Answer:
The vertex is the point (-6,-34)
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
In this problem we have
[tex]y=x^{2}+12x+2[/tex]
Convert in vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y-2=x^{2}+12x[/tex]
Complete the square . Remember to balance the equation by adding the same constants to each side.
[tex]y-2+36=x^{2}+12x+36[/tex]
[tex]y+34=x^{2}+12x+36[/tex]
Rewrite as perfect squares
[tex]y+34=(x+6)^{2}[/tex]
[tex]y=(x+6)^{2}-34[/tex]
The vertex is the point (-6,-34)
Question about Radicals.
Answer:
Conjugate
Step-by-step explanation:
Those are conjugates. In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign. They will always come in pairs. Same with imaginary numbers.
This question might be confusing to me because it talks about Unknown angle problems with Algebra and I may need help on this, please.
Answer:
40 = x
Step-by-step explanation:
They reflect each other like a mirror, so set 120 equal to 3x, then simply divide by 3 to get your answer.
Please help! Brainliest if correct!
Answer:
x:(x +15)
Step-by-step explanation:
The corresponding sides that are in proportion are apparently ...
PS:PQ = PT:PR
PT = x
PR = x+15
so the proportion of interest is ...
28:40 = x:(x+15)
draw a diagram for this statement
eight percent of the 320 students like sports
use your diagram to determine the number of students who do not like sports
Approximately 26 out of 320 students like sports. Therefore, about 294 students do not like sports.
Explanation:To draw a diagram for the given statement, we begin with understanding that the total of 320 students represents 100%. Therefore, if 8% of the students like sports, we would multiply 320 by 0.08 (or 8%).
The calculation would be:
320 * 0.08 = 25.6
However, because we cannot have a fractional student, we round this figure to 26. This implies that about 26 students like sports.
To calculate the number of students who do not like sports, subtract the number that do from the total, which is 320. That calculation would be:
320 - 26 = 294
Therefore, approximately 294 students do not like sports.
Learn more about Percentages here:https://brainly.com/question/30697911
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Half of the students in a freshman class are 14 years old one third are 15 and the rest are 13 . Is the mean age greater than or less than the median age
Answer:
the mean age is greater
Step-by-step explanation:
The mean age is ...
(1/2)14 + (1/3)15 + (1/6)13 = 14 1/6
The median age is 14. (half the students are 14 or younger)
The mean age is greater.
_____
1 -1/2 -1/3 = 6/6 -3/6 -2/6 = 1/6 . . . . . 1/6 of the students are 13.
Answer:
Step-by-step explanation:
Given that half of the students in a freshman class are 14 years old one third are 15 and the rest are 13
If no of students are n, then we have
n/2 have ages as 14, n/3 as 15 and remaining n/6 as 13.
Average would be total/n
= [tex]\frac{\frac{14n}{2}+\frac{15n}{3} +\frac{13n}{6} }{n} \\=7+5+\frac{13}{6} =14.67[/tex]
Median would be middle entry when arranged in ascending order hence = 14
Mean > median
Each cone of the hourglass has a height of 15 millimeters. The total height of the sand within the top portion of the hourglass is 45 millimeters. The radius of both cylinder and cone is 6 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
Answer:
The answer is 126 seconds.
Step-by-step explanation:
Volume of the cone is given as:
[tex]\frac{1}{3} \pi r^{2} h[/tex]
Volume of cylinder is given as:
[tex]\pi r^{2} h[/tex]
We can find the total volume of the sand by adding volume of cone and volume of cylinder.
Height for cylinder is 30 mm (as we will subtract the cone height from 45mm that is 45-15=30)
Total volume of sand = [tex]\pi /3*(6^{2})*(15)[/tex] + [tex]\pi *(6)^{2}*(30)[/tex] = 1260π mm³
Given is - Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second.
So, for all the sand to drip down, it will take [tex]\frac{1260\pi }{10\pi }[/tex]= 126 seconds.
Could someone check that I did this correctly? It's about complex numbers. Thank you!
Answer:
All your steps are correct. Well done!
A country has 50 million people, 30 million of whom are adults. Of the adults, 5 million are not interested in working, another 5 million are interested in working but have given up looking for work, and 5 million are still looking for work. Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time. What is this country's labor force participation rate?
Answer:
66.7% is the answer.
Step-by-step explanation:
A country has 50 million people, 30 million of whom are adults.
