Answer:
x = 72
Step-by-step explanation:
3/8=27/x
cross multiply
3*x=3x 27*8=216
divide
216/3=x
x=72
Calculate the next term in the geometric sequence that is calculated with a ratio of 19 if the current term is 38
Answer:
Step-by-step explanation:
The next term is going to be simply 38*19 = 722
The series is geometric which means that you multiply from one term to get to the next.
The ratio of 19, and the current term is 38. So to get to the next term, multiply 38 * 19
A real estate agent has 1717 properties that she shows. She feels that there is a 60`% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling no more than 55 properties in one week. Round your answer to four decimal places.
Answer:
[tex]P(x \le 5) = 0.0110[/tex]
Step-by-step explanation:
Given
[tex]n = 17[/tex] -- number of properties
[tex]p = 60\%[/tex] --- probability of selling a property
Required
[tex]P(x \le 5)[/tex]
The question is an illustration of binomial probability, and it is calculated using:
[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(x \le 5) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3) +P(x = 4) +P(x = 5)[/tex]
[tex]P(x=0 ) = ^{17}C_0 * (60\%)^0 * (1 - 60\%)^{17-0} = 1.71798692*10^{-7}[/tex]
[tex]P(x=1 ) = ^{17}C_1 * (60\%)^1 * (1 - 60\%)^{17-1} = 0.00000438086[/tex]
[tex]P(x=2 ) = ^{17}C_2 * (60\%)^2 * (1 - 60\%)^{17-1} = 0.00005257039[/tex]
[tex]P(x=3 ) = ^{17}C_3 * (60\%)^3 * (1 - 60\%)^{17-3} = 0.00039427799[/tex]
[tex]P(x=4 ) = ^{17}C_4 * (60\%)^4 * (1 - 60\%)^{17-4} = 0.00206995948[/tex]
[tex]P(x=5 ) = ^{17}C_5 * (60\%)^5 * (1 - 60\%)^{17-5} = 0.008072842[/tex]
So, we have:
[tex]P(x \le 5) = 1.71798692*10^{-7}+0.00000438086+0.00005257039+0.00039427799+0.00206995948+0.008072842[/tex]
[tex]P(x \le 5) = 0.01059420251[/tex]
[tex]P(x \le 5) = 0.0110[/tex]
A researcher is interested in exploring the relationship between calcium intake and weight loss. Two different groups, each with 25 dieters, are chosen for the study.
Group A is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day.
Group B is required to follow the same diet and exercise regimen, but with no supplemental calcium. After six months on the program, the members of Group A had lost a mean of 12.7 pounds with a standard deviation of 2.2 pounds. The members of Group B had lost a mean of 10.8 pounds with a standard deviation 2.0 pounds during the same time period. Assume that the population variances are not the same.
Create and interpret a 95% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not.
Answer:
(0.7044 ; 3.0956)
Step-by-step explanation:
Given:
GROUP A:
n1 = 25
x1 = 12.7
s1 = 2.2
GROUP B :
n2 = 25
x2 = 10.8
s2= 2.0
The obtain the confidence interval assuming unequal population variance :
(x1 - x2) ± tα/2[√(s1²/n1 + s2²/n2)]
The degree of freedom :
df = (s1²/n1 + s2²/n2)² ÷ (s1²/n1)²/n1-1 + (s2²/n2)²/n2-1
The degree of freedom :
(2.2²/25 + 2²/25)² ÷ (2.2²/25)²/24 + (2²/25)²/24
df = 0.12503296 ÷ (0.0015617 + 0.0010666)
df = 47.57 ;
df = 48
Tcritical value ; α = 95% ; df = 48
Tcritical = 2.0106
C.I = (12.7 - 10.8) ± 2.0106[√(2.2²/25 + 2²/25)]
C.I = 1.9 ± (2.0106 * 0.5946427)
C.I = 1.9 ± 1.1955887
C. I = (0.7044 ; 3.0956)
Did any one know this?
