Answer:
50 inches
Explanation:
Let the length of the steel bar when it was formed = y
Steel bars shrink 8% when cooled from furnace temperature to room temperature.
[tex]\begin{gathered} \text{Room Temperature Length}=(100-8)\%\text{ of y} \\ =92\%y \\ =0.92y \end{gathered}[/tex]Given that a cooled steel bar is 46 in. long, then:
[tex]0.92y=46[/tex]Divide both sides by 0.92.
[tex]\begin{gathered} \frac{0.92y}{0.92}=\frac{46}{0.92} \\ y=50\;in. \end{gathered}[/tex]The steel bar was 50 in. long when it was formed.
Fill in the missing values to make the equations true.(a) log, 9-log, 11 = log5(b) log45 + log4 = log, 45(c) 5log72 = log7
(a)
[tex]\log _59-\log _511=\log _{5_{}}(\frac{9}{11})\text{ (}\because\log a-\log b=\log (\frac{a}{b})[/tex]Thus, the required value in the blank in 9/11/
(b)
[tex]\log _45+\log _4(9)=\log _445\text{ (}\because\log a+\log b=\log ab)[/tex]Thus, the required value in the blank is 9.
(c)
[tex]\begin{gathered} 5\log _72=\log _72^5(\because a\log b=\log b^a) \\ =\log _732 \end{gathered}[/tex]Thus, the requried value in the blank is 32.
Number of adult tickets sold = Number of child tickets sold =
Given:
Total ticket = 321
Total collection = $3535
Adult ticket price = $15
Child ticket price = $5
Find-:
(1)
Number of adult tickets sold
(2)
Number of child tickets sold
Explanation-:
Let the number of adult tickets = x
Let the number of child tickets = y
If the total ticket is 321 then,
[tex]x+y=321........................(1)[/tex]Price for adult ticket is:
[tex]=15x[/tex]The price for child ticket is:
[tex]=5y[/tex]total price is $3535 then,
[tex]15x+5y=3535...................(2)[/tex]From eq(1)
[tex]\begin{gathered} x+y=321 \\ \\ 5x+5y=1605..............(3) \end{gathered}[/tex]So eq(2) - eq(3) is:
[tex]\begin{gathered} (15x+5y)-(5x+5y)=3535-1605 \\ \\ 15x-5x+5y-5y=1930 \\ \\ 15x-5x=1930 \\ \\ 10x=1930 \\ \\ x=\frac{1930}{10} \\ \\ x=193 \end{gathered}[/tex]Put the value in eq(1) then,
[tex]\begin{gathered} x+y=321 \\ \\ 193+y=321 \\ \\ y=321-193 \\ \\ y=128 \end{gathered}[/tex]So,
Number of adult tickets = 193
Number of child tickets = 128
Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood chipped path running through their yard. What wouldbe the area of his rink if it is triangular-shaped with sides of length 18 feet, 20 feet, and 22 feet? Round to the nearest square foot.
In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:
[tex]A=\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}[/tex]Where p is the semi-perimeter.
So, calculating the value of p and then the area of the triangle, we have:
[tex]\begin{gathered} p=\frac{a+b+c}{2}=\frac{18+20+22}{2}=\frac{60}{2}=30 \\ A=\sqrt{30\left(12\right)\left(10\right)\left(8\right)} \\ A=\sqrt{28800} \\ A=169.7\text{ ft^^b2} \end{gathered}[/tex]Rounding to the nearest square foot, the area is 170 ft².
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment n=10, p=0.2, x=2
The binomial probability of x successes is 0.302.
