Answer:
B. 0.024
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
Of 100, 20 were in the bottom thid. So
[tex]p_B = \frac{20}{100} = 0.2[/tex]
[tex]s_B = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
Of 100, 10 were in the bottom third, so:
[tex]p_A = \frac{10}{100} = 0.1[/tex]
[tex]s_A = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
To determine this, you test the hypotheses H0 : p1 = p2 , Ha : p1 > p2.
Can also be rewritten as:
[tex]H_0: p_B - p_A = 0[/tex]
[tex]H_1: p_B - p_A > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample:
[tex]X = p_B - p_A = 0.2 - 0.1 = 0.1[/tex]
[tex]s_A = \sqrt{s_A^2+s_B^2} = \sqrt{0.03^2+0.04^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of proportions of at least 0.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.976.
1 - 0.976 = 0.024, so the p-value is given by option B.
The p-value of the test is 0.024 < 0.05(standard significance level), which means that there is enough evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Which of the following is written as a rational function
The function written in the rational form is, C. F(x) = (x - 5)/3x
What are rational numbers?Rational numbers are subsets of real numbers which can be written in the form of p/q, where q ≠ 0. As at q = 0 it is undefined.
Similarly, A rational expression is also written in the form of p/q, where p and q are algebraic expressions and q ≠ 0.
From the given options, F(x) is written in the form p/q,
Where, p = x - 5 and q = 3x.
Therefore, The rational function is, F(x) = (x - 5)/3x, where x ≠ 0.
As at x = 0 the function is undefined.
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Which of the following expressions has a value of 4? A. (16 – 12)² B. – | – 4 | C. (96 ÷ 8) – 2³ D. 24 – 42
A. (16 - 12)² = 4² = 4 · 4 = 16
B. -|-4| = -4
C. (96 : 8) - 2³ = 12 - 8 = 4
D. 24 - 42 = -(42 - 24) = -18
or 2⁴ - 4² = 16 - 16 = 0
The correct answer is C
Evaluate-2 xy, if x= - 4 and y= 1.
Answer:
8
Step-by-step explanation:
-2 xy
Let x = -4 and y = 1
-2 (-4)*(1)
8(1)
8
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
V10
Answer: 2=
=
Submit Answer
Answer:
x=2*sqrt(5)
Step-by-step explanation:
Since the triangle is isosceles, the other side of the triangle is sqrt(10) too. By using Pythagoras theorem, we have 10+10=x^2, x=2*sqrt(5).
How do I find the Derivative of a Function where the x is a number?
If I was to find d/dx g(1) for example, would I first find the value of the function g(x) at x=1 and then find the derivative of that which becomes 0 because the result would probably be a constant. Or do I first find the derivative of g(x) and then plug in x=1 to calculate it?
Thanks
Given a function g(x), its derivative, if it exists, is equal to the limit
[tex]g'(x) = \displaystyle\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]
The limit is some expression that is itself a function of x. Then the derivative of g(x) at x = 1 is obtained by just plugging x = 1. In other words, find g'(x) - and this can be done with or without taking a limit - then evaluate g' (1).
Alternatively, you can directly find the derivative at a point by computing the limit
[tex]g'(1) = \displaystyle\lim_{h\to0}\frac{g(1+h)-g(1)}h[/tex]
But this is essentially the same as the first method, we're just replacing x with 1.
Yet another way is to compute the limit
[tex]g'(1) = \displaystyle\lim_{x\to1}\frac{g(x)-g(1)}{x-1}[/tex]
but this is really the same limit with h = x - 1.
You do not compute g (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some number, you care about the derivative of a function that depends on a variable.
solve for x the triangles are the same
Answer: x=8
Step-by-step explanation:
So to begin with we need to find the connection being that they are the same triangle but with a dilation. We need to find the dilation by matching the new angles with each other H=E F=C and D=G. We need to find the relation ship between CD and FG. 65 divided by 24= 2.6 take ED and multiply 2.6 to find HG. HG= 91. Now we need to find x. 8 times x+ 3=91. Find the closest eight multiple to 91 which is 8 times 8= 88 and add 3 to see it makes 91.
8 is your answer.
Answer with the explanation step by step
Answer:
The answer is A. [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex].
Step-by-step explanation:
To find the difference of this problem, start by simplifying the denominator, which will look like [tex]\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}[/tex]. Next, multiply [tex]\frac{3}{x+7}[/tex] by [tex]\frac{x-7}{x-7}[/tex] to create a fraction with a common denominator in order to subtract from [tex]\frac{42}{(x+7)(x-7)}[/tex]. The problem will now look like [tex]\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}[/tex].
Then, simplify the terms in the problem by first multiplying [tex]\frac{3}{x+7}[/tex] and [tex]\frac{x-7}{x-7}[/tex], which will look like [tex]\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}[/tex]. The next step is to combine the numerators over the common denominator, which will look like [tex]\frac{3(x-7)-42}{(x+7)(x-7)}[/tex].
Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of [tex]3(x-7)-42[/tex], which will look like [tex]\frac{3(x-7-14)}{(x+7)(x-7)}[/tex]. Then, subtract 14 from -7, which will look like [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex]. The final answer will be [tex]\frac{3(x-21)}{(x+7)(x-7)}[/tex].
Find the surface area of the cylinder in terms of T. 9 cm 19 cm Not drawn to scale O 211.5 cm 2 0 382.57 cm 2. O 333 77 cm2 o 504 лcm
Answer:
hey the answer is cylinder= 211.5л!
Combine these radicals.
Anyone can help pls
write down the relation between the scales of temperature i.e degree Fahrenheit and degree Celsius in form of function and also write it's inverse
Answer:
C=（9F-32）/5
inverse：
Step-by-step explanation:
the cost of a ford is 2/13 of the cost of a rolls Royce. If the current price of a rolls Royce is $211 250, what is the cost of a ford ?
An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data from an article in Engineering Horizons (Spring 1990) indicated that 117 of 484 new engineering graduates were planning graduate study. Are the data from Engineering Horizons consistent with the claim reported by Fortune
Answer:
unless this is a stats question and you are suggesting that you have bad sampling techniques being used
117/484 is about 24% that is 100% under the "about 50%" stated in the article
Step-by-step explanation:
5. The average weight of a blue whale is 4 x 105 pounds. The average weight of an elephant is 1 x 10 pounds. How many more times heavier is a blue whale than an elephant in pounds?
Answer:
42 more times
Step-by-step explanation:
1) 4×105=420 (pounds)-blue whale
2) 1×10=10 (pounds)- elephant
3) 420:10=42
The amount of times that the blue whale is more heavier than the elephant in pounds is; 40 times heavier.
We are given;Average weight of blue whale; W_w = 4 × 10^(5) pounds
Average weight of elephant; w_e = 1 × 10⁴ pounds
Now, we want to find how much more heavier the blue whale is than the elephant. Thus we will just divide W_w by W_e to get;W_w/W_e = (4 × 10^(5))/(1 × 10⁴)
According to laws of exponents;
a¹²/a³ = a¹² ¯ ³ = a^(9)
Applying that to our question gives;
4(10^(5 - 4)) = 4 × 10 = 40
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plz help me this will be appreciated
Answer:
1. h
2. b
3. a
4. d
5. c
Step-by-step explanation:
all answers are straight forward. only the last (5) is phrased a bit strangely. I would have said "reflect across a horizontal line".
Solve for x. The triangles are similar.
A. 5
B. 10
C. 4
D. 8
Answer: D) 8
Work Shown:
32/24 = 2x/12
32*12 = 24*2x
384 = 48x
48x = 384
x = 384/48
x = 8
The correct option is Option D: the value of x is 8
What are similar triangles?The triangles whose corresponding angles are equal and the corresponding sides are in equal proportiion are called similar triangles.
If two triangles are similar
then a₁/a₂=b₁/b₂=c₁/c₂
where a₁, b₁, and c₁ are the sides of one triangle
a₂, b₂, and c₂ are the sides of another triangle
Here it is given that
triangles ΔJLK and ΔRJS are similar.
so by the property of similar triangles,
JR/JL = JS/JK = RS/KL
Given that JR=24
JL=32
JS=12
JK=2x
By using the property
JR/JL = JS/JK
⇒ 24/32 = 12/2x
⇒2x= 12*32/24
⇒2x=16
⇒x=16/2
⇒x=8
Therefore the value of x is 8.
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Find the missing angles indicated by small letters in each of the diagram.
Answer:
a) X=75°
y= 105°
b) b= 120°
a=45°
d) r=75°
q=37°
p= 37°
e) y=100°
X= 143°
Step-by-step explanation:
soln no. a
here,
X+50+55=180(sum of all angle of triangle)
or, X= 180-105
or, X= 75°
again,
X+y = 180 (straight angle)
or, y= 180-75
or, y= 105°
soln no b
here,
b+60=180(straight angle)
or, b = 180 - 60
or, b = 120°
again,
a+60+75=180(sum of all angle of triangle)
or, a = 180- 135
or, a = 45°
soln no. d
here,
r=70°( alternate angle)
again,
73°+q+r=180( sum of all angle of triangle)
or,q=180-143
or,q=37°
again,
p=q=37(alternate angle)
soln no. e
y+80=180(straight angle)
or,y= 180-80
or, y = 100°
again,
63+80+<RMB=180(sum of all angles of triangle)
or, 143+<RMB=180
or, <RMB=180-143
or,<RMB= 37°
again,
X+ <RMB= 180(straight angle)
or,X= 180°-37°
or, X = 143°
17
Ax+2y=12
8x +32 y=144
For what value of A will the system of equations above
have no solutions?
Answer:
Hello,
a=0.5
Step-by-step explanation:
[tex]\left \{ \begin{array}{ccc}ax+2y&=&12\\8x+32y&=&144\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}ax+2y&=&12\\x+4y&=&18\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}(1-2a)x&=&-6\\x+4y&=&18\\\end{array}\right.\\\\if\ 1-2a\neq 0\ (or\ a\neq \dfrac{1}{2} )\ then\\\left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{18-\dfrac{6}{2a-1}}{4} \\\end{array}\right.\\\\[/tex]
[tex]\Longleftrightarrow\ \left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{ 3(3a-2)}{2a-1} \\\end{array}\right.\\\\[/tex]
else\
[tex]a=\dfrac{1}{2} \\\Longleftrightarrow\ \left \{ \begin{array}{ccc}\dfrac{1}{2} x+2y&=&12\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}x+4y&=&24\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}0=6\ !!!!!\\\end{array}\right.\\\\Syetem\ has\ no\ solution\\[/tex]
Find the HCF of: 5a²b² and 9x³y³
Answer:
1
Step-by-step explanation:
To do this, we can first look at each factor of each number.
For 5a²b², we can split this up into three parts: 5, a², and b². The factors of 5 are 1 and 5, the factors of a² are 1, a, and a² (because a*a = a² and a²*1 = a²), and the factors of b² are 1, b, and b²
For 9x³y³, the factors for 9 are 1, 3, and 9, the factors of x³ are 1, x, x², and x³ (because x * x² = x³ and x³ * 1 = x³), and the factors of y³ are 1, y, y², and y³.
The only number that is a factor of at least 1 item in each number is 1. Therefore, 1 is the HCF
Another way of looking at this is seeing that a, b, x, and y are all different variables with nothing to connect them, so as a result, they will have no common factors except for 1
PLS HELP Leo is looking at two different savings plans. The first plan requires an initial deposit of $500 and grows at an annual interest rate of 2.5%. The second plan requires an initial deposit of $400 and interest grows continuously at a rate of 2% per year. Leo wrote a system of equations to represent the account balance of either plan, y, after x years. Which two equations are part of the system?
OPTIONS ARE BELOW
Answer:
First and Second option choices
Step-by-step Explanation:
1st case:
Initial deposit (P) = 500
Annual interest rate (r) = 2.5%
Account balance after x years, y = P(1+r/100)×
y = 500(1+2.5/100)×
y = 500(1+0.025)×
y = 500(1.025)×
2nd case:
Initial deposit (P) = 400
Annual interest rate (r) = 2%
Account balance after x years, y = P(1+r/100)×
y = 400(1+2/100)×
y = 400(1+0.02)×
y = 400(1.02)×
The correct option is (A) and (B)
What are Equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).
Parts of an EquationThere are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation. Look at the image below to understand the parts of an equation.
Initial deposit (P) = 500
Annual interest rate (r) = 2.5%
Account balance after x years, y = P(1+r/100)^×
y = 500(1+2.5/100^)×
y = 500(1+0.025)^×
y = 500(1.025)^×
again,
Initial deposit (P) = 400
Annual interest rate (r) = 2%
Account balance after x years, y = P(1+r/100)×
y = 400(1+2/100)^×
y = 400(1+0.02)^×
y = 400(1.02)^×
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EFGH is an isosceles trapezoid and EFGI is a parallelogram. If m∠IEF = 36°, then m∠HGI = ° (Blank 1).
The base angles of an isosceles trapezoid are equal; For EFGI to be a parallelogram, the measure of [tex]\angle HGI[/tex] is: 108 degrees
Given that:
[tex]\angle IEF = 36^o[/tex]
IEF and GHI are the base angles of the trapezoid.
So:
[tex]\angle GHI = \angle IEF = 36^o[/tex]
Also:
[tex]\triangle GHI[/tex] is an isosceles triangle.
This means that:
[tex]\angle GHI = \angle HIG = 36^o[/tex] --- base angles of an isosceles triangle
So:
[tex]\angle GHI + \angle HIG + \angle HGI = 180[/tex] --- sum of angles in a triangle
Substitute known values
[tex]36 + 36+ \angle HGI = 180[/tex]
[tex]72 + \angle HGI = 180[/tex]
Collect like terms
[tex]\angle HGI = 180-72[/tex]
[tex]\angle HGI = 108[/tex]
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1. Identify each number as rational or irrational. Give a reason for your choice.
Part I: The number 0.35 is a(n) _I
number because
Answer:
rational
Step-by-step explanation:
it can be written as a fraction
Rose has $83. She is saving up for a new bike. If she saves $15 per week, how much money will she have after 8 weeks?
How much money does Rose have after 8 weeks? Solve on paper, then enter your answer on Zearn.
Rose has $
after 8 weeks.
Answer:
$203
Step-by-step explanation:
15x8=$120
120+83=$203
The altitude a (in feet) of a plane t minutes after liftoff is given by a = 3400t + 600. How many minutes after liftoff is the plane at an altitude of 21,000 feet
Answer:
6
Step-by-step explanation:
Altitude = 3400t +600
21,000 = 3400t +600
21000-600= 3400t
20400/3400 = 3400t/3400
t= 6
Answered by Gauthmath
A juice machine is set to dispense 16 ounces of juice. The amount of juice
dispensed is normally distributed, with a mean of 16.15 ounces and a
standard deviation of 0.25 ounces. In which range will the amount of juice
dispensed be found 68% of the time?
Answer: A): 15.90 ounces to 16.4 ounces.
Step-by-step explanation:
Considering the standard deviation is 0.25 ounces. The mean of the juice is 16.15 ounces. Additionally, 68% is one standard deviation away from the mean.
With that being said, you would do the following calculations:
[tex]16.15-0.25=15.90\\\\16.15+0.25=16.40[/tex]
This question relates to The Empirical Rule and understanding how it works. A brief summary is that within one standard deviation of the mean, that is where 68% of the data lies. Two standards deviations is 95%. And three standard deviations is 99.5%.
The formula: [tex]u\frac{+}{-} o[/tex]
the mean PLUS OR MINUS the standard deviation.
Answer:
A
Step-by-step explanation:
Find the measures of the indicated angle
Answer:
76
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin ? = 32/33
Taking the inverse sin of each side
sin ^-1( sin ?) = sin^-1 (32/33)
? =75.85888
To the nearest degree
? = 76
The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 61 and standard deviation of 9.8 grams per mililiter. a. What is the probability that the amount of collagen is greater than 60 grams per milliliter
Answer:
45.94%
Step-by-step explanation:
Probability-Above 45.94%
Z =0.1
x= 61
µ 60
σ 9.8
Write the following expression
as a
simplified polynomial in standard form.
2(x – 5)^2 + 2(x – 5) + 5
Answer:
2x^2 - 18x + 45
Step-by-step explanation:
Standard form is ax^2 + bx + c
Expand the (x-5)^2 = (x-5)(x-5) --
x^2 - 5x - 5x + 25
x^2 - 10x + 25
So we now have
2(x^2 - 10x + 25) + 2(x-5) + 5
From here, distribute the 2 to each term in x^2 - 10x + 25, and distribute the 2 to each term in x - 5.
2x^2 - 20x + 50 + 2x - 10 + 5
Combine like terms
2x^2 - 20x + 2x + 50 - 10 + 5
2x^2 - 18x + 40 + 5
2x^2 - 18x + 45
Find the value of b.
A. 57
B. 123
C. 50
D. 61.5
Answer:
please i need educere answers
Step-by-step explanation:
i have one day left and i cannot finish please reply with any way to contact you
1. Simplifying Equation Below
please help!!
Answer: 0
Step-by-step explanation:
In this equation 0/y would equal 0, no matter what y is. 0/y means that there's 0 items out of y items (ex: substitute y with 2, it would be 0/2). Beginning with 1*0 (one times zero) the answer there would be 0. Since we already know that 0/y equals 0, the rest of the equation would be 0 - 0 which would equal to 0. Hope this explanation helps :)
[tex]\\ \sf\longmapsto 0-\dfrac{0}{y}[/tex]
[tex]\\ \sf\longmapsto \dfrac{0-0}{y}[/tex]
[tex]\\ \sf\longmapsto \dfrac{0}{y}[/tex]
[tex]\\ \sf\longmapsto \infty[/tex]
[tex]\\ \sf\longmapsto 0[/tex]
write down the first 3 term of each sequence described by the sequence with first term 8 and difference -7
Answer:
8,1,-6
Step-by-step explanation:
8 + (-7)
= 8-7 = 1
1 + (-7) = 1 - 7 = -6
The first three terms are 8, 1,-6
Answered by Gauthmath
