Answer: The equation that has a graph which is a parabola with a vertex at (5, 3) would be y = (x – 5)^2 + 3. The general form of a parabola which the vertex is not in the origin is expressed as y = a(x - h)^2 + k where (h,k) represents the vertex.
The vertices of a parabola is the maximum or the minimum point on the parabola.
The equation (a) [tex]\mathbf{y = (x - 5)^2 + 3}[/tex] has a vertex at (5,3)
The equation of a parabola is represented as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
Where:
[tex]\mathbf{Vertex = (h,k)}[/tex]
The vertex is given as:
[tex]\mathbf{Vertex = (5,3)}[/tex]
This means that:
[tex]\mathbf{(h,k) = (5,3)}[/tex]
Substitute these values in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = a(x - 5)^2 + 3}[/tex]
By comparing the options,
[tex]\mathbf{y = (x - 5)^2 + 3}[/tex] has the same vertex as [tex]\mathbf{y = a(x - 5)^2 + 3}[/tex]
Hence, [tex]\mathbf{y = (x - 5)^2 + 3}[/tex] has a vertex at (5,3)
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The number of rows in an auditorium can be represented by the function f(x) = 80x. The number of seats in each row can be represented by the function g(x) = x + 7. Which function represents the total number of seats, h(x) = f(x)g(x)?
Answer:
[tex]h(x) = 80x^2 + 560x[/tex]
Step-by-step explanation:
To find the function h(x), that represents the total number of seats, we just need to multiply the functions f(x) (number of rows) and g(x) (number of seats per row):
[tex]h(x) = f(x) * g(x)[/tex]
[tex]h(x) = 80x * (x+7)[/tex]
[tex]h(x) = 80x*x + 80x*7[/tex]
[tex]h(x) = 80x^2 + 560x[/tex]
So the function that represents the total number of seats is:
[tex]h(x) = 80x^2 + 560x[/tex]
Answer: A
Step-by-step explanation:
A department store finds that in a random sample of 200 customers, 60% of the sampled customers had browsed its website prior to visiting the store. Based on this data, a 90% confidence interval for the population proportion of customers that browse the store’s website prior to visiting the store will be between
Answer:
between 108-110?
Step-by-step explanation:
60% or 200 = 120 people
90% of 120 = 108
question doesnt look complete so this is the best I could come up with...♀️
If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is?
A. 33
B. 40
C. 49
D. 61
E. 84
Answer:
D
Step-by-step explanation:
3x, 4y, and 7z must be equal to the LCM of 3, 4, and 7 in order to be the smallest value. The LCM is 84 which means x = 28, y = 21 and z = 12. 28 + 21 + 12 = 61.
Answer:
61
Step-by-step explanation:
3x=4y=7z
x =4/3 y
x = 7/3 z
Since they have to be integers
y and z must be multiples of 3
y = 7/4 z
Since they have to be integers
z must be multiple of 4
Z must be a multiple of 12
Let z = 12
Then
y = 7/4 *12
y = 21
x = 7/3 *12
x = 28
x+y+z
28+ 21+12
61
What is the area of the circle shown below? Please
answer quickly! 20 points
Answer:
A =1017.9 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi * (18)^2
Using the pi button
A =1017.87602 cm^2
Rounding to 1 decimal place
A =1017.9 cm^2
Mr. Rosenberger asked his students to use the distributive property to rewrite the expression 18 (24) by using friendlier numbers. The table below shows the expressions that four students created. Expressions Created by Students Student Expression Aaron 10 + 8 times 4 + 20 Brian 10 + 8 (4 + 20) Cece 18 (4 + 6) Diana 18 (4 + 20)
Answer:
diana
Step-by-step explanation:
Answer:
I think it’s Diana I’m sorry if I’m wrong :P
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
Answer:
Length = 47 in
Radius = 47/π in
Step-by-step explanation:
Let 'h' be the length of the package, and 'r' be the radius of the cross section.
