For this case we must find the solution set of the given inequalities:
Inequality 1:
[tex]3 (2x + 1)> 21[/tex]
Applying distributive property on the left side of inequality:
[tex]6x + 3> 21[/tex]
Subtracting 3 from both sides of the inequality:
[tex]6x> 21-3\\6x> 18[/tex]
Dividing by 6 on both sides of the inequality:
[tex]x> \frac {18} {6}\\x> 3[/tex]
Thus, the solution is given by all the values of "x" greater than 3.
Inequality 2:
[tex]4x + 3 <3x + 7[/tex]
Subtracting 3x from both sides of the inequality:
[tex]4x-3x + 3 <7\\x + 3 <7[/tex]
Subtracting 3 from both sides of the inequality:
[tex]x <7-3\\x <4[/tex]
Thus, the solution is given by all values of x less than 4.
The solution set is given by the union of the two solutions, that is, all real numbers.
Answer:
All real numbers
Write the solution to the given inequality in interval notation.
A) [2,∞)
B) (-∞,2]
C) (-∞,2)
D) (2,∞)
Answer:
The answer should be C.
Answer:
c
Step-by-step explanation:
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.
Write a differential equation that is satisfied by y
A small town has 3,500 inhabitants. At 8 AM, 280 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round your final answer to one decimal place.)
Answer:
a) dy/dt = ky(1-y)
b) 3:36pm
Step-by-step explanation:
a) Let the number of people who have heard the rumor = p
Let those who have not heard the rumor= q
Total population = p+q
Fraction of those that heard the rumor = p/p+q = y
Fraction of those who did not hear the rumor = q/p+q = 1-y
The rate at which the rumor spreads = dy/dt
dy/dt varies directly to y(1-y)
dy/dt = ky(1-y) where k is a constant
b) Recall that dy/dt = ky(1-y)
y(t) = y/(y+(1-y) e^-kt)
At 8 am , t= 0
y = p/ p+q
y(0) = 280/3500
y(0) = 0.08
By noon(12pm), t = 4
At this time half of the population has heard the rumor
y(4) = 0.5
Recall that y(t) = y/(y+(1-y) e^-kt)
y(t) = y0/(y0+(1-y0) e^-kt)
y(t) = 0.08/(0.08+(1-0.08) e^-kt)
y(t) = 0.08/(0.08+0 92 e^-kt)
To find k, put y(4) = 0.5 into the equation
y(4) = y/(y+(1-y) e^-4k)
0.5 = 0.08/(0.08+0.92e^-4k)
0.08 + 0.92e^-4k = 0.08/0.5
0.92e^-4k = 0.16 - 0.08
0.92e^-4k = 0.08
e^-4k = 0.08/0.92
e^-4k = 0.087
-4k = ln(0.087)
-4k = -2.422
k = -2.422/ -4
k = 0.611
y(t) = 0.08/(0.08+ 0.92 e^-0.611t)
The time by which 90% of the population would have heard the rumor is
0.9 = 0.08/(0.08+0.92e^-0.611t)
0.08 + 0.92e^-0.611t = 0.08/0.9
0.92e^-0.611t= (0.08/0.9) - 0.08
e^-0.611t = [(0.08/0.9)-0.08] / 0.92
e^-0.611t = 0.00966
-0.611t = ln(0.00966)
-0.611t = -4.640
t = -4.640/ -0.611
t = 7.6hrs
t = 7 hrs + (0.6*60)mins
t= 7 hrs + 36mins
t = 7hrs 36 mins
Therefore 8 am + 7 hrs 36 mins = 3:36pm
The time by which 90% of the rumor spreads = 3:36pm
The differential equation for the spread of a rumor, given the rate is proportional to the product of the fraction of the population who have heard the rumor and the fraction that has not, is dy/dt = k * y * (1 - y). To solve when 90% will have heard it, we find k using initial conditions and integrate to find the time.
Explanation:To create a differential equation for the spread of the rumor we can say that the rate of spread, which is the derivative of the fraction of the population that has heard the rumor with respect to time (dy/dt), is proportional to the product of the fraction of the population that has heard the rumor (y) and the fraction that has not heard the rumor (1 - y). This gives us the differential equation dy/dt = k * y * (1 - y), where k is the proportionality constant.
