Answer:
calls first evening = 26
calls second evening = 80
calls third evening = 20
Step-by-step explanation:
Let x = calls third evening
x+6 = calls first evening
4x = calls second evening
x+6 + 4x + x = total calls = 126
Combine like terms
6x+6 = 126
Subtract 6 from each side
6x =120
Divide by 6
6x/6 =120/6
x = 20
x+6 = calls first evening = 20+6 = 26
4x = calls second evening = 4*20 = 80
Let x = calls third evening = 20
What is 4sqrt7^3 in exponential form?
Answer:
[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]
Step-by-step explanation:
[tex]4 (\sqrt{7} )^3[/tex]
Square root can be written as a power.
[tex]4(7^{\frac{1}{2} })^3[/tex]
Multiply the exponents.
[tex]4(7^{\frac{3}{2} })[/tex]
Answer:
A (7^3/4)
Step-by-step explanation:
ed 2020
Find the total area of the prism.
Answer:
A=1,728
Step-by-step explanation:
To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.
The width is 12, the hight is 12, and the depth is 12 so you can write
A=12*12*12
Multiply 12 by 12
A=144*12
Multiply 12 by 144 to get your final total area
A=1,728
Hope this helps, feel free to ask follow-up questions if confused.
Have a good day! :)
In the diagram, line a is the perpendicular bisector of KM. Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 6 x + 4. Line segment K N is 9 x minus 5. Line segment N M is 7 x + 7. What is the length of KM? 22 units 40 units 44 units 80 units
Answer:
D. 80 :)
Step-by-step explanation:
The solution is : The value of segment LM is 9x + 5.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
Consider the image below.
A perpendicular bisector is a line segment that bisects another line segment into two equal parts and is perpendicular to this line segment.
So from the diagram below we know:
KL = LM
line a is ⊥ to KM
∠NLK = 90°
Since the angle measure of ∠NKL is not provided we cannot determine the value of x.
So, the value of segment LM is 9x + 5.
To learn more on angle click:
brainly.com/question/28451077
#SPJ7
Complete question:
Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 9 x +5. Line segment K N is 14 x minus 3. What is the length of segment LM? units
The amount of flow through a solenoid valve in an automobile's pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Four different levels (low, fair, moderate, and high) of each factor were chosen, and a single observation on flow was made for each combination of levels.A) The resulting data set consisted of how many observations?
B) Is this an enumerative or analytic study? Explain.
Answer:
A) 64 observations
B) analytic study
Step-by-step explanation:
Given:
There are 3 number of factors i.e. armature length, spring load, and bobbin depth.
There are 4 levels i.e. low, fair, moderate, and high
There is a single i.e. 1 observation on flow made for each combination of levels.
A)
To find:
Number of observations.
There are 4 levels so these 4 levels are to be considered for each factor.
Number of observations = 4.4.4 = 64
For example if we represent low fair moderate and high as L,F,M,H
and factors armature length, spring load, and bobbin depth as a,s,b
Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]
So resulting data set has 64 observations.
B)
This is analytic study.
The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.
Mary wants to make brownies to make brownies she needs 7/12 of a cup of flour per batch of brownies if Mary has 7 cups of flour then how many batches of brownies can mary make?
━━━━━━━☆☆━━━━━━━
▹ Answer
12
▹ Step-by-Step Explanation
[tex]7/\frac{7}{12} \\\\= 7 * \frac{12}{7} \\\\= \frac{84}{7} \\\\= 12[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
PLZ IM ON THE CLOCK!!!!! A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month? $457.50 $460.00 $462.50 $572.50
Answer:
460
Step-by-step explanation:
Answer:
460
Step-by-step explanation:
Explain how to use the vertex and the value of “A” to determine the range of an absolute value function. PLEASE HELP!!
Answer:
First, a absolute value function is something like:
y = f(x) = IxI
remember how this work:
if x ≥ 0, IxI = x
if x ≤ 0, IxI = -x
Notice that I0I = 0.
And the range of this function is all the possible values of y.
For example for the parent function IxI, the range will be all the positive reals and the zero.
First, if A is the value of the vertex of the absolute function, then we know that A is the maximum or the minimum value of the function.
