Answer:
The y-intercept is y = -4.
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
Step-by-step explanation:
Quadratic equation:
Has the following format:
[tex]y = ax^2 + bx + c[/tex]
The y-intercept is c.
Finding the x-intercepts:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
In this question:
The quadratic equation is [tex]2x^2 - 7x - 4[/tex], which has [tex]a = 2, b = -7, c = -4[/tex]. This means that the y-intercept is y = -4.
x-intercepts:
[tex]\Delta = (-7)^2-4(2)(-4) = 81[/tex]
[tex]x_{1} = \frac{-(-7) + \sqrt{81}}{2*2} = 4[/tex]
[tex]x_{2} = \frac{-(-7) - \sqrt{81}}{2*2} = -\frac{1}{2}[/tex]
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
Vertex:
[tex]x_{v} = -\frac{(-7)}{2*2} = \frac{7}{4}[/tex]
[tex]y_{v} = -\frac{81}{4(2)} = -\frac{81}{8}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
Slope = 4
Y-intercept = -1
Answer:
y = 4x -1
Step-by-step explanation:
You use the equation y = mx + b
m is the slope, so you just substitute 4 for m, and b is the y-intercept, so you substitute -1 for b
Find the midpoint of line segment
Step-by-step explanation:
[tex]midpoint = ( \frac{4.9 + - 5.2}{2} , \: \frac{ - 1.3 + - 0.6}{2} ) \\ = ( - 0.15, \: - 0.95)[/tex]
Add the fraction : 3/5 + 5 2/5 + 1/6
Answer:
37/6 or 6 1/6
Step-by-step explanation:
make all the denominators the same and add the numerators
The number of students attending summer school at a local community college has been decreasing each year by 7%. If 847 students currently attend summer school at this rate continues, find the number of students attending summer school in 4 years.
Answer:
≈ 634
Step-by-step explanation:
n = 847(1 * .07)^4
n = 847(0.93)^4
n = 633.60005247
n ≈ 634
A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 using B. The average gas mileage for A was 36 mpg, and 42 mpg for B. Assume population standard deviations for A and B are respectively 6 and 8. A. Find the point estimate. (2 pts) B. Find the margin of error. (3 pts) C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)
Answer:
a) -6 mpg.
b) 2.77 mpg
c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
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]
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.
Gas mileage A: Mean 36, standard deviation 6, sample of 50:
So
[tex]\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485[/tex]
Gas mileage B: Mean 42, standard deviation 8, sample of 50:
So
[tex]\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314[/tex]
Distribution of the difference:
Mean:
[tex]\mu = \mu_A - \mu_B = 36 - 42 = -6[/tex]
Standard error:
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142[/tex]
A. Find the point estimate.
This is the difference of means, that is, -6 mpg.
B. Find the margin of error
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs = 1.96*1.4142 = 2.77[/tex]
The margin of error is of 2.77 mpg
C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)
The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg
The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg
The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
For every 1000 videos a channel gets it makes £2.50 from ad revenue. How many videos will the channel need to make £1
Answer: 400 videos
Step-by-step explanation:
1000/1 x 1/2.5 = 400
Mike drinks 2/5 of a litre of juice each day.Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.Mike buys enough juice to last for 7 days.What is the lowest price Mike can pay for this juice?Show how you decide.
Presume we have this sack of marbles. There are 4 green marbles, 3 red marbles, 2 blue marbles, and 1 yellow marble.
What is the probability of pulling a red marble, given a blue marble was pulled before without replacement?
Answer:
There is a 33.3% chance you will pull a red marble after pulling a blue one.
Step-by-step explanation:
There are a total of 10 marbles in the sack. A blue marble is removed from the bag without being replaced, leaving 9 in the sack. 3 of the marbles left are red. To find the probability of pulling a red marble, we divide the number of red marbles by the number of total marbles.
3/9 = 1/3 = 0.333 = 33.3%
Does anyone know
How to do probability?
Probability is simply how likely something is to happen.
Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The best example for understanding probability is flipping a coin:
There are two possible outcomes—heads or tails.
What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.You might intuitively know that the likelihood is half/half, or 50%.
Tips
The probability of an event can only be between 0 and 1 and can also be written as a percentage.
4. A zoo is open for 10 1/2 hours every day. There
are two security guards on duty at a time and each
shift is 3 1/2 hours. How many shifts are there per
day?
A. 1 shift
B. 2 shifts
C. 3 shifts
D. 4 shifts
Answer:
C
Step-by-step explanation:
This can come from process of elimination, 1 shift is not enough. 2 shifts, 3 1/2 + 3 1/2 is 7, meaning it still isn't enough. 4 shifts 7 + 7 is 14, making it to much.
Find the volume of this sphere.
