Answer:
-74
Step-by-step explanation:
f(x) = -2x^2 +8x -10
Let x = -4
f(-4) = -2 ( -4)^2 +8(-4) -10
= -2(16) -32-10
= -32 -32-10
= -74
What is the coordinate of the midpoint of segment AC
Answer:
-5.5
Step-by-step explanation:
[tex]\frac{-7+-4}{2}\\\\\frac{-11}{2}\\\\-5.5[/tex]
What is the best definition of the domain of a relation
Answer:
All of the values that can go into a relation or function (input) are called the domain. ... The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.
A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence interval for the population mean. Round your answers to one decimal place. ( , ) b. Assume that the same sample mean was obtained from a sample of items. Provide a confidence interval for the population mean. Round your answers to two decimal places. ( , ) c. What is the effect of a larger sample size on the interval estimate? Larger sample provides a - Select your answer - margin of error.
Answer:
(a): The 95% confidence interval is (46.4, 53.6)
(b): The 95% confidence interval is (47.9, 52.1)
(c): Larger sample gives a smaller margin of error.
Step-by-step explanation:
Given
[tex]n = 30[/tex] -- sample size
[tex]\bar x = 50[/tex] -- sample mean
[tex]\sigma = 10[/tex] --- sample standard deviation
Solving (a): The confidence interval of the population mean
Calculate the standard error
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{10}{\sqrt {30}}[/tex]
[tex]\sigma_x = \frac{10}{5.478}[/tex]
[tex]\sigma_x = 1.825[/tex]
The 95% confidence interval for the z value is:
[tex]z = 1.960[/tex]
Calculate margin of error (E)
[tex]E = z * \sigma_x[/tex]
[tex]E = 1.960 * 1.825[/tex]
[tex]E = 3.577[/tex]
The confidence bound is:
[tex]Lower = \bar x - E[/tex]
[tex]Lower = 50 - 3.577[/tex]
[tex]Lower = 46.423[/tex]
[tex]Lower = 46.4[/tex] --- approximated
[tex]Upper = \bar x + E[/tex]
[tex]Upper = 50 + 3.577[/tex]
[tex]Upper = 53.577[/tex]
[tex]Upper = 53.6[/tex] --- approximated
So, the 95% confidence interval is (46.4, 53.6)
Solving (b): The confidence interval of the population mean if mean = 90
First, calculate the standard error of the mean
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{10}{\sqrt {90}}[/tex]
[tex]\sigma_x = \frac{10}{9.49}[/tex]
[tex]\sigma_x = 1.054[/tex]
The 95% confidence interval for the z value is:
[tex]z = 1.960[/tex]
Calculate margin of error (E)
[tex]E = z * \sigma_x[/tex]
[tex]E = 1.960 * 1.054[/tex]
[tex]E = 2.06584[/tex]
The confidence bound is:
[tex]Lower = \bar x - E[/tex]
[tex]Lower = 50 - 2.06584[/tex]
[tex]Lower = 47.93416[/tex]
[tex]Lower = 47.9[/tex] --- approximated
[tex]Upper = \bar x + E[/tex]
[tex]Upper = 50 + 2.06584[/tex]
[tex]Upper = 52.06584[/tex]
[tex]Upper = 52.1[/tex] --- approximated
So, the 95% confidence interval is (47.9, 52.1)
Solving (c): Effect of larger sample size on margin of error
In (a), we have:
[tex]n = 30[/tex] [tex]E = 3.577[/tex]
In (b), we have:
[tex]n = 90[/tex] [tex]E = 2.06584[/tex]
Notice that the margin of error decreases when the sample size increases.
Determine by inspection (i.e., without performing any calculations) whether a linear system with the given augmented matrix has a unique solution, infinitely many solutions, or no solution. 1 2 3 4 5 6 7 6 5 4 3 2 8 8 8 8 8 8
Answer:
Infinitely Many Solutions
Step-by-step explanation:
Given
[tex]\left[\begin{array}{cccccc}1&2&3&4&5&6\\7&6&5&4&3&2\\8&8&8&8&8&8\end{array}\right][/tex]
Required
Determine the type of solution
From the matrix, we have:
3 non-zero rows and 5 variables (the last column is the result)
When the number of variables is more than the number of non-zero rows, then such system has infinitely many solutions
i.e.
