The statement; the area of a rectangle is 6 if and only if its length and width are 3 and 2 is true
Area of rectangleLength = 3Width = 2Area of a rectangle = length × width
= 3 × 2
= 6
Therefore, the area of a rectangle is 6 if and only if its length and width are 3 and 2 is true
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How does an earthquake of magnitude 7.8 compare in intensity with an earthquake of magnitude 3.7 on the Richter scale? Round to the nearest whole number.
Answer:
1000 * 10th sqrt of 10 or about 12589 times more powerful?
Step-by-step explanation:
Answer:v 31623
Step-by-step explanation:
Four students are working on a Math problem to find the soulution to 2x-3=11. Each student got a different answer. The four answers were 5,6,7 and 8. Which of these numbers make the equation true?
Answer:
7
Step-by-step explanation:
2x-3=11
Move the -3 to the right side by adding 3 to both sides of the equation
2x=14
Divide both sides by 2 to get x by itself
x=7
Answer:
7
Step-by-step explanation:
2x -3 = 11
2x = 14 . . . . add 3
x = 7 . . . . . . divide by 2
The number 7 makes the equation true when substituted for x.
Here are summary statistics for randomly selected weights of newborn girls: nequals153, x overbarequals31.5 hg, sequals7.1 hg. Construct a confidence interval estimate of the mean. Use a 90% confidence level. Are these results very different from the confidence interval 30.4 hgless thanmuless than32.8 hg with only 15 sample values, x overbarequals31.6 hg, and sequals2.7 hg?
Answer:
yes it is little different from the confidence interval (30.4 ≤μ≤ 32.8) changes statistics
90% confidence interval estimate of the mean is
(30.1048 , 33.0952)
Step-by-step explanation:
Step(I):-
Given sample size 'n' = 153
Given mean of the sample x⁻ = 31.5
Sample standard deviation 'S' = 7.1 h g
90% confidence interval estimate of the mean is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 153-1 =152
t₀.₀₅ =1.9757
Step(ii)
90% confidence interval estimate of the mean is
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
[tex](31.5 - 1.9757 } \frac{7.1}{\sqrt{153} } , 31.5 + 1.9757 \frac{7.1}{\sqrt{153} } )[/tex]
( 31.5 - 1.1340 , 31.5 + 1.1340)
(30.366 , 32.634)
90% confidence interval estimate of the mean is
(30.4 , 32.6)
b)
Given sample size 'n' = 15
Given mean of the sample x⁻ = 31.6
Sample standard deviation 'S' = 2.7 h g
90% confidence interval estimate of the mean is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 15-1 =14
t₀.₀₅ =2.1448
90% confidence interval estimate of the mean is
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]
[tex](31.6 - 2.1448 } \frac{2.7}{\sqrt{15} } , 31.6 + 2.1448 \frac{2.7}{\sqrt{15} } )[/tex]
( 31.6 - 1.4952 , 31.6 + 1.4952)
(30.1048 , 33.0952)
Conclusion:-
yes it is little different from the confidence interval (30.4 ≤μ≤32.8)
The weight of a box of cereal can vary by of an ounce and still be sold as a full box. Each box is supposed to contain 18 ounces of cereal. Which graph represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes?
Answer:
Its B
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
Its B on edge
A new landowner has a triangular piece of flat land she wishes to fence. Starting at the first corner, she measures the first side to be 5.7 m long and is directed 0.3 radians north of east. From the second corner, the second side is 9 m long and is directed 0.9 radians west of north. What is the length of the third side of the fence?
Answer:
The length of the third side of fence is 11.4 m
Step-by-step explanation:
Solution:-
- We are to mow a triangular piece of land. We are given the description of motion and the orientation of land-mower while fencing.
- From one corner of the triangular land, the land-mower travels H1 = 5.7 m at θ1 = 0.3 radians north of east. We will use trigonometric ratios to determine the amount traveled ( B1 ) in the east direction.
