The pooled estimate of the variance is 187.650 and the test statistic is -2.32
Pooled estimate of the varianceThe dataset is given as:
Regular price 138 124 89 112 116 123 98
Reduced price 124 134 154 135 118 126 133 132
Let the regular price be dataset 1 and the reduced price be dataset 2.
So, we have:
#1: 138 124 89 112 116 123 98
#2: 124 134 154 135 118 126 133 132
Calculate the sample means and the sample standard deviations using a graphing calculator.
#1
[tex]\sigma_1 = 16.56[/tex]
[tex]\bar x_1 = 114.29[/tex]
[tex]\sigma_1^2 = 274.24[/tex]
#2
[tex]\sigma_2 = 10.65[/tex]
[tex]\bar x_2 = 132[/tex]
[tex]\sigma_2^2 = 113.43[/tex]
The pooled estimate of the variance is:
[tex]\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}[/tex]
This gives
[tex]\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}[/tex]
Evaluate the factors
[tex]\sigma_p^2 = \frac{2439.45}{13}[/tex]
Divide
[tex]\sigma_p^2 = 187.65[/tex]
Hence, the pooled estimate of the variance is 187.650
The test statisticThis is calculated using:
[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]
This gives
[tex]t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}[/tex]
This gives
[tex]t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}[/tex]
Evaluate the product
[tex]t = \frac{-17.71}{\sqrt{58.08214}}[/tex]
Evaluate the exponent
[tex]t = \frac{-17.71}{7.62}[/tex]
Divide
t = -2.32
Hence, the test statistic is -2.32
The decision about the null hypothesisThe critical value at 0.025 significance level is -1.96
-2.32 is less than -1.96
This means that we accept the null hypothesis
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simplify (x^-1y^2)(-3x^2y^0)
Please help and explain
We have [tex]x^{-n} = \frac1{x^n}[/tex] if [tex]n[/tex] is a positive integer and [tex]x\neq0[/tex], as well as [tex]x^0 = 1[/tex] if [tex]x\neq0[/tex]. So right away we can simplify to
[tex]\left(x^{-1} y^2\right) \left(-3 x^2 y^0\right) = \left(\dfrac{y^2}x\right) \left(-3x^2\right) = -\dfrac{3x^2y^2}x[/tex]
If [tex]x=0[/tex], then the starting expression is undefined. So we accept that [tex]x=0[/tex], in which case [tex]\frac xx = 1[/tex], and the overall expression simplifies to
[tex]\left(x^{-1} y^2\right) \left(-3 x^2 y^0\right) = \boxed{-3xy^2}[/tex]
Compare using <,=,or >.
-5/12 and -3/4
Answer:
-9/12 < -5/12
Step-by-step explanation:
-5/12 = -5/12
-3/4 = -9/12
-9/12 < -5/12
Suppose that a classroom has 4 light bulbs. The probability that each individual light bulbs work is 0. 6. Suppose that each light bulb works independently of the other light bulbs. What is the probability that none of the 4 light bulbs work?.
Answer:
(0.4)⁴
Step-by-step explanation:
• The probability that each individual light bulbs work is :
1 - 0. 6 = 0.4
Then
•• the probability that none of the 4 light bulbs work is :
(0.4)×(0.4)×(0.4)×(0.4)
= (0.4)⁴
= 0.0256
please help me
i dont understand this
Answer and Explanation:
Area is the measure of how large a 2-dimensional space is.
For example, a 6 × 2 grid of eggs contains 12 egg spaces.
In math, the unit for area is always a linear measurement squared (for example [tex]m^2[/tex], [tex]cm^2[/tex], and [tex]ft^2[/tex]).
Perimeter is the measurement of the border of a space.
For example, the fence around a 5 × 10 ft garden can be solved for by adding up each individual side of fencing (see the attached image).
The unit for perimeter is always a linear measurement, like m, cm, or ft.
Using this knowledge, for question a, simply multiply the side lengths to get the area. Remember to use [tex]ft^2[/tex] as the unit.
For question b, the answer is perimeter, since it is measuring the border length of the model court.
For question c, the answer is area, since it is measuring the size of the model court's wooden floor.
