Answer:
72 feet
Step-by-step explanation:
We have that the vertex at the origin in an upward concave is:
y = a * x ^ 2, we solve for a:
a = y / (x ^ 2)
Thus:
The points from the origin (0,0) are (-48, 8) and (48, 8), we replace:
a = 8 / (48 ^ 2) = 1/288
Therefore the equation would be:
y = (1/288) * x ^ 2
288 * y = x ^ 2
Now, be distance above the vertex to put the receiver, which would be the focus, we have:
4 * p = 288
we replace:
4 * p = 288
p = 288/4
p = 72
The receiver should be placed at [tex](x,y) = (0, 72)\,[ft][/tex].
We assume that the paraboloid is centered at the origin of a rectangular system of coordinates, then we have the following standard equation of the parabola is:
[tex]4\cdot p \cdot y = x^{2}[/tex] (1)
Where:
[tex]x[/tex] - Horizontal distance with respect to origin, in feet. [tex]y[/tex] - Vertical distance with respect to origin, in feet. [tex]p[/tex] - Distance between vertex and origin, in feet.The coordinates of the vertex are expressed by [tex](x,y) = (0, p)[/tex].
If we know that [tex]x = 48[/tex] and [tex]y = 8[/tex], then the coordinates of the vertex are, respectively:
[tex]4\cdot p\cdot 8 = 48^{2}[/tex]
[tex]p = 72\,ft[/tex]
The receiver should be placed at [tex](x,y) = (0, 72)\,[ft][/tex].
To learn more on parabolae, we kindly invite to check this verified question: https://brainly.com/question/8495268
30 POINTS IF ANSWERED IN THE NEXT FIVE MINUTES. Ms. Roth has made 200 headbands and is deciding what price to charge for them. She knows that she will sell more if the price is lower. To estimate the number she can expect to sell, she uses the function defined as ()=200−1.5, where is the price in dollars. Which choice describes a function, (), that models the total sales in dollars she can expect?
Answer:
198.5
Step-by-step explanation:
() = 200 - 1.5
() = 198.5
im not sure if this is what you are asking, but i hope it helps
Answer:
S=p(200-1.5)
College students were given three choices of pizza toppings and asked to choose one favorite Results are shown in the table toppings Sremam 15 24 28 28 15 1 11 23 28 cheese meat 23 15 veggie Estimate the probability that a randomly selected student who is a junior or senior prefers veggie. Round the answer to the nearest thousandth
A. 371
B. 220
C. 395
D. 662
Answer:
B. 0.220
Step-by-step explanation:
The table is presented properly below:
[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]
Number of junior students who prefers veggies =23
Number of senior students who prefers veggies =28
Total =23+28=51
Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie
=51/232
=0.220 (to the nearest thousandth)
The correct option is B.
if 1/u=1/f-1/v is the formula Express f as the subject of the formula
Answer:
[tex]f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }\\[/tex]
Step-by-step explanation:
[tex]1/u=1/f-1/v\\\frac{1}{f} = \frac{1}{u} +\frac{1}{v}\\Divide- both- sides- by; 1\\\frac{1}{f} \div \frac{1}{1} = ( \frac{1}{u} +\frac{1}{v}) \div \frac{1}{1}\\\\f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }[/tex]
Find the cost to asphalt a circular racetrack if asphalt costs $90 per 100 f2. (Use 3.14 for it. Round to the nearest dollar.) r = 80 ft R = 145 ft
Small circle in a large circle
r= 80 ft
R=145 ft
Y
R
(Use 3.1 4 for a.)
Answer:
$41,330
Step-by-step explanation:
To find the cost to asphalt a circular path, first, calculate the area of the circular path:
Area of circular path = area of big circle (A1) - Area of small circle (A2)
Area of circle = πr²
Radius of big circle (R) = 145 ft
Area of big circle (A1) = 3.14*145²
= 3.14*21,025
A1 = 66,018.5 ft²
Radius of small circle (r) = 80ft
Area of small circle (A2) = 3.14*80²
= 3.14*6,400
A2 = 20,096 ft²
=>Area of path = 66,018.5 - 20,096 = 45,922.5 ft²
If 100ft = $90
45,922.5 ft = x
Cross multiply and find x (cost to asphalt the circular path)
100*x = 45,922.5*90
100x = 4,133,025
Divide both sides by 100
x = 4,133,025/100
x = $41,330.25
To the nearest dollar, $41,330 is needed to asphalt the circular path
help one more for my friend lollllll well maybe 2 more
Answer:
8 : 1
Step-by-step explanation:
The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...
raspberry juice : lemon-lime soda = 8 : 1
Answer:
D
Step-by-step explanation:
raspberry : lemon lime soda::8:1
What is the length of Line segment B C?