[tex]cos ( theta_1 ) = \frac{B_1}{H_1}[/tex]
Where,
B1: Is the base length of the right angle triangle
H1: Hypotenuse of the right angle triangle
Therefore,
[tex]B_1 = H_1*cos ( theta_1 )\\\\B_1 = 5.7*cos ( 0.3 )\\\\B_1 = 5.44541 m[/tex]
- Similarly, from the other corner of the triangular land. The land-mower moves a lateral distance of H2 = 9m and directed θ2 = 0.9 radians north of west. We will use trigonometric ratios to determine the amount traveled ( B2 ) in the west direction.
[tex]cos ( theta_2 ) = \frac{B_2}{H_2} \\[/tex]
Where,
B2: Is the base length of the right angle triangle
H2: Hypotenuse of the right angle triangle
Therefore,
[tex]B_2 = H_2*cos ( theta_2 )\\\\B_2 = 9*cos(0.9)\\\\B_2 = 5.59448 m[/tex]
- The total length of the third side of the fence would be the sum of bases of the two right angles formed by the land-mower motion at each corner.
[tex]L = B_1 + B_2\\\\L = 5.44541 + 5.59448\\\\L = 11.4 m[/tex]
Find the product of all positive integer values of $c$ such that $3x^2+7x+c=0$ has two real roots. I will award a lot of points
Answer: 24
Step-by-step explanation:
Let's find one solution:
3x² + 7x + c = 0
a=3 b=7 c=c
First, let's find c so that it has REAL ROOTS.
⇒ Discriminant (b² - 4ac) ≥ 0
7² - 4(3)c ≥ 0
49 - 12c ≥ 0
-12c ≥ -49
[tex]c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}[/tex]
Since c must be a positive integer, 1 ≤ c ≤ 4
Example: c = 4
3x² + 7x + 4 = 0
(3x + 4)(x + 1) = 0
x = -4/3, x = -1 Real Roots!
You need to use Quadratic Formula to solve for c = {1, 2, 3}
Valid solutions for c are: {1, 2, 3, 4)
Their product is: 1 x 2 x 3 x 4 = 24
Answer:
$3x^2+7x+c=0$
comparing above equation with ax²+bx+c
a=3
b=7
c=1
using quadratic equation formula
[tex]x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{ 2a} [/tex]
x=(-7+-√(7²-4×3×1))/(2×3)
x=(-7+-√13)/6
taking positive
x=(-7+√13)/6=
taking negative
x=(-7-√13)/6=
Find the values of b and c so g(x)=6x^2+bx+c has a vertex of (7,-9).
Answer:
b = -84
c = 285
Step-by-step explanation:
Given that:
[tex]g(x)=6x^2+bx+c[/tex]
Vertex of (7, -9).
To find:
Value of b and c = ?
Solution:
It can be seen that the given equation is of a parabola.
Standard equation of a parabola is given as:
[tex]y =Ax^2+Bx+C[/tex]
x coordinate of vertex is given as:
[tex]h=\dfrac{-B}{2A}[/tex]
Here, A = 6, B = b and C = c, h = 7 and k = -9
[tex]7=\dfrac{-b}{2\times 6}\\\Rightarrow b = -84[/tex]
So, the equation of given parabola becomes:
[tex]y=6x^2-84x+c[/tex]
Now, putting the value of vertex in the equation to find c.
[tex]-9=6\times 7^2-84\times 7+c\\\Rightarrow -9=294-588+c\\\Rightarrow -9=-294+c\\\Rightarrow c = 285[/tex]
So, the answer is :
b = -84
c = 285
I don't know what to do.
Answer:
104.93 in
Step-by-step explanation:
When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:
sin23° = 41/x
xsin23° = 41
x = 41/sin23°
x = 104.931
Determine whether the given value is from a discrete or continuous data set. When a car is randomly selected, it is found to have 8 windows. Choose the correct answer below. A. A discrete data set because there are a finite number of possible values. B. A continuous data set because there are infinitely many possible values and those values cannot be counted. C. A continuous data set because there are infinitely many possible values and those values can be counted. D. The data set is neither continuous nor discrete.
Answer:
A discrete data set because there are a finite number of possible values.
Step-by-step explanation:
We are given the following data set below;
When a car is randomly selected, it is found to have 8 windows.