Now, if the arms of the graph open up, then we know that A is the minimum of the function, and the range will be:
y ≥ A
Or all the real values equal to or larger than A.
if the arms of the graph open downwards, then A is the maximum of the function, and we have that the range is:
y ≤ A
Or "All the real values equal to or smaller than A"
Which of the following is an exterior angle of triangle BHE? Yes or no
Answer:
Im not 100% sure, but I think it is:
No
No
No
Yes
-6+4q+(-6q)−6+4q+(−6q)minus, 6, plus, 4, q, plus, left parenthesis, minus, 6, q, right parenthesis ?
Answer:
-16-5q
Step-by-step explanation:
-6+4q-6q-6+4q-6q-6+4q-6q= -18-6q
Answer:C
Step-by-step explanation: 100% correct I did it on Khan Academy
surface area of a equilateral by hand
surface area of a equilateral by hand a 140.4 cm and 9cm
which formula would be used to find the measure of angle 1
Answer:
Option (4)
Step-by-step explanation:
By the Angle of intersecting secants,
"If two lines intersect outside a circle, then the measure of the angle between these lines or secants will be one half of the difference between the intercepted arcs."
From the picture attached,
Angle between the secants = ∠1
Measure of intercepted arcs are a° and b°.
By this theorem,
m∠1 = [tex]\frac{1}{2}(a-b)[/tex]
Option (4) will be the answer.
What is the Greatest Common Factor GCF between two expressions?
Answer:
The GCF is the largest expression that is factor of all expressions
Answer:
The GCF of two expressions is the greatest expression that is a factor of both the expressions.
Step-by-step explanation:
For example 7x² and 14x.
7x² = 1, 7, x, x
14x = 2, 7, x
The greatest common factor of the two expressions is 7x.
Jacob needs to know if the volume of a storage bin is under 3,000 cubic feet. The
dimensions of the bin are 17 ft. X 15 ft. x 10 ft.
a. Is the bin under 3,000 cubic ft.?
b. If yes, by how much?
Answer:
It is less than 3000 ft^3 by 450 ft^3
Step-by-step explanation:
The volume of the bin
V = l*w*h
V = 17*15*10
V =2550 ft^3
If it less than 3000 ft^3
V = 3000- 2550 =450 ft^3
If is less by 450 ft^3
Answer:
Let’s first multiply all the numbers given
Since it wants the volume we need to use the formula
LxWxH
17x15x10=2,550
Part A: yes the bin is under 3,000
Part B: by 450 more because if you subtract 3,000 and 2,550 you will get 450
Hope this helps! :)
express 3.222......in p/q form
Answer:
3.22222...... = [tex]\frac{29}{9}[/tex]
Step-by-step explanation:
In this question we have to convert the number given in recurrent decimals into fraction.
Recurrent decimal number is 3.22222.......
Let x = 3.2222......... -------(1)
Multiply this expression by 10.
10x = 32.2222........... -------(2)
Now subtract the expression (1) from (2),
10x = 32.22222.....
x = 3.22222.......
9x = 29
x = [tex]\frac{29}{9}[/tex]
Therefore, recurrent decimal number can be written as [tex]\frac{29}{9}[/tex] which is in the form of [tex]\frac{p}{q}[/tex].
A movie earned $438 million at the box office in
2013. That is 24% more than book of the same
name earned. Estimate how much the book
earned?
Round your answer to the nearest hundredth of
a million dollars.
Answer:
332.88 million
Step-by-step explanation:
you do the thing
A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?
Answer: 0.0548
Step-by-step explanation:
Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.
Let [tex]\overline{X}[/tex] represents the sample mean GPA for each student.
Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:
[tex]P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548[/tex]
hence, the required probability is 0.0548.
g Suppose that three hypothesis tests are carried out, each using significance level 0.05. What is the worst-case probability of a type I error in at least one of these tests?
Answer:
The worst-case probability is 0.05
Step-by-step explanation:
The given significance level ([tex]\alpha[/tex]) = 0.05
since Probability of a type I error is [tex]\alpha[/tex]
∴ P (type I error) = 0.05
0.05 will be the worst-case probability of a type I error in at least one of the tests.
