Answers
Answer:
1/2
Step-by-step explanation:
● 1/4 + 4(1/2 - 3/4 )^2
To make it easier convert the fractions to decimal numbers.
● 1/4 = 0.25
● 1/2 = 0.5
● 3/4 = 0.75
So the expression will be:
● 0.25 + 4(0.5 - 0.75)^2
Calculte first 0.5-0.75 (0.5-0.75= -0.25)
● 0.25 + 4 × (-0.25)^2
-0.25^2 is the same as 0.25^2
● 0.25 + 4 × (0.25)^2
0.25^2 is 0.0625
● 0.25 + 4×0.0625
Multiplication has the priority (4 ×0.0625) wich is 0.25
● 0.25 + 0.25
● 0.5
0.5 is 1/2
So the answer 1/2
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}+4(\frac{1}{2}-\frac{3}{4})^2\\\frac{1}{4}+4(\frac{2-3}{4})^2\\\frac{1}{4}+4(\frac{-1}{4})^2\\\frac{1}{4}+4(\frac{1}{16})\\\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]
Related Questions
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple
Answers
Answer:
Step-by-step explanation:
Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.
So, to answer the first question, [tex]6^2[/tex] is a perfect square.
(a,b,c) is a Pythagorean triple means the following
[tex]a^2+b^2=c^2[/tex]
Here, it means that
[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]
Thank you.
Answer:
Its B
Step-by-step explanation:
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 16]
Answers
Answer:
C = 4
Step-by-step explanation:
solution:
f(x) can be differentiated on (0,16)
By mean value theorem
= f(16) = 4
= f(0) = 0
= f(b) - f(a)/b - a
= f(4) - f(0)/ f(16) - f(0)
= f'(c) = 1/2√C
= 1/2√C = 4/16
= 1/2√C = 1/4
= 4 = 2√C
= √C = 4/2
we make c the subject of the formula and also eliminate the square root
= √C = 2
= C = 2²
= C = 4
Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.)
Required:
a. Find the probability that the first card is a face card and the second is NOT a face card.
b. Find the probability that they are both face cards.
c. Find the probability that the second is a face card given the first is NOT a face card.
Answers
Answer:
The answer is below
Step-by-step explanation:
There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards
a. Find the probability that the first card is a face card and the second is NOT a face card.
There are 12 first card, the probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:
The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card) = 12/52 × 40/51 = 40/221
b) Find the probability that they are both face cards.
The probability that the first card is a face card is 12/52.
Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:
The probability that they are both face cards = P(first is face card) × P(second is face card) = 12/52 × 11/51 = 11/221
c) Find the probability that the second is a face card given the first is NOT a face card.
The probability that the first card is not a face card = 40/52
Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:
The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card) = 40/52 × 12/51 = 40/221
In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard. Compute the test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Answers
Answer:
The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.
Step-by-step explanation:
We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.
In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.
Let [tex]p_1[/tex] = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.
[tex]p_2[/tex] = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex] {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = [tex]\frac{24}{90}[/tex] = 0.27
[tex]\hat p_2[/tex] = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = [tex]\frac{42}{380}[/tex] = 0.11
[tex]n_1[/tex] = sample of cars driven at high altitudes = 90
[tex]n_2[/tex] = sample of cars driven at low altitudes = 380
So, the test statistics = [tex]\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }[/tex]
= 3.234
The value of z-test statistics is 3.234.
p-value problem. Suppose the director of manufacturing at a clothing factory needs to determine wheteher a new machine is producing a particulcar type of cloth according to the manufacturer s specification which indicate that the cloth should have mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds. THe p value for this hypothesis testing scenario is
Answers
Answer:
The P-Value is 0.07186
Step-by-step explanation:
GIven that :
Mean = 70
standard deviation = 3.5
sample size n = 49
sample mean = 69.1
The null hypothesis and the alternative hypothesis can be computed as follows;
[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]
The standard z score formula can be expressed as follows;
[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]
[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]
[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]
z = -1.8
Since the test is two tailed and using the Level of significance = 0.05
P- value = 2 × P( Z< - 1.8)
From normal tables
P- value = 2 × (0.03593)
The P-Value is 0.07186
i need help will rate you branliest
Answers
Answer:
d. The graph of g(x) is the graph of f(x) reflected over the x-axis.
