Answer:
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
Step-by-step explanation:
We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).
New machine
Sample mean x₁ = 25
Sample variance s₁ = 27
Sample size n₁ = 45
Old machine
Sample mean x₂ = 23
Sample variance s₂ = 7,56
Sample size n₂ = 36
Test Hypothesis:
Null hypothesis H₀ x₂ - x₁ = d = 0
Alternative hypothesis Hₐ x₂ - x₁ < 0
CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂
s₁ = 27 ⇒ s₁² = 729
n₁ = 45 ⇒ s₁² / n₁ = 16,2
s₂ = 7,56 ⇒ s₂² = 57,15
n₂ = 36 ⇒ s₂² / n₂ = 1,5876
√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175
z(s) = (23 - 25 )/4,2175
z(s) = - 0,4742
Comparing z(s) and z(c)
|z(s)| < | z(c)|
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean
what is a negative number that has an absolute value greater than 3?
Answer:
x > -3
Step-by-step explanation:
Any negative number greater than -3 will have an absolute value greater than 3.
(4x - 3) × (x + 2)=0
Hi,
AxB = 0 means A=0. or B=0
so 2 solutions :
4x-3= 0
4x=3
x = 3/4
and x+2 = 0.
x= -2
solutions are : -2 +and 3/4
2 answers
1) -2
2) -3/4
Look at the image for the question?
Answer:
Surface area = the sum of the area of all six sides:
(11 · 10) + (11 · 10) + (11 · 8) + (11 · 8) + (8 · 10) + (8 · 10)
= 110 + 110 + 88 + 88 + 80 + 80
= 220 + 176 + 160
= 556 ft²
Answer:
556 ft^2
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(lw+wh+lh) where h is the height l is the length and w is the width
SA = 2( 11*10+10*8+11*8)
= 2(110+80+88)
=2(278)
=556 ft^2
As part of an enterprise day, Guramar and Gurnam baked 4 cakes. They gave 1/2 of one cake away to the staff. In the morning they sold 2 1/3 cakes and in the afternoon they sold 1 1/8. How much cake did they have left?
9514 1404 393
Answer:
1/24 of a cake
Step-by-step explanation:
The remaining amount of cake was ...
4 -1/2 -2 1/3 -1 1/8 = 4 -12/24 -2 8/24 - 1 3/24 = (4 -2 -1) -(12 +8 +3)/24
= 1 -23/24 = 1/24
1/24 of a cake was left
_____
Basically, crumbs.
Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out - squares from each corner. The length of the original piece of cardboard is more than the width. If the volume of the box is , determine the dimensions of the original piece of cardboard.
Question is not complete, so i have attached it.
Answer:
Length = 30 inches
Width = 22 inches
Step-by-step explanation:
Let the width of rectangular sheet be x inches.
Let the length of the sheet be (x + 8) inches.
Now, after she cuts 4 inches squares from each corner, she will get a box of length: x + 8 - 4 - 4 = x inches , width: (x - 8) inches and height 4 inches.
Now, volume of a cube is;
V = lwh
Thus;
V = x(x - 8)(4)
We are told that the volume of the box is 2640 in³
Thus;
x(x - 8)(4) = 2640
Divide both sides by 4 to get;
x(x - 8) = 660
x² - 8x - 660 = 0
Using quadratic formula, we have;
x = 30 or - 22.
We will use x = 30 as the other one is negative.
Since we earlier deduced that she will get a box of will get a box of length: x inches , width: (x - 8) inches
Thus,
Length = 30 inches
Width = 30 - 8 = 22 inches
Suppose you finance a home in the amount of $425,000 at 4.3% compounded monthly for 30 years. Calculate your payment.
Answer: $1,540,194.30 .
Step-by-step explanation:
The formula to calculate the accumulated amount earned on principal (P) at rate of interest (r)[ in decimal] compounded monthly after t years :
[tex]A=P(1+\dfrac{r}{12})^{12t}[/tex]
Given: P= $425,000
r= 4.3% = 0.043
t= 30 years
[tex]A=425000(1+\dfrac{0.043}{12})^{12(30)}\\\\=425000(1.003583)^{360}\\\\=425000\times3.62398657958\approx1540194.30[/tex]
Hence, the payment would be $1,540,194.30 .
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%
Assuming that the loss of ability to recall learned material is a first-order process with a halflife of 35 days. Compute the number of days required to forget 90% of the material that you have learned today. Report to 1 decimal place.