For the functions f(x)=2x^2+3x+9 and g(x)=−3x+10 find (f⋅g)(x) and (f⋅g)(1)
Step-by-step explanation:
f(x)=2x²+3x+9
g(x) = - 3x + 10
In order to find (f⋅g)(1) first find (f⋅g)(x)
To find (f⋅g)(x) substitute g(x) into f(x) , that's for every x in f (x) replace it by g (x)
We have
(f⋅g)(x) = 2( - 3x + 10)² + 3(- 3x + 10) + 9
Expand
(f⋅g)(x) = 2( 9x² - 60x + 100) - 9x + 30 + 9
= 18x² - 120x + 200 - 9x + 30 + 9
Group like terms
(f⋅g)(x) = 18x² - 120x - 9x + 200 + 30 + 9
(f⋅g)(x) = 18x² - 129x + 239
To find (f⋅g)(1) substitute 1 into (f⋅g)(x)
That's
(f⋅g)(1) = 18(1)² - 129(1) + 239
= 18 - 129 + 239
We have the final answer as
(f⋅g)(1) = 128Hope this helps you
Which ideas from the excerpt would be most appropriate to include in a summary? Select three options. Popular novels from the past often ask provocative questions that are important to consider today. Many Americans have given up and say that the nation is no longer great or a land of dreams. John Wayne, nicknamed Duke, was an iconic Hollywood actor and filmmaker. President Reagan believed that John Wayne would argue that he was not the last American hero, because there are many more. Duke Wayne died as a symbol of the Hollywood dream industry.
Answer:
Short answer A,B,D
Step-by-step explanation:
The ideas from the excerpt would be most appropriate to include in a summary are;
Popular novels from the past often ask provocative questions that are important to consider today. Many Americans have given up and say that the nation is no longer great or a land of dreams. President Reagan believed that John Wayne would argue that he was not the last American hero, because there are many more. What is a summary of a passage?Summary is known to be a form of quick or short review of what has happened in a specific passage.
The summary is regarded as a statement that present the main points of a passage as seen above.
Learn more about novels from
https://brainly.com/question/19599489
These are the weekly wages paid to staff in a hotel. £245 £140 £525 £163 £195 £174 £140 What is the range of these wages? £ What is the mean wage?
Answer:
Range of wages is £140 to £525.
Mean wage = £226
Step-by-step explanation:
Given:
Weekly wages paid to the staff are :
£245, £140, £525, £163, £195, £174 and £140.
To find:
Range of these wages = ?
Mean wage = ?
Solution:
First of all, let us learn about the range of wages and mean wage.
Range of wages has a minimum pay and a maximum pay.
Here, if we have a look £140 is the minimum pay and
£525 is the maximum pay.
So, range of wages is £140 to £525.
Mean wage means the average of all the wages given to the staff.
Mean is defined as the formula:
[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]
Here, Sum of all observations mean sum of the wages of all the staff members.
Number of observations mean the number of staff members i.e. 7 here.
Applying the formula:
[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]
So, the answer is:
Range of wages is £140 to £525.
Mean wage = £226
What is the slope of the line x = 4?
Answer:
slope is undefined
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis.
The slope of a vertical line is undefined
Answer:
Undefined
Step-by-step explanation:
If the line is strait up like x = 4 that means it is undefined.
Can someone help me with this one
Answer:
b^2
------
2a
Step-by-step explanation:
-6ab^3 10b
-------------- * -----------
5a -24 ab^2
Rewriting
-6ab^3 10b
-------------- * -----------
-24 ab^2 5a
Canceling like terms
b 2b
-------------- * -----------
4 a
Canceling the 2 and 4
b b
-------------- * -----------
2 a
b^2
------
2a
Answer:
b²/2a
Step-by-step explanation:
[(-6ab³)/5a]*[(10b)/(-24ab²)]
-60ab^4/-120a²b²= ( when divide ,subtract the exponents)
b²/2a
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Item 25
The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function.
0
1
2
3
4
5
6
7
8
9
10
Answer:
5
Step-by-step explanation:
The temperature, T^0Celcius, of an object, t minutes after it is removed from a head source, is given byT=55e^((-0.1t) )+15. Find the temperature of the object at the instant it is removed from the heat source.
Answer:
60°C
Step-by-step explanation:
This is a great example of a problem that looks really complicated, but can be broken down and easily understood!
First, we want to know the temperature the instant it is removed from the heat source. In that case, the time that has elapsed after it has been removed is 0, so we're looking for:
[tex]T(0)=55e^{-0.1(0))}+15=55e^{0}+15[/tex]
Now, any number raised to to the power of zero is 1, so this becomes:
[tex]T(0)=55(1)+15=60[/tex]
For more information on why any number raised to the zero power is 1, I highly recommend researching if it interests you. One of the most intuitive ways is to think of the pattern of exponents:
[tex]3^{3}=3*3*3=27[/tex]
[tex]3^{2}=3*3=9[/tex]
[tex]3^{1}=3[/tex]
You might notice that with each decrease in power, it can be read as dividing the expression by three, so following that pattern gives:
[tex]3^{0}=\frac{3}{3}=1[/tex]
And if we follow the division pattern, we do end up going into negative exponents correctly:
[tex]3^{-1}=\frac{1}{3^{1}}[/tex]
[tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex]
[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex]
what is the measure of SR?
Answer:
RS = 8
Step-by-step explanation:
Given:
Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16
Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8
To find the measure of RS, we need to find the value of x.
Thus, recall the "Two Secant Theorem"
According to the theorem,
(RS + RQ)*RQ = (PU + PQ)*PQ
Thus,
[tex] (3x - 5 + 8)*8 = (7 + 9)*9 [/tex]
[tex] (3x + 3)*8 = (16)*9 [/tex]
[tex] 24x + 24 = 144 [/tex]
Subtract 24 from both sides
[tex] 24x + 24 - 24 = 144 - 24 [/tex]
[tex] 24x = 120 [/tex]
Divide both sides by 24
[tex] \frac{24x}{24} = \frac{120}{24} [/tex]
[tex] x = 5 [/tex]
Plug in the value of x into (3x - 5) to find the measure of RS
RS = 3(5) - 5 = 15 - 7
RS = 8
please help me out with these questions. Its trigonometry.
Find the value of the lettered angles
In case the pic's not clear;
[tex] \cos \alpha = \sin(50 + \alpha ) [/tex]
Answer: i) θ = 30°, 60°, 210°, & 240°
ii) θ = 20° & 200°
Step-by-step explanation:
i) sin (2θ) = cos 30°
[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]
To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above. θ = 30°, 60°, 210°, 240°
If you need ALL of the solutions (more than one rotation), add 180n to the solutions. θ = 30° + 180n & 60° + 180n
*********************************************************************************************
ii) cos α = sin (50 + α)
Use the Identity: cos α = sin (90 - α)
Use Transitive Property to get: sin (50° + α) = sin (90° - α)
50° + α = 90° - α
50° + 2α = 90°
2α = 40°
α = 20°
To find all solutions for one rotation, add 360/2 = 180 to the solution above.
α = 20°, 200°
If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n
verify sin4x - sin2x = cos4x-cos2x
Answer:
sin⁴x - sin²x = cos⁴x - cos²x
Solve the right hand side of the equation
That's
sin⁴x - sin²x
From trigonometric identities
sin²x = 1 - cos²xSo we have
sin⁴x - ( 1 - cos²x)
sin⁴x - 1 + cos²x
sin⁴x = ( sin²x)(sin²x)
That is
( sin²x)(sin²x)
So we have
( 1 - cos²x)(1 - cos²x) - 1 + cos²x
Expand
1 - cos²x - cos²x + cos⁴x - 1 + cos²x
1 - 2cos²x + cos⁴x - 1 + cos²x
Group like terms
That's
cos⁴x - 2cos²x + cos²x + 1 - 1
Simplify
We have the final answer as
cos⁴x - cos²xSo we have
cos⁴x - cos²x = cos⁴x - cos²xSince the right hand side is equal to the left hand side the identity is true
Hope this helps you
Which represents the solution of the graphed system of equations, y=x^2-2x and y=-2x-1
Answer:
x = √(-1) = i
Since the value of √(-1) is not real.
The system has no real solution.
