Answer:
Step-by-step explanation:
Focus: (6,4)
Directrix lies 6 units below the focus, so the parabola opens upwards and focal length p = 6/2 = 3.
The equation of the directrix is y = -2.
The vertex is halfway between focus and directrix, at (6,1).
Equation of the parabola:
y = (1/(4p))(x-6)²+1 = (1/12)(x-6)²+1
The equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
What are parabolas?Parabolas are used to represent a quadratic equation in the vertex form
The given parameters are:
Focus = (6,4)
Directrix (x) = 6 units below the focus,
Start by calculating the focal length (p)
[tex]p = \frac x2[/tex]
This gives
[tex]p = \frac 62[/tex]
[tex]p = 3[/tex]
Next, calculate the vertex as follows:
[tex](h,k) = (6,2/2)[/tex]
Simplify
[tex](h,k) = (6,1)[/tex]
The equation of the parabola is then calculated a:
[tex]y = \frac{1}{4p}(x - h)^2 + k[/tex]
So, we have:
[tex]y = \frac{1}{4*3}(x - 6)^2 + 1[/tex]
Simplify
[tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Hence, the equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Read more about parabola at:
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For what values of y: Is the value of the fraction 5−2y 12 always greater than the value of 1−6y?
Answer:
[tex](5 - 2y) \div 12 > 1 - 6y[/tex]
[tex]5 - 2y > 12 - 72y[/tex]
[tex] - 7 > - 70y[/tex]
[tex]7 < 70y[/tex]
[tex]y > 1 \div 10 = 0.1[/tex]
Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of µ with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)? Would it be valid to select all of your water specimens from a single rainfall? Explain.
Answer:
The number of rainfalls is [tex]n =96[/tex]
The answer to the second question is no it will not be valid this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid.
Step-by-step explanation:
from the question we are told that
The standard deviation is [tex]\sigma = 0.5[/tex]
The margin of error is [tex]E = 0.1[/tex]
Given that the confidence level is 95% then we can evaluate the level of significance as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Next we will obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2[/tex]
substituting values
[tex]n = [\frac{1.96 * 0.5 }{ 0.1} ]^2[/tex]
[tex]n =96[/tex]
The answer to the second question is no the validity is null this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid
The range of values for x?
Answer:
x = 32
but
I would say anything from 30 to 33
but truly i have no clue about the range
Step-by-step explanation:
3x-9=87 (because 180 -93 =87)
3x = 96
x = 32
Answer:
it is 32
Step-by-step explanation:
The College Board conducted research studies to estimate the mean SAT score in 2016 and its standard deviation. The estimated mean was 1020 points out of 1600 possible points, and the estimated standard deviation was 192 points. Assume SAT scores follow a normal distribution. Using the Empirical Rule, about 95% of the scores lie between which two values?
a. 768 to 1358
b. 636 to 1404
c. 620 to 1520
d. 828 to 1212
e. 724 to 1486
Answer:
its B. 636 to 1404
Step-by-step explanation:
Using the Empirical Rule, about 95% of the scores lie between values 636 to 1404. The correct option is c.
What is standard deviation?The standard deviation of a set of values is a measure of its variation or dispersion. The square root of the variance, which is the average of the squared differences from the mean, is used to calculate it.
According to the Empirical Rule, approximately 68% of the data for a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this case, the mean SAT score is 1020, with a standard deviation of 192. As a result, roughly 95% of the scores fall within two standard deviations of the mean, or between
(1020 - 2(192)) and (1020 + 2(192)).
Calculating, we get:
Lower bound: 1020 - 2(192) = 636
Upper bound: 1020 + 2(192) = 1404
Therefore, the answer is (b) 636 to 1404.
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7x to the power of 2 is a what is it
a) monomial
b) binomial
c) Trinomial
Find out vector product of 3i+8j-5k and -2i+9j+7k.
9514 1404 393
Answer:
101i -11j +43k
Step-by-step explanation:
A suitable calculator can find the cross product for you, or you can evaluate the determinant ...
