Answer:
The answer to the best prediction is 115.04
Step-by-step explanation:
We have to:
x = 102
They also tell us that:
y = 5.9 + 1.07 * x
If we replace we have:
y = 5.9 + 1.07 * (102)
y = 115.04
Therefore, the best predicted value of ModifyingAbove and with caret given that the older child has an IQ of 102 is 115.04
what is the axis of symmetry of f(x)=-3(x+2)^2+4
Answer:
line passes through the vertex
Step-by-step explanation:
f(x)=-3(x+2)^2+4
x=-2 it is the x of the vertex
How many solutions does the system have? { y = − 3 x + 9 3 y = − 9 x + 9 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=−3x+9 3y=−9x+9
Answer:
no solutions
Step-by-step explanation:
y = − 3 x + 9
3 y = − 9 x + 9
Multiply the first equation by -3
-3(y )=-3( − 3 x + 9)
-3y = 9x -27
3 y = − 9 x + 9
-------------------------
0 = 0 -18
0 = -18
This is never true so there are no solutions
Answer:
for kahn academy -- b -- ( no solutions)
Step-by-step explanation:
2. A line passes through the point (0,4).
The gradient of this line is 2.
Write down the equation of this line
Answer:
[tex]\boxed{y = 2x+4}[/tex]
Step-by-step explanation:
Gradient = m = 2
Y-intercept = b = 4 (Because here x = 0 as in the point (0,4))
So, the equation becomes
=> [tex]y = mx+b[/tex]
=> [tex]y = 2x+4[/tex]
Sample annual salaries (in thousands of dollars) for employees at a company are listed. 51 53 48 62 34 34 51 53 48 30 62 51 46 (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a $5000 raise. Find the sample mean and sample standard deviation for the revised data set. (c) Each employee in the sample takes a pay cut of $2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?
Answer:
Mean increase or decrease (same quantity) according to the quantity of the increment or reduction
As all elements were equally affected the standard deviation will remain the same
Step-by-step explanation:
For the original set of salaries: ( In thousands of $ )
51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46
Mean = μ₀ = 47,92
Standard deviation = σ = 9,56
If we raise all salaries in the same amount ( 5 000 $ ), the nw set becomes
56,58,53,67,39,39,56,58,53,35,67,56,51
Mean = μ₀´ = 52,92
Standard deviation = σ´ = 9,56
And if we reduce salaries in the same quantity ( 2000 $ ) the set is
49,51,46,60,32,32,49,51,46,28,60,49,44
Mean μ₀´´ = 45,92
Standard deviation σ´´ = 9,56
What we observe
1.-The uniform increase of salaries, increase the mean in the same amount
2.-The uniform reduction of salaries, reduce the mean in the same quantity
3.-The standard deviation in all the sets remains the same.
We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the data spread around the mean will be the same
Any uniform change in the data will directly affect the mean value
Uniform changes in values in data set will keep standard deviation constant
Pamela is 7years older than jiri. The sum of their age is 91. What is Jori’s age
Answer:
[tex]\boxed{\sf \ \ \text{Jori is 42} \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's not J Jori's age
Pamela is 7 years older than Jori so here age is J + 7
The sum of their age is 91 so
J + ( J + 7 ) = 91
<=>
2J + 7 = 91 subtract 7
2J = 91 - 7 = 84 divide by 2
J = 84/2 = 42
So Jori is 42 and Pamela is 49
hope this helps
The slope of the line passing through the points (7, 5) and (21, 15) is
Answer:
5/7
Step-by-step explanation:
We are given two points so we can find the slope by using
m = (y2-y1)/(x2-x1)
= (15-5)/(21-7)
=10/14
5/7
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
23.14
Step-by-step explanation:
Solve for the area of the figure by dividing it up into parts. You can divide into a half-circle and a triangle
Half-Circle
The diameter is 6. This means that the radius is 3. Use the formula for area of a circle. Divide the answer by two since you only have a half-circle.