Which function represents a reflection of f(x) = 2*
Answer:
h(x)=2x-1
Step-by-step explanation:
The Given function is
f(x) =2*(0.35)* x
→y=0.7* x→Pre image
The line passes through first and third quadrant.
it is equation of straight line passing through origin and slope =0.7.
When this line is reflected over y axis , the equation of new line will be
→y= - 0.7 x⇒image
Slope of image will be = -0.7
The Image passes through Second and fourth Quadrant.
B = 54°, c = 15, a =_?___ (Round answers to
the nearest hundredth.)
Answer:
a ≈ 8.82
Step-by-step explanation:
using the cosine ratio in the right triangle
cos54° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{a}{15}[/tex] ( multiply both sides by 15 )
15 × cos54° = a , then
a ≈8.82 ( to the nearest hundredth )
The magnitude of the electrical force acting between a 2.4 × 10–8 c charge and a 1.8 × 10–6 c charge that are separated by 0.008 m is n, rounded to the tenths place.
The magnitude of the electrical force acting between both the given charges which are separated by 0.008 m is 6.07 N.
Given Charges 2.4*[tex]10^{-8} C[/tex] and 1.8 *[tex]10^{-6} C[/tex] that are separated by 0.008 m.
We have to find the magnitude of the electrical force acting between the charges. Magnitude is the property which determines the size of an object or process. Force is an influence that can change the direction of an object.
To find the magnitude we have to use Coulomb's law which says that
[tex]F_{E}=K*(q_{1}*q_{2}/d^{2}[/tex]
where K is Coulomb's constant whose value is [tex]8.9910^{9}Nm^{2} C^{2}[/tex].
[tex]q_{1}[/tex]=[tex]2.6*10^{-8} C[/tex] and
[tex]q_{2}=1.8*10^{-6} C[/tex] are the electric charges.
d=0.008m is the separation distance between the charges.
Putting the values in the given formula we get:
[tex]F_{E} =8.99(10)^{9}Nm^{2}/C^{2} *(2.4(10)^{-8}C(1.8(10)^{-6}C)/(0.008m)^{2}[/tex]
=6.07 N
Hence the magnitude of force acting between [tex]2.4*10^{-8} C[/tex] and [tex]1.8*10^{-6}C[/tex] is 6.07 N.
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Answer:
6.1Step-by-step explanation:
Please assist me with this problem
Answer:
x = 192
Step-by-step explanation:
The three right triangles in the figure are all similar, so their sides are proportional.
ProportionThe length marked x is the long side of the smallest triangle, and the short side of the middle-size triangle. The long side of the middle-size triangle is ...
400 -144 = 256
We now have enough information to write the proportion ...
long side/short side = x/144 = 256/x
Multiplying by 144x gives ...
x² = (144)(256)
x = √(144×256) = 12×16 = 192
The length x is 192 units.
Grogg has two bags of marbles, each of which contains some red marbles and some blue marbles (and no marbles of any other color). The ratio of red marbles to blue marbles in the first bag is 3:5. The ratio of red marbles to blue marbles in the second bag is 3:2. When the two bags of marbles are mixed together, the ratio of red marbles to blue marbles is 11:9. What is the ratio of the number of marbles in the first bag to the number of marbles in the second bag?
The ratio of the number of marbles in the first bag to the number of marbles in the second bag is 2:7.
How to determine the required ratio?First of all, we would assign the variables x and y to the marbles in the first and second bag respectively. Also, let F and S represents the first and second bag respectively.
For the first bag, we have:
Ratio = 3:5 = 3x:5x = 3x + 5x = 8x
For the first bag, we have:
Ratio = 3:2 = 3y:2y = 3y + 2y = 5y
Tabulating these values, we have:
Red Blue
First bag 3x 5x
Second bag 3y 2y
The two red marbles = 3x + 3y.
The two blue marbles = 5x + 2y.
Next, we would write the ratio of the total red marbles to the total blue marbles:
Total red/Total blue = 11/9
(3x + 3y)/(5x + 2y) = 11/9
Cross-multiplying, we have:
27x + 27y = 55x + 22y
27y - 22y = 55x - 27x
5y = 28x
y = 28x/5
y = (28/5)x
y = 5.6x
Remember from the second bag, S = 5y:
S = 5(5.6x)
S = 28x.
Thus, the ratio of the number of marbles in the first bag to the number of marbles in the second bag is given by:
F/S = 8x/28x
F/S = 8/28
F/S = 2/7
F:S = 2:7.
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help me please ASAP
Answer:
on the percentage of the buses on time ,30 is not included
Answer:
the numbering on the y axis
c=pd for d pls help with steps
The given equation, when solved for d gives d = c/p
Subject of formulaeFrom the question, we are to solve for d in the given equation
The given equation is
c = pd
To solve for d, we will divide both sides by p
c/p = (pd)/p
c/p = d
∴ d = c/p
Hence, the given equation, when solved for d gives d = c/p
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** Which of the following is parallel to the line 2x + 4y = 16 (A) y = 2x + 5 (B) y = -x + 4 (C) y = -x + 8 (D) y = 2x + 5 =-
Answer:
None of them.
Step-by-step explanation:
Each and every straight line is of one kind in terms of its pattern: it can be presented in the view of [tex]y = kx + b[/tex]: [tex]k[/tex] is the slope or gradient of the line, [tex]b[/tex] is the y-intercept of the line. I will not let the cat out of the bag if I say that any parallel lines do not intersect one another, hence they should have the same value of coefficient [tex]k[/tex].
[tex]2x + 4y = 16 \Leftrightarrow x + 2y = 8 \Leftrightarrow 2y = -x + 8 \Leftrightarrow y = - \frac{1}{2}x + 4[/tex]
Therefore, our line has [tex]k = - \frac{1}{2}[/tex] and [tex]b = 4[/tex] coefficients.
(A) [tex]k = 2, b = 5;[/tex]
(B) [tex]k = -1, b = 4;[/tex]
(С) [tex]k = -1, b = 8;[/tex]
(D) [tex]k = 2, b = 5;[/tex]
Recapitulating this: none of them have the same coefficient [tex]k[/tex], thus none of them suit us.
Find the missing part of the
unit rate:
21 Cards
3 Piles
=
[?] cards
Pile
Answer:
7
Step-by-step explanation:
Given,
3 Piles = 21 cards
1 Pile = (21 ÷ 3) cards
= 7 cards.
Answer:
7
Step-by-step explanation:
Because there is 7 cards in 1 pile. it follows the ratio of 7:1
Find the value of x:
Answer:
x=20
Step-by-step explanation:
a) isolate the variable
K-8=12
10-4=6
Which expression is equivalent to[tex]18x\sqrt{14x^8}/6\sqrt{7x^4[/tex] if [tex]x\neq 0[/tex]
a. [tex]12x^4\sqrt{2}\\[/tex]
b. [tex]3x^4\sqrt{2}[/tex]
c. [tex]3x^4\sqrt{7}[/tex]
d. [tex]3x\sqrt{2}[/tex]
The equivalent expression is [tex]3x^4\sqrt{2}[/tex] . Option B
How to determine the expression
Given the expression
= [tex]\frac{18x\sqrt{14x^8} }{6\sqrt{7x^4} }[/tex]
Divide the multipliers, we have
= [tex]\frac{3x\sqrt{14x^8} }{7x^4}[/tex]
Let factorize the numerator in square root
= [tex]\frac{3x \sqrt{7x^4 * 2x^4} }{7x^4}[/tex]
Eliminate the like factor in both the numerator and denominator
= [tex]3\sqrt{2x^4}[/tex]
Let's bring forth the 'x' factor, we have
= [tex]3x^4\sqrt{2}[/tex]
Thus, the equivalent expression [tex]3x^4\sqrt{2}[/tex] . Option B
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Need solution ~
[tex] \sf \hookrightarrow24x =( 96 \div 2) + (55 - 50 - 4 + 5 - 6)[/tex]
[tex]24x =( 96 \div 2) + (55 - 50 - 4 + 5 - 6) \\ \\ 24 x = 48 + 0 \\ \\ 24x = 48 \\ \\ x = \frac{48}{24} \\ \\ x = 2.[/tex]
It was a 5ft. by 5ft. sandbox. how many square feet would mr. potato head be able to walk inside the box?
25 square feet would mr. potato head be able to walk inside the box.
What is square ?A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is side square.Each side of square is 90° .Given,
length and breadth of sandbox is 5 ft.
Now, We apply formula of area of square.