Answer:
5.3 days
Step-by-step explanation:
Let us assume the loss of ability to recall a learned material = 100%
Formula to calculate number of days = time(t) =
t = t½ × Log½(Nt/No)
Nt = Ending Amount
No = Beginning Amount
t½ = Half life
t = Time elapsed
Therefore, we have the following values from the questions:
Half life (t½)= 35 days
Initial or beginning amount = 100%
Ending amount = 90%
t = t½ × Log½ (Nt/No)
t = 35 × Log ½(90/100)
t = 5.3201082705768 days
Approximately = 5.3 days
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (Enter your answer using interval notation.)
Answer:
(-∞,-3) and (3,∞)
Step-by-step explanation:
f(x) = x³ − 27x + 3
1. Find the critical points
(a) Calculate the first derivative of the function.
f'(x) = 3x² -27
(b) Factor the first derivative
f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)
(c) Find the zeros
3(x + 3) (x - 3) = 0
x + 3 = 0 x - 3 = 0
x = -3 x = 3
The critical points are at x = -3 and x = 3.
2. Find the local extrema
(a) x = -3
f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57
(b) x = 3
f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51
The local extrema are at (-3,57) and (3,-51).
3, Identify the local extrema as maxima or minima
Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)
f'(-4) = 3x² -27 = 3(4)² - 27 = 21
f'(0) = 3(0)² -27 = -27
f'(4) = 3(4)² - 27 = 51
The function is increasing on the intervals (-∞,-3) and (3,∞).
The graph below shows the critical points of your function.
1) Given P(A) = 0.3 and P(B) = 0.5, do the following.
(a) If A and B are mutually exclusive events, compute P(A or B).
(b) If P(A and B) = 0.2, compute P(A or B).
2) Given P(A) = 0.4 and P(B) = 0.2, do the following.
(a) If A and B are independent events, compute P(A and B).
(b) If P(A | B) = 0.7, compute P(A and B).
Answer:
1) a) 0.8
b) 0.6
2) a) 0.08
b) 0.14
Step-by-step explanation:
1) Given
[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]
Let us learn about a formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]
(a) If A and B are mutually exclusive i.e. no common thing in the two events.
In other words:
[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]
(b) P(A and B) = 0.2
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]
*************************************
1) Given
[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]
Let us learn about a formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex] for dependent events
[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.
(a) If A and B are independent events :
Using the above formula for independent events:
[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]
(b) [tex]P(A / B) = 0.7[/tex]
Using above formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]
Someone please help me with this
Answer:
Step-by-step explanation:
Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 75 quarts of 3% butterfat milk. The mixture should contain ___ quarts of the 4% butterfat milk.
Answer:
50
Step-by-step explanation:
The amount of 4% butterfat milk is equal to x quarts , When 1% butterfat milk is equal to 75-x. The amount of butterfat in 4% butterfat milk is x/100*4=0.04x
The amount of butterflat in 1% butterfat milk is (75-x)/100= 0,75-0.01x
1The amount of butterflat in 75 quarts of 3% butterfat milk (our desired mixture) is 75/100*3= 2.25
This quantity (2.25) is the sum of butterfat from 4% butterfat milk and 1% butterfat milk(the sum of 0.04x and 0.75-0.01x)
the equation is
0.04x+0.75-0.01x=2.25
0.03x=1.5
x=50
#2. Given the following conditional statement; which answer is
represents the biconditional statement: "If Mr. Anderson is a ninja, then
he can run like Naruto."
Mr. Anderson is a ninja iff he can run like Naruto.
Mr. Anderson can run like Naruto iff he is a ninja.
Mr. Anderson is Naruto iff he can run like a ninja.
Answer:
Mr. Anderson can run like Naruto iff he is a ninja.
Step-by-step explanation:
This is because, in the statement "If Mr. Anderson is a ninja, then he can run like Naruto.", the sub-statement, "he can run like Naruto.", depends on the sub-statement 'If Mr Anderson is a Ninja'. This means that although Mr. Anderson is a Ninja, he can only run like Naruto if and only if he is a Ninja implying that if Mr Anderson is not a Ninja, he cannot run like Naruto.
So, Mr Anderson can run like Naruto iff he is a Ninja is the correct answer
Answer:
1
Step-by-step explanation:
In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014. (a) Write a differential equation to describe the relationship.\
Answer: i don’t kno I’m 6 years old
Step-by-step explanation:
given the vector with a manitude of 9m at an angle a of -80 degrees, decompose this vector into two vector components oarallel to the x axis with a slope of
Answer:
We have the magnitude, M, and the angle A.
(The angle is always measured from the +x-axis)
Then we have that:
x = M*cos(A)
y = M*sin(A)
in this case:
M = 9m
A = -80°
x = 9m*cos(-80°) = 1.562
y = 9m*sin(-80) = -8.86m
Now, the component parallel to the x axis is:
x = 9m*cos(-80°) = 1.562 m
And the slope of something parallel to the x-axis is always zero, as this is a constant line.
