Answer:
denominator zeros are excluded
Step-by-step explanation:
The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.
The exclusions of interest are generally those values of the variable that make any denominator be zero.
__
Example:
f(x) = (2/(x-3)) / (4/(x -6))
has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...
f(x) = (x -6)/(2(x -3))
but x=6 remains excluded from the domain because of its effect in the original function definition.
_____
Additional comment
If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.
Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.
which of the following correctly shows the quotient of 75 divided by 5?
Answer:
15
Step-by-step explanation:
in multiplication we have given form of expression
Dividend(D) = Quotient(Q) x Divisor(d) + Remainder(r)
The number which is getting divided is called dividend
divisor is the number which divides the dividend.
quotient is the No. of times a dividend is divisible by divisor.
if dividend is not completely divisible by divisor then leftover after quotient * divisor is remainder.
value of remainder should be always less than divisor.
In the problem given
Dividend is 75
divisor is 5
so by the given above expression
Dividend(D) = Quotient(Q) * Divisor(d) + Remainder(r) ----> 1
we know that 15*5 = 75
75 = 15*5 + 0
comparing with the expression 1
we have q = 15
r = 0
Thus, quotient is 15.
If you come across this please try to solve the attachment below.
Answer:
Area of each triangle = 4 * 1.5 = 6 sq cm
Area of all 4 triangle = 4 * 6 = 24 sq cm
Step-by-step explanation:
A college entrance exam company determined that a score of 24 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 24.5 on the college entrance exam with a standard deviation of 3.3.
a) Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 24 on the math portion of the exam?
b) State the appropriate null and alternative hypotheses.
Answer:
a) The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance
Null hypothesis is accepted at 0.01% level of significance
They score is above 24 on the math portion of the exam
b)
Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school
H₀: μ = 24
Alternative Hypothesis: H₁: μ ≠ 24
Step-by-step explanation:
Step(i):-
Given random sample 'n' = 250
Given data sample mean x⁻ = 24.5
Standard deviation = 3.3
Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school
H₀: μ = 24
Alternative Hypothesis: H₁: μ ≠ 24
test statistic
[tex]Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{24.5 - 24}{\frac{3.3}{\sqrt{250} } } = \frac{0.5}{0.2087} = 2.397[/tex]
a) 99% or 0.01% level of significance
Level of significance ∝ = 0.01
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} =2.576[/tex]
The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance
Null hypothesis is accepted at 0.01% level of significance
They score is above 24 on the math portion of the exam
b) 95% or 0.05% level of significance
Level of significance ∝ = 0.05
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
The Z -value 2.397 > 1.96 at 95% or 0.05% level of significance
Null hypothesis is Rejected at 0.05% level of significance
They score is below 24 on the math portion of the exam
Una tirolina de 26 m de largo está atada entre dos postes que están separados por 24 m. Si Manuela monta la tirolina desde el primer poste a una altura de 50 m, ¿cuál es la diferencia entre los dos postes?
Answer:
The difference between the heights of the poles is 10m
Step-by-step explanation:
The distance between poles is 24 m
The length of the cable is 26m
You first use the Pythagoras' theorem to calculate the vertical distance between the end of one pole and the end of the other one.
[tex]c_2=\sqrt{h^2-c_1^2}\\\\c_2=\sqrt{(26m)^2-(24m)^2}=\sqrt{100}m=10m[/tex]
The difference between the heights of the poles is 10m
The higher pole has height of 50m
Then, the lower pole has a height of 50m - 10m = 40m
A triangular prism. The rectangular sides are 5 feet by 4 feet, 5 feet by 5 feet, and 5 feet by 3 feet. The triangular sides have a base of 4 feet and height of 3 feet. [Not drawn to scale] 60 square feet 72 square feet 82 square feet 84 square feet
Answer:
72ft²
Step-by-step explanation:
Calculate the area of each face and then sum them.
area of base = 4 × 5 = 20 ft²
area of back = 5 × 3 = 15 ft²
area of sloping face = 5 × 5 = 25 ft²
area of 2 triangular faces = 2 × × 4 × 3 = 4 × 3 = 12 ft²
Thus
surface area = 20 + 15 + 25 + 12 = 72 ft²
Write an equation in slope-intercept form of the line shown
Y=
Can someone help with the answer??
Answer:
y= -1/2 + 1
Step-by-step explanation:
It starts at +1 which is the B in y=mx+b. B is where a point touches the y-axis.
starting at a point: (-2,2), it goes down 1, and right 2. which now the slope is -1/2 because it is going down.
Given the sample data below, test the claim that the proportion of male voters who plan to vote Republican at the next presidential election is 15 percentage points more than the percentage of female voters who plan to vote Republican. Assume all requirements are met. Use the P-value method of testing hypotheses.
Men: n1 = 250, x1 = 146
Women: n2 = 202, x2 = 103
Answer:
[tex]z=\frac{0.584-0.510 -0.15}{\sqrt{0.551(1-0.551)(\frac{1}{250}+\frac{1}{202})}}=-1.615[/tex]
The p value would be given by:
[tex]p_v =P(Z<-1.615)= 0.0531[/tex]
The p value if is compared with a significance of 5% we see that is higher than 0.05 so then at this significance level we have enough evidence to conclude that the true difference in the proportion of males in favor is 15% more than the % of females in favor
Step-by-step explanation:
Information provided
[tex]X_{1}=146[/tex] represent the number of male in favor
[tex]X_{2}=103[/tex] represent the number of female in favor
[tex]n_{1}=250[/tex] sample of males selected
[tex]n_{2}=203[/tex] sample of females selected
[tex]p_{1}=\frac{146}{250}=0.584[/tex] represent the proportion of males in favor
[tex]p_{2}=\frac{103}{202}=0.510[/tex] represent the proportion of females in favor
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic
[tex]p_v[/tex] represent the value
System of hypothesis
We want to test if the proportion of males in favor is 0.15 point above the proportion of females, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} - p_{2} \geq 0.15[/tex]
Alternative hypothesis:[tex]p_{1} - p_{2} <0.15[/tex]
The statistic is given by:
[tex]z=\frac{p_{1}-p_{2} -0.15}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{146+103}{250+202}=0.551[/tex]
Replacing the info given we got:
[tex]z=\frac{0.584-0.510 -0.15}{\sqrt{0.551(1-0.551)(\frac{1}{250}+\frac{1}{202})}}=-1.615[/tex]
The p value would be given by:
[tex]p_v =P(Z<-1.615)= 0.0531[/tex]
The p value if is compared with a significance of 5% we see that is higher than 0.05 so then at this significance level we have enough evidence to conclude that the true difference in the proportion of males in favor is 15% more than the % of females in favor
help i needs hep will mar brainliest!
Answer:
B
Step-by-step explanation:
Have a wonderful day hope this helps
Reading and similar triangles
In the diagram below of MADE, B is a point on AE and C
is a point on AD such that BC is parallel to ED. AC = x - 5,
AB = 15, BE = 40,, and AD = 2x + 3. Find the value of x
and the length of CD
A
Answer:
x = 12.8CD = 20.8Step-by-step explanation:
The parallel lines create similar triangles, so corresponding sides are proportional.
AC/AD = AB/AE
(x -5)/(2x +3) = 15/(15+40)
Cross-multiplying gives ...
55(x -5) = 15(2x +3)
55x -275 = 30x +45 . . . . eliminate parentheses
25x = 320 . . . . . . . . . . . . add 275-30x
x = 12.8 . . . . . . . . . . . . . . .divide by 25
__
CD = AD -AC = (2x +3) -(x -5) = x +8 = 12.8 +8
CD = 20.8
What is the area of the trapezoid? If necessary, round your answer to the nearest tenth. A trapezoid with bottom side length of 8.5 feet, top side length of 5.5 feet, and height of 6.5 feet. 35.8 feet squared 45.5 feet squared 46.8 feet squared 55.3 feet squared
Answer:
45.5 sq. feet
Step-by-step explanation:
Area of trapezoid is given by 1/2(sum of parallel sides) * height of trapezoid.
In the problem
Parallel sides are bottom and top sides with length of 8.5 feet and 5.5 feet
Thus sum of Parallel sides = 8.5 feet + 5.5 feet = 14 feet
Height = 6.5 feet.
Thus,
area of trapezoid = 1/2*(14)* 6.5 feet = 7*6.5 feet = 45.5 sq. feet
The area of the trapezoid is whose sides are 8.5 feet and 5.5 feet with a height of 6.5 feet is 45.5 feet squared.
What is the area of a trapezoid?A trapezoid is a quadrilateral with parallel opposite sides and a height.
Mathematically, the area of a trapezoid can be calculated by using the expression:
[tex]\mathbf{Area \ of\ a \ trapezoid = \dfrac{1}{2}(a+b)\times h}[/tex]
where:
a and b =the two parallel sides of the trapezoidh = height[tex]\mathbf{Area \ of\ a \ trapezoid = \dfrac{1}{2}(8.5+5.5)\times 6.5}[/tex]
[tex]\mathbf{Area \ of\ a \ trapezoid = \dfrac{1}{2}(14)\times 6.5}[/tex]
[tex]\mathbf{Area \ of\ a \ trapezoid = 45.5 \ ft^2}[/tex]
Learn more about calculating the area of a trapezoid here:
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Brian invests £4000 into his bank account.
