[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{-11} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{8}{2(-2)}~~,~~-11-\cfrac{8^2}{4(-2)} \right)\implies \left( 2~~,~~-11+\cfrac{64}{8} \right) \\\\\\ (2~~,~~-11+8)\implies (2~~,~~-3)[/tex]
the surface area of this rectangular prism is 28 square centimeters. What is the value of p?
Answer:
4
Step-by-step explanation:
Since the value of the total prism is 28, and you know that there are two sides which are 2 from 2x1. Then you can subtract 4 from 28. You would have 4 sides left, 2 of which are px1 and the other 2 are 2xp. The total results would be 2p+4p which is 6p=24.
Round 8.077 to nearest thousand
Answer:
Your answer is 8,077
Step-by-step explanation:
What you do is you take 8.077 and times it by 1,000.
8.077*1,000=8,077 as your answer.
Answer:
It equals 0, I hope this helps yoU!
When 1,250^3/4 is written in simplest radical form, which value remains under the radical?
A. 2
B. 5
C. 6
D. 8
HELP IM ABT TO FAIL :)
Answer:
15/36
Step-by-step explanation:
One hack that I used is I looked at all of the options in the first row and added the number one less 6 times
I basically did
5+(5-1)+(5-2)+(5-3)+(5-4)
5+4+3+2+1
15
HELP!!!!!! Determine the equation of the line with slope −4 that passes through the point M(−2, 1).
Answer:
y = -4x - 7Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = -4 and the point M(-2, 1).
The equation of a line:
[tex]y=-4x+b[/tex]
Put the coordinates of the point M to the equation of a line:
[tex]1=-4(-2)+b[/tex]
[tex]1=8+b[/tex] subtract 8 from both sides
[tex]-7=b\to b=-7[/tex]
Finally:
[tex]y=-4x-7[/tex]
Mrs. Eskew saved her money for 37 years and had $2,119,784 in the bank. She used her money to go a vacation for a month and spent $278,389. How much did she have left after her vacation?
Mrs. Eskew will have $1,841,395 left after subtracting the vacation expense of $278,389 from her initial savings of $2,119,784.
The student is asking how much money Mrs. Eskew will have left after spending part of her savings on a vacation. To find out, we simply need to subtract the amount spent on the vacation from the total amount she had saved. Mrs. Eskew started with $2,119,784 in the bank. After spending $278,389 on her vacation, we can calculate her remaining balance as follows:
$2,119,784 - $278,389 = $1,841,395.
Therefore, Mrs. Eskew will have $1,841,395 left after her vacation.
find the difference of the given polynomials (8x^2-3x+1/3)-(2x^2-8x+3/5)
Answer:
[tex]\boxed{\bold{6x^2+5x-\frac{4}{15}}}[/tex]
Explanation:
[ Step One ] Remove Parenthesis: (a) = a
[tex]\bold{8x^2-3x+\frac{1}{3}-\left(2x^2-8x+\frac{3}{5}\right)}[/tex]
[ Step Two ] Simplify: [tex]\bold{-\left(2x^2-8x+\frac{3}{5}\right): \ -2x^2+8x-\frac{3}{5}}[/tex]
[tex]\bold{8x^2-3x+\frac{1}{3}-2x^2+8x-\frac{3}{5}}[/tex]
[ Step Three ] Simplify [tex]\bold{8x^2-3x+\frac{1}{3}-2x^2+8x-\frac{3}{5}: \ 6x^2+5x+\frac{1}{3}-\frac{3}{5}}[/tex]
[tex]\bold{6x^2+5x-\frac{4}{15}}[/tex]
[ [tex]\boxed{\bold{Final \ Answer}}[/tex] ]
➤ [tex]\bold{6x^2+5x-\frac{4}{15}}[/tex]
[tex]\boxed{\bold{Mordancy}}[/tex]
Plz help !!!!!!!!!!!!!!
Answer: a) 21
Step-by-step explanation:
2A - 3B ; A = 6, B = -3
2(6) - 3(-3)
= 12 - -9
= 12 + 9
= 21
Mr.Walden wrote the expression. He asked his students to write an equivalent expression of simplified form.