5 × 5 = 25 ft²
Therefore, 25 ft² would mr. potato head be able to walk inside the box.
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I’m confused, can someone explain?
Answer:
-3 < x < 7
Step-by-step explanation:
The domain of a graph is all of the x-values that are included in the function. Since the graph is continuous (one connected line), you can determine the domain by identifying the x-values associated with the line's endpoints. These values are x = -3 and x = 7. Remember, the x-value located on a closed dot is not included in the domain. Therefore, the domain of the graph is -3 < x < 7.
Which statement about this figure is true?
It has reflectional symmetry with one line of symmetry
It has rotational symmetry with an angle of rotation of 90%
It has no reflectional symmetry
It has no rotational symmetry
Option C. The truth statement about the figure is that it has no reflectional symmetry.
What is reflectional symmetry?
This is the term that is also used to refer to mirror symmetry. It is known to be used in respect to reflections.
The shape that we have here can be seen that it does not have this type of symmetry.
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coach tim needs to fill five
volleyballs with air. if each
volleyball has a diameter of 8
inches, what is the total volume
of air that coach tim will
need? round to the nearest
whole number
The total volume of air that coach Tim will need to fill is [tex]1,340^{3} inches[/tex].
To find the total volume of air that coach Tim will need:
The formula of volume = [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × [tex]r^{3}[/tex]
Given - Diameter of volleyball = 8 inches
So, the radius of volleyball = [tex]\frac{8}{2}[/tex] = 4 inches
Now, put the values in the formula of volume as follows:
[tex]\frac{4}{3} * \pi * 4^{3}[/tex]
[tex]\frac{4}{3} * \pi * 64[/tex]
[tex]\frac{4}{3} * 3.14 * 64\\\frac{4}{3} * 201.06\\4 * 67.02\\268.08[/tex]
To find total volume = [tex]268.08 * 5[/tex]
[tex]= 1340.4[/tex]
Rounding off to the nearest whole number = [tex]1,340^{3} inches[/tex]
Therefore, the total volume of air that coach Tim will need to fill is [tex]1,340^{3} inches[/tex].
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11. Multiple choice. Determine the volume of a cube with a side
length of 14 cm.
A. 196 cm²
12
SL
B. 196 cm³
cm
C. 14 cm²
D. 2744 cm³
3
Answer:
D
Step-by-step explanation:
the volume (V) of a cube is calculated as
V = s³ ( s is the side length ) , then
V = 14³ = 2744 cm³
Answer:
D. 2744 cm³
Step-by-step explanation:
volume can be found by multiplying length × width × height
because we know that this is a cube, all side lengths are the same (meaning length, width, and height will all be the same)
so, we know our side length is 14cm, meaning that all of our measurements {length/width/height} are 14cm
length × width × height = volume
14 × 14 × 14 = 2744
when we write volume, we write it as cubed (x³)
{similarly, when we write area, we write it as squared (x²)}
so, we would write the volume of this cube to be 2744 cm³
(option D)
hope this helps! have a lovely day :)
The Dysons love to give parties. Last Friday, they gave a party and the doorbell rang 15 times. At the first ring, one guest arrived. Each time the doorbell rang after that, two more guests arrived than the time before. On Saturday they had another party. At the first ring of the doorbell a single guest arrived, at the second ring two guests appeared, at the third ring three guests and so on. If the doorbell rang 20 times Saturday night, how many guests attended? Was this party bigger than Friday's party? How do you know? 2. Draw a picture to show one way to solve this problem.
The number of guests on Saturday is 210 and it is greater than the party of Friday (15 guests)
Calculations and ParametersLast Friday had 15 guests
The sum total of guests on Saturday= 210 guests (using Arithmetic progression)
Using the arithmetic progression sum formula:
1 * 20 + (20 * 19/2) * 1= 210
Therefore, 210 > 15, so we can conclude that the Saturday night party was bigger than Friday's own.
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Complete the following constructions. leave all construction arcs on your paper.
-5 5/6-(-2 1/3)+5 1/6
Answer: 1.66666666667
If we changed the 2 to a 5 in the domain restriction x < 2 what would happen to the graph?
Answer:
what would happen is that the dotted line that is at 2 and down right now would go up to 5
Hope This Helps!!!