[tex]Variables > Non\ zero\ rows[/tex]
[tex]5 > 3[/tex]
How many square feet does the paint need to cover?
Answer:
62 square feet
Step-by-step explanation:
9 x 8 = 72
5 x 2 = 10
72 - 10 = 62
A membership committee for a local community group consists of twenty-two individuals. a. If a task force of eight members of this committee must be formed to investigate the membership rules, how many different task force groups might possibly be formed
Answer:
319,770 different task force groups might possibly be formed
Step-by-step explanation:
The order in which the members of the task force are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Groups of 8 from a set of 22. So
[tex]C_{22,8} = \frac{22!}{8!(22-8)!} = 319770[/tex]
319,770 different task force groups might possibly be formed
According to a survey about 82% of a highly satisfied with their jobs at 45 engineers were surveyed how many reported that they were highly satisfied?
4. Gravetter/Wallnau/Forzano, Essentials - Chapter 6 - End-of-chapter question 4 A psychology class consists of 32 freshmen and 48 sophomores. If the professor selects names from the class list using random sampling. What is the probability that the first student selected will be a freshman
Answer:
ANS.1
Freshmen F = 32
Sophomore S = 48
Total students = 80 students
P(F) = Favorables cases/Total cases
= 32/80
Hope this helps!
Answer:
32/80 or 2/5 simplified
Step-by-step explanation:
P(Freshman) = 32/80 or 2/5 simplified
If correct ill give brainly
Answer:
Hello! answer: x = 16
Step-by-step explanation:
16 × 16 = 256
12 × 12 = 144
256 + 144 = 400
√400 = 20 therefore x = 16 hope that helps!
Answer:
23
Step-by-step explanation:
The monthly family income of a family is $15,000. They spend 28% of their monthly income on food. How much do they spend on food each month?
Answer - $
(fill in the value)
Answer:
$1000 each month.
Step-by-step explanation:
$1000 because 12 month and 1 month=$1000 the family have $3000.
In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws. In a random sample of 588 men, 307 favored stricter gun control laws. Can it be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women
Answer:
The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women
Step-by-step explanation:
Before solving the question, we need to understand the central limit theorem, and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Test if a lower proportion of men favor stricter gun control than women:
At the null hypothesis, we test if the proportion is the same, that is, the difference of the proportions if 0. So
[tex]H_0: p_M - p_W = 0[/tex]
At the alternative hypothesis, we test if it is less, that is, the subtraction of the proportions is negative. So
[tex]H_1: p_M - p_W < 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws.
This means that:
[tex]p_W = \frac{313}{564} = 0.555[/tex]
[tex]s_W = \sqrt{\frac{0.555*0.445}{564}} = 0.0209[/tex]
In a random sample of 588 men, 307 favored stricter gun control laws.
This means that:
[tex]p_M = \frac{307}{588} = 0.522[/tex]
[tex]s_M = \sqrt{\frac{0.522*0.478}{588}} = 0.0206[/tex]
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_M - p_W = 0.522 - 0.555 = -0.033[/tex]
[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0206^2+0.0209^2} = 0.029[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.033 - 0}{0.029}[/tex]
[tex]z = -1.12[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion difference greater than 0.033, which is the p-value of z = -1.12.
Looking at the z-table, z = -1.12 has a p-value of 0.1314.
The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women
Question 1 of 25
This table shows the population of owls in a park in different years. The
quadratic regression equation that models these data is
y -1,34x2 - 10,75x - 11.3
Year
Number of owls
1
0
2
2
3
7
4
14
6
4
Using this model, the predicted number of owls in year 8 is about - 11. Does
this prediction make sense? Why or why not?
PREVIOUS
Answer:
No, it doesn't make sense, as we cannot have a negative population of owls.
Step-by-step explanation:
Obtaining a the quadratic model :
y = -1,34x2 - 10,75x - 11.3 ; by fitting the data above ;
To obtain the number of owls after 8 years, we have ;
y = -1,34x2 + 10,75x - 11.3
put x = 8 in the equation
y = -1,34(8)^2 + 10.75(8) - 11.3
y = - 85.76 + 86 - 11.3
y = - 11.06
y = - 11
This figure dies not make sense, as we cannot have a negative population of a certain specie such as owls at any given time.
Answer:
No, because you can't have a negative number of owls.
