Answer:
The cost of the dining set = $200
Step-by-step explanation:
Let
Cost of the dining set=x
Sixty percent of the cost of the dining set
= 60% of x
=60/100 * x
= 0.6x
One half the cost of the dining set decreased by $180.
=1 1/2 of x - 180
= 1.5 * x - 180
= 1.5x - 180
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180
0.6x = 1.5x - 180
Collect like terms
0.6x - 1.5x = -180
-0.9x = -180
Divide both sides by -0.9
x= -180 / -0.9
=200
x= $200
Check:
0.6x
= 0.6(200)
=120
1.5x - 180
=1.5(200) - 180
= 300 - 180
=120
Solve application problems using quadratic equations. A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.
Hello, let's note a this positive real number.
The sum of the square is
[tex]a^2+(a-4)^2[/tex]
right?
So, we need to solve
[tex]a^2+(a-4)^2=72[/tex]
We will develop, simplify.
Let's do it!
[tex]a^2+(a-4)^2=72\\\\a^2+a^2-8a+16=72\\\\2a^2-8a+16-72=0\\\\2(a^2-4a-28)=0\\\\a^2-4a-28=0[/tex]
Now, we can use several methods to move forward. Let's complete the square.
[tex]a^2-4a=a^2-2*2*a=(a-2)^2-2^2=(a-2)^2-4[/tex]
So,
[tex]a^2-4a-28=0\\\\(a-2)^2-4-28=0\\\\(a-2)^2=32=4^2*2\\\\a-2=\pm4\sqrt{2}\\\\a = 2(1+2\sqrt{2}) \ \ or \ \ a = 2(1-2\sqrt{2})[/tex]
As a should be positive, the solution is
[tex]\Large \boxed{\sf \bf \ \ a = 2(1+2\sqrt{2}) \ \ }[/tex]
and the other number is
[tex]2(1+2\sqrt{2})-4=2(2\sqrt{2}-1)[/tex]
Thank you.
Rodell wants to find the favorite gaming app among the students at his school. He decides to poll the thirty students
on his football team and the fifteen students on his basketball team to gather the data. What is wrong with Rodell's
method for collecting his data?
Rodell only polled fellow athletes, this sample does not represent nonathletes at the school.
* Rodell needs a larger sample size than two sports teams to represent a whole school.
Rodell polled everyone on his teams; he should have only polled every other student for it to be a true sample.
Rodell’s polling method only included fall and winter sports, he should have also included a spring sport like
baseball
(it’s not B on edge, don’t answer if you don’t know thanks)
Rodell needs a larger sample size than two sports teams to represent a whole school.
Important Information : Study is conducted about favourite gaming app among students at school, 30 & 15 students of football & basketball team are polled.
Finding : Issue in Rodell's method of collecting data
The issue in this sampling : Rodell needs a larger sample size than two sports teams to represent a whole school.
Sample selected from universe should be very carefully chosen, to be a good representative of universe.
Here, Rodell has chosen only two sports' team members as sample for the study of favourite gaming app. Such kind of sample having more uneven concentration of any type of population members doesn't denote sample being a good representative of population.
To learn more Sampling, refer https://brainly.com/question/24842573?referrer=searchResults
Your manufacturing plant produces air bags, and it is known that 20% of them are defective. Five air bags are tested. (a) Find the probability that two of them are defective. (Round your answer to four decimal places.)
Answer:
1.0000
Step-by-step explanation:
It is know that 20% of air bags produced by the manufacturing plant are defective.
20% of x
Therefore, the probability that two are defective will be
20/100 × 5
0.2×5=1.0000
Shirley wants to find the distance her unicycle moves on the sidewalk when the tire makes one complete revolution. If the diameter of her unicycle tire is 14 inches, find the distance the unicycle moves in one complete revolution. Use as an approximation for pi.
Answer:
44 in
Step-by-step explanation:
The circumference of the tire will be the same as the distance the unicycle moves in one complete revolution.