How to calculate the probability of x successes?Since we are dealing with a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Given: n=10, p=0.2, x=2
The failures can be calculated using q = 1 - p = 1 - 0.2 = 0.8
P(x = 2) = 10C2 x 0.2² x 0.8¹⁰⁻²
= 10!/(10-2)! 2! x 0.2² x 0.8⁸
= 10!/(8!2!) x 0.2² x 0.8^8
= 10x9x8!/(8!2!) x 0.2² x 0.8⁸
= 45 x 0.2² x 0.8⁸
= 0.302
Therefore, the probability of x successes in 10 trials is 0.302
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find the slope of the line that passes through (10,2) and (2,10)
Translate and solve: The difference of a and 7 is 11
Answer:
(B)a=18
Explanation:
The difference of a and 7 translated as an expression is:
[tex]a-7[/tex]Thus, the equation is:
[tex]a-7=11[/tex]To solve for a, add 7 to both sides of the equation:
[tex]\begin{gathered} a-7+7=11+7 \\ a=18 \end{gathered}[/tex]The correct choice is B.
By what factor does the population grow every 2 years? Use rhis information to fill out the table.By what factor does the population grow every year? explain how you know, and use this information to complete the table.
From the table, we see that:
• Year 0 has a population of 10,
,• Year 2 has a population of 20.
So after two years, the population of fish is doubled.
1) By year 4, we will have double the population of year 2, so the population will be 2*20 = 40.
2) To function that describes the growth of the population is:
[tex]P(t)=P_0\cdot r^t._{}[/tex]Where P_0 is the initial population and r is the growth factor.
We know that after two years, the population of fish is doubled:
[tex]P(t+2)=2\cdot P(t)\text{.}[/tex]Using the formula above evaluated in t + 2, we have:
[tex]P(t+2)=P_0\cdot r^{t+2}=(P_0\cdot r^t)\cdot r^2=P(t)\cdot r^2[/tex]Equalling the last two equations, we have:
[tex]P(t+2)=2\cdot P(t)=P(t)\cdot r^2\text{.}[/tex]Solving for r the last equation, we have:
[tex]\begin{gathered} 2=r^2, \\ r=\sqrt[]{2}\text{.} \end{gathered}[/tex]So the growth factor is r = √2.
Answer:
1. 40
2. √2
Northeast Hospital’s Radiology Department is considering replacing an old inefficient X-ray machine with a state-of-the-art digital X-ray machine. The new machine would provide higher quality X-rays in less time and at a lower cost per X-ray. It would also require less power and would use a color laser printer to produce easily readable X-ray images. Instead of investing the funds in the new X-ray machine, the Laboratory Department is lobbying the hospital’s management to buy a new DNA analyzer.
The classification of each cost item as a differential cost, a sunk cost, an opportunity cost, or None, is as follows:
Cost Classification1. Cost of the old X-ray machine Sunk cost
2. The salary of the head of the Radiology Dept. None
3. The salary of the head of the Laboratory Dept. None
4. Cost of the new color laser printer Differential cost
5. Rent on the space occupied by Radiology None
6. The cost of maintaining the old machine Differential cost
7. Benefits from a new DNA analyzer Opportunity cost
8. Cost of electricity to run the X-ray machines Differential cost
9. Cost of X-ray film used in the old machine Sunk cost
What are differential cost, sunk cost, and opportunity cost?A differential cost is a cost that arises as the cost difference between two alternatives.
A sunk cost is an irrelevant cost in managerial decisions because it has been incurred already and future decisions cannot overturn it.
An opportunity cost is a benefit that is lost when an alternative is not chosen.
Thus, the above cost classifications depend on the decision to replace the old X-ray machine with a new machine (new X-ray or new DNA analyzer).
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Question Completion:Required Classify each item as a differential cost, a sunk cost, or an opportunity cost in the decision to replace the old X-ray machine with a new machine. If none of the categories apply for a particular item, select "None".
1. Cost of the old X-ray machine
2. The salary of the head of the Radiology Department
3. The salary of the head of the Laboratory Department
4. Cost of the new color laser printer
5. Rent on the space occupied by Radiology
6. The cost of maintaining the old machine
7. Benefits from a new DNA analyzer
8. Cost of electricity to run the X-ray machines
9. Cost of X-ray film used in the old machine
3(2x+4) - 2(4x-1)=20A. x=5B. x=-5C. x=3D. x=-3
we have the following:
[tex]3(2x+4)-2\left(4x-1\right)=20[/tex]solving for x:
[tex]\begin{gathered} 3(2x+4)-2\left(4x-1\right)=20 \\ 6x+12-8x+2=20 \\ -2x=20-12-2 \\ -2x=6 \\ x=\frac{6}{-2} \\ x=-3 \end{gathered}[/tex]The answer is x = -3
Question 8 of 10According to this diagram, what is tan 62°?
In this problem, we want to determine tangent of 62 degrees.
Recall the identity of tangent:
[tex]\tan\theta=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]We are given the triangle:
Since we are referencing 62 degrees, the arrow pointing away from the 62 degrees is headed toward the opposite side. Therefore, the opposite side is 15, and the adjacent side is 8.
[tex]\tan62=\frac{15}{8}[/tex]Tangent of 62 degrees is 15/8.
Blackgrass black graph is the of y=f(x) chose the equation for the red graph
The Solution:
The correct answer is [option A]
Given:
Required:
To determine the equation of the red graph if the black graph function is y = f(x).
The correctb
Can you tell me if im right or wrong
I will begin typing in the answer tab. It will take me approximately _
Which of the following is equivalent to - sin ¹1?A. sin ¹111OB. - sin(-11)OC. sin(-11)D. sinReset Selection
The correct option is C.
In a recent year, 24.8% of all registered doctors were female. If there were 54,100 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
To solve for total number of registered doctors:
Explanation:
The questions says, "24.8% of all registered doctors are females"
(Consider, total number of registered doctors as x)
that's,
[tex]\begin{gathered} 24.8\text{ \% of the x are female registered doctor} \\ 24.8\text{ \% of x = 54,100} \end{gathered}[/tex]Mathematically,
[tex]\begin{gathered} \frac{24.8}{100}.x=54,100 \\ \text{cross multiply} \\ 24.8x=54,100\text{ x 100} \\ 24.8x=5410000 \\ \frac{24.8x}{24.8}=\frac{5410000}{24.8} \\ x=218145.16 \\ x\approx218,145\text{ (nearest whole number)} \end{gathered}[/tex]Therefore the total number of registered doctors ≈ 218,145
Which graph represents the equation X =2?
ANSWER and EXPLANATION
We are given x = 2.
To plot the graph of x = 2, it is important to note that the value of x does not change for this equation.
x is always 2 regardless of the value of y.
This means that we are going to plot a straight line that will straight up (and down as well) at x = 2.
The graph therefore is:
Determine the required value of a missing probability to make the distribution a discrete probability distribution… p(4) =
The table given showed the discrete probability distribution for random variables 3 to 6 and their corresponding probability except for the probability of 4
It should be noted that for a probability distribution, the cummulative probabibility (that is the sum of all the probability) must be equal to one.
This means that
[tex]P(3)+P(4)+P(5)+P(6)=1[/tex]From the given table, it can be seen that
[tex]\begin{gathered} P(3)=0.32 \\ P(4)=\text{?} \\ P(5)=0.17 \\ P(6)=0.26 \end{gathered}[/tex]Then, p(4) is calculated below
[tex]\begin{gathered} P(3)+P(4)+P(5)+P(6)=1 \\ 0.32+P(4)+0.17+0.26=1 \\ P(4)+0.32+0.17+0.26=1_{} \\ P(4)+0.75=1 \\ P(4)=1-0.75 \\ P(4)=0.25 \end{gathered}[/tex]Hence, P(4) is 0.25
what is the correct base and coefficient for the function:
The general form of a logarithmic function is:
[tex]y=a\cdot\log _b(x)[/tex]Where a is the coefficient and b is the base. In the given picture, we can see that the coefficient is equal to 1, while the base is equal to 2.
You have a bag full of 4 green marbles and 1 blue marble. You pick a marble out at random. If it's blue, you stopbecause you win 20 points. If not, you get another chance. Without replacing the green marble, you pick again. It'sblue, you win 10 points, otherwise you lose 20 points. Let X be the number of points you eam in this game. If you playedthis game 100 times, how many points can you expect to win (or lose)?
As per given by the question,
There are given that, 4 green marbles and 1 blue marble contains in a box and pick a marble at randomly.