He receives 7% per year compound interest.
How many years will it take for Brian to have more than £8000?
Answer:
It will take for Brian 7.14 years.
Step-by-step explanation:
I=PRT
4,000=8,000*7/100*T
4,000=560T (then you divide 560 from both sides.)
T=7.14
Is (0,7) a solution for the equation 2x + y = 6
Answer:
no
Step-by-step explanation:
plug numbers into equation
2x + y = 6
2*0 + 7 = 6
0+7=6
7=6
False
Answer:
0.7 is not a solution for the equation 2x+y = 6
Step-by-step explanation:
If you calculate it....
2 x 0 + 7 = 6
does not make any sense because
2 x 0 = 0
0 + 7 = 7 not 6
please answer fast im having trouble please help
Answer:
For the first question the answer is B
For the second question the answer is 15
Step-by-step explanation:
In the picture we can see that 45 is equal to 3 z's, which can also be written as 45 = 3z. Now that we know that 45 = 3z, we can divide both sides by 3 so that we know what z equals.
45 (/3) = 3z (/3)
15 = z
Now we can see that z is equal to 15
Answer:
The answer is B
Step-by-step explanation: 45 is =3z because it shows three triangles in the expression and three z variables so when you add all the variable together you get 3z, hence 45=3z. And the value of z is 1 because like all variables unless the expression accounts for the number of variable they all start out to have only one.
Whoever answers CORRECTLY will get Brainliest. Do not answer if you don’t know. Don’t guess either. I want all correct answers. I’m on limited time here so I apologize if I come off as rude. If you cannot see all the words zoom out and then zoom in again so you’ll be able to solve the whole problem. Thank you in advance and God Loves you!
Answer: 18 cm^2
Step-by-step explanation:
There are four equal triangle and a rectangle.
Formula of a rectangle = b * h = 2*3 = 6
Formula of triangle = [tex]\frac{bh}{2}[/tex] but there four of them so we times them by 4, this leaves us with 2 (b * h) = 2(2*3) = 12
Area of pentagon = area of all triangles + rectangle
Area of pentagon = 12 + 6 = 18
Hope this helps.
Answer:
* Area of Pentagon ⇒ 18 cm^2 *
Step-by-step explanation:
Two of this triangles area are the same provided they are present with similar height and base length. They form a larger triangle such that, for the simplicity, let us start with finding the area of this larger triangle;
Area of Triangle ⇒ 1/2 * base * height ⇒ 1/2 * 6 * 2 ⇒ 6 cm^2
Now there is a similar issue with another two triangles, but they are present to not form a larger triangle. We could imagine that they are next to one another however, and solve for this larger triangle's area;
Area of Triangle ⇒ 1/2 * base * height ⇒ 1/2 * 4 * 3 = 6 cm^2
The last remaining shape is a rectangle, present with dimensions 3 by 2 centimeters such that it's area would be;
Area of Rectangle ⇒ base * height ⇒ 3 * 2 = 6 cm^2
The area of the pentagon is, consecutively;
Area of Pentagon ⇒ 6 + 6 + 6 = 18 cm^2
Which phrase represents the algebraic expression – 0472
the product of one-fourth and a number, plus seven
the product of seven and a number
the product of one-fourth and seven, plus a number
the product of seven and one-fourth
The human eye has different levels of sensitivity for different wavelengths of light. We can measure this sensitivity by comparing it (in percentages) to the highest possible sensitivity. S(w), left parenthesis, w, right parenthesis models sensitivity as a function of wavelength w (in nanometers). Match each statement with the feature of the graph that most closely corresponds to it. Feature Statement
Answer:
1. A wavelength of 320
2.the human eye 560
3.As the wavelength grows beyond 560
Step-by-step explanation:
W=560
The feature of the graph that most closely corresponds to it is W=560.
We have given that,
The human eye has different levels of sensitivity to different wavelengths of light.
We can measure this sensitivity by comparing it (in percentages) to the highest possible sensitivity. S(w), left parenthesis, w, right parenthesis models sensitivity as a function of wavelength w (in nanometers).
What is wavelength?The distance between successive crests of a wave especially points in a sound wave or electromagnetic wave.
Therefore the correct matches are given below,
1. A wavelength of 320
2. The human eye 560
3. As the wavelength grows beyond 560
W=560
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What is 9+10 please help I have 1 minute left, please
Answer:
21
Step-by-step explanation:
9 = 3*3
10 = 5*2
5*3 = 15
2*3 = 6
15 + 6 = 21
Which statement about a sphere is true?
Answer:
it is 3D
Step-by-step explanation:
Answer:
Its 3 dimensional
Step-by-step explanation:
I took the test
Help please
The best answer gets brainliest.