The length and girth combined are:
[tex]L+G=141=h+2\pi r\\h=141-2\pi r[/tex]
The volume of the cylindrical package is:
[tex]V=A_b*h\\V=\pi r^2*h[/tex]
Rewriting the volume as a function of 'r':
[tex]V=\pi r^2*h\\V=\pi r^2*(141-2\pi r)\\V=141\pi r^2-2\pi^2 r^3[/tex]
The value of 'r' for which the derivate of the volume function is zero yields the maximum volume:
[tex]V=141\pi r^2-2\pi^2 r^3\\\frac{dV}{dr}=282\pi r-6\pi^2r^2=0\\ 6\pi r=282\\r=\frac{47}{\pi} \ in[/tex]
The length is:
[tex]h=141-2\pi r=141-2\pi*\frac{47}{\pi}\\h=47\ in[/tex]
The dimensions that yield the maximum volume are:
Length = 47 in
Radius = 47/π in
Management at a home improvement store randomly selected 95 customers and observed their shopping habits.They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store.
a. number of items-discrete: total time-discrete
b. number of items-continuous; total time-discrete
c. number of items-continuous; total time-continuous
d. number of items-discrete; total time-continuous
Answer:
d. number of items-discrete; total time-continuous
Step-by-step explanation:
Continuous:
Real numbers, can be integer, decimal, etc.
Discrete:
Only integer(countable values). So can be 0,1,2...
In this question:
You can purchase 0, 1, 2,...,10,...,100,... items, so the number of items is discrete.
You can spend for example, 0.5 hours in the store, or 2.5 minutes, that is, can be decimal numbers. So the total time is continuous
The correct answer is:
d. number of items-discrete; total time-continuous
Your drawer contains 10 red socks and 7 blue socks. You pick 3 socks without replacement. What's the probability that at least two socks will be different colors?
Answer:
105/136 ≈ 0.772
Step-by-step explanation:
There are 3 socks and 2 colors, so they are either all the same color or 2 will be different colors.
P(different colors)
= 1 − P(same color)
= 1 − ₁₀C₃/₁₇C₃ − ₇C₃/₁₇C₃
= 1 − 120/680 − 35/680
= 1 − 155/680
= 1 − 31/136
= 105/136
≈ 0.772
A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some type of after school activity. Find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.
Answer:
The interval is [tex]0.7187 < p < 2.421[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 100[/tex]
The population proportion is [tex]p = 0.81[/tex]
The confidence level is C = 98%
The level of significance is mathematically evaluated as
[tex]\alpha = 100 -98[/tex]
[tex]\alpha = 2%[/tex]%
[tex]\alpha = 0.02[/tex]
Here this level of significance represented the left and the right tail
The degree of freedom is evaluated as
[tex]df = n-1[/tex]
substituting value
[tex]df = 100 - 1[/tex]
[tex]df = 99[/tex]
Since we require the critical value of one tail in order to evaluate the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2
The critical value of [tex]\frac{\alpha}{2}[/tex] and the evaluated degree of freedom is
[tex]t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33[/tex]
this is obtained from the critical value table
The standard error is mathematically evaluated as
[tex]SE = \sqrt{\frac{p(1-p )}{n} }[/tex]
substituting value
[tex]SE = \sqrt{\frac{0.81(1-0.81 )}{100} }[/tex]
[tex]SE = 0.0392[/tex]
The 98% confidence interval is evaluated as
[tex]p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }[/tex]
substituting value
[tex]0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392[/tex]
[tex]0.7187 < p < 2.421[/tex]
What is the next number in the sequence.
1,121,12321, 1234321
The next number in the sequence is _____
Answer:
123454321
Step-by-step explanation:
it's a palendrome, made out of a number of numbers in the sqquence.
if y varies inversely as the square of x, and when y = 4/63 find y when y varies inversely as the square of x = 3, and when find y when x=5
Answer:
Step-by-step explanation:
In order to solve this, we'll set up a proportion.
