Answer:
-4 · [tex]4^{7}[/tex]
Step-by-step explanation:
A research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years. When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years
a) What is the population of interest in this situation?
b) How many samples were described?
c) Is the average age of 37 years a parameter or a statistic?
d) Tell whether this information represents a quantitative or qualitative variable? - age of the visitor - whether the visitor has a season pass
e) What possible explanation is there for the large difference in age between the two samples?
Answer:
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic.
(d) The above information represents a quantitative variable.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
Step-by-step explanation:
We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.
When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.
(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.
(b) Two samples are described in the above situation, that is;
A survey of 100 randomly selected park visitors on a weekday in May.A survey of 100 randomly selected park visitors on a Saturday in May.(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e. [tex]\bar X_1[/tex] = 37 years.
(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.
(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.
But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at time t hours is given by a function A(t) and the amount in Vat B is given by B(t). The two vats contain the same amount of water at t=0. You have a formula for the rate of flow for Vat A and the amount in Vat B: Vat A rate of flow: A(t)-3t2+24t-21 Vat B amount: B(t)-2t2+16t+40
(a) Find all times at which the graph of A(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum of A(t) smaller t= 1 gives a local minimum larger t= 7 l maximum
(b) Let D(t)-B(t)-A(t). Determine all times at which D(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum. (Round your times to two digits after the decimal.) xgives a Select x gives a Select smaller t- larger t=
(c) Use the fact trruntain the same amount of water at ta0 to find the formula for A(), the amount in Vat A at time t Enter a number
(d) At what time is the water level in Vat A rising most rapidly? t- hours
(e) what is the highest water level in Vat A during the interval from t=0 to t=10 hours? gallons
(f) What is the highest rate at which water flows into Vat B during the interval from t-0 to t-10 hours? gallons per hour
(g) How much water flows into VatA during the interval from t=1 to t-8 hours? gallons
Note: The first file attached contains the clear and complete question
Answer:
a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7
A(t) has a local maximum at t=7
A(t) has a local minimum at t=1
b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74
D(t) has a local maximum at t=1.59
D(t) has a local minimum at t=7.74
c) A(t) = (-t^3) + 8(t^2) -21t + 40
d) The water level in vat A is rising most rapidly at t = 4 hrs
e) 138 gallons
f) 18 gallons per hour
g) 98 gallons
Step-by-step explanation:
For clarity and easiness of expression, the calculations are handwritten and attached as files below.
Each step is neatly expressed and solutions to each part of the question are clearly written
If 7 - y = 6, then y=
Answer:
y=1
Step-by-step explanation:
7-y=6
6+1=7
7-1=6
Hope this helps:)
Stay Safe
Answer:
y =1
Step-by-step explanation:
7 - y = 6
Subtract 7 from each side
7 - y-7 = 6 -7
-y = -1
Multiply each side by -1
-y*-1 = -1 *-1
y = 1
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
(3х^2y^3)^3 =
3x^5y^6
9х^6y^9
27x^5y^6
27x^6y^9
Answer:
27x^6y^9
Step-by-step explanation:
The outside exponent multiplies all of the inside exponents. The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
(3x^2y^3) = (3^3)(x^(2·3))(y^(3·3)) = 27x^6y^9
Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, x3 = 188, x5 = 6.6, and x6 = 10. Use these data to predict x4 (advertising costs) and find an 80% confidence interval for your prediction. (Use 2 decimal places.)
Answer:
The advertising cost, X₄ = 5.626 million
The 80% confidence limits for X₄ is (5.041 , 6.100)
The 80% prediction limits for X₄ is (4.048 , 7.094)
Step-by-step explanation:
Using MINITAB
The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆
Predictor Coef SE Coef T P
Constant 4.142 1.626 2.55 0.019
X₁ 0.043089 0.009466 4.55 0.000
X₂ -0.7998 0.2515 -3.18 0.005
X₃ 0.000590 0.004221 0.14 0.890
X₅ -0.6606 0.1542 -4.28 0.000
X₆ 0.0574 0.1254 0.46 0.652
S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 5 345.966 69.193 59.42 0.000
Residual Error 21 24.454 1.164
Total 26 370.420
Source DF Seq SS
X₁ 1 309.464
X₂ 1 8.699
X₃ 1 5.994
X₅ 1 21.566
X₆ 1 0.244
Unusual Observation
Obs X₁ X₄ Fit SE Fit Residual St Resid
17 398 5.500 7.714 0.641 -2.214 -2.55 R
27 400 7.000 7.366 1.025 -0.336 -1.00 X
Where R is observation with a large standardized residual.
Where X is observation whose X values give it large influence.