Firstly, as we know that the discrete data is that data that have countable or finite values, and also we can observe at a point value.
On the other hand, the continuous data is that data in which there is a range of values and we can't count or observe each and every value.
So, in our question; as we can observe that we can count all the windows and it is also a finite number which means that the given data set is a discrete data set because there are a finite number of possible values.
Talk about why you think it is sometimes important to represent a procedure mathematcally. Give an example in life that a mathematcal procedure helped you solve a problem. In this procedure, what is independent quanity, what is dependent quanity?
Answer:
See Explanation
Step-by-step explanation:
Representing a procedure mathematically enables us to model life situations, solve for the unknown variables, and interpret back into the given situation for implementation.
A typical example is determining the gallons of gasoline a car would consume at a certain speed.
In this example, the independent variable is the driving speed, and the dependent variable is the gasoline consumption.
Gasoline consumption will either increase or decrease based on the speed of the car. The speed of the car is not affected by gasoline consumption.
Which of the following (x,y) pairs is the solution for the system of equations x+2y=4 and -2x+y=7
Answer:
(-2 ,3)
Step-by-step explanation:
Step 1: Rewrite first equation
x = 4 - 2y
-2x + y = 7
Step 2: Substitution
-2(4 - 2y) + y = 7
Step 3: Solve y
-8 + 4y + y = 7
-8 + 5y = 7
5y = 15
y = 3
Step 3: Plug in y to find x
x + 2(3) = 4
x + 6 = 4
x = -2
Solve the system of equations for the variables: x+2y-z=3 x+y-2z= -1
Answer:
z=0
x= -5
y=4
Step-by-step explanation:
Check the attachment please
Hope this helps :)
Step-by-step explanation:
x + 2y − z = 3
x + y − 2z = -1
There are three variables but only two equations, so this system of equations is undefined. We cannot solve for the variables, but we can eliminate one of them and reduce this to a single equation.
Double the first equation:
2x + 4y − 2z = 6
Subtract the second equation.
(2x + 4y − 2z) − (x + y − 2z) = (6) − (-1)
2x + 4y − 2z − x − y + 2z = 7
x + 3y = 7
What number must you add to complete the square?
X^2 + 8x= 11
A. 12
B. 16
c. 8
D. 4
Answer:
16
Step-by-step explanation:
X^2 + 8x= 11
Take the coefficient of x
8
Divide by 2
8/2 =4
Square it
4^2 = 16
Add 16 to each side
(0, 3) and (-2, -1)
Write an equation in slope intercept from of the line that passes through the given points.
Answer:
y = 2x + 3
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (-1 - 3)/(-2 - 0)
m = -4/-2
m = 2
y = 2x + b
Step 2: Rewrite equation
y = 2x + 3
*You are given y-intercept (0, 3), so simply add it to your equation.
Need help with this as soon as possible.
Answer:
after 9 weeks it would become 9*1+10=19 inches
and after w weeks it will be w*1+10 inches tall
hope this helps
Step-by-step explanation:
Answer:
a) 19 inches
b) 10+w inches
Step-by-step explanation:
The equation for this problem is 10 + w. In the first part, w = 9, so the plant is 19 inches tall.
Two vehicles begin traveling at the same time. Vehicle A travels at 45
miles per hour (MPH) for two hours. Vehicle B travels at 80 MPH for
one hour. Which vehicle travels the farthest, and how much farther
does it travel?
Answer:
The answer is A because 45x2= 90 miles and 80×1 = 80 miles and 90-80= 10 so Vehicle A travels 10 miled farther than Vehicle B. Hope that helps!
Vehicle which travels the farthest is vehicle A and the distance it travels farther is 10 miles.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Speed of vehicle A = 45 miles per hour
Speed of vehicle B = 80 miles per hour
Vehicle A travels for 2 hours.
Total distance travelled = Speed × Time = 45 × 2 = 90 miles
Vehicle B travels for 1 hour.
Distance travelled = 80 miles
Vehicle A travels farthest since the distance is greater for A.
Difference in the distance = 90 - 80 = 10 miles
Hence the vehicle A travels 10 miles farther.