Step-by-step explanation:
Geometry need to find the lengths of DE , EF AND DF , respectively? ASAP
Answer:
option D
because every length is one fifth of the corresponding length of the bigger triangle
there are 12 space suits that fit into one box. how many are needed for 2400 space suits
Answer:
200 boxes
Step-by-step explanation:
We can use ratios to solve
12 suits 2400 suits
------------ = ------------
1 box x boxes
Using cross products
12x = 1*2400
12x = 2400
Divide by 12
12x/12 = 2400/12
x =200
We need 200 boxes
Answer:
200
Step-by-step explanation:
1 box = 12
Box? = 2400.
DIVIDE
Hello guys can somebody please help me solve this equation
Answer:
a) cosA=5/13 b) sinA=12/13
Step-by-step explanation:
Look at the needed angle, then use SOHCAHTOA!
Answer:
cos A = 5/13, sin A = 12/13
Step-by-step explanation:
Watch the picture for help.
sin A = a/c (According to the picture)
cos A = b/c (According to the picture)
If post are space 5 feet apart and how many posts are needed for 60 feet of straight line fence
Step-by-step explanation:
Math is a language
say you plant two posts that are 5ft apart and you want to get up to 60ft
right now you've covered 5ft and now have 60 - 5 = 55ft to go.
you plant the next one: 55 - 5 = 50ft to go
instead of subtracting many times and counting hiw many times we've subtracted, we can use division
60ft / 5ft = 12 posts
to verify, you can multiply 5 and 12 which is the same as adding 5 + 5 + 5 + 5 +... + 5 = 5ft x 12 Posts= 60ft in total length
There are 12 posts for 60 feet of straight line fence.
Here,
Given that,
Post are space 5 feet apart.
We have to find number of posts for 60 feet of straight line fence.
What is Division method?
This method of distributing a group of things into equal parts is termed as division.
Now,
We can division method to find number of posts for 60 feet of straight line fence.
Here, Post are space 5 feet apart.
Number of posts = [tex]\frac{60}{5} = 12[/tex]
Hence, There are 12 posts for 60 feet of straight line fence.
Learn more about the Division method visit:
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This question has two parts.
Many artists incorporate geometric shapes into their art. An artist wants to make a sculpture shaped like a cone with a height of 4.2 inches and a radius of 2.5 inches. The artist needs to know the volume of the sculpture to purchase the correct amount of materials.
Part A. Which equation should the artist use to calculate the volume of the cone with the given measurements?
1. V=4/5π (2.5)³
2.V=π(2.5)²(4.2)
3.V=1/3 (2.5)² (4.2)
4.V=1/3π (2.5)²(4.2)
B.What is the Volume Of The Cone?
Answer:
D
Step-by-step explanation:
shaped like a cone
Cone = 1/3
v = 1/3 x 3.14 x 2.5^2 x 4.2
v =27.475
The equation should the artist use to calculate the volume of the
cone is, 4. V=1/3π (2.5)²(4.2)
What is a cone?A cone is a three-dimensional geometric object with a smooth, curved top and a flat base. As a cone's height increases, its radius gradually decreases until it reaches a particular point.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, An artist is making a sculpture shaped like a cone having a radius of 2.5 inches and a height of 4.2 inches.
We know The volume of a cone is (1/3)πr²h.
Therefore, The volume of the cone would be,
= (1/3)π(2.5)²×4.2 cubic inches.
learn more about cones here :
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How do you apply frequency distribution table in real life?
Answer:
As a statistical tool, a frequency distribution provides a visual representation for the distribution of observations within a particular test. Analysts often use frequency distribution to visualize or illustrate the data collected in a sample.
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Answer:
snafnjnfnEWfnwenlfnwenflwenlfewfwefư
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Find the circumference of this circle
ysing 3 for a
C ~ [?]
20
C=πα
Answer:
[tex]2*\pi *10=62.83185307[/tex]
[tex]20/2 = 10[/tex]
[tex](Radius)[/tex][tex]Or the C = \pi*d[/tex]
62.83185307 is the answer
Answer:
C≈60
Step-by-step explanation:
remember circumference formula
[tex] \displaystyle C = 2\pi r[/tex]
given that,d=20 therefore r would be 20/2=10 thus substitute:
[tex] \displaystyle C = 2\pi .10[/tex]
simplify mutilation:
[tex] \displaystyle C = 20\pi [/tex]
substitute the given value of π:
[tex] \displaystyle C = 20.3[/tex]
simplify multiplication:
[tex] \displaystyle C = 60[/tex]
and we are done!