[tex]\left|\begin{array}{ccc}i&j&k\\3&8&-5\\-2&9&7\end{array}\right|=i(8\cdot7-9(-5))-j(3\cdot7-(-2)(-5))+k(3\cdot9-(-2)(8))\\\\=\boxed{101i-11j+43k}[/tex]
Please show detailed work if possible-that will help me to better understand the questions
start with this expression:
f(x) = 2x2 − x − 10
1st- What are the x-intercepts of the graph of f(x)? Show work on how to get this
2nd- Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Show work on how to get this
Part C: What are the steps you would use to graph f(x)? show how you can use the answers obtained in Part A and Part B to draw a graph
Answer:
We are given the function:
[tex]f(x)=2x^2-x-10[/tex]
[tex]Here,\\a=2, b=-1,c=-10[/tex]
1. X-intercepts are the points at which the graph of a function intersects or cuts the x-axis. Since the x-intercept always lies on the x-axis, its ordinate or y-coordinate will always be 0. Since the function is quadratic, it will have at most 2 x-intercepts.
In order to find the x intercept, we basically solve for x at y=0:
[tex]f(x)=2x^2-x-10\\As\ y=0,\\0=2x^2-x-10\\2x^2-x-10=0\\ 2x^2-5x+4x-10=0\\x(2x-5)+2(2x-5)=0\\(x+2)(2x-5)=0\\Hence,\\Individually:\\x=-2,\ x=\frac{5}{2}[/tex]
Hence, the x-intercepts of the parabola of f(x) is (-2,0),(2.5,0)
2. The vertex of parabola is determined as maximum or minimum, solely on how it opens. This depends on the nature of the co-efficient of the x^2 term or 'a'. If a is positive the parabola opens upwards (minimum point) and downwards (maximum point) if negative. Hence, here as a=2, the parabola opens upwards and its vertex is minimum.
[tex]Vertex=(\frac{-b}{2a},\frac{-D}{4a})\\Hence,\\D=b^2-4ac\\Substituting\ a=2,b=-1,c=-10:\\D=(-1)^2-4*2*-10=1+80=81\\Hence,\\Vertex\ of\ f(x)=(\frac{-(-1)}{2*2},\frac{-81}{4*2})=(\frac{1}{4},\frac{-81}{8})[/tex]
3. [Please refer to the attachment]
From the graph, we observe that the parabola cuts the x-axis at (-2,0),(2.5,0). Also, its clear that the axis of symmetry passes through [tex](\frac{1}{4},\frac{-81}{8})[/tex], which is its minimum point.
Answer:
A chord of a circle is 9cm long if it's distance from the centre of the circle is 5cm calculate the radius of the circle
anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
The limit of a function is the value it approaches.
In #37, as x approaches infinity (far to the right), the curve f(x) approaches 1. As x approaches negative infinity (far to the left), the curve f(x) approaches -1.
lim(x→∞) f(x) = 1
lim(x→-∞) f(x) = -1
In #38, as x approaches infinity (far to the right), the curve f(x) approaches 2. As x approaches negative infinity (far to the left), the curve f(x) approaches -3.
lim(x→∞) f(x) = 2
lim(x→-∞) f(x) = -3
michaela has h hair ties. michaela's sister has triple the number of hair ties that michaela has. choose the expression that shows how many hair bows michaela's sister has
Answer:
[tex]S = 3 h[/tex]
Step-by-step explanation:
Let M represent Michaela hair tier and S represents Michaela sister's
Given
M = h
S = Triple of M
Required
Determine an expression for S
From the given parameters, we have that;
S = Triple of M
Mathematically, this implies;
[tex]S = 3 * M[/tex]
Substitute h for M
[tex]S = 3 * h[/tex]
[tex]S = 3 h[/tex]
Hence, the expression for Michaela sister' is [tex]S = 3 h[/tex]
i will give brainliest and 5 stars if you help ASAP
Shyla's research shows that 8 empty cans make 1/4 pound of aluminum. Shyla wants to know how many cans does it take to make 5 pounds of aluminum. How many cans are there per pound of aluminum?
