Answer:
A: 19
Step-by-step explanation:
For this, we can complete the square. We first look at the first 2 terms,
t^2 and -6t.
We know that [tex](t-3)^2[/tex] will include terms.
[tex](t-3)^2 = t^2 - 6t + 9[/tex]
But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:
[tex]m(t) = (t-3)^2 - 9 +28[/tex]
[tex]m(t) = (t-3)^2 +19[/tex]
Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.
1.
a. AABC has a right angle at B, BC = 4, and has an area of 10 square units. What is the
length of AB?
Answer:
5 unitsStep-by-step explanation:
A right angled triangle is a triangle that has one of this angles to be 90°. According to the ΔABC, the angle at B is 90°.
Area of a triangle = 1/2 * base * height
According to the diagram shown, the base is BC and the height is AB which is the required side.
Area of the triangle = 1/2 * BC * AB
Given area of the triangle = 10 square units
BC = 4 units
AB is the required length.
Substituting this values into the formula above;
10 = 1/2 * 4 * AB
10 = 2AB
Dividing both sides by 2
2AB/2 = 10/2
AB = 5 units
Hence the length of AB is 5 units.
Which polynomial is prime? x2 + 9 x2 – 25 3x2 – 27 2x2 – 8
This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).
Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.
Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.
Answer:
A
Step-by-step explanation:
because it has a + sign
Assume that adults have IQ scores that are normally distributed with a mean of and a standard deviation . Find the probability that a randomly selected adult has an IQ between 81 and 119 .
Complete Question
Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.
Answer:
The probability is [tex]P( x_1 < X < x_2) = 0.79474[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is σ = 15.
The mean μ= 100
The range we are considering is [tex]x_1 = 81 , \ x_2 = 119[/tex]
Now given that IQ scores are normally distributed
Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as
[tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]
So
[tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )[/tex]
substituting values
[tex]P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )[/tex]
[tex]P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )[/tex]
[tex]P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )[/tex]
From the standardized Z table
[tex]P(Z <-1.2667 ) = 0.10263[/tex]
And [tex]P(Z <1.2667 ) = 0.89737[/tex]
So
[tex]P( x_1 < X < x_2) = 0.89737 - 0.10263[/tex]
[tex]P( x_1 < X < x_2) = 0.79474[/tex]
paul worked 50 hours last week. if he earns $10 per hour plus time-and-a-half for any hours worked beyond 40 in a week, how much did he earn last week?
Answer: 4150
Step-by-step explanation:
You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!
For a data set with Mean -20, SD-3 find the Z scores for each of the following raw scores: 23, 17, 15, 22, 30. 23: 17: 15: 22: 30:
A. 23
B. 17
C. 15
D. 22
E. 30
4. Look at your result from the previous question in regards to raw score of 15
Answer:
A. 1
B. -1
C. -1.67
D. 0.67
E. 3.33
Step-by-step explanation:
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 20 , SD = 3 while x represents the individual values
A. 23
Z = (23-20)/3 = 3/3 = 1
B. 17
z = (17-20)/3 = -3/3 = -1
C. 15
z = (15-20)/3 = -5/3 = -1.67
D. 22
z = (22-20)/3 = 2/3 = 0.67
E. 30
z = (30-20)/3 = 10/3 = 3.33
Consider the following. x = t − 2 sin(t), y = 1 − 2 cos(t), 0 ≤ t ≤ 2π Set up an integral that represents the length of the curve. 2π 0 dt Use your calculator to find the length correct to four decimal places.
Answer:
L = 13.3649
Step-by-step explanation:
We are given;
x = t − 2 sin(t)
dx/dt = 1 - 2 cos(t)
Also, y = 1 − 2 cos(t)
dy/dt = 2 sin(t)
0 ≤ t ≤ 2π
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (0,2π)∫√((1 - 2 cos(t))² + (2 sin(t))²)dt
L = (0,2π)∫√(1 - 4cos(t) + 4cos²(t) + 4sin²(t))dt
L = (0,2π)∫√(1 - 4cos(t) + 4(cos²(t) + sin²(t)))dt
From trigonometry, we know that;
cos²t + sin²t = 1.