Answer:
option D
Brianna
Step-by-step explanation:
Given in the question the expression wrote by Mr.Walden
[tex]\frac{p^{-5} }{q^{0} }[/tex]
To write the simplified form of this expression we will use negative rule of exponent
[tex]b^{-n}[/tex]= 1 / [tex]b^{n}[/tex]
[tex]q^{-5} = \frac{1}{q^{5} }[/tex]
so,
[tex]\frac{1}{q^{5} x q^{0} }[/tex]
[tex]\frac{1}{q^{5} p^{0} }[/tex]
Only Brianna wrote right simplification of the expression written by Mr.Walden
Terrence randomly sampled 400 people and asked them if they prefer spring or fall. The results of his sample yielded an estimated population proportion of 43% who prefer spring. Deena randomly sampled 1,200 people and asked them if they prefer spring or fall. The results of her sample also yielded an estimated population proportion of 43% who prefer spring.
If Terrence and Deena use the same confidence level, which statement best describes the results of their margin of error calculations?
Terrence’s margin of error will be exactly three times as large as Deena’s.
Deena’s margin of error is half the amount of Terrence’s.
If Terrence samples 800 more people, his margin of error will be the same as Deena’s.
If Deena samples 400 fewer people, her margin of error would be exactly half the amount of Terrence’s.
on edge it's C. If Terrence samples 800 more people, his margin of error will be the same as Deena’s.
Answer:
Step-by-step explanation:
Margin of error is calculated as
Critical value multiplied by Std error of sample
= Critical value multiplied by square root of (variance/sample size)
Hence Margin of error
=[tex]z/t*(\frac{\sigma}{\sqrt{n} } )[/tex]
Thus square root of n is inversely proportion to margin of error.
Thus we have margin of error of Terrena would be square root of 3 times that of Deena
Thus option a, b and d are wrong
C is right because when sample sizes equal, the margin of error also would be equal.
if a patient checks in at at 1:25 and seen at 1:54. how long did patient wait in waiting area?
Answer: " 29 minutes. "
_____________________________________________
Step-by-step explanation:
_____________________________________________
54 minutes (minus) 25 minutes =
54
- 25
_____________________________________________
29 minutes.
_____________________________________________
Answer 29 minutes
step by step solution:
patient seen at = 1:54
patient check in at = 1:25
waiting time= 1:54 - 1:25= 0: 29
Are the following equations (1,2,3) one solution, infinitely many solutions, or no solution for each one? Please and Thank You
1.
y-3x=5
y=3x+5
2.
y=6x+2
y=6x-2
3.
y=5x+9
y=3x-2
1.when you change the first equation to the form it is the same as the second which means infinite solutions
y-3x=5 --->y=3x+5 then set them equal to find many possible solutions
2.this is no solution because the slopes are the same when you combine these equation the 2's cancel out and you ar left with y=12x which cannot be solved
3.when everything is different there is one solution
during a softball game kay hit a fly ball the function f(x) = -16t^2 + 64t + 4 describes the height of the softball in feet. make a table of values for the function and then graph it.
The graph is attached.
To graph a parabola we need to know the following:
- If the parabola is open upwards or downwards
- They axis intercepts (if they exist)
- The vertex position (point)
We are given the function:
[tex]f(t)=-16t^{2}+64t+4[/tex]
Where,
[tex]a=-16\\b=64\\c=4[/tex]
For this case, the coefficient of the quadratic term (a) is negative, it means that the parabola opens downwards.
Finding the axis interception points:
Making the function equal to 0, we can find the x-axis (t) intercepts, but since the equation is a function of the time, we will only consider the positive values, so:
[tex]f(t)=-16t^{2}+64t+4\\0=-16t^{2}+64t+4\\-16t^{2}+64t+4=0[/tex]
Using the quadratic equation:
[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}\\\\\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}=\frac{-64+-\sqrt{4096+256} }{-32}\\\\\frac{-64+-\sqrt{4096+256} }{-32}=\frac{-64+-(65.96) }{-32}\\\\t1=\frac{-64+(65.96) }{-32}=-0.06\\\\t2=\frac{-64-(65.96) }{-32}=4.0615[/tex]
So, at t=4.0615 the height of the softball will be 0.
Since we will work only with positive values of "x", since we are working with a function of time:
Let's start from "t" equals to 0 to "t" equals to 4.0615.