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Please check my answer! The faculty at a particular school have attended up to an average 4 years of college with a standard deviation of 2 years. Faculty members who are in the lower 10% of the distribution will be offered the opportunity to obtain additional training. A faculty member must have attended less than ___________ years of school to qualify for the training. Round your answer to the year. My answer: 1 – 0.10 = 0.90 0.9 - 0.5 = 0.40 z-score = 1.28 (corresponds with 0.3997) x = (1.28)(2) + 4 = 7 years (rounded)
Answer:
1 year
Step-by-step explanation:
1. Convert 10% into a z-score, using a calculator or whateva
2. Z = -1.281551 ( you can find this by doing the following equation: (x - mean) / (standard deviation)
3. Hence -1.281551 = (x - 4) / 2 or, x = 1.436898, ( rounded to the nearest year ) = 1 year
F (X) = x² - 2x and 6(x) = 3x+1
A) Find F(g(-4))
B) Find F(g(x)) simply
C) find g^-1 (x)
Part A
g(x) = 3x+1
g(-4) = 3(-4)+1 ... every x replaced with -4
g(-4) = -12+1
g(-4) = -11
Plug this into the f(x) function
f(x) = x^2 - 2x
f( g(-4) ) = (g(-4))^2 - 2( g(-4) )
f( g(-4) ) = (-11)^2 - 2(-11)
f( g(-4) ) = 121 + 22
f( g(-4) ) = 143 is the answer====================================================
Part B
Plug the g(x) function into the f(x) function
f(x) = x^2 - 2x
f( g(x) ) = ( g(x) )^2 - 2( g(x) ) ... replace every x with g(x)
f( g(x) ) = (3x+1)^2 - 2(3x+1)
f( g(x) ) = (9x^2+6x+1) + (-6x-2)
f( g(x) ) = 9x^2+6x+1-6x-2
f( g(x) ) = 9x^2-1 is the answerNote that we can plug x = -4 into this result and we would get
f( g(x) ) = 9x^2-1
f( g(-4) ) = 9(-4)^2-1
f( g(-4) ) = 9(16)-1
f( g(-4) ) = 144-1
f( g(-4) ) = 143 which was the result from part A
====================================================
Part C
Replace g(x) with y. Then swap x and y. Afterward, solve for y to get the inverse.
[tex]g(x) = 3x+1\\\\y = 3x+1\\\\x = 3y+1\\\\3y+1 = x\\\\3y = x-1\\\\y = \frac{1}{3}(x-1)\\\\y = \frac{1}{3}x-\frac{1}{3}\\\\g^{-1}(x) = \frac{1}{3}x-\frac{1}{3}\\\\[/tex]
Suppose that you have 9 cards. 5 are green and 4 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 4 yellow cards are numbered 1, 2, 3, and 4. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, and without replacement. • G1 = first card is green • G2 = second card is green a) Draw a tree diagram of the situation. (Enter your answers as fractions.) b) Enter the probability as a fraction. P(G1 AND G2) = c)Enter the probability as a fraction. P(at least one green) = d)Enter the probability as a fraction. P(G2 | G1) = _______.
The probability of picking greens on both occasions will be 5/18.
How to explain the probability?The probability of picking greens cards will be:
= 5/9 × 4/8
= 5/18
The probability of picking at least one green will be:
= 1 - P(both aren't green)
= 1 - (4/9 × 3/8)
= 1 - 1/6.
= 5/6
From the tree diagram, the probability as a fraction of P(G2 | G1) will be:
= 4/8 = 1/2
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Find the slope and y-intercept: 4x-y+6=0
Answer:
The slope is 4, and the y-intercept is 6.
Step-by-step explanation:
The equation of the line is generally written as y = mx + b.
Where m is the slope, and b is the y-intercept.
4x - y + 6 = 0
Solve for y.
- y = 0 - 4x - 6
y = -1(-4x - 6)
y = 4x + 6
The slope of the line is 4, and the y-intercept of the line is 6.
Answer:
Y-intercept is (0,6). The slope is 4
Step-by-step explanation:
are the two triangles below similar
Answer:
Hey!
Your answer is YES!
AKA the Last Option on your screen!
Step-by-step explanation:
It is this because...
They both have the angles 105 in it...
And looking at the other angle on the smaller one (25)
50 + 25 = 75 ... 180 - 75 = 105
WE HAVE 105 as an angle on the larger triangle...which makes them SIMILAR but congruent Angles!
It cant be the "corresponding sides" as we do not have the notations (lines intersecting the sides) that let us know that the lines are the same.
Hope this helps!
A lady buys bananas at 3 Rs 5 and sells them at 2 Rs for Rs 5; find her gain percent.
Answer:
50%
Step-by-step explanation:
Cost of 3 bananas= Rs. 5 ⇒ cost of 1 banana= Rs. 5/3
Selling price of 2 bananas= Rs. 5 ⇒ selling price of 1 banana= Rs. 5/2
Gain= Rs. (5/2- 5/3)= Rs. (15/6- 10/6)= Rs. 5/6
Gain %= 5/6÷5/3 × 100%= 50%
If the 2412 leaves are not a random sample, but the researchers treated the 2412 leaves as a random sample, this most likely made the data more:_____________.1. accurate, but not precise2. precise, but not accurate3. neither4. both accurate and precise
Answer:
2. Precise but not accurate
Step-by-step explanation:
In a high precision, low accuracy case study, the measurements are all close to each other (high agreement between the measurements) but not near/or close to the center of the distribution (how close a measurement is to the correct value for that measurement)
In the North Area Mall, 18 of the 90 stores sell shoes. If that same ratio holds true for the University Mall and 9 stores there sell shoes, how many stores are at University Mall?
Answer:
18/90=9/x and to find x use proportion so first 90*9=18x and 810=18x and x-45
Step-by-step explanation:
Answer:
45 stores are at University Mall
Step-by-step explanation:
The ratio of malls that sell shoes at North Area mall are 18 out of 90, which simplifies to one fifth of stores. Since the same ratio holds for the University Mall, and 9 is half of 18, the amount of stores at University Mall is 45 because 45 is half of 90.
HElp 64 points and Brainlyiest to who ever can solve the problem question on the picture
Which property was applied in this step?
Addition Property of Equality
O Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equalit
Answer:
Addition Property of Equality
Step-by-step explanation:
You are adding 3/4 to both sides to isolate the x.
Your bank balance is $102.35 and you've just made purchases for $20, $33.33, and $52.80. You then make deposits of $25 and $24.75. What's your new balance?
A. 565.77
B. 54102
C. $45.97
D. 551.22
Answer:
C
Step-by-step explanation:
102.35-20-33.33-52.80+25+24.75
45.97
PLS HELP ASAP!!!!........
Answer:
aaaaha pues
Step-by-step explanation:
Answer:
what happened
Step-by-step explanation:
please i need this answer right now !!!! Dx
Answer: the answer is d sin30degrees equal 5/x because sin is opposite over hyponuese
Please answer this correctly
Answer:
The second question
Step-by-step explanation:
The orca starts at -25 meters. She goes up 25 meters.
up 25 = +25
-25+25=0
Answer:
Option 2
Step-by-step explanation:
The orca swims at the elevation of -25 meters. The orca swims up 25 meters higher than before.
-25 + 25 = 0
Suppose that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6. Find the 95% confidence interval of the mean score for all bowlers in this league, using the accompanying data set of 10 random scores. Round your answers to two decimal places and use ascending order. Score 86 86 93 88 98 107 93 75 89
Answer:
A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].
Step-by-step explanation:
Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.
We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.
The accompanying data set of 9 random scores in ascending order is given as; 75, 86, 86, 88, 89, 93, 93, 98, 107
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean score = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{815}{9}[/tex] = 90.56
[tex]\sigma[/tex] = population standard deviation = 6
n = sample of random scores = 9
[tex]\mu[/tex] = population mean score for all bowlers
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]90.56-1.96 \times {\frac{6}{\sqrt{9} } }[/tex] , [tex]90.56+1.96 \times {\frac{6}{\sqrt{9} } }[/tex] ]
= [86.64 , 94.48]
Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].