Answer:
840
Step-by-step explanation:
the volume of a rectangular prism is the base(width)height
Solve the equation (y-10)^2=0
Answer:
y=10
Step-by-step explanation:
(y-10)^2=0
Take the square root of each side
sqrt((y-10)^2)=sqrt(0)
y-10 =0
Add 10 to each side
y-10+10=0+10
y = 10
Quiz 1
1,700
Possiblem
A circle has a radius of 10. An arc in this circle has a central angle of 72.
What is the length of the arc?
Either enter an exact answer in terms of 7 or use 3.14 for 7 and enter your answer as a decimal.
Skill Sum
Circle basi
Arc measu
Arc length
Ouiz 1
Unit test
4 of 5 •••
Answer:
Length of arc=4π
Step-by-step explanation:
Length of arc=¤/360 x 2xπxr
Where:
¤=72
r=10
Length of arc=72/360 x 2xπx10
Length of arc=0.2 x 20π
Length of arc=4π
Leah has a 22 ounce coffee. she drinks 7 ounces. enter the percentage of ounces Leah has left of her coffee. round your answer to the nearest hundredth.
Answer:
The percentage of ounces Leah has left of her coffee is 68.18%.
Step-by-step explanation:
The decrease percentage is computed using the formula:
[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]
It is provided that Leah originally had 22 ounce coffee.
Then she drinks 7 ounces of coffee.
Decrease = 7 ounces
Original = 22 ounces
Compute the percentage of ounces Leah has left of her coffee as follows:
[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]
[tex]=\frac{22-7}{22}\times 100\\\\=\frac{15}{22}\times 100\\\\=68.1818182\%\\\\\approx 68.18\%[/tex]
Thus, the percentage of ounces Leah has left of her coffee is 68.18%.
Which of the following best describes the equation below? y=-6x+7
Answer:
y=-6x+7 (Negative Slope)
Step-by-step explanation:
This equation is in slope intercept form.
7= y-intercept
-6= slope
This means that when you plot this on a graph, your slope will be negative.
Find the horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.
y = −3
y = −1
y = 3
y = 1
Answer:
y = 3
Step-by-step explanation:
y = (3x² + 3x + 6) / (x² + 1)
The power of the numerator and denominator are equal, so as x approaches infinity, y approaches the ratio of the leading coefficients.
y = 3/1
The horizontal asymptote will be;
⇒ y = 3
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The algebraic expression is,
''The horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.''
Now,
We can formulate;
⇒ f (x) = ( 3x² + 3x + 6 ) / (x² + 1)
Hence, We get the horizontal asymptote as;
We know that;
A function f is said to have a horizontal asymptote y = a;
⇒ [tex]\lim_{x \to \infty} f (x) = a[/tex]
So, We get;
⇒ [tex]\lim_{x \to \infty} f (x) = \lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1}[/tex]
⇒ [tex]\lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1} = \lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)}[/tex]
⇒ [tex]\lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)} = 3[/tex]
⇒ y = 3
Thus, The horizontal asymptote will be;
⇒ y = 3
Learn more about the divide visit:
https://brainly.com/question/315081
#SPJ2
1 third plus 1/2 -1/5 equals
Answer: 0.63333333333
Step-by-step explanation: Use a calculator.
Answer: 19/30
Step-by-step explanation:
You want to find a common denominator that works for all fractions and add a subtract them and the simplify
(please break it down for me to understand):)
*I got 0.00040404 on calculator but I need fraction not decimal trying to understand how to get the fraction*
[tex] \frac{1}{50} \times \frac{2}{99} = \frac{1}{2475} [/tex]
Answer:
1/50 times 2/99 = 2/4950
divide numerator and denominator by 2 and the answer you should get is 1/2475 and in decimal form it equals 0.00040404040404040
Step-by-step explanation:
This is the question with the answer choices. Is it correct?
Step-by-step explanation:
A question is asked with options for answers, but in reality, there is only one question stating that it is correct.
I need to Simplify (3mn)^4
9514 1404 393
Answer:
81m^4·n^4
Step-by-step explanation:
"Simplify" in this context means "remove parentheses." The applicable rule of exponents is ...
