probability of between $90 and $120.
c. more than $140140-100/12
= P(Z>3.3333)
= 0.000429
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