Of the adults, 5 million are not interested in working.
5 million are interested in working but have given up looking for work.
5 million are still looking for work.
Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time.
Total labor force = Employed people + Unemployed people
=> 15 million+ 5 million = 20 million
The labor force participation rate is [tex]\frac{20million}{30million} \times100[/tex]
= 66.66% ≈ 66.7%.
The labor force participation rate of the country is 66.7%, calculated by dividing the number of employed and actively seeking employment individuals (20 million) by the total adult population (30 million) and multiplying by 100.
To calculate the labor force participation rate, we include only those adults who are either employed or actively seeking employment. In the given scenario, the country has 30 million adults. Out of these, 5 million are not interested in working, 5 million have given up looking for work, and there are 15 million employed (10 million full-time and 5 million part-time). Therefore, the labor force includes those employed full-time, employed part-time, and those actively looking for work, adding up to 20 million.
The labor force participation rate is calculated by dividing the number of people in the labor force (20 million) by the total adult population (30 million) and multiplying the result by 100 to convert it into a percentage:
Labor Force Participation Rate = (Number in labor force ÷ Total adult population) x 100
Labor Force Participation Rate = (20 million ÷ 30 million) x 100
Labor Force Participation Rate = (2÷3) x 100
Labor Force Participation Rate = 66.7%
Find the GCF of the following numbers:
n and (n-1), where n is a natural number, greater than 1.
13 POINTS! NEED ANSWER QUICK! THANKS!!
Answer:
1
Step-by-step explanation:
The numbers are mutually prime, so the GCF is 1.
Answer:
1
Step-by-step explanation:
n-1 and n are consecutive integers.
Examples of consecutive pairs:
(7,8)
(10,11)
(100,101)
and so on...
The remainder will always be 1 when doing n divided by n-1.
n=(n-1)(1)+1.
All this is here to try to convince you that n and n-1 will only have common factor of 1.
Please help with #12
Answer:
a. 1 1/8 b. 8/9
Step-by-step explanation:
You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:
[tex]\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}[/tex]
Cross multiplying gives you:
[tex]\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}[/tex]
The 3's on the right cancel out nicely, leaving you with
[tex]\frac{2}{3}x=\frac{1}{4}[/tex]
To solve for x, multiply both sides by 3/2:
[tex]\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}[/tex] gives you
[tex]x=\frac{3}{8}[/tex]
That means that the road is still missing 3/8 of a mile til it's finished. The length of the road is found by adding the 3/4 to the 3/8:
[tex]\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}[/tex]
So the road is a total of 1 1/8 miles long.
For b. we need to find out how much of 1 1/8 is 1 mile:
1 mile = x * 9/8 and
x = 8/9. When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.
I really need this answer
Answer:
D
Step-by-step explanation:
If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.
The answer is:
If the red line has a slope of 3, the slope of the red line will also be 3.
So, the correct option is, D. 3
Why?We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.
So, if two lines are parallel, and one of them (the red line) has a slope of 3, the slope of the other line (the green line) will also be 3.
Have a nice day!
Stone Pine Corporation, a calendar year taxpayer, has ending inventory of $150,000 on December 31, 20X2. During the year 20X2, the corporation purchased additional inventory of $375,000. If cost of goods sold for 20X2 is $470,000, what was the beginning inventory at January 1, 20X2?
Answer:
beginning inventory is $245000
Step-by-step explanation:
Given data
ending inventory = $150,000
purchased additional inventory = $375,000
goods sold = $470,000
to find out
beginning inventory
solution
according to question beginning inventory is calculated by this formula i.e.
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase .....................1
now put all value cost of goods sold, ending inventory and amount of inventory purchase in equation 1 and we get beginning inventory
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase
beginning inventory = ( 470000 + 150000 ) - 375000
beginning inventory = 245000
so beginning inventory is $245000
What is the equation of the line with m = 2.5 and b = 7? A. y = −2.5x − 7 B. y = 2.5x −7 C. y = −2.5x + 7 D. y = 2.5x + 7
Answer:
y=2.5x+7
Step-by-step explanation:
You are basically being asked to use slope-intercept form for linear equations. It says y=mx+b where m is the slope and b is the y-intercept.
Plug in 2.5 for m and 7 for b giving you y=2.5x+7.
The equation is: y = mx + b
y = 2.5x + 7
so it's option D.
In formulating hypotheses for a statistical test of significance, the null hypothesis is often
A) A statement of “no effect” or “no difference.
B) The probability of observing the data you actually obtained.
C) A statement that the data are all
D) 0. 0.05.
Answer:
A) A statement of “no effect” or “no difference.
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.
16%
32%
34%
84%
Answer:
The answer is 16%
Step-by-step explanation:
Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes
so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean
Use the probability table:
The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes
= Probability of z being outside 1 SD from mean
= 1 - Probability of z within 1 SD from mean
= 1 - 0.84
= 0.16 or 16%....
A bag contains 12 red marbles, 5 yellow marbles, and 15 green marbles. How many additional red marbles must be added to the 32 marbles already in the bag so that the probability of randomly drawing a red marble is ?
Answer:
18 red marbles.
Step-by-step explanation:
The complete question asks the probability of randomly drawing a red marble is 3/5?
Let x be the number of red marbles that must be added.
To find x we will do the following:
[tex]\frac{x+12}{x+32} =\frac{3}{5}[/tex]
=>[tex]5(x+12)=3(x+32)[/tex]
=> [tex]5x+60=3x+96[/tex]
=> [tex]2x=36[/tex]
This gives x = 18
Hence, 18 red marbles will be added to the bag.
Please help *image attached*
Answer:x=25
Step-by-step explanation:
One line is 180 , AB equals 180 ,angle AD is 110,180-110=70
So corner O on line DC is 70 and angle CE is 60. 60+70=130
180-130=50, 2x=50,50/2=25
Three fourths of a gasoline storage tank is emptied by filling each of five trucks with the same amount of fuel what part of the total capacity of the storage tank did each vehicle receive
Answer:
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
Step-by-step explanation:
we know that
To find out what part of the total capacity of the storage tank that each vehicle received, divide three fourths by five
so
[tex]\frac{(3/4)}{5}=\frac{3}{20}[/tex]
therefore
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
A widget company produces 25 widgets a day,5 of which are defective.Find the probability of selecting 5 widgets from the 25 produced where none are defective
Answer:
1/5
Step-by-step explanation:
The probability of selecting 5 widgets from the 25 produced where none are defective is 0.2914.
To calculate the probability of selecting 5 non-defective widgets from the 25 produced.
The number of ways to choose 5 non-defective widgets:
[tex]\[ \binom{20}{5} = \frac{20!}{5!(20-5)!} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{1860480}{120} \][/tex]
= 15504
The total number of ways to choose 5 widgets from the 25 produced:
[tex]\[ \binom{25}{5} = \frac{25!}{5!(25-5)!} \][/tex]
[tex]\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{7893600}{120} \][/tex]
= 53130
The probability:
Probability = (Number of ways to choose 5 non-defective widgets)/(Total number of ways to choose 5 widgets)
[tex]\[ = \frac{15504}{53130} \][/tex]
[tex]\[ = 0.2914 \][/tex]
Complete question:
A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.
The problem is in the pictures, please show step by step how to do it. Thanks! :)
Answer:
-4,-5/2
Step-by-step explanation:
2x^2+3x-20 =0
2x^2+8x-5x-20 =0
2x(x+4)-5(x+4) =0
(x+4)(2x-5) =0
Either,
x+4=0
x=-4
Or,
2x-5=0
2x=5
x=5/2
[tex]2x^2+3x-20=0\\2x^2+8x-5x-20=0\\2x(x+4)-5(x+4)=0\\(2x-5)(x+4)=0\\x=\dfrac{5}{2} \vee x=-4[/tex]
Select the correct answer.
What is the sum of
The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
- 6 ⁴/₅ and 6 ⁴/₅
Convert the mixed fraction number into a fraction number. Then we have
- 6 ⁴/₅ = -34/5
6 ⁴/₅ = 34/5
Then the sum of the expressions will be given as,
⇒ - 34/5 + 34/5
⇒ 0
The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.
More about the Algebra link is given below.
https://brainly.com/question/953809
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Use division of numbers in scientific notation to answer the question.
(8.64 × 104)
(2.4 × 102)
What is the quotient in scientific notation?
