Answers
Answer: The correct answer is:
_________________________
The given "graph" in the bottom right, lowest corner
Step-by-step explanation:
_________________________
Note: When there is only one (1) equation give for a graph;
and/or: only one (1) "inequality given";
we look for the symbol.
If the symbol is "not" an "equals" symbol (i.e. not an: = symbol) ;
we check for the type of "inequality" symbol.
If there is a: "less than" (<) ; or a "greater than" (>) symbol; the graph of the "inequality" will have "dashed lines" (since there will be a "boundary").
If there is an "inequality" that is a: "less than or equal to" (≤) ;
or a: "greater than or equal to" (≥) ;
→ then there will be not be a dashed line when graphed;
but rather—a "solid line" ; since "less than or equal to" ;
or "greater than or equal to" —is similar to:
"up to AND including"; or: "lesser/fewer than AND including".).
_________________________
Note: We are given the "inequality" :
→ " y < x² + 4x " .
_________________________________
Note that we have a "less than" symbol (< ) ; so the graph will have a:
"solid line" [and not a "dotted line".].
_________________________________
Note that all of the graphs among our 4 answer choices have "dotted lines".
Not that all values (all x and y coordinated) within the "shaded portion" of the corresponding graph are considered part of the graph.
As such, given any point within the shaded part, the x and y coordinates must match the inequality (i.e. the given inequality must be true when one puts in the "x-coordinate" and "y-coordinate" into the "given inequality" :
→ " y < x² + 4x " .
_________________________
Likewise, we can take any point within the "white, unshaded" portion of any of the graph, and take the "x-coordinate" and "y-coordinate" of that point, and the inequality: → " y < x² + 4x " ; will not hold true when the "x-coordinate" and "y-coordinate" values of that point— are substituted into the "inequality".
_________________________
{Note: Answer is continued on images attached.}.
Wishing you the best!
Related Questions
How do u solve this?
Answers
Answer:
0
Step-by-step explanation:
Tuesday : -1/2
Wednesday + 3/4
Thursday : -3/8
Add them together
-1/2 + 3/4- 3/8
Get a common denominator
-4/8 + 6/8 - 3/8
-1/8
The closest integer value to -1/8 is 0
What is a word problem for 15 minus 28?
Answers
Answer:
A word problem for that would be Sam had 28 chocolates and Bob took away 15. How many does Sam have left?
Step-by-step explanation:
I don't know how to show work for writing a word problem. Sorry
Answer:
Step-by-step explanation:
Jane has $15 in her bank account. She wrote a $28 check for buying a fiction book. How much is her balance now?
What’s the correct answer for this question?
Answers
Answer:
A: 97π/18 m
Step-by-step explanation:
Central Angle = 97°
In radians:
97° = 97π/180
Now
S = r∅
S = (10)(97π/180)
S = 97π/18 m
Answer:
The answer is option 1.
Step-by-step explanation:
Given that the formula for length of Arc is Arc = θ/360×2×π×r when r represents the radius of circle. Then, you have to substitute the following values into the formula :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
Let θ = ∠VCW = 97°,
Let r = 10m,
[tex]arc = \frac{97}{360} \times 2 \times \pi \times 10[/tex]
[tex]arc = \frac{97}{360} \times 20 \times \pi[/tex]
[tex]arc = \frac{97}{18} \pi \: m[/tex]
Please answer this correctly
Answers
Answer:
326
Step-by-step explanation:
l x w
7x8
25x6
4x30
326
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone. What probability distribution describes this situation and what are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
Answers
Answer:
We use the binomial distribution to describe this situation.
The mean number of phone sales is 749.7 with a standard deviation of 15.
Step-by-step explanation:
For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.
This means that [tex]p = \frac{35}{50} = 0.7[/tex]
What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
1071 shoppers, so [tex]n = 1071[/tex]
Mean
[tex]E(X) = 1071*0.7 = 749.7[/tex]
Standard deviation
[tex]\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15[/tex]
The mean number of phone sales is 749.7 with a standard deviation of 15.
6(4x - 3) - 30
24x - 18 = 30
24% -18 + 18 = 30 + 18
24x = 48
24x 48
24 24
X = 2
Original Equation
Step 1
Step 2
Step 3
Step 4
Step 5
Which of these is not part of the solution process?