Answer:
x sqrt(2)
Step-by-step explanation:
sqrt(a) / sqrt(b) = sqrt(a/b)
sqrt( 14 x^3) / sqrt(7x)
sqrt(14x^3/7x)
sqrt(2x^2)
sqrt(ab) = sqrt(a)sqrt(b)
sqrt(x^2) sqrt(2)
x sqrt(2)
Kesley works at a nursery she has 157 beads that she wants to share equally between 16 children for a necklace making activity.
How many beads will each child have and how many beads will be left over
Each child will get 9 pieces with 13 pieces left.
What is division?
'Division is a method of distributing a group of things into equal parts.'
According to the given problem,
Number of beads Kesley has = 157
Number of children to be shared between = 16
Number of beads in possession of each child = 157 ÷ 16
= 9
Number of beads divided equally = 144
Remaining beans = 157 - 144
= 13
Hence, we can conclude that out of 157 beans, 144 is divided equally among 16 children with each child getting 9 pieces.
Learn more about division here:
https://brainly.com/question/25502096
#SPJ2
which of the rolling equations have exactly one solutions ?
ps: (click the picture to see answer choices)
Answer:
All have exactly one solution
Step-by-step explanation:
a) -13x + 12 = 13x - 13
+13x +13x
-------------------------------
12 = 26x - 13
+13 +13
-------------------
25 = 26x
----- ------
26 26
25/26 = x
b) 12x + 12 = 13x - 12
-12x -12x
-----------------------
12 = x - 12
+12 +12
-----------------
24 = x
c) 12x + 12 = 13x + 12
-12x -12x
-----------------------------
12 = x + 12
0 = x
d) -13x + 12 = 13x + 13
+13x +13x
-----------------------------
12 = 26x + 13
-13 -13
-----------------------
-1 = 26x
--- -----
26 26
-1/26 = x
The equation y = 4x represents the relationship between time, x, and distance traveled, y. Which table represents
this relationship?
x
y
y
x
y
*
y
* 1
0
4
4
1
4
2
8
0
O
o
2
8
2
8
4
8
4
16
من
12
3
16
5
12
8
32
N
9514 1404 393
Answer:
D
Step-by-step explanation:
Choose the table in which all of the y-values are 4 times the corresponding x-values.
If there is a row in a table in which y is not 4x, reject that table. For example, in the first row of the first table we have x=0, so y = 4(0) = 0, but the table has y=4. The first table can be rejected.
Answer:D got the question and got it right
Step-by-step explanation:
x y
2 8
4 16
8 32
I NEED HELP PLEASE ASAP!!
Answer:
Option B, 1
Step-by-step explanation:
tan 45° = 1/1 = 1
in a school every student have two participate at least one of the activities athletes or music in a class of 50 students 30 participate in athlete and 25 students participate in music
Answer:
In a class of 50 students, 30 participated in athletics and 25 participated in music. Drawing a Venn- diagram , calculate how many students ...
Answer:
ok
Step-by-step explanation:
t7y7y8 I am not going out for the
Please help me with this question
Answer:
The sum of 1/6 and 1/7 would be 13/42, or, if you wanted the answer in decimal form rounded to the nearest hundredth, it would be about 0.31.
To find the sum of 1/6 and 1/7, we cannot simply add the numerators together and maintain the same denominator. This is because 1/6 and 1/7 have different denominators, so we don't know which denominator to maintain!
To fix this we need to find a number that is divisible by both 6 and 7. One easy way to do this is to multiply the two numbers together:
6 x 7 = 42
If we were to change the denominator to 42 for each fraction, we could add the numerators together and maintain a denominator of 42. However, this means we must change the numerator of each fraction along with its denominator.
Let's start with 1/6. We can multiply 6 by 7 to obtain 42, but this means we also have to multiply 1 by 7 to keep the fraction proportionate. If the fraction does not maintain the same proportion, it will be a completely different fraction!
We know that 1 x 7 = 7, so it is safe to say that 1/6 is equal to 7/42.