Step-by-step explanation:
The solution to the system of equations is at the point where they intercept each other.
y1 = y2
For the given equation;
y=x^2-2x and y=-2x-1
To get the where they intercept, we will equal both equations;
y=x^2-2x = -2x-1
x^2 - 2x = -2x - 1
x^2 - 2x + 2x + 1 =0
x^2 +1 = 0
x^2 = -1
x = √(-1) = i
Since the value of √(-1) is not real.
The system has no real solution.
A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09 *Note: An increase in film speed would lower the value of the observation in microjoules per square inch. We may also assume the speeds of the film follow a normal distribution. Use this information to construct a 98% interval estimate for the difference in mean speed of the films. Does decreasing the thickness of the film increase the speed of the film?
Answer:
A 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Step-by-step explanation:
We are given that Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured.
For the 25-mil film, the sample data result is: Mean Standard deviation 1.15 0.11 and For the 20-mil film the data yield: Mean Standard deviation 1.06 0.09.
Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;
P.Q. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean speed for the 25-mil film = 1.15
[tex]\bar X_1[/tex] = sample mean speed for the 20-mil film = 1.06
[tex]s_1[/tex] = sample standard deviation for the 25-mil film = 0.11
[tex]s_2[/tex] = sample standard deviation for the 20-mil film = 0.09
[tex]n_1[/tex] = sample of 25-mil film = 8
[tex]n_2[/tex] = sample of 20-mil film = 8
[tex]\mu_1[/tex] = population mean speed for the 25-mil film
[tex]\mu_2[/tex] = population mean speed for the 20-mil film
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(8-1)\times 0.11^{2}+ (8-1)\times 0.09^{2}}{8+8-2} }[/tex] = 0.1005
Here for constructing a 98% confidence interval we have used a Two-sample t-test statistics because we don't know about population standard deviations.
So, 98% confidence interval for the difference in population means, ([tex]\mu_1-\mu_2[/tex]) is;
P(-2.624 < [tex]t_1_4[/tex] < 2.624) = 0.98 {As the critical value of t at 14 degrees of
freedom are -2.624 & 2.624 with P = 1%}
P(-2.624 < [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < 2.624) = 0.98
P( [tex]-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < [tex]2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ) = 0.98
P( [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] < ([tex]\mu_1-\mu_2[/tex]) < [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ) = 0.98
98% confidence interval for ([tex]\mu_1-\mu_2[/tex]) = [ [tex](\bar X_1-\bar X_2)-2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] , [tex](\bar X_1-\bar X_2)+2.624 \times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ]
= [ [tex](1.15-1.06)-2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] , [tex](1.15-1.06)+2.624 \times {0.1005 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }[/tex] ]
= [-0.042, 0.222]
Therefore, a 98% confidence interval estimate for the difference in mean speed of the films is [-0.042, 0.222].
Since the above interval contains 0; this means that decreasing the thickness of the film doesn't increase the speed of the film.
43.
Some of the ingredients used by a baker for making 1 dozen
normal sponge cakes are listed below:
225g unsalted butter; 4 eggs; 125ml milk;
2 tsp vanilla extract; 264g plain flour
To make fully vegetarian cakes, the baker replaces each egg
with an additional 30g of plain flour.
The baker got an order for 100 normal cakes and 60 vegetarian
cakes. How much kilograms of flour would the baker need to
complete the order?
Answer:
4.12 kg
Step-by-step explanation:
Regular cakes:
1 dozen normal sponge cakes: 264 g plain flour
Vegetarian cakes:
1 dozen cakes: 264 g plain flour
4 eggs are replaced by 4 * 30 g of flour = 120 g flour
total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g
Proportion for regular cakes:
12 cakes to 264 g flour = 100 cakes to x grams flour
12/264 = 100/x
12x = 26400
x = 2200
2200 g flour for 100 regular cakes
Proportion for vegetarian cakes:
12 cakes to 384 g flour = 60 cakes to y grams flour
12/384 = 60/y
12y = 384 * 60
12y = 23040
y = 1920
1920 g flour for 60 vegetarian cakes
Total flour needed:
2200 g + 1920 g = 4120 g
4120 g * 1 kg/(1000 g) = 4.12 kg
Answer: 4.12 kg