Since y is inversely related to the square of x, therefore:
y=4/63 ----->9 (square of x)
y=? ---------->25 (square of x)
According to the inverse relation:
y=4/63------->25
y=?------------->9 and y=4/175
Your friend decides to flip a coin repeatedly to analyze whether the probability of a head on each flip is one half . He flips the coin 15 times and observes a head 6 times. He concludes that the probability of a head for this coin is 6/15 = 0.40 and the coin is not balanced. What is a correct interpretation?
A. Probability doesn't prove anything about the coin because probability is subjective.
B. A coin is balanced as long as the probability of each outcome is closer to 0.5 than it is to 1 or 0.
C. Environmental conditions such as temperature and humidity can cause the results of flipping a balanced coin to be skewed and thus appear unbalanced.
D. In the short run, the proportion of a given outcome can fluctuate a lot. A long run of observations is needed to accurately calculate the probability of flipping heads.
B. A coin is balanced as long as the probability of each outcome is closer to 0.5 than it is to 1 or 0.
Neither of the others seem like a suitable answer
Answer:
B
Step-by-step explanation:
For a study regarding mean cadence, two-way ANOVA was used. The two factors were walking device (none, standard walker, rolling walker) and dual task (being required to respond vocally to a signal or no dual task required). Results of two-way ANOVA showed that there was no evidence of interaction between the factors. However, according to the article, "the ANOVA conducted on the cadence data revealed a main effect of walking device." When the hypothesis regarding no difference in mean cadence according to which, if any, walking device was used, the sample F was 30.94, with d.f.N = 2 and d.f.D = 18. Further, the P-value for the result was reported to be less than 0.05.
Required:
What is the conclusion regarding any difference in mean cadence according to the factor "walking device used"?
Answer:
Step-by-step explanation:
With regards to the factor 'walking device used', the ANOVA conducted on the cadence data revealed a main effect of walking device, and also with the results of the experiment giving rise to a p - value less than 0.05, we can reject the null hypothesis which says, there is no effect of the walking device factor.
We can thus conclude that there is not enough statistics evidence to prove that there is no interaction between the two factors or that there is no effect of the walking device given the cadence data.
If segment ac and segment bc are tangent to circle o,find the value of x
Answer:
160°
Step-by-step explanation:
1/2 (Major arc AB - Minor arc AB) = 20°
Major arc AB = 200°
Minor arc AB = 160°
central angle = minor arc AB = 160°
The value of variable x is,
⇒ x = 150°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Line segment ac and segment bc are tangent to circle O.
Now, We get;
∠A + ∠B + ∠C + ∠O = 360°
90° + 90° + 30° + x = 360°
x = 360° - 210°
x = 150°
Hence, The value of variable x is,
⇒ x = 150°
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Find the first five terms in sequences with the following nth terms. 6n+3
Answer:
33
Step-by-step explanation:
An = 6n+3
so the first five terms in sequences is A5= 6*5 +3 = 33
2a -a + 1 =
x + y + x + 2 =
2(x + 4) + 2x =
3x + 2(x - 2) =
Answer:
Step-by-step explanation:
Please, share the instructions that come with each problem. Thanks.
2a -a + 1 = can be simplified to a + 1.
x + y + x + 2 = cannot be simplified.
2(x + 4) + 2x =
3x + 2(x - 2) = can be expanded and then simplified:
3x + 2x - 4 = 5x - 4
Assume that military aircraft use ejection seats designed for men weighing between 141.8 lb and 218 lb. If women's weights are normally distributed with a mean of 173.6 lb and a standard deviation of 49.8 lb, what percentage of women have weights that are within those limits? Are many women excluded with those specifications?
Answer:
[tex]P(141.8<X<218)=P(\frac{141.8-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{218-\mu}{\sigma})=P(\frac{141.8-173.6}{49.8}<Z<\frac{218-173.6}{49.8})=P(-0.639<z<0.892)[/tex]
And we can find this probability with this difference and using the normal standard table:
[tex]P(-0.639<z<0.892)=P(z<0.892)-P(z<-0.639)=0.814-0.261= 0.553[/tex]
Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(173.6,49.8)[/tex]
Where [tex]\mu=173.6[/tex] and [tex]\sigma=49.8[/tex]
We are interested on this probability
[tex]P(141.8<X<2188)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(141.8<X<218)=P(\frac{141.8-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{218-\mu}{\sigma})=P(\frac{141.8-173.6}{49.8}<Z<\frac{218-173.6}{49.8})=P(-0.639<z<0.892)[/tex]
And we can find this probability with this difference and using the normal standard table:
[tex]P(-0.639<z<0.892)=P(z<0.892)-P(z<-0.639)=0.814-0.261= 0.553[/tex]
Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women
At the candle factory, 10 out of 100 produced candles in the sample are defective. Find a point estimate of the probability that a fault free candle is produced.
Answer:
p=0.9
Step-by-step explanation:
Total Sample of Candles =100
Number of defective Candles = 10
Therefore, the number of fault-free candles =100-10=90
A point estimate of the probability that a fault-free candle is produced is:
[tex]p=\dfrac{90}{100}\\\\ p=0.9[/tex]
Answer:
thank u
Step-by-step explanation:
Need help with this question thanks!
How do i work out what 6/7 of 77 is?
Answer:
First of all "of " means multiplication
To calculate 6/7 of 77 multiply 6/7 by 77
That is
6/7 × 77
= 6 × 11 = 66
Hope this helps you
Answer:
66
Step-by-step explanation:
6/7 × 77
Multiply.
462/7
Divide.
= 66
Identify the axis of symmetry of the given quadratic
y= -3x^2 - 12
Answer:
[tex]\frac{d}{dy}(-3x^{2} -12) = -6x[/tex]
0 = -6x
0 = x
[tex]-3(0)^{2} -12 = -12[/tex]
(0,-12)
Step-by-step explanation:
Last year, a soft drink manufacturer had 22% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 22% of the population will like the new soft drink. 1. Using α = .05, test to determine if more than 22% of the population will like the new soft drink. 2. What should be the critical value(s)? 3. If there is more than one, please enter the positive one. (please keep at least 4 digits after the decimal point).
Answer:
Critical value zc = 1.6449.
As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that more than 22% of the population will like the new soft drink.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22\\[/tex]
The significance level is 0.05.
The sample has a size n=400.
The sample proportion is p=0.25.
[tex]p=X/n=100/400=0.25[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{400}}\\\\\\ \sigma_p=\sqrt{0.000429}=0.0207[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.25-0.22-0.5/400}{0.0207}=\dfrac{0.0288}{0.0207}=1.3881[/tex]
As this is a right-tailed test, there is only one critical value and it is, for a significance level of 0.05, zc=1.6449.
As the test statistic z=1.3881 is smaller than the critical value zc=1.6449, it falls in the acceptance region and the null hypothesis is failed to be rejected.
Given that the sum of the first n terms of the provided series is 6560 determine the value of n (2,6,18,54....)
Answer:
n = 8
Step-by-step explanation:
The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.