A. Using the associative property
B. Adding 18 to both sides to isolate the variable term
C. Dividing both sides by 24 to isolate the variable
D. Using the distributive property
Answers
Answer:
A-using the associative property
Step-by-step explanation:
Suppose that y = 5 x plus 4 and it is required that y be within 0.005 units of 8. For what values of x will this be true?
Answers
Answer:
so we have an inequality for y -
7.995<y<8.005
Then now we need in inequality for x
(y-4)/5 = x
so that means that so if we have (7.995-4)/5 we get 3.995/5 = 7.99
so we have our first 7.99<x<b
Now we solve for b
So that means that 5.005/5 = 1.001
since we are changing it we switch our signs
from 7.99<x<1.001
we do 7.99>x>1.001
therefore
1.001<x<7.99
Answer:
0.795 [tex]\leq[/tex] y [tex]\leq[/tex] 0.805
Step-by-step explanation:
8 = 5x + 4
5x = 4
x = 4/5 or 0.800
therefore 0.800 + .005 and 0.800 - .005 =
0.795 [tex]\leq[/tex] y [tex]\leq[/tex] 0.805
Temperature transducers of certain type are shipped in batches of 50. A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:
2 1 2 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
0 4 2 1 3 1 1 3 41 2 3 2 2 8 4 5 1 3 1
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 2 3
a. Determine frequencies and relative frequencies for the observed values of x = number of non-conforming transducers in a batch. (Round your relative frequencies to three decimal places.)
b. What proportion of batches in the sample have at most four non-conforming transducers? (Round your answer to three decimal places.)
Answers
Answer:
a.
Number: 0, 1, 2, 3, 4, 5, 6, 7, 8
Frequency: 6, 12, 13, 15, 5, 3, 3, 1, 1
b. The proportion of the batches that have at most is 0.864
Step-by-step explanation:
a. The given data are;
2 1 2 3 1 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 2 3
The frequencies are;
x fx
0 6
1 12
2 13
3 15
4 5
5 3
6 3
7 1
8 1
The relative frequency are;
x Rfx
0 0.102
1 0.203
2 0.220
3 0.254
4 0.085
5 0.051
6 0.051
7 0.017
8 0.017
b. The proportion of the batches that have at most 4 is given as follows;
The number of the batches that have at most 4 = 6 + 12 + 13 + 15 + 5 = 51
Therefore, the proportion of the batches that have at most 4 = 51 / 59 = 0.864.
Daniel deposits $300 into an account that earns 16% interest annually. Which equation can be used to model his account balance, y, after x years?
Answers
Answer:
[tex]y=300(1+0.16)^x[/tex]
Step-by-step explanation:
This account can be modeled using the compound interest formula.the compound interest formula is expressed as[tex]A= P(1+r )^t[/tex]
Where
A =final amount = y
P=initial principal balance = $300
r=interest rate = 16%= 0.16
t=number of time periods elapsed= x
Hence the equation to model his account balance/ final amount A (y) after time (x) years is
[tex]y=300(1+0.16)^x[/tex]
A gumball machine has 100 red gumballs. If the red gumballs are 25% of the total number of gumballs, how many gumballs are in the gumball machine?
Answers
Answer: 400
Step-by-step explanation:
25% is equal to one quarter (1/4). If theres 100 red gumballs then there must be 300 more gumballs in the machine because a quarter of a number is always even.
The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2.
Required:
a. Estimate at 5% level of significance whether the true average shrinkage percentage U: is greater than 17.5 and write your conclusion.
b. Report the p-value.
Answers
Answer:
a) [tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
b) [tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
Part b
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
What’s the correct answer for this?
Answers
Answer:
D.
Step-by-step explanation:
Since opposite angles of a quadrilateral inscribes in a circle add up to 180°
So,
<P + <N = 180°
2x+2x-12 = 180°
4x = 180+12
4x = 192
Dividing both sides by 4
x = 48
Now
<P = 2(48)
<P = 96
Now
<N = 2(48)-12
<N = 96-12
<N = 84
Tameka can make 32 beads with 4 sheets of paper. Right now she only has 3 sheets of paper. How many beads can Tameka make?