Thus;
L = (0,2π)∫√(1 - 4cos(t) + 4)dt
L = (0,2π)∫√(5 - 4cos(t))dt
Using online integral calculator, we have;
L = 13.3649
Given m = - 1/4 & the point (4, 5)which of the following is the point slope form of the equation?
Answer:
y - 5 = -1/4(x - 4)
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
To find the point slope form, plug in the point given and the slope.
y - y1 = m(x - x1)
y - 5 = -1/4(x - 4)
Calculating the degrees of freedom, the sample variance, and the estimated standard error for evaluations.
using the t statistic.
With another study, where you also plan on evaluating a mean using the t statistic, you have a sample of n = 21 that has an SS of 500. What is the variance for the sample?
A. 5.00
B. 22. 36
C. 25
D. 250,000
Answer:
The variance is [tex]\sigma ^2 =25[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 21
The sum of squares is [tex]SS = 500[/tex]
Generally the variance is mathematically represented as
[tex]\sigma ^2 = \frac{SS}{n- 1}[/tex]
substituting values
[tex]\sigma ^2 = \frac{ 500}{21- 1}[/tex]
[tex]\sigma ^2 =25[/tex]
Which is greater than 4?
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
Please solve this question by using the strategy Elimination Method or Solve By Substitution. This is the math equation: 1/2x+y=15 and -x-1/3y=-6
2nd Question: 5/6x+1/3y=0 and 1/2x-2/3y=3
First pair of equations :
[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]x+2y=30\ ..(iii)[/tex]
By Elimination Method, Add (i) and (ii) (term with x eliminate), we get
[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]
put y= 14.4 in (iii), we get
[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]
hence, x=1.2 and y =14.4
Second pair of equations :
[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]
Elimination Method, Add (i) and (ii) (term with y eliminate) , we get
[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]
put [tex]x=\dfrac{18}{13}[/tex] in (i), we get
[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]
hence, [tex]x=\dfrac{18}{13}[/tex] and [tex]y=\dfrac{-45}{13}[/tex] .
solve the following equations
x-1=6/x
Answer:
or,x2-x=6
or,x2-x-6=0
or,x2-3x+2x-6=0
or,x(x-3)+2(x-3)=0
or,(x-3)(x+2)=0
so either x=3
or x=-2
A random sample of size results in a sample mean of and a sample standard deviation of . An independent sample of size results in a sample mean of and sample standard deviation of . Does this constitute sufficient evidence to conclude that the population means differ at the level of significance?
Answer:
A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.
Step-by-step explanation:
Which, if any, pair of sides are parallel? AB II DC and AD II BC Cannot be determined AB II DC only AD II BC only
Answer:
120%
Step-by-step explanation:
The volume of ice-cream in the cone is half the volume of the cone. The cone has a 3 cm radius and
6 cm height. What is the depth of the ice-cream, correct to two decimal places?
m
3 cm
Ice-cream
6 cm
depth of
ice-cream
5cm
Answer:
h = 5 cm
Step-by-step explanation:
Given that,
The volume of ice-cream in the cone is half the volume of the cone.
Volume of cone is given by :
[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]
r is radius of cone, r = 3 cm
h is height of cone, h = 6 cm
So,
[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]
Let [tex]V_i[/tex] is the volume of icecream in the cone. So,
[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]
Let H be the depth of the icecream.
Two triangles formed by the cone and the icecream will be similiar. SO,
[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]
So, volume of icecream in the cone is :
[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]
or
h = 5 cm
So, the depth of the ice-cream is 5 cm.
