Answer:
Z-score for 34-week baby = 0.643
Z-score for 41-week baby = 1.154
Baby weight of 41-week is more than the baby weight of 34-week in the gestation period.
Step-by-step explanation:
Given - Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3100 grams and a standard deviation of 390 grams. If a 34-week gestation period baby weighs 2950 grams and a 41-week gestation period baby weighs 3550 grams
To find - Find the corresponding z-scores. Which baby weighs more relative to the gestation period.
Proof -
Given that,
In between period of 32 to 35 weeks
Mean = 2500
Standard deviation = 700
In between after a period of 40 weeks
Mean = 3100
Standard deviation = 390
Now,
For a 34-week baby,
X = 2950
For a 41-week baby,
X = 3550
Now,
Z-score = (X - mean) / Standard deviation
Now,
For a 34-week baby,
Z - score = (2950 - 2500) / 700 = 0.643
For a 41-week baby,
Z-score = (3550 - 3100) / 390 = 1.154
∴ we get
Z-score for 34-week baby = 0.643
Z-score for 41-week baby = 1.154
As 1.154 > 0.643
So,
Baby weight of 41-week is more than baby weight of 34-week in the gestation period.
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.
Which equations could you use to find the price of one tire patch? Select all that apply.
4x – 1.9 = 22.2
4x – 22.2 = 1.9
4x + 1.9 = 22.2
4x + 22.2 = –1.9
22.2 – 4x = 1.9
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Step-by-step explanation:
Define the variable:
Let x be the cost of one tire patch (in dollars).Given information:
Number of tire patches purchased = 4Total amount available to spend = $22.20Amount remaining after sale = $1.90First equation
The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:
⇒ 4x + $1.90 = $22.20
⇒ 4x + 1.9 = 22.2
Second equation
The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:
⇒ $22.20 - 4x = $1.90
⇒ 22.2 - 4x = 1.9
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Step-by-step explanation:
Find the average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3.
Simplify your answer as much as possible.
The average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3 is
a(x)= -13
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends. Following is the formula for the average rate of change:
a(x) = [f(b) - f(a)]/(b - a)
where,
a(x) = Average Rate of Change
f(a) = Function Value at a
f(b) = Function Value at b
Given,
g (x)=-2x³ +5x² from x=2 to x = 3
Average rate of change is a(x)
g (x)=-2x³ +5x²
Put x=2 in the above equation
g(2)= -2(2)³+5(2)²
= -16+20
=4
g(2)=4
Now, put x=3 in the above equation
g(3)= -2(3)³+5(3)²
= -57+45
= -9
We know that,
Average rate of change a(x)= (g(b)-g(a))/(b-a)
a(x)= g(3)-g(2)/(3-2)
a(x)= (-9-4)/1
a(x)= -13
Therefore, the average rate of change a(x)= -13
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The maximum weight, w, that an elevator can hold is 2200 pounds. Which inequality represents the situation?
Answer: w ≤ 2200 would represent the situation
For g(x) = 12x - 2, evaluate g (1).
A. -1
B. 1
C. 2
D. -2
Answer:
B
Step-by-step explanation:
g(x) = 12x - 2
g(1/4) = 12(1/4) - 2 ==> plug in 1/4 for x
g(1/4) = 12 * 1/4 - 2
g(1/4) = 12/4 - 2
g(1/4) = 3 - 2
g(1/4) = 1 ==> B
Answer:
Step-by-step explanation:
To evaluate g(1) for the function g(x) = 12x - 2, you can substitute the value 1 for x in the function:
g(1) = 12(1) - 2
g(1) = 12 - 2
g(1) = 10
Therefore, g(1) = 10. B
Algebraically prove that x^3 + 9 / x^3+8 = 1 + 1/x^3 +8 , where x ≠ -2
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Determine which statements are the converse, inverse, and contrapositive of the following statement.
If a figure is a square, it is a polygon.
Answer:
Step-by-step explanation:
There are 99 males and 121 females participating in a marathon. What percent of the participants are female?