(ab)^c = (a^c)(b^c)
__
[tex](3mn)^4=3^4m^4n^4=\boxed{81m^4n^4}[/tex]
At 12.5 mph how long will it take her to go 4.5 miles
Answer:
asdasd
Step-by-step explanation:
miles ÷ miles/hour = hours
Just divide the miles by the mph
4.5/12.5 = 0.36 hours
(0.36 hours)(60 min/hour) = 21.6 minutes
(0.6 minutes)(60 seconds/minute) = 36 seconds
Time: 21 minutes 36 seconds
Answer:
0.36 hours
Step-by-step explanation:
Miles ÷ Miles/hour = hours
4.5 miles ÷ 12.5 mph = 0.36 hours
You need tile on one wall in your kitchen. The wall measures 12 feet by 5 feet. The tile cost $2 a square foot. How much money will it cost for the tile on the kitchen wall?
Answer:
$120
Step-by-step explanation:
Area of wall: 12*5=60 square feet
price = 60*2=$120
Which of the following it true about the graph below?
Answer:
B
Step-by-step explanation:
choose brainliest
Suppose shirts are one of 3 colors (red, blue and green) and pants are either black or brown. An outfit consists of a shirt and pants. What is the minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits
You solve this question by finding the maximum possible number of different combinations, then adding one extra person.
3 possible shirts * 2 possible pants for each shirt = 6 combinations of pants and shirts.
6 + 1 = 7
Therefore, the minimum is:
7 People
Between the years of 1947 and 1956 earthenware jars containing what are known as the Dead Sea scrolls were found in caves along the coast of Jerusalem in the Dead Sea. Upon radiometric testing it was found that the scrolls were wrapped in material that contained about 79 percent of the original carbon-14.archeologists estimated that the scrolls are about 1900 years old. Are they right ?
Answer:
The scroll is 1949 years old, thus the archeologists are right.
Step-by-step explanation:
The decay equation of ¹⁴C is:
[tex] A = A_{0}e^{-\lambda*t} [/tex] (1)
Where:
A₀: is the initial activity
A: is the activity after a time t = 79%*A₀
λ: is the decay rate
The decay rate is:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where [tex]t_{1/2}[/tex]: is the half-life of ¹⁴C = 5730 y
By entering equation (2) into equation (1) we can find the age of the scrolls.
[tex] A = A_{0}e^{-\lambda*t} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t} [/tex]
Since, A = 79%*A₀, we have:
[tex]\frac{79}{100}A_{0} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]
[tex]ln(\frac{79}{100}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]
Solving the above equation for t:
[tex]t = -\frac{ln(79/100)}{\frac{ln(2)}{t_{1/2}}}[/tex]
[tex]t = -\frac{ln(75/100)}{\frac{ln(2)}{5730 y}} = 1949 y[/tex]
Hence, the scroll is 1949 years old, thus the archeologists are right.
I hope it helps you!
Answer:
The hypothesis is correct.
Step-by-step explanation:
Using the half-life equation, the number of years (1,900) can be substituted for t and the half-life (5,730) can be substituted for h. Since the original amount is not known but the percent remaining is known, any value can be used for the original amount. Using 100 will be the easiest. Plugging these values into the equation gives 79.47 remaining. If 79.47 of the original 100 units are left, that is 79.47 percent. Since radiometric dating gives an estimate of age, the archeologists’ hypothesis is correct.
Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. 500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of adults residents of this city who have cell phones.
Answer:
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 500, \pi = \frac{421}{500} = 0.842[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874[/tex]
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
The 95% confidence interval is (0.81,0.874) and this can be determined by using the confidence interval formula and using the given data.
Given :
500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones.95% confidence level.The formula for the confidence interval is given by:
[tex]\rm CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex] --- (1)
where the value of p is given by:
[tex]\rm p =\dfrac{421}{500}=0.842[/tex]
Now, the value of z for 95% confidence interval is given by:
[tex]\rm p-value = 1-\dfrac{0.05}{2}=0.975[/tex]
So, the z value regarding the p-value 0.975 is 1.96.
Now, substitute the value of z, p, and n in the expression (1).
[tex]\rm CI = 0.842\pm 1.96\sqrt{\dfrac{0.842(1-0.842)}{500}}[/tex]
The upper limit is 0.81 and the lower limit is 0.874 and this can be determined by simplifying the above expression.
So, the 95% confidence interval is (0.81,0.874).
For more information, refer to the link given below:
https://brainly.com/question/23044118
The table shows the relationship, "Taiga reads 250 words Which equation models this relationship?
per minute."
O wm = 250
The independent variable, the number of minutes he
O w = 250m
reads, causes a change in the dependent variable, the
O m = 250w
number of words read.