Step-by-step explanation:
The standard transformation
g(x) = - f(x)
is a simple reflection about the x-axis.
So the answer is the last option.
Answer:
Last one
Step-by-step explanation:
The function we are interested in are g(x) and f(x).
● g(x)= (-1/x)
● f(x)= 1/x
Notice what happens when we input the same values in both functions.
● g(1) = -1/1 = -1
● f(x) = 1/1 = 1
●g(2) = -1/2 = -0.5
● f(2) = 1/2 = 0.5
Notice that we get opposite values by imputing the same number.
Wich means:
●f(x) = -g(x)
So the graph of g(x) is the graph of f(x) reflected over the x axis.
Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l
Answers
Answer:
B. j(kl)
Step-by-step explanation:
(jk)l
We can change the order we multiply and still get the same result
j(kl)
Answer:
Step-by-step explanation:
its B i did it
1. What happened when you had a negative plus a negative, (-a) + (-b)?
I
2. What happened when you had a positive plus a negative, a + (-b)?
***Is this the same as a positive minus a positive, a - b?
3. What happened when you had a positive minus a negative, a - (-b)?
4. What happened when you had a negative minus a negative, (-a) - (-b)?
Answers
Answer:
See Explanation
Step-by-step explanation:
1.
What happens when negative adds to negative; e.g (-a) + (-b)
First, we need to simplify the expression
[tex](-a) + (-b)[/tex]
Open the brackets
[tex]-a - b[/tex]
Factorize
[tex]-(a+b)[/tex]
So, what happens is that: the two numbers are added together and the result is negated;
E.g.
[tex](-5) + (-3) = -(5 + 3) = -8[/tex]
2.
What happens when positive is added to negative; e.g. a + (-b)
First, we need to simplify the expression
[tex]a + (-b)[/tex]
Open the brackets
[tex]a - b[/tex]
So, what happens is that: the negative number is subtracted from the positive number
And Yes; [tex]a + (-b)[/tex] is the same as [tex]a - b[/tex] (As shown above)
E.g.
[tex]5 + (-3) = 5 - 3 =2[/tex]
3.
What happens when to positive minus a negative; e.g. a - (-b)
First, we need to simplify the expression
[tex]a - (-b)[/tex]
Open the brackets
[tex]a + b[/tex]
So, what happens is that; the two numbers are added together.
E.g.
[tex]5 - (-3) = 5 + 3 = 8[/tex]
4.
What happens when negative minus a negative; e.g. (-a) - (-b)
First, we need to simplify the expression
[tex](-a) - (-b)[/tex]
Open the brackets
[tex]-a + b[/tex]
Reorder
[tex]b - a[/tex]
So, what happens is that; the first number is subtracted from the second.
E.g.
[tex](-5) - (-3) = 3-5 = -2[/tex]
Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes. What does Chebyshev's Theorem say about the percentage of employees with commuting times between 54 minutes and 72minutes?
Answers
Answer: At-least 89% of employees with commuting times between 54 minutes and 72 minutes .
Step-by-step explanation:
Given: Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes.
Now, 54 minutes = (63 - 9) minutes
= (63 -3(3)) minutes
= Mean - 3 standard deviation
72 minutes = (63 + 9) minutes
=63 +3(3) minutes
= Mean + 3 standard deviation
According to Chebyshev's theorem, at least [tex]\dfrac{8}{9}[/tex] of the data lie within 3 standard deviations of the mean.
i.e. The percentage of employees with commuting times between 54 minutes and 72 minutes = [tex]\dfrac{8}{9}\times100\approx89\%[/tex]
Hence, at-least 89% of employees with commuting times between 54 minutes and 72 minutes .
Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)
Answers
Answer:
Step-by-step explanation:
From the given information;
let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c
SO, using the Pythagoras theorem
a² = c² + 177²
By taking the differentiation of both sides with respect to time t , we have
[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]
[tex]a = \sqrt{ 5041+31329}[/tex]
[tex]a = \sqrt{ 36370}[/tex]
a = 190.71
SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]
Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:
[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]
[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]
[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]
[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex] to the nearest hundredth.
Which statement best describes a sequence? a.All sequences have a common difference. b.A sequence is always infinite. c.A sequence is an ordered list. d.A sequence is always arithmetic or geometric.
Answers
Answer:
C
Step-by-step explanation:
A sequence is defined as a list of numbers or objects in a special order.
They may be arithmetic or geometric or neither.
For example
0, 1, 4, 9, 16, 25, ..... ← is the sequence of square numbers.
Note it is neither arithmetic or geometric.
Please answer this correctly without making mistakes
Answers
Answer:
so to get a third you divide it by 3
first convert it to fraction
so it is 26/3
so do 26/3 divided by 3
so we do keep switch flip
26/3*1/3
so answer is 26/9 or 2 8/9
Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{2 \ 8/9 \ tablespoons \ of \ red \ chilies }}[/tex]
Step-by-step explanation:
8 2/3 tablespoons of red chilies is required for a recipe.
One-third of the original recipe would mean that the quantity of red chilies will be also one-third.
8 2/3 × 1/3
Convert to an improper fraction.
26/3 × 1/3
Multiply the fractions.
26/(3 × 3) = 26/9
Convert to a mixed fraction.
26/9 = 2 8/9
(Algebra) HELP ME ASAP PLZ
Answers
Answer:
no solution because the answer will be p=2
10 - [ 8p + 3 ] = 9 [ 2p - 5 ]
10 - 8p - 3 = [ 2p - 5 ]
-8p + 10 - 3 = [ 2p - 5 ]
p = 2 We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, the following 2 terms will change sign:
8p, 3
Step-by-step explanation:
Use the graph showing Debra's account balance to answer the question that follows. ^
About how long will it take for Debra's account balance to equal $60?
A - 6 months
B - 6 years
C - 3 months
D - 3 years
Answers
Answer: 2 years
Step-by-step explanation:
In the given graph, we have
Account Balance ($) on y-axis
Time (years) on x-axis.
To know the time taken to get a balance of $60 , we check the point corresponding to 60 at y-axis and then join it to the line of the function and stop.
Then from there we drop a line to x-axis.
We get x=2.
That is it will take 2 years to get $60 balance in Debra's account.
So the correct answer is 2 years.
One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?
Answers
Answer:
The [tex]L_{ACL}[/tex] of the player is [tex]L_{ACL} = 56.82 \ mm[/tex]
Step-by-step explanation:
From the question we are told that
The relationship between the length [tex]L_{ACL}[/tex] to the height is
[tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]
The height of the basketball player is [tex]h = 2.13 \ m = 2130 \ mm[/tex]
Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is
[tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]
[tex]L_{ACL} = 56.82 \ mm[/tex]
Find the length of a square with a perimeter of 48cmeter
Answers
Answer:
12
Step-by-step explanation:
Perimeter of a square:
4(L)
L = Length
=> 4(L) = 48
=> 4L = 48
=> 4L/4 = 48/4
=> L = 12
The length of the square is 12 cm.
Answer:
12
Step-by-step explanation:
Since the lengths of the sides of a square are equal, divide the perimeter by 4
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answers
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not solve the equation.
x2+3x−18=0
Answers
Answer:
Step-by-step explanation:
Hello, "the constant term has been written on the right side", it means that we add 18 to both sides to get.
[tex]x^2+3x-18=0\\\\x^2+3x=18\\\\\text{We can see the beginning of } (x+\dfrac{3}{2})^2 \\\\x^2+3x=(x+\dfrac{3}{2})^2-\dfrac{3^3}{2^2}=18\\\\(x+\dfrac{3}{2})^2=18+\dfrac{9}{4}=\dfrac{18*4+9}{4}=\dfrac{81}{4}[/tex]
Hope this helps.