Enter your answer in the box.
_____%
The art museum is 8 1/2 miles from Alison's house. Alison has ridden her bike 2/3 of the way there so far. How far has she gone?
Alison has traveled six miles on her bike.
What is the distance?Distance is defined as the product of speed and time.
To find how far Alison has ridden her bike, we need to first convert 8 1/2 miles to miles as a mixed number.
We can do this by multiplying the fractional part of the mixed number by the denominator of the fraction:
8 1/2 miles = 8 miles + (1/2 x 2) miles = 8 miles + 1 mile = 9 miles
We can now multiply this distance by 2/3 to find how far Alison has ridden her bike:
9 miles x 2/3 = 6 miles
Therefore, she has ridden her bike 6 miles.
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O For a period of time, an island's
population grows exponentially. If the
continuous growth rate is 3% per year and
the current population is 1,767, what will
the population be 10 years from now?
0.03 - 10
≈2,385
5,867
A) 1767e
3) 1767e0.12.
C) 442e0.03-10
D) 1767e0.09
10
≈
≈597
0.09 - 10
≈4,346
valuate each expression
The population of the island after 10 years will be approximately 2385.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].
Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.
Given, an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.
∴ The population be 10 years from now will be,
[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].
We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.
[tex]y_{10} = 1767e^{0.3}[/tex].
[tex]y_{10} = 1767\times1.35[/tex].
[tex]y_{10} = 2385[/tex].
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Draw the dilation of ABCD using center D and scale factor 1/3. Label the dilation IJKL
According to question.
Given data,
The dilation of ABCD using centre D
And scale factor 1/3
Lebel the dilation IJKL.
With the help of figure,
The dilation of ABCD shown in the figure,
The centre of D shown in the figure,
when EFGH, IJKL are obtained from scaling factor ½,1/3 respectively,
then,
ABCD≈EFGH
and
ABCD≈IJKL
Therefore,
EFGH≈IJKL
(Quadrilaterals similar to the same quadrilateral)
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The length of a shirt is 80 cm. Fatima needs to buy a fabric twice this length. What length of the fabric must she buy?
Answer:
160 cm
Step-by-step explanation:
the question says twice this length
the length is 80 cm, therefore
[tex]80 \times 2 = 160[/tex]
This is because the question is dimply asking you to double the length of the shirt
determine whether the improper integral diverges or converges. evaluate the integral if it converges. 14/(x-8^2
Therefore ,the answer of this integration problem comes out to be 4/9.
Integrity, what is it?To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.
Here,
Given :
=> [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]
=> substitute x- 8 =u
=>du/dt =d(x-8)/dx = 1
=>du/dt =1
=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]
Substituting x- 8 =u
=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]
=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex] ]
=> 14( -1/9) + 1/7)
=> 14 ( ( 9 -7 ) / 63 )
=> 14 (2/63)
=> 28/63
=>4/9
Therefore ,the answer of this integration problem comes out to be 4/9.
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5. A person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh
only 30 pounds on the moon. If Haresh weighs 54 pounds on Earth, how much would he weigh on the
moon?
When Haresh weighs 54 pounds on Earth, his weigh on the moon will be 9 pounds.
How to calculate the value of the weight?From the information, person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh only 30 pounds on the moon.
The constant of proportionality will be:
= 180 / 30.
= 6..
Therefore, Haresh weighs 54 pounds on Earth, his weigh on the moon will be:
= 54 / 6
= 9 pounds.
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Aaliyah invests $7,000.00 at 4% simple interest for 1103 days.
How much interest is earned over the 1103 day period?
The interest earned over the 1103 day period is _______
How much is in the account at the end of the 1103 day period?
Aaliyah will have __________
in the account at the end of the 1103 day period.
The interest earned over the 1103 day period is $840
Aaliyah will have $7840 in the account at the end of the 1103 day period.
What is simple interest?Simple interest is defined as the amount of money that is paid to an individual following an investment that is made to an account.