A = πr²
A = π(3)²
A = 9π
A = 28.274
28.274/2 = 14.137
Triangle
The base is 3 and the height 6. Use the formula for area of a triangle.
A = 1/2bh
A = 1/2(6)(3)
A = 3(3)
A = 9
Add the two areas together.
14.137 + 9 = 23.137 ≈ 23.14
The area is 23.14.
Answer:
23 sq. unitsStep-by-step explanation:
The figure consists of a semi circle and a triangle
Area of the figure = Area of semi circle + Area of triangle
Area of semi circle is 1/2πr²
where r is the radius
radius = diameter/2
radius = 6/2 = 3
Area of semi circle is
1/2π(3)²
1/2×9π
14.14 sq. units
Area of a triangle is 1/2×b×h
h is the height
b is the base
h is 6
b is 3
Area of triangle is
1/2×3×6
9 sq. units
Area of figure is
14.14 + 9
= 23.14
Which is 23 sq. units to the nearest hundredth
Hope this helps you.
A line through the points (2, -9) and (j, 17) is parallel to the line 2x + 3y = 21. What is the value of j?
Answer:
j = -37
Step-by-step explanation:
First find the slope of 2x + 3y = 21
Solve for y
Subtract 2x from each side
2x-2x + 3y =-2x+ 21
3y = -2x+21
Divide by 3
3y/3 = -2x /3 + 21/3
y = -2/3 x +7
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
m = -2/3
The slope of parallel lines are equal
Using the two points
m = (y2-y1)/(x2-x1)
-2/3 = (17 - -9)/(j-2)
-2/3 = (17 +9)/(j-2)
Using cross products
-2(j-2) = 3 ( 17+9)
-2j +4 = 26*3
-2j +4 = 78
Subtract 4 each side
-2j = 78-4
-2j = 74
Divide by -2
-2j/-2 = 74/-2
j = -37
7.1 A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings.
Answer:
1.875
Step-by-step explanation:
To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.
In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:
[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]
[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]
[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]
Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:
[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]
[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]
[tex]E_2 = 1 + \frac{7}{8}[/tex]
[tex]E_2 = \frac{15}{8} = 1.875[/tex]
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
QUESTION 2
Find Percent Increase:
The original price for a product is $53.93 and the sale's tax rate is 29%. Find the amount of tax and the total selling price. Round to the nearest cent.
A $15.64 and $69.57
B. $38.29 and 592.22
C. $15.64 and $38.29
D. $16.78 and $70.21
QUESTION 3
Find Future Value Using Simple Interest Formula:
Chad got a student loan for $10,000 at 8% annual simple interest. How much does he owe after two years?
A $12,800
B. $10,800
C. $11,600
D. $11,664
Answer:
QUESTION 2 -> Correct option: A.
QUESTION 3 -> Correct option: C.
Step-by-step explanation:
QUESTION 2
To find the amount of tax we just need to multiply the tax rate by the original price of the product:
[tex]Tax = 29\% * 53.93[/tex]
[tex]Tax = 0.29 * 53.93[/tex]
[tex]Tax =\$15.64[/tex]
Then, to find the total selling price, we need to sum the original price to the tax value:
[tex]Total = tax + price[/tex]
[tex]Total = 15.64 + 53.93[/tex]
[tex]Total = \$69.57[/tex]
Correct option: A.
QUESTION 3
To find the final value after 2 years, we can use the formula:
[tex]P = Po * (1 + r*t)[/tex]
Where P is the final value, Po is the inicial value, r is the interest and t is the amount of time. Then, we have that:
[tex]P = 10000 * (1 + 0.08 * 2)[/tex]
[tex]P = \$11600[/tex]
Correct option: C.
what is the difference of rational expressions below 6x/x-3 - 5/x
Answer:
[tex]$ \frac{6x^2-5x+15 }{x^2-3x} $[/tex]
Step-by-step explanation:
[tex]$\frac{6x}{x-3} -\frac{5}{x} $[/tex]
[tex]$\frac{6x(x)}{x(x-3)} -\frac{5(x-3)}{x(x-3)} $[/tex]
[tex]$\frac{6x^2}{x^2-3x} -\frac{5x-15}{x^2-3x} $[/tex]
[tex]$ \frac{6x^2-5x+15 }{x^2-3x} $[/tex]
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below? Make sure your answer is in reduced form.
Answer:
B.
Step-by-step explanation:
First, notice that we can cancel out an x in the second term. Thus:
[tex]\displaystyle \frac{3x^2}{x^2+x} =\frac{3x^2}{x(x+1)} =\frac{3x}{x+1}[/tex]
As with the last question, change the sign to multiplication and "flip" the second term:
[tex]\displaystyle \frac{2x-1}{x+1}\cdot \frac{x+1}{3x}[/tex]
Multiply straight across:
[tex]\displaystyle =\frac{(2x-1)(x+1)}{(x+1)(3x)}[/tex]
We can cancel the (x + 1) term:
[tex]\displaystyle =\frac{2x-1}{3x}[/tex]
This cannot be simplified further. Hence, our answer is B.
Answer:
It is B)
Step-by-step explanation:
Ap3x Approved
A random variable X counts the number of successes in 20 independent trials. The probability that any one trial is unsuccessful is 0.42. What is the probability of exactly eight successful trials
Answer:
[tex] P(X=8)[/tex]
And using the probability mass function we got:
[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=20, p=1-0.42=0.58)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=8)[/tex]
And using the probability mass function we got:
[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]
The probability of exactly eight successful trials is 0.0486 and this can be determined by using the formula of the probability mass function.
Given :
A random variable X counts the number of successes in 20 independent trials.The probability that any one trial is unsuccessful is 0.42.According to the binomial distribution, the probability mass function is given by:
[tex]\rm P(X) = \; (^nC_x )(p^x)(1-p)^{n-x}[/tex]
where the value of n is 20 and the value of (p = 1 - 0.42 = 0.58).
Now, substitute the values of known terms in the above expression of probability mass function.
[tex]\rm P(X=8) = \; (^{20}C_8 )((0.58)^8)(1-0.58)^{20-8}[/tex]
Simplify the above expression in order to determine the probability of exactly eight successful trials.
P(X = 8) = 0.0486
For more information, refer to the link given below:
https://brainly.com/question/23017717
A rectangular prism made of wood has a length of 10 centimeters, a width of 8 centimeters, and a height of 12 centimeters. A rectangular hole
with a length of 2 centimeters and a width of 3 centimeters is cut through the prism as shown. What is the volume of the resulting figure?
3 cm
2 cm
12 cm
8 cm
10 cm
Answer: its B 888 cm
Step-by-step explanation: hope this helps let me know if wrong ill fix it
Name the object that exhibits rotational symmetry. Question 7 options: sunglasses tent Ferris wheel a pair of scissors
The answer is Ferris wheel, since it is a circular object and will display symmetry even when rotated.
I NEED HELP PLEASE, THANKS! :)
A discus is thrown from a height of 4 feet with an initial velocity of 65 ft/s at an angle of 44° with the horizontal. How long will it take for the discus to reach the ground? (Show work)
Answer:
2.908 s
Step-by-step explanation:
The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.
For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...
h(t) = -16t² +v₀t +s₀
where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.
0 = -16t² +65sin(44°) +4
Dividing by -16 gives ...
0 = t^2 -2.82205t -0.2500
Using the quadratic formula, we find ...
t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099
t ≈ 2.90802
It will take about 2.908 seconds for the discus to reach the ground.
_____
Comment on the question
You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.
A- y=-2x-4
B- y=2x+4
C- y=-2x+4
D- y= 2x-4
Answer:
A. y=-2x-4
Step-by-step explanation:
The slope is negative when the line is going down from up.
Options B and D are wrong.
The y-intercept is (0, -4) as shown in the graph.
Option C is wrong.
y = mx + b
y = -2x - 4
The point (3, 6) is on the graph of y= 5f(2(x+3))-4 . Find the original point on the graph of y=f(x).
Answer:
(12, 2) is the original point on the graph of [tex]y=f(x)[/tex].
Step-by-step explanation:
Given:
[tex]y= 5f(2(x+3))-4[/tex] has a point (3, 6) on its graph.
To find:
Original point on graph [tex]y=f(x)[/tex] = ?.
Solution:
We are given that The point (3, 6) is on the graph of [tex]y= 5f(2(x+3))-4[/tex]
If we put x = 3 and y = 6 in [tex]y= 5f(2(x+3))-4[/tex], it will satisfy the equation.
Let us the put the values and observe:
[tex]6= 5f(2(3+3))-4\\\Rightarrow 6= 5f(2(6))-4\\\Rightarrow 6= 5f(12)-4\\\Rightarrow 6+4=5f(12)\\\Rightarrow 5f(12)= 6+4\\\Rightarrow 5f(12)= 10\\\Rightarrow f(12)= \dfrac{10}{5}\\\Rightarrow f(12)= 2\\OR\\\Rightarrow 2=f(12)[/tex]
Now, let us compare the above with the following:
[tex]y=f(x)[/tex]
we get y = 2 and x = 12
So, the original point on graph of [tex]y=f(x)[/tex] is (12, 2).
-73 + 28
Can anybody help me with this
Answer:
-45 is the answer
Step-by-step explanation:
PLZZ MARK BRAINLIEST
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Answer:
t = 5.6 day
t =5 days 14 hours 24 minutes
Step-by-step explanation:
Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.
N = N•e(-kt)
N• = 25
K = 0.1229
Then
N = 25/2 = 12.5
The reason because at the half life , it's original value will decrease to half.
Let's solve for the half life t
N = N•e(-kt)
12.5 = 25e(-0.1229t)
12.5/25 = e(-0.1229t)
0.5 = e(-0.1229t)
In 0.5 =-0.1229t
-0.69314 = -0.1229t
-0.69314/-0.1229 = t
5.6399 = t
To the nearest tenth
5.6 days = t
Solve the system by graphing (Simplify your answer completely.)
Will someone please help me with this and give an explanation on how you got it? I don’t understand.
{x+y=8
{x-y=4
Answer:
(6,2)
Step-by-step explanation:
1) convert both equations to slope intercept form:
y=-x+8
and
y=x-4
now graph both equations separately by intercepts:
x int: 0=-x+8
-8=-x
8=x
y int: y=0+8
y=8
so the two coordinate points for first equation are (0,8) and (8,0)
lets move on two second equation: y=x-4
x int: 0=x-4
4=x
y int y=0-4
y=-4
so the 2 coordinate points are (4,0) and (0,4)
lets graph these two equations and see where they intersect:
(see graph below), the intersection is at (6,2) so (6,2) is our answer
hope this helps
Solve for x.
Simplify your answer as much as possible.
The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers. This is the data from a sample of the previous recruits: 7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4 a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data. b. Find the mean, median, mode, and range. c. Is it appropriate to use a normal distribution to model this data? d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages. d1. What percent of new recruits would be taller than 72 inches? d2. What percent of new recruits would be shorter than 67.5 inches? d3. What percent of new recruits would be between 69 and 72 inches? d4. Between what two heights would capture 95% of new recruits?? By using statistics are the numbers changed to whole numbers?
Answer:
60-|||
61-
62-||
62
64-|||
65
66
67-|
68-|||
69-|
70-||
71
72-||
73
74-||
75
76-||
77
78-|
This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches
Step-by-step explanation:
Anybody get this? Thanks in advanced