So, evaluating we have:
[tex]f(0)=-16(0)^{2}+64(0)+4=4\\\\f(1)=-16(1)^{2}+64(1)+4=52\\\\f(2)=-16(2)^{2}+64(2)+4=68\\\\f(3)=-16(3)^{2}+64(3)+4=52\\\\f(4.061)=-16(4.0615)^{2}+64(4.0615)+4=0.0034=0[/tex]
Finally, we can conclude that:
- The softball reach its maximum height at t equals to 2. (68 feet)
- The softball hits the ground at t equals to 4.0615 (0 feet)
- At t equals to 0, the height of the softball is equal to 4 feet.
See the attached image for the graphic.
Have a nice day!
How many decameters are there in 4.5 kilometers
There are 100 decameters (dam) in a kilometer (km).
4.5km x 100dam = 450 decameters
Answer: 450 decameters
assume that random guesses are made for 8 multiple choice questions on an SAT test, so that there are n=9 trials, each with probability of success (correct) given by p=0.6. find the indicated probability for the number of correct answers. find the probability that the number x of correct answers is fewer than 4.
Answer:
[tex]P(x<4)=0.0994[/tex]
Step-by-step explanation:
If we call x the number of correct questions obtained in the 9 attempts, then:
x is a discrete random variable that can be modeled by a binomial probability distribution p, with n = 9 trials.
So, the p of x successes has the following formula.
[tex]P(x) =\frac{n!}{x!(n-x)!}*p^x(1-p)^{n-x}[/tex]
Where:
n = 9
p = 0.6
We are looking for P(x<4)
By definition:
[tex]P(x<4) = P(x\leq3) = P(0) + P(1) + P(2) +P(3)[/tex]
Then:
[tex]P(x\leq3)=\sum_{x=0}^{3} \frac{9!}{x!(9-x)!}*(0.6)^x(1-0.6)^{9-x}[/tex]
[tex]P(x\leq3)=0.0994[/tex]
Probabilities are used to determine the chances of an event
The probability that the number of correct answers is fewer than 4 is 0.0994
The given parameters are:
[tex]n = 9[/tex]
[tex]p =0.6[/tex]
The probability is a binomial probability, and it is calculated using:
[tex]P(x) = ^nC_x p^x (1 - p)^{n -x}[/tex]
Fewer than 4 means: x = 0, 1, 2 and 3
So, we have:
[tex]P(x<4) = ^9C_0 \times 0.6^0 \times (1 - 0.6)^{9 -0} +^9C_1 \times 0.6^1 \times(1 - 0.6)^{9 -1} +^9C_2 \times 0.6^2\times (1 - 0.6)^{9 -2} +^9C_3 \times 0.6^3\times (1 - 0.6)^{9 -3}[/tex]
This gives
[tex]P(x<4) = 1 \times 0.6^0 \times (1 - 0.6)^9 + 9 \times 0.6^1 \times(1 - 0.6)^8 +36 \times 0.6^2 \times (1 - 0.6)^7 +84 \times 0.6^3 \times (1 - 0.6)^6[/tex]
Using a calculator,
[tex]P(x<4) = 0.099352576[/tex]
Approximate
[tex]P(x<4) = 0.0994[/tex]
Hence, the probability that the number of correct answers is fewer than 4 is 0.0994
Read more about binomial probabilities at:
https://brainly.com/question/23498586
Please help!!!!! Will give brainliest!!!
See the attached picture:
Explain how to write a linear equation for a line on a graph.
Use y = mx + b.
m represents the slope of the line.
the slope equals rise over run.
in other words, count the number of vertical and horizontal units from one point to another point on the line.
if you have the y-intercept and a point, you can also solve for m.
b represents the y-intercept.
find the point on the graph where x = 0.
b is the value of y.
for example, if the y-intercept was (0,4) then b would equal 4.
x and y represent a point on the graph.
pick any point on the graph and plug it in.
for example, if the point (1,2) is on the graph then x = 1 and y = 2.
The width of a rectangle, in feet, is represented by (3x-1.5). The length of the rectangle, in feet, is represented by (1.25x+3). Find the perimeter of the rectangle.
Answer:
P = 8.5 x + 3 ft
Step-by-step explanation:
To find the perimeter, we use the formula
P =2(l+w) where l is the length and w is the width
P =2 (1.25x+3 + 3x-1.5)
Combine like terms
P = 2( 4.25x +1.5)
Distribute the 2
P = 8.5 x + 3 ft
The perimeter of the rectangle in terms of x is [tex]\( {\frac{17}{2}x + 3} \)[/tex].