Answers
Answer:
24 beads
Step-by-step explanation:
beads in 4 sheet=32
beads in 1 sheet=32/4=8
beads in 3 sheet=8*3=24
Answer:
Assuming that you can make the same number of beads with 1 sheet of paper, Tameka can make 24 beads with 3 sheets of paper.
The differential equation below models the temperature of a 91°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. dy dt = − 1 53 (y − 17)\
Answers
Answer:
[tex]t \approx 17.690\,min[/tex]
Step-by-step explanation:
This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:
[tex]\frac{dy}{dt} = - \frac{1}{53} \cdot (y - 17)[/tex]
[tex]\frac{dy}{y-17} = -\frac{1}{53} \, dt[/tex]
[tex]\int\limits^{y}_{y_{o}} {\frac{dy}{y-17} } = -\frac{1}{53} \int\limits^{t}_{0}\, dx[/tex]
[tex]\ln \left |\frac{y-17}{y_{o}-17} \right | = -\frac{1}{53} \cdot t[/tex]
[tex]\frac{y-17}{y_{o}-17} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]y = 17 + (y_{o} - 17) \cdot e^{-\frac{1}{53}\cdot t }[/tex]
The solution of the differential equation is:
[tex]y = 17 + 74\cdot e^{-\frac{1}{53}\cdot t }[/tex]
Where:
[tex]y[/tex] - Temperature, measured in °C.
[tex]t[/tex] - Time, measured in minutes.
The time when the cup of coffee has the temperature of 70 °C is:
[tex]70 = 17 + 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]53 = 74 \cdot e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\frac{53}{74} = e^{-\frac{1}{53}\cdot t }[/tex]
[tex]\ln \frac{53}{74} = -\frac{1}{53}\cdot t[/tex]
[tex]t = - 53\cdot \ln \frac{53}{74}[/tex]
[tex]t \approx 17.690\,min[/tex]
please help me explain your answer only answer if you are sure
Answers
Answer:
The answer of top prism is 262
and down prism is 478
The upper figure is triangular prism.
so, we use bh+2ls+lb formula
B=5
h=3
s=4
l=19
Now,
surface area of triangular prism = bh+2ls+lb
= 5×3+2×19×4+19×5
= 262
The down figure is rectangular prism.
so, we use 2lw+2lh+2hw
l=5
h=6
w=19
Now,
The area of rectangular prism = 2lw+2lh+2hw
= 2×5×19+2×19×6+2×5×6
= 478
A bag contains 1p,20 and 5p coins 3/8 of the bag are 1p coins There are as many 5p coins as 1p coins in the bag. There are 640 coins in total. Work out the number of 20 coins in the bag
Answers
Answer:
160 off 20p coins
Step-by-step explanation:
1 p, 20 p, 5 p coins1 p= 3/8 of the bag5 p= 1 p= 3/8 of the bagtotal coins= 64020 p coins= 640 - 640*(3/8+3/8)= 640*(1- 6/8)= 640 * 2/8= 640* 1/4= 160
20p coins = 640 -640*(3/8+3/8)=640*(-16/8)=640 *2/8=640*1/4=160
For which x is f(x)?=-3
-7
-4
4
5
Answers
Answer:
B.
✔ -4
Step-by-step explanation:
E 2021
Henry, Brian and Colin share some sweets in the ratio 6:4:1. Henry gets 25 more sweets than Colin. How many sweets are there altogether?
Answers
Answer:
There are 55 sweets in total.
Step-by-step explanation:
The total number of sweets is t.
Henry, Brian and Colin share some sweets in the ratio 6:4:1.
This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).
Brian earns [tex]\frac{4}{11}[/tex] of the total.
Colin earns [tex]\frac{1}{11}[/tex] of the total
Henry gets 25 more sweets than Colin.
Henry earns [tex]\frac{6t}{11}[/tex]
Colin earns [tex]\frac{t}{11}[/tex]
So
[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]
Multiplying everything by 1
[tex]6t = t + 275[/tex]
[tex]5t = 275[/tex]
[tex]t = \frac{275}{5}[/tex]
[tex]t = 55[/tex]
There are 55 sweets in total.