Will give brainliest pls help!!!!
Answer:
3rd option
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{5}{3}[/tex] and c = - 3 , then
y = - [tex]\frac{5}{3}[/tex] x - 3 ← equation of line
11. Two of every 7 birds landing on
Mischa's feeder are sparrows. Today,
42 birds landed on her feeder. How
many of the birds would you expect to
be sparrows?
A 6
B 12
C 21
D 35
Answer:
B) 12
Step-by-step explanation:
2/7 is the original ratio
7 × 6 = 42
2 × 6 = 12
Please show how you did it so I can learn :)
Answer:
[tex] x_{1} = 3 + \sqrt {6} [/tex]
[tex] x_{2} = 3 - \sqrt {6} [/tex]
Step-by-step explanation:
Given the quadratic equation;
x² - 6x + 3 = 0
To find the roots of the quadratic equation, we would use the quadratic formula;
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 1, b = -6 and c = 3
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the formula, we have;
[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]
[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]
[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]
[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]
[tex] x_{1} = 3 + \sqrt {6} [/tex]
Or
[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]
[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]
[tex] x_{2} = 3 - \sqrt {6} [/tex]
The equation for line r can be written as y=-1/4x+3. Line s which is parallel to lone r includes the point (-4,3). What is the equation of line s?
Answer:
[tex]y=-\frac{1}{4}x+2[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form:[tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope of line S using line R (m)
[tex]y=-\frac{1}{4} x+3[/tex]
We can identify clearly that the slope of the line is [tex]-\frac{1}{4}[/tex], as it is in the place of m. Because parallel lines always have the same slope, the slope of line S would also be [tex]-\frac{1}{4}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{1}{4}x+b[/tex]
2) Determine the y-intercept of line S (b)
[tex]y=-\frac{1}{4}x+b[/tex]
Plug in the given point (-4,3) and solve for b
[tex]3=-\frac{1}{4}(-4)+b\\3=1+b[/tex]
Subtract 1 from both sides to isolate b
[tex]3-1=1+b-1\\2=b[/tex]
Therefore, the y-intercept is 2. Plug this back into [tex]y=-\frac{1}{4}x+b[/tex]:
[tex]y=-\frac{1}{4}x+2[/tex]
I hope this helps!
substitution method y= 3x-2 and 2x-3y=16
solution (__), (__)
thanks
Answer:
i got (-10/7, -44/7)
The volume of a right circular cylinder with radius r and height h is Vrh. Is the volume an increasing or decreasing function of the radius at a fixed height%E2%80%8B (assume r0 and h%E2%80%8B0)?
Answer:
The rate of change of volume of the cone with respect to radius is [tex]\frac{2}{3}\pi\times rh\\[/tex].
Step-by-step explanation:
radius of come = r
height of cone = h
Volume of cone
[tex]V = \frac{1}{3}\pi\times r^2 h[/tex]
As the height is constant, the rate of change of volume with respect to radius is given by the derivative of volume with respect to radius.
[tex]\frac{dV}{dr}=\frac{1}{3}\pi\times {2r}h\\\\\frac{dV}{dr}=\frac{2}{3}\pi\times rh\\\\[/tex]
how many days are there in xweeks and x days
Answer:
7 DAYS IN A WEEK
Step-by-step explanation:
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDA
7 DAYS
Answer:
it depends... What is X in this situation?
Step-by-step explanation:
A week has seven days.
A day has one day..?
I dont know how to help you, Sorry
NEED ASAP! What is m
Answer:
B = 31.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan B = opp / adj
tan B = 28.2 / 45.8
taking the inverse tan of each side
tan ^ -1 ( tan B) = tan ^-1 (28.2/45.8)
B =31.62145
Rounding to the nearest tenth
B = 31.6
Someone please help me
Answer:
David had x amount of M&M's. He then ate 15 of them for snack. Now David only has 35 M&M's left. How many M&M's did David have in the beginning?
Step-by-step explanation:
Answer:
X= 20
Step-by-step explanation:
Hannah has 35 marbles. Hannah gives away 15 marbles. How many marbles does Hannah have left? Solve the equation X- 15=35.
Can someone please help me with this I'm really stuck!!!
Answer:
we use side of triangle to find area and divide by 2 so first one is 15*15+ 8*15/2 225+60=285