Five regular six-sided dice are rolled. How many ways are there to roll the dice so that the total of the numbers on the five dice is 14
If five regular six sided dice are rolled then there are 540 ways through which sum of numbers coming after rolling will be 14.
Given Five regular six sided dices are rolled.
From stars and bars the number of n tuples of natural numbers summing up to k is given by
[tex](k-1\\n-1)[/tex]
For k=14 and n=5
[tex](14-1 \\5-1)[/tex]
=[tex](13\\4)[/tex]
=715
Some of these will contains a number greater than 6.To get the number of 5 tuples that correspond to 5 rolls of a six sided dice we need to subtract from 715.
Total 5 tuples summing up to 14 for which no element is greater the 6 is given as under:
N=[tex](13/4)-5(6/3)-5(5/3)-5(4/3)-5(3/3)[/tex]
where last term comes from the 5 tuples containing one 10 and fours'
=715-100-50-20-5
=540
Hence there are 540 such ways which sum to 14 when five six sided dices are rolled.
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Glenn the owner of a hardware store originally paid $54.60 for 15 tool sets. at his year-end clearance sale he sold the last tool set for$24.00 how much money did he lose on the last tool set
The amount of money that Glenn lost on last tool set is $30.60.
Given sale value of 15 tool set 1 year before is $54.60 and the sale value of last tool at year end is $24.00 by Glenn.
Sale value is the price which we get by selling the good including the profit and cost of the product.
In this question it is given that 15 tools sets, it does not mean that 15 sets are sold.
Using the formula
Amount lose=Original amount paid- selling price.
Now put the values in the formula:
Amount lose=$54.60-$24.00
Amount lose=$30.60.
Hence the amount of money he lost on the last tool set is $30.60.
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Which linear equation would produce a y-intercept of (0, - 7) and a slope of 5?
a.)
y = 5x - 7
b.)
y = -5x + 7
c.)
y = -7x + 5
d.)
y = 7x - 5
Answer:
a.) y = 5x - 7
Explanation:
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
insert values
[tex]\sf y - (-7) = 5(x - 0)[/tex]
simplify
[tex]\sf y + 7 = 5x[/tex]
rewrite
[tex]\sf y = 5x - 7[/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Which linear equation would produce a y-int. of (0,-7) and a slope of 5?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Take the second co-ordinate of the point (0,-7), this is your y-intercept.
Next, just put it into y=mx+b in the place of b.
[tex]\bf{y=mx-7}[/tex] | now put in the slope, 5
[tex]\bf{y=5x-7}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y=5x-7}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]
∞
For every 3 kids movies, there will be how many horror movies?
kids movies = 24
horror= 32
Answer:
The answer will be 8
Step-by-step explanation:
SInce you notice there is movies with an 8 difference....
Answer:
4 horror movies
Step-by-step explanation:
This seems to be a problem related to ratios. We are given that, for every 24 kids' movies, there are 32 horror movies. We need to figure out how many horror movies there would be if there were just 3 kids' movies. We can set up an equation using proportions:
[tex]\frac{24}{32}=\frac{3}{x}[/tex]
We don't know how many horror movies there would be so we can let this quantity equal x. Now, we can cross multiply and solve for our unknown:
[tex]24x = 3*32\\24x = 96\\x = 4[/tex]
This means that there are 4 horror movies
(05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to
answer the following questions:
y > 5x + 5
y>-2x+1
Part A: Describe the graph of the system, including shading and the types of lines graphed.
Provide a description of the solution area. (6 points)
Part B: Is the point (-2, 5) included in the solution area for the system? Justify your answer
mathematically. (4 points)
(10 points)
The point (-2, 5) is not included in the solution area
The graph of the inequalitiesThe system of inequalities is given as:
y > 5x + 5
y > -2x+1
See attachment for the graph.
Since the inequalities use the greater than symbol, then the lines of the inequalities would be a dotted line and the upper part would be shaded
The solution areaThe point is given as:
(-2, 5)
The point (-2, 5) is not in the shaded area of the system of inequalities
Hence, the point is not included in the solution area
Mathematically, we have:
5 > 5 * -2 + 5 ⇒ 5 > -5 --- true
5 > -2 * -2 +1 ⇒ 5 > 5 --- false
Since both inequalities are not true, then the point is justified
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