Answer:
given,
AB= 17
AC= 8
angle BCA =90°
as it is a Right angled triangle ,
taking reference angle BAC
we get,h=AB=17
b=AC=8
p=BC=?
now by the Pythagoras theorem we get,
p=
[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]
so,p=
[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]
[tex] = \sqrt{225} [/tex]
=15 is the answer....
hope its wht u r searching for....
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f(x) = x4 − 8x3 + 7
Answer:
D
Step-by-step explanation:
Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (1 comma 0 ), (3 comma 2 ), and (1 comma 2 )about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
Answer: Volume = [tex]\frac{20\pi }{3}[/tex]
Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be
V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]
For this case, the region generated by the conditions proposed above is shown in the attachment.
Because it is revolting around the y-axis, the formula will be:
[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]
Since it is given points, first find the function for points (3,2) and (1,0):
m = [tex]\frac{2-0}{3-1}[/tex] = 1
[tex]y-y_{0} = m(x-x_{0})[/tex]
y - 0 = 1(x-1)
y = x - 1
As it is rotating around y:
x = y + 1
This is R(y).
r(y) = 1, the lower limit of the region.
The volume will be calculated as:
[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]
[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]
[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]
[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]
[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]
[tex]V=\frac{20\pi }{3}[/tex]
The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].
What is the y-intercept of the line given by the equation below? y = 4x – 6 A. (4, 0) B. (–6, 0) C. (0, –6) D. (0, 4)
Hey there! :)
Answer:
C. (0, -6).
Step-by-step explanation:
In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.
In this instance:
y = 4x - 6
The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).
-------------------------------------------------------------------------------------------
The y-intercept can also be solved for by substituting in 0 for x:
y = 4(0) - 6
y = 0 - 6
y = -6.
Answer:
C. (0, –6)
Step-by-step explanation:
y = 4x - 6
The equation is:
y = mx + b
where b is the y-intercept.
In this case, - 6 is the vertical intercept.
Do not confuse from (-6, 0) because that represents an x-intercept.
x=-4
Tell whether it’s graph is a horizontal or a vertical line
Answer:
Vertical Line
Step-by-step explanation:
A vertical line is x = [a number]
A horizontal line is y = [a number]
Answer:
vertical line
Step-by-step explanation:
A vertical line is of the form
x =
All the x values are the same and the y value changes
x = -4 is a vertical line
Q(x)= 2x+2 R(x)=x^2-1 find (r•q)(5) and (q•r)(5)
Answer:
Q(x) = 4
R(x) = 0
Step-by-step explanation:
Q(x) = 2x + 2 ----- (1)
R(x) = x² - 1 -------- (2)
i) For (R * Q)(5) and [(Q * R)], we have as follow:
[(x² - 1)(2x + 2)] (5)
= (2x³ + 2x² - 2x - 2)(5)
= x³ + x² - x - 1
When x = -1
x³ + x² - x - 1 = 0
∴ (x³ + x² - x - 1) ÷ (x + 1) = x² - 1
If x + 1 = 0
x = -1
and x² - 1 = 0
x = 1
From (1), when x= 1: Q(x) = 4
From (2), when x= 1 or -1: R(x) = 0
This expression gives the solutions to which quadratic equation?
Answer:
Hey there! Your answer would be: [tex]3x^2+4=x[/tex]
The quadratic formula is (-b±√(b²-4ac))/(2a), and helps us find roots to a quadratic equation.
All quadratic equations can be written in the [tex]ax^2+bx+c[/tex] form, and a, b, and c, are numbers we need for the quadratic equation.
Our given quadratic equation is 1±√(-1)²-4(3)(4)/2(3)
We can see that b is -1, as -b is positive 1.
That gives us [tex]ax^2+-1x+c[/tex], which can be simplified to [tex]ax^2-x+c[/tex].
We can see that a is 3, because 2a=6, so a has to be 3.
That gives us [tex]3x^2-x+c[/tex]
Finally, we see that 4 is equal to b, clearly shown in the numerator of this fraction.
Which gives us a final answer of [tex]3x^2-x+4[/tex], or [tex]3x^2+4=x[/tex]
3. Given the polynomial p(x) = x^4 - 2x^3 -7x^2 + 18x – 18 a. Without long division, find the remainder if P is divided by x+1. b. If one zero of P is 1-i, find the remaining zeros of P. c. Write P in factored form.
