Step-by-step explanation:
Let breadth be x,
then length is 2x cm,
perimeter of rectangle=2(l+b),
48=2(2x+x),
48÷2=3x
24=3x
24÷3=x
8cm =x,
B=8cm
L=2×8=16cm
Answer:
length =2x
breadth= let x be breadth
Perimeter = 48cm
now
Perimeter = 2 (l+b)
or, 48 cm = 2 (2x+x)
or, 48cm= 4x + 2x
or, 48 cm = 6x
or, 48cm÷6 =x
x = 8 cm
breadth= 8cm
length = 8 ×2 =16cm
Which of the following methods of sampling is an example of a stratified random sample?
A. Randomly choosing a name from a list of names in the population and then choosing every tenth name thereafter.
B. From 500 names of members of a population in a hat drawing 50 names from the hat without looking.
C. Dividing a target population of students by grade level and choosing the first 25 names from each group.
D. Dividing a population of adults into males and females and randomly choosing a sample proportional to the numbers in each group.
Answer: D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
Which equation can be used to find x, the length of the hypotenuse of the right 18 + 24 = x 18 squared + 24 = x (18 + 24) squared = x squared 18 squared + 24 squared = x squared
Answer:
18² + 24² = x²
Step-by-step explanation:
Using the Pythagorean theorem, with legs a and b, and hypotenuse c, the equation is:
a² + b² = c²
If the legs measure 18 and 24, and the hypotenuse has length x, then you get:
18² + 24² = x²
Answer:
D
Step-by-step explanation:
A list of pulse rates is 70, 64, 80, 74,92. What is the median for this list?
Answer:
64 70 74 80 92
Answer = 74
Step-by-step explanation:
The median is when you have an order of numbers in ascending order (smallest to largest) then you find the middle number
Hope this helps :)
If anything is incorrect then please comment and I shall change the answer to the correct one
Median for the given data 70, 64, 80, 74,92 is equals to 74.
What is median?"Median is defined as the central value of the given data after arranging them into ascending or descending order."
According to the question,
Given data for pulse rates = 70, 64, 80, 74,92
Arrange the data in ascending order we get,
64, 70 , 74, 80, 92
Number of pulse rate reading is 5 , which is an odd number.
Therefore, median is the central value.
Median for the given data = 74
Hence, median for the given data 70, 64, 80, 74,92 is equals to 74.
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596 is divisible by 2?
a.yes
b.no
Answer:
It's yes
Step-by-step explanation:
Answer:
yep
Step-by-step explanation:
number is even, so it can be evenly divided by 2. :)
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
Express the quotient of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]
Answer:
Solution : [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
Step-by-step explanation:
[tex]-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right][/tex]
Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,
[tex]\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}[/tex]
=[tex]-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] ÷ [tex]2\sqrt{2}\left(0-1\right)i[/tex]
= [tex]3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)[/tex] ÷ [tex]-2\sqrt{2}i[/tex]
= [tex]\frac{3\left(1-i\right)}{\sqrt{2}}[/tex]÷ [tex]2\sqrt{2}i[/tex] = [tex]-3-3i[/tex] ÷ [tex]4[/tex] = [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
As you can see your solution is the last option.
Find 14.6 + 8.52
I really need help !!!!
Answer:
[tex]14.6 + 8.52 \\ = 23.12[/tex]
Do phone surveys provide adequate coverage of households with respect to one particular parameter? The parameter is the proportion of households without children. If telephone surveys provide adequate coverage of households, then p , the proportion of households without children in the set of all future samples reached by phone, must be equal to the proportion of households without children in the population of all households. Suppose that Thomas, a market analyst, contacts a simple random sample of 300 households as part of a national telephone survey. Of the households contacted, 129 households, or 43 %, have no children and 57 % have at least one child. The most recent census indicates that 48 % of all households have no children and 52 % have at least one child.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Based on the result of his test , Thomas should fail to reject null hypothesis at a significance level of 0.01. Thomas sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
Step-by-step explanation:
From the question we see that the p-value is greater than the level of significance (0.01 )so we fail to reject the null hypothesis.