We can apply the same logic to 1/7. Since 7 x 6 is 42 we need to multiply 1 by 6 along with 7. Note: you cannot multiply each number by 7 this time, because 7 x 7 would be 49, not 42. In multiplying the numerator and denominator by 6 we know that 1/7 = 6/42.
Now we have an equation of:
6/42 + 7/42
Now we can add it as we would normally by adding the numerators and keeping the denominator to get:
6/42 + 7/42 = 13/42
If you needed the answer in decimal form it would be about 0.3095238095, or 0.31 rounded to the nearest hundredth.
I hope this helped.
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate
Answer:
YWX = DFE
Step-by-step explanation:
AAS means angle angle side. so, we need 2 angles and 1 side.
we have 1 side and one angle confirmed.
so, we need one of the other two angles (W or Y vs. F or D) confirmed.
they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.
Question 7 Multiple Choice Worth 1 points)
(01.01 LC)
Evaluate the expression 28 - 472 - 10-2
0 11
O 27
O 56
O 59
PLS HELP!!!
Solve x^2 – 4 = 5 by graphing the related function.
A) There are two solutions: 3 and –3.
B) There are two solutions: ±1.
C) There is one solution: 1
D) There are no real number solutions.
Answer:
A
Step-by-step explanation:
Because we can rearrange the equation and get:
x²=5+4
x²=9
[tex]x = \sqrt{9} [/tex]
[tex]x = + 3 \: \: or \: \: - 3[/tex]
Helpppp please !! Thank you :)
Answer: Because they are corresponding angles (second option is the answer).
Answer:
second option...because they are corresponding angles..
STEP BY STEP EXPLANATION: corresponding angles are formed when two parallel lines are intersected by the transversal
the corresponding angles are 2 and 6
Convert 653 in base 7 to base 10
Determine whether the following events are mutually exclusive. Choosing a student who is a French major or a chemistry major from a nearby university to participate in a research study. (Assume that each student only has one major.)
A. Mutually Exclusive
B. Not Mutually Exclusive
Answer:
A. Mutually Exclusive
Step-by-step explanation:
Mutually exclusive events:
Two events are mutually exclusive if they cannot happen together, that is, supposing the events are A and B:
[tex]P(A \cap B) = 0[/tex]
Choosing a student who is a French major or a chemistry major
Since each student only has one major, the student cannot be both a French and a Chemistry major, that is, [tex]P(A \cap B) = 0[/tex], so they are mutually exclusive and the correct answer is given by option A.
What must be true about the discriminant of this quadratic equation for the mentioned values of k? Assume p>0.
value of the discriminant k > 0
Options:
B^2 - 4ac= 0
B^2 - 4ac is greater than 0
B^2 - 4ac is less than 0
Answer:
Step-by-step explanation:b
No real roots. Roots will have imaginary numbers. This means the quadratic is either always above the axis, or always below.
One real root. The graph touches the x -axis in one place. →
Two real roots. The graph crosses the x -axis twice.
Given h(x) = -x + 1, find h(0).
Answer:
Answer:
1
Step-by-step explanation:
Given,
h ( x ) = - x + 1
To find : h ( 0 ) = ?
h ( 0 )
= - ( 0 ) + 1
= 1
Answer: 1
Step-by-step explanation:
h(x) = -x + 1
To Find = h(0)
= -(0) + 1
= 1
Answered by GauthMath if you like pls heart it and comment thanks
How long will it take for money to double if it is invested at 7% compounded monthly?
10x^3 - 25x^2 + 20
How to factor this
5(2x^2-x-2)(x-2)
Step-by-step
Answer: [tex]5(\frac{10x^3}{5}+\frac{-25x^2}{5}+\frac{20}{5}) \\\\5(2x^3-5x^2+4)\\\\5(2x^2-x-2)(x-2)[/tex]
How many edges are there?