Answer:
(a) remainder is -40
(b) The remaining zeroes are (x+3) and (x-3)
Step-by-step explanation:
p(x) = x^4 - 2x^3 -7x^2 + 18x – 18
(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely
let x + 1 = 0 => x = -1
remainder
= P(-1)
= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18
= 1 +2 -7-18-18
= -40
remainder is -40
(b)
If one zero is 1-i, then the conjugate 1+i is another zero.
in other words,
(x-1+i) and (x-1-i) are both factors.
whose product = (x^2-2x+2)
Divide p(x) by (x^2-2x+2) gives
p(x) by (x^2-2x+2)
= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)
= x^2 -9
= (x+3) * (x-3)
The remaining zeroes are (x+3) and (x-3)
Use Newton's method to estimate the requested solution of the equation. Start with given value of X0 and then give x2 as the estimated solution.
x3 + 5x +2 = 0; x0 = -1; Find the one real solution.
Answer:
-0.3913Step-by-step explanation:
Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;
[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]
[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]
If [tex]x_0 = 1\\[/tex]
We will iterate using the formula;
[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]
Given f(x) = x³ + 5x +2
f(x0) = f(-1) = (-1)³ + 5(-1) +2
f(-1) = -1 -5 +2
f(-1) = -4
f'(x) = 3x²+5
f'(-1) = 3(-1)²+5
f'(-1) = 8
[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]
f(-0.5) = (-0.5)³ + 5(-0.5) +2
f(-0.5) = -0.125-2.5+2
f(-0.5) = -0.625
f'(-0.5) = 3(-0.5)²+5
f'(-0.5) = 3(0.25)+5
f'(-0.5) = 0.75+5
f'(-0.5) = 5.75
[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]
The estimated solution is -0.3913 (to 4dp)
Ms. Stone decided to purchase 2 reusable bottles instead. When she got to the counter, she realized she had $10.15, only ⅝ of the money she needed for the purchase. How much does 1 bottle cost?
Answer:
The price of one reusable bottle is $8.12
Step-by-steetp explanation:
Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.
So the cost of what she wants to purchase will be called x.
Mathematically
⅝ * x = 10.15
X = (10.15*8)/5
X = 81.2/5
X= 16.24
The price of the two bottles is $16.24
So the price if one bottle will be calculated as follows.
2 bottles=$ 16.24
One bottle= $16.24/2
One bottle= $8.12
The price of one reusable bottle is $8.12
From Andy's house to Billy's hometown you can travel by 3 roads. And to get from Billy's hometown to Willie's house you can travel by 5 roads. How many possible ways are there to travel from Andy's house to Willie's house?
Answer:
15
Step-by-step explanation:
You can go from Andy to Billy by 3 roads.
For each of those 3 roads, you can go from Billy to Willie by 5 roads.
3 * 5 = 15
Answer: 15
The solid below is made from 1 centimeter cubes. Find the total surface area of the solid. Be sure to include the correct unit in your answer.
Answer:
62 [tex]cm^{2}[/tex]
Step-by-step explanation:
A 1 centimetre cube implies that its length = width = height = 1 cm.
Thus, the area of a surface of the cube = length × length
= 1 × 1
= 1 [tex]cm^{2}[/tex]
Considering the views or parts of the given solid;
Surface area of its left side = Surface area of its right side = 1 × 10
= 10 [tex]cm^{2}[/tex]
Surface area of the front elevation = Surface area of its back = 1 × 9
= 9 [tex]cm^{2}[/tex]
Surface area of its plan = Surface area of its bottom = 1 × 12
= 12 [tex]cm^{2}[/tex]
Total surface area of the solid = 10 + 10 + 9 + 9 + 12 + 12
= 62 [tex]cm^{2}[/tex]
The total surface area of the solid is 62 [tex]cm^{2}[/tex].
Suppose 47G% of the doctors in a hospital are surgeons. If a sample of 460460 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%5%
Answer:
3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.47, n = 460, \mu = 0.47, s = \sqrt{\frac{0.47*0.53}{460}} = 0.0233[/tex]
What is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%
Sample proportion lower than 0.47 - 0.05 = 0.42 or higher than 0.47 + 0.05 = 0.52.
Since they are equidistant from the mean of 0.47 they are equal. So we find one of them, and multiply by two.
Lower than 0.42:
pvalue of Z when X = 0.42. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.47}{0.0233}[/tex]
[tex]Z = -2.15[/tex]
[tex]Z = -2.15[/tex] has a pvalue of 0.0158
2*0.0158 = 0.0316
3.16% probability that the sample proportion of surgeons will differ from the population proportion by greater than 5%
what happens to the value of the expression n+15n as n decreases? answer
Answer:
The value will decrease.
Step-by-step explanation:
Identify a pair of vertical angles in the figure
A. Angle ADE and Angle ADB
B. Angle EDC and angle DBA
C. angle ADE and angle EDC
D. Angle ADE and angle BDC
Answer:
A pair of vertical angles are ADE and BDC. Vertical angles are located across from each other.
Answer:
D. Angle ADE and angle BDC
Step-by-step explanation:
Vertically opposite angles are equal.
Angle ADE and angle BDC are a pair of vertical angles.
If f(x) = 4x – 8 and g(x) = 5x + 6, find (f - g)(x).
Answer:
(f - g)(x) = -x - 14
Step-by-step explanation:
Step 1: Plug in equations
4x - 8 - (5x + 6)
Step 2; Distribute negative
4x - 8 - 5x - 6
Step 3: Combine like terms
-x - 14
Answer:
-x-14
Step-by-step explanation:
Hope this helps
3. A tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below.
30°
300 feet
Tunne
How long is the tunnel?
Answer:
173.20 ft
Step-by-step explanation:
[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]
if 2 1/5 of a number is 5. what is the number
Answer:
2
Step-by-step explanation:
5÷2 1/5 = 2
Answer:
2 3/11
Step-by-step explanation:
To find the original number, we need to divide 5 by 2 1/5.
5/ 2 1/5
Convert 2 1/5 to an improper fraction:
11/5
5/ 11/5
When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.
5*5/11
25/11
2 3/11
An inverse variation includes the point (-8,-19). Which point would also belong in this inverse variation? A. (-19,-8) B. (-8,19) C. (-19,8) D. (8,-19)
Answer:
(A) (-19,-8)
Step-by-step explanation:
Given that the graph is an inverse variation.
The equation of variation is:
[tex]x=\dfrac{k}{y}[/tex]
Since point (-8, -19) is on the graph
[tex]-8=\dfrac{k}{-19}\\k=152[/tex]
Therefore, the equation connecting x and y is:
[tex]x=\dfrac{152}{y}[/tex]
[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]
Therefore, the point that is also on the graph is:
(A) (-19,-8)
please help me, i will give you brainliest
Answer:
4
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
JN* NK = LN * NM
3x = 2*6
3x = 12
Divide by 3
3x/3 =12/3
x =4
whats the answer ???? help dude
Answer:
C. 44 °
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
180 - 88 = 92
Angles in a triangle add up to 180 degrees.
y + y + 92 = 180
y + y = 88
2y = 88
y = 88/2
y = 44
Answer:
The answer is 46"
Step-by-step explanation:
A triangle is 180 degrees
so u already know one side
180"-88" is 92
then divide 92 by 2 which is 46
Answer: 46"
Find the 55th term of the following arithmetic sequence.
7, 10, 13, 16, ...
The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.
This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.
a(n) = a(1) + d( n- 1)
d = 3
This is the formula of an arithmetic sequence.
an = a(1) + d( n- 1)
Substitute in the values of
a(1) = 7 and
d = 3
a(n) = 7 + 3 ( n- 1)
Simplify each term.
a(n) = 7 + 3n- 3
Subtract 3 from 7.
a(n) = 3n + 4
The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.
Substitute in the value of n to find the nth term.
a(55) = 3 (55) + 4
Multiply 3 by 55 .
a(55) = 165 + 4
Add 165 and 4.
a(55) = 169
Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.
To learn more about Aritmetic sequence
https://brainly.com/question/6561461
#SPJ1
If m is 21 inches, j is 28 inches, and ∠K measures 90°, then find k using the Law of Cosines. Round your answer to the nearest tenth.
Answer:
35 inches
Step-by-step explanation:
The right angle and the given measures in the ratio 3:4 tell you this is a 3:4:5 right triangle. k = 7·5 = 35 inches.
__
Using the Law of Cosines, ...
k² = m² +j² -2mj·cos(K)
k² = 21² +28² -2·21·28·cos(90°) = 441 +784 -0 = 1225
k = √1225 = 35
The length of k is 35 inches.
Answer:
35 Inches
Step-by-step explanation:
Instead of using the Law of Cosines, you can use the Pythagorean Theorem; or A^2 + B^2 = C^2 because angle K is 90 degrees. The equation would look like:
21^2 + 28^2 = C^2
441 + 784 = C^2 Square Each Term
1,225 = C^2 Simplify
35 = C Find Square Root
k = 35 In This Situation, k is C
3. A photograph is 40 cm long and 20 cm wide. Find its area.
Answer:
Area = 40×20
=800Step-by-step explanation:
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 30 meters cubed A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? 10 meters cubed 20 meters cubed 30 meters cubed 40 meters cubed
Answer:
30 m^3
Step-by-step explanation:
Answer:
B. 20m3
Step-by-step explanation:
i dont know if its correct, hope it is tho