Help Me PLEASE!!!
A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?
Answers
Answer:
P = 0.5207
Step-by-step explanation:
First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.
Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).
So, the probability that just the first card is a diamond or an ace is calculated as:
[tex]P_1=\frac{16}{52}*\frac{36}{52}=0.2130[/tex]
At the same way, the probability that just the second card is a diamond or an ace is:
[tex]P_2=\frac{36}{52}*\frac{16}{52}=0.2130[/tex]
Finally, the probability that both cards are diamonds or aces is:
[tex]P_3=\frac{16}{52}*\frac{16}{52}=0.0947[/tex]
Therefore, the probability that at least one of the cards is a diamond or an ace is:
[tex]P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207[/tex]
Watermelon A is 2 kg lighter than watermelon B and it weighs one fifth of the weight of watermelon C. Watermelons A and C together are 3 times as heavy as watermelon B. How heavy is each watermelon?
Answers
Answer:
A: 2 kgB: 4 kgC: 10 kgStep-by-step explanation:
We can write some equations to describe the given relationships:
A = B - 2 . . . . . A is 2 kg lighter than B
A = C/5 . . . . . . A is 1/5 the weight of C
A+C = 3B . . . . together, A and C are 3 times the weight of B
__
Let's solve for A.
B = A+2 . . . from the first equation
C = 5A . . . . from the second equation
A +5A = 3(A+2) . . . . substituting for B and C in the third equation
6A = 3A +6
3A = 6
A = 2
__
B = A+2 = 4
C = 5A = 10
Watermelon A weighs 2 kg; B weighs 4 kg; and C weighs 10 kg.
Answer:
2 kg 4 kg 10 kg
I BLESS THE EYES!
The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i. Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.
Calculate R.
(A) 1.23
(B) 1.56
(C) 1.60
(D) 1.74
(E) 1.94
Answers
Answer:
Step-by-step explanation:
image attached (representing first perpetuity on number line)
Present value is 7.21
[tex]7.21=\frac{1}{1-u^2} \\\\1-\frac{1}{7.21} =u^2\\\\\frac{6.21}{7.21} =(1+i)^{-2}\\\\(1+i)^2=\frac{7.21}{6.21} \\\\(i+1)=\sqrt{\frac{7.21}{6.21} }\\\\ i=\sqrt{\frac{7.21}{6.21} } -1\\\\=0.77511297[/tex]
image attached (representing second perpetuity on number line)
we have ,
[tex]7.21=\frac{Ru}{1-u^3}[/tex]
Here,
[tex]V=\frac{1}{1+i}[/tex]i
i = 0.077511297 + 0.01
[tex]\therefore V =\frac{1}{1.087511295} =(1.087511297)^-^1\\\\7.21=\frac{R(1.087511297)^-^1}{1-(1.087511297)^-^3} \\\\7.21=4.132664645R\\\\R=\frac{7.21}{4.132664645} \\\\R= 1.7446370\approx1.74[/tex]
Therefore, value of R is 1.74
A soccer field is a rectangle 30 meters wide and 120 meters long.The coach asks players to run from one corner to the corner diagonally across. What is the distance to the nearest tenth of a mile
Answers
Answer:
123.7 meters
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 30. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
30^2 + 120^2 = c^2
c=123.7
Find the population mean or sample mean as indicated.
Sample: 17, 11, 8, 12, 22
Answers
Answer:
mean:12
Step-by-step explanation:
The population mean or sample mean as indicated in the given samples is 14
What is mean?A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.
Mathematically,
Mean = Sum of the observations/number of observations
Now the given sample is,
17, 11, 8, 12, 22
So, Number of sample = 5
Thus, Mean = Sum of the sample /number of sample
Mean = (17 + 11 + 8 + 12 + 22) / 5
⇒ Mean = 70/5
⇒ Mean = 14
Thus, the population mean or sample mean as indicated in the given samples is 14
To learn more about mean :
https://brainly.com/question/21479395
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2. En la ciudad de Quito, en la temporada fría, se registran temperaturas que van desde los 5 °C hasta los 18 °C. En la temporada cálida, el registro de la temperatura va desde los 4 °C hasta los 30 °C.
a. Representamos estas temperaturas en forma de intervalo y como conjunto.
b. ¿A qué intervalo pertenece la temperatura de la ciudad de Quito?
c. ¿Qué temperaturas son comunes en las temporadas fría y cálida?
d. ¿Qué temperaturas son posibles solo en la temporada fría?
e. ¿Qué temperaturas son posibles solo en la temporada cálida?