3.6 × 102
6.24 × 102
1.104 × 107
2.0736 × 109
Answer:
[tex]3.6*10^{2}[/tex]
Step-by-step explanation:
we have
[tex]\frac{8.64*10^{4}}{2.4*10^{2}}=\frac{8.64}{2.4}*10^{4-2}\\ \\=3.6*10^{2}[/tex]
Answer:
A) 3.6 × 10^2
Step-by-step explanation:
Got it right in the instruction on Edge 2021 ;D
Identify the three similar triangles in the figure we should to name the verticals in the correct order
Answer: ΔABC ~ ΔBDC ~ ΔADB
Step-by-step explanation:
Match the degrees of each angle:
In ΔABC: ∠A = 60° , ∠B = 90° , ∠C = 30°
In ΔBDC: ∠B = 60° , ∠D = 90° , ∠C = 30°
In ΔADB: ∠A = 60° , ∠D = 90° , ∠B = 30°
Answer:
See below.
Step-by-step explanation:
Triangle ABC is similar to triangle ADB is similar to triangle BDC.
I SEE YALL LOOKING BUT NOT HELPING PLEASE SOMEONE
Answer:
the pitcure isnt clear.
Given the geometric sequence where a1 = 4 and the common ratio is 3, what is the domain for n?
A) All integers where n ≥ 1
B) All integers where > 1
C) All integers where n ≥ 4
D) All real numbers
Answer:
The correct option is A.
Step-by-step explanation:
According to statement a1 = 4 and r = 3. This shows that r is greater than 1.
If r is greater than 1 than it includes integers greater than 1 or equal to 1. It does not include all the real numbers because real numbers include negative numbers also.
If starting value is 4,if we put n=0, then we get 4, but if we put a negative value than we would get a number which is not a part of our sequence. Thus the correct option is All integers where n ≥ 1....
Answer:
The answer is A. All integers where n > 1
Step-by-step explanation:
The domian for n is restricted and cannot be less than 1 and the domain is the x value while 4 would be a y value.
Geometry: write a two column proof
Step-by-step explanation:
[tex]\angle1\ and\ \angle 2\ \text{are complementary}\to m\angle1+m\angle2=90^o\\\\m\angle ACX=m\angle1+m\angle2=90^o\to XA^{\to}\perp XC^{\to}[/tex]
Use the following net to find the surface area of the solid figure it represents.
For this case we have that by definition, the surface area of a cylinder is given by:[tex]SA = LA + 2B[/tex]
Where:
LA: It is the lateral area of the cylinder
B: It is the area of the base
We have as data that:
[tex]LA = 75.36 \ cm ^ 2\\B = 28.26 \ cm ^ 2[/tex]
Substituting:
[tex]SA = 75.36 + 2 (28.26)\\SA = 75.36 + 56.52\\SA = 131.88[/tex]
Finally, the surface area is:
[tex]131.88 \ cm ^ 2[/tex]
Answer:
Option D
Answer:
The solid formed is a cylinder
The total surface area is [tex]131.88cm^2[/tex]
Step-by-step explanation:
The given net is made up of a rectangle and two circles.
The total surface area is the area of the rectangle plus the area of the two circles.
This implies that:
[tex]S.A=75.36+2(28.26)[/tex]
[tex]\implies S.A=75.36+56.52[/tex]
[tex]\implies S.A=131.88cm^2[/tex]
The rectangular surface can be folded into the curved surface of a cylinder with the two circles becoming the lid.
YO PLZ HELP ASAP!!! MARKIN BRAINIEST!!!
Answer:
My estimate would be D, if you view 0, -23 as the vertex and compare the other values, the values on D show the most similarities.
Definitely not B since it's exponential.
NEED HELP WITH A MATH QUESTION
Answer:
33π square units
Step-by-step explanation:
The area of a sector is given by this formula. The larger sector angle is 2π-π/6 = 11π/6 radians.
A = (1/2)r²θ = (1/2)6²(11π/6) = 33π . . . . square units
Answer:
Area of larger sector = 33π units²
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where 'r' is the radius of circle
To find the area of circle
Here r = 6 units
Area = πr²
= π * 6²
= 36π units²
To find area of large sector
The central angle of larger sector = 360 - 30 = 330
Area of larger circle = (330/360) * area of circle
= (330/360) * 36π
= 33π units²
Simplify 4/25 divided by 5/7
Answer: 28/125
Step-by-step explanation: To divide two fractions, flip the second fraction and multiply. The equation will be:
4/25 x 7/5
Multiply the numerators by the numerators and the denominators by the denominators.
4 x 7 = 28 (numerator)
25 x 5 = 125 (denominator)
Put into a fraction.
28/125