Answer:
a) point (2, 1) is when the ball is on it's way down at 2 seconds
b) vertex (1, 2) is the highest the ball goes, which is 2 at 1 second.
c) y-intercept (0, 1) at time zero the ball is starting at a height of 1.
d) Points (0, 1) and (2, 1) are the points at which the ball starts and when it is in the same position from the ground as when it started, which is 1.
e) zero (x-int) is when the ball hits the ground at 2.5 seconds.
Step-by-step explanation:
Answer:
See below
step by step explanation
A. (2 , 1 ) is point on the parabola . It represents that the height of the ball after 2 second have passed.
b. The vertex is at ( 1 , 2 ) . It represent that the maximum height of the ball which is 2 units to at t = 1 second
c. The y - intercept is ( 0 , 1 ) . It represent that the initial height of ball at t = 0 second is 1 unit.
d. Point ( 0 , 1 ) and ( 2 , 1 )
This point represent the set of point having equal height at two different time. It represents how long before the ball reaches the same height from the starting point.
e. The zero or x - intercept is ( 2.5 , 0 )
It represent the time taken by ball before it reaches the ground.
Hope this helps...
Best regards!!
which of the following is equivalent to [ (x^ 2 y^ 3 )^ -2/ (x^ 6 y^ 3 z)^3]? worth 60 points!
Answer:
[tex]\dfrac{1}{x^{48}y^{36}z^{6}}[/tex]
Step-by-step explanation:
[tex] (\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 = [/tex]
[tex] = (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3 [/tex]
[tex] = (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3 [/tex]
[tex]= (\dfrac{1}{x^{16}y^{12}z^{2}})^3[/tex]
[tex]= \dfrac{1}{x^{48}y^{36}z^{6}}[/tex]
Answer:
[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]
Step-by-step explanation:
[tex]\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3[/tex]
[tex]\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }[/tex]
[tex]\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }[/tex]
[tex]\displaystyle \frac{x^{-48} y^{-36}}{z^6 }[/tex]
[tex]\displaystyle \frac{1}{x^{48}y^{36}z^6}[/tex]
Which option is it??????
Answer:
both the equation and it's inverse are functions
Which equation represents the line that passes through (-8,11) and
0 v= - 3 5x + 6
Oy=-x+16
Ov=-X-49
Oy - 11x +71
Answer:
Step-by-step explanation:
Hello,
the line passes through (-8,11) means than y = 11 for x = -8
I believe that you wanted to write the first one as below
[tex]y=-\dfrac{5}{8}x+6[/tex]
in that case for x = -8
y = - 5 * - 1 + 6 = 5 + 6 = 11
hope this helps
The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
First we need to find the slope
m = (y2-y1)/ (x2-x1)
= (7/2 -11)/(4--8)
= (7/2 - 22/2)/(4+8)
= (-15/2)/(12)
= -15/24
Divide top and bottom by 3
-5/8
Then we can use point slope form to write the equation
y-y1 = m (x-x1)
y- 11 =-5/8(x--8)
y- 11 =-5/8(x+8)
Distribute
y-11 =-5/8 x -5
Add 11 to each side
y-11 = -5/8x -5+11
y = -5/8x +6
Hence, The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).
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first correct answer gets best marks and make it short not super-long please and hurry
Answer:
b > 3 2/15
Step-by-step explanation:
To make it easier to solve convert the mixed fraction to a fraction.
2 3/5 = 13/5
Now, multiply the fraction by 3/3 so that you will have a common denominator.
13/5 × 3/3 = 39/15
Now you solve for b.
39/15 < b - 8/15
39/15 + 8/15 < (b - 8/15) + 8/15
47/15 < b
b > 47/15
Convert the fraction to a mixed fraction to find the answer
47/15 = 3 2/15
b > 3 2/15
[tex]Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = 0.$ Find\[\frac{u}{v} + \frac{v}{u}.\][/tex]
By the factor theorem,
[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]
Now,
[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]
[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]
So we have
[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]
The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
What is the sum and product of the roots of the quadratic equation?If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then
Sum of the roots = [tex]\frac{-b}{a}[/tex]
And,
Product of the roots = [tex]\frac{c}{a}[/tex]
According to the given question.
We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]
On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].