Thank you.
Answer:
2.25.
Step-by-step explanation:
x^2 + 3x - 18 = 0
First, we need to write the constant on the right of the equation. So, we add 18 to both sides.
x^2 + 3x = 18.
Now, we find the number that will complete the square. It will be [tex](\frac{b}{2} )^2[/tex].
In this case, b = 3.
[tex](\frac{3}{2} )^2[/tex]
= (1.5)^2
= 2.25.
So, the number that will complete the square to solve the equation is 2.25, or 2 and 1/4, or 9/4.
Hope this helps!
y=mx+6 , solve for m
Answers
Answer:
m = [tex]\frac{y-6}{x}[/tex]
Step-by-step explanation:
Given
y = mx + 6 ( subtract 6 from both sides )
y - 6 = mx ( divide both sides by x )
[tex]\frac{y-6}{x}[/tex] = m
Plz answer quickkkk help will give 5 star rate if answer is right nd will say thx
Answers
Answer:
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s):
(−6,0)
y-intercept(s):
(0,3)
So I would say -6 and 0 and 2 are in domain
Answer:
-6, 0 ,2 are in the domain
Step-by-step explanation:
The domain is what values that x can take
There are no restrictions on the values that x can take
All real numbers are in the domain
-6, 0 ,2 are in the domain
Find the sum of the even numbers between 199 to 1999
Answers
[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]
The Sum is 989100.
what is sum of Even numbers?The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.
The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)
Given:
a1 = 200
an= 1998
So, using formula
S= n(a1 + an)/2
now,
d=2
an= a1+(n-1)d
1998= 200 + (n-1) 2
1998-200= (n-1)2
1798/2=n-1
n= 900
S900= 900( 200 + 1998)/2
=450*2198
= 989100
Hence, the sum is 989100.
Learn more about this concept here:
https://brainly.com/question/18837188
#SPJ2
solve the following equations for x (3x-6)=18
Answers
Answer:
x = 8
Step-by-step explanation:
Hello!
What we do to one side of the equation we have to do to the other side.
3x - 6 = 18
Add 6 to both sides
3x = 24
Divide both sides by 3
x = 8
The answer is 8
Hope this helps!
Answer:
x=8
Step-by-step explanation:
(3x-6)=18
Add 6 to each side
(3x-6+6)=18+6
3x= 24
Divide by 3
3x/3 = 24/3
x = 8
4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25
Answers
Answer:
a) Means: 24 and 2; Extremes: 4 and 12
b) Means: 6 and 16; Extremes: 24 and 4
c) Means: 8 and 8; Extremes: 4 and 16
d) Means: 50 and 3; Extremes: 6 and 25
Step-by-step explanation:
The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:
a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.
The Means are the values that appear in the middle of the one line expression, that is: b and c.
Recall as well that the proportion can also be written with fractions:
a : b = c : d is the same as: a / b = c / d
so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.
if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!
Answers
Answer:
5
----------
( n+1)(n+2)
Step-by-step explanation:
5
----------
n ( n+1)
Replace n with n+1
5
----------
(n+1) ( n+1+1)
5
----------
( n+1)(n+2)
We replace every 'n' with n+1 and simplify
[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]
Should I read Fruit's Basket? I need something to keep me busy.
Answers
Answer: Yes
Explanation: Yes because, sometimes you need to do stuff to get things of your head
Find the interquartile range of the data in the dot plot below. players blob:mo-extension://5f64da0e-f444-4fa8-b754-95
Answers
Answer:
[tex]IQR=Q_{3}-Q_{1}[/tex]
Step-by-step explanation:
The inter-quartile range is a measure of dispersion of a data set.
It is the difference between the third and the first quartile.
[tex]IQR=Q_{3}-Q_{1}[/tex]
The 1st quartile (Q₁) is well defined as the mid-value amid the minimum figure and the median of the data set. The 2nd quartile (Q₂) is the median of the data. The 3rd quartile (Q₃) is the mid-value amid the median and the maximum figure of the data set.
2
Select the correct answer.
which number is the additive Inverse of -10 ?
O A 10 1
Ос. о
OD. -41
Reset
Next
Answers
Answer:
[tex]\boxed{\sf 10}[/tex]
Step-by-step explanation:
The additive number of any number is the number when added to the number gives a result of zero.
So, if we add 10 to -10 we get a result of zero.
=> -10+10
=> Zero
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 83 units of a small appliance with a standard deviation of 5 units. During the same point in time last year, a random sample of 49 stores had mean sales of 78 units with standard deviation 3 units.Required:Construct a 95 percent confidence interval for the difference in population means.
Answers
Answer:
The 95% confidence interval for the difference in population means is (−26.325175 , 36.325175)
Step-by-step explanation:
Given that :
sample size n₁ = 36
sample mean [tex]\over\ x[/tex]₁ = 83
standard deviation [tex]\sigma[/tex]₁ = 5
sample size n₂ = 49
sample mean [tex]\over\ x[/tex]₂= 78
standard deviation [tex]\sigma[/tex]₂ = 3
The objective is to construct a 95% confidence interval for the difference in the population means
Let the population means be [tex]\mu_1[/tex] and [tex]\mu_2[/tex]
The 95% confidence interval or the difference in population means can be calculated by using the formula;
[tex](\overline{x_1} - \overline{x_2}) \pm t_{\alpha /2} \ \times s_{p}[/tex]
where;
the pooled standard deviation [tex]s_{p} = \dfrac{(n_1-1)s_1^2+(n_2-1)s^2_2}{n_1+n_2-2}[/tex]
[tex]s_{p} = \dfrac{(36-1)5^2+(49-1)3^2}{36+49-2}[/tex]
[tex]s_{p} = \dfrac{(35)25+(48)9}{83}[/tex]
[tex]s_{p} = \dfrac{875+432}{83}[/tex]
[tex]s_{p} = \dfrac{1307}{83}[/tex]
[tex]s_p[/tex] = 15.75
degree of freedom = [tex]n_1 +n_2 -2[/tex]
degree of freedom = 36+49 -2
degree of freedom = 85 - 2
degree of freedom = 83
The Critical t- value 95% CI at df = 83 is
t critical = T.INV.2T(0.05, 83) = 1.9889
Therefore, for the population mean , we have:
= (83 - 78) ± (1.9889 × 15.75)
= 5 ± 31.325175
= 5 - 31.325175 , 5 + 31.325175
= (−26.325175 , 36.325175)
PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?
Answers
Answer:
8) 1.962 miles
9) (-2, -1.5)
10) 0.515 miles
Step-by-step explanation:
√(-9 - 5)² + (1 - -4)² = 14.866
14.866 x .132 = 1.962
(-9+5)/2, (1 + -4)/2
-4/2, -3/2
-2, -3/2
√(-2 - 1)² + (-3/2 - -4)² = 3.905
3.905 x .132 = 0.515 miles
The scale on a scale drawing is 1 : 30. What should you do with each measurement on the drawing to get the actual dimensions? Provide an example of a drawing that uses this scale. Include both the original and new dimensions.
Answers
Answer:
see below
Step-by-step explanation:
For the first question, you should multiply the scale dimension by 30 to get the actual dimension. This is because the scale is 1:30 where the scale dimension is the 1 and the actual dimension is 30, so therefore, the scale dimension is 1/30th of the actual dimension, so to get the actual dimension, we can multiply the scale dimension by 30. I'm not totally sure how to attach pictures from my phone on my computer (sorry) but an example of a drawing could be two rectangles, the first (this is the scale drawing) having dimensions of 1 by 2 units and the second (this is the actual drawing) having dimensions of 30 by 60 units. I hope this helps!
