The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).
Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.
From the given information,
Let n=101 represents the size of the sample.
Let [tex]\bar{x}[/tex]= 12.9 represents the mean of the sample.
Let s= 3.2 represents the standard deviation of the sample.
Degrees of freedom:
df = n-1
df= 101-1
df= 100
The critical value of t at 0.2 level of significance with 100 degrees of freedom is,
[tex]\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end[/tex]
The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:
[tex]\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end[/tex]
Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).
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Given AB=10cm, CD=11cm, and AD=39cm, find the length of BC
Answer:
BC = 18 cm
Step-by-step explanation:
As we can see from the diagram:
AB + BC + CD = AD
⇒ 10 cm + BC + 11 cm = 39 cm
⇒ BC + 21 cm = 39 cm
⇒ BC = 39 cm - 21 cm
⇒ BC = 18 cm
Solve for m. 3/4m>−12 m>−16 m<−16 m>−9 m<−9
Answer: m > -16
Step-by-step explanation:
[tex]\frac{3}{4}m > -12\\\\m > -\frac{4}{3}(12)=-16[/tex]
If the side length of of rectangle is 3x-3 and the top length is 6, how do I write a linear equation the represents the area and a linear equation that represents the perimeter, all measurements are in cm if that is useful.
Perimeter of the rectangle is: 6x + 6 cm
Area of the rectangle is: 18x - 18 cm²
What is the Area and Perimeter of a Rectangle?Area = (length)(width)
Perimeter = 2(length + width).
Given the following:
Length of rectangle = 3x - 3
Width = 6
Area = (3x - 3)(6)
Area = 18x - 18 cm²
Perimeter = 2(3x - 3 + 6) = 2(3x + 3)
Perimeter = 6x + 6 cm
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Express the formula in terms of the height, Use that formula to find the height when the volume is and the radius is
The formula to find the height of the Cylinder is; h = V/(πr²) and at V = 45π and r = 3, we have; h = 5
How to change the subject of the formula?We are given the formula for volume of a cylinder as;
V = πr²h
where;
h is height
r is radius
To make h the subject, let us divide both sides by πr² to get;
V/(πr²) = h
At V = 45π and r = 3, we have;
h = 45π/(πr²)
h = 45/3²
h = 5
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How do i find the slope of these points? (−4, 3) and (2, 9)
Answer:
Divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Step-by-step explanation:
Answer:
The value of the slope b/n these two pts. will be 1.
Step-by-step explanation:
Greetings !
For finding slope from two points of a line (x₁, y₁) and (x₂, y₂), we use the formula (y₂ - y₁) / (x₂ - x₁).
Thus, m=(y₂ - y₁) / (x₂ - x₁)
m=(9-3)/(2-(-4))m=6/6m=1.Convert 45 32’ 55” into decimal degrees to the nearest two decimal places
The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
Converting degrees into decimalThe given degree is:
45⁰ 32' 55''
This can be converted to decimal as shown below
[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]
This can be simplified further as:
[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]
Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
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If you apply the changes below to the exponential parent function f(x)=2^x, what is the equation of the new function? Shifts five units to the right, Shifts seven units down
the equation of the new function is:
[tex]g(x) = 2^{x - 5} - 7[/tex]
What is the equation of the new function?We have a function:
[tex]f(x) = 2^x[/tex]
And we want to shift it five units to the right, and seven units down, then the new function will be:
[tex]g(x) = f(x - 5) - 7[/tex]
If we now replace f(x), we get:
[tex]g(x) = 2^{x - 5} - 7[/tex]
That is the equation of the new function.
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The Apollo space program lasted from 1967 until 1972 and included 13 missions.The missions lasted from as little as Z hours to as long as 30ours.The duration of each flight is listed below. 9 195 241 295 142% 142% 147 a.Expain why the flight times b.Find Mean and the Median of flight times c.Find range and the standard deviation of flight times
The mean and the median based on the information given will be 166.08 and 195.
How to calculate the value?It should be noted that the mean is also the average. It's gotten by adding all the numbers and dividing by 13. This will be 166.08.
The median is simply the middle number. This will be 195.
The range will be:
= 301 - 7
= 294
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18. Find the value of 3x² x 2(x-3y) divide by 6 when x is 6 and y is 1
Answer:
11664
Step by Step:
Evaluate for x=6,y=1
3(6^2)(6^2)(6−(3)(1))
3(6^2)(6^2)(6−(3)(1))
=11664
Which is the only state that uses to calculate its area
Answer:
The answer is circle.
Step-by-step explanation:
For all the rest of the shapes, we use certain base x height formulas. Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula [tex]\pi r^{2}[/tex] where r= radius.
Question is attached as an image
The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].
The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].
What are the general and particular solutions of the logistic equation?