This means that Thomas has sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
The equation before the problem is
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²
X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²
The right side of the equation now has a common denominator
The next step is to factorize the left side of the equation.
(X+b/2a)²= ( b²-4ac)/4a²
Squaring both sides
X+b/2a= √(b²-4ac)/√4a²
Final equation
X=( -b+√(b²-4ac))/2a
Or
X=( -b-√(b²-4ac))/2a
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
First find the critical points of f :
[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]
[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]
so the point (1, 0) is the only critical point, at which we have
[tex]f(1,0)=-7[/tex]
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]
Find the critical points of g :
[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]
[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]
[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]
where n is any integer. We get 4 critical points in the interval [0, 2π) at
[tex]t=0\implies f(10,0)=155[/tex]
[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]
[tex]t=\pi\implies f(-10,0)=235[/tex]
[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]
So f has a minimum of -7 and a maximum of 299.
plz help brainliest to correct answer
Answer:
-2 would be right next to -3 because its negative and -1 would be right next to -2, 2 would be two points away from 0 bc its a whole number
Select the correct answer from each drop-down menu. The gasoline prices in seven states are $1.96, $2.09, $1.79, $1.61, $1.75, $2.11, and $1.84. The median gasoline price is _____. The difference of the first and third quartiles in this set of gas prices is ______ .
Answer:
The median is 1.84 and the difference between the first and third quartile is 0.34
Step-by-step explanation:
When you write them out 1.84 is the median (middle number). To find the difference I just subtracted the third quartile (2.09) by the first quartile (1.75)
========================================================
Explanation:
Original data set = {1.96, 2.09, 1.79, 1.61, 1.75, 2.11, 1.84}
Sorted data set = {1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11}
Notice that 1.84 is in the middle of the sorted set. Three values are smaller than it, and three values are larger than it.
Therefore, 1.84 is the median.
The values {1.61, 1.75, 1.79} are smaller than the median. We'll call this set L for lower set.
The values {1.96, 2.09, 2.11} are larger than the median. We'll call this set U for upper set.
From set L = {1.61, 1.75, 1.79}, the median here is 1.75. This is the value of the first quartile Q1
The value of Q3 is 2.09 as it is in the direct middle of set U = {1.96, 2.09, 2.11}
The interquartile range (IQR) is the difference of Q3 and Q1
IQR = Q3 - Q1
IQR = 2.09 - 1.75
IQR = 0.34
Find the value of x.
A. 86
B. 172
C. 94
D. 188
Answer:
188
Step-by-step explanation:
Tangent Chord Angle = 1/2Intercepted Arc
94 = 1/2 x
Multiply by 2
2*94 =x
188 =x
Select the best answer for the question . 7. At a public swimming pool , the probability that an employee is a lifeguard is P(L) = 0.85 , and the probability that an employee is a teenager is P(T) = 0.58 . What's the probability that an employee is a lifeguard , given that the employee is a teenager ? O A. There isn't enough information given. O B. 1.47 OC. 0.68 O D.0.49
Answer:
D) 0.49
Step-by-step explanation:
0.85 * 0.58 = 0.49
The probability is:
D 0.49
the cost of 1 kg tomato is RS . 75.Find the cost of 14 kg
Answer:
Cost of 1kg tomato=rs.75
Cost of 14kg tomato=(75×14)
rs.1050
What is the volume of the sphere shown below with a radius of 6?
A. 483 Cu, units
B. 2887 cu units
C. 1627 cu units
D. 14431 Cu, units
Answer:
B
Step-by-step explanation:
Volume of the sphere = (4/3)*pi*6^3=288*pi
Answer:
288 pi units^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi (6)^3
V = 4/3 pi (216)
V = 288 pi units^3
The number 42 has the prime factorization 2.3.7. Thus 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors):
1.42, 2 · 21,3 · 14, and 6. 7.
Required:
List the distinct ways the number 770 can be written as a product of two positive integer factors.
Answer:
Step-by-step explanation:
770 = 2*5*7*11
So they are:
2*385
10*77
5*154
7*110
14*55
11*70
22*35
Evaluate the expression for q = -2. 8q=
Answer:
-16
Step-by-step explanation:
8q
Let q = -2
8*-2
-16
Which expresses 1.5 as a percent?