We get
[tex]a = 3\\b = 5\\and\\c = 7[/tex]
Also, u and v are the solutions of the quadratic equation.
⇒ u and v are the roots of the given quadratic equation.
Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].
And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].
Therefore,
[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)
[tex]uv=\frac{7}{3}[/tex] ....(iii) (product of the roots)
Now,
[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex] ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])
Therefore,
[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex] (from (i) and (ii))
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]
Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
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A taste test asks people from Texas and California which pasta they preferred brand a or brand b this table shows the results. A person is randomly selected for those tested. What is the probability that the person is from Texas given that the person prefers Brand b? Round your answer to two decimal places.
Answer: I just did it and the answer is 0.43
Step-by-step explanation:
Using it's concept, it is found that the probability that the person is from Texas given that the person prefers Brand b is given by:
A. 0.43.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 105 people prefer brand B, and of those, 45 are from Texas, hence:
p = 45/105 = 0.43.
Which means that option A is correct.
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PQR shown in the figure below is transformed into STU by a dilation with center (0, 0) and a scale factor of 3
Answer:
Step-by-step explanation:
Given question is incomplete; here is the complete question.
∆ PQR shown in the figure below is transformed into ∆ STU by a dilation with center (0, 0) and a scale factor of 3.
Complete the following tasks,
- Draw ΔSTU on the same set of axes.
- Fill in the coordinates of the vertices of ΔSTU.
- Complete the statement that compares the two triangles.
When ΔPQR is transformed into ΔSTU by a dilation with center (0, 0) and a scale factor of 3,
Rule to followed to get the vertices of ΔSTU,
(x, y) → (3x, 3y)
P(1, 1) → S(3, 3)
Q(3, 2) → T(9, 6)
R(3, 1) → U(9, 3)
Length of QR = 2 - 1 = 1 unit
Length of PQ = [tex]\sqrt{(3-1)^2+(2-1)^2}=\sqrt{5}[/tex] units
Length of PR = 3 - 1 = 2 units
Length of ST = [tex]\sqrt{(9-3)^2+(6-3)^2}=3\sqrt{5}[/tex] units
Length of TU = 6 - 3 = 3 units
Length of SU = 9 - 3 = 6 units
Therefore, ratio of the corresponding sides of ΔPQR and ΔSTU,
[tex]\frac{\text{PQ}}{\text{ST}}=\frac{\text{QR}}{\text{TU}}=\frac{\text{PR}}{\text{SU}}[/tex]
[tex]\frac{\sqrt{5}}{3\sqrt{5}}=\frac{1}{3}=\frac{2}{6}[/tex]
[tex]\frac{1}{3}=\frac{1}{3}=\frac{1}{3}[/tex]
Since ratio of the corresponding sides are same,
Therefore, ΔPQR and ΔSTU are similar.
Solve. 8x² + 5 = 35 Round to the nearest hundredth. Enter your answers in the boxes. The solutions are approximately and .
Answer:
x=1.94
x = - 1.94
Step-by-step explanation:
8x² + 5 = 35
Subtract 5 from each side
8x² + 5-5 = 35-5
8x² = 30
Divide each side by 8
8x² /8 = 30/8
x² = 15/4
Take the square root of each side
sqrt( x²) = ±sqrt(15/4)
x = ±sqrt(15/4)
x=1.93649
x = - 1.93649
To the nearest hundredth
x=1.94
x = - 1.94
Answer:
1.94
Step-by-step explanation:
[tex]8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\[/tex]
≈ ±1.94
Please help ASAP! I’ll give brainliest:))
Answer with explanation:
After dilation about the origin(0,0) with the scale factor of 'k" , the image of the original point (x,y) becomes (kx,ky)
From the given graph, the coordinates of point C = (0,6) [Since it lies on y-axis , the x-coordinate is zero]
After a dilation about the origin(0,0) with the scale factor of [tex]\dfrac{1}{2}[/tex], the new point will be [tex](\dfrac{1}{2}\times0,\dfrac{1}{2}\times6)=(0,3)[/tex]
Now plot this point on y-axis at y=3 as given in the attachment.
please help me explain this correctly..
Answer:
Yes, the ordered pair is correct.
Explanation:
You can check the if the ordered pair by substituting the values into the equation. If you substitute the ordered pair (1, 3), then you can make sure the ordered pair is correct. The equation with the substitution will be 3 = 1 + 2, which results in the true equation 3 = 3, therefore the ordered pair is correct.