Answer:
They will need 160 cans to make 5 lbs
32 cans for 1 lbs
Step-by-step explanation:
We can use ratios to solve
8 cans x cans
--------------- = ---------------
1/4 lbs 5 lbs
Using cross products
8 * 5 = 1/4x
40 = 1/4 x
Multiply each side by 4
4 * 40 = 1/4 x * 4
160 =x
They will need 160 cans to make 5 lbs
8 cans x cans
--------------- = ---------------
1/4 lbs 1 lbs
Using cross products
8 * 1 = 1/4x
Multiply each side by 4
8*4 = x
32 cans for 1 lbs
Answer:
32 cans per pound of aluminum
160 cans per 5 pounds of aluminum
Step-by-step explanation:
will make it short and simple.
8 empty cans can make 1/4 pound of aluminum.
therefore... 8 x 4 = 32 cans per pound of aluminum.
Number of cans to make 5 pounds of aluminum = 32 x 5
= 160 cans per 5 pounds of aluminum
Which of the following statements about shapes of histograms is true?
a. A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size.
b. A negatively skewed histogram is one with a long tail extending to the left.
c. A positively skewed histogram is one with a long tail extending to the right.
d. All of these choices are true
Answer:
d. all of these choices are true
Step-by-step explanation:
Histograms have 3 outstanding shapes:
1. they are syymetric:
this is to say that from the middle of the histogram if you cut it into two or half, each side is an exact close representation of the other side.
2. they are positively skewed to the right:
That is it has a long tail that goes off towards the right.
3. they are negativly skewed to the left:
They have a long tail that goes off to the left.
therefore from the question option d is the best answer since a, b, c describes the shape of a histogram.
Find the minimum turning point of y = x^2 + x - 12
Answer:
(x+4)(x-3)
Step-by-step explanation:
x^2+x-12
=x^2+(4-3)x-12
=x^2+4x-3x-12
=x (x+4)-3 (x+4)
=(x+4)(x-3)
Answer:x=6
Step-by-step explanation:
What word phrase can you use to represent the algebraic expression 7x?
A. 7 more than a number x
B. the product of 7 and a number x
C. the quotient of 7 and a number x
D. 7 less than a number x
Answer:
B. the product of 7 and a number x
Step-by-step explanation:
7x is 7 multiplied by x.
Answer:
b is the product
Step-by-step explanation:
A teacher writes the algebraic expression 24C + 5m + 19.99 to represent the cost
of supplies she purchased for her classroom. She bought 24 packages of colored
pencils, 5 packages of markers, and a beanbag chair. Identify any variables,
coefficients, and terms in the expression. Tell what each represents.
Answer:
variables: m ,c
coefficients, 24, 5
terms 24c,5m,19.99
24C represents the cost of the colored pencils
24 packages at a cost of c each
5m represents the cost of the markers
5 packages of markers at a cost of m each
19.99 for the bean bag chair
Step-by-step explanation:
24C + 5m + 19.99
variables: m ,c
coefficients, 24, 5
terms 24c,5m,19.99
24C represents the cost of the colored pencils
24 packages at a cost of c each
5m represents the cost of the markers
5 packages of markers at a cost of m each
19.99 for the bean bag chair
The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.
Answer:
64 : 729
Step-by-step explanation:
Ratio of surface area
= (ratio of linear dimensions) ^2
= 1.6^2 : 5.4^2
= 256 : 2916
= 64 : 729
4 + (-13)
Yajmmsmssjsjsjjsnssnsnnsnsxxdddddddd
Answer:
-9
Step-by-step explanation:
4 + (-13)
=> 4 - 13
=> -9
Assume a significance level of alpha = 0.05 and use the given information to complete parts (a) and (b) below. Original claim: The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm. The hypothesis test results in aP-value of 0.2761.a. State a conclusion about the null hypothesis.(Reject H0 or fail to reject H0.) Choose the correct answer below.A. Fail to reject H0 because the P-value is less than or equal to alphaα.B. Reject H0 because the P-value is less than or equal to alphaα.C.Fail to reject H0 because the P-value is greater than alphaα.D. Reject H0 because the P-value is greater than alphaα.b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?A. The standard deviation of pulse rates of the group of adult males is more than 11 bpm.B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.C. The standard deviation of pulse rates of the group of adult males is less than or equal to 11 bpm.D. There is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.