Predicted values for new Observations
New
Obs Fit SE Fit 80% Cl 80% Pl
1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)
Values of Predictors for New Observations
New
Obs X₁ X₂ X₃ X₅ X₆
1 163 2.40 188 6.60 10.0
∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)
After 2 hours, there are 1,400 mL of fluids remaining in a patient’s IV. The fluids drip at a rate of 300 mL per hour. Let x be the time passed, in hours, and y be the amount of fluid left in the IV, in mL. Write a linear function that models this scenario.
Answer:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Step-by-step explanation:
We want to set up a linear function like this one:
[tex]y = mx+b[/tex]
Where y is the amount of fluid left, m the slope and b the initial amount. From the info given we know thatm = -300. And we also have the following condition:
[tex] y(2) = 1400[/tex]
Using this condition we got:
[tex]1400= -300*2 +b[/tex]
And solving for b we got:
[tex] b= 1400+ 600= 2000[/tex]
So then our linear function is given by:
[tex] y = -300x +2000[/tex]
Where y is the amount of fluid left and x the number of hours ellapsing
Please answer this question !! 20 points and brainliest !!
Answer:
yes, they are parallel; the general form equation differs only in the constant.
Step-by-step explanation:
Subtract y from the first equation and multiply by 2.
y -y = 1/2x -y +3
0 = x -2y +6
x -2y +6 = 0 . . . . . put in general form
Compared to the second equation, we see the only difference is in the constant, +6 vs. -8.
This means the lines are parallel.
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a $1 charge to play the game, what is the game’s expected value?
Answer:
1/5
Step-by-step explanation:
i had a similar question
For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).
So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars
So you lose 1/3 dollars on average with each game
since you have no limited rolls u put 1/5
this from another question but both same just different numbers
How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the 95% confidence interval of the population proportion
Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
Which of the functions below could have created this graph?
Answer:
i don't know if this is right or not i did to much work to put it all down but i pretty sure it's C.
Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? A: x^2 + 8x – 308 = 0 B: x^2 – 8x + 308 = 0 C: x^2 + 8x + 308 = 0 D: x^2 − 8x − 308 = 0
Answer:
A
Step-by-step explanation:
The smaller negative integer is x.
The larger one is x+8, since they are 8 units apart.
The equation would be:
x*(x+8)=308
Let's simplify it by distributing.
x^2+8x=308
Subtract 308 from both sides.
x^2+8x-308=0
Therefore, the answer would be A.
There are 11 apples in a basket. 9 of these apples are green. The rest of them are red. What is the ratio of red apples to all apples in the basket? What is the ratio of red apples to green apples?
Answer:
Red apples to all apples =2/11
Red apples to green apples =2/9
Step-by-step explanation:
There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples
The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11
The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9
Answer:
Red apples to all apples =2/11
Red apples to green apples =2/9
Step-by-step explanation:
There are 11 total apples 9 of them are green and the rest are red so there are 11-9=2 red apples
The ratio of red apples to all apples = number of red apples ÷ total apples number = 2÷11
The ratio of red apples to green apples = number of red apples ÷ number of green apples = 2÷9
Step-by-step explanation:
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
To examine the effect of high-dose green tea extract on weight loss, researchers conducted a randomized, double-blind trial on a random sample of 115 women with obesity from Taiwan. Some of these women were randomly assigned to the main treatment group taking a high-dose green tea extract ("EGCG") daily for 12 weeks. The published abstract of this 2015 study reports that, "Significant weight loss, from 76.8 ± 11.3 kg to 75.7 ± 11.5 kg (p = 0.025), was observed in the treatment group after 12 weeks of high-dose EGCG treatment."
Which of the following inference procedures would be used to reach the quoted conclusion?
a. Z procedure for a proportion
b. Chi-square for two-way tables
c. Chi-square for goodness of fit
d. Two sample t procedure for two means
e. One sample or matched-pairs t procedure for a mean
f. ANOVA for several means
Answer:
d. Two sample t procedure for two means.
Step-by-step explanation:
The study have a treatment group, which is the group of women that are taking the high dose of green tea extract, and a control group, in order to compare. They are assigned randomly to each group.
Then, the difference fo the two sample means is calculated and a t-test is performed in order to conclude if the two populations means are significantly different.
Apparently they are significantly different, as this is the conclusion with a P-value of 0.025.
A cylindrical tank has a radius of 2 m and a height of 9 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)
Answer:
3,325,140 Joules
Step-by-step explanation:
Work done by the pump = Force applied to pump * distance covered by the water.
Since Force = mass * acceleration due to gravity
Force = (density of water * volume of the tank) * acceleration due to gravity
F =ρVg
Workdone = (ρVg )* d
Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m
[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]
Workdone by the pump = 1000 * 113.10 * 9.8 * 3
Workdone by the pump = 3,325,140Joules
You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.
A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.
Answer:
Step-by-step explanation:
Given that :
The probability of winning is 0.8
i.e P(winning) = 0.8
Then P(losing) = 0.2
a) Y ~ Geometric distribution
[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]
b) Y ~ Negative Binomial Distribution
[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]
c) Y ~ Binomial Distribution;
n = 100 ; P = 0.8
[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]
Do consumers spend more on a trip to Target or Walmart? Suppose researchers interested in this question collected a systematic sample for 84 Target customers and 80 Walmart customers by asking customers for their purchase amount as they left the store. Using the given summary statistics, researchers calculated a 95% confidence interval for the mean difference between Target and Walmart purchase amounts. The interval was ($negative 15.05,$negative 2.95). Explain in context what this interval means.
Answer:
Step-by-step explanation:
Confidence interval for the difference between two population means is written in the form,
difference in sample means ± margin of error
The difference in sample means is the point estimate for the difference in population means. In the given scenario, the point estimate is the difference in mean amount spent by the sampled customers on a trip to Target or Walmart.
Since the interval was (- $15.05,$2.95), it means that the lower limit is - $15.05 and the upper limit us $2.95.
Therefore, the 95% confidence interval is providing a range that we are 95% confident that the true difference in mean amount spent by Target customers and Walmart customers falls between - $15.05 and $2.95
A cognitive psychologist would like to evaluate the claim that the omega-3 fatty acids can help improve memory in normal adult humans. One group of participants is given a large dose of fish extract containing the Omega-3 (500 mg), and a second group is given a placebo containing no Omega-3 (0 mg). The researcher asks each participant to read the front page of a local newspaper thoroughly every morning and to take their prescribed dosage (of either Omega-3 or placebo) immediately afterwards. The researcher gives each participant a memory test at the end of two weeks and records how many news items each participant remembers from the past three weeks of news. Answer the following:
A) What names would you give the independent and dependent variables;
B) Is the dependent variable discrete or continuous?
C) What scale of measurement (nominal, ordinal, interval or ratio; and continuous or discrete) is used to measure the independent variable?
D) What research method is being used (experimental or observational)? Explain why you conclude that the research method is one or the other.
Answer:
(a)
Independent Variable- Dosage of Omega-3 Fatty AcidsDependent Variable - Number of news item remembered(b)Discrete
(c)Ratio Scale and Discrete Variable
(d) Experimental Method
Step-by-step explanation:
The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.
(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).
The memory test involves measuring the number of items each participant remembers from the past three weeks of news.
Therefore:
Independent Variable- Dosage of Omega-3Dependent Variable - Number of news item remembered(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.
(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.
Since the dosage is given in multiples of 50mg, it is a discrete variable.
(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.
Indigo Depot is having a clearance sale of their summer items. A swimsuit that originally cost $120 before any discount is on sale for 15% off. If the swimsuit is then put on clearance for an additional 40% off the sale price, what is the final price? Round your answer to the nearest cent, if necessary.
Answer:
20
Step-by-step explanation:
Answer:
$61.20
Step-by-step explanation:
15% sale:
$120 - 15%= $120*0.85= $10240% sale:
$102 - 40%= $102*0.6= $61.20Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
laura quiere cúbrir con papel de china una puerta como la que se muestran el dibujo cuánto centímetros cuadrados es la que tendra que cubrir con papel de china
Answer:
Necesita cubrir 4800 cm^2.
Step-by-step explanation:
La pregunta está incompleta:
Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo. Las medidas son 80 cm de largo y 60 cm de ancho.
Tenemos que calcular la superficie de la puerta, cuyas medidas son 80 cm de largo y 60 cm de ancho.
Para calcular el área simplemente multiplicamos las medidas de ambos lados:
[tex]A=80\,cm\cdot 60\,cm=4800\,cm^2[/tex]
Suppose that it costs $200 per day to search for chanterelle mushrooms at Pt. Reyes National Seashore. On an average day, the total weight of mushrooms M found at Pt. Reyes is M = 100x-x^2 pounds ,where x is the number of people mushroom hunting on that day. Chanterelles can be sold for $60 per pound. How many more people will go mushroom hunting than is socially optimal?
Answer:
For an overall profit, we need at least 97 people to go mushroom hunting.
Any number of people that is more than the socially optimal number should go mushroom hunting on any given day.
Step-by-step explanation:
The socially optimal number of people that will go mushroom hunting is the number where amount spent to go mushroom hunting equally balances the amount obtained by selling the mushrooms obtained.
If x people go mushroom hunting in a day, the total cost of hunting for that day = 200x
The amount of mushroom obtained is given as
M = (100x - x²) in pounds
The selling price of 1 pound = $60
The cost of M pounds = 60M = 60(100x - x²)
= (6000x - 60x²)
At socially optimal number,
200x = 6000x - 60x²
60x² - 6000x + 200x = 0
60x² - 5800x = 0
x(60x - 5800)
x = 0 or (60x - 5800) = 0
x = 0 or x = (5800/60) = 96.67
Socially optimal number of people = 0 or 96.67
For realistic purposes, we take the socially optimal number of people that went mushroom hunting as 96.67
Any number above this number will result in an overall profit, and any number below it results in an overall loss.
So, for an overall profit, we need at least 97 people to go mushroom hunting.
Hope this Helps!!
Answer:
48 people
Step-by-step explanation:
When allocating resources to a particular task it is important to assign optimal units of resources.
In this scenario if the people hunting mushrooms are too many they will not make profit. But an optimal number will guarantee everyone makes positive profit.
Optimal = (M÷x)Px - 200= 0
Optimal= {(100x -x^2) ÷ x} * 60 = 200
Optimal = 6000 - 60x = 200
x= 96.666~ 97 people
However to maximise profit MTB = MTC
Socially Optimal quantity = 60(100x - x^2) -200
∂(Socially Optimal amount) ÷ ∂ x= 6000 - 120x - 200
x = 48.33~ 48 people
So 48 more people go mushroom hunting than is socially optimal
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
winnie and kevin like to create their own triathlon courses to challenge each other. last weekend, winnie created a course that included a swim of 3/4 of a mile, a bike ride of 57/4 miles and a run of 13/4 miles. how long was the course winnie created?
Please help. I’ll mark you as brainliest if correct . I don’t understand this math problem. Thank you .
Answer:
That can be factored as
(x -1 (1/3) ) * ( x +3) * (x -4/5)
and the zeroes are located at:
x = 1.33333333... x = -3 and x = .8
Step-by-step explanation:
Answer:
[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]
Step-by-step explanation:
We need to factorise the following function
[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]
-3 is a trivial solution, we can notice that f(-3)=0
so we can factorise by (x+3)
let s note a, b and c real and let s write
[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]
[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]
let s identify...
the terms in [tex]x^3[/tex]
15 = a
the terms in [tex]x^2[/tex]
13 = b + 3a
the terms in x
-80 = 3b+c
the constant terms
48 = 3c
so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32
so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]
[tex]\Delta=32^2-4*15*16=64[/tex]
so the roots of [tex](15x^2-32x+16)[/tex] are
[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]
and
[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]
so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]
the zeros are -3, 4/5, 4/3
Select the correct answer from each drop-down menu. A quadrilateral has vertices A(11, -7), B(9, -4), C(11, -1), and D(13, -4). Quadrilateral ABCD is a . If the vertex C(11, -1) were shifted to the point C′(11, 1), quadrilateral ABC′D would be a .
Answer:
Quadrilateral ABCD is a Quadrilateral with four equal sides so either a rhombus or square
But
Quadrilateral ABC'D is a quadrilateral with two adjacent sides equal so it's a kite shape
Step-by-step explanation:
(11, -7), B(9, -4), C(11, -1), and D(13, -4).
Let's take out the values of x and y coordinate with the way they are arranged
X = 11,9,11,13
Y = -7,-4,-1,-4
So we observe that distance of the coordinates on either x is 2 units and y is 3 units.
But when the the value was changed to
C′(11, 1), (11, -7), B(9, -4), C′(11, 1), and D(13, -4).
There was difference of 2 unit and 4 unit making the new shape a kite.
The diagram attached explain better
Answer:
1. rhombus with non-perpendicular adjacent sides
2. kite
Step-by-step explanation:
i just got it right on edmentum.
Please mark as brainliest.
Which equation has two real solutions?
A. x2 = –100
B. 5x2 = 1
C. 6x2 + 17 = 11
D. 7(x2 + 6) = 42
Answer:
B. 5x² = 1Step-by-step explanation:
A. x² = –100
This equation has no solution because x² is always positive.
B. 5x² = 1
then x² = 1/5
then x = 1/(√5) or x = -1/(√5)
C. 6x² + 17 = 11
then 6x² = 11 - 17 = -6
then x² = -6/6 = -1
This equation has no solution because x² is always positive.
D. 7(x + 6) = 42
then x + 6 = 42/7 = 6
then x = 6 - 6 = 0
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:)