It has a common ratio of 3 => [tex] \frac{6}{2} = \frac{18}{6} = \frac{54}{18} = 3 [/tex]
Thus, the sum of the first n terms of a geometric sequence is given as [tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
Where,
[tex] a_1 [/tex] = first term of the series = 2
r = common ratio = 3
[tex] S_n [/tex] = sum of the first n terms = 6,560
Plug in the above values into the formula
[tex]6,560 = \frac{2(1 - 3^n)}{1 - 3}[/tex]
[tex] 6,560 = \frac{2(1 - 3^n)}{-2} [/tex]
[tex] 6,560 = \frac{1 - 3^n}{-1} [/tex]
Multiply both sides by -1
[tex] -6,560 = 1 - 3^n [/tex]
Subtract 1 from both sides
[tex] -6,560 - 1 = - 3^n [/tex]
[tex] -6,561 = - 3^n [/tex]
[tex] 6,561 = 3^n [/tex]
Evaluate
[tex] 3^8 = 3^n [/tex]
3 cancels 3
[tex] 8 = n [/tex]
The value of n = 8
Please answer this correctly without making mistakes
ANSWER :
Percentage = 50%
(if it odd and even then its 100%)
Answer:
100%
Step-by-step explanation:
There is a 100% chance rolling an odd or even since all the faces of this die are odd or even.
Graph the system of linear equations.
-{ y = 4x+ 5 and y = 2x + 2.
Answer:
work shown and pictured
You are walking directly away from your house. You are 555 miles away from your house when you start walking, so you can determine your distance from your house by adding 555 to the number of miles you have walked. In the equation below, xxx represents the number of miles you have walked, and yyy represents your distance from home in miles. The relationship between these two variables can be expressed by the following equation: y=x+5y=x+5y, equals, x, plus, 5 Identify the dependent and independent variables. Dependent variable Independent variable Your distance from home Number of miles you walk
Answer:
Dependent variable is Your distance from home(y)Independent variable is Number of miles you walk(x)Step-by-step explanation:
x represents the number of miles you have walked
y represents your distance from home in miles.
The relationship between these two variables can be expressed by the following equation: y=x+5
The dependent variable is that whose value changes whenever the value of the independent variable is changed.
From the equation above:
When x=1, y=1+5=6 milesWhen x=3, y=3+5=8 milesWe can clearly see that y changes for different values of x.
Therefore:
Dependent variable is Your distance from home(y)Independent variable is Number of miles you walk(x)Answer:
1dependant
2independant
Step-by-step explanation:
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The
longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox.
In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function
to model the hours of daylight hours on certain days of the year in New York City.
Identify the independent and dependent variables find amplitude and the period of the function create a trigonometric function that describes the hours of sunlight for each day of the year and then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
independent: day number; dependent: hours of daylight
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
1.79 fewer hours on Feb 10
Step-by-step explanation:
a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).
__
b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,
March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...
d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
__
c) d(41) = 10.34, so February 10 will have ...
12.13 -10.34 = 1.79
hours less daylight.
Chase scored 14 points on Monday, and he doubled his score each day thereafter. How many points did he score on Thursday?
Answer:
112
Step-by-step explanation:
Original Score equals 14 right?
If chase doubles his original Score daily it will be
14*2 (Tuesday)=28
28×2 (Wednesday)=56
56×2 (Thursday)=112
Therefore,
Chase's Final score Equals 112
The number of points did he score on Thursday is 112.
Given that,
Chase scored 14 points on Monday. And he doubled his score each day thereafter.Based on the above information, the calculation is as follows:
On Monday = 14
On Tuesday = (14) (2) = 28
On Wednesday = (28) (2) = 56
On Thursday = (56) (2) = 112
Therefore, we can conclude that the number of points did he score on Thursday is 112.
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Need help with the problem 77
Hey there! :)
Answer:
∠A = 15.6°
Step-by-step explanation:
Use trigonometry to solve for ∠A. Since this involves the opposite and adjacent sides, tangent will be used. Therefore:
24/86 = arc tan x (inverse of tangent)
0.279 = arc tan x
x = 15.59° ≈ 15.6°.
Therefore:
∠A = 15.6°
What is the constant of proportionality in the equation Y = x/9?
Answer:
1/9
Step-by-step explanation:
Separate the fraction (1/9) from the variable x:
y = (1/9)x.
1/9 is the constant of proportionality.