Answer: 44ft^2
Step-by-step explanation:
plug it into the equation, h=11, b=8
so A=1/2(11)(8) = 44ft^2
Find the x-intercept of the line 3x + 19y = -18
Answer:
Step-by-step explanation:
Sarai wants to make latkes for
the Hanukkah party. The recipe
says she will need 6 potatoes to
make 16 latkes. Sarai wants to
make 40 latkes. How many
potatoes will she need?
Answer:
The correct answer is 15 potatoes.
Step-by-step explanation:
To solve this problem, we can determine the unit rate and use proportions. We know that Sarai needs 6 potatoes for 16 latkes. We want to know how many potatoes she will need to make 40 latkes. Let's call this unknown value x. We can set up the following equation:
6 potatoes/16 latkes = x potatoes/40 latkes
To solve this equation, we can first simplify the left side to find the unit rate.
3 potatoes/8 latkes = x potatoes/40 latkes
To solve, we can recognize that 40 latkes is 5 times the amount shown in the unit rate (8 latkes), which means that we need 5 times the amount of potatoes.
3 potatoes * 5 = 15 potatoes
Therefore, the correct answer is 15 potatoes. Note that you could have also just solved the equation for x to find your answer as well.
Check out the questions linked below for some more examples of unit rates and using proportions:
https://brainly.com/question/16115741
https://brainly.com/question/29431442
If Cadence earns $66.50 washing cars for 7 hours, how much would she make washing cars for 9 hours?
Answer:$85.5
Step-by-step explanation:
So divide 66.50 by 7 and that will get you 9.5 then multiply that by 9 which is then 85.5
a) If 6^x = 216’
find the value of x.
Answer: x=3
Step-by-step explanation:
6*6=36
36*6=216
6*6*6=216
6*6*6=[tex]6^{2}[/tex]
[tex]6^{x} =6^{3}[/tex]
x=3
Answer:
Step-by-step explanation:
we need to find a base for 216 that is equal to 6.
216 / 6 = 36
36 / 6 = 6,
So 6 * 6 = 36 and 36 * 6 = 216.
From this we know that 216 = 6^3
6^x = 6^3
x=3
13,140 divided by 12
Answer:
1095
Step-by-step explanation:
the probability of heads of a coin is , and this bias is itself the realization of a random variable which is uniformly distributed on the interval . to estimate the bias of this coin. we flip it times, and define the (observed) random variable as the number of heads in this experiment. throughout this problem, you may find the following formula useful: for every positive integers , given the observation , calculate the posterior distribution of the bias . that is, find the conditional distribution of , given . for ,
The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746
What is conditional distribution formula?In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)
What is full conditional distribution?The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).
1) fY|N(y∣N=3)=84 y^6 (1-y)^3
2)0.0636363
To learn more about conditional distribution visit
https://brainly.com/question/14310262
#SPJ4
A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them. Conduct a hypothesis test at the 5% level.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.
Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.
Let p1 be the proportion of local seniors and p2 national seniors.
H₀ : p₁ = p₂
Hₐ : p₁ > p₂
(right tailed test at 5% significance level)
Group I II
Success 69 60 129
Total 100 100 200
p 0.69 0.6 0.645
q 0.31 0.4 0.355
se 0.046249324 0.048989795 0.033836002
p diff 0.09
Std error 0.03384
Z 2.659574468 0
p 0.00391
we find that p value is 0.00391 < 0.05
Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.
To learn more about hypothesis test refer here
https://brainly.com/question/15980493
#SPJ4
The following equation was solved incorrectly by a student
-2 (am + 4) = 22
The solution for the given equation is am = -15.
What is an equation?An equation is formed by equating an expression with another expression or a constant. An equation consists of variables, coefficients, and constants.Depending upon the degree of the variable, the equation is defined.Calculation:The given equation is -2(am + 4) = 22
On simplifying the given equation for its solution, we get
-2(am + 4) = 22
⇒ -2am - 8 = 22
⇒ -2am = 22 + 8
⇒ -2am = 30
∴ am = -30/2 = -15
So, the solution for the given equation is -15.
Learn more about an equation here:
https://brainly.com/question/25678139
#SPJ1
Mr. Martinez has a 16-ounce Starbucks drink. He drinks 10 ounces. What is the percent of ounces Mr. Martinez has left of his drink?
well, he has left only 6 oz.
now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]
Mark pays out his debt at regular intervals every 6 months. He pays $500 each time. If the interest on the loan is 2% compounded semi-annually and he still has 8 years left to pay off the debt, how much does he still owe?