In this question we are before a type of ordinary differential equation known as equation with separable variables, that is to say, that variables t and y can be separated at each side of the expression in order to find a solution:
dy / dt = 3 · y · (1 - y /14)
dy / [(- 3 / 14 ) · y · (y - 14)] = dt
Then, we simplify the expression by partial fractions and integrate the resulting expression:
- (1 / 14) ∫ dy / y + (1 / 14)∫ dy / (y - 14) = - (14 / 3)∫ dt
- (1 / 14) · ㏑ |y| + (1 / 14) · ㏑ |y - 14| = - (14 / 3) · t + C, where C is the integration constant.
㏑ |(y - 14) / y| = - (14 / 3) · t + C
[tex]1 - \frac{14}{y} = C\cdot e^{-\frac{14\cdot t}{3} }[/tex]
[tex]\frac{14}{y} = 1 - C \cdot e^{-\frac{14\cdot t}{3} }[/tex]
[tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex]
The general solution of the logistic equation is [tex]y(t) = \frac{14}{1 - C\cdot e^{-\frac{14\cdot t}{3} }}[/tex].
If y(0) = 10, then the particular solution of the differential equation is:
10 = 14 /(1 - C)
1 - C = 1.4
C = - 0.4
The particular solution of the logistic equation is [tex]y(t) = \frac{14}{1 + 0.4 \cdot e^{-\frac{14\cdot t}{3} }}[/tex].
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Landscape artists frequently hand-draw their landscape layouts (blueprints) because this allows them more creativity and precision over their plans. Although done by hand, the layouts must be extremely accurate in terms of angles and distances.
a. A landscape artist has drawn the outline of a house. Describe three different ways to make sure the corners of the house are right angles.
b. A bench needs to be placed in the exact middle of two trees. Describe three different methods the designer can use to find out where to place the bench.
c. The landscape designer has drawn an angle on one side of the yard and wants to draw the same angle on the other side. Describe three different ways he can do this.
The information given about the landscape is illustrated below:
How to explain the landscape?a. You'll need a measuring tape, two range poles, pegs, and three people.
The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.
Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.
B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.
Method 2; By use of a compass to bisect the distance between both points.
Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.
C The three different ways he can do this.
1) by using a protractor
2) by finding a point
3) by extending the line of the angle until it reaches the other side of the field.
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In the following diagram, line m is parallel to line n and line q intersects the parallel lines at
Answer:
108°
Step-by-step explanation:
We know for a theorem that A = B, so:
4x + 28 = 2x + 68
Isolating the x:
2x = 40
x = 20
Now let's plug in the equation for A:
4(20) + 28 = 108°
What is the equation of the line that passes through the point (5,4) and has a slope of 2
Hello,
[tex]y = ax + b[/tex]
We know the slope is 2 so :
[tex]y = 2x + b[/tex]
The equation of the line that passes through the point (5,4) so :
[tex]4 = 2 \times 5 + b[/tex]
[tex]4 = 10 + b[/tex]
[tex]b = 4 - 10[/tex]
[tex]b = - 6[/tex]
The equation of the line that passes through the point (5,4) and has a slope of 2 is :
[tex]y = 2x - 6[/tex]
y = 2x - 6
Step-by-step explanation:Most lines are written in slope-intercept form, but we can use slope-point form in situations like this.
Slope-Point Form
The formula for slope-point form is [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]. So, we can plug in the information we have, the point and slope.
y - 4 = 2(x - 5)This is an equation for the line given to us. However, this form can be simplified further.
Slope-Intercept Form
Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find the most simplified form of the equation we need to use the properties of equality.
First, distribute the 2
y - 4 = 2x - 10Next, add 4 to both sides
y = 2x - 6Now, we have the equation for the line in slope-intercept form. Both of the equations technically meet the requirements for the question, but slope-intercept is more common to use.
on a number line, suppose point E has a quotient of -1, and EG = 12. what are the possible coordinates of point G?
-13, or +11, because they are both 12 places away from -1.
Please help! Solve this
The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1
How to solve the equation?The equation is given as:
[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]
Split the equation as follows:
[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]
[tex]y = 1 + x^2[/tex]
Next, we plot the graph of both equations (see attachment)
From the attached graph, the intersection point is (1, 2)
Remove the y value
x = 1
Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1
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You need 30 quarts of water based paint to paint the interior of a house. If the price ofa gallon of paint is $22, how much will cost the paint for the interior of the house?
An auction website charges $1 for a bid. The bidding starts at 1¢ and goes up 1c at a time. A television that is worth
$2000 is won, on average, with a bid of $160. You make one bid at random.
Find the expected value of the outcome of the bid. (Write as an exact decimal, with a negative sign, if necessary.)
Expected Value: $
The expected value of the outcome of the bid is $0.18
So let's start by counting how many bids are placed up to a total of 160.
100*160 = 16000.
What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)
Your odds of winning are 1/16000 (1 bid out of 16000).
If you win, your profit is 1920 ($2000 minus $80.00).
1920/16000 is $0.12
Your cost to enter the auction is $1, and your average winning offer is $0.12.
The result is $0.18 (0.12-1=-0.88).