To solve the problem for when 90% of the population will hear the rumor, we must first find the value of k using the initial conditions provided. At 8 AM, y(0) = 280/3500 and at noon, which is 4 hours later, y(4) = 0.5. Using this information, we can integrate the differential equation to find k and then use it to determine when 90% (i.e., y(t) = 0.9) of the population will have heard the rumor, applying appropriate integration and exponential growth techniques.
Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 28%. Use a 0.05 significance level to test that claim.
Answer:
The percentage of blue candies is equal to 28%.
Step-by-step explanation:
Sample size = n = 1000
21% of them are blue
So, No. of blue candies = [tex]21\% \times 100 =\frac{21}{100} \times 100=21[/tex]
Claim : The percentage of blue candies is equal to 28%.
[tex]H_0:\mu = 0.28\\H_a:\mu \neq 0.28[/tex]
We will use one sample proportion test
[tex]\widehat{p}=\frac{x}{n}[/tex]
[tex]\widehat{p}=\frac{21}{100}[/tex]
[tex]\widehat{p}=0.21[/tex]
Formula of test statistic =[tex]\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
=[tex]\frac{0.21-0.28}{\sqrt{\frac{0.28(1-0.28)}{100}}}[/tex]
=−1.55
Now refer the p value from the z table
p value =0.0606
α =0.05
So, p value > α
So, we failed to reject null hypothesis
So, the percentage of blue candies is equal to 28%.
Given the problem, first, we denote the sample size, observed proportion of blue candies, claimed proportion of blue candies, and significance level as:
- n = 100
- p_observed = 0.21
- p_claimed = 0.28
- significance_level = 0.05
Our first step in the hypothesis testing process is to calculate the standard error. We do this using the formula:
standard_error = sqrt((p_claimed*(1 - p_claimed))/n)
which gives us a standard error of approximately 0.0449. The standard error measures the variability or dispersion of our sample proportion from the claimed proportion.
Next, we will calculate the z-score, which measures the number of standard deviations an observation (or in this case, the sample proportion) is away from the mean, or the claimed proportion. We do this using the formula:
z = (p_observed - p_claimed)/standard_error
which gives us a z-score of approximately -1.559. The negative sign indicates that the observed proportion is less than the hypothesized proportion.
Then, we need to calculate the p-value. The p-value is the probability of getting a sample as extreme, or more extreme, than the one we have, assuming the null hypothesis is true. In other words, it is the likelihood of observing our sample data if the candy company's claim of 28% blue candies is accurate.
As the observed proportion is less than the hypothesized proportion, we calculate the cumulative probability up to the z-score. Doing this gives us a p-value of approximately 0.0595.
Finally, we need to determine whether to accept or reject the null hypothesis based on the p-value and the significance level.
Here, we can see our p-value is slightly larger than the given significance level (0.0595 > 0.05), thus, we do not reject the null hypothesis. This means there is not enough evidence at the 5% significance level to reject the candy company's claim that 28% of their candies are blue.
In conclusion, given our sample and the given significance level, our analysis does not provide sufficient evidence to say with 95% confidence that the company's claim is false. Our data does not contradict the company's claimed proportion of 28%.
In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?(A) xy(B) x + y(C) 1/(x + y)(D) xy/(x + y)(E) (x + y)/xy
Answer:
(D) xy/(x + y)
Step-by-step explanation:
To find r in terms of x and y
Given,
two resistors with resistances x and y are connected in parallelr is the combined resistance of these two resistorsthe reciprocal of r is equal to the sum of the reciprocals of x and yThen,
1/r = 1/x + 1/y
1/r = (y + x)/xy
Find the reciprocal of both sides
r = xy/(x + y)
The right answer is option (D) xy/(x + y)
Yolanda is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of 'English is Fun' she sells. Suppose that x and y are related by the equation y=1900+80x.
a. What is the change in Yolanda's total pay for each copy of 'English is Fun' she sells?
b. What is Yolanda's total pay if she doesn't sell any copies of 'English is Fun'?