A. not enough information
B. 15
C. 7
D. 10
The number of edges in the given figure is 15. The correct option is B.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The shape is made up of the triangular prism and the trapezoidal prism the total number of edges in the shape will be 15.
Therefore, the number of edges in the given figure is 15. The correct option is B.
To know more about geometry follow
https://brainly.com/question/25766008
#SPJ2
what is Newton's Law of Cooling?
Answer:
Newton's law of coming states that the rate at which an object cools is proportional to the differences in temperature between the object and the object's surroundings.
Answer:
It is the rate of heat loss of a body that is directly proportional to the difference in the temperatures between the body and its surroundings. Q= h* A* (T(object) -T(environment) )
find the missing length indicated
Answer:
Step-by-step explanation:
192
Answer:
Step-by-step explanation:
Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
please give me correct answer
Answer:
answer of question number 1 is 2400, 2880, 3600 respectively.
answer of question number 2 is 1384 and 1680.
Step-by-step explanation:
100×24=2400
120×24=2880
150×24=3600
692×2=1384
420×4=1680
How many centilitres are in 156000m^3
9514 1404 393
Answer:
1.56×10^10 cL
Step-by-step explanation:
There are 1000 liters in a cubic meter, so 10^5 centiliters in a cubic meter. The 1.56×10^5 cubic meters will then have ...
(1.56×10^5 m^3)×(10^5 cL/m^3) = 1.56×10^10 cL
_____
That's 15,600,000,000 cL.
"Centi-" is a prefix meaning 1/100.
1) A book contains 192 pages. A boy reads x complete pages everyday.if he has not finished the book after 10days, find the highest possible value of x
9514 1404 393
Answer:
19
Step-by-step explanation:
After x days, the boy will have read 10x. If this is less than 192, we have ...
10x < 192
x < 192/10
x < 19.2
If x is an integer, the largest possible value x could have is 19.
write your answer in simplest radical form
Answer:
n = 8√2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Opposite = 4√6
Hypothenus = n =?
The value of n can be obtained by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 60 = 4√6 / n
√3/2 = 4√6 / n
Cross multiply
n × √3 = 2 × 4√6
n × √3 = 8√6
Divide both side by √3
n = 8√6 / √3
Rationalise
n = 8√6 / √3 × (√3/√3)
n = 8√(6×3) / 3
n = 8√18 / 3
Recall
√18 = √(9×2) = √9 × √2 = 3√2
Thus,
n = 8√18 / 3
n = 8 × 3√2 / 3
n = 8√2
You can run at a speed of 4 mph and swim at a speed of 2 mph and are located on the shore, 6 miles east of an island that is 1 mile north of the shoreline. How far (in mi) should you run west to minimize the time needed to reach the island
9514 1404 393
Answer:
5.423 miles
Step-by-step explanation:
Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:
d² = 1² +(6 -x)² = x² -12x +37
d = √(x² -12x +37)
The total travel time is the sum of times running and swimming. Each time is found from ...
time = distance/speed
total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)
__
The total time will be minimized when its derivative with respect to x is zero.
t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0
Multiplying by 4 and combining fractions, we can see the numerator will be ...
√(x² -12x +37) +2x -12 = 0
Subtracting the radical term and squaring both sides, we get ...
4x² -48x +144 = x² -12x +37
3x² -36x +107 = 0
The quadratic formula tells us the smaller of the two roots is ...
x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi
You should run 5.423 miles west to minimize the time needed to reach the island.
__
A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.
A pool can be filled with water by a large pipe within six hours .A smaller pipe will take 9 hours to fill the pool.How long will it take to fill the pool if the two pipes operate together
Answer:
3.6 hours
Step-by-step explanation:
The formula is
1/a+1/b = 1/c where a and b are the times working along and c is the time working together
1/6 + 1/9 = 1/c
Multiply by 36c to clear the fractions
36c (1/6 + 1/9 = 1/c)
6c +4c = 36
10c = 36
Divide by 10
10c/10 = 36/10
c = 3.6 hours working together