Answer:
a
The correct option is B
b
The correct option is D
Step-by-step explanation:
From the question we are told that
The level of significance is [tex]\alpha = 0.05[/tex]
The p-value is [tex]p = 0.2761[/tex]
Considering question b
Given that the [tex]p< \alpha[/tex] then the null hypothesis is rejected
Considering question b
Given that the original claim is The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm
Then the null hypothesis is [tex]H_o : \sigma = 11[/tex]
The reason why the null hypothesis is write like this above is because a null hypothesis expression can not contain only a > or a < but only allows = [tex]\le , \ and \ \ge[/tex]
and the alternative hypothesis is [tex]H_a : \sigma > 11[/tex]
Now given that the null hypothesis is rejected, it mean that there is sufficient evidence to support original claim
A 12 ounce bag of rice costs $4.08. A 16-ounce bag of the same rice costs $5.76. Which bag is the better by
and by how much
Answer:
16 once is the better one.
Answer: 12-ounce bag is better by $0.02 per ounce
Concept:
When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].
In finding [price per object], simply do [Total price / number of objects].
Solve:
A 12-ounce bag of rice costs $4.08
Total price / number of objects = 4.08 / 12 = $0.34 per ounce
A 16-ounce bag of rice costs $5.76
Total price / number of objects = 5.76 / 16 = $0.36 per ounce
$0.36 - $0.34 = $0.02
$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.
Hope this helps!! :)
Please let me know if you have any questions
mean is 1250
variance is 120
finding the probability between 970 and 1320
[tex] find p{970 < x < 1320}[/tex]
Although you said the variance is 120, I suspect you meant to say standard deviation. If that's the case, then
P(970 < x < 1320)
= P((970 - 1250)/120 < (x - 1250)/120 < (1320 - 1250)/120)
≈ P(-2.3333 < z < 0.5833)
= P(z < 0.5833) - P(z < -2.3333)
≈ 0.72012 - 0.009815
≈ 0.7104
If you really did mean variance, then
P(970 < x < 1320)
= P((970 - 1250)/√120 < (x - 1250)/√120 < (1320 - 1250)/√120)
≈ P(-25.5604 < z < 6.3901)
= P(z < 6.3901) - P(z < -25.5604)
≈ 1 - 0
≈ 1
Any help is appreciated.
No links pls
Answer:
its b plz give brainlist
Step-by-step explanation:
PLEASE ANSWER ASAP!!
Question is in the picture as well as the answer choices
any unrelated answers will be reported
Answer:
c
Step-by-step explanation
Find the length of a square with a perimeter of 48cmeter
Answer:
12
Step-by-step explanation:
Perimeter of a square:
4(L)
L = Length
=> 4(L) = 48
=> 4L = 48
=> 4L/4 = 48/4
=> L = 12
The length of the square is 12 cm.
Answer:
12
Step-by-step explanation:
Since the lengths of the sides of a square are equal, divide the perimeter by 4
The triangle shown on the graph above is rotated 90 degrees clockwise about the original to form triangle P’Q’R which of the following are the (x,y) coordinates of the point P’
Hey there! I'm happy to help!
When rotating a point 90 degrees clockwise about the origin, our original point (x,y) becomes (-y,x), because it is now at a negative y-value.
We see that our point P is at (1,2). We can use this rotation formula to find the coordinates of P' (the new spot where P is)/
(x,y)⇒(-y,x)
(1,2)⇒(-2,1)
Therefore, the coordinates of the point P' are (-2,1).
Have a wonderful day! :D
Find the particular solution of the differential equation that satisfies the initial condition(s). (Remember to use absolute values where appropriate.) f ''(x) = 4 x2 , f '(1) = 2, f(1) = 5
Looks like either [tex]f''(x)=4x^2[/tex] or [tex]f''(x)=\frac4{x^2}[/tex]...