To find out how much Mark still owes on his debt, we need to calculate the amount of interest that has accrued on the loan over the time that he has been paying it off. The interest on the loan is compounded semi-annually, so the amount of interest that accrues on the loan will be added to the principal every six months. Since Mark has been paying off his debt for 8 years and the interest is compounded semi-annually, he will have made 16 payments of $500.
To calculate the total amount of interest that has accrued on the loan, we need to know the original principal amount of the loan. Since we don't have that information, we won't be able to calculate the exact amount that Mark still owes on his debt. However, we can use the information that we have to make an educated guess.
If Mark has been making payments of $500 every six months for eight years, then he has paid a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest payments. If the interest on the loan is 2% compounded semi-annually, then the total amount of interest that has accrued on the loan over the past eight years is $8000 x 2% = $<<80002*.01=160>>160. This means that the original principal amount of the loan was $8000 - $160 = $<<8000-160=7840>>7840.
Since Mark still has 8 years left to pay off the debt, and he is making payments of $500 every six months, he will need to make a total of 8 years x 2 payments per year = <<82=16>>16 more payments of $500 to pay off the debt. This means that he will have to pay a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest over the next eight years.
Since the total amount of interest that has accrued on the loan over the past eight years was $160, the total amount of interest that will accrue on the loan over the next eight years is also $160. This means that the total amount of interest that Mark will have to pay over the next eight years is $160 x 2 = $<<160*2=320>>320.
Adding the amount of interest that Mark will have to pay over the next eight years to the amount of principal that he will have to pay, we find that the total amount that Mark will owe on the loan over the next eight years is $8000 + $320 = $<<8000+320=8320>>8320.
Therefore, if Mark has been paying off his debt for eight years and still has eight years left to pay, he still owes a total of $8320 on the loan.
18. In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile)
and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15. Assuming that
this sample is representative of the cars in use, construct a 98% confidence interval estimate of
the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide
emissions be less than 0.165 g/mi, can we safely conclude that this requirement is being met?
Assume the population is normally distributed.
We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.
What is Normally distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
results obtained are 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15
[tex]\overline {X} = \frac{0.06 + 0.11 + 0.16 + 0.15 + 0.14 + 0.08 + 0.15}{7}\\\\ \overline {X} = 0.1214\\[/tex]
[tex]S=\sqrt[2]{\frac{0.0091}{n-1} } \\\\S= \sqrt[2]{\frac{0.0091}{7-1} }\\\\S=0.039\\\\n-1 = 6\\\\E= 3.143 * \frac{0.039}{\sqrt[2]{7} } \\\\E= 0.0462\\\\[/tex]
The confidence interval ⇾ 0.0752 < µ < 0.1676
We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.
To know more about Normally distribution visit,
https://brainly.com/question/23418254
#SPJ1
What is the x-intercept of 4x+2y=6?
decide if the events are mutually exclusive. explain your reasoning based on a venn diagram. event a: randomly rolling greater than 3 with a six-sided die. event b: randomly rolling less than 5 with a six-sided die.
Analyzing the events a and b given in the question , the events are not mutually exclusive events, which are also called intersecting events in terms of venn diagram.
What is mutually exclusive event?Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. The probability of an occurrence if A and B are mutually exclusive is indicated by P(A Or B) or P. (A U B).
What is mutually inclusive or intersecting event?Mutually inclusive events permit the occurrence of both occurrences simultaneously or inside a single trial. It refers to events that are required to take place simultaneously by a rule or a natural law. When two occurrences are mutually inclusive, they cannot happen separately.
Here, the events a and b can occur simultaneously, since we can get a number greater than 3 and less than 5 at the same time while rolling a dice randomly.
To learn more about mutually exclusive events visit:
https://brainly.com/question/28565577
#SPJ4
Fill in the blank. Given O below, you can conclude that DF is congruent to ____.
In the given circle with center O, DF is congruent to BC.
What is congruent?
When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.
Consider the given circle with center O.
We have to find DF is congruent to which line.
Let point E and A are the midpoints of chord DF and BC.
There is angle 90 degrees on both the points.