1.5%
15%
150%
0.015%
Answer:
150%
Step-by-step explanation:
is the correct answer
A ball is dropped from a height of 14 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. (a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter an exact number.)
Answer:
Hello,
742/27 (ft)
Step-by-step explanation:
[tex]h_1=14\\\\h_2=\dfrac{14}{3} \\\\h_3=\dfrac{14}{9} \\\\h_4=\dfrac{14}{27} \\\\[/tex]
[tex]d=14+2*\dfrac{14}{3} +2*\dfrac{14}{9} +2*\dfrac{14}{27} \\=14*(1+\dfrac{1}{3}+\dfrac{2}{9} +\dfrac{2}{27} )\\=14*\dfrac{53}{27} \\=\dfrac{742}{27} \\[/tex]
The total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
What is the total distance?
Distance is a numerical measurement of how far apart objects or points are. It is the actual length of the path travelled from one point to another.
Here given that,
A ball is dropped from a height of [tex]14[/tex] ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
So, after striking with the ground it covers the distance [tex]14[/tex] ft. so it rebounds to the height is [tex]\frac{1}{3}(14)[/tex].
Then again it hits the ground and covers the distance [tex]\frac{1}{3}(14)[/tex] and again after rebounding it goes to the height is
[tex]\frac{1(1)}{3(3)}.(14)=\frac{(1)^2}{(3)^2}(14)[/tex]
Then it falls the same distance and goes back to the height
[tex]\frac{1}{3}[/tex] ×[tex](\frac{(1)^2}{(3)^2})[/tex] ×[tex]14[/tex] = [tex]\frac{(1)^3}{(3)^3}(14)[/tex]
So, the total distance travelled is
[tex]14+2[\frac{1}{3}(14)+(\frac{1}{3})^2(14)+(\frac{1}{3})^3(14)+...][/tex]
We take the sum is twice because it goes back to the particular height and falls to the same distance.
[tex]S=14+2(\frac{\frac{1}{3}(14)}{1-\frac{1}{3}})\\\\\\S=\frac{a}{1-r}\\\\\\S=14+2(\frac{\frac{14}{3}}{\frac{2}{3}})\\\\S=14+2(\frac{14}{2})\\\\S=14+2(7)\\\\S=14+14\\\\S=28ft[/tex]
Hence, the total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
To know more about thetotal distance
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A population culture begins with 20 strands of bacteria and then doubles every 4 hours. This can be modeled by , where t is time in hours. How many strands of bacteria are present at 20 hours?
Question 13 options:
A)
425 strands of bacteria
B)
567 strands of bacteria
C)
640 strands of bacteria
D)
375 strands of bacteria
Answer:
C) 640 strands of bacteria
Step-by-step explanation:
We are told in the question that the population doubles every 4 hours
Hence, formula to solve this question =
P(t) = Po × 2^t/k
From the question, we have the following information:
Beginning amount (Po) = 20 strands of bacteria
Rate(k) = 4 hours
Time(t) = 20 hours
Ending time (P(t)) = unknown
Ending amount = 20 × 2^20/4
= 20 × 2^5
= 20 × 320
= 640 strands of bacteria.
Therefore, the number of strands left after 20 hours is 640 strands of bacteria.
A photography store develops 320 pictures on Monday, 564 on Tuesday, 281 on Wednesday, and 473
on Thursday. If the store typically averages at least 420 pictures daily, how many pictures would need to
be developed on Friday?
Answer:
462 pictures
Step-by-step explanation:
Average (mean) is calculated by adding up all the values and dividing by how many values there are, therefore to have an average 420 pictures daily, the sum of the 5 days must be: 5x420 = 2100
The current sum is: 320 + 564 + 281 + 473 = 1638
Therefore the number for Friday is 2100 - 1638 = 462 pictures.
Hope this helped!
Fill in the blanks and explain the pattern
0,1,1,2,3,5,__,__,21,34,55
Answer:
8,13
Step-by-step explanation:
Look at the pattern :
0,1,1,2,3,5,...,...,21,34,55.