How do I solve |10-5| ?
Answer:
5
Step-by-step explanation:
Subtract
5
from
10
.
|
5
|
The absolute value is the distance between a number and zero. The distance between
0
and
5
is
5
.
5
What does the tape measure say Measurement # 4 is?
Answer:
It looks like 6 and one eighth of an inch.
Picking a card and spinning a spinner are independent events.
True
False
Answer:
True
Step-by-step explanation:
Both happened in different times and are seprate events
Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043 Keith reads that the mean nap is 22 minutes. The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. 1.39 or 1.43 or 2.88 or 0.70
Answer:
The t-statistic is [tex]t = 0.6956[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 22 \ minutes[/tex]
The standard deviation is [tex]s = 7.043[/tex]
The given data is 23, 35, 17, 30, 20, and 19.
Generally the sample mean is mathematically evaluated as
[tex]\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}[/tex]
[tex]\= x =24[/tex]
The t-statistic is mathematically evaluated as
[tex]t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }[/tex]
=> [tex]t = 0.6956[/tex]
Answer: 0.70
Step-by-step explanation:
Solve for x step by step:
2(4x-3)-8=4+2x
Answer:
3
Step-by-step explanation:
2(4x-3)-8=4+2x
8x - 6 - 8 = 4 + 2x
8x - 2x = 4 + 6 + 8
6x = 18
x = 18/6
x = 3
Answer:
[tex]2(4x - 3) - 8 = 4 + 2x \\ 2 \times 4x + 2 \times - 3 - 8 = 4 + 2x \\ according \: to \: bodmas \: first \: \times then + or - \\ so \\ 8x - 6 - 8 = 4 + 2x \\ 8x - 14 = 4 + 2x \\ 8x - 2x = 4 + 14 \\ 6x = 18 \\ x = \frac{18}{6} \\ x = 3 \\ thank \: you[/tex]
Complete the pattern ___ 8,579 ____85.7 8.57____
Answer:
the next one is .857 I hope this helps you :)
Solve the following system of equations.
2x + y = 3
x = 2y-1
ANSWER: ______
plz help me
(1,1) is your answer.
Work is shown below.
Any questions? Feel free to ask.
Answer: (1,1)
Step-by-step explanation:
A researcher was interested in whether a new sports drink could change people's running endurance. For one week, 6 participants continued with their normal routine and then their endurance was measured. The following week, the same participants were instructed to drink the new sports drink an hour before their endurance was measured. Below are your data.
Week I 90 100 110 110 85 95
Week 2 100 110 110 120 95 95
What type of analysis would be used on the above data?
a. Z-test
b. One sample t-test
c. Independent samples t-test
d. Dependent samples t-test
Answer:
The correct option is (d).
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have 2 measurements on the same item, person or thing. We should also use this test if we have 2 items that are being measured with a unique condition.
For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.
In this case, the same participants are selected for both the trials.
And the difference between the endurance before and after the usage of the new sports drink are noted.
Thus, the analysis that would be used on the data is the Dependent samples t-test.
Find the missing side or angle.
Round to the nearest tenth.
Answer:
[tex] b = 2.7 [/tex]
Step-by-step explanation:
Given:
< C = 53°
< B = 80°
a = 2
Required:
Find b
Solution:
The question given suggests we are given measures for a ∆.
To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.
=> A = 180 - (53 + 80) = 47°
Law of Sines: [tex] \frac{a}{sin(A} = \frac{b}{sin(B} [/tex]
Plug in the values into the formula
[tex] \frac{2}{sin(47} = \frac{b}{sin(80} [/tex]
Cross multiply
[tex] 2*sin(80) = b*sin(47) [/tex]
Divide both sides by sin(47) to make b the subject of formula
[tex] \frac{2*sin(80)}{sin(47} = b [/tex]
[tex] 2.69 = b [/tex]
[tex] b = 2.7 [/tex] (nearest tenth)
Write the standard form of the equation of the circle with radius 3 and center (−4,−10)
Answer:
(x + 4)² + (y + 10)² = 9
Step-by-step explanation:
The standard equation of a circle is written as seen below
(x - h)² + (y - k)² = r²
Where (h,k) is at the center and r is the radius
We want to find the standard equation of a circle that has a radius of 3 and a center at (-4,-10)
Remember r = radius so r = 3
and (h,k) is at center so h = -4 and k = -10
Now to find the standard equation of the circle we simply plug in the values of the variables (h,k and r) into the standard equation of a circle formula.