The amount of money invested = $7,000.00
The rate of interest= 4%
The time of investment = 1103 = 3 years
Simple interest = P×T×R/100
= 7000×4×3/100
= 84000/100
= $840
The amount of money that is in the account at the end of the 1103 day period = 7000 + 840 = $7,840
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Let M be the amount of money left on the card, t weeks after the beginning of the fall semester. enter a linear equation to model the data. use week 0 and week 14 to calculate the slope. round your slope to 2 decimal places.
The amount of money on the card decreases by $1.43 per week. The slope is a measure of the steepness of a line
The slope can be positive, negative, or zero. A positive slope means that the line slopes upward from left to right, which means that the value of the dependent variable (in this case, M) increases as the value of the independent variable (t) increases. A negative slope means that the line slopes downward from left to right, which means that the value of the dependent variable decreases as the value of the independent variable increases.
To find the linear equation that models the data, we need to find the slope of the line. The slope is calculated by using the formula:
slope =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]
Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points on the line. In this case, we can use week 0 and week 14 as our two points. Let's say that at week 0, M = $100 and at week 14, M = $80. Then the slope would be:
slope = ($80 - $100) / (14 - 0) = -$20 / 14 = -$1.43
So the linear equation that models the data is:
M = -$1.43 * t + $100
The missing part in the question is shown in the attachment.
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Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait.The random variable S follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For a sample of values randomly selected from the distribution of S, the average of the sample will be 4.66.The probability is 0.66 that a value randomly selected from the distribution of S will be close to the mean.For a sample of values randomly selected from the distribution of S, the average of the sample will vary from the population mean by no more than 4.66.
Step-by-step explanation:
correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For
I NEED HELP ASAPPPPPP
Answer:
2.5
Step-by-step explanation:
m is the gradient
to find this we do the change in y/change in x
using the first 2 values we have been given:
change in y= 15-10
change in x= 4-2
5/2= 2.5
the gradient in 2.5
Graph by finding the x and y intercepts using a table
-3x-6y=0
Answer: see below
Step-by-step explanation:
x=0 -3(0)-6y=0 -6y=0 y=0
x=1 -3(1)-6y=0 -4-6y=0 -6y=4 y=4/6 or 2/3
x=2 -3(2)-6y=0 -6-6y=0 -6y=6 y=-1
x=3 -3(3)-6y=0 -9-6y=0 -6y=9 y= -9/6 or -3/2
x=-1 -3(-1)-6y=0 3-6y=0 -6y=-3 y=1/2
x y
-1 1/2
0 0
1 -2/3
2 -1
3 -1 1/2
Using the income statement below, calculate the following profitability ratios for Western Bookkeeping and Tax Service. Assume that stockholder's equity equals $441,600 and total assets equal $640,000.
Profit margin ratio
Return on equity ratio
Asset turnover ratio
Write the profit margin and return on equity ratios as a percent, rounded to the nearest percent. Write the asset turnover ratio as a decimal, rounded to two decimal places.
The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:
Profit margin ratio = 8%Return on equity ratio = 8%Asset turnover ratio = 0.75.What are profitability ratios?Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.
Some of the common profitability ratios include:
Gross Profit MarginOperating Income RatioNet Income RatioReturn on Investment (ROI)Return on EquityReturn on Total AssetsAsset turnover RatioEarnings per share.Stockholders' equity = $442,600
Total assets = $640,000
Net sales = $480,000
Net income = $36,000
Profit margin ratio = Net income/Net Sales x 100
= $36,000/$480,000 x 100
= 7.5%
= 8%
Return on equity ratio = Net income/Shareholders' Equity x 100
= $36,000/$442,600 x 100
= 8.13%
= 8%
Asset turnover ratio = Net Sales/Total Assets
= $480,000/$640,000
= 0.75
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A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? hint: look at the difference between number of people and cost to get cost per person and then cost without people
How much does each person cost?
Write an equation to show cost, c, of a bus with x number of people on it
Answer:
Base rate: $120
Rate: $2 per person
Equation: f(x)=2x+120
Step-by-step explanation:
If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40. This means, [tex]\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}[/tex].
