Answer:
The probability that the next mattress sold is either king or queen-size is P=0.8.
Step-by-step explanation:
We have 3 types of matress: queen size (Q), king size (K) and twin size (T).
We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.
We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:
[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]
We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:
[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]
Finally, we know that the sum of probablities has to be 1, or 100%.
[tex]P_Q+P_K+P_T=1[/tex]
We can solve this by sustitution:
[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]
Now we know the probabilities of each of the matress types.
The probability that the next matress sold is either king or queen-size is:
[tex]P_K+P_Q=0.6+0.2=0.8[/tex]
Please answer this correctly
Answer:
662
Step-by-step explanation:
l x w
10x41
6x22
8x15
662
NFL player Gerald Sensabaugh recorded a 46 inch standing vertical jump at the 2005 NFL Combine, at that time the highest for any NFL player in the history of the Combine. Sensabaugh weighed about 200 lb when he set the record. Part A What was his speed as he left the floor
Answer:
His speed as he left the floor is 4.83 m/s.
Step-by-step explanation:
Given: 46 inches = 1.1684 m and mass = 200 lb = 90.7185 Kg.
From the third equation of motion under free fall,
[tex]V^{2}[/tex] = [tex]U^{2}[/tex] - 2gs
Where; V is the final velocity (0), U is the initial velocity (unknown), g is the value of gravity - 10 m/[tex]s^{2}[/tex] and s is the distance = 1.1684 m.
Then;
0 = [tex]U^{2}[/tex] - 2gs
[tex]U^{2}[/tex] = 2gs
= 2 × 10 × 1.1684
= 23.368
⇒ U = [tex]\sqrt{23.368}[/tex]
= 4.8340 m/s
The initial velocity, U = 4.83 m/s.
Therefore, his speed as he left the floor is 4.83 m/s.
Answer:
His speed as he left the floor is 4.83 m/s.
Step-by-step explanation:
What is the center of the circle?
Answer:The point from which circle is drawn is called center of circle.
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...
If f(x) = 5x + 7 and g(x) = sqrt(x + 6) , which statement is true? A) 9 is NOT in the domain of f g B) 9 IS in the domain of f g
Answer 9 is in the domain of f g
Step-by-step explanation:
Suppose parts are of two varieties: good (with probability 90/92) and slightly defective (with probability 2/92). Parts are produced one after the other. What is the probability that at least 3 parts must be produced until there is a slightly defective part produced
Answer:
95.69%
Step-by-step explanation:
We have X is the number of parts produced up to (and including) the first slightly defective part. So, X is Geometric (2/92), which would be the following:
P (X => 3) = Summation i = 3, up to infinity of {[(90/92)^(i-1)] * (2/92)}
We replace and solve and we are left with:
P (X => 3) = (2/92) * (90/92)^(3-1) * 1/(1 - 90/92)
P (X => 3) = 0.9569
Which means that the probability that at least 3 parts must be produced until there is a slightly defective part produced is 95.69%
simplify 2x+x+x+2y times 3y times y
Answer:
12 x y² + 6 y³
Step-by-step explanation:
Step(i):-
Given ( 2 x + x + x + 2 y ) times 3 y times y
( 2 x + x + x + 2 y ) × 3 y × y = ( 4 x + 2 y) × 3 y × y = ( 4 x + 2 y) 3 y²
By applying Distributive property
( a + b ) c = a . c + b . c
= 4 x . 3 y² + 2 y . 3 y²
= 12 x y² + 6 y³
Final answer:-
( 2 x + x + x + 2 y ) times 3 y times y = 12 x y² + 6 y³
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Square root is finding what number times what gets your goal.
10 x 10 = 100 so 100 squared is 10.
5 x 5 = 25 so 25 squared is 5.
4 x 4 = 16 so 15 squared is 4.
You get it? :)
Have a nice day!
Mo has some red and green sweets He eats 1/3 of the sweets ¾ of the sweets left over are green Mo buys himself 30 more green sweets. There are now 162 green sweets. How many sweets did Mo start with?
Answer:
176 sweets
Step-by-step explanation:
162 - 30 = 132 this finds the 3/4 before he purchased more sweets.
132 divided by 3 = 44 This finds how many thirds their are. (We do 3 not 4 because 1/4 is already gone and there are only 3rds lefts.)
44 x 4 = 176 This finds the total before he purchased more.
Hope this helps!
Complete the transformation on the rectangle ABCD shown and choose the resulting vector: Use [ABCD]
edgen.
last option
The previous transformation could be classified as a
✔ reflection across the y–axis
.
Step-by-step explanation:
Answer:
D. [3, -1, -1, 3, 4, 4, 1, 1]
Reflection across the y–axis
Step-by-step explanation:
Please mark as Brainliest!
Does coordinate s or coordinate t represent a greater number?
Answer:
t
Step-by-step explanation:
both t and s represent x axis value, t is greater as is on the right side from s
Answer: t
Step-by-step explanation: khan academy
Bonnie volunteers to bring bags of candy to her child's class for the Halloween party. She buys a bag containing 240, a bag containing 624, and a bag containing 336 pieces. Age needs to use all the candy to create identical treat bags. How many treat bags can bonnie make so that each one has the same number and variety of candy? How many of each type of candy will be in each bag?
Answer:
Number of bags that Bonnie can make so that each one has the same number of candies = 48
Number of candies from bag I in each of the treat bag = 5
Number of candies from bag II in each of the treat bag = 13
Number of candies from bag III in each of the treat bag = 7
Step-by-step explanation:
Given: One bag (I) has 240 candies, one bag (II) has 624 candies and one bag (III) has 336 candies
To find: Number of bags that Bonnie can make so that each one has the same number of candies and number of each type of candies in each bag
Solution:
[tex]240=2^4\times 3\times 5\\624=2^4\times3\times13\\336=2^4\times3\times7[/tex]
Highest common factor (H.C.F) = [tex]2^4\times3=48[/tex]
So,
Number of bags that bonnie can make so that each one has the same number of candies = 48
Now,
[tex]\frac{240}{48}=5\\ \frac{240}{48}=13\\\frac{240}{48}=7[/tex]
Number of candies from bag I in each of the treat bag = 5
Number of candies from bag II in each of the treat bag = 13
Number of candies from bag III in each of the treat bag = 7
Identify the range of the function shown in the graph
Answer:
D Y is all real numbers
Step-by-step explanation:
When looking at the y axis, you can see that if the graph were to be bigger, the line would keep going. This means y will never stop.
Express each percent as a fraction in simplest form.
a. 85%
b. 5 72%
c. 12.55%
Answer:
(a) 17/20 b.5/18/25 c. 1.255
what is the last three
Answer:
20:30 goes to 8:12
the rest goes to 6:18
Step-by-step explanation:
i may be wrong
Answer:
7:12 is equivalent to 6:18
20:30 is equivalent to 8:12
5:15 is equivalent to 6:18
Step-by-step explanation:
plz mark brainliest
Lester worked 12 hours last week at the grocery store and earned $93.00. If he continues to earn the same hourly pay, how many additional hours must he work to earn another $62.00?
A. 9 hours
B. 10 hours
C. 11 hours
D. 8 hours
Answer:
8 hours
Step-by-step explanation:
We can use a ratio to solve
12 hours x hours
---------- = ------------
93 dollars 62 dollars
Using cross products
12 * 62 = 93x
Divide each side by 93
12*62/93 = 93x/93
8 = x
8 hours
Need answers to 32 and 33
How would I start this?
Answer:
(0, ∞)
Step-by-step explanation:
A good place to start is by visualizing what the graph looks like on a number line.
For x > 0, it is an open circle at x=0, and shading to the right extending to infinity.
__
So, the left end of the interval is 0, but 0 is not included in the interval.
The right end of the interval is infinity, but there is no such number, so "infinity" is not included in the interval.
"Not included" means you use round brackets ( ) for the corresponding end of the interval. ("Included" would mean you use square brackets [ ].)
So, the interval 0 < x < ∞ is written in interval notation as ...
