Answer:
The IV will run [tex]66.67 \ ml /hr[/tex]
Step-by-step explanation:
From the question we are told that
The mass of Magnesium sulfate is [tex]m_g = 30 \ g[/tex]
The volume of the Magnesium sulfate [tex]V_R = 500ml[/tex]
The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is [tex]R = 4g/hr[/tex]
The concentration of Magnesium sulfate in Lactated Ringers is mathematically evaluated as
[tex]C_m = \frac{m_g}{V_R}[/tex]
substituting values
[tex]C_m = \frac{30}{500}[/tex]
[tex]C_m = 0.06\ g/ ml[/tex]
This implies that
0.06 g of Magnesium sulfate is in every 1 ml of Lactated Ringers
So 4 g of Magnesium sulfate is in x ml of Lactated Ringers
So
[tex]x = \frac{4}{0.06}[/tex]
[tex]x = 66.67 \ ml[/tex]
So the amount of the solution in ml that is been infused in 1 hour is
[tex]66.67 \ ml /hr[/tex]
The sum of an infinite geometric sequence is seven times the value of its first term.
a) Find the common ratio of the sequence.
b) Find the least number of terms of the sequence that must be added in order for the sum to exceed half the value of
the infinite sum.
Answer:
a). r = [tex]\frac{6}{7}[/tex]
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,
[tex]S_{\inf}=\frac{a}{1-r}[/tex]
Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.
[tex]7a=\frac{a}{1-r}[/tex]
[tex]7=\frac{1}{1-r}[/tex]
7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r = [tex]\frac{6}{7}[/tex]
b). Since sum of n terms of the geometric sequence is given by,
[tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]
If the sum of n terms of this sequence is more than half the value of the infinite sum.
[tex]\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}[/tex] > [tex]\frac{7a}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}[/tex]
[tex]\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}[/tex]
[tex]1-(\frac{6}{7})^{n}> \frac{1}{2}[/tex]
[tex]-(\frac{6}{7})^{n}> -\frac{1}{2}[/tex]
[tex](\frac{6}{7})^{n}< \frac{1}{2}[/tex]
[tex](0.85714)^{n}< (0.5)[/tex]
n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n > [tex]\frac{0.30102}{0.06695}[/tex]
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.
prove each identify
cos X(tanX+cotX) =cscX
Answer:
Step-by-step explanation:
cos X(tanX+cotX) =cscX
cos X(sinx/cosx +cosx/sinx) =cscx
cos X (sin²+cos²/cossin)=cscx
cosx(1/cossin)=cscx
cross out cosines
1/sinx=cscx
How do you write or break down this decimal:
45.50 =
Step-by-step explanation:
45.50
Converting decimal
45.50 x 100 = 4550
A florist currently makes a profit of $20 on each of her celebration bouquets and sells a average of 30 bouquets every week
Answer:
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW;
A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.
CHECK THE ATTACHMENT FOR THE GRAPH
EXPLANATION;
FIRST QUESTION:
From the graph maximum profit is the value gotten where p(X) has maximum value, and the maximum value is observed at y- axis at P(X)to be 675.
Thefore, maximum profit the florist will earn from celebration bouquet is $675.
SECOND QUESTION:
Break even is the exact point that profit p(x) is observed as zero.
Checking the given g graph the point where there is zero value of p(X) is observed at x=20 and x= -10 but we can only pick the positive value which is x=20
Therefore, the florist will break even after 20 one- dollar decreases
THIRD QUESTION;
The interval of number of one dollar decreases can be observed at the point where we have the value of P(x) been more than zero, looking at the given graph, the P(x) has its value greater than zero at the interval 0 to 20.Therefore, it can be concluded that the interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)
Answer:
Step-by-step explanation:
(2)/(5) and (1)/(x)common denominator =10 find the value of x
Answer:
[tex]x=5/48[/tex]
Step-by-step explanation:
[tex]2/5 + 1/x =10[/tex]
[tex]1/x=10-2/5[/tex]
[tex]1/x=48/5[/tex]
[tex]48x=5[/tex]
[tex]x=5/48[/tex]
Answer:
[tex]x = \frac{5}{48} [/tex]
Step-by-step explanation:
[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\
use \: \: \: \: cross \: \: \: multiply
\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.
Answer:
a) The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
We are 95% confident that the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is within 9,009 and 10,585 steps.
b) No, we can not use the confidence interval to estimate the probability of individual values. It can onlybe used to make inference about the population mean.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=9,797.
Ths sample standard deviation is s=2,313.