These values correspond to a base rate for the bus of $120.
The function for the cost per bus with x number of people on it would be:
[tex]f(x)=2x+100[/tex]
This can be checked by using the values given in the problem:
[tex]f(30)=2(30)+120=180\\f(50)=2(50)+120=220[/tex]
The base rate of $120 and $2 per person satisfies the given equation and established values.
Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.
Given: BD ≅ BF
DE⊥BC
F K ⊥ AB
Prove: ED ≅ F K
The triangle ΔBHK and ΔBDE are congruent with each other. Then the side length ED is equal to the side length HK.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
Replace F with H.
The triangles ΔBHK and ΔBDE are shown.
In triangles ΔBHK and ΔBDE, then we have
BD ≅ BH (Given)
∠HBK = ∠DBE (Common angle)
∠BHK = ∠BDE = 90° (Right angle)
The triangle ΔBHK and ΔBDE are harmonious with one another. Then, at that point, the side length ED is equivalent to the side length HK.
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Can someone help me with this question????
Answer:
[tex]P = \boxed{\sf 4000}[/tex]
[tex]r=\boxed{\sf 0.03}[/tex]
[tex]n=\boxed{\sf 4}[/tex]
[tex]t=\boxed{\sf 5}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
If you invest $4,000 then the principal amount is $4,000. As P represents the principal amount:
[tex]\implies P = \boxed{\sf 4000}[/tex]
The interest is 3%. 3% = 3/100 = 0.03. Therefore:
[tex]\implies r=\boxed{\sf 0.03}[/tex]
"n" represents the number of times interest is applied per year.
Therefore, if the interest is applied quarterly then:
[tex]\implies n=\boxed{\sf 4}[/tex]
"t" represents the time in years. Therefore, if you plan to leave the money in the account for 5 years then:
[tex]\implies t=\boxed{\sf 5}[/tex]
-----------------------------------------------------------------------------------------
To calculate the amount in the account after 5 years, substitute the values into the formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.03}{4}\right)^{4 \times 5}[/tex]
[tex]\implies A=4000\left(1+0.0075\right)^{20}[/tex]
[tex]\implies A=4000\left(1.0075\right)^{20}[/tex]
[tex]\implies A=4000(1.16118414...)[/tex]
[tex]\implies A=\$4644.74[/tex]
on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.
How to find the day to take the dose ?From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:
Day Time
First dose Monday 9 am
Second dose Monday 9 pm
Third dose Tuesday 9 am
Fourth dose Tuesday 9 pm
Fifth dose Wednesday 9 am
Sixth dose Wednesday 9 pm
Seventh dose Thursday 9 am
Therese will therefore take the seventh dose at 9 am on Thursday.
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A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 820-meter head start. When the start gun is fired the hare begins running at a constant speed of 7.5 meters per second and the tortoise begins crawling at a constant speed of 4.5 meters per second.
a. Write an expression in terms of t that represents the hare's distance from the starting line (in meters)
b. Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters).
c. Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
a. The hare's distance from the starting line is represented by the expression 7.5t.
b. The tortoise's distance from the starting line is represented by the expression 4.5t+820.
c. The number of meters the tortoise is ahead of the hare is represented by the expression 4.5t+820-7.5t.
In the race, the hare is running at a constant speed of 7.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to run that distance. This is represented by the expression 7.5t, where t is the time in seconds it takes the hare to run.
Similarly, the tortoise is crawling at a constant speed of 4.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to crawl that distance, plus the 820-meter head start they were given. This is represented by the expression 4.5t+820, where t is the time in seconds it takes the tortoise to crawl.
To find the number of meters the tortoise is ahead of the hare, we subtract the hare's distance from the starting line from the tortoise's distance from the starting line, which gives us the expression 4.5t+820-7.5t.
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Four times a number is equal to the number increased by 12. Find the number
Answer:
number is 4
Step-by-step explanation:
let n be the number then 4 times the number is 4n and
4n = n + 12 ( subtract n from both sides )
3n = 12 ( divide both sides by 3 )
n = 4
that is the number is 4
Twenty percent of U.S. adults have some type of mental illness. You randomly select 6 U.S. adults. Find the probability that the number of adults having some type of mental illness is:
a)exactly two
b)at least one
c)less than three
d)find the mean, variance, and standard deviation for this distribution
The mean is 1.2 ,variance is 0.96 and standard deviation of the given data is 96 square root.we can find all these data by using formula of probability.
what is probability?Probability means possibility.It is a branch that deals with occurrence of random event.The value is given in the probability from 0 to 1.Probability is how likely something is to happen.It is used in real life for analysis data.we can find probability to favorable outcomes divided by total outcomes.
What is difference between standard deviation and variation?Standard deviation measures how far apart numbers are in a data set.Variance gives us the actual value to how much the numbers in a data set vary from the mean.The variance is equal to the square standard deviation and standard deviation is the square root of the variance.
NOW we have data
Person(ill)=20% =0.20 n=6
For Exactly two p(x) =2
now we get 24.58% by using binomial theorem and putting value in the formula.
NOW for at least one p(x)>1 By putting value we get 0.7379.
Now for less than three p(x<30) we get 0.9011
Now to find mean
Mean=person (ill) multiply n
Mean = 0.20 * 6
Mean= 1.2
Variance= 1.2*0.80
=0.96
IN the last we find standard deviation.it will be 96 square root.
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Eileen is making lemonade with water and lemon concentrate. What percent of each mixture is
lemon concentrate?
a. The ratio of water to lemon concentrate is 3 to 1.
b. Eileen mixes 4 parts water for each part of lemon concentrate.
c. 4 out of every 5 cups of the mixture is water.
a) The percentage of lemon is 25%
b) The percentage of lemon is 20%
c) The percentage of lemon is 20%
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
a)
Water : Lemon = 3 : 1
Percent of lemon concentrate:
= 1/4 x 100
= 25%
b)
1 part of lemon = 4 part of water
Percent of lemon.
= 1/5 x 100
= 20%
c)
Cups of lemon = 1
Cups of water = 4
Percent of lemon.
= 1/5 x 100
= 20%
Thus,
The percent of each answer is given above.
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Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, what is the value of s?
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.
Define midpoint.The point that divides a line segment into two equal halves is known as the midway in geometry. A point that divides a line segment into two equal halves is the midpoint of the segment. In other words, the line segment's midpoint is precisely in the middle. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
Given,
VZ = s + 14
WY = s
VZ bisects WY
VZ = 2WY
s + 14 = 2(s)
s + 14 = 2s
2s - s = 14
s = 14
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.
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so I am still very confused because when I do it the same it tells me I am wrong did I do something wrong my assignment is DUE TODAY!!!!!!!!! :(
PLEASE HELP ME NOW :(
Answer:
7.5 minutes
4/3 km
Step-by-step explanation:
Use a proportion.
2 km is to 3 min as 5 km is to x min
2/3 = 5/x
2x = 3 × 5
2x = 15
x = 7.5
Answer: 7.5 minutes
2 km is to 3 min as x km is to 2 min
2/3 = x/2
3x = 2 × 2
3x = 4
x = 4/3
Answer: 4/3 km
solve: 2cos(x)+sqrt2=0 less than x less than 2pi
Check all that apply.
a.pi/4
b.3pi/4
c.5pi/4
d.7pi/4
The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:
c.5pi/4
d.7pi/4
What is the solution about?To solve this equation, we can start by isolating the cosine term on one side of the equation:
[tex]2cos(x) = -\sqrt{2[/tex]
[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]
The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).
The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].
Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:
[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]
where k is an integer.
Substituting the values from the given choices into this equation, we find that the possible solutions are:
[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]
Therefore, the correct answer is c. and d.
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Answer:
b.3pi/4
c.5pi/4
Step-by-step explanation: