[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{h}{-3}~~,~~\stackrel{k}{4})\qquad \implies f(x) = a[x-(-3)]^2+4\implies f(x) = a(x+3)^2+4 \\\\\\ \textit{we know that} \begin{cases} x=0\\ f(x) = -5 \end{cases}\implies -5=a(0+3)^2+4\implies -5=9a+4 \\\\\\ -9=9a\implies \cfrac{-9}{9}=a\implies \boxed{-1=a}~\hfill \blacktriangleright f(x)=-(x+3)^2+4 \blacktriangleleft[/tex]
At a concert the ratio of adults to children is 4:5. There are 720 children in a concert how many adults are there?
BRAINLIEST QUEATION !!
Answer:
576 adults
Step-by-step explanation:
The 5 part of the ratio relates to 720 children, then
720 ÷ 5 = 144 ← value of 1 part of the ratio , then
4 parts = 4 × 144 = 576 ← number of adults
Answer:
576
Step-by-step explanation:
Adults : Children
4 : 5
x : 720
Let the number of adults be x.
Use cross multiplication.
[tex]4 : 5\\ x : 720\\[/tex]
[tex]4 *720=5*x[/tex]
[tex]\frac{4*720}{5} =\frac{5x}{5}[/tex]
4 × 144 = x
576 = x
Hope this helps you.
Let me know if you have any other questions :-)
Simplify the following expression
3x + 2(x +6) -4 -2x
A. 3x + 2
B. 7x + 8
C. 3x + 8
D.7x + 10
Answer:
C
Step-by-step explanation:
3x+2(x+6)-4-2x.
First, we do the parenthesis.
This gives us: 3x+2x+12-4-2x.
Then, we reorder so like terms are together.
This gives us: 3x+2x-2x+12-4.
Then, we combine like terms.
This gives us: 3x+8, which is C.
1. The following sets of data shows the mean marks of 43 interviewees from a certain job interview that was conducted by a HR Consulting Firm in Mombasa: 23, 45, 79, 15, 47, 64, 33, 26, 34, 46, 31, 29, 49, 25, 45, 43, 39, 45, 22, 26, 28, 36, 42 Using the concept of sampling distribution, what sample size will give at least a 0.95 probability that the sample mean is greater than $8 of the population mean?
Using the Central Limit Theorem, it is found that a sample size of 13 is needed.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, using a calculator:
The mean is [tex]\mu = 37.9[/tex]The standard deviation is [tex]\sigma = 14.07[/tex]The sample size needed is n when [tex]s = 4[/tex], as by the Empirical Rule, 95% of the measures are within 2 standard errors of the mean, hence [tex]2s = 8 \rightarrow s = 4[/tex]
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
[tex]4 = \frac{14.07}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 14.07[/tex]
[tex]\sqrt{n} = \frac{14.07}{4}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{14.07}{4}\right)^2[/tex]
[tex]n = 12.37[/tex]
Rounding up, a sample size of 13 is needed.
A similar problem is given at https://brainly.com/question/24663213
help on math review edu
Answer:
Answer is A
Step-by-step explanation:
Subtract 47 from both sides to get 0
3x² - 18x - 42 = 0
Use Quadratic formula to get
[tex]3+\sqrt{23} \\3-\sqrt{23}[/tex]
Answer:
Step-by-step explanation:
Subtract and simplify. 12 3\8 − 9 1\8 =
Answer:
[tex]3\dfrac{1}{4} \ \ or \ \ 3,25[/tex]
Step-by-step explanation:
[tex]\displaystyle12 \frac{3}{8} -9\frac{1}{8} =12-9+\frac{3}{8} -\frac{1}{8} =3+\frac{2}{8} =3\frac{1}{4} \ \ or \ \ 3,25[/tex]
If it takes you 2 1/2 hours to assemble one unit, how many units will you complete in 15 hours? (Change 2 1/2 to improper fraction first)
Answer:37.5
Step-by-step explanation:
2 1/2 as an improper fraction is 5/2
If i'm wrong tell me please i hope this helped you
The graph of g(x) = x + 2 is a translation of the graph of the parent function 2 units [ A. right , B. left , C. up , D. down ].