The sample size is N=61.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2313}{\sqrt{61}}=\dfrac{2313}{7.81}=296.15[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=61-1=60[/tex]
The t-value for a 99% confidence interval and 61 degrees of freedom is t=2.66.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.66 \cdot 296.15=787.84[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 9797-787.84=9009\\\\UL=M+t \cdot s_M = 9797+787.84=10585[/tex]
The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
b) The value of 8,500 steps is outside the confidence interval, but this means that it is an unusual value for the mean number of steps for all people in New York City who wear an activity tracker.
We can not use the confidence interval to estimate the probability of individual values.
The activity tracking devices.
The activity tracker re those devices such as watches and a bands that tells you about your physical activity such as skipping, running, and walking. They simply count the steps and tell you about the daily goals and targets. They are quite effective for monitoring blood pressure and more.
Thus answer is 9,009, 10,585 workers, 9,009, and 10,585 steps and population mean.
As per the question, the smart trackers are used by the new york people on a daily basis and they measure the footsteps of the people. A sample of random 61 people was taken and selected on the basis of the tracers. It was found that with these statistical tests a 99% confidence interval was taken for the mean on a typical workday for all people working in City that is 9,009, 10,585. The 95% confidence that the mean number of steps taken by workers of the City was within 9,009 and 10,585 steps.The confidence interval can be used to estimate the probability of the individual values. It can be used for drawing inferences for the population mean.Learn more about the trackers are electronic.
brainly.com/question/17434350.
Is –57 + 19 positive or negative?plz answerrrrrr ill mark 1st as brainliest
Answer: negative
Step-by-step explanation:
because –57 + 19= -38
and negative plus positive is negative
so the answer is negative
Hope this helps :)
Answer:
Negative
Compare the absolute values (how far the number is away from zero)
57 is bigger than 19
since 57 is negative and bigger than 19 when they add the sum will still be negative
Step-by-step explanation:
Help me please and thanks
Hey there! :)
Answer:
B.
Step-by-step explanation:
To find the solution to the inequality, we can begin by solving for 'x':
2x + 1 ≥ 3
Subtract 1 from both sides:
2x ≥ 2
Divide both sides by 2:
x ≥ 1.
This means that the graph must contain all values of x greater or equal to one. The only number line that shows solutions greater than 1 is B.
What is an equation of the line that is parallel to y = 9 – 5x and passes through (0, 8)?
Answer:
y = 8 - 5x
Step-by-step explanation:
both equations shares the same gradient as they are parallel
from y= 9-5x, the gradient is -5
subst x = 0, y=8, and m= -5 into the y = mx + c to find the value of c
8 = (-5)(0) + c
c= 8
therefore the eqn is y = 8 - 5x
I need help please HELP ME
Answer:
-3
Step-by-step explanation:
Because -3x-3=9 and 9+8= 17. 17 is greater than 14
The function h(t) = -4.92f^2 + 17.69f + 575 is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range?
Answer:
rounded to 3 decimal places ...
domain: [0, 12.757]range: [0, 590.901]Step-by-step explanation:
The function can be put into vertex form:
h(t) = -4.92(t -(1769/984))^2 +575 +4.92(1769/984)^2
h(t) ≈ -4.92(t -1.79776)^2 +590.90122
The value of h(t) is zero for ...
t = √(590.90122/4.92) +1.79776 ≈ 12.75686
For practical purposes, the domain of the function is those values of t between the time the object is tossed and the time it hits the ground. That is, the domain is ...
0 ≤ t ≤ 12.75686
The range is the set of useful vertical heights, so extends from 0 to the maximum height, given by the vertex.
The range is 0 ≤ h(t) ≤ 590.90122.
_____
Alternate interpretation of the question
The function h(t) is defined for all values of t, so that could be considered the domain.
The function h(t) only gives values less than its vertex value, so the range could be considered to extend from negative infinity to that maximum.
Ralph is 3 times as old as Sara. In 4 years, Ralph will be only tice as old as Sara will be then.
If x represents Sara's age now, which of the following expressions represents Ralph's age in four years?
A. 3x
B. 2x+4
C. 3x+4
Answer:
In 6 years, Ralph will be only twice as old as Sara
Step-by-step explanation:
Answer:
The answer is C, 3x+4
Step-by-step explanation:
The “in four years” part translates to +4. The 3x translates to 3 times his current age. Hope this helped :)
Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. How fast does a man have to run to be in the top 1% of runners?
Answer:
To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 93, \sigma = 16[/tex]
How fast does a man have to run to be in the top 1% of runners?
The lower the time, the faster they are. So the man has to be at most in the 1st percentile, which is X when Z has a pvalue of 0.01. So he has to run in at most X seconds, and X is found when Z = -2.327. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.327 = \frac{X - 93}{16}[/tex]
[tex]X - 93 = -2.327*16[/tex]
[tex]X = 55.768[/tex]
To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.