Given the width of the rectangle is (3x - 1.5) feet and the length is (1.25x + 3) feet, we can substitute these expressions into the perimeter formula.
First, let's express the width and length in terms of xwith rational numbers to avoid dealing with decimals:
Width [tex]\( w = 3x - \frac{3}{2} \)[/tex]
Length [tex]\( l = \frac{5}{4}x + 3 \)[/tex]
Now, we can calculate the perimeter:
[tex]\( P = 2(l + w) \)\\ \( P = 2 \left( \left( \frac{5}{4}x + 3 \right) + (3x - \frac{3}{2}) \right) \)\\ \( P = 2 \left( \frac{5}{4}x + 3 + 3x - \frac{3}{2} \right) \)\\ \( P = 2 \left( \frac{5}{4}x + 3x + 3 - \frac{3}{2} \right) \)\\ \( P = 2 \left( \frac{5}{4}x + \frac{12}{4}x + \frac{6}{2} - \frac{3}{2} \right) \)\\ \( P = 2 \left( \frac{17}{4}x + \frac{3}{2} \right) \)\\ \( P = 2 \times \frac{17}{4}x + 2 \times \frac{3}{2} \)\\ \( P = \frac{34}{4}x + 3 \)\\ \( P = \frac{17}{2}x + 3 \)[/tex]
perimeter = [tex]\( {\frac{17}{2}x + 3} \)[/tex].
one day reeva baked several dozen muffins. the next day she made 8 dozen more muffins. if she made 20 dozen muffins in all, how many dozen did she make the first day?
Answer: 12 Dozens of Muffins
Step-by-step explanation:
An easy way to do this is to work backwards. 20(Total number of muffins) - 8(Muffins made in the second day) = 12(Muffins made in the first day) that means that she made 12 dozens, or a dozen dozens!
Write 31 in tens and ones
Answer:
3 tens and 1 ones
Step-by-step explanation:
3 tens would be
3 x 10
which is 30
and 1 one is 1
30 + 1 = 31
Hope this helps! Please mark Brainliest! Thanks!!
If x+3/3 = y + 2/2 then x/3 =
Show work
Answer:
y/2
Step-by-step explanation:
(x+3)/3=(y+2)/2
(x+3-3)/3=(y+2-2)/2 adding the denominator to numerator
x/3=y/2
Danny's office ordered a sandwich tray for lunch. The tray had 4 turkey sandwiches, 7 ham sandwiches, and 6 tuna sandwiches. If Danny randomly picked a sandwich off the tray without looking, what is the probability that he picked a ham sandwich? A. B. C. D.
Step-by-step explanation:
The total amount of sandwiches on the tray is 4+7+6. This makes 17. This will be the denominator of our fraction which we are going to use for the probability.
There are 7 ham sandwiches on the tray, therefore the probability that he will pick a ham sandwich is 7/17.
Brainliest? :)
Final answer:
The probability that Danny picked a ham sandwich is 7/17, since there are 7 ham sandwiches out of a total of 17 sandwiches on the tray.
Explanation:
The question is about calculating the probability that Danny picked a ham sandwich. To determine this, we count the total number of sandwiches and then count the number of ham sandwiches.
Total number of sandwiches = 4 turkey + 7 ham + 6 tuna = 17 sandwiches.
Since there are 7 ham sandwiches, the probability (P) that Danny picks a ham sandwich is calculated by dividing the number of ham sandwiches by the total number of sandwiches.
P(ham sandwich) = Number of ham sandwiches / Total number of sandwiches
P(ham sandwich) = 7 / 17
Therefore, the probability that Danny picked a ham sandwich is 7/17.
ronen selects 75 random products to test their quality he found that 6 products had defects how many out of 3000 should ronen predict have defects
Answer: About 43
Step-by-step explanation:
in each 75 there is 6 mistakes so 75-6=69
then if you divide 3000 by 69 you get 43 im pretty sure
To predict the number of defective products out of 3000, Ronen can use proportions. He found 6 defects in a sample of 75 products, which scales up to approximately 240 defects in 3000 products.