Answer: a) $80 b)$1900
Step-by-step explanation:
a) change in Yolanda total pay y, for each 'English is fun' sold x, i.e ∆y/∆x = dy/dx
y = 1900+80x
differentiating the equation above
dy/dx = 80
Therefore, dy/dx = $80
change in Yolanda total pay y, for each 'English is fun' sold x, is $80
b) if she doesn't sell any copy of ' English is fun ',x=0
Therefore,
y = 1900 + 80x
Substituting x = 0, into the equation above
y = 1900 = $1900
Therefore her total pay is $1900 if she did not sell any ' English is fun'
Meg is walking around her neighborhood. She stands 150 meters from the grocery store, and she wants to know the distance between the store and the bank.
Which answer is closest to the distance between the store and the bank?
Answer:
162.5 meters
Step-by-step explanation:
With respect to the angle given, the side from Meg to Store (150m) is the side that is "opposite" to the angle.
The side from Store to Bank is the side that is "adjacent" to the angle.
So, we have Opposite side and want to know the Adjacent side.
Which trigonometric ratio relates "opposite" to "adjacent"??
Yes, it is Tan!
We write the trig equation and solve for the distance (letting it be x):
[tex]Tan(42.71)=\frac{Opposite}{Adjacent}=\frac{150}{x}\\x=\frac{150}{Tan(42.71)}\\x=162.49[/tex]
Rounding the answer to 1 decimal place, it is:
162.5 meters
The temperature T of an object in degrees Fahrenheit after t minutes is represented by the equation T(t) = 69e−0.0174t + 79. To the nearest degree, what is the temperature of the object after one and a half hours?
To determine the temperature of an object after a specific time using the given equation T(t) = 69e−0.0174t + 79, you replace t with the desired time in minutes and calculate the result. In case of one and a half hours (90 minutes), the temperature can be found using T(90) = 69e−0.0174*90 + 79.
Explanation:The subject of this question is mathematics, more specifically an application of exponential decay in the context of temperature change. The equation T(t) = 69e−0.0174t + 79 represents the temperature T of an object after time t in minutes. To find the temperature after one and a half hours, we need to convert this to minutes because the given equation uses time in minutes. One and a half hours is equivalent to 90 minutes. So we will plug t=90 into the equation:
T(90) = 69e−0.0174*90 + 79.
Around this value to the nearest degree will give us the desired temperature in degrees Fahrenheit after one and a half hours.
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The temperature of the object after one and a half hours is approximately [tex]\( {93^\circ} \)[/tex] Fahrenheit.
To find the temperature of the object after one and a half hours, we need to substitute t = 90 minutes into the equation [tex]\( T(t) = 69e^{-0.0174t} + 79 \)[/tex], since there are 60 minutes in an hour and a half.
Let's calculate:
[tex]\[ T(90) = 69e^{-0.0174 \times 90} + 79 \]\[ T(90) = 69e^{-1.566} + 79 \][/tex]
Using a calculator:
[tex]\[ T(90) \approx 69 \times 0.208 + 79 \]\[ T(90) \approx 14.352 + 79 \]\[ T(90) \approx 93.352 \][/tex]
Identify the fraction that is equivalent to 5 __ 9 1. 20\ 45 2. 25\36 3.25\ 45 4. 30\45
Answer:
3. 25/45
Step-by-step explanation:
[tex]\dfrac{5}{9}=\dfrac{5\cdot 5}{5\cdot 9}=\bf{\dfrac{25}{45}}[/tex]
Find an equation of the line through the given point and perpendicular to the given line
Y=2x-2 and (-3, 5)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is
y = 2x - 2
Comparing with the slope intercept form,
Slope, m = 2
This means that the slope of the line that is perpendicular to it is -1/2
The given points are (-3, 5)
To determine c,
We will substitute m = -1/2, y = 5 and x = - 3 into the equation, y = mx + c
It becomes
5 = -1/2 × - 3 + c
5 = - 3/2 + c
c = 5 + 3/2
c = 13/2
The equation becomes
y = -x/2 + 13/2
5.6% CompleteToolbox 55.6% complete This is a Single Choice Question; skip ahead to question content A B C D E Confirm Drainage tubing comes in large rolls. At your hardware store, you cut tubing to the lengths the customers want. You also provide customers with the volume of their tubing because they need to fill tubing with gravel as they install it. The tubing’s inside radius is 2 inches. Which of the following is an expression for the volume of L feet of drainage tubing, in cubic feet? 0.09L 3.14L 6.28L 12.56L 150.72L
Answer: V = 0.09L feet^3
Step-by-step explanation:
The tubing has the shape of a cylinder. Formula for determining the volume of a cylinder is
Volume of cylinder = πr^2h
Where π = 22/7 or 3.14
r = the inner radius of the drainage tubing. It is given as 2 inches. We would convert the 2 inches to feets
If 12 inches = 1 foot,
2 inches will be 2/12 inches
h = height of the cylinder and it is replaced by L in feets. L is the length of the cut drainage tubing.