A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. Based on these data, the computed two-sample t statistic is:
Answer:
I think the complete question should be:
A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard well known treatment. After a suitable period of time, the reduction in blood pressure for each subject was recorded.
Treatment group n = 21, x1 mean = 23.48, sd = 8.01
Control group n = 23, x2 = 18.52, sd = 7.15
Based on these data, the computed two-sample t statistic is:
Step-by-step explanation:
Since the variances to be calculated from the sd are unequal we use this formula:
t statistics = (x1 - x2) / [(sd1²/n1) + (sd2²/n2) where n1 = 21, x1 mean = 23.48, sd1 = 8.01, n2 = 23, x2 = 18.52, sd2 = 7.15
Thus, we have
test statistic= (23.48-18.52) / [(8.01²/21) + (7.15²/23)]
Test statistics = 4.96 / (324.36/21)+(51.12/23)]
Test statistics = 4.96/ (15.45+2.43)
t statistic = 4.96 / 17.88
t statistics = 0.2774
I hope that helps, you can use this to solve for tours if the values are not the same
Graph g(x)=f(x+1) when f(x) =4x-2
[tex]g(x)=4(x+1)-2[/tex]
[tex]g(x)=4x+4-2[/tex]
[tex]g(x)=4x+2[/tex]
Image attached below for graph.
Breakfast Bar’s scrambled egg recipe uses 8 eggs to feed 5 people. How many eggs are they going to need to serve 100 people on Saturday morning?
Explain the steps you would use to solve the problem.
Answer:
800 eggs
Step-by-step explanation:
You would first thing about the starting numbers, Then look at the number 100 and multiply by 8. This would give you 800. This means that you will need 800 eggs to serve 100 people.
Brainliest is greatly appreciated
Answered by: Skylar
6/8/2020
9:59 AM (Eastern Time)
Answer:
the answer is 12.5 i know because i divided 100 by 8 and got 12.5 then multiply then got 100
Step-by-step explanation:
got it right just did the test
Fractions - Addition : 3/7 + 1/56
Explanation needed
[tex]answer = \frac{25}{56} \\ solution \\ \frac{3}{7} + \frac{1}{56} \\ = \frac{3 \times 8 + 1}{56} \\ = \frac{24 + 1}{56} \\ = \frac{25}{56} \\ hope \: it \: helps \: \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
25/56
Step-by-step explanation:
3/7 + 1/56
We have to find the L.C.M of 7 and 56
The L.C.M of 7 and 56 is 56
Now, we have to change the denominators to 56
we dont need to change the denominator of 1/56 to 56 as it is already 56
[tex]\frac{3}{7}[/tex] * [tex]\frac{8}{8}[/tex] = [tex]\frac{24}{56}[/tex]
Now we can add the fractions
[tex]\frac{24}{56} + \frac{1}{56}[/tex] [tex]= \frac{25}{56}[/tex]
Hope it helped :>
• Write this number as a fraction:178.25
Answer: 178 1/4 or 713/4
Step-by-step explanation:
178.25 = 178+0.25 = 178+25/100
gcd(25,100) = 25
178.25 = 178+(25/25)/(100/25) = 178+1/4 = 713/4
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer: h = -(16t + 3)(t - 2)
h(0) = 6
h(1) = 19
h(2) = 0
Step-by-step explanation:
Factor the equation by finding two numbers whose
product = a×c and sum = b, then replace the b value with those two numbers and factor the equation.
h = -16t² + 29t + 6
a=-16 b=29 c=6 a×c = -96 b = 29
32 × -3 = 96 32 + (-3) = 29
h = -16t² + 32t -3t + 6
h = -16t(t - 2) -3(t - 2)
h = (-16t - 3) (t - 2)
h = -(16t + 3)(t - 2)
h(0) = -[16(0) + 3] [0 - 2]
= -(3)(-2)
= 6
h(1) = -[16(1) + 3] [1 - 2]
= -(19)(-1)
= 19
h(2) = -[16(2) + 3] [2 - 2]
= -(35)(0)
= 0
A gum ball machine has 22 red 18 white 10 blue and 23 green. What chances of pulling out a red
Step-by-step explanation:
Total gum balls = 22 + 18 + 10 + 23 = 73
Probability of red gum = 22/73
Write the quotient in simplest form. Type answer as integer or a fraction
Answer:
[tex]-\dfrac{1}{26}[/tex]
Step-by-step explanation:
[tex]-\dfrac{12}{13}\div 24=\\\\-\dfrac{12}{13} \times \dfrac{1}{24}=\\\\-\dfrac{12}{13\times 24}=\\\\-\dfrac{1}{26}[/tex]
Hope this helps!