Thus the expected value of the outcome of the bid is $0.18
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In Hawaii”s Kona iron man competition, Gretchen swims the first 7/8 of a mile in 70 minutes. At this pace, how many minutes will it take for Gretchen to swim the entire 2 2/5 mile course
It would Gretchen 192 minutes to swim the entire 2 2/5 mile course.
What is speed?
Speed is distance divided by the time taken to cover the distance.
In this case, we can determine distance covered in a minute by dividing the speed by the distance, which is distance of 7/8 mile(i.e. 0.825 mile) over the time take to cover the distance.
speed per minute=0.825/70
speed per minute=0.0125 mile/minute
With this, we can determine the time in minutes it would take to cover 2.4 miles(2/5=0.4)
0.0125=2.4/time
0.0125*time=2.4
time=2.4/0.0125
time=192 minutes
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Question about a rational expression
The equation is -9=6/v
In the explanation, it tells me to multiply v on both sides. My question is why do you multiply v on both sides and not 6?
When I did the problem I multiplied 6 on both sides and got -54=v, but apparently the answer is -2/3 so I’m confused as to why you multiply v on both sides and not 6.
A cube has it's one edge 5 cm and a cuboid measures 4m multiple 3m multiple 2m which has a greate surface area and how much ?
Answer:
Gievn that l=3m,b=5m,h=4m
L.S.A=2(l+b)h
=2×(3.5)×4
=2×8×4
=64sq.m
Step-by-step explanation:
Please please Help!
Need Answer to Multiple Choice! Brainliest!
The scores on the ACT exam are normally distributed with a mean of 21 and a standard
deviation of 5. If we selected a random sample of 37 test takers, what is the probability that the
sample mean of those test takers who would be less than a 19.8?
a) .0721
b) .5000
c) .0808
d) .0582
Answer:
a) 0.0721
Step-by-step explanation:
Let the random variable X be the score on the ACT exam.
Given:
mean (μ) = 21standard deviation (σ) = 5Therefore, the random variable X is normally distributed:
[tex]X \sim\textsf{N}(21,5^2)[/tex]
Z-score for a sample mean
[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]
[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]
Given:
[tex]\overline{x}[/tex] = 19.8μ = 21σ = 5n = 37Therefore, the test statistic is:
[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]
Using the Z-tables to find the probability:
[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]
find the slope of this line
AC and BD intersect at point E which is inside the circle. Find the measure of Arc AB if Arc CD = 60 degrees and Angle CED = 35 degrees.
Th measure of arc AB will be 60 degrees
Circle theoremThe figure shown shows a circle with lines AC and BD intersecting the circle at the point E
From the figure given the measure of the arc AB is congruent to the arc CD.Given that the measure of arc CD is 60 degrees, hence the measure of arc AB will also be 60 degrees
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What is the measure of ABC in the figure below?
Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.
Hence, option D is the correct answer.
What is the measure of ABC in the figure below?Two angles are called complementary when their measures add to 90 degrees.
From the diagram; Angle ABD and Angle DBC are complementary angles that add up to make 90 degrees.
Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.
Hence, option D is the correct answer.
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Please help me answer this question, 20 POINTS!
Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
It's 4 buns & 5 cakes
Hope my explanation to the other one helps, if not, you can draw them; while following the steps & you may get it better.
E.g draw a box for the bun & a circle for the cake, then, adding them up to get the 95p. Also, you keep taking away from 435p
explain me the formula for a point that forms a partiton of a ratio on a segment in the 2nd grade real numbers.
Let’s say the ratio a:b, our formula those becomes
{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}
From the question, we can identify that
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
The partition point is (-7/2, 23/4)
How to determine the partition point?The given parameters are:
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
The partition point is calculated as:
(x, y) = ((bx1 + ax2)/(a + b) ,( by1+ay2)/a+b)
So, we have:
(x, y) = ((3 * -6 + 1 * 4)/(1 + 3) ,(3 * 8 + 1 * -1)/1+3)
Evaluate
(x, y) = (-14/4, 23/4)
Simplify
(x, y) = (-7/2, 23/4)
Hence, the partition point is (-7/2, 23/4)
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How many proportional relationships are shown in the coordinate plane below/
Answer:
I wish I could I didnt do good with this in math
At some department store, all suits are reduced 20% from the retail price. If a man purchased a suit that originally retailed for 231.20 how much did he save?
well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]
Anyone know the answer please teach me
Answer: Look at step by step
Step-by-step explanation:
(a) There are 119 stocks that increased in price out of 246 stocks so the probability of selecting a stock that is increased in price is 119/246 = 48.37%
(b) There are 112 stocks where it pays dividends so the probability so the probability of selecting a stock that pays dividends is 112/246 = 45.53%
(c) There are 49 stocks which satisfy the question so the probability is 49/246 = 19.92%
(e) There are 34 stocks which increase in price and pay dividends out of the 119 stocks that increase in price so the probability is 34/119 = 28.57%
(f) Using the same logic as (e), the probability is 85/134 = 63.43%
(g) From the requirements, we see that 49 stocks don't satisfy the requirements, so the probability is (246-49)/246 = 80.08%