Two lines intersect to form 4 angles. Angles 2 and 4 are vertical angles with angle 2 = 4x + 12 and angle 4 = 7x - 6. a) Find x. b) What is the measure of angle 2 ?
Answer:
Does this help?
Step-by-step explanation:
2 = 4x + 12 and angle 4 = 7x - 6
Use the slope-intercept form to find the slope and y-intercept.
Slope: 0
y-intercept: 4
Use the slope-intercept form to find the slope and y-intercept.
Slope: 0
y-intercept: 2
Use the slope-intercept form to find the slope and y-intercept.
Slope: 0
y-intercept: 4
Graph 2= 4x + 12
Slope: Undefined
y-intercept: No y-intercept
Plot each graph on the same coordinate system.
4=
2=
4=
2= 4x + 12
4= 7x − 6
Simplify the expression 12k-2+6k
A. 16k2
B. 10k+6
C. 18k-2
D. 16k
Answer:
16k so it is D
Step-by-step explanation:
How is 5,328 represented in expanded notation
Answer:
5000
300
20
8
would be your answer :)
Angles R and S are complementary if m <R=65.3 what is the measure of <S?
Answer:
Step-by-step explanation:
if angles are complementary, that means they add up to 90º
if one is 65.3, then the other is just 90 - 65.3
<S = 90º - <R
<S = 90º - 65.3º
<S = 24.7º
The volume of the cylinder pi cm.^3. What is the volume of a cone with the same base and height as the cylinder
The Retail Advertising and Marketing Association would like to estimate the average amount of money that a person spends for Mother's Day with a 99% confidence interval and a margin of error within plus or minus $6. Assuming the standard deviation for spending on Mother's Day is $36, the required sample size is ________.
A) 313 B) 284 C) 210 D) 239
Answer:
D) 239
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Required sample size:
Is n
n is found when [tex]M = 6[/tex]
We have that [tex]\sigma = 36[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 2.575*\frac{36}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 36*2.575[/tex]
Simplifying by 6
[tex]\sqrt{n} = 6*2.575[/tex]
[tex](\sqrt{n})^{2} = (6*2.575)^{2}[/tex]
[tex]n = 238.7[/tex]
We round up, and the answer is 239.
Evaluate 8j-k+14 when j=0.25 and k=1
Hey Mate
Substitute
8(.25)-1+14
2-1+14
1+14
15
Hope it helps
So the right answer is 15.
Look at the attached picture
Hope it will help you
This diagram is a scale drawing of a store. To the nearest 50 square feet, what is the area of the actual store
Answer:
2500 ft²
Step-by-step explanation:
The missing area at lower right in the diagram has dimensions ...
(4 -2 1/4) by (3 -1 3/4) = (1 3/4) by (1 1/4)
Then the area of that "missing" space is ...
(1.75)(1.25) = 2.1875 . . . . square inches.
The area of the enclosing rectangle is ...
(4 in)(3 in) = 12 square inches
Then the area in the diagram representing the store is ...
12 in² -2.1875 in² = 9.8125 in²
__
Each square inch on the diagram represents an actual area of ...
(1 in)×(1 in) ⇒ (16 ft)×(16 ft) = 256 ft²
Then the actual store area is ...
9.8125(256 ft²) = 2512 ft²
Rounded to the nearest 50 ft², this is 2500 ft².
$5000 was invested into an account that earns an annual rate of 4.75%. If money is compounded monthly, how much will the account be worth after 3 years?
Answer:
$5764.14
Step-by-step explanation:
The future value formula is useful here.
FV = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.
FV = $5000(1 +.0475/12)^(12·3) = $5764.14
The account will be worth $5764.14 after 3 years.
What is the value of x in the equation
3x - y = 30, when y = 15?
Answer:
x = 15
Step-by-step explanation:
3x - y = 30
Let y = 15
3x - 15 = 30
Add 15 to each side
3x-15+15 = 30+15
3x= 45
Divide each side by 3
3x/3=45/3
x = 15
Answer
x=15Step-by-step explanation:
[tex]3x - y = 30 \\ 3x = 30 + y \\ x = \frac{30 + y}{3} \\ \\ [/tex]
[tex]y = 15[/tex]
[tex]x = \frac{30 + y}{3} \\ x = \frac{30 + 15}{3} \\ x = \frac{45}{3} \\ x = 15[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Volume of a rectangular prism is 15.75 in.³ the base has an area 10.5 in.² what is the height of the prism?
Answer:
Volume of a rectangular prism is 15.75 in.³ the base has an area 10.5 in.²
We also have:
Volume of a rectangular prism (V) = base area x height
=> height = V/base area = 15.75/10.5 = 1.5 in
Hope this helps!
:)