In the first case, integrate both sides twice to get
[tex]f''(x)=4x^2\implies f'(x)=\dfrac43x^3+C_1\implies f(x)=\dfrac13x^4+C_1x+C_2[/tex]
Then the initial conditions give
[tex]f'(1)=2\implies 2=\dfrac43\cdot1^3+C_1\implies C_1=\dfrac23[/tex]
[tex]f(1)=5\implies 5=\dfrac13\cdot1^4+C_1\cdot1+C_2\implies C_2=4[/tex]
so that the particular solution is
[tex]f(x)=\dfrac{x^4}3+\dfrac{2x}3+4[/tex]
If instead [tex]f''(x)=\frac4{x^2}[/tex], we have
[tex]f''(x)=\dfrac4{x^2}\implies f'(x)=-\dfrac4x+C_1\implies f(x)=-4\ln|x|+C_1x+C_2[/tex]
[tex]f'(1)=2\implies 2=-\dfrac41+C_1\implies C_1=6[/tex]
[tex]f(1)=5\implies 5=-4\ln|1|+C_1\cdot1+C_2\implies C_2=-1[/tex]
[tex]\implies f(x)=-4\ln|x|+6x-1[/tex]
F(x, y, z) = (x + yz)i + (y + xz)j + (z + xy)k, Find the divergence of the vector field.
The divergence of F is
div(F ) = ∂(x + yz)/∂x + ∂(y + xz)/∂y + ∂(z + xy)/∂z
div(F ) = 1 + 1 + 1
div(F ) = 3
The divergence of the vector field is equal to 3
Data;
(x+yz)i(y + xz)j(z+xy)kDivergence of Vector FieldTo find the divergence of the vector field, we have to differentiate the i, j and k component of the vector.
[tex]div F = \frac{\delta}{\delta x} (x+yz) + \frac{\delta}{\delta y} (y + xz) + \frac{\delta}{\delta z} (z + xy)\\div F = (1+0)+(1+0)+(1+0)\\div F = 1 + 1 + 1 \\div F = 3[/tex]
The divergence of the vector field is equal to 3
Learn more on divrgence of vector field here;
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Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Answer:
9 m
Step-by-step explanation:
Given that
Width of rectangular flower garden, w = 4 m
Perimeter of rectangular flower garden, p = 26 m
To find:
Length of Lisa's flower garden = ?
Solution:
First of all, let us understand perimeter, length and width of a rectangle.
Let ABCD be a rectangle. Please refer to the attached image.
Opposite sides of a rectangle are equal to each other.
AB = CD = Length
Let the length be [tex]l[/tex] m.
BC = DA = Width = 4 m
Perimeter of a closed image is equal to the sum of all the sides of the image.
So, perimeter of ABCD:
[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]
[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 12 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer:
129 [tex]cm^2/s[/tex]
Step-by-step explanation:
Increasing rate of length, [tex]\frac{dl}{dt}[/tex]= 9 cm/s
Increasing rate of width, [tex]\frac{dw}{dt}[/tex] = 7 cm/s
Length, l = 12 cm
Width, w = 5 cm
To find:
Rate of increase of area of rectangle at above given points.
Solution:
Formula for area of a rectangle is given as:
[tex]Area = Length \times Width[/tex]
OR
[tex]A = l \times w[/tex]
Differentiating w.r.to t:
[tex]\dfrac{d}{dt}A = \dfrac{d}{dt}(l \times w)\\\Rightarrow \dfrac{d}{dt}A = w \times \dfrac{d}{dt}l +l \times \dfrac{d}{dt}w[/tex]
Putting the values:
[tex]\Rightarrow \dfrac{dA}{dt} = 5 \times 9 + 12 \times 7\\\Rightarrow \dfrac{dA}{dt} = 45 + 84\\\Rightarrow \bold{\dfrac{dA}{dt} = 129\ cm^2/sec}[/tex]
Find three different numbers such that the
HCF of each pair of these numbers is greater
than 1 but the HCF of all three numbers is 1.
[Hint: For instance, the numbers 6, 10 and
15 satisfy the conditions.]
6, 10, 15
15,21,35
35, 55, 77
77, 91, 143
143, 187, 221
I can go on forever
There are different possibilities
fridays high temp was -1. the low temp was -5. what was the difference between the high and low temps
Answer:
4
Step-by-step explanation:
count up from -5 to -1
so -5,-4,-3,-2,-1 and there are four numbers excluding-5