Answer:
A: -21
Step-by-step explanation:
Vertex of a quadratic function:
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]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic function:
[tex]g(x) = x^2 - 6x - 12[/tex]
So [tex]a = 1, b = -6, c = -12[/tex].
Minimum value:
This is the y-value of the vertex. So
[tex]\Delta = b^2-4ac = (-6)^2 - 4(1)(-12) = 36+48 = 84[/tex]
[tex]y_{v} = -\frac{\Delta}{4a} = -\frac{84}{4} = -21[/tex]
The minimum value is -21, and the correct answer is given by option A.
12 ducks fly overhead. Each of 6 hunters picks one duck at random to aim at and kills it with probability 0.6. What's the expected number of hunters who hit the duck they aim at?
Answer:
The expected number of hunters who hit the duck they aim at is 3.6
Step-by-step explanation:
Given;
number of hunters, n = 6
the probability of killing a duck, p = 0.6
The expected number of hunters who hit the duck they aim at?
In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.
The expected number of hunters who hit the duck they aim at is calculated as follows;
E = np
E = 0.6 x 6
E = 3.6
Therefore, the expected number of hunters who hit the duck they aim at is 3.6
Which expression is equivalent to 3/56x^7y^5 , if x ≠0 and y≠0
Answer:
[tex]2x^2y\sqrt[3]{7xy^2}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{56x^7y^5}[/tex]
Required
Solve
Expand
[tex]\sqrt[3]{8*7*x^6*x*y^3*y^2}[/tex]
Rewrite as:
[tex]\sqrt[3]{8*x^6*y^3*7*x*y^2}[/tex]
Split
[tex]\sqrt[3]{8*x^6*y^3} *\sqrt[3]{7*x*y^2}[/tex]
Express 8 as 2^3
[tex]\sqrt[3]{2^3*x^6*y^3} *\sqrt[3]{7*x*y^2}[/tex]
Apply law of indices
[tex]2^{(3/3)}*x^{(6/3)}*y^{(3/3)} *\sqrt[3]{7*x*y^2}[/tex]
[tex]2*x^2*y *\sqrt[3]{7*x*y^2}[/tex]
[tex]2x^2y *\sqrt[3]{7xy^2}[/tex]
[tex]2x^2y\sqrt[3]{7xy^2}[/tex]
Solve x2 + 13x + 22 = 0 using the quadratic formula.
x^2 + 13x + 22 = 0
( x + 11 )( x + 2 ) = 0
x = - 11 Or x = - 2
It takes Miguel 18 minutes to finish reading 4 pages of a book. How long does it take him to finish reading 30 pages
Answer: 135 minutes or 2 hours and 15 minutes
Step-by-step explanation:
4/18 = 30/ x
Solve for duh 'x'
The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below.
Robert, 1.11 Juan, 1.66 Susan, –1.9 Joel, 0.00 Jan, –0.65 Linda, 1.46
(a) Which of these students scored above the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(b) Which of these students scored on the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(c) Which of these students scored below the mean?
a. Jan
b. Joel
c. Juan
d. Linda
e. Robert
f. Susan
(d) If the mean score was ? = 156 with standard deviation ? = 24, what was the final exam score for each student? (Round your answers to the nearest whole number.)
a. Janb. Joelc. Juand. Lindae. Robertf. Susan
Answer:
a)
b. Joel
c. Juan
d. Linda
b)
b. Joel
c)
a. Jan
f.Susan
d)
a. Jan: 140
b. Joel: 156
c. Juan: 196
d. Linda: 191
e. Robert: 183
f. Susan: 110
Step-by-step explanation:
Z-score:
In a set 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]
The Z-score measures how many standard deviations the measure is from the mean, positive z-scores are above the mean, negative are below the mean and 0 is the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Question a:
Robert, Juan and Linda had positive z-scores, so they scored above the mean, and the correct options are c,d,e.
(b) Which of these students scored on the mean?
Joel, which had a z-score of 0, so the correct option is b.
(c) Which of these students scored below the mean?
Jan and Susan had negative z-scores, so them, options a and f.
Question d:
We have that [tex]\mu = 156, \sigma = 24[/tex], so we have to find X for each student.
Jan:
Z = -0.65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.65 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = -0.65*24[/tex]
[tex]X = 140[/tex]
b. Joel
Z = 0, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 0*24[/tex]
[tex]X = 156[/tex]
c. Juan
Z = 1.66, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.66 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.66*24[/tex]
[tex]X = 196[/tex]
d. Linda
Z = 1.46. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.46 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.46*24[/tex]
[tex]X = 191[/tex]
e. Robert
Z = 1.11. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.11 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = 1.11*24[/tex]
[tex]X = 183[/tex]
f. Susan
Z = -1.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.9 = \frac{X - 156}{24}[/tex]
[tex]X - 156 = -1.9*24[/tex]
[tex]X = 110[/tex]
HELP PLEASE giving out brainilest
9514 1404 393
Answer:
160 cm³
Step-by-step explanation:
The ratio of the linear dimensions is the square root of the ratio of areas:
scale factor B/A= √(64/144) = 8/12 = 2/3
The ratio of volumes is the cube of the scale factor:
(volume B)/(volume A) = (2/3)³ = 8/27
Then the volume of pyramid B is ...
volume B = (volume A) × (volume B)/(volume A)
= (540 cm³) × (8/27) = 160 cm³ . . . . volume of pyramid B
_____
Equivalently, the ratio of volumes is the 3/2 power of the ratio of areas.
Vb = Va(64/144)^(3/2) = (540 cm³)(4/9)^(3/2) = (540)(8/27) cm³ = 160 cm³
PLEASE HELP ASAP I NEED THIS LIKE RIGHT NOW NO LINKS OR WILL BE REPORTED! SHOW ALL OF YOUR WORK! 3. The area of the square rug is 484 feet squared. (a) What is the length of one side? Write it as a square root. SHOW ALL OF YOUR WORK. (Hint: How do you find the area of a square? What is the equation?) (b) write the area as a number squared SHOW ALL OF YOUR WORK
Answer:
well,
it's more than (20ft)²
bc 20*20 =400
21² = 21 * 21 = 441
getting closer...
22² = 22 * 22 = 484
[tex] \sqrt{484} = {22}^{2} [/tex]
yet, we arrived, short trip tough, pls leave the bus in an orderly manner
HELP ME PLZ WILL MARK U AS BRAINLIEST
Answer:
Step-by-step explanation:
a)
The mean for ground floor is 20.67
The mean for balcony is 15.8
b)
the difference between the means is ground floor - balcony
20.67 - 15.8 = 4.87
You can talk about it yourself for part c
Somebody Please Help!!!
Step-by-step explanation:
11. shape 1 => A = ½×17×10=85m²
shape 2=> A = 17×9 =153 m²
total area = 238 m²
12. shape 1 => A = 7×3= 21 m²
shape 2=> A = 3×2 = 6 m²
total area = 27 m²
PLZ HELP ASAP
The white triangle drawn on the road sign in the picture has a height of 8 and a base of 5 which formula would be correct to find the area of this triangle
1) A= 1/2 (8) (5)
2) A=2(8)+2(5)
3) A=1/2(8+8)(5+5)
4) A=2(8)(8)+2(5)(5)
Answer:
[tex]\text{1) }\frac{1}{2}(8)(5)[/tex]
Step-by-step explanation:
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is equal to [tex]A=\frac{1}{2}bh[/tex]. Since we're given a base of 5 and a height of 8, the area is given by [tex]\boxed{\text{1) }\frac{1}{2}(8)(5)}[/tex].
Can you help? What do you think ??
Answer:
The amount of money one may spend in a month may be greater than that of ones monthly payment especially when the payment is at a lower rate.
The time it takes to build a house (T), varies directly with the floor area (A), and inversely with the number of workers (W). What is the equation that models this situation?
Answer:
T = k * (A/W)
Step-by-step explanation:
Someone pls help…. We need to find m angle f
Answer:
m<F = 95°
Step-by-step explanation:
We'll begin by calculating the value of x. This can be obtained as follow:
m<C = 50
m<A = (10x – 5)
m<B = m<G = (2x + 15)
m<C + m<A + m<B = 180 (Sum of angles in a triangle)
50 + (10x – 5) + (2x + 15) = 180
50 + 10x – 5 + 2x + 15 = 180
50 – 5 + 15 + 10x + 2x = 180
60 + 12x = 180
Collect like terms
12x = 180 – 60
12x = 120
Divide both side by 12
x = 120 / 12
x = 10
Finally, we shall determine the value of m<F. This can be obtained as follow:
m<F = m<A
But
m<A = 10x – 5
x = 10
Therefore,
m<F = 10x – 5
m<F = 10(10) – 5
m<F = 100 – 5
m<F = 95°
please answer thanks
Answer:
ED = 31
DT = 20
Step-by-step explanation:
m< ESD = 90-52=38°
the distance ED = 40×tan 38° = 31.25 = 31
ET = 40 x tan (90-38) = 40×tan 52°
= 51.19= 51
the distance DT = 51-31 = 20
Pablo deposits $5000 into an account that pays simple interest at a rate of 3% per year. How much interest will he be paid in the first 6years?
Answer:
$5900
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is time (in years)Step-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 3% = 0.03
t = 6
Step 2: Find Interest
Substitute in variables [Simple Interest Rate Formula]: A = 5000(1 + 0.03 · 6)(Parenthesis) Multiply: A = 5000(1 + 0.18)(Parenthesis) Add: A = 5000(1.18)Multiply: A = 5900
Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
Answer:
The relationship between the above two triangles is SAS and they are congruent
Christian Robbie are construction arytenoids stained glass window whose length is 7.3 inches longer than its width if the area of the window is 596.9 in.² find the width and the length
Answer:
w ≈ 21.053 inches
l ≈ 28.353 inches
Step-by-step explanation:
When setting the temperature of a refrigerator, is -1 or -5 the coldest!
Answer:
-5 is the answer
Step-by-step explanation:
Answer:
-5 corresponds to the coldest temperature here.
Step-by-step explanation:
-5 is to the left of -1 on a number line and is therefore smaller than -1.
Three fifths of the adults at a party are male.
There are 40 adults at the party.
How many of the adults are male?
hich is the graph of the linear equation x – 2y = 6?
On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, 3) and (6, 0).
Answer:
B or graph 2
Step-by-step explanation:
when y = 0 then x = 6
when x = 0 then y = -3
find those points
Answer: b
question
hich is the graph of the linear equation x – 2y = 6?
On a coordinate plane, a line goes through points (negative 6, 0) and (0, 3).
On a coordinate plane, a line goes through points (0, negative 3) and (6, 0).
On a coordinate plane, a line goes through points (negative 6, 0) and (0, negative 3).
On a coordinate plane, a line goes through points (0, 3) and (6, 0).
14.
Find the domain of
x ¹ -2 / x + 1
Answer:
?????????????????????????
The difference between the measures of two complementary angles is 56 determine the measures of the two angles. The larger angle has a measure of? And the smaller angle has a measure of?
Answer:
Larger angle= 73, smaller angle= 17
Step-by-step explanation:
I wrote an equation, and x is the measure of one of the angles
90=2x-56
90+56=2x-56+56
146=2x
73=x
One of the angles is 73, so subtract 53 from 73 to find the second angle. 73+56=17
You can make sure it adds up to a complementary angle by seeing if 17+73=90
The ratio of boys to girls in Mr. Johnsons after school club is the same as the ratio is the same to the ratio of boys to girls in Mr. Greene's after school club. There are 4 boys and 12 girls in Mr. Johnsons club. There are 6 boys in Mr. Greene's club. How many girls are in Ms. Greene's club?
Answer:
18 GIRLS
Step-by-step explanation:
1. Lets write a fraction (4 boys/12 girls)
[tex]\frac{4 \\boys}{12 \\ \\girls}[/tex]
2. Now lets plug the value in
[tex]\frac{6 \\boys}{x girls}[/tex]
3. In the original equation, the amount of girls is 3 times the amount of boys
4. multiply 6 and 3 = 18
5. 18 girls
Answer:
18 <3
Step-by-step explanation:
What is the area of the triangle
Answer:
60m^2 is the answer im pretty sure
Step-by-step explanation:
yeah man thats it
What is the solution of StartRoot x + 2 EndRoot minus 15 = negative 3?
9514 1404 393
Answer:
x = 142
Step-by-step explanation:
You want to find x such that ...
[tex]\sqrt{x+2} -15=-3\qquad\text{given}\\\\\sqrt{x+2} =12\qquad\text{add 15}\\\\x+2=144\qquad\text{square both sides}\\\\\boxed{x=142}\qquad\text{subtract 2 to get x by itself}[/tex]
Answer:
a
Step-by-step explanation:
Determine the value of x.
1) 14.75
2)15.25
3)11.92
4)18.56
Find the area of this shape!!
Answer:
if you assume one box as 1 m^2
then area of the shape is 54 m^2
but i am not sure if this is correct answer
44%adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
Answer:
.101501615
.84982392
.901244701
Step-by-step explanation:
For this question use a binomial distribtuion
a.
12C3*.44³*(1-.44)⁹= .101501615
b.
to find at least 4 find the probability of less than 4 and take its compliment
12C0*(1-.44)¹²+12C1*.44*(1-.44)¹¹+12C2*.44²*(1-.44)¹⁰+12C3*.44³*(1-.44)⁹= .15017608
1-.15017608=.84982392
c.
To find less than eight's probability find the proability of at least 8 and take its compliment
12C8*.44⁸(1-.44)⁴+12C9*.44⁹(1-.44)³+12C10*.44¹⁰(1-.44)²+12C11*.44¹¹*(1-.44)+12C12*.44¹²= .098755299
1-.098755299= .901244701
An unknown radioactive material is measured to have a half life of 3 months. When the material was first found, there was 2000mg. a) Write an equation that models the mass of the material, t months. b) Use your equation to determine the mass of material in 4 year c) Calculate around how many months it will take to have 750 mg left
Answer:
OK!!.
N=N(½)ⁿ
n= Time/half life
N=Remaining Mass
N°=Initial Mass or Mass before decay.
t= time taken to decay(Its in Months in this case)
t½= Half Life of the Material. This is the time taken to decay to half its initial value.
N°= 2000mg
a).Equation that Models this is
since n=t/t½
N=N°(½)ⁿ =
N=N°(½)^t/t¹'². This should be your answer.
b). We're asked to find the remaining mass of substance in 4years.
t= 4years
Our Half life is in Months... So we gotta convert or time t from year to Months too.
4yrs === 4x12 = 48Months.
N° was given as 2000mg
N=N°(½)^t/t½
N= 2000(½)^48/3
N=2000(½)^16
Using your calc to evaluate (½)^16... Then multiply by 2000
N=0.0305mg will remain after 4years.
Or After 16Half Lives since 1 half life is 3months
c). We're looking for t this time
N=N°(½)^t/t½
Since it asked for 750mg to remain ... 750 is now our N --- Remaining Mass
750 = 2000(½)t/3
To Isolate "t" and make it the subject
750/2000 = (½)^t/3
0.375 = (½)^t/3
Taking ln(natural log) of both sides
Ln(0.375) = Ln(0.5)^t/3
From the rule of logarithm...
You can bring the power (I.e t/3) to the front
You'll have
Ln(0.375) = t/3Ln(0.5)
Dividing both sides by Ln(0.5) to isolate t
Ln(0.375)/Ln(0.5) = t/3
t/3 = 1.415
t= 3x1.415
t=4.25months.
Have a great day.
Hope this helps... I'm open to questions if you have any too.
5:Pretest 5 Spatial Thinking
A point P has coordinates (-5, 4). What are its new coordinates after reflecting point P over the x-axis?
(-5, 4)
(-5,-4)
(5-4)
(5, 4)
Given:
The coordinates of point P are (-5,4).
Point P is reflected over the x-axis.
To find:
The new coordinates after the reflection.
Solution:
If a point is reflected across the x-axis, then the rule of reflection is:
[tex](x,y)\to (x,-y)[/tex]
Using this rule, we get
[tex]P(-5,4)\to P'(-5,-4)[/tex]
The new coordinates of point P after the reflection over the x-axis are (-5,-4).
Therefore, the correct option is B.