If you’re good at statistics please help
Answer:
Step-by-step explanation:
probabilty distribution= interval of x/total area of the distribution
OR P(x)= frequency of x/total frequency(N)*the interval of x(w)
x f probabilty f/N*w
16 10 0.2
17 16 0.32
18 20 0.4
19 4 0.08
w is the width of the bar( interval) 17-16=1
N=10+16+20+4=50
( only need to draw histogram)
solve the system with elimination 4x+3y=1 -3x-6y=3
Answer:
x = 1, y = -1
Step-by-step explanation:
If we have the two equations:
[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.
[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex] by 2 and y is gone (as -6y + 6y = 0).
So let's multiply the equation [tex]4x+3y=1[/tex] by 2.
[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]
Now we can add these equations
[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]
------------------------
[tex]5x = 5[/tex]
Dividing both sides by 5, we get [tex]x = 1[/tex].
Now we can substitute x into an equation to find y.
[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]
Hope this helped!
Ughhh this is hard for me!
Answer:
(x+4)/3. When x is 5 the answer is 3
Step-by-step explanation:
PLEASE HELP ASAP! - 14 POINTS
Answer:
False
Step-by-step explanation:
the answer is false because
year 1 to 2 is $18
year 2 to 3 is $17
year 3 to 4 is $18
year 4 to 5 is $17
false because simple interest always has the same money not a pattern
Snoopy has a spoon that measures out 2(3)/(4) cups of sugar with every scoop. Snoopy takes 5(1)/(3) scoops with this spoon. How many cups of sugar does Snoopy scoop out?
33/64 cups of sugar does snoopy scoop out.
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.
The amount of sugar needed = 2 3/4 cups
Amount of sugar per scoop = 5 1/3 cups/scoop
So, number of cups of sugar scoops
= cups of sugar needed/ cups of sugar per scoop
=11/4 /16/3
=11/4 *3/16
=33/64
Hence, 33/64 cups of sugar does snoopy scoop out.
Learn more about this concept here:
https://brainly.com/question/25936585
#SPJ1
Polar coordinates: which is not the same?
Answer:
The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.
Step-by-step explanation:
Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.
Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.
Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)
We know that :
7.518 - 1.236 = 6.282 = ( About ) 2π
5.047 + 1.236 = 6.283 = ( About ) 2π
1.236 + 1.906 = 3.142 = ( About ) 2π
Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).
Assume that blood pressure readings are normally distributed with a mean of 117and a standard deviation of 6.4.If 64people are randomly selected, find the probability that their mean blood pressure will be less than 119.Round to four decimal places.
Answer:
0.9938
Step-by-step explanation:
We can find this probability using a test statistic.
The test statistic to use is the z-scores
Mathematically;
z-score = (x-mean)/SD/√n
from the question, x = 119 , mean = 117 , SD = 6.4 and n = 64
Plugging these values in the z-score equation above, we have;
z-score = (119-117)/6.4/√64
z-score = 2/6.4/8
z-score = 2.5
The probability we want to find is;
P(z < 2.5)
we can get this value from the standard normal distribution table
Thus; P(z < 2.5) = 0.99379
Which to four decimal places = 0.9938
reciprocal of dash and dash remains same
Answer:
-1 and 1
Step-by-step explanation:
Reciprocal means "one divided by...".
1/-1 = -1 and 1/1 = 1
A company will need to replace 35% of their computers this year. If they replaced 140 computers this year, how many computers do they have in total?
Hi
35/100= 140/ X
X = 100*140 /35
X= 14000/35
X= 400
There are 400 computer in the compagny.
5/2 + 6g = 11/4 solve it
Answer:
g = [tex]\frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{2}[/tex] + 6g = [tex]\frac{11}{4}[/tex]
Multiply through by 4 to clear the fractions
10 + 24g = 11 ( subtract 10 from both sides )
24g = 1 ( divide both sides by 24 )
g = [tex]\frac{1}{24}[/tex]
Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons. We have a random sample of 20 children from the city, with a mean of 4.6 years of piano lessons and a standard deviation of 2.2 years. Required:Explicitly state and check all conditions necessary for inference on these data.
Answer:
The condition are
The Null hypothesis is [tex]H_o : \mu = 5[/tex]
The Alternative hypothesis is [tex]H_a : \mu < 5[/tex]
The check revealed that
There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5 \ year[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 4.6 \ years[/tex]
The standard deviation is [tex]\sigma = 2.2 \ years[/tex]
The Null hypothesis is [tex]H_o : \mu = 5[/tex]
The Alternative hypothesis is [tex]H_a : \mu < 5[/tex]
So i will be making use of [tex]\alpha = 0.05[/tex] level of significance to test this claim
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_\alpha = 1.645[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }[/tex]
[tex]t = -0.8131[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis
This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
50 POINTS!!! i WILL GIVE BRAINLISET IF YOU ANSWER FAST Find the domain for the rational function f of x equals quantity x minus 3 over quantity 4 times x minus 1. (−∞, 3)(3, ∞) (−∞, −3)( −3, ∞) negative infinity to one fourth and one fourth to infinity negative infinity to negative one fourth and negative one fourth to infinity
Answer:
[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]
The answer is C.
Step-by-step explanation:
We are given the rational function:
[tex]\displaystyle f(x) = \frac{x-3}{4x-1}[/tex]
In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:
[tex]\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = \frac{1}{4} \end{aligned}[/tex]
Therefore, the domain is all real number except for x = 1/4.
In interval notation, this is:
[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]
The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.
In conclusion, our answer is C.
Answer:
The third one
Step-by-step explanation:
Find secα, if sinα=−2/3 and 3π/2 <α<2π . Also the α=alpha symbol
Answer:
Step-by-step explanation:
Given sinα=−2/3, before we can get secα, we need to get the value of α first from sinα=−2/3.
[tex]sin \alpha = -2/3[/tex]
Taking the arcsin of both sides
[tex]sin^{-1}(sin\alpha) = sin^{-1} -2/3\\ \\\alpha = sin^{-1} -2/3\\ \\\alpha = -41.8^0[/tex]
Since sin is negative in the 3rd and 4th quadrant. In the 3rd quadrant;
α = 180°+41.8°
α = 221.8° which is between the range 270°<α<360°
secα = sec 221.8°
secα = 1/cos 221.8
secα = 1.34
Martin currently has a balance of $948 in an account he has held for 20 years. He opened the account with an initial deposit of $600. What is the simple interest on the account?
A - 1.8%
B - 2.9%
C - 3.2%
D - 7.9%
Find x in each triangle
Answer:
x=20
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
21 ^2 + x^2 = 29^2
441+x^2 =841
Subtract 441 from each side
x^2 = 841-441
x^2 = 400
Take the square root of each side
sqrt(x^2) = sqrt(400)
x = 20
Answer:
[tex]\boxed{x = 20}[/tex]
Step-by-step explanation:
Hey there!
Well to find x we need to use the Pythagorean Theorem, which is.
[tex]a^2 + b^2 = c^2[/tex]
We have a which is 21 and 29 which is c.
[tex](21)^2 + x^2 = (29)^2[/tex]
[tex]441 + x^2 = 841[/tex]
[tex]-441[/tex]
[tex]x^2 = 400[/tex]
[tex]x = 20[/tex]
So the missing side "x" is 20.
Hope this helps :)
Find three consecutive integers such that the sum of the largest and 5 times the smallest is -244. Find the smallest integer.
Let the largest integer equal x, the 3rd number ( smallest-number) would be x - 2
The sum of the two would be:
X + 5(x-2) = -244
Simplify:
X + 5x -10
Combine like terms
6x -10 = -244
Add 10 to both sides:
6x = -234
Divide both sides by 6
X = -234/6
X = -39
The smallest number is x-2 = -39-2 = -41
The answer is -41