An expression for the volume of L feets of drainage tubing will be
V = πr^2L
= 3.14 × (2/12)^2 × L
= 3.14 × 4/144 × L
V = 0.087L feet^3
V = 0.09L feet^3
The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be p = 0.3. If a random sample of 10 residents shows that 1 or fewer favor this proposal, we will conclude that p < 0.3.
a. Find the probability of type I error if the true proportion is p = 0.3.
b. Find the probability of committing a type II error with this procedure if p = 0.2.
c. What is the power of this procedure if the true proportion is p = 0.2?
Answer:
b
Step-by-step explanation:
you first got twerk and this is workable because my wife left me for this reason
The exponential models describe the population of the indicated country, A, in millions, t years after 2006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
A) Country 1: A= 126.4e^0.001t
B) Country 2: A= 1091.5e^0.016t
C) Country 3: A= 143.6 e^-0.005t
D) Country 4: A= 27.6 e^0.025t
Answer:
Step-by-step explanation:
Country 4 has the highest growth rate, as it has the largest exponent in its growth function.
The growth rate of each country is given by the coefficient in the exponent of the exponential equation. The greatest growth rate is for Country 4, which has a growth rate of 2.5% each year.
Explanation:The growth rate of each country is represented by the coefficient in the exponent in each exponential equation. The coefficients represent the yearly percentage increase in population. Looking at the four models given, the coefficients are 0.001 for country 1, 0.016 for country 2, -0.005 for country 3, and 0.025 for country 4. Note that the coefficient for country 3 is negative, indicating that the population is actually decreasing each year. Hence, it can be concluded that Country 4 has the greatest growth rate, which is 0.025 or 2.5% each year (when the coefficient is expressed as a percentage).
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Fill in the missing amounts in the balance sheet after the following transactions. You start with $2,500 in cash and in owner's equity.
a. You purchase testing equipment for $815.
b. You purchace product for $500 and then sell it for $1750.00.
c. You receive next month's utility bill for $185.00.
d. You pay the rent by check for $300.
Total assets: $3,450
Total liabilities and equity: $3,450
Explanation:
Cash: $2635
Equipment: $815
Total assets: $3,450
Accounts Payable: $185
Owner's Equity: $3,450 - $185 = $3,265
Total liabilities and equity: $3,450
the guy up there didn't understand.
Brainliest?
If George put $600 in a savings account at a simple interest rate for each year. What was his interest rate, r, if after 3 years he had a total of 708$
Answer:
6%
Step-by-step explanation:
The multiplier on George's money is ...
$708/$600 = 1.18
This value is ...
1 + rt = 1.18 . . . . . for t = 3
3r = 0.18 . . . . . . subtract 1; next divide by 3
r = 0.06 = 6%
The simple interest rate on George's account is 6%.
Two jets leave an air base at the same time and travel in opposite directions. One jet travels 100 miles an hour faster than the other. If the two jets are 3924 miles apart after3 hours, what is the rate of each jet?
Answer: speed of jet A is 704 miles per hour
speed of jet B is 604 miles per hour
Step-by-step explanation:
Let the jets be jet A and jet B
Jet A and Jet B leave an air base at the same time and travel in opposite directions.