The chords DF and chord BC are on the same distance from the center of the circle which is 3.09.
So, the chords DF and BC are of same measure.
Therefore, the chord BC is congruent to DF.
Hence, in the given circle with center O, DF is congruent to BC.
To know more about congruent, click on the link
https://brainly.com/question/2938476
#SPJ1
The playing time X of classical CDs has the normal distribution with a mean of 54 and a standard deviation of 5; the N(54, 5) distribution. What is the relative frequency of classical CDs with a playing time X between 44 and 54 minutes? (2 points)
a)47.5%
b)52.5%
c)50%
d)81.5%
Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 44 and 54 minutes is 0.8150= 81.5%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The relative frequency of classical CDs with playing time X between 44 and 54 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 44, hence:
X = 54:
Z = 3
Z = 3 has a p-value of 0.9987.
X = 54:
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8150
More can be learned about the normal distribution at brainly.com/question/4079902
#SPJ4
The data below consist of 25 samples of 4 observations each on the lengths of particular bolts manufactured for use in a large aircraft. The target length of these bolts is 37 centimeters. Answer the below questions and show all hand written, SPSS (screenshots) or excel work.
a) Is the process in statistical control?
b) If not in statistical control, why? Explain.
c) Given that the tolerance of these bolts is + .01 centimeters, determine the
i. Cp
ii. CpK values of this process and the
iii. Sigma level Samples
Samples
Sub 1
Sub 2
Sub 3
Sub 4
1
36.99
37.02
37.04
37.01
2
37.01
37.04
37.03
36.98
3
36.98
37.03
37.03
36.99
4
37.00
37.00
37.00
36.98
5
36.98
36.99
36.99
36.96
6
36.99
36.96
36.94
36.97
7
36.98
36.97
37.01
36.96
8
36.93
36.96
36.96
36.93
9
36.91
36.99
36.95
36.92
10
36.97
36.99
36.95
36.94
11
37.05
37.05
37.05
37.05
12
37.00
37.04
37.11
37.05
13
37.05
37.04
37.06
37.04
14
37.08
37.08
37.03
37.08
15
37.08
36.99
37.07
37.06
16
36.93
36.99
37.03
37.03
17
37.06
36.94
37.06
36.98
18
36.94
36.96
36.96
37.01
19
37.01
36.98
37.03
37.00
20
37.03
37.07
36.99
37.03
21
36.99
36.99
37.01
37.00
22
37.01
37.00
37.00
36.99
23
37.02
37.00
37.00
37.00
24
37.01
37.01
37.00
37.03
25
36.99
37.00
37.00
36.99
Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.
(a) The process is not a statistical process .
b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.
(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74
and Tolerance = 0.01 USL LSL = 0.01
After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995
cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686
(ii) Cp = min (Cpu, CP).
Cpu = 37.005-37 0.073 = 0.06849
CPL = 0.06859
Срк = 2 × 0.06849 = 0.024
The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).
This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).
The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.
To learn more about statistical process visit:
https://brainly.com/question/13008883
#SPJ4
Solve:
3250/156 = y/40
Answer:
y = 833.(3) .3 repeatingStep-by-step explanation:
the fraction is a division, we solve with an equation
3250 : 156 = y : 40
y = 3250 × 40 : 156
y = 833.(3) 3 repeating
--------------------------
check
3250 : 156 = 833.(3) : 40
20,83333333333333 = 20,83333333333333
the answer is good
find the critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom.
The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.
The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.
To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.
Step 1: Go to the chi-square distribution calculator.
Step 2: Enter the degrees of freedom, which is 10 in this case.
Step 3: Enter the confidence level, which is 99% in this case.
Step 4: Click the “Calculate” button.
Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.
Learn more about confidence interval here
https://brainly.com/question/24131141
#SPJ4
what is 70x+10=200 pretty pls help
Answer: 19/7
Step-by-step explanation:
Your goal is to isolate x or get x by itself.
Move all other variables to the opposite side.