Halle en metros cuadrados la cantidad de cartón necesaria para elaborar el sólido que se muestra:: POR FIS ES DE UNA EVALUACION ALGUIEN QUE ME AYUDEEE:).
Answer:
La cantidad de cartón necesaria para hacer el sólido es de 165 m² de cartón.
Step-by-step explanation:
La figura en la pregunta consta de tres formas
1) Una pirámide cuadrada
Altura inclinada = 5 m
Longitud lateral base = 3 m
2) un cubo
Longitud lateral, s = 3 m
3) Un prisma rectangular
Longitud = 6 m
Altura = 3 m
Ancho = 3 m
El área de superficie de la pirámide cuadrada, [tex]S_P[/tex] = 2 × Altura inclinada × Longitud del lado base
[tex]S_P[/tex] = 2 × 5 × 3 = 30 m²
El área de superficie del cubo, [tex]S_C[/tex] = 6 ×(Longitud lateral, s)²
[tex]S_c[/tex] = 6 × 3² = 54 m²
El área de superficie del prisma rectangular, [tex]S_R[/tex] = 4 × largo × alto + ancho × alto
[tex]S_R[/tex] = 4 × 6 × 3 + 3 × 3 = 81 m²
La cantidad de cartón necesaria para hacer el sólido, [tex]S_S[/tex] = [tex]S_P[/tex] + [tex]S_C[/tex] + [tex]S_R[/tex]
[tex]S_S[/tex] = 30 + 54 + 81 = 165 m².
La superficie del cartón necesaria para construir el sólido es de 165 m².
Look at photo please don't understand
Does anyone understand this
Please answer quickly!
Answer:
a) 18.6%
b) 598,230
Step-by-step explanation:
a) In the first part of the question, you are given two population values and asked to find the percentage difference between them. A formula you can use for that is ...
percentage difference = (difference)/(original value) × 100%
The difference of interest is the difference between the 2011 population and the 2001 population
difference = 510,000 -430,000 = 80,000
The original value is the 2001 population, so the percentage difference is ...
percentage difference = 80,000/430,000 × 100% = 0.1860 × 100% = 18.6%
This is a positive value, so represents an increase.
The percentage increase in population from 2001 to 2011 was 18.6%.
__
b) In the second part, you are given the percentage difference and asked to find the new value. We can rearrange the above formula to find the difference:
difference = (percentage difference)/100% × original value
Then the difference between the 2021 population and the 2011 population will be ...
difference = (17.3%)/100% × 510,000 = 0.173 × 510,000 = 88,230
So, the population in 2021 is expected to be 88,230 more than in 2011:
2021 population = 520,000 +88,230 = 598,230
The predicted population in 2021 is 592,230.
ASAP! I really need help with this question! Please do not send nonsense answers. Full solutions please!
Answer:
first option
Step-by-step explanation:
Given
[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]
Multiply through by x² to clear the fractions
15x + 6x² = 9 ( subtract 9 from both sides )
6x² + 15x - 9 = 0 ( divide through by 3 )
2x² + 5x - 3 = 0 ← in standard form
Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 5
The factors are + 6 and - 1
Use these factors to slit the x- term
2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(2x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5
Solution set is { - 3, 0.5 }
Please please help me
Answer:
A = 189 cm²Step-by-step explanation:
The area of a parallelogram is equal to the product of the length of its side and the height of the parallelogram perpendicular to that side.
H = 9 cm
S = 21 cm
A = S•H = 21 cm • 9 cm = 189 cm²
Function (True/False)
Answer:
yes it is a function
Step-by-step explanation:
Mathematics
In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.
Answer:
False
Step-by-step explanation:
A function has only 1 y value for any given x value.
You can use the "vertical line test" to check if a graph is of a function. Move a vertical line (you can use the edge of a ruler) from left to right across the graph. If at any point the line intersects the curve in two or more places, the curve is not a function.
PLEASE HELP. WILL MARK BRAINIEST!!! 1. What shape should Kylee use to draw the swimming pool on the diagram? 2.If Kylee wanted to put the swimming pool directly between the flower beds, at what point would the center of the swimming pool be? 3.Use the point you identified in Part 1 to write an equation that will draw the swimming pool on the diagram so that it is directly between the flower beds. 4.Can Kylee place the swimming pool directly between the flower beds? Use the equation you wrote in Part 3 prove or disprove that the swimming pool will touch one of the flower beds. (Hint: Plug in points that are on a flower bed to check if they are also on the circle.) 5.Where can Kylee put the pool? Write an equation that will draw the pool on the diagram so that it does not touch anything.
Answer:
1) A rectangular shape
2) Point (30, 50)
3) (x - 30)² + (y - 50)² = 10²
4) Yes, the swimming pool will touch the flower beds
5) Point (45, 25)
Step-by-step explanation:
1) Given the number of shapes that are rectangles (4) and the number of circular shapes (1) to conserve more space Kylee should drw the swimming pool with a rectangular shape
2) So as to avoid touching the flowerbeds which are 20 feet apart, the center of the swimming pool will be moved slightly up to (30, 50)
3) The equation that will draw the swimming pool is the equation of a circle, given as follows
(x - h)² + (y - k)² = r²
Where (h, k) is the coordinate of the center of the circle, and r is the radius of the circle,
Given that the diameter, D, of the circle = 20 feet, the radius, r = D/2 = 20/2 = 10 feet
The equation of the circle is therefore;
(x - 30)² + (y - 50)² = 10²
4) The coordinates of the center of the flower bed is (30, 45) which gives
(x - 30)² + (y - 45)² = 10²
Where the coordinates of the side of the flower pot is (20, 45), we have;
(20 - 30)² + (45 - 45)² = 10²
(-10)² = 10² = r²
Hence, point (20, 45) is on the circle
The other flower bed side has coordinates (40, 45) which gives
(40 - 30)² + (45 - 45)² = 10²
10² = r² = 10²
Point (40, 45) is also on the circle
Therefore, the swimming pool will touch the flower beds
5) At point (45, 25), we have;
(x - 45)² + (y - 25)² = 10²
The closest point is the patio with coordinates (40, 15) which gives;
(40 - 45)² + (15 - 25)² = 10² = 100
(-5)² + (-10)² = 125 > 100
Therefore, point (40, 15), is not on the circle.
What is the surface area of the regular pyramid? What is the surface area of a square pyramid with a height of 10.4 m and a base side length of 12.4 m? a. 141.4 cm c. 167.4 m b. 162.4 cm d. 188.4 cm
Answer:
A. 141.4 cm
Step-by-step explanation:
The piramide is 141.4cm
Of the 30 people riding the bus to work today, 3 rode a bike to work yesterday, 7 drove a car to work yesterday, and the rest rode the bus to work yesterday. If one of the 30 people riding the bus to work today is selected at random, what is the probability that the person selected will ride the bus to work tomorrow?
Answer:
2/3Step-by-step explanation:
This is a probability question and we have to calculate the sample size.
given the sample size S= 30
3 rode a bike
7 drove a car
20 rode bus
The probability of selecting a person that will take a bus is
[tex]Pr(bus)= 20/30= 2/3[/tex]
Tom and Harry live 24km from each other, which on the map is 5 cm Given that the distance on the map between Harry and the Sea view is 4cm Find the actual distance between Harry and the Sea view.
Answer:
19.5 km
Step-by-step explanation:
the actual distance between Harry and the Sea view:
if 24 km is 5 cm on map
24*4/5= 19.5 km
If cos0=-3/5 in quadrant II, what is sin0
Answer:
[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.
Step-by-step explanation:
By the Pythagorean Trigonometric Identity:
[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.
In this question:
[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].
Therefore:
[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].
Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.
According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this
It was already found (using the Pythagorean Trigonometric Identity) that:
[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].
Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:
[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].
Pls answer QUICKLY I need this
Answer:
pretty sure this is right
Your family used two full tanks ofgasoline on a road trip. Your car drives about 25 miles per gallon, andthe tank holds 12 gallons of gasoline.a. Find the approximate number of gallons of gasoline used on the trip.b. Find the approximate number of miles you drove on the trip.c. Calculate Assume gasoline costs $1.50 per gallon. How much didyou spend per mile on gasoline?d. Apply You have $20 to spend on gasoline for another trip. The trip is350 miles. You spend the same amount per mile on gasoline as onthe first trip. Do you have enough money for gasoline? Explain.