Let x = the speed of Jet A
Let y = the speed of jet B
One jet travels 100 miles an hour faster than the other. Let Jet A be the faster Jet. This means that
x = y + 100 - - - - - -1
If the two jets are 3924 miles apart after 3 hours, this means that both Jet A and Jet B travelled a total distance of 3924 miles after 3 hours.
Distance travelled = speed × time
Therefore,
Distance travelled by Jet A in 3 hours will be x × 3 = 3x miles.
Distance travelled by Jet B in 3 hours will be y × 3 = 3y miles.
Therefore, total distance is
3x + 3y = 3924 - - - - - - - -2
Substituting equation 1 into equation 2, it becomes
3(y+100) + 3y = 3924
3y + 300 + 3y = 3924
6y = 3924 - 300 = 3624
y = 3624/6 = 604 miles per hour
x = y + 100 = 604 + 100
x = 704 miles per hour
With no air resistance, the time, t, it takes an object to fall h feet, can be determined by the equation t = square root of h/4. What is the height when the time to reach the ground is 25 seconds?
Answer:
10,000 ft
Step-by-step explanation:
We can solve the given relation for h:
[tex]t=\dfrac{\sqrt{h}}{4}\\\\4t=\sqrt{h}\\\\h=16t^2[/tex]
Putting t=25 into this formula, we get ...
h = 16(25²) = 10,000
With no air resistance the object will take 25 seconds to fall from 10,000 feet.
A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?
A. 120
B. 240
C. 480
D. 600
E. 1200
Answer: E. 1200
Step-by-step explanation:
Given : A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts.
i.e. No. of choices for different salads= 8 -----(1)
No. of choices for different main courses = 5 ----(2)
No. of choices for different desserts = 6
When we choose two different desserts then we use permutation(repeatition not allowed) :
[tex]^6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6\times5\times4!}{4!}=6\times5=30[/tex]----(3)
[∵ No. of ways to choose r things out of n =[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex] ]
If customers choose one salad, one main course and two different desserts for their meal , then By Fundamental principle of counting (Multiply (1) , (2) and (3)), the number of different meals are possible :-
[tex]8\times5\times30\\\\=1200[/tex]
Hence, the correct answer is E. 1200 .
Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1 1/2 times her regular pay. How much does Joelle earn for a week in which she works 42 hours? *How much does Joelle earn for a week in which she works 42 hour?
A. $126.00
B. $315.00
C. $322.50
D. $378.00
E. $472.
Final answer:
Joelle would earn $322.50 for a week in which she works 42 hours.
Explanation:
To calculate Joelle's earnings for a week in which she works 42 hours, we need to determine the regular pay for the first 40 hours and the overtime pay for the additional 2 hours.
Regular pay for 40 hours = $7.50/hour x 40 hours = $300
Overtime pay for 2 hours = 1.5 x $7.50/hour x 2 hours = $22.50
Therefore, Joelle's total earnings for a week of 42 hours would be $300 (regular pay) + $22.50 (overtime pay) = $322.50.
The correct answer is C. $322.50. Joelle earns $322.50 for a week in which she works 42 hours.
To calculate Joelle's earnings for the week, we need to consider both her regular pay for the first 40 hours and her overtime pay for the additional hours worked beyond 40 hours.
First, let's calculate her regular pay for 40 hours:
Joelle's regular pay rate is $7.50 per hour. Therefore, for 40 hours, her regular pay is calculated as:
Regular pay = Hourly pay rate × Number of regular hours
Regular pay = $7.50/hour ×40 hours
Regular pay = $300.00
Next, we calculate her overtime pay for the 2 hours of overtime work. Joelle earns 1 1/2 times her regular pay rate for overtime hours. So her overtime pay rate is:
Overtime pay rate = 1 1/2 × Regular pay rate
Overtime pay rate = 1.5 × $7.50/hour
Overtime pay rate = $11.25/hour
Now, we calculate her overtime pay for the 2 hours of overtime work:
Overtime pay = Overtime pay rate × Number of overtime hours
Overtime pay = $11.25/hour × 2 hours
Overtime pay = $22.50
Finally, we add her regular pay and overtime pay to find her total earnings for the week:
Total earnings = Regular pay + Overtime pay
Total earnings = $300.00 + $22.50
Total earnings = $322.50
Therefore, Joelle earns $322.50 for a week in which she works 42 hours.
Two bike riders left each other and started to ride in opposite directions. Two hours later they were 54 miles apart. If one of them averaged twice the average rate of the other, what was the rate of each?
Answer:
The speed of right going rider is 9 mph
The speed of left going rider is 18 mph
Step-by-step explanation:
Given as :
The total distance apart both the riders = 54 miles
Let The speed of right going rider = x mph
and The speed of left going rider = 2 x mph
The Distance cover by right going rider = D miles
The Distance cover by left going rider = 54 - D miles
Total time for both = 2 hours
So, Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]
Or , Distance = speed × Time
For right going rider
D = x × 2
For left going rider
54 - D = 2 x × 2
Or, from first equation
54 - 2 x = 4 x
or, 54 = 4 x + 2 x
or, 6 x = 54
∴ x = [tex]\frac{54}{6}[/tex]
I.e x = 9 mph
So, The speed of right going rider = 9 mph
and The speed of left going rider = 2 × 9 = 18 mph
Hence The speed of right going rider is 9 mph
and The speed of left going rider is 18 mph answer
Victor Malaba has a net income of $1,240 per month. If he spends $150 on food, $244 on a car payment , $300 on rent, and $50 on savings, what percent of his net income can he spend on other things?
Answer:
40%
Step-by-step explanation:
The amount of income allocated to the items listed totals $744, so there is $496 he can spend on other things. As a percentage of income, that is ...
496/1240 × 100% = 40%
Malaba can spend 40% of his net income on other things.
one number is 5 more than twice the other number. if the sum of the two numbers is 32 find the two numbers
Answer:
9 and 23
Step-by-step explanation:
You can adjust the problem a little bit and make it easier to solve.
Subtracting 5 from the larger number makes it twice the smaller, and their sum be 32-5 = 27. So 27 is 3 times the smaller number, 9, and the larger is 32-9 = 23, which is 5 more than two times 9.
The two numbers are 9 and 23.
_____
You can let x represent "the other number". Then "one number" is 2x+5, and their sum is ...
(x) +(2x+5) = 32
3x +5 = 32
3x = 27 . . . . . subtract 5
x = 9 . . . . . . . divide by 3
(This working out should look familiar if you followed the above verbal solution.)
"One number" is 27 and "the other number" is 9.
Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone. If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is
a. 0.10
b. 0.90
c. 0.50
d. None of these choices.
Answer:
Option a, 0.10
Step-by-step explanation:
Given that of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.
i.e. out of 500 customers 50 customers purchased
Hence probability for any random customer to purchase = [tex]\frac{50}{500} =0.10[/tex]
Thus we find that if the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is
Option a)
0.10
This is based on the assumption that the past pattern of purchase determines the probabiltiy
PLZ HURRY IT'S URGENT!!
f the chance of rain for tomorrow is 40%, what is the chance that it will NOT rain?
Note: You can choose more than one answer.
40%
10%
60%
100%
Answer:
OPTION C: 60%
Step-by-step explanation:
Chances of raining the next day + Chances that it will not rain = 100%
One of them should definitely be true.
So, if the chance of it raining tomorrow is 40% then there is 60% chance that it will not rain tomorrow.
This can also seen as follows:
Probability of rain tomorrow + Probability of no rain = 1
Given Probability of rain tomorrow = 40% = [tex]$ \frac{40}{100} = \frac{2}{5} $[/tex]
Probability of no rain tomorrow = 1 - Probability of rain tomorrow
⇒ Probability of no rain = 1 - [tex]$ \frac{2}{5} $[/tex]
⇒ Probability of no rain = [tex]$ \frac{3}{5} $[/tex]
Expressing it as percentage: [tex]$ \frac{3}{5} \times 100 $[/tex] = 60%.
Help me please! All questions answer. Step by step explain it please....!!!
Answer:
Part 1) Option A. The graph of g(x) has the lesser y-intercept
Part 2) Option B. (2,4)
Part 3) Option B. 62.5 miles per hour
Part 4) Option A. The functions will intersect at x=-2 and at x=1
Step-by-step explanation:
Part 1)
Let
x ----->the number of years
g(x) ----> the expected value in dollars of televisions
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
In the function g(x)
The slope is
[tex]m=-\$90\ per\ year[/tex] ---> is negative because is a decreasing function
The y-intercept is
[tex]b=\$360[/tex]
substitute
[tex]g(x)=-90x+360[/tex]
Find the x-intercept (value of x when the value of the function is equal to zero)
For g(x)=0
[tex]0=-90x+360[/tex]
[tex]x=4[/tex]
The x-intercept is the point (4,0)
The y-intercept is the point (0,360)
Function f(x)
we have
[tex]f(x)=100(-x+4)[/tex]
[tex]f(x)=-100x+400[/tex]
Find the x-intercept (value of x when the value of the function is equal to zero)
For f(x)=0
[tex]0=-100x+400[/tex]
[tex]x=4[/tex]
The x-intercept is the point (4,0)
The y-intercept is the point (0,400) (value of f(x) when the value of x is zero)
Compare the intercepts both functions
The y-intercept is the same in both functions
The y-intercept is greater in the function f(x)
therefore
The graph of g(x) has the lesser y-intercept
Part 2) we have the equation of the line
[tex]4x-3y=-4[/tex]
Remember that
If a ordered pair is on the given line, then the ordered pair must satisfy the given line
Verify each case
a) (4,4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(4)-3(4)=-4[/tex]
[tex]4=-4[/tex] ---> is not true
so
the ordered pair not satisfy the equation
therefore
the ordered pair is not on the line
b) (2,4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(2)-3(4)=-4[/tex]
[tex]-4=-4[/tex] ---> is true
so
the ordered pair satisfy the equation
therefore
the ordered pair is on the line
c) (2,-4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(2)-3(-4)=-4[/tex]
[tex]20=-4[/tex] ---> is not true
so
the ordered pair not satisfy the equation
therefore
the ordered pair is not on the line
d) (4,-4)
Substitute the value of x and the value of y in the equation and compare the result
[tex]4(4)-3(-4)=-4[/tex]
[tex]28=-4[/tex] ---> is not true
so
the ordered pair not satisfy the equation
therefore
the ordered pair is not on the line
Part 3) we know that
The formula to calculate the average rate of change using the graph is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]f(a)=f(2)=75\ mi[/tex]
[tex]f(b)=f(4)=200\ mi[/tex]
[tex]a=2\ h[/tex]
[tex]b=4\ h[/tex]
Substitute
[tex]\frac{200-75}{4-2}=125/2=62.5 mi/h[/tex]
Part 4) we know that
The solution of the equation
f(x)=g(x)
are the x-coordinates of the intersection points both graphs
In this problem
If the solutions are x=-2 and x=1
then
The functions will intersect at x=-2 and at x=1
A newborn baby has extremely low birth weight if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was 810 grams. This sample mean is an unbiased estimator of the mean weight m in the population of extremely low birth weight babies. This means that:
a. when the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean.
b. as we take larger and larger samples from this population the sample mean, x-bar, will get closer and closer to the population mean.
c. in many samples from this population, the many values of x-bar will have a distribution that is close to Noral.
d. in many births from this population the many values of x-bar will be equal to m.
The statements mostly describe properties of an unbiased estimator in statistics, which typically involves large sample sizes, the mean of the sampling distribution being equivalent to the population mean, and the distribution of sample means approaching a normal distribution. One incorrect statement suggests that each individual sample mean will be equivalent to the population mean.