Now,
Here pick a marble out at random, so first pick a marble for blue;
Then,
Total number of green marbles is 4, and the total number of blue marble is 1, and;
The total numbers of marbles in a bag is, 4+1=5.
So,
For pick the blue marble from 5 marble,
Now,
[tex]\begin{gathered} 5_{C_1}=\frac{5!}{1!\times(5-1)!} \\ =\frac{5!}{1!\times4!} \\ =\frac{5\times4!}{1!\times4!} \\ =5 \end{gathered}[/tex]Now, for pick the green marble from 5 marbles.
Here, total green marble is 4.
So,
[tex]\begin{gathered} 5_{C_4}=\frac{5!}{4!\times(5-4)!} \\ =\frac{5\times4!}{4!\times1!} \\ =5 \end{gathered}[/tex]Now,
From the question, there are clearly mention that if pick a blue, then stop because you won 20 points.
So,
Probability of the blue marble that won the 20 points.
then,
[tex]\begin{gathered} P(x=20)=\frac{total\text{ number of blue marble}}{\text{total number of marble}} \\ P(x=20)=\frac{1}{5} \end{gathered}[/tex]Now,
There are also mention that, pick a green marbles without replacing and if its blue then win the 10 points,
So,
probability of the blue marbles that won 10 pointss is,
[tex]P(x=10)=\frac{1}{4}[/tex]Now,
Here, find the probability that no points for the first green ball is,
[tex]P(x=0)=\frac{4}{5}[/tex]Now,
If you played this game 100 time, then the probability is,
[tex]\begin{gathered} P(x=0)+_{}P(x=10)+P(x=20)=\frac{4}{5}+\frac{1}{4}+\frac{1}{5} \\ =1.25 \end{gathered}[/tex]now,
For 100 times,
[tex]1.25\times100=125\text{ points.}[/tex]Hence, 125 points can you expect to win.
Answers asap please
x ≥ 1 or x ≥ 3 is inequality of equations .
What do you mean by inequality?
The allocation of opportunities and resources among the people who make up a society in an unequal and/or unfair manner is known as inequality. Different persons and contexts may interpret the word "inequality" differently.The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. It is an illustration of inequity. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.9 - 4x ≥ 5
4x ≥ 9 - 5
4x ≥ 4
x ≥ 1
4( - 1 + x) -6 ≥ 2
-4 + 4x - 6 ≥ 2
4x ≥ 2 + 8
4x ≥ 10
x ≥ 10/4
x ≥ 5/2
x ≥ 2.5
x ≥ 1 or x ≥ 3
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Michelle can wash dry and fold 5 loads of laundry in 3 1/2 hours. what is the average amount of time it takes Michelle to do one load of laundry
Jodie is an event planner who believeseach person requires 3.75 feet ofpersonal space at her events. Her nextevent will be at a venue that measures40 feet by 75 feet. How many peopleshould she include on the guest list?
The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
Kindly help with these questions.
use the information provided to write the equation of each circle. center: (12,-13)point on circle: (18, -13)
Answer:
[tex](x-12)^2+(y+13)^2=36[/tex]Explanation:
Given:
• Center: (12,-13)
,• Point on circle: (18, -13)
First, we find the length of the radius.
[tex]\begin{gathered} r=\sqrt[]{(18-12)^2+(-13-(-13)_{})^2} \\ =\sqrt[]{(6)^2} \\ r=6\text{ units} \end{gathered}[/tex]The general equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the centre, (h,k)=(12,-13) and r=6, we have:
[tex]\begin{gathered} (x-12)^2+(y-(-13))^2=6^2 \\ (x-12)^2+(y+13)^2=36 \end{gathered}[/tex]The equation of the circle is:
[tex](x-12)^2+(y+13)^2=36[/tex](h) through (5,0), y-intercepto 0
We first need to calculate the slope of the line.
m=(0-0)/(5-0)=0 since the slope is equal to zero we have that the line is horizontal.Then the equation is
[tex](y-0)=0(x-0)\Rightarrow y=0[/tex]the equation is y=0
How do we determine the number of hours each family used the sprinklers?
Given:
The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The combined usage of sprinkler is 40 hours. The resulting water output is 1250L.