Find the circumference with the formula C = [tex]\pi[/tex]d, where d is the diameter
Plug in the values:
C = [tex]\pi[/tex](14)
C = approx. 44 in
The boiling point of jet fuel is 329°F. Rounded to the nearest degree, what is the temperature in degrees Celsius? Use the formula C = 59(F – 32), where C represents degrees Celsius and F represents degrees Fahrenheit. A. 165°C B. 183°C C. 201°C D. 535°C
Answer:
17523° Celsius
Step-by-step explanation:
using the formula c=59(F-32), you have to plug the 329 into F like so-
C=59(329-32)
and then you're free to calculate! first you distribute the 59 like so...
C= (59 times 329)(59 times -32) getting C=19411-1888 which u then solve again to get 17523° Celsius
You measure 46 watermelons' weights, and find they have a mean weight of 60 ounces. Assume the population standard deviation is 8.5 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places.
Answer:
A 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .
Step-by-step explanation:
We are given that you measure 46 watermelons' weights, and find they have a mean weight of 60 ounces.
Assume the population standard deviation is 8.5 ounces.
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 weight = 60 ounces
[tex]\sigma[/tex] = population standard deviation = 8.5 ounces
n = sample of watermelons = 46
[tex]\mu[/tex] = population mean watermelon weight
Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.
So, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99
P( [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99
99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] , [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ]
= [ [tex]60-2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] , [tex]60+2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] ]
= [56.77 ounces, 63.23 ounces]
Therefore, a 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .
The coordinates on a map for City A are (57, 11) and those for City B are (121, 79). Note that coordinates represent miles. Find the distance between the cities to the nearest mile.
Answer:
93 miles
Step-by-step explanation:
Use the distance formula:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
Plug in the values:
d = [tex]\sqrt{(121 - 57)^2 + (79 - 11)^2}[/tex]
d = [tex]\sqrt{4096 + 4624}[/tex]
d = [tex]\sqrt{8720}[/tex]
d = 93.4
= 93 miles
Answer:
93 miles.
Step-by-step explanation:
To find this answer, we can use the distance formula: D= SQ root of (X2 - X1)^2 + (Y2-Y1)^2
Then, we have to plug in the corrdinates accordingly:
D = SQ root of (121 - 57)^2 + (79 - 11)^2
D = SQ root of (64^2) + (68^2)
D = SQ root of 4096 + 4624
D = SQ root of 8720
D = 93.3809402394
D rounded to the nearest mle is 93 miles
Hope this helps :)
1. Which of the following describes the end behavior of the function ƒ(x) = x^4 + 3x^3 – 2x + 7?
Hello, when x tends to [tex]\infty[/tex] the term with the highest degree will lead the behaviour.
In other words.
[tex]\displaystyle \lim_{x\rightarrow+\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow+\infty} {x^4}\\\\=+\infty\\\\\\\displaystyle \lim_{x\rightarrow-\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow-\infty} {x^4}\\\\=+\infty[/tex]
So, the answer B is correct.
Thank you.
As x → - ∞, then y → ∞ and x → ∞, then y → ∞. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = x⁴ + 3x³ - 2x + 7
If the value of x approaches the negative infinity, then the value of the function will be
f(x) = x⁴ + 3x³ - 2x + 7
We know that the value of (x⁴ - 2x) is greater than the value of 3x³. Then the value of the function will approach the positive infinity.
If the value of x approaches the positive infinity, then the value of the function will be
f(x) = x⁴ + 3x³ - 2x + 7
We know that the value of (x⁴ + 3x³) is greater than the value of 2x. Then the value of the function will approach the positive infinity.
Thus, As x → - ∞, then y → ∞ and x → ∞, then y → ∞.
Then the correct option is B.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) are given below. Find a 99% confidence interval on the difference in mean life. Which brand would you prefer based on this calculation?
Answer:
-727.5034 and 2464.2534
Step-by-step explanation:
Find explanation in the attachment
PLS HELP ASAP!! For brainliest answer!!!!
Round 765 mm to the nearest 100mm
Answer:
It is over then 749mm. so 800mm.
If it is less or same as 749mm, It is 700mm.
Answer:
[tex]\huge \boxed{\mathrm{800 \ mm}}[/tex]
Step-by-step explanation:
765 mm to nearest 100 mm would be to round up 765 to nearest hundred.
765 rounded up to nearest hundred’s place would be 800.
The place after 7 is 6, which is higher or equal to 5, so we add 1 to the hundred’s place followed by zeros.
six coins in your pocket: 5 cents, 10 cents, 20 cents, 50 cents, $1, $2. How many different sums of money can you make?
Answer:
You can make 64 different sums (which includes a sum of $0 using none of the coins).
Step-by-step explanation:
The number of sums you can make is equal to:
⁶C₀ + ⁶C₁ + ⁶C₂ + ⁶C₃ + ⁶C₄ + ⁶C₅ +⁶C₆ = 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64
The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
Answer:
irrational
Step-by-step explanation:
A = s^2
s^2 = 24,200
[tex] s = \sqrt{24200} [/tex]
[tex] s = \sqrt{242 \times 100} [/tex]
[tex] s = \sqrt{100 \times 121 \times 2} [/tex]
[tex] s = 10 \times 11\sqrt{2} [/tex]
[tex] s = 110\sqrt{2} [/tex]
P = 4s
[tex] P = 4 \times 100 \sqrt{2} [/tex]
[tex] P = 440 \sqrt{2} [/tex]
The perimeter is irrational.
if a number is doubled, and 16 is added to it, the resault is 40. what is the number
Answer:
The number is 12
Step-by-step explanation:
Let x = number
2x+16 = 40
Subtract 16 from each side
2x+16-16 =40-16
2x = 24
Divide by 2
2x/2 =24/2
x = 12
Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².
[1 3]
[-3 1]
Hello, let's note A the matrix, we need to find [tex]\lambda[/tex] such that A[tex]\lambda[/tex]=[tex]\lambda[/tex] I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as
[tex]\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0[/tex]
We just need to solve this equation using the discriminant.
[tex]\Delta=b^2-4ac=2^2-40=-36=(6i)^2[/tex]
And then the eigenvalues are.
[tex]\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}[/tex]
To find the basis, we have to solve the system of equations.
[tex]A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}[/tex]
[tex]A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}[/tex]
Thank you
Write the decimal number in numerical form: Six hundred eighty-two ten-
thousandths
Answer: 0.0682
Definition
Numerical: It's involving only numbers.
This means we will convert this number from word into numbers.
Answer:
Step-by-step explanation:
682.010
Please help me please thank you
Answer:
x = 15
Step-by-step explanation:
angles 2 and 4 are supplementary so they add up to 180
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15
Answer:
x=15
Step-by-step explanation:
Angles 2 and 4 are same-side interior angles. This means that if they are supplementary angles, then the lines A and B are parallel.
Supplementary angles, when added together, will equal a total of 180°. Set up an equation in which the angles are added and are equal to 180:
[tex](2x+10)+(4x+80)=180[/tex]
Solve for x. Remove the parentheses and combine like terms:
[tex]2x+10+4x+80=180\\\\2x+4x+10+80=180\\\\6x+90=180[/tex]
Work to isolate the variable, x. Subtract 90 from both sides:
[tex]6x+90-90=180-90\\\\6x=90[/tex]
Isolate x. Divide both sides by 6:
[tex]\frac{6x}{6}=\frac{90}{6} \\\\x=15[/tex]
The value of x is 15.