In two sample surveys 125 people were asked about their favorite fruit in the survey 40 people chose apples 64 choose oranges and 21 chose bananas in the second 34 chose apples 63 chose oranges 19 Joe’s banana marine inferred before is this a French trooper by us on the data explain
Answer:
Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.
hope it help please mark me as brainliest
What’s the correct answer for this? Select all that apply
Answer:
B and C
Step-by-step explanation:
The correct options are :
A cross-section that is perpendicular to the base of a cube.
A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.
In both the cases the length and the width of the section are equal
Which value of y makes the equation y/9=12 true
Answer:
108
Step-by-step explanation:
9 times 12 is 108
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.48 ppm and a standard deviation of 3.25 ppm. Suppose that you draw a random sample of 10 printers.
Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 18.06 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion)
Answer:
0.288
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740[/tex]
Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.
This is 1 subtracted by the pvalue of Z when X = 18.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18.06 - 17.48}{1.027740}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.712
1 - 0.712 = 0.288
The answer is 0.288
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 53 units of a small appliance with a standard deviation of 12 units. During the same point in time last year, a random sample of 49 stores had mean sales of 41 units with standard deviation 6 units.
It is of interest to construct a 95 percent confidence interval for the difference in population means ?1??2, where ?1 is the mean of this year's sales and ?2 is the mean of last year's sales.
Enter values below rounded to three decimal places.
(a) The estimate is: _________ .
(b) The standard error is: ____________________ .
Answer:
The 95% confidence interval for the difference of means is (7.67, 16.33).
The estimate is Md = 12.
The standard error is sM_d = 2.176.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.
The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.
The difference between sample means is Md=12.
[tex]M_d=M_1-M_2=53-41=12[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{36}+\dfrac{6^2}{49}}\\\\\\s_{M_d}=\sqrt{4+0.735}=\sqrt{4.735}=2.176[/tex]
The degrees of freedom are:
[tex]df=n_1+n_2-1=36+49-2=83[/tex]
The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.
The margin of error (MOE) can be calculated as:
[tex]MOE=t \cdot s_{M_d}=1.989 \cdot 2.176=4.328[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 12-4.328=7.67\\\\UL=M_d+t \cdot s_{M_d} = 12+4.328=16.33[/tex]
The 95% confidence interval for the difference of means is (7.67, 16.33).
An accident Investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid
marks, d, was 117ft. Use the formula s = 24d to find s, the speed of the vehicle before the brakes were applied. Fund
Answer:
2,808
Step-by-step explanation:
since 117 = d then we would just plug that into the equation of s = 24d and get s = 24(117), after that you would just solve.
Answer:
53
Step-by-step explanation:
Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 3 = 0. (Round your answer to four decimal places.) x2 =?
Answer:
[tex]x_{2} = 0.0000[/tex]
Step-by-step explanation:
The formula for the Newton's method is:
[tex]x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}[/tex]
Where [tex]f' (x_{i})[/tex] is the first derivative of the function evaluated in [tex]x_{i}[/tex].
[tex]x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}[/tex]
Lastly, the value of [tex]x_{2}[/tex] is determined by replacing [tex]x_{1}[/tex] with its numerical value:
[tex]x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}[/tex]
[tex]x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}[/tex]
[tex]x_{2} = 0.0000[/tex]
In planning a restaurant, it is estimated that a profit of $8 per seat will be made if the number of seats is no more than 50 inclusive. On the other hand, the profit on each seat will decrease 10 cents for each seat above 50.
a) Find the number of seats that will produce the maximum profit.
b) What is the maximum profit?
Answer:
a. 65 seats
b. $422.50
Step-by-step explanation:
We have the following two functions:
8 * x, {0 <= x <= 50}
x * (8 - 0.1 * (x - 50)), {x> 50}, solving we have:
-0.1 * x ^ 2 + 13 * x, {x> 50}
Now we derive both functions and we are left with:
8, {0 <= x <= 50}
-0.2 * x + 13 {x> 50}
we cannot equal to 0 the first function that is equal to 0, because it would be inconsistent, therefore we equal the second function to 0:
-0.2 * x + 13 = 0
0.2 * x = - 13
x = -13 / -0.2
x = 65
Now, test for increasing and decreasing on the intervals (0.65) and (65, infinity)
p '(60) = -0.2 * (60) + 13 = 1
since this value is positive the profit is increasing on (0.65)
p '(70) = -0.2 * (70) + 13 = -1
becuase this value is negative the profit is decreasing on (65, infinity)
Therefore 65 seats are needed to maximize profit
The maximum value would be:
P (65) = 0.1 * (65 ^ 2) + 13 * 65 = 422.5
That is, the maximum value is $ 422.50