Answer:
The appropriate hypotheses for performing a significance test is:
[tex]H_0: \mu = 51[/tex]
[tex]H_1: \mu > 51[/tex]
Step-by-step explanation:
Last year, the mean score on the state’s math test was 51. The administrators have trained the teachers in a new method of teaching math hoping to raise the scores on this standardized test this year.
At the null hypothesis, we test if the mean score this year is the same as last year, that is:
[tex]H_0: \mu = 51[/tex]
At the alternate hypothesis, we test if the mean score improved this year from last, that is:
[tex]H_1: \mu > 51[/tex]
The appropriate hypotheses for performing a significance test is:
[tex]H_0: \mu = 51[/tex]
[tex]H_1: \mu > 51[/tex]
Find the length of AB. A 0140 AB = [?] 140° 8 m B Round your answer to the nearest hundredth.
[tex]\huge{ \mathfrak{ \underline{ Answer} \: \: ✓ }}[/tex]
Radius (r) = 8mAngle made at centre [tex](\theta)[/tex] = 140°[tex] \boxed{ \mathrm{length \: \: of \: \: arc = \dfrac{ \theta}{360 \degree} \times 2\pi r}}[/tex]
[tex] \dfrac{140}{360} \times 2 \times 3.14 \times 8[/tex][tex] \dfrac{7}{18} \times 50.24[/tex][tex] \dfrac{351.64}{18} [/tex][tex]19.54 \:m[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
Length of arc AB on circle is 30.72 m.
What is circular arc?A circular arc is an arc between two different points. If the two points are not diametrically opposed, one of these arcs, the minor arc, forms an angle of less than π radians (180 degrees) with the center of the circle. The other circular arc, the main arc, makes an angle greater than π radians. An arc is defined as a portion or segment of the circumference. A straight line connecting the two ends of an arc is called a chord. If the arc length is exactly half the circle, it is called a half arc.
Given,
Circle with center O
Radius of circle OA = OB = 8m
Angle made by minor arc AB on center of circle α = 140°
then angle made by main arc AB = 360° - 140° = 220°
π = 180°
1° = π/180°
220° = 220°π/180°
220° = 11π/9
220° = 3.84 Rad
Length of arc on circle
= Radius of circle × angle made by the arc on center of circle in radians
= 8 × 3.84
= 30.72 m
Hence, 30.72 m is length of the arc AB.
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How many American adults must be interviewed to estimate the proportion of all American adults who actively try to avoid drinking regular soda or pop within 0.01 margin of error with 95% confidence using the large-sample confidence interval
Answer:
9604 American adults must be interviewed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How many adults must be interviewed for the margin of error to be 0.01?
This is n, which is found for M = 0.01.
We have no estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample size will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.01 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.01})^2[/tex]
[tex]n = 9604[/tex]
9604 American adults must be interviewed.
giving branliest for correct person.. incorrect doesnt get points or branliest..
Answer:
A
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
Need help due in 10!
Answer:
1. (28-2)x
2.(12+6)x
3.(15+1)x
Step-by-step explanation:
beth is 2 years older than jimmy, and in 3 years the sum of their ages will be twice as much as the sum of their ages 3 yrs ago. fing their present ages
Answer: 10
Step-by-step explanation:
What is the zero of r(x)
=
8/3X-16
Answer:
x = 6
Step-by-step explanation:
(8/3)x - 16 = 0
Add 16 to both sides
(8/3)x = 16
Multiply both sides by 3/8
x = 16(3/8)
x = 6
For what value of x is quadrilateral CDEF a parallelogram?
Answer:
x = 2.
Step-by-step explanation:
If its a parallelogram then the diagonal will be bisected so:
4x + 7 = 10x - 5
7 + 5 = 10x - 4x
12 = 6x
x = 2.
find x and y. give answer in insimplified radical form, not decimal.
Finding x,
We will use Pythagoras theorem to determine the value of x:
[tex]9^{2} = {8}^{2} + {x}^{2} \\ 81 = 64 + {x}^{2} \\ 81 - 64 = {x}^{2} \\ {x}^{2} = 17 \\ x = \sqrt{17} [/tex]
Finding y,
We have to determine the angle, at the bottom left of the bigger triangle.
Using sine rule,
[tex] \frac{9}{sin(90)} = \frac{8}{sin(z)} \\ sin(z) = 0.8889 \\ z = {sin}^{ - 1} (0.8889) \\ z = 62.73[/tex]
To find the angle on the smaller triangle,
[tex]a = 90 - 62.73 \\ a = 27.27[/tex]
Finding the missing length of y,
[tex] \frac{ \sqrt{17} }{sin(62.73)} = \frac{m}{sin(27.27)} \\ m = 2[/tex]
So y = 2 + 8, y = 10
2/5 of a number is 2/5 greater than 1/3 of a number? What is the number?
Answer:
5
Step-by-step explanation:
The cost of 6 pens is $3.60. What would 2 dozen cost?
$14.40. And then you have the tax. :D
Have A Great Day.
The cost of 2 dozen pens will be "$14.4".
Given:
Cost of 6 pens,
$3.60As we know,
1 dozen = 12then,
12 dozen = [tex]12\times 2[/tex]= [tex]24[/tex]
Now,
→ The cost of 1 pen will be:
= [tex]\frac{3.60}{6}[/tex]
= [tex]0.6[/tex] ($)
hence,
→ The cost of 24 pens (2 dozen) will be:
= [tex]0.6\times 24[/tex]
= [tex]14.4[/tex] ($)
Thus the above solution is right.
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Tell whether one figure is a reflection of the other figure
yes or no
Answer:
No
Step-by-step explanation:
Currently, there are 1,460 wolves in Scataway National Park. If the population of wolves is growing at a rate of 6% every year,
which function represents the number of wolves in Scataway National Park in tyears?
OA W0 = 1,460(1.06)
B. WO = 1,460(0.94)
OC M6 = 1,460(0.06)
OD. WO = (1,460)(1.06)
Answer:
[tex]P(t) = 1460(1.06)^t[/tex]
Step-by-step explanation:
Exponential equation for population growth:
The exponential equation for a population after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial population and r is the growth rate, as a decimal.
Currently, there are 1,460 wolves in Scataway National Park.
This means that [tex]P(0) = 1460[/tex]
Growing at a rate of 6% every year:
This means that [tex]r = 0.06[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 1460(1+0.06)^t[/tex]
[tex]P(t) = 1460(1.06)^t[/tex]
Answer:
Step-by-step explanation:
Arrivals of cars at a gas station follow a Poisson distribution. During a given 5-minute period, one car arrived at the station. Find the probability that it arrived during the last 30 seconds of the 5-minute period g.
Answer:
0.9 = 90% probability that it arrived during the last 30 seconds of the 5-minute period.
Step-by-step explanation:
The car is equally as likely to arrive during each second of the interval, which means that the uniform distribution is used to solve this question.
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distribution has two bounds, a and b, and the probability of finding a value higher than x is given by:
[tex]P(X \geq x) = \frac{b - x}{b - a}[/tex]
5-minute period
This means that [tex]a = 0, b = 5*60 = 300[/tex]
Find the probability that it arrived during the last 30 seconds of the 5-minute period.
300 - 30 = 270. So
[tex]P(X \geq 270) = \frac{300 - 270}{300 - 0} = 0.9[/tex]
0.9 = 90% probability that it arrived during the last 30 seconds of the 5-minute period.
By what percent will a fraction increase if its numerator is INCREASED by 60% and its denominator is decreased by 20%?
Please Help will give Brainliest!!!!!!
Answer:
100%
Step-by-step explanation:
let , a/b is a fraction
=> a+60% = 1.6 a
and b-20% = 0.8b
so, the new fraction is
(1.6a) /(0.8b) = 2(a/b)
from a/b to 2(a/b) => increase 100%
What is the area? PLEASE HELP
Answer:
14mm×20mm=280mm²
14mm×12mm/2=84mm²
3.14×10²mm=314mm²
280m²+84mm²+314mm²=678mm²
Answer:
521mm^2
Step-by-step explanation:
First, separate the shapes.
-Half circle= diameter of 20, radius 10
-Rectangle= 14x20
-Triangle= (32-20)x14= 12x14
Then, calculate
Circle equation= (pi)r^2= (pi)(10)^2= 314.16 -> divide by 2 for half circle= 157.1
Rectangle= 14x20=280
Triangle= (12x14)=168 -> Divide by two because it's a triangle= 84
Add 157 + 280 + 84 and you get 521
Alonzo deposits 300 into an account that pays simple interest at a rate of 4% per year . How much interest will he be paid in the first 4 years
Answer:
1200 was is interested in the first 4years
Convert 600 bags of cement to tons
Answer:
the 600 bags of cement would weigh 25.5826 tonnes
Answer:
600-90 lb bags of cement weigh 27 tons
Step-by-step explanation:
You don't say how much each bag weighs. Let's suppose that that weight is 90 lb.
Then:
90 lb 1 ton
----------- * -------------- = 9/200 ton/bag
1 bag 2000 lb
Now multiply this by 600 bags:
9 tons 600 bags
--------------- * ------------------ = 27 tons
200 bags 1
600-90 lb bags of cement weigh 27 tons
If X = 14 units and h = 7 units, then what is the area of the triangle shown above?
A. 196 square units
B. 98 square units
C. 24.5 square units
D. 49 square units
Please help me
Answer:
B
Step-by-step explanation:
Answer:
B is the answer 98 square units
NO LINKS. Find the segment length indicated. Assume that lines which appear to be tangent are tangent. PLEASE SHOW WORK!!
Answer:
? = 9.2
Step-by-step explanation:
The angle between a tangent and radius at the point of contact is 90°
Then the triangle shown is right with legs ? , 6.9 and hypotenuse = (6.9 + 4.2) = 11.5
Using Pythagoras' identity in the right triangle
?² + 6.9² = 11.5²
?² + 47.61 = 132.25 ( subtract 47.61 from both sides )
?² = 84.64 ( take the square root of both sides )
? = [tex]\sqrt{84.64}[/tex] = 9.2
Answer:
Solution given:
BC=BD=6.9 units
AD=4.6units
Now
AB=4.6+6.9=11.5units.
we have
<C=90°[the line from the tangent is perpendicular to the radius of circle]
we know that ∆ABC is a right angled triangle.
hypotenuse [h]=AB=11.5units
base[b]=BC=6.9 units
perpendicular [p]=x units
By using Pythagoras law
h²=p² +b²
11.5²=x²+6.9²
x²=11.5²-6.9²
x²=84.64
x=[tex] \sqrt{86.64} [/tex]=9.2
Sothe segment length indicated is 9.2 units.
A professor pays 25 cents for each blackboard error made in lecture to the student who pointsout the error. In a career ofnyears filled with blackboard errors, the total amount in dollarspaid can be approximated by a Gaussian random variableYnwith expected value 40nandand variance 100n. What is the probability that 20exceeds 1000
Answer:
The correct answer is "0.0000039110".
Step-by-step explanation:
The given values are:
[tex]Y_n\rightarrow N(\mu, \sigma^2)[/tex]
[tex]\mu = 40n[/tex]
[tex]\sigma^2=100n[/tex]
[tex]n=20[/tex]
then,
The required probability will be:
= [tex]P(Y_{20}>1000)[/tex]
= [tex]P(\frac{Y_{20}-\mu}{\sigma} >\frac{1000-40\times 20}{\sqrt{100\times 20} } )[/tex]
= [tex]P(Z>\frac{1000-800}{44.7214} )[/tex]
= [tex]P(Z>\frac{200}{44.7214} )[/tex]
= [tex]P(Z>4.47)[/tex]
By using the table, we get
= [tex]0.0000039110[/tex]
Which of the following ordered pairs are solutions to the system of equations below?
(3x + 5y = 14
y = 1/2x + 5)
O (2.4)
0 (-2,4)
O (2,6)
O (-2,6)
Answer:
(- 2, 4 )
Step-by-step explanation:
Given the 2 equations
3x + 5y = 14 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
3x + 5([tex]\frac{1}{2}[/tex] x + 5) = 14
3x + [tex]\frac{5}{2}[/tex] x + 25 = 14
[tex]\frac{11}{2}[/tex] x + 25 = 14 ( subtract 25 from both sides )
[tex]\frac{11}{2}[/tex] x = - 11 ( multiply both sides by 2 )
11x = - 22 ( divide both sides by 11 )
x = - 2
Substitute x = - 2 into (2) for corresponding value of y
y = [tex]\frac{1}{2}[/tex] × - 2 + 5 = - 1 + 5 = 4
solution is (- 2, 4 )
Can someone please help?
9514 1404 393
Answer:
x > 3 : bothx < 3 : g onlyx = 3 : f onlyx ≠ 3 : g onlyStep-by-step explanation:
The attached number lines show the domains of each function.
x > 3 — both number lines are included
x < 3 — only the g(x) domain is included
x = 3 — only the f(x) domain is included
x ≠ 3 — only the g(x) domain is included in the entire region
What is Mary's location if she travels 3 units left and 4 units up from (5, 0)?
A - (2, 5)
B - (8, 6)
C - (2, 4)
D - (8, 5)
Answer:
here is the right answer
C- (2,4)
Subtract the sum of 13 and 6 from 40. *
HELP PLS HELP PLS HELP PLS HELP PLS
Answer:
Step-by-step explanation:
Surface area of a cube of side-length 0.5m
= 6(0.5)^2 = 6(0.25) = 1.5 sq.m.
Find the area of the shape. Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal.
Answer:
314
Step-by-step explanation:
First, find the diameter which is 10 and square it. Then, multiply by pi or 3.14 to get 314.
(IF THIS HELPED PLEASE GIVE BRAINLIEST!)
Find each angle measure.
Figures are not drawn.!!
Answer: See explanation
Step-by-step explanation:
1 . 61
2 124
3 27
4 29
1 4/5 is an example of a (n)
Answer:
Mixed Fraction
Step-by-step explanation:
A mixed fraction is a fraction with a whole number attached to it like 5 1/5 or 3 1/2
[tex]1\frac{4}{5}[/tex] is an example of a mixed fraction.
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers.
A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.
Properties of Mixed Numbers :
1. It is partly a whole number.
2. It is partly a fraction.
[tex]1\frac{4}{5}[/tex] is an example of a mixed fraction.
In [tex]1\frac{4}{5}[/tex] , 2 is the quotient, 4 is the remainder.
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Please help!!!! ASAP!! I’ll give brainliest!!!
Answer:
First column 35
Second column 60
It is 91.6083916% likely that the soil sample contains organic matter
Step-by-step explanation:
700 -655= 35
300 -240= 60
655 +60 = 715
715÷655 = 0.916083916
0.916083916 x 100 = 91.6083916%
Let Y1 denote the weight of a bulk item stocked by a supplier, with a uniform distribution over the interval (0, 1). The random variable Y2 denotes the weight of the item sold and is assumed to have a uniform distribution over the interval (0, y1), where y1 is a specific value of Y1. If the supplier stocked 5 6 ton, what amount in tons could be expected to be sold during the week
Answer:
5/12 ton
Step-by-step explanation:
Y1 ( uniform random variable ) : ( 0, 1 )
Y2 ( uniform distribution ) ; ( 0, y1 )
supplier stocked ; 5/6 ton
Determine the amount of tons expected to be sold
F ( y2 | y1 ) = 1 / y1
E ( y2 | y1 = 5/6 )
The number of tons expected to be sold = 5/12 ton
attached below is the detailed solution