70x+10-10=200-10
70x=190
Divide both sides by 70
x= 19/7
Answer:
[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]
Step-by-step explanation:
To do this you need to:
1. Subtract 10 from both sides {As shown below}
[tex]70x+10-10=200-10[/tex]
2. Simplify {As shown below}
[tex]70x=190[/tex]
3. Divide both sides by the same factor {As shown below}
[tex]\frac{70x}{70} = \frac{190}{70}[/tex]
4. Simplify {As shown below}
{a. Cancel terms that are in both the numerator and the denominator}
{b. Divide the numbers}
[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]
{Please give Brainliest}
Experience has shown that a certain lie detector will show a positive reading (indicates a lie) 10% of the time when a person is telling the truth and 95% of the time when a person is lying. Suppose that a random sample of 5 suspects is subjected to a lie detector test regarding a recent crime. The probability of observing no positive reading if all suspects are telling the truth is: (a) 0.00 (b) 0.23 (c) 0.41 (d) 0.59 (e) 0.77
The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.
Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:
(90%)^5 = (0.9)^5 = 0.59049.
The correct answer is therefore (d) 0.59.
Learn more about probability, here https://brainly.com/question/30034780
#SPJ4
Mark got a new job with a starting salary of $32,000. If he gets a yearly raise
of 2%. find Marks salary after 25 years
Answer:
Mark's salary after 25 years is $52,499.39
Step-by-step explanation:
This situation can be modelled exponentially. We are given the starting amount, 32000, and the annual growth rate, 2%. This means that, for every year that passes, we'd have [tex][(32000)(1.02)][/tex] $ as the salary. As such, the model would be [tex]S(t) = 32000(1.02)^t[/tex]. We want to find Mark's salary 25 years from the starting point, t=25. Having developed a model for this situation, we can simply plug in 25 for t:
[tex]S(25) = 32000(1.02)^{(25)}[/tex]
[tex]S(25) = 52499.39[/tex]
Help me pls asappp……
Answer:
a. (0,1)
b. slope is -2
y-1=-2x
Step-by-step explanation:
10. Which of the following sets of ordered pairs does not describe a function?
A
((7,-2), (5, 0), (3, 3), (1, -2)}
B
((7, 2), (5, 4), (3, 6), (1, 8))
C ((7, 2), (7, 0), (3,-2), (1,4)}
D ((7, 7),(5, 5), (3, 3), (1, 1))
Answer:
C {(7, 2), (7, 0), (3,-2), (1,4)}
Step-by-step explanation:
In a function, x = 7 can't be at both 2 and 0 because it would not pass the vertical line test.
1. What is the volume of a rectangular prism with a length of 15 yards, a width of 8 yards, and a height of 5 yards?
2. A teacher purchased a fish tank for her classroom. The dimensions of the tank are 36 inches by 60 inches by 48 inches. What is the maximum amount of water that the tank can hold?
Answer:
1. 600 yd^3
2. 103,680 in^3
Step-by-step explanation:
1. To find volume we do l*w*h
(15)(8)(5)
120(5)
600 yards^3
2. We also find the volume for this
(36)(60)(48)
2160(48)
103680 in^3
Hopes this helps
Help!!!
A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner
is divided into two equal sections labeled A and B. Nigel will spin each spinner one
time.
How many of the possible outcomes have a number less than 3 or an A?
Hint: first write out the sample space (you should have 10)
Which samples have a number less than 3 or an A?
Answer:
There are 5 possible outcomes when the first spinner is spun, and 2 possible outcomes when the second spinner is spun. Therefore, the sample space of possible outcomes when both spinners are spun is 5 x 2 = <<5*2=10>>10.
The possible outcomes are:
1A
1B
2A
2B
3A
3B
4A
4B
5A
5B
Of these, 3A, 2A, 1A, and 4B have a number less than 3 or an A. Therefore, there are 4 possible outcomes that have a number less than 3 or an A.
Step-by-step explanation:
Which inequality matches the graph?
Answer:
2n + 5 ≤ 7 The first choice
Step-by-step explanation:
2n + 5 ≤ 7 Subtract 5 from both sides.
2n + 5 - 5 ≤ 7 - 5
2n ≤ 2 Divide both sides by 2
[tex]\frac{2n}{2}[/tex] ≤ [tex]\frac{2}{2}[/tex]
n [tex]\leq[/tex] 1
Answer:
2x +5 ≤ 7
I hope my answer helps you.
a box contains ten sealed envelopes numbered 1, . . . , 10. the first six contain no money, the next two each contains $5, and there is a $10 bill in each of the last two. a sample of size 3 is selected with replacement (so we have a random sample), and you get the largest amount in any of the envelopes selected. if x1, x2, and x3 denote the amounts in the selected envelopes, the statistic of interest is m
When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.
Given that,
A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.
We know that,
The probability distribution will be
P(X=0) = 5/10
P(X=5) = 3/10
P(X=10) = 2/10
In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.
The expected value is
E =0(5/10)+5(3/10)+10(2/10) = 3.5
The variance is
V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25
Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.
To learn more about statistic visit: https://brainly.com/question/15006619
#SPJ4
Compute the directional derivatives of the following functions along unit vectors at the indicated points in directions parallel to the given vector. (a) rx, y) = x^y, (Xo, yo) = (e, e), d = 8i + 15j (b) f(x, y, z) = e^x + yz, (Xo, yo, Zo) = (1, 1, 1), d = (1,-4, 4) (c) f(x, y, z) = xyz, (xo, yo, Zo) = (1, 0, 1), d = (1, 0,-1)
The derivative of given function is D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814
We have to find the directional derivative of the given function
f(x,y,z) = yz+e^x at (x0,y0,z0)=(1,1,1) in the direction of the vector
d⃗ =(3,−5,5)
Find the gradient of the function and evaluate it at the given point:
To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.
∇f= (∂f/∂x,∂f/∂y,∂f/∂z)
∂f/∂x = ∂( yz+e^x )/∂x
The derivative of a sum/difference is the sum/difference of derivatives:
∂f/∂x = ∂( yz)/∂x +∂(e^x )/∂x since the derivative of y and z with respect of x is zero.
∂f/∂x = e^x The derivative of exponential is d(e^x)/dx=e^x.
Similarly
d(yz+e^x)/dy = z and d(yz+e^x)/dz = y
∇(yz+e^x)(x0,y0,z0)=(e^x,z,y)
Finally plug in the point we get the result
∇(yz+e^x)|(x0,y0,z0)=(1,1,1)=(e,1,1)
∇(yz+ex)|(x0,y0,z0)=(1,1,1)=(e,1,1)
Now we Find the length of the vector: |d⃗ |=((3)^2+(−5)^2+(5)^2)^1/2 =(59)^1/2
To normalize the vector, divide each component by length:
d = ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)
Finally, the directional derivative is the dot product of the gradient and the normalized vector:
D(yz+e^x)d(1,1,1) = (e,1,1). ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)
D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814
learn more about of derivative here
https://brainly.com/question/14860134
#SPJ4
Which polynomial is the product of (4x−3)(x2+2x−6)?
The polynomial that is the product of (4x−3)(x²+2x−6) is 4x³ + 5x² - 30x + 18
Which polynomial is the product of (4x − 3)(x² + 2x − 6)?A polynomial simply refers to the expression that is composed of constant, variables, and exponents that are combined by mathematical operations.
The product of the polynomial will be:
= (4x −3)(x² + 2x − 6)
= 4x³ + 8x² - 24x - 3x² - 6x + 18
= 4x³ + 5x² - 30x + 18
The product is 4x³ + 5x² - 30x + 18.
Learn more about polynomial on:
brainly.com/question/2833285
#SPJ1
A card is drawn randomly from a standard 52-card deck. Find the following: Write all answers as simplified fractions (not mixed numbers). Probability the card drawn is a face card _____
Probability the card drawn is not a face card. ____
Odds in favor of drawing a face card ______
Odds against drawing a face card _____
The probability the card drawn is a face card is 3/13. The probability the card drawn is not a face card is 10/13. The odds in favor of drawing a face card is 3/10. The odds against drawing a face card are 10/3.
There are 52 cards in a standard deck, and 12 of them are face cards (jack, queen, and king). Therefore, the probability of drawing a face card is 12/52, or 3/13.
The probability of not drawing a face card is 1 minus the probability of drawing a face card. Since the probability of drawing a face card is 3/13, the probability of not drawing a face card is 1 - 3/13, which is 10/13.
The odds in favor of drawing a face card are 3:10, or 3/10. The odds against drawing a face card are 10:3, or 10/3.
In summary:
The probability the card drawn is a face card: 3/13
The probability the card drawn is not a face card: 10/13
Odds in favor of drawing a face card: 3/10
Odds against drawing a face card: 10/3
To know more about probability visit :
brainly.com/question/11234923?referrer=searchResults
#SPJ4