(0, ∞)
Identify which of the following is NOT equivalent to 2 3/4
Answer:
Step-by-step explanation:
mabey its c
The equation which is equivalent to [tex]2^{\frac{2}{3} }[/tex] will be equal to [tex]\sqrt[4]{2^3}[/tex]. Hence, option C is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
[tex]2^{\frac{2}{3} }[/tex] = 1.68
Now, let's check the options,
A.
[tex](2^{\frac{1}{4} } )^{\frac{1}{2} }[/tex] = 1.09 ≠ 1.68, hence this is incorrect.
B.
[tex]2\frac{1}{4}*2\frac{1}{2}[/tex] = 9/4 × 5/2 = 5.625 ≠ 1.68, hence, this is incorrect.
C.
[tex]\sqrt[4]{2^3}[/tex] = 1.68 = 1.68, hence, this is correct.
D.
√8 = 2.82 ≠ 1.68, hence, this is incorrect.
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Alex and Bryan are giving an exam. The probability Alex gets an A is 0.9, the probability Bryan gets an A is 0.8 and the probability Alex gets an A and Bryan doesn't get an A is 0.1. What is the probability that either Alex or Bryan get an A.
Answer:
The probability that either Alex or Bryan get an A is 0.9
Step-by-step explanation:
Before we proceed to answer, we shall be making some important notation;
Let A = event of Alex getting an A
Let B = event of Bryan getting an A
From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1
We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)
We can use the addition theorem here;
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) .......................(i)
Also,
P(A) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) .........................(ii)
We can insert ii into i and we have;
P(A ∪ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) + P(B) - P(A ∩ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9
An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously.
(a) Which investment will ear more interest in 5 yr?
(b) How much more will the better plan earn?
Answer:
a. 6% one is better
b. $12,285.95
Step-by-step explanation:
a. For determining which investment earn more first we have to calculate both the investment which are as follows
a. Based on compound quarterly, the amount is find out by using the following formula
[tex]Amount = {Present\ value\times (1 + interest\ rate)} ^{number\ of\ years}[/tex]
where,
Present value is $50,000
Interest rate is = [tex]\frac{0.06}{4}[/tex] = 0.015
And, the number of years is
= [tex]4\times4[/tex]
= 16
So, the amount is
[tex]= \$50,000 \times (1 + 0.015)^{16}[/tex]
= $63,449.28
And, based on compounded continuously, the amount is determined by using the following formula
[tex]Amount = Present\ value\times e^{rt}[/tex]
[tex]= \$50,000 \times e.^{0575(4)}[/tex]
= $51,163.33
Therefore, The the investment at 6% is better
b. Now the difference in earning is
= $63,449.28 - $51,163.33
= $12,285.95
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
For 90:
9 10p coins
7 10p coins and 1 20p coin
5 10p coins and 2 20 p coins
3 10p coins and 3 20p coins
For 60:
6 10p coins
4 10p coins and 1 20p coin
2 10p coins and 2 20p coins
3 20p coins
Step-by-step explanation:
Answer:
For 90 is having each containing both the 20 and10 for 2 boxes then the rest each a 20&10
For 60 is two 20s and two10
Step-by-step explanation:
Hope it helps
Billy's age is twice Joe's age and the sum of their ages is 45. How old is Billy?
Answer:
30 years old
Step-by-step explanation:
Joe's age can be set to x. Since Billy is twice as old as Joe, his age can be set to 2x. They add up to 45. You can set up an equation, 2x+x=45.
Simplify the equation.
3x=45, x=15
Joe is 15. Billy is 2(15)=30.
Does the frequency distribution appear to have a normal distribution? Explain. Temperature (degreesF) Frequency 35 dash 39 1 40 dash 44 4 45 dash 49 9 50 dash 54 13 Temperature (degreesF) Frequency 55 dash 59 9 60 dash 64 2 65 dash 69 1 Choose the correct answer below. A. No, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is not symmetric. B. No, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric. C. Yes, because the frequencies start low, proceed to one or two high frequencies, then increase to a maximum, and the distribution is not symmetric. D. Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.
Answer:
D. Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.
Step-by-step explanation:
Hello!
The given frequency distribution for temperatures.