Use 3 for TT.
V
3
જ
V ~ [?]cm
V = Tr3
10 cm
Enter
9514 1404 393
Answer:
500 cm³
Step-by-step explanation:
The diameter of the sphere is shown as 10 cm, so its radius is 5 cm. Using the given numbers in the given formula, you find the volume to be ...
V = (4/3)(3)(5 cm)³ = 4(125 cm³) = 500 cm³
Alex has 5 1/5cups of dog food. A serving of dog food is 4/5cup.
How many servings does Alex have?
O A.
8
55
serving
B. 4; servings
O c. 5 servings
OD.
D. 67 servings
5 servings looked It up
Alex has 5 1/5cups of dog food. A serving of dog food is 4/5cup. Therefore, Alex has 4 servings.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Alex has 5 1/5 cups of dog food. A serving of dog food is 4/5 cup.
[tex]5\dfrac{1}{5} = \dfrac{26}{5}\\\\= \dfrac{26}{5}/ \dfrac{4}{5} \\\\= \dfrac{26}{5}\times \dfrac{5}{4} \\\\=\dfrac{26}{4}[/tex]
Therefore, Alex has 4 servings.
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In how many ways can the letters A, C, E, G, K, S be arranged
Answer:720
Step-by-step explanation:Now let's imagine we are filling them with letters. There are six places we can put the first letter, so after we've placed one letter, we have six different outcomes.
There are then five remaining gaps for the second letter, so we have 5*6=30 different outcomes after two letters.
There are four spaces for the third letter, three for the fourth letter, two for the fifth letter and finally we have to put the sixth letter in the remaining gap.
So we end up with 6*5*4*3*2*1=720 ways to arrange six different letters.
This is called the factorial function, and is denoted by an exclamation mark. The factorial function is defined as the number of ways to arrange n different options and is calculated as n! = 1*2*3*…*(n-1)*n, with a extra bit that 0!=1 as there is one way to arrange a set of 0 objects (this comes into play later in statistics).
Please help me with this it is very important to my grade
Answer:
Option B is correct
Step-by-step explanation:
[tex] \sf \longmapsto \: \frac{{x}^{3} - {y}^{3} }{4} \\ \sf \longmapsto \: \frac{ {4}^{3} - {2}^{3} }{4} \\ \sf \longmapsto \: \frac{64 - 8}{4} \\ \sf \longmapsto \: \frac{56}{4} \: \: \: \: \: \: \: \: \\ \sf \longmapsto \: 14[/tex]
help please please help
Answer:
2/10 (A)
Step-by-step explanation:
i need to know what this movie is, what is the name of this move.
Answer:
Step-by-step explanation:
Percy Jakcson maybe?
I need help plz I don’t know how to do this
Answer:
(2,4)
Step-by-step explanation:
3x-2(-2)=x
3x-4=x
-4= -2x
x=2
y=3(2)-2
y=6-2
y=4
(2,4)
what is the value of n?
Answer:
5?
Step-by-step explanation:
Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
D
45
53
28
sin D=
sin E=
COS DE
COS E =
Answer:
sin D = 28/53
sin E =45/53
cos D =45/53
cos E =28/53
Find the measures of the angles given
Answer:
BCD = 60
ABD - 90
Step-by-step explanation:
BCD)
BC and CD are the same length on in the circle, they are the radius. Therefor, all angles will be the same at 60
ABD)
All angles together are 180
You know 2 Angles, A at 30 and D at 60
180 - 30 - 60 = Angle B
90 = Angle B
Azul spun a tri-color spinner twice. What is the probability that the spinner landed on the colors blue and green in any order? BB, BG, BY, GB, GG, GY, YB, YG, YY 2 ON 3 Acvate Win Gettings to
Answer:
The Probability that the spinner landed on the colors blue and green in any order = 2/9
Step-by-step explanation:
Given - Azul spun a tri-color spinner twice.
To find - What is the probability that the spinner landed on the colors blue and green in any order?
Solution -
Given that,
A tri-color spinner spun twice
So,
The Sample Space, S = {BB, BG, BY, GB, GG, GY, YB, YG, YY}
⇒n(S) = 9
Now,
Let A be an event that the spinner landed on the colors blue and green
So,
A = {BG, GB}
⇒n(A) = 2
Now,
Probability that the spinner landed on the colors blue and green in any order = n(A) ÷ n(S)
= 2 ÷ 9
∴ we get
The Probability that the spinner landed on the colors blue and green in any order = 2/9
It would be nice if someone helped!
Thank you I’m advanced
Answer: 243 inches squared.
Step-by-step explanation: I could be wrong but here's my answer
The heights of 4 different people are: 1.55m, 1.52m, 1.81m, and 1.91m. The range of these
heights is:
A circle has an equation (x+2)2+(y−5)2=64. What is 34 of its area.
Answer:
3/4 of the area of the circle is of [tex]48\pi[/tex] squared units.
Step-by-step explanation:
Equation of a circle:
The equation of a circle has the following format:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In which the center is [tex](x_0,y_0)[/tex] and r is the radius.
Area of a circle:
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Circle (x+2)² + (y-5)² = 64
Comparing with the standard equation, we have that:
[tex]r^2 = 64[/tex]
Area of the circle:
[tex]A = \pi r^2 = 64\pi[/tex]
What is 3/4 of its area?
[tex]\frac{3A}{4} = \frac{3*64\pi}{4} = 3*16\pi = 48\pi[/tex]
3/4 of the area of the circle is of [tex]48\pi[/tex] squared units.
explain why you rename 4 1/4 to find 4 1/4- 3/4
Answer:
Because it is a mixed fraction and it should be renamed in order to solve your problem, for the other one CAN NOT be converted into a mixed fraction.
A: $521.80
B:513.60
C: 467.90
D: 435.70
Answer:
I think it´s A $521.80
Step-by-step explanation:
O2) Work out 30% of £5.80.
Answer:
1.74
Step-by-step explanation:
Multiply 5.80 times .30
Answer:
1.74
Step-by-step explanation:
To solve this, lets multiply the value by the percentage.
Our value is 5.8
And our percentage is 30%.
Lets convert this into a decimal, to do this, divide 30 by 100:
30/100
=
0.3
Now that we have the percentage in decimal form, multiply it by the 5.8:
5.8*0.3
=
1.74
This is your answer!
Hope this helps! :)
find 5 consecutive odd numbers where the sum of the first three numbers is 15 greater than the sum of two numbers
Answer:
The five odd numbers are:
23, 25, 27, 29, and 31
Step-by-step explanation:
A random odd number is written as:
2*n + 1
Where n is an integer.
Then 5 consecutive odd numbers will be:
2*n + 1
2*(n + 1) + 1
2*(n + 2) + 1
2*(n + 3) + 1
2*(n + 4) + 1
Now we want that the sum of the first 3 numbers to be 15 greater than the sum of the two last numbers, then:
(2*n + 1) + (2*(n + 1) + 1) + (2*(n + 2) + 1) = 15 + (2*(n + 3) + 1) + (2*(n + 4) + 1)
Now we just need to solve this for n:
(2*n + 1) + (2*n + 3) + (2*n + 5) = 15 + (2*n + 7) + (2*n + 9)
6*n + 9 = (15 + 7 + 9) + 4*n
6*n - 4*n = 15 + 7 + 9 - 9
2*n = 15 + 7 = 22
n = 22/2 = 11
Then the five numbers are:
(2*11 + 1) = 23
(2*(11 + 1) + 1) = 25
(2*(11 + 2) + 1) = 27
(2*(11 + 3) + 1) = 29
(2*(11 + 4) + 1) = 31
Suppose Hailey has taken four exams and made 86, 94, 76, and 81. If each exam counts equally, what does Hailey need to make on her fifth test to have an overall average of 85?
Answer:
She has to get a score of 88 on that test
Step-by-step explanation:
Take the average of the other grades, and that gives you 84.25. So she has to think about what rating she gives it is 85, and the rating is 88.
Hailey needs to score an 88 on the last exam in order to get an average of 85.
The overall average is the mean and the mean is calculated by adding up all the scores and then dividing by the number of exams.
There are 5 exams but only 4 scores. The 5th score will be denoted, "x" and the average we are looking for is 85.
The fifth score should therefore be:
Overall score = Sum of 5 exams / 5
85 = (86 + 94 + 76 + 81 + x) / 5
85 x 5 = 337 + x
425 = 337 + x
x = 425 - 337
= 88
In conclusion, Hailey needs a score of 88 on the fifth exam.
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What is the volume of the following rectangular prism? 8 units 5 1/4 units2
Answer:
84 units²
Step-by-step explanation:
v = 8 * 5 1/4 * 2
v = 84 units²
The volume of the rectangular prism is 42 cubic units.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
To find the volume of a rectangular prism, you need to multiply the height of the prism by the base area.
The height of the prism is given as 8 units.
The base area is given as 5 1/4 units².
To convert the mixed fraction to an improper fraction, we multiply the whole number (5) by the denominator (4), then add the numerator (1).
5 1/4 = (5 x 4 + 1) / 4 = 21/4
Now, we can calculate the volume of the rectangular prism:
Volume = height x base area
Volume = 8 x 21/4
Volume = 168/4
Volume = 42
Therefore, the volume of the rectangular prism is 42 cubic units.
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