Answers
Answer:
(See explanation below for further detail/Véase la explicación abajo para mayores detalles)
Step-by-step explanation:
(This exercise is written in Spanish and explanations will be held in such language)
a) Las temperaturas quedan representadas a continuación:
Quito - Temporada Fría
Intervalo
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada fría)
Conjunto
[tex]C = \{\forall t \in \mathbb {R}| 5 \leq t \leq 18\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada fría)
Quito - Temporada Cálida
Intervalo
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada cálida)
Conjunto
[tex]H = \{\forall t \in \mathbb {R}| 4 \leq t \leq 30\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada cálida)
b) La temperatura de la ciudad de Quito pertenece esencialmente a dos intervalos:
Intervalo de Temporada Fría:
[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex]
Intervalo de Temporada Cálida:
[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex]
c) Toda temperatura mayor o igual que 4 °C y menor o igual que 30 °C.
d) Temperaturas mayores o iguales a 5 °C y menores o iguales a 18 °C.
e) Temperaturas mayores o iguales a 4 °C y menores o iguales a 30 °C.
Write a quadratic function f whose zeros are −6 and −1.
Answers
Answer:
y = (x+6) (x+1) or in quadratic form: y = x² + 7x + 6
Step-by-step explanation:
22,056 people went to the baseball game on Sunday. Half as many people came on money. How many people were at the baseball game on Sunday and Monday altogether?
Answers
Answer:
33084
Step-by-step explanation:
22056 divided by 2 =11028
altogether (on sunday and monday) the total amount would be..
22056+11028=33084
Answer:
33084
Step-by-step explanation:
If 22056 people came to the game on Sunday and Half as many people came on Monday, you do
22056 divided by 2. this is how many people cam on monday
Add this answer to 22056 and this is how many people came on both days.
Plz help me :(
Prove for any value of y the value of expression y^4−(y^2−9)(y^2+9) is divisible by 9.
Answers
PROOF:
[tex]y^4-(y^2-9)(y^2+9)\\=y^4 -(y^4-81)\\=y^4-y^4+81\\=81[/tex]
And 81 is ALWAYS divisible by 9
Answer:
Its 9*9
Step-by-step explanation:
The equation equals 81 and 9*9=81.
Have a great day! :)
36°
I
80°
w
m
What equation can be used to calculate the measure of angle ? Describe, in words, the
process you would use to find
Answers
Answer:
44°
Step-by-step explanation:
A pair of angles formed from the intersection of two lines opposite to each other at the point of intersection (vertex) is called vertically opposite angles. These vertically opposite angles are congruent to each other (that means they are equal).
Since opposite angles are equal, the equation needed to calculate w is given as:
80° = 36° + w
w = 80° - 36°
w = 44°
New York City is known for it's tourist attractions and high priced real estate. The mean hotel room rate is $202 per night. Assume that the room rates are normally distributed with a standard deviation of $70.What is the probability that a hotel room costs between $210 and $290?
Answers
Answer:
[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]
And we can find this probability with this difference
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]
And we can find the difference with the normal standard distirbution or excel:
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]
Step-by-step explanation:
Let X the random variable that represent the hotel room cost of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(202,70)[/tex]
Where [tex]\mu=202[/tex] and [tex]\sigma=70[/tex]
We are interested on this probability
[tex]P(210<X<290)[/tex]
The z score formula is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the formula we got:
[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]
And we can find this probability with this difference
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]
And we can find the difference with the normal standard distirbution or excel:
[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]
HELP ME QUICK!! The best answer I will mark brainlest!
Answers
Answer: 1. (4, 8); 2. (3, 4)
Step-by-step explanation: I tried to get this to you fast but I can give you an explaination if you would like one :)