To see if the distribution appears to have a normal distribution you have to draw a histogram using the information. Check attachment.
As you can see, the distribution appears symmetric, it starts low and proceeds to grow until it reaches its maximum point (f(4)=13) and then starts to decrease to low frequencies. The right tail decreases a little more than the left one but it is almost symmetrical.
I hope this helps!
Laura placed a bucket of water in her garden. Over the course of a week, she watched the water evaporate and recorded the volume of water left in the bucket each day.
Laura found the linear model that best fit the data was V=5.00−0.25n, where n is the number of days since she first placed the bucket and V is the volume of water, in liters, remaining in the bucket.
How many liters of water evaporated from the bucket every day?
How may liters where inside the bucket when Laura first placed it in the garden?
Answer:
1. 0.5 L; 2. 5.00 L
Step-by-step explanation:
V = 5.00 - 0.5n
If you include units, the equation becomes
V(in litres) = 5.00 L - (0.5 L/day) × (n days)
1. Rate of evaporation
When you include the units, it becomes easier to see that the water is evaporating at a rate of 0.5 L/day.
That is, 0.5 L of water evaporates each day.
The negative sign shows that the volume of water is decreasing.
2. Volume at the beginning
At the beginning of the experiment, n = 0. Then
V = 5.00 -0.5×0 = 5.00 - 0 = 5.00 L
The bucket originally contained 5.00 L of water.
Let:T : ℝ3→ℝ3 be the transformation that projects each vector x=(x1,x2,x3)onto the plane
x2=0,
so
T(x)=(x1 ,0 ,x3). Show that T is a linear transformation.
The first property for T to be linear is
T(0) =_________________________________________________
Check if this property is satisfied for T.T(x1, x2, x3) =(x1, 0,x3)
T(0,0,0) = ( _____ ,_____, _,_______) ,
So, is the first property satisfied?
Yes 0r No
The second property for T to be linear is T(cu+dv)=______(see choices below)___________________________________________for all vectors(u and v)i n the domain of T and all scalars c, d
cT(u)+dT(v)
dT(u)+cT(v)dT(u)−cT(v)
cT(u)−dT(v)
for all vectors
u,
v in the domain of T and all scalars c, d.
Check if this property is satisfied for T. Let u=(u1, u2, u3) and v =(v1, v2, v3).
T(cu+dv)=(cu1+dv1, 0, cu3+dv3) =(cu1, _______, _________) +(dv1, ________, _________)
Factor out the scalar in each ordered triple.
T(cu+dv) = ____(u1, 0, u3) + ______(v1, 0,v3)
Further simplify the previous equation.
T(cu+dv) = c
▼
(choices pick one)
T(v)
T(u)+d
▼
(choices for the arrow above pick one)
T(v)
T(u)
So, is the second property satisfied?
Yes
No
Thus, T ▼
is
is not
linear.
Answer:
Step-by-step explanation:
A linear transformation must satisfy the following properties.
- T(0) = 0.
- For vector a,b then T(a+b) = T(a) + T(b).
- For a vector a and a scalar r, it must happen that T(ra) = rT(a)
In this case we have that T(a,b,c) = (a,0,c).
Note that T(0) = T(0,0,0) = (0,0,0) = 0. So, the first property holds.
Let [tex] a=(a_1,a_2,a_3), b=(b_1,b_2,b_3) [/tex]. Then
[tex]T(a+b) = T((a_1+b_1,a_2+b_2,a_3+b_3)) = (a_1+b_1,0,a_3+b_3) = (a_1,0,a_3)+(b_1,0,b_3) = T(a) + T(b)[/tex]
So the second property holds.
Finally, let r be a scalar and let [tex] a=(a_1,a_2,a_3)[/tex]. Then
[tex] T(ra) = T((ra_1,ra_2,ra_3)) = (ra_1,0,ra_3) = r(a_1,0,a_3)= rT(a)[/tex]
So, the three properties hold, and therefore, T is a linear transformation.
It is true that T represents a linear transformation
How to determine if T is a linear transformationA linear transformation is such that have the following properties
T(0) = 0.If u and v are vectors, then T(u+v) = T(u) + T(v).If u is a vector and r is a scalar, then T(ru) = rT(u)For the first property, we have:
T(x1,x2,x3) = (x1,0,x3)
The above property becomes
T(0) = T(0,0,0)
T(0) = (0,0,0)
T(0)= 0.
So, we can conclude that the first property of the linear transformation is satisfied
For the second property, we make use of the following:
u = (u1, u2, u3) and b = (v1,v2,v3)
The above property becomes
T(u + v) = T(u1 + v1, u2 + v2, u3 + v3)
Expand
T(u + v) = T(u1 + v1, 0, u3 + v3)
Expand
T(u + v) = (u1,0,u3) + (v1, 0, v3)
Simplify
T(u + v) = T(u) + T(v)
The above means that the second property is also satisfied
Recall that:
u = (u1, u2, u3)
So, we have:
T(ru) = (ru1, ru2, ru3)
Where r is a scalar
Expand
T(ru) = (ru1, 0, ru3)
Further, expand
T(ru) = r(u1, 0, u3)
So, we have:
T(ru) = rT(u)
The above means that, the third property is also satisfied
Hence, T represents a linear transformation
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Determine whether the underlined number is a statistic or a parameter. In a study of all 1963 employees at a college, it is found that "40%" own a computer. Choose the correct statement below.
1. Parameter because the value is a numerical measurement describing a characteristic of a population
2. Statistic because the value is a numerical measurement describing a characteristic of a population
3. Statistic because the value is a numerical measurement describing a characteristic of a sample.
4. Parameter because the value is a numerical measurement describing a characteristic of a sample.
Answer:
1. Parameter because the value is a numerical measurement describing a characteristic of a population
Step-by-step explanation:
A parameter is a fixed measure which describes the whole population while a statistic is a characteristic of a sample (which is a portion of the target population).
In a study of all 1963 employees at a college, it is found that "40%" own a computer.
The study involved the entire population of employees in the college, therefore the result describes the computer owning characteristics of the whole population under study. It is therefore a parameter.
The correct option is 1.
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the favorite sports of respondents are identified as 100 for basketball comma 200 for baseball comma 300 for football comma and 400 for anything else. The average (mean) is calculated for 597 respondents and the result is 256.1 .The data are at the _________________
level of measurement.
Answer:
The data are at the Nominal level of measurement.
The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement.
Step-by-step explanation:
The objective here is to Identify the level of measurement of the data, and explain what is wrong with the given calculation.
a)
The data are at the Nominal level of measurement due to the fact that it portrays the qualitative levels of naming and representing different hierarchies from 100 basketball, 200 basketball, 300 football, 400 anything else
b) We are being informed that, the average (mean) is calculated for 597 respondents and the result is 256.1.
The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement. At nominal level this type of data set do not measure at all , it is not significant to compute their average (mean).
a business owes $8,000 on a loan. every month, the business pays half of the amount remaining on the loan. how much will the business pay in the six-month?
Answer:
$7875
Step-by-step explanation:
1 Month 4000 Paid
2 Months 2000 Paid
3 Months 1000 Paid
4 Months 500 Paid
5 Months 250 Paid
6 Months 125 paid
Total = $7875 Paid
Hope this helped ;)
Solve (x - 3)2 = 49. Select the values of x.
52
DONE
Answer:
Step-by-step explanation:
[tex](x-3)^2=49[/tex]
<=>
[tex](x-3)^2-49=0\\\\<=> (x-3)^2-7^2=0\\\\<=> (x-3-7)(x-3+7)=0\\<=> (x-10)(x+4)=0\\<=> x -10=0\ or \ x+4=0\\<=> x = 10 \ or\ x = -4[/tex]
solutions are -4 and 10
do not hesitate if you need further explanation
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Please answer this correctly
Answer:
# of pages # of magazines
1-20 7
21-40 4
Step-by-step explanation:
Numbers 1 through 20:
10, 11, 14, 16, 17, 17, 20 (7 numbers)
Numbers 21 through 40:
21, 28, 29, 32 (4 numbers)