O w + m = 250
Minutes
(m)
Words
(w)
250
500
750
1000
9514 1404 393
Answer:
w = 250m
Step-by-step explanation:
As the problem statement tells you, the independent variable, the number of minutes he reads, causes a change in the dependent variable, the number of words read. This is modeled by ...
w = 250m
Answer: B. w = 250m
Step-by-step explanation: i answered the question and got it right :)
uppose a 95% confidence interval for the average forearm length of men was (24cm, 27cm). How would we then interpret this interval? 95% of all men have a forearm length between 24cm and 27cm. In confidence intervals calculated from many random samples, 95% would contain a sample average forearm length between 24cm and 27cm. The average forearm length of all men is between 24cm and 27cm 95% of the time. 95% of men in this sample of 9 men have a forearm length between 24cm and 27cm. In confidence intervals calculated from many random samples, 95% would contain the average forearm length for all
Answer:
in many random samples, 95% of the confidence intervals will contain a sample average between 24cm and 27cm.
Step-by-step explanation:
We then interpret this interval that 95% would contain a sample average forearm length between 24cm and 27cm.
What is average?The average is defined as the mean equal to the ratio of the sum of the values of a given number to the total number of values in the set.
The formula for finding the average of given numbers or values is very simple. We just need to add all the numbers and divide the result by the given number of values. So the formula for mean in mathematics is given as follows:
Mean = sum of values/ number of values
Suppose we have given n as number of values like x1, x2, x3 ,..., xn. The average or mean of the given data is equal to:
Mean = (x1 x2 x3 … xn)/n
To learn more about average, refer;
https://brainly.com/question/1375440
#SPJ2
Suppose that there are 100 MBA students in the first-year class. Of these students, 20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience. Suppose that a first-year MBA student is selected at random. (a) What is the probability that this student has at least four years of work experience
Answer:
(a)0.5
(b)0.625
Step-by-step explanation:
Out of 100 MBA students
20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience.Total Sample Space, n(S)=100
(a)Let event A be the event that an MBA student has at least four years of work experience.
n(A)=15+35=50
Therefore:
[tex]P(A)=\dfrac{n(A)}{n(S)} =\dfrac{50}{100}=0.5[/tex]
The probability that this student has at least four years of work experience is 0.5.
(b)Conditional probability that given that a student has at least three years of work experience,this student has at least four years of work experience.
P(at least 4 years|the student has at least three years of experience)
[tex]=\dfrac{50/100}{80/100} =\dfrac{5}{8}=0.625[/tex]
The probability that a randomly selected first-year MBA student has at least four years of work experience is 0.5 or 50%.
Explanation:The question involves the concept of probability in statistics, a part of Mathematics. Here, we are given that there are a total of 100 first-year MBA students. The number of students with at least four years of work experience combines the students with four years and five or more years of work experience. Thus, the students with at least four years of work experience are 15 (four years of work experience) + 35 (five or more years of work experience), which equals 50.
The probability is determined by dividing the number of favorable outcomes by the total number of outcomes. Hence, the probability that a randomly selected first-year MBA student has at least four years of work experience is calculated as 50 (students with at least four years' experience) divided by 100 (total students), which equals 0.5 or 50%.
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ3
A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3. If nickel plating costs $1 per cm2 and silver plating costs $3 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length
Answer:
Base= 5.09 cm x 5.09 cm; height = 1.69 cm
Step-by-step explanation:
-> materials has a square base of side length, dimension will be: x . x = x²
'y' represents height
->For dimensions of 4 silver plated sides= xy each
->dimensions of the nickel plated top= x²
Volume = yx²
44=yx² => y= 44/x²
Cost of the sides will be( 4 * xy * $3 )
Cost of the top and the bottom will be (2 * x² * $1)
For the Total cost: 12xy + 2x²
substituting value of 'y' in above equation,
=> Total cost = 12x (44/x²) + 2x² = 528 / x + 2x²
To Minimum critical point => d [cost] / dx = 0
=> - 528/x² + 4x =0
132/x² - x =0
132 - x³ = 0
x³ = 132
Taking cube root on both sides
∛x³ = ∛(132)
x= 5.09
=> y = 44/5.09² =>1.69
Dimensions of the box :
Base= 5.09 cm x 5.09 cm; height = 1.69 cm
A random sample of n = 4 scores is selected from a population with a mean of 50 and a standard deviation of 12. If the sample mean is 56, what is the z-score for this sample mean?
The z-score for the sample mean in this case is 0.5, which is calculated using the z-score formula, Z = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the standard deviation.
Explanation:The subject here pertains to the calculation of a z-score, which is a statistical measurement describing a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.