Equation of a circle: (x - h)² + (y - k)² = r²
r = 3, h = -4 and k = -10
Plug in values
(x - (-4))² + (y - (-10))² = 3²
Simplify
(x + 4)² + (y + 10)² = 9
And we are done!
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
An online polling site posed this question: "How much stock do you put in long-range weather forecasts?" Among its Web site users, 38, 528 chose to respond Complete parts (a) through (c) below.
a. Among the responses received, 3% answered with "a lot". What is the actual number of responses consisting of "a lot"?
b. Among the responses received, 18, 566 consisted of "very little or none". What percentage of responses consisted of "very little or none"?
c. Because the sample size of 38, 528 is so large, can we conclude that about 3% of the general population puts "a lot" of stock in long-range weather forecasts? Why or why not?
A. No, because the sample is a voluntary response sample, so the sample is not likely to be representative of the population.
B. Yes, because the sample is so large, the margin of error is negligible.
C. No, because even though the sample size is so large, there is still a margin of error.
D. Yes, because the sample size is large enough so that the sample is representative of the population.
Answer:
(a) 1155.84
(b) 48.2%
(c) D
Step-by-step explanation:
The number of total responses is, N = 38,528.
(a)
It is provided that 3% answered with "a lot".
Compute the actual number of responses consisting of "a lot" as follows:
n (a lot) = N × P (a lot)
= 38528 × 0.03
= 1155.84
Thus, the actual number of responses consisting of "a lot" is 1155.84.
(b)
The number of responses consisting of "very little or none" is,
n (very little or none) = 18,566
Compute the percentage of responses consisted of "very little or none" as follows:
[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]
[tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]
The percentage is: 0.482 × 100% = 48.2%.
Thus, the percentage of responses consisted of "very little or none" is 48.2%.
(c)
As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.
Thus, making the sample statistic an unbiased estimator of the population parameter.
And proving that the sample is a true representative of the population.
Thus, the correct option is (D).
Which relationships have the same constant of proportionality between y and x as the equation 3y=2x? SELECT 3 ANSWERS
*Correct Question:
Which relationships have the same constant of proportionality between y and x as the equation 3y=27x?
Answer:
A, B, C
Step-by-step explanation:
Given that [tex] 3y = 27x [/tex] , we can simplify to get a proportionality statement that exists between X and y. Thus
[tex] 3y = 27x [/tex]
Divide both sides by 3
[tex] \frac{3y}{3} = \frac{27x}{3} [/tex]
[tex] y = 9x [/tex]
Thus, we can say, y would always be 9 times the quantity of x.
From the options given, examine which options have this proportionality statement as well.
Option A, y = 9x is same as the statement.
Option B, 2y = 18x, conforms to the same statement. If we simply further, we would have y = 9x
Option C, the graph shows that when x = 1, y = 9. This also confirms to the same constant of proportionality in the given equation.
Option D and E do not have same constant of proportionality.
The right options are A, B, and C.
The graph below represents the function f.
f(x)
if g is a quadratic function with a positive leading coefficient and a vertex at (0,3), which statement is true?
А.
The function fintersects the x-axis at two points, and the function g never intersects the x-axis.
B
The function fintersects the x-axis at two points, and the function g intersects the x-axis at only one point.
c.
Both of the functions fand g intersect the x-axis at only one point.
D
Both of the functions fand g intersect the x-axis at exactly two points.
Answer: А.
The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
In the graph we can see f(x), first let's do some analysis of the graph.
First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.
The arms of the graph go up, so the leading coefficient of f(x) is positive.
The vertex of f(x) is near (-0.5, -2)
The roots are at x = -2 and x = 1. (intersects the x-axis at two points)
Now, we know that:
g(x) has a positive leading coefficient, and a vertex at (0, 3)
As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.
As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.
so:
f(x) intersects the x-axis at two points
g(x) does not intersect the x-axis.
The correct option is A.
Answer:
The answer is A.) The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
I took the test and got it right.
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation? 0.1 1 10
Answer:
1
Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.
Given that the image and the preimage of the triangle are congruent, their
dimensions are the same.
The scale factor of dilation of an image of a triangle that is congruent to the pre-image is; 1Reasons:
Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.
Given that the image and the preimage are congruent, we have;
AB ≅ A'B'
BC ≅ B'C'
AC ≅ A'C'
By definition of congruency, we have;
AB = A'B'
BC = B'C'
AC = A'C'
The scale factor of dilation is given as follows;
[tex]\displaystyle Scale \ factor = \mathbf{ \frac{A'B'}{AB}} = \frac{AB}{AB} = 1[/tex]Therefore;
If the image is congruent to the pre-image, the scale factor of dilation is; 1Learn more about dilation transformation here:
https://brainly.com/question/5453159