The graph of g(x) = 3(–x) is the graph of the parent function stretched vertically and reflected across the [ A. x-axis, B. y-axis ].
The graph of g(x) = (5x) is a [ A. vertical stretch, B. vertical compression, C. horizontal stretch ,D. horizontal compression ] of the graph of the parent function.
Answer:
Step-by-step explanation:
1. C
2. B
3. D
Dr. Smith can see 12 patients in 2 hours. At this rate, how long would it take him to see 96 patients?
OA. 576 hours
Step-by-step explanation:
set up a proportion
12 patients. 96 patients
---------------- = ------------------
2 hours. ?
96 • 12 = 1152
1152 ÷ 2 = 576 hours
Answer:
16hours
Step-by-step explanation:
12=2
96=x
crossmultiply
12x=192
x=192÷12
x=16
Please help and give real answers it would be much appreciated
Answer:
x = 8, x = 10
Step-by-step explanation:
[tex]\sqrt{4x - 31}[/tex] = x - 7 ( square both sides )
4x - 31 = (x - 7)² ← expand using FOIL
4x - 31 = x² - 14x + 49 ( sub 4x - 31 from both sides )
0 = x² - 18x + 80 ← in standard form
0 = (x - 8)(x - 10) ← in factored form
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x - 10 = 0 ⇒ x = 10
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 8
left side = [tex]\sqrt{4(8)-31 }[/tex] = [tex]\sqrt{32-31}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 8 - 7 = 1
Then x = 8 is a solution
x = 10
left side = [tex]\sqrt{4(10)-31}[/tex] = [tex]\sqrt{40-31}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = 10 - 7 = 3
Then x = 10 is a solution
can someone please help me with this one question!
Answer:
RST≈TSR FOR YOU PLAESE RANK ME HELPING HAND
which of the following explains why 2/3(x+3)=2/3(x-6)has no solution
Answer:
D. The coefficients are the same, and the constants are different
Step-by-step explanation:
This means that because we have the same coefficient (2/3), if we wanted the same equation, the constants (x +/- #) would have to be the same, and since they are not in this instance, that makes the equation false, and therefore has no solution
Round to 2 decimal places 0.966
Answer:
Step-by-step explanation:
round to 2 places 0.966: 1.00
The largest frog in the world is the goliath, It can grow to be 12 inches long. The smallest frog in the world is about 2.5% as log as the goliath. About how long is the smallest frog in the world
Answer:
0.3 inches
Step-by-step explanation:
2.5% = 0.025
The smallest frog is 12 * 0.025 inches, which is 0.3 inches.
50 pencils cost £3. How much would 8 pencils
cost
What is the answer
Answer:
0.48£
Step-by-step explanation:
(3x8)/50=0.48£
When bisecting segments and angles, which step is the same?
Yesterday, there were 96 problems assigned for math homework. Hanson got 72 out of 96 problems correct. What percentage did Hanson get correct?
Answer:
He got 75% correct
Step-by-step explanation:
72/96 = 3/4 = 0.75
0.75 × 100 = 75%
Evaluate the expression -2
Answer: 2x for x=3: 2(3) = 6.
Step-by-step explanation:
What is an equation of the line that passes through the points (-2,1) and (6,-7)
4) 4+ 1 =
a) 5
b) 572
12
c) 51
d) 572
6
12
Answer:
4+1=5
Step-by-step explanation:
Note down the below rules
(+)(+)=(+)(-)(+)=(-)(+)(-)=(-)(-)(-)=(+)A dealership is allowing residents to test drive the following vehicles: 2 sports cars, 3 vans, and 3 trucks. If you select a random car to test drive, what are the odds it is not a sports car? Write your answer in the form a:b as a fully reduced ratio.
Answer:3:1
Step-by-step explanation:
There are 2 sports cars out of a total of 8 total cars, so there are 2 favorable outcomes, and 8−2=6 unfavorable outcomes.
The odds against choosing a sports car are 6:2.
Both numbers are divisible by 2, so this ratio can be simplified to 3:1.
Select the correct answer
Consider the given solids with the dimensions shown. Which solids are similar?
Aonly figure 1 and figure 2
B.only figure 2 and figure 3
c.only figure 1 and figure 3
D. all three figures
E none of the figures
only figure 1 and figure 3 are similar.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
In figure 1, two of the sides (16 and 9 ) are perfect square and third is not.