Ronen found that 6 out of 75 products had defects in a random sample. To predict how many out of 3000 products would have defects, we can set up a proportion because we are assuming that the sample proportion will be representative of the larger population. Here's the step-by-step explanation:
First, establish the proportion of defective products in the sample: 6 defects / 75 products.Next, set this equal to x (the number we want to find) over 3000 products: 6/75 = x/3000.Cross multiply to solve for x: (6 * 3000) = (75 * x).Do the multiplication: 18000 = 75x.Finally, divide both sides by 75 to find x: 18000 / 75 = x.This calculates to 240. Therefore, Ronen can predict that approximately 240 out of 3000 products will have defects.
Convert 3.2 grams to milligrams.
0.0032 mg
32 mg
320 mg
3,200 mg
Answer:
3200
Step-by-step explanation:
multiply the mass value by 1000
Answer:
3,200 WILL BE YOUR ANSWER
Step-by-step explanation:
I HOPE 6THAT HELPS
Simplify 4(1/2 + 5/4)+ -5
Answer:
2
Step-by-step explanation:
Hopefully this helps.
Mr. Caldwell divides 72 students into 12 groups. Solve the equation 72/s =12 find the number of students in each group.
Answer:
6
Step-by-step explanation:
72 divided by grops of 12 so 72/12 =6
if you are trying to find out what is s it is 864 if not then no i multipled 12 and 72 and got 864 and then i divieded it and it was right . Again sorry if this is not what you were looking for
is the function linear or non-linear?
Answer:
Linear
Step-by-step explanation:
It is linear because it is a straight line.
Answer:
Linear
Step-by-step explanation:
The function is linear because it is a straight line.
Each week, Kelly pays $68.45 in federal income tax, $22.81 in state income tax, and $18.75 in other taxes. Which is the best estimate for the payroll tax Kelly pays each month?
Kelly's estimated monthly payroll tax is $475.94, which is found by adding together all of her weekly taxes and then multiplying by the average number of weeks in a month.
Explanation:To estimate the amount of payroll tax Kelly pays each month, we first need to find out how much she pays weekly and then multiply it by the number of weeks in a month on average.
Firstly, we add together all of the weekly taxes she pays, which includes federal income tax ($68.45), state income tax ($22.81), and other taxes ($18.75). The sum equals $110.01.
Then, to convert this weekly tax to a monthly estimation, we multiply by an average of 4.33 weeks in a month (since not every month is precisely 4 weeks). Therefore, $110.01 * 4.33 is approximately $475.94.
Therefore, the best estimation for the monthly payroll tax that Kelly pays is $475.94.
Learn more about Payroll Tax here:https://brainly.com/question/9497135
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Find the values of x and y. Leave answers in simplest radical form.
[tex] \sin(60°) = \frac{x}{14} \Leftrightarrow x = 14 \sin(60°) = \frac{14 \sqrt{3} }{2} = 7 \sqrt{3} \\ \cos(60°) = \frac{y}{14} \Leftrightarrow y = 14\cos(60°) = \frac{14}{2} = 7[/tex]
To factor the expression x³ - y³ into factors of the lowest possible order, we can use the formula for factoring a difference of cubes: a³ - b³ = (a - b)(a² + ab + b²). In this case, we have x³ - y³, so our factors are (x - y)(x² + xy + y²). These are the factors using complex coefficients.
Explanation:To factor the expression x³ - y³ into factors of the lowest possible order, we can use the formula for factoring a difference of cubes: a³ - b³ = (a - b)(a² + ab + b²). In this case, we have x³ - y³, so our factors are (x - y)(x² + xy + y²).
These are the factors using complex coefficients. To find the factors using real coefficients, we can use the fact that a complex conjugate pair of roots will always have real coefficients. Therefore, the factors using real coefficients will be (x - y)(x² + xy + y²).
What is the measure of ∠L ? A right triangle L M N. Angle M is marked as a right angle. Side L M is labeled as 18 inches. Side L N is labeled as 60 inches.
Answer:
72.54°
Step-by-step explanation:
Given that triangle LMN is a right-angle triangle and LM=18 inches and LN =60 inches then;
applying the cosine rule
cos ∠L=Adjacent/hypotenuse
cos∠L=18/60
cos∠L=0.3
cos⁻¹ ∠L= 72.54°
Answer:
72.54°
Step-by-step explanation: