Answer:
[tex]z= 2 \ and \ z = \frac{-20}{3}[/tex]
Step-by-step explanation:
For the given expression to be undefined, it means that the denominator of the expression must be equal to zero
Hence;
[tex]6z^2+14z-80 = 0[/tex]
On factorizing:
[tex]6z^2+14z-80=0\\3z^2+7z-40 = 0\\3z^2-6z+20z-40 = 0\\3z(z-2)+20(z-2) = 0\\(3z+20)(z-2) =0\\(z-2)=0 \ and \ (3z+20)=0\\z= 2 \ and \ z = \frac{-20}{3}[/tex]
n rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=3 and BC=11, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.
*see attachment for clearer diagram
Answer:
16.5
Step-by-step explanation:
BC = 11
AB = 3
Area of the shaded region = area of ∆AEB + area of ∆CED
Area of a triangle is given as,
A = ½*base*height
Find the area of each triangle and add together
✔️Area of ∆AEB = ½*bh
Where,
base (b) = 3
height (h) = ½(BC) = ½(11) = 5.5
Area of ∆AEB = ½*3*5.5 = 8.25
✔️Area of ∆CED = ½*bh
Where,
b = 3
h = ½(BC) = ½(11) = 5.5
Area of ∆CED = ½*3*5.5 = 8.25
✅Area of the shaded region = area of ∆AEB + area of ∆CED
= 8.25 + 8.25
= 16.5
How much state tax is withheld from $36,200 if the tax rate is 4%?
Answer:
$1448
Step-by-step explanation:
Tax=rate*amount=(4/100)*36200=1448
If f(x)=x-2 and g(x)=2x-6, then g(4)/f(3)
Answer:
2
Step-by-step explanation:
g(x) = 2x - 6
g(4) = 2*4 - 6
g(4) = 2
f(x) = x - 2
f(3) = 3 - 2
f(3) = 1
Thus g (4) / f (3) = 2 / 1 = 2
The value of the function g (4) / f (3) is 2.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
We are given the function as;
f(x)=x-2 and g(x)=2x-6, then we need to find g(4)/f(3)
Therefore, g(x) = 2x - 6
g(4) = 2*4 - 6
g(4) = 2
Similalry,
f(x) = x - 2
f(3) = 3 - 2
f(3) = 1
Thus we have the value of function as
g (4) / f (3) = 2 / 1
g (4) / f (3) = 2
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How many real solutions does this system of equations have? x2 +3 = y
3х — у+1 = 0
Answer:
Step-by-step explanation:
y = x²+3
y = 3x+1
x² + 3 = 3x +1
x² - 3x + 2 = 0
(x-2)(x-1) = 0
x = 2, 1
Two solutions
(2,7) and (1,4)
Hi I need help :( I can’t figure these out
Step-by-step explanation:
I do don't either ok wjshjddshsj
Refer to this design web of a car manufacturer’s experiment. Which of the following statements are true? Check all that apply.
A confounding variable is the use of cruise control.
A confounding variable is the weather conditions.
A confounding variable is the participants’ reporting on their fuel efficiency.
There are no confounding variables in this experiment.
A confounding variable is the speed at which the participants drive on the course.
Answer:
2.3,5
Step-by-step explanation:
Both the 2nd and 3rd statement is true. Because of both statement is closely analyzed up during design process of automobile.
How do car manufacturers design cars?The process of creating the outside (and, to some degree, interior) of motor vehicles, such as cars, motorbikes, trucks, buses, coaches, and vans, is known as automotive design.Although a big team from many various disciplines, including automotive engineering, normally works on the functional design and development of a contemporary motor vehicle, design jobs are not always linked to educational requirements for professional- or chartered-engineer status. In this context, automotive design primarily focuses on improving the visual appeal or aesthetics of vehicles while also getting involved in the development of product concepts. Designers with degrees in industrial design or transportation design who have an artistic background often work in the field of automotive design professionally.Learn more about Automobile design refer :
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Use the formul
a (a+b)2=a2+2ab+b2 to expand the (4x+3y)2
Answer:
[tex] {(4x + 3y)}^{2} \\ = {(4x)}^{2} + 2 \times 4x + 3y + {(3y)}^{2} \\ 16 {x}^{2} + 24xy + 9 {y}^{2} \\ thank \: you[/tex]
What is the minimum perimeter of a rectangle with an area of 625 mm^2
3)
Write an inequality for the graph below. If necessary, use
<= for < or >= for.
Kinda stuck and running out of time
Answer:
Step-by-step explanation:
if a pendrive is bought for 1200 and sold at 25% profit find the profit amount
Answer: Profit = $300
Step-by-step explanation:
Given information
Original Price = $1200
Profit rate = 25%
Given expression
Profit amount = Profit rate × Original price
Substitute values into the expression
Profit amount = 25% × 1200
Profit amount = $300
Hope this helps!! :)
Please let me know if you have any questions
Which polynomial function is best represented by the graph?
ƒ(x) = –x(x – 1)4
ƒ(x) = x2(x + 1)3
ƒ(x) = x2(x – 1)3
ƒ(x) = x(x – 1)4
Answer: ƒ(x) = x2(x – 1)3
10 times as much as 9
Answer:
90
Step-by-step explanation:
10 x 9
=> 90
10 times 9 is 90.
Which expression is equivalent to sqrt of (6x^5 z)^3/ 4x^4 z^2
Answer:
[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]
I hope I helped you^_^
A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.
Answer:
About 6,785 people will be infected about nine months.
Step-by-step explanation:
We can write an exponential function to represent the situation. The standard exponential function is given by:
[tex]\displaystyle f(x) = a(r)^x[/tex]
Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.
3,124 people have already been infected. Thus, our initial value a = 3124.
And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.
Hence, our function is:
[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]
Then after nine months, the total amount of infected people will be f(9):
[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]
Use a calculator:
[tex]\displaystyle f(9) \approx 6785[/tex]
About 6,785 people will be infected about nine months.
Answer:
7,022
Step-by-step explanation:
Process control and acceptance sampling procedures are most closely related to _____. a. analysis of variance procedures b. hypothesis testing procedures c. interval estimation procedures d. linear regression procedures
Solve for y 2y+1>-9/5y-6
Answer: All real numbers
Step-by-step explanation:
Let's find the critical points of the inequality.
2y2+1=
−9
5
y−6
2y2+1−(
−9
5
y−6)=
−9
5
y−6−(
−9
5
y−6)(Subtract (-9)/5y-6 from both sides)
2y2+
9
5
y+7=0
For this equation: a=2, b=1.8, c=7
2y2+1.8y+7=0
y=
−b±√b2−4ac
2a
(Use quadratic formula with a=2, b=1.8, c=7)
y=
−(1.8)±√(1.8)2−4(2)(7)
2(2)
y=
−1.8±√−52.76
4
Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
OAmalOHopeO
A data set includes data from student evaluations of courses. The summary statistics are n=89, x=3.44, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
H0: μ=3.50
H1: μ>3.50
B.
H0: μ=3.50
H1: μ<3.50
C.
H0: μ≠3.50
H1: μ=3.50
D.
H0: μ=3.50
H1: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)
We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0
The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.
We go with answer choice D to form the null and alternative hypotheses.
The sign ≠ in the alternative hypothesis tell us that we have a two tail test.
---------------------------------------
Let's compute the test statistic
z = (xbar - mu)/(s/sqrt(n))
z = (3.44 - 3.50)/(0.67/sqrt(89))
z = -0.84483413122896
z = -0.84
The test statistic is roughly -0.84
---------------------------------------
Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.
Use a calculator or a Z table to determine that
P(Z < -0.84) = 0.2005
which is approximate
Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401
The p-value is roughly 0.401
-----------------------------------------
Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.
The conclusion based on that means that μ=3.50 must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50
Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *
12/24
Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.
Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24
Step Three: Add our new fractions: 3/24+8/24= 12/24
Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten
I hope I've help!
Working at home: According to the U.S Census Bureau, 34% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 170 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Answer:
The answer is "0.340".
Step-by-step explanation:
[tex]n = 500\\\\x = 170[/tex]
Using formula:
[tex]\to \hat{p} = \frac{x}{n} = \frac{170}{500}=\frac{17}{50} =0.340[/tex]
Express 18 hours to 2 days in its lowest term
Answer:
1 : 3
Step-by-step explanation:
We know that 1 days is 24 hours
2 days = 2*24 = 48 hours
16 hours : 48 hours
Divide each by 16
16/16 : 48/16
1 : 3
Answer:
[tex]3 : 8[/tex]
Step-by-step explanation:
[tex]18h : 2d \\ 18h : 2 \times 24h \\ 18 :48 \\ 3 : 8[/tex]
A(3, 7), B(5, 7), C(3-7), D(5, -7)
what is the area ?
Answer:
28 square units.
Step-by-step explanation:
This is a rectangle with sides (7 - (-7) and (5 - 3)
= 14 by 2
= 28 unit^2.
find the two intersection points
(x+1)^2 +(y+2)^2 = 16
3x+ 4y = 1
Show your steps please
Answer:
Our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Step-by-step explanation:
We want to find where the two graphs given by the equations:
[tex]\displaystyle (x+1)^2+(y+2)^2 = 16\text{ and } 3x+4y=1[/tex]
Intersect.
When they intersect, their x- and y-values are equivalent. So, we can solve one equation for y and substitute it into the other and solve for x.
Since the linear equation is easier to solve, solve it for y:
[tex]\displaystyle y = -\frac{3}{4} x + \frac{1}{4}[/tex]
Substitute this into the first equation:
[tex]\displaystyle (x+1)^2 + \left(\left(-\frac{3}{4}x + \frac{1}{4}\right) +2\right)^2 = 16[/tex]
Simplify:
[tex]\displaystyle (x+1)^2 + \left(-\frac{3}{4} x + \frac{9}{4}\right)^2 = 16[/tex]
Square. We can use the perfect square trinomial pattern:
[tex]\displaystyle \underbrace{(x^2 + 2x+1)}_{(a+b)^2=a^2+2ab+b^2} + \underbrace{\left(\frac{9}{16}x^2-\frac{27}{8}x+\frac{81}{16}\right)}_{(a+b)^2=a^2+2ab+b^2} = 16[/tex]
Multiply both sides by 16:
[tex](16x^2+32x+16)+(9x^2-54x+81) = 256[/tex]
Combine like terms:
[tex]25x^2+-22x+97=256[/tex]
Isolate the equation:
[tex]\displaystyle 25x^2 - 22x -159=0[/tex]
We can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 25, b = -22, and c = -159. Substitute:
[tex]\displaystyle x = \frac{-(-22)\pm\sqrt{(-22)^2-4(25)(-159)}}{2(25)}[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} x &= \frac{22\pm\sqrt{16384}}{50} \\ \\ &= \frac{22\pm 128}{50}\\ \\ &=\frac{11\pm 64}{25}\end{aligned}[/tex]
Hence, our two solutions are:
[tex]\displaystyle x_1 = \frac{11+64}{25} = 3\text{ and } x_2 = \frac{11-64}{25} =-\frac{53}{25}[/tex]
We have our two x-coordinates.
To find the y-coordinates, we can simply substitute it into the linear equation and evaluate. Thus:
[tex]\displaystyle y_1 = -\frac{3}{4}(3)+\frac{1}{4} = -2[/tex]
And:
[tex]\displaystyle y _2 = -\frac{3}{4}\left(-\frac{53}{25}\right) +\frac{1}{4} = \frac{46}{25}[/tex]
Thus, our two intersection points are:
[tex]\displaystyle (3, -2) \text{ and } \left(-\frac{53}{25}, \frac{46}{25}\right)[/tex]
Suppose that appearances of a foe to battle (that is, a random encounter) in a role-playing game occur according to a Poisson process, and the average rate equals one appearance per two minutes. Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
Answer:
Rate parameter of [tex]\mu = 0.5[/tex]
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
One appearance per two minutes.
This means that [tex]m = 2[/tex]
Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
[tex]\mu = \frac{1}{m} = \frac{1}{2} = 0.5[/tex]
So
Rate parameter of [tex]\mu = 0.5[/tex]
A telephone call arrived at a switchboard at random within a one-minute interval. The switch board was fully busy for 10 seconds into this one-minute period. What is the probability that the call arrived when the switchboard was not fully busy
Answer:
50/60 = .8333= 83.33%
Step-by-step explanation:
The probability that the call arrived when the switchboard was not fully busy is 0.75.
What is Normal Distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Given:
Here X follows uniform distribution with parameter a and b.
Where,
a = 0 and b = 1.
Then,
The density function of Y is given by:
P( 15 < Y ≤ 60)
or, P( 0.25 < Y ≤ 1)
So, P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]
= [tex][y]^1 _ {0.25}[/tex]
= (1- 0.25)
= 0.75
Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.
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For an ordered pair left parenthesis x comma y right parenthesis in a relation, the x element represents the
Answer:
the x éléments représente the domain
x represents the value on the x-axis and the coordinate is also known as abscissa.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).
Here x represents the value on the x-axis and the coordinate is also known as abscissa.
More about the coordinate geometry link is given below.
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on a 25 square grid how many squares need to be shaded to make 60% shaded
Answer:
15 squares
Step-by-step explanation:
60/100 * 25 = 15
Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.
Answer:
Step-by-step explanation:
The remainder when f(x) is divided by x + 3 would be 76.
What is remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x).
We have been given a function;
[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]
We need to find the remainder when f(x) is divided by x + 3.
So, Let p(x) = x + 3
p(x) = 0
x + 3 = 0
x = -3
Substitute in the given function f(x);
[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]
Thus, the remainder when f(x) is divided by x + 3 would be 76.
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a test has 10 multiple-choice questions with 6 choices each, followed by 35 true/false questions. if a student guesses on each equation, how many ways can he answer the questions on the test
Answer:
6¹⁰×2³⁵
Step-by-step explanation:
he has 6 choices for the first multiple choice question.
and for each of those he had again 6 more choices to answer the second question. 6×6 = 36
so, for all 10 multiple choice questions he answer in
6¹⁰ different ways = 60466176 ways
then there are 35 true/false questions, which are Bausch again multiple choice questions but with only 2 options instead of 6.
so we get 2³⁵ different possibilities. a huge number.
and they're possible for each of the 60466176 ways of the multiple choice part.
so, in total we have
6¹⁰×2³⁵ different answer possibilities.
please help me with this question!