Given the sample mean (56), population mean (50), and standard deviation (12), and the formula for the z-score, which is Z = (X - μ) / σ, we can compute for the z-score as follows:
- X is the raw score which is 56- μ is the population mean which is 50- σ is the population standard deviation which is 12Substituting these values into the equation, we have: Z = (56 - 50) / 12 = 0.5. Hence, the z-score of the sample mean is 0.5.
Learn more about Z-score Calculation here:https://brainly.com/question/34836468
#SPJ3
Vitamins in Milk - Milk is a good source of many vitamins that can help us stay healthy. FDA recommends that the average vitamin A concentration for whole milk should be 202 micrograms per liter.
A first study in 2016 collected a sample of 35 whole milk bottles and found the average vitamin A concentration was 206.83 micrograms per liter with a standard deviation of 10 micrograms per liter.
A medical researcher wants to determine if the mean vitamin A concentration in whole milk is more than 202 micrograms per liter. The null and alternative hypothesis are given by
H0 : μ = 202 vs HA: μ > 202.
The effect size for this first study is 0.483 and the p-value is 0.0036.
1. A new study of 100 whole milk bottles reports a p-value of 0.00056 and an effect size of 0.4342. Does the new study confirm or conflict with the results of the first study?
O Conflict, because the effect size is smaller.
O Conflict, because the p-value is much smaller.
O Confirm, because the effect size is comparable.
O Confirm, because the p-value is much smaller.
Answer:
O Confirm, because the p-value is much smaller.
Step-by-step explanation:
The p-value is the probability used to determine whether to accept or reject an null hypothesis. Higher p-value means that there is evidence in favour of the null hypothesis while smaller p-value means that there is stronger evidence in favour of the alternative hypothesis. For the case above, the p-value is smaller which means that the new study confirms the results of the first study which also have a small p-value.
Simplify 8(x - 4).
A. 8x-4
B. 8x-32
C. x-32
D. x-4
Answer:
8x-32
Step-by-step explanation:
Because 8 multiples X and gives 8x and also multiples-4 and gives you -32
:.8x-32
Find the inverse of the function: { (3,5), (1, 6), ( -1, 7), (-3, 8)}
Answer:
{(5,3) , (6,1), (7,-1), (8,-3)}
Step-by-step explanation:
inverse of (x,y) is (y,x)
inverse of { (3,5), (1, 6), ( -1, 7), (-3, 8)} is
{(5,3) , (6,1), (7,-1), (8,-3)}
Outdoor Luggage, Inc., makes high-end hard-sided luggage for sports equipment. Data concerning three of the company’s most popular models appear below. Ski Guard Golf Guard Fishing GuardSelling price per unit $ 270 $ 350 $ 185 Variable cost per unit $ 155 $ 210 $ 65 Plastic injection molding machine processingtime required to produce one unit 7 minutes 9 minutes 12 minutes Pounds of plastic pellets per unit 11 pounds 15 pounds 13 pounds Required:1. If we assume that the total time available on the plastic injection molding machine is the constraint in the production process, how much contribution margin per minute of the constrained resource is earned by each product? 2. Which product offers the most profitable use of the plastic injection molding machine?3. If we assume that a severe shortage of plastic pellets has required the company to cut back its production so much that its new constraint has become the total available pounds of plastic pellets, how much contribution margin per pound of the constrained resource is earned by each product? 4. Which product offers the most profitable use of the plastic pellets?5. Which product has the largest contribution margin per unit?
Find the attachment for complete solution
The annual energy consumption of the town where Camilla lives in creases at a rate that is onal at any time to the energy consumption at that time. The town consumed 4.4 trillion ually after 5 years. British thermal units (BTUs) initially, and it consumed 5.5 trillion BTUs ann What is the town's annual energy consumption, in trillionso f BTUs, after 9 years?
Answer:
6.575 trillion BTUs
Step-by-step explanation:
Let represent the annual energy consumption of the town as E
The rate of annual energy consumption * energy consumption at time past
dE/dt * E
dE/dt =K
k = the proportionality constant
c= the integration constant
(dE/dt=) kdt
lnE = kt + c
E(t) = e^kt+c ⇒ e^c e^kt e^c is a constant, and e^c = E₀
E(t) = E₀ e^kt
The initial consumption of energy is E(0)=4.4TBTU
set t = 0 then
4.4 = E₀ e⇒ E₀ (1)
E₀ = 4.4
E (t) = 4.4e^kt
The consumption after 5 years is t = 5, e(5) = 5.5TBTU
so,
E(5) = 5.5 = 4.4e^k(5)
e^5k = 5/4
We now take the log 5kln = ln(5/4)
5k(1) = ln(5/4)
k = 1/5 ln(5/4) = 0.04463
We find the town's annual energy consumption, after 9 years
we set t=9
E(9) = 4.4e^0.04463(9)
= 4.4(1.494301) = 6.5749TBTUs
Therefore the annual energy consumption of the town after 9 years is
= 6.575 trillion BTUs
A fair dice is rolled.
Work out the probability of getting a multiple of 3.
Give your answer in its simplest form.
Answer:
2/6 or 1/3
Step-by-step explanation:
3 and 6 are multiples of 3
so that is 2 out of 6 numbers on a fair dice.
Consider a sampling distribution with p equals 0.15p=0.15 and samples of size n each. Using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion. a. For a random sample of size n equals 5000n=5000. b. For a random sample of size n equals 1000n=1000. c. For a random sample of size n equals 500n=500.
Answer:
[tex]a.\ \mu_p=750\ \ , \sigma_p=0.005\\\\b.\ \mu_p=150\ \ , \sigma_p=0.0113\\\\c.\ \mu_p=75\ \ , \sigma_p=0.0160[/tex]
Step-by-step explanation:
a. Given p=0.15.
-The mean of a sampling proportion of n=5000 is calculated as:
[tex]\mu_p=np\\\\=0.15\times 5000\\\\=750[/tex]
-The standard deviation is calculated using the formula:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.15(1-0.15)}{5000}}\\\\=0.0050[/tex]
Hence, the sample mean is μ=750 and standard deviation is σ=0.0050
b. Given that p=0.15 and n=1000
#The mean of a sampling proportion of n=1000 is calculated as:
[tex]\mu_p=np\\\\=1000\times 0.15\\\\\\=150[/tex]
#-The standard deviation is calculated as follows:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{1000}}\\\\\\=0.0113[/tex]
Hence, the sample mean is μ=150 and standard deviation is σ=0.0113
c. For p=0.15 and n=500
#The mean is calculated as follows:
[tex]\mu_p=np\\\\\\=0.15\times 500\\\\=75[/tex]
#The standard deviation of the sample proportion is calculated as:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\\\=\sqrt{\frac{0.15\times 0.85}{500}}\\\\\\=0.0160[/tex]
Hence, the sample mean is μ=75 and standard deviation is σ=0.0160
6.- Find the area under the standard normal distribution: to the left of z=-1.55.
Answer:
[tex] P(z<-1.55)=0.0606[/tex]
Step-by-step explanation:
For this case we want to find this probability:
[tex] P(z<-1.55)[/tex]
Because they want the area to the left of the value. We need to remember that the normal standard distribution have a mean of 0 and a deviation of 1.
We can use the following excel code: =NORM.DIST(-1.55,0,1,TRUE)
And we got:
[tex] P(z<-1.55)=0.0606[/tex]
The other possibility is use the normal standard table and we got a similar result.
f(x) = 10x-4 and g(x) = . What is the value of f(g(-4))?
This is a composite function problem in high school mathematics. To solve the problem, first evaluate g(-4), then substitute that result into the function f(x). Using these steps, the composite function f(g(-4)) equals -114.
Explanation:First, it is crucial to identify that this is a question involving composite functions, specifically applying the function f(g(x)). In this case, the function g(x) is not provided in the question, so I'll assume we have a typo. If g(x) has been given as 3x + 1, then g(-4) would equal -11. We substitute -11 into the function f(x)=10x-4, we get f(-11)=10*(-11)-4, which results in f(-11)=-114.
The composite function f(g(-4)) is thus -114.
Learn more about Composite Functions here:https://brainly.com/question/30143914
#SPJ2
Choose the function that represents the data in the table.
A.Y= 0.5x^2+6
B. Y= 0.5^x+6
C. Y= 0.5x+ 6
D. Y= x^0.5+ 6
Given:
It is given that the function represents the data in the table.
We need to determine the function.
Slope:
The slope can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute the coordinates (1,6.5) and (4,8) in the above formula, we get;
[tex]m=\frac{8-6.5}{4-1}[/tex]
[tex]m=\frac{1.5}{3}[/tex]
[tex]m=0.5[/tex]
Thus, the slope is 0.5
y - intercept:
The y - intercept is the value of y when x = 0.
Thus, from the table, when x = 0 the corresponding y value is 6.
Therefore, the y - intercept is [tex]b=6[/tex]
Equation of the function:
The equation of the function can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values [tex]m=0.5[/tex] and [tex]b=6[/tex], we get;
[tex]y=0.5x+6[/tex]
Thus, the equation of the function is [tex]y=0.5x+6[/tex]
Hence, Option C is the correct answer.