Answer:
a. 24
b.600
c.36
d. No
Step-by-step explanation:
a.You know the approximate number of gallons is about 24 gallons because each tank holds twelve and your family used 2 of them.
b. You know you drove about 600 miles. This is because you used 24 gallons And each gallon should get you 25 miles. multiply The 2 together to get 600 miles. Or you could set a thing like 1/25=24/x and solve for x.
c. It cost 36 dollars because each gallon is 1.5 and you used 24 gallons so mul the two together to get 36
d. First find the amount of gallons used by dividing 350 by 25 to get 14. Then multiply 14 by 1.5 to get 21. 21 is greater than 20 so you don’t have enough money.
A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number. From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are choise 13,14 13,14,15 15,16,17 16,17
Answer:
5
Step-by-step explanation:
Please answer it now in two minutes
Answer: 3.2 yd
Step-by-step explanation:
Notice that TWV is a right triangle.
Segment TU is not needed to answer this question.
∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6
[tex]\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}[/tex]
Your math teacher caught you text messaging in class, again, so the teacher is making you give a presentation to your math class next week. Your assignment is to analyze the scatter plot that shows people's ages and the number of text messages sent in a day. In 3-5 sentences, explain what you see in the scatter plot below.
Answer: If a scatterplot is included in the assignment
The dots plotted on the graph might closely follow the graph of exponential decline. There is a large number of texts per day by 19-20-21 year-olds, but the number seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.
Step-by-step explanation: Look at some graphs of exponential decay. Also consider harmonic and hyperbolic decay. The trend in the data is evident. The main challenge is to look at the data and create an equation that models it.
Assume that an opinion poll conducted in a 1998 congressional race found that on election eve, 54% of the voters supported Congressman Stevens and 44% supported challenger Jones. Also assume that the poll had a +/- 3% margin of error. What would the pollster be able to safely predict?
Answer:
Congressman Stevens will win the race
Step-by-step explanation:
Considering the margin of error, the possible outcomes for each candidate would be:
Congressman Stevens: from (54 - 3)% to (54+3)%
Challenger Jones: from (44 - 3)% to (44+3)%
Congressman Stevens: from 51% to 57%
Challenger Jones: from 41% to 47%
Therefore, even considering the margin of error, the pollster would be able to safely predict that Congressman Stevens will win the race.
juice is $1.79 for 8-4.23 ounce boxes. What is the unit price
Answer:
I believe the unit price would be 2.39 per unit
Step-by-step explanation:
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
Answer:
x = 5 is the solution
Step-by-step explanation:
See the attachment for table values.
f(x) = g(x) for x = 5
The solution to the equation ...
2.5x -10.5 = 64(0.5^x)
is x = 5.
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method.
Construct and interpret the 95% confidence interval. Select the correct choice below and fill in the answer boxes within your choice.
(Round to three decimal places as needed.)
A. The proportion of students who eat cauliflower on Jane's campus is between___ and __ 95% of the time.
B.There is a 95% chance that the proportion of students who eat cauliflower in Jane's sample is between __ and __.
C. There is a 95% chance that the proportion of students who eat cauliflower on Jane's campus is between __ and__.
D. One is 95% confident that the proportion of students who eat cauliflower on Jane's campus is between __ and __.
Answer:
A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].
Step-by-step explanation:
We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of students who eat cauliflower
n = sample of students
p = population proportion of students who eat cauliflower
Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.
So, 95% confidence interval for the population proportion, p 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{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;
[tex]n = n + Z^{2}__(\frac{_\alpha}{2})[/tex]
n = [tex]24 + 1.96^{2}[/tex] = 27.842
[tex]\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}[/tex] = [tex]\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}[/tex] = 0.141
95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] , [tex]0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }[/tex] ]
= [0.012, 0.270]
Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].
The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.
14) Marty weighs 64
pounds and Nathan weighs
4
76 pounds. How much more does Nathan weigh
2
than Marty?
Answer:
Nathan weighs 12 more pounds than Marty.
Step-by-step explanation:
If Marty weighs 64 pounds and Nathan weighs 76 pounds, we can subtract the weight of Marty from Nathan to get our answer.
[tex]76-64=12[/tex]
In case Nathan was actually 476 pounds, the answer would be 412.