As you see the number in the pattern was made by the sum of 2 numbers behind it. Then, the blanks must be filled by :
3 + 5 = 88 + 5 = 13So, the blanks must be filled by 8 and 13
Answer:
In the two blanks would be 8, 13.
The pattern is practically the Fibonacci Code.
Step-by-step explanation:
The Fibonacci Code is a mathematical sequencing in which you start with two numbers and add them together to make the third number, then you add the third number and the second number together. Practically you keep adding each new sum and the number before it in the sequence to find the next new sum.
After 55 in this pattern, the pattern would go 89, 144, 233, 377, 610, 987,...
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Answer:
x + 2y = 8.
Step-by-step explanation:
Line goes through (-4, 0) and (4, -4).
The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.
Since we are looking for the equation of the line parallel to that line, the slope will be the same.
We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.
3 = (-1/2) * 2 + b
b - 1 = 3
b = 4.
So, we have y = -1/2x + 4.
1/2x + y = 4
x + 2y = 8.
Hope this helps!
ANSWEAr
x + 2y = 8
because it is
Please help me with this on the picture
9514 1404 393
Answer:
(x, y) ⇒ (y+1, 7-x) . . . rotation 90° CW about (4, 3)
or
(x, y) ⇒ (y+1, x+1) . . . glide reflection across y=x; and translation (1, 1)
Step-by-step explanation:
The figure is apparently rotated 90° clockwise. This can be accomplished a couple of ways: (1) rotation 90° CW about some center; (2) reflection across the line y=x. Because of the symmetry of the figure, we cannot tell which of these is used.
Rotation
The center of rotation can be found by looking at the perpendicular bisectors of the segments joining a vertex and its image. One such segment has endpoints (1, 6) and (7, 6), so is a horizontal line with midpoint (4, 6). The perpendicular bisector of that is x=4.
Another segment joining a point with its image has endpoints (5, 6) and (7, 2). Its midpoint is (6, 4), and the slope of the bisector through that point is 1/2. It intersects the line x=4 at (4, 3), the center of rotation.
Rotation 90° CW about the origin is the transformation (x, y) ⇒ (y, -x), so rotation of (x, y) 90° about the point (4, 3) will be the transformation ...
(x, y) ⇒ ((y -3) +4, (-(x -4) +3) = (y +1, 7 -x)
The transformation A to B is rotation 90° CW about (4, 3):
(x, y) ⇒ (y +1, 7 -x).
__
Reflection
Simple reflection across the line y=x is the transformation (x, y) ⇒ (y, x). Applying that transformation, we see that an additional translation of 1 unit right and one unit up is required. The complete transformation is a "glide reflection", a reflection followed by a translation.
The transformation A to B is a glide reflection across the line y=x with a translation up 1 and right 1:
(x, y) ⇒ (y +1, x +1).
Consider the given function and the given interval.
f(x) = 8 sin x - 4 sin 2x, [0,pi]
(a) Find the average value f ave of f on the given interval.
(b) Find c such that f ave = f(c).
(a) The average value of f(x) on the closed interval [0, π] is
[tex]\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}[/tex]
(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :
8 sin(c) - 4 sin(2c) = 16/π
8 sin(c) - 8 sin(c) cos(c) = 16/π
sin(c) - sin(c) cos(c) = 2/π
Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.
x power 8 + x power 4 + 1
factorize
Answer:
[tex]1(x {}^{8} + x {}^{4} + 1)[/tex]
Step-by-step explanation:
[tex]x {}^{8} + {x}^{4} + 1 =1( x {}^{8} + x {}^{2} + 1)[/tex]
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
Let x1 represent a quantitative independent variable and x2 represent a dummy variable for a 2-level qualitative independent variable. Which of the following models is the equation that produces two parallel curves, one for each level of your QL variable?
A. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2
B. E(y) = ?0 + ?1x1 + ?3x2
C. E(y) = ?0 + ?x11 + ?3x2 + ?4x1x2
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Answer:
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Step-by-step explanation:
Quantitative variables are measured in terms of numbers, and figures. Independent variables are those which are reason for change in other variables. Dummy variables are numerical that represents categorical data. The range of these variables is small and they can take on only two quantitative values.