To find:
The number of hours each family used the sprinkler.
Solution:
Let Martinez family used sprinkler for x hours and Green family used sprinkler for y hours.
Since the combined usage of sprinklers is 40 hours. So,
[tex]x+y=40...\left(i\right)[/tex]The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The resulting water output is 1250L. So,
[tex]\begin{gathered} 25x+35y=1250 \\ 5x+7y=250...\left(ii\right) \end{gathered}[/tex]Multiply (i) by 7 and subtract from (ii), to get:
[tex]\begin{gathered} 5x+7y-7\left(x+y\right)=250-7\left(40\right) \\ 5x+7y-7x-7y=250-280 \\ -2x=-30 \\ x=\frac{-30}{-2} \\ x=15 \end{gathered}[/tex]Now, we get x = 15, Put x = 15 in the equation (i):
[tex]\begin{gathered} 15+y=40 \\ y=40-15 \\ y=25 \end{gathered}[/tex]Thus, x = 15, y = 25.
I need help with a word problem in algebra 2 please
We were given the following information:
Plan 1
Cost = $175
It has unlimited call & texts as well as 15gb
Plan 2
Cost = $50 per month
It has unlimited call & texts as well as 6gb
After 6gb, data is charged $5 per gb
From this we have the following equations:
[tex]undefined[/tex]In the given figure, find the mesure of angle BCD
Since the sum of angles in a triangle is 180°, it follows that;
[tex]\begin{gathered} 4x+3x+2x=180 \\ 9x=180 \\ \text{ Divide both sides of the equation by }9 \\ \frac{9x}{9}=\frac{180}{9} \\ x=20 \end{gathered}[/tex]Since line segment AB is parallel to the line segment CD, it follows from the Corresponding angles theorem that:
[tex]\begin{gathered} \angle{B}=\angle{BCD} \\ \text{ Therefore:} \\ \angle{BCD}=4x \\ \text{ Substitute }x=20\text{ into the equation} \\ \angle{BCD}=4\times20=80 \end{gathered}[/tex]Therefore, The req
Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 362 with 54 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
We have to find the 80% confidence interval for a population proportion.
The sample size is n = 362 and the number of successes is X = 54.
Then, the sample proportion is p = 0.149171.
[tex]p=\frac{X}{n}=\frac{54}{362}\approx0.149171[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_s=\sqrt{\frac{p(1-p)}{n}} \\ \sigma_s=\sqrt{\frac{0.149171*0.850829}{362}} \\ \sigma_s=\sqrt{0.000351} \\ \sigma_s=0.018724 \end{gathered}[/tex]The critical z-value for a 80% confidence interval is z = 1.281552.
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z\cdot\sigma_s=0.149171-1.281552\cdot0.018724\approx0.1492-0.0240=0.1252[/tex][tex]UL=p+z\cdot\sigma_s=0.1492+0.0240=0.1732[/tex]As the we need to express it as a trilinear inequality, we can write the 80% confidence interval for the population proportion (π) as:
[tex]0.125<\pi<0.173[/tex]Answer: 0.125 < π < 0.173
Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find AU (BNC).{
Solution:
Given that;
[tex]\begin{gathered} A=\left\{0,2,4,6\right\} \\ B=\left\{1,2,3,4,5\right\} \\ C=\left\{1,3,5,7\right\} \end{gathered}[/tex]For B∩C, i.e . common elements between bot sets
[tex]B\cap C=\lbrace1,3,5\rbrace[/tex]Then, A∪(B∪C), i.e. all the elements in A and B∩C
[tex]A∪\left(B∪C\right)=\lbrace0,1,2,3,4,5,6\rbrace[/tex]Hence, A∪(B∪C) is
[tex]\begin{equation*} \lbrace0,1,2,3,4,5,6\rbrace \end{equation*}[/tex]i have to find is they similar or not. help im lost
First we have to find the missing angle on each case.
In the first triangle we have
180°-(28°+80°)=72°
In the second triangle we have
180°-(28°+71°)=81°
Since the values of the angles are not the same for both triangles they are not similar.