:Done
If you want to check your work, insert the value of x into the angles, and add them. If the answer is 180, then the value of x is true:
[tex]2x+10\\\\2(15)+10\\\\30+10\\\\40[/tex]
∠2=40
[tex]4x+80\\\\4(15)+80\\\\60+80\\\\140[/tex]
∠4=140
∠2+∠4=180
40+140=180
The value of x is true.
Complete the table of values for the following function.
Answer/Step-by-step explanation:
To complete the table, given the function, [tex] f(x) = \frac{1}{3}x^2 [/tex], plug in each value of x to find f(x).
Thus:
x = -6
[tex] f(-6) = \frac{1}{3}(-6)^2 = \frac{1}{3}(36) [/tex]
[tex] f(-6) = 12 [/tex]
[tex] f(-3) = \frac{1}{3}(-3)^2 = \frac{1}{3}(9) [/tex]
[tex] f(-3) = 3 [/tex]
[tex] f(0) = \frac{1}{3}(0)^2 = \frac{1}{3}(0) [/tex]
[tex] f(0) = 0 [/tex]
[tex] f(3) = \frac{1}{3}(3)^2 = \frac{1}{3}(9) [/tex]
[tex] f(3) = 3 [/tex]
[tex] f(6) = \frac{1}{3}(6)^2 = \frac{1}{3}(36) [/tex]
[tex] f(6) = 12 [/tex]
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 32. Is Theodore correct? Yes, the triangles are similar with a scale factor of 32. No, the triangles are similar with a scale factor of 21. No, the triangles are similar with a scale factor of 23. No, the triangles are similar with a scale factor of 43.
Answer:
Yes, the triangles are simirar with a scale factor of 3/2.
Step-by-step explanation:
We find the scale factor by dividing corresponding sides:
12/8=3/2
18/12=3/2
24/16=3/2
Find the angle measure x in the figure
Answer:
x = 25
Step-by-step explanation:
Make use of the fact that the sum of angle measures in a triangle is 180°.
(2x+15)° +(3x+5)° +(x+10)° = 180°
6x +30 = 180 . . . collect terms, divide by °
x +5 = 30 . . . . . . divide by 6
x = 25 . . . . . . . . . subtract 5
_____
Check
This value of x makes the angle measures be ...
A = (x+10)° = 35°
B = (3x+5)° = 80°
C = (2x+15)° = 65°
These angles total 180°.
Describe the sampling distribution of p(hat). Assume the size of the population is 30,000.n=800, p=0.6a) Determine the mean of the sampling distributionb) Dtermine the standard deviation of the sampling distribution
Answer:
Standard deviation of the binomial distribution
= [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]
Step-by-step explanation:
Explanation:-
Given size 'n' = 800
The population proportion 'p'=0.6
Let 'X' be the random variable of the binomial distribution
a) mean of the binomial distribution = n p = 800 ×0.6
μ = 480
b) variance of the binomial distribution
= n p q
= 800 X 0.6 ×0.4
σ² = 192
Standard deviation of the binomial distribution
σ = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]
Simplify please and show steps:
Sec (x) tan (x) csc (x) cot (x) sin (x) cos (x)
Answer:
The answer is 1Step-by-step explanation:
First of all transform the expression using trigonometric identities
That's
[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]
[tex] \csc(x ) = \frac{1}{ \sin(x) } [/tex]
[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]
So we have
[tex] \frac{1}{ \cos(x) } \times \tan(x) \times \frac{1}{ \sin(x) } \times \frac{1}{ \tan(x) } \times \sin(x) \times \cos(x) [/tex]
Reduce the expression with tan x
We have
[tex] \frac{1}{ \cos(x) } \times \cos(x) \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]
Reduce the expression with cos x
That's
[tex]1 \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]
Reduce the expression with sin x
We have
[tex]1 \times 1[/tex]
We have the final answer as
1Hope this helps you
Olivia has a big bag of 324 skittles.She divides the bag into thirds for herself and 2 friends.How many Skittles will each person get?
Answer:
108 skittles
Step-by-step explanation:
If she divides a bag of 324 skittles between 3 people, then we want to find a third of 324 - aka [tex]324\div3[/tex].
324 divided by 3 is 108, so each person will get 108 skittles.
Hope this helped!
Find out the mystery sequence hidden in the diminoes,dominoes, decide which number should replace the question mark.
Answer:
80?
Step-by-step explanation:
i counted the numbers on the first domino and that would be the first number, counted on the second one that would be the second number but since c had a two digit number they added the first number of the two digit number to the first domino number and that is what i did with d
hope it's correct:)
Answer:
80
Step-by-step explanation:
Basically, the first domino represents the tens place of the number and the second domino represents the units place. For a, we see that there are 3 dots on the first domino and 4 dots on the second domino so the number is 30 + 4 = 34. The same goes for b. For c, there are 6 tens and 11 ones so the number is 60 + 11 = 71. For d, there are 7 tens and 10 ones so the number is 70 + 10 = 80.
In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted for misconduct. How many people were in the sample
Answer: 200
Step-by-step explanation:
given data:
In a sample 76 people or 38% voted the mayor to be prosecuted.
solution:
how many people were in that sample
if 38% = 76 people
therefore;
let
p = total number of people
76/p = 38/100
cross multiply both sides
38p = 7600
divide both sides by 38
38p /38 = 7600 /38
p = 200
the number of people in the sample original was 200.
Assume that adults have IQ scores that are normally distributed with a mean 105 of and a standard deviation 20 . Find the probability that a randomly selected adult has an IQ between 88 and 122 .
Answer:
0.6048
Step-by-step explanation:
Given the following :
Assume a normal distribution :
Mean (m) = 105
Standard deviation (sd) = 20
Find the probability that a randomly selected adult has an IQ between 88 and 122 .
Z = (x - m) / sd
For IQ score of 88:
Z = (88 - 105) / 20
Z = (-17) / 20
Z = - 0.85
For IQ score of 122:
Z = (122 - 105) / 20
Z = (17) / 20
Z = 0.85
P(-0.85<Z<0.85) = P(Z < 0.85) - P(Z < - 0.85)
P(-0.85<Z<0.85) = (0.8023 - 0.1977)
P(-0.85<Z<0.85) = 0.6048
solve this asap plsss Giving 20 points ty <3
Answer:
24
Step-by-step explanation:
first 2×2=4
then 16÷4
4×6
24
Help me with this two problems please
(The problema are in a picture):
Answer:
Hey there!
I would prefer method two.
Both methods give the right solution, but method two is more straightforward. Instead of distributing, you simply divide and don't need to do as much work.
Let me know if this helps :)
Does the table show a direct proportional relationship? If so, what is the constant of proportionality? X 4 7 12 Y 32 56 96
equation is y = 8x
=============================================
Explanation:
Divide each x and y pair like so: y/x
If we get the same result each time, then we have a direct proportion.
y/x = 32/4 = 8
y/x = 56/7 = 8
y/x = 96/12 = 8
Each time we get the same result 8, which is the constant of proportionality. The table does show a direct proportional relationship. The equation is y = 8x which is in the form y = kx. The k value is the constant of proportionality. So k = y/x.
Find the
(i) Radius of the smaller sector.
(ii) Perimeter of the shape.
(iii) The angle
Answer:
Radius of the smaller sector = 12 cmPerimeter of the shape = 68 cmAngel = 47.72° (Approx)Step-by-step explanation:
Computation:
Length of arc = Θ/360[2πr]
20 = Θ/360(2)(22/7)(24)
Θ = 47.72°
Angel = 47.72° (Approx)
Length of arc = Θ/360[2πR]
10 = [47.72 / 360][2][22/7][R]
R = 12 cm
Radius of the smaller sector = 12 cm
Perimeter of the shape = 20 + 24 + 24
Perimeter of the shape = 68 cm