If we take the ratio of three side as
16:9:12
(4)²:(3)²:(2√3)²
Similarly, In figure 3 two of the sides (64 and 36 ) are perfect square and third is not.
If we take the ratio of three side as
64:36:48
(8)²:(6)²:(4√3)²
Comparing the ratios of both figure, the figure 3 has twice the measurement of figure 1 sides.
Hence, only figure 1 and 3 are similar.
Learn more about this concept here:
https://brainly.com/question/12670209
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Steve drives at a constant speed of 59.3 mph. How far should he expect to drive in 7/8 hr?
Answer:
51.9 miles
Step-by-step explanation:
distance = speed * time
d = 59.3 * 7/8
d = 51.8875 miles
rounded
51.9 miles
A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories. Determine how many calories 14 brownies would have. Round to the nearest calorie
The number of calories in 14 brownies is 233 calories.
The first step is to determine the average calorie in 1 brownie.
Average calorie = 50 calories / 3 = 16.667 calories
In order to determine the number of calories in 14 brownies, multiply the average calorie by 14 brownies.
Total calories = 16.67 x 14 = 233 calories
A similar question was answered here: https://brainly.com/question/15420908
PLEASE HELP WITH THIS ONE QUESTION
Answer:
(x-1) (x-4) is the answer
Which expressions are equivalent to (13x+x−53x)−(−43x+2) ?
Answer:
4x+2
Step-by-step explanation:
(13x+x−53x)−(−43x+2)
Group all the same variables on each side.
(-39x)-(-43x+2)
-39x+43x+2
4x+2
Hope this helps :)
Answer: x-2 & -2-x+2x
Step-by-step explanation:
a rectangle is made by joining two squares adjacent to each other as shown below. if one squared has an area of 144 squared centimeters what is the area of the rectangle?
Answer:
Hello! After reading your question I have deduced that the correct answer is 288² cm.
Step-by-step explanation:
The way I came to this conclusion was as follows:
Firstly:
If said rectangle is two squares put side by side (adjacent), then a valid assumption is that both squares are the same size.
This is because all four sides of a square have to be equal.
Thus if the two squares are joined together on one side, then all the other sides of both the squares will be the same length.
Thus both of the squares are going to be the same size, so they will have the same area.
Secondly:
If the area of one square is 144² cm then the area of the other square should also be 144² cm.
Thus if you combine the areas of both the squares, that make up the rectangle, you are left with the area of the rectangle being 288² cm.
I hope this helped!
Help help help help help help help help
Answer:
7
Step-by-step explanation:
15-8 is 7
16-8 is 7
17-10 is 7
18-11 is 7
this fits the eqation.
hope this helps you
Octavia is making cotton candy. She uses 17.5 cups of sugar to make 5 bags of cotton candy. At this rate, how many cups of sugar are used to make 1 bag of cotton candy?
Answer:
3.5 cups of sugar per bag.
Step-by-step explanation:
17.5/5
3.5 cups of sugar are used to make 1 bag of cotton candy
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
For 5 bags of candy = 17.5 cups of sugar needed
and, For 1 bags of candy
=17.5/ 5
=3.5 cups of sugar needed
hence, 3.5 cups of sugar are used to make 1 bag of cotton candy
Learn more about unitary method here:
https://brainly.com/question/22056199
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please i need help
How many rows of seats are inside the theater? Enter your answer in the box.
Answer:
24 rows
Step-by-step explanation:
384 seats in total, and 16 chairs in a row, so 384/ 16=
24 rows
Hope this helps!
LMK if it does
After watching some fish 55 feet below the surface of the water, a scuba diver went up 25 feet to explore a coral reef. Use a number line to help you create an equation that shows the location of the coral reef in relation to the water's surface.︎︎︎︎︎︎︎ ︎︎︎︎
It might be A
I really dont know lol
Answer:
The answer is C.
Step-by-step explanation:
Consider 5 1/2 as 5.5 to make it less confusing. Now, subtract 8 from 5.5.
5.5 - 8
=> -2.5
Now, let's turn -2.5 back in fraction form.
=> -2 1/2
Therefore, C is the answer