Answer:
Reject the null hypothesis because the value of null is outside the interval.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron. What is the standardized score for a binding site position of 2.03 microns? (Enter your answer rounded to one decimal place.)
Answer:
The values is
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2.45[/tex]
The standard deviation is [tex]\sigma = 0.35 \ mi[/tex]
The random value is [tex]x = 2.03[/tex]
The standardized score for a binding site position of 2.03 microns is mathematically represented as
[tex]z-score = \frac{x - \mu}{ \sigma }[/tex]
=> [tex]z-score = \frac{2.03 - 2.45}{ 0.35}[/tex]
=> [tex]z-score = -1.2[/tex]
Simplify 10 - [14 = (3 + 4) · 2]+3
Answer:
There is a typo near the equal sign.
There can be two different answers if we think that = sign as + or -.
First way: Making = as +
=> 10 - [14 + (3+4) x 2] +3
=> 10 - [14 + 7 x 2] + 3
=> 10 - [14 + 14] + 3
=> 10 - 28 + 3
=> 10 + 3 - 28
=> 13 - 28
=> -15
=> So, -15 is the answer if we consider "=" sign as "+" sign.
Second way: Making = as -
=> 10 - [14 - (3+4) x 2] + 3
=> 10 - [14 - 7 x 2] + 3
=> 10 - [14 - 14] + 3
=> 10 - 0 + 3
=> 10 + 3
=> 13
=> So, 13 is the answer if we consider "=" sign as "-" sign.
Which is the graph of g(x) = (0.5)x + 3 – 4?
Answer:
Graph (A)
Step-by-step explanation:
Given question is incomplete; find the question in the attachment.
Given function is g(x) = [tex](0.5)^{x+3}-4[/tex]
Parent function of the given function is,
f(x) = [tex](0.5)^{x}[/tex]
When the function 'f' is shifted by 3 units left over the x-axis, translated function will be,
h(x) = f(x+3) = [tex](0.5)^{x+3}[/tex]
When h(x) is shifted 4 units down, translated function will be,
g(x) = h(x) - 4
g(x) = [tex](0.5)^{x+3}-4[/tex]
g(x) has a y-intercept as (-4).
From the given graphs, Graph A shows the y-intercept as (-4).
Therefore, Graph A will be the answer.
Answer:
The Answer A is correct
Step-by-step explanation:
I took the edg2020 test
The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP
Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............
Step-by-step explanation:
From the first statement,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6 -----------------------------------1
second statement
sum of the next 4 terms inclusive
T₉ = ⁹/₂(2a + 8d ) = 69
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
divide through by 18 to reduce to lowest time
a + 4d = 11 ------------------------------------------2
Now solve the two equation simultaneously to find a and d
a + 2d = 6
a + 4d = 11
-2d = -5
d = ⁵/₂.
Now substitute for d to get a
a + 2(⁵/₂) = 6
a + 5 = 6
a = 6 - 5
a = 1.
Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............
The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
What is sequence?
An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
The sum of the first 5 terms of an AP is 30,
Write the equations as shown below,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6
T₉ = ⁹/₂(2a + 8d ) = 69 (sum of the next 4 terms inclusive)
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
a + 4d = 11
Solve the equation as shown below,
d = ⁵/₂, and a = 1.
Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
To know more about the sequence:
https://brainly.com/question/28615767
#SPJ5
HELPP PLEASEE ��2222 is the diameter of a circle. The coordinates are �(−2, −3) and �(−12, −5). At what coordinate is the center of the circle located? A. (5, 1) B. (−5, −1) C. (−4, −7) D. (−7, −4)
Answer:
(-7, -4) which is your answer D in the list of options
Step-by-step explanation:
The center of the circle should be located half way in between the given points on the plane.
Then the center ahs to be located half way for the x coordinates of both points:
half way between -12 and -2 (notice that there is a difference of 10 units between them), therefore half way would be at 5 units to the right from the furthest point, that is -12 + 5 = -7
Similarly, for the y coordinate, we see that the difference is between -5 and -3 (a difference of two units) therefore the center point will be located half way (that is one unit) up from the lowest y coordinate: -5 + 1 = -4
Then the center of the circle is located at (-7, -4)
Someone PLEASE help!
Step-by-step explanation:
[tex]f(f(x)) = f( {x}^{2} + 4)[/tex]
[tex] = {( {x}^{2} + 4) }^{2} + 4[/tex]
[tex] = {x}^{4} + 4 {x}^{2} + 16 + 4[/tex]
[tex] = {x}^{4} + 8 {x}^{2} + 20[/tex]
A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat
Answer:
2 servings of salad and 1 serving of soup
Step-by-step explanation:
In the given scenario the aim is to minimise the fat content of the food combination.
Fat content of soup is 3mg while fat content of salad is 2 mg.
Using Soup as 0 and Salad as 2 will not give the required vitamin content
The logical step will be to keep servings of soup to the minimum.
Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1
1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.
This will not work because amount of vitamin B complex is not up to 10 mg
2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat
This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.
Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving
Lynn estimates roof jon 1500,bo estimates 2400. What's the ratio to lynn to bo
Answer:
5:8
Step-by-step explanation:
If I understand your question correctly, we have 1500/2400=15/24=5/8, so we have Lynn:Bo is 5:8, however, in the future please be more clear.
What is "estimates roof jon"? And, instead of saying "ratio to lynn to bo" say "What is the ratio of the estimates?" or whatever you're asking. If this answer is wrong, you only have yourself to blame.
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.966 grams and a standard deviation of 0.315 grams. Find the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less.
Answer:
The probability is [tex]P(X \le 0.305 ) = 0.01795[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.966 \ grams[/tex]
The standard deviation is [tex]\sigma = 0.315 \ grams[/tex]
Given that the amounts of nicotine in a certain brand of cigarette are normally distributed
Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )[/tex]
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )[/tex]
From the z-table(reference calculator dot net ) value of [tex]P(Z >-2.0984 ) =0.98205[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205[/tex]
=> [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795[/tex]
=> [tex]P(X \le 0.305 ) = 0.01795[/tex]
Could someone help me pls! And could you explain if possible? Thanks you
Answer:
3%
Step-by-step explanation:
1. Set up the equation
6(0.18) + 12x = 18(0.08)
2. Simplify
1.08 + 12x = 1.44
3. Solve
12x = 0.36
x = 0.03
0.03 = 3%
−(−49) = −49 true or false?
If you have a piece of glass that is 12in X 12in - how many square feet is it?
Answer:
1 square foot is the answer
Answer:
1 ft^2
Step-by-step explanation:
We know 12 inches = 1 ft
12 inches by 12 inches
1 ft by 1 ft
The area is 1 * 1 = 1 ft^2
Solve x/10 = -7 A. x = 3 B. x = -0.7 C. x = -17 D. x = -70
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
Calculate two iterations of Newton's Method for the function using the given initial guess. (Round your answers to four decimal places.) f(x) = x2 − 5, x1 = 2n xn f(xn) f '(xn) f(xn)/f '(xn) xn − f(xn)/f '(xn)1 2
Answer:
Step-by-step explanation:
Given that:
[tex]\mathsf{f(x) = x^2 -5 } \\ \\ \mathsf{x_1 = 2}[/tex]
The derivative of the first function of (x) is:
[tex]\mathsf{f'(x) =2x }[/tex]
According to Newton's Raphson method for function formula:
[tex]{\mathrm{x_{n+1} = x_n - \dfrac{f(x_n)}{f'(x_n)}}[/tex]
where;
[tex]\mathbf{x_1 =2}[/tex]
The first iteration is as follows:
[tex]\mathtt{f(x_1) = (2)^2 - 5} \\ \\ \mathbf{f(x_1) = -1}[/tex]
[tex]\mathtt{f'(x_1) = 2(2)} \\ \\ \mathbf{ = 4}[/tex]
[tex]\mathtt{\dfrac{f(x_1)}{f'(x_1)}} = \dfrac{-1}{4}}[/tex]
[tex]\mathbf{\dfrac{f(x_1)}{f'(x_1)} =-0.25}[/tex]
[tex]\mathtt{x_1 - \dfrac{f(x_1)}{f'(x_1)}} = \mathtt{2 - (-0.25)}}[/tex]
[tex]\mathbf{x_1 - \dfrac{f(x_1)}{f'(x_1)} = 2.25}[/tex]
Therefore;
[tex]\mathbf{x_2 = 2.25}[/tex]
For the second iteration;
[tex]\mathtt f(x_2) = (2.25)^2 -5}[/tex]
[tex]\mathtt f(x_2) = 5.0625-5}[/tex]
[tex]\mathbf{ f(x_2) =0.0625}[/tex]
[tex]\mathtt{f'(x_2)= 2(2.25)}[/tex]
[tex]\mathbf{f'(x_2)= 4.5}[/tex]
[tex]\mathtt{ \dfrac{f(x_2)}{f'(x_2)}} = \dfrac{0.0625}{4.5}}[/tex]
[tex]\mathbf{ \dfrac{f(x_2)}{f'(x_2)} = 0.01389}[/tex]
[tex]\mathtt{x_2 - \dfrac{f(x_2)}{f'(x_2)}} = \mathtt{2.25 -0.01389}}[/tex]
[tex]\mathbf{x_2 - \dfrac{f(x_2)}{f'(x_2)} = 2.2361}}[/tex]
Therefore, [tex]\mathbf{x_3 = 2.2361}[/tex]
x
Find the value
of x. Show
3
10
your work.
Step-by-step explanation:
Hello, there!!!
Let ABC be a Right angled triangle,
where, AB = 3
BC= 10
and AC= x
now,
As the triangle is a Right angled triangle, taking angle C asrefrence angle. we get,
h= AC = x
p= AB = 3
b= BC= 10
now, by Pythagoras relation we get,
[tex]h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
[tex]or ,\: h = \sqrt{ {3}^{2} + {10}^{2} } [/tex]
by simplifying it we get,
h = 10.44030
Therefore, the answer is x= 10.
Hope it helps...
Molly’s house is located at point X. Molly wants Sophia and Cole to meet at her house because she thinks it is the same distance from Sophia’s house and Cole’s house. Which could prove that Molly’s house is the samedistance from Sophia’s and Cole’s houses?
Answer:
Cole's House
Step-by-step explanation:
Cole house is closer because molly and Sophia can go there together because there both girls
What is the probability of the spinner landing on an odd number? A spinner is split into 4 equal parts labeled 1, 2, 3, and 4. One-fourth One-third One-half Three-fourths
Answer:
One half, or 1/2.
There are an equal amount of odd numbers as there are even numbers on the spinner.
Answer:
C. 1/2
One-half
Find the product . Write your answer in exponential form 8^-2•8^-9
Answer:
8^-11
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
Then we have ...
(8^(-2))·(8^(-9)) = 8^(-2-9) = 8^-11
If you invest $ 30 , 700 with an annual interest rate of 8.9 % , compounded daily, how much would you have at the end of 4 years?
Answer: $43,823.37
Step-by-step explanation:
Formula to calculate the accumulated amount earned on principal (P) at rate of interest (r) compounded daily after t years :
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
As per given , we have
P= $ 30,700
r= 8.9 % = 0.089
t= 4 years
[tex]A=30700(1+\dfrac{0.089}{365})^{365(4)}\\\\=30700(1+0.0002438)^{365(4)}\\\\=30700(1.0002438)^{1460}\\\\=30700(1.42747138525)\\\\=43823.3715272\approx43823.37[/tex]
Hence, the amount at the end of 4 years would be $43,823.37 .
What is the value of this expression when x = -6 and y = — 1/2? 4(x^2+3) -2y A. -131 B. -35 C. 57 1/2 D. 157
Answer:
D
Step-by-step explanation:
[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]
The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
4(x² + 3) - 2y
Substitute x = -6 and y = -1/2 to find the value of expression,
= 4 ((-6)² + 3) - 2(-1/2)
= 4 (36 + 3) + 1
= 4 x 39 + 1
= 156 + 1
= 157
The required value of the expression is 157.
To know more about Algebraic expression on:
https://brainly.com/question/19245500
#SPJ2
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
step by step
given length=6
so area of square is given by s2 i.e 6^2
=6×6
=36 (Ans)
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $15.59$ and $15.6$ so each division is $\frac{15.60-15.59}{10}=0.001$
A is 5 division from $15.59$, so, A is $15.59+5\times 0.001=15.595$
similarly, C is 4 division behind $15.59$ so it is $15.590-4\times0.001=15.586$
and B is $15.601$
i need help will rate you branliest
Answer:
D. the bottom one is the answer, because hyperbola is two curves that curve infinitely
Help Quick Please. Will give brainliest.
Answer:
72[tex]\sqrt{3}[/tex] units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = ST = a = 12 and h = RS
To calculate RS use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )
RS = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²
how to find the roots of a quadratic equation -10x^2 + 0x +250
Answer:
Step-by-step explanation:
The first thing you want to do is to factor in any quadratic equation.
So, -10(x^2-25)
Now, we see this is a special case, whenever we see a equation in this case, x^2 - b^2, we factor it to this (x+b)(x-b)
So, -10(x+5)(x-5)
x = -5 and x = 5
A la propiedad fundamental de las proporcionas, comprueba si las siguientes son o no hay elementos a) 5/7 a 15/21 b) 20/7 a 5/3 c) 16/8 a 4/2
Answer:
fucuvucybycych tcy bic ttx TV ubtx4 cub yceec inivtxr xxv kb
Step-by-step explanation:
t tcextvtcbu6gt CNN tx r.c tct yvrr TV unu9gvt e tch r,e xxv t u.un4crcuv3cinycycr xxv yctzrctvtcrzecycyvubr xiu nyfex tut uhyh
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
Complete Question
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
a.
The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen’s d.
b.
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
c.
The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen’s d.
d.
The larger sample is less likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
Answer:
The Cohen's d value is [tex]d = 0.895[/tex]
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample mean of each population is [tex]M = 84[/tex]
The variance of each population is [tex]s^2 = 20[/tex]
The first sample size is [tex]n_1 = 10[/tex]
The second sample size is [tex]n_2 = 20[/tex]
The null hypothesis is [tex]H_o : \mu = 80[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]s = \sqrt{20 }[/tex]
=> [tex]s = 4.47[/tex]
The first test statistics is evaluated as
[tex]t_1 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_1} } }[/tex]
=> [tex]t_1 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{10} } }[/tex]
=> [tex]t_1 = 2.8298[/tex]
The second test statistics is evaluated as
[tex]t_2 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_2} } }[/tex]
=> [tex]t_2 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{20} } }[/tex]
=> [tex]t_2 = 4.0[/tex]
The sample with the larger test statistics (sample size) will more likely reject the null hypothesis
Generally the Cohen's d value is mathematically evaluated as
[tex]d = \frac{M - \mu }{s }[/tex]
=> [tex]d = \frac{ 84 - 80 }{4.47 }[/tex]
=> [tex]d = 0.895[/tex]
Given that the the sample mean and sample size are the same for both sample the Cohen's d value will be the same
1 If a = p^1/3-p^-1/3
prove that: a^3 + 3a = p - 1/p
Hello, please consider the following.
We know that
[tex]a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}[/tex]
And we can write that.
[tex](p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})[/tex]
It means that, by replacing p by [tex]p^{1/3}[/tex]
[tex](p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\<=>\boxed{ a^3+3a=p-\dfrac{1}{p} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Solve this problem using the Trigonometric identities (secA+1)(SecA-1)= tan^2A
Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
[PLEASE HELP] Consider this function, f(x) = 2X - 6.
Match each transformation of f (x) with its descriptions..
Answer:
Find answer below
Step-by-step explanation:
f(x)=2x-6
Domain of 2x-6: {solution:-∞<x<∞, interval notation: -∞, ∞}
Range of 2x-6: {solution:-∞<f(x)<∞, interval notation: -∞, ∞}
Parity of 2x-6: Neither even nor odd
Axis interception points of 2x-6: x intercepts : (3, 0) y intercepts (0, -6)
inverse of 2x-6: x/2+6/2
slope of 2x-6: m=2
Plotting : y=2x-6