Explanation:This question pertains to the concept of statistical estimation. The statements reflect the properties of an unbiased estimator in a simple random sample from the population. Let's analyze each choice:
When the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean. This statement is true. The mean of the sampling distribution (expected value of sample means) should be equal to the population mean if the estimator is unbiased. As we take larger and larger samples from this population the sample mean, x-bar, will get closer and closer to the population mean. This statement is true. It is based on the law of large numbers which implies that as the sample size increases, the sample mean converges to the population mean. In many samples from this population, the many values of x-bar will have a distribution that is close to normal. This statement is usually true due to the central limit theorem which states that when samples of sufficiently large size are taken, the distribution of sample means tends to approach normal distribution. In many births from this population, the many values of x-bar will be equal to m. This statement is false. Each individual sample mean (x-bar) will not be equal to the population mean (m), but the average of many x-bars from many samples will be close to m if the estimator is unbiased.Learn more about Unbiased Estimator here:https://brainly.com/question/32063886
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The sample mean is an unbiased estimator of the population mean when the sample is a simple random sample; the mean of the sampling distribution of the sample mean will equal the population mean.
The student's question relates to the concept of an unbiased estimator in statistics, particularly the sample mean as an unbiased estimator of the population mean. The correct statement that defines an unbiased estimator is:
a. when the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean.This means that if you were to take many samples from the population and calculate the mean of each sample, the average of all these sample means would be equal to the population mean. This property is fundamental in inferential statistics for making generalizations about a population from a sample.
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?A. 1.5B. 1.7C. 2.3D. 2.5E. 3.0
Answer:
Q = 1.84
Step-by-step explanation:
If we poured 0,5 gallon of mixture A with 0.5 gallon of mixture B we will get a gallon of:
( 15 + 50 )/ 2 = 32.5 %
Now by ule of three
If with 0, 5 gl of A we get 32.5 %
?? x 30
x = (0.5)*(0.3)/ 0.325
x = 0,462 gl t get a mixture of 30%
Then for 4 gl
Q = 4 * 0.462
Q = 1.84
What is the output value for the following function if the input value is 1?
y = 3x + 1
32
0
5
4
Answer:
Output value for the following function is 4
Step-by-step explanation:
Given:
The input value are the value of x
[tex]y = 3x + 1[/tex]
Input value is 1
We substitute the value 1 for the input variable x in the given function.
[tex]y = 3x + 1[/tex]
[tex]y = 3(1) + 1[/tex]
[tex]y = 3 + 1[/tex]
[tex]y = 4[/tex]
The output value are the value of y
Therefore, for an input of 1, we have an output of 4.
Liliana used 444 dark power crystals to raise 141414 zombie soldiers. She wants to know how many zombie soldiers (z)(z)left parenthesis, z, right parenthesis she can raise with 101010 dark power crystals. How many zombie soldiers can Liliana raise with 101010 power crystals?
Question is bit incorrect, Correct question is given below.
Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) she can raise with 10 dark power crystals. How many zombie soldiers can Liliana raise with 10 power crystals?
Answer:
Liliana can raise 35 zombie soldiers.
Step-by-step explanation:
Let the number of zombie soldiers raised by 10 dark power crystals be 'z'.
Zombie raised by 4 power crystals = 14
Since the number of zombie and power crystals are in direct proportion.
Therefore, we get
[tex]\frac{z}{10}=\frac{14}{4}[/tex]
Multiply 10 on both the sides, we get
[tex]z=\frac{14}{4}\times 10 = 35[/tex]
Hence, Liliana can raise 35 zombie soldiers.
Answer:
35 Zombie Soldiers
Step-by-step explanation:
Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is 1 50 and is independent from one topic to the next. If you discuss 17 topics, how surprising would it be to find that you match on at least one of them? (Round your answer to four decimal places.)
Answer:
0.2907
Step-by-step explanation:
Given that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on.
Since each topic is independent we find that probability for success in each topic = constant = 1/50 = 0.02
X no of topics that match is binomial with n = 17 and p = 0.02
Required probability
= Probability to find that you match on at least one of them
=[tex]P(X\geq 1)\\=1-P(X=0)\\=1-(1-0.02)^{17} \\=0.2907[/tex]
It would not be surprising as probability is reasonably large.
In the past month, Abdul rented 4 video games and 3 DVDs. The rental price for each video game was $3.20. The rental price for each DVD was $3.80. What is the total amount that Abdul spent on video game and DVD rentals in the past month?
Answer:
$24.20
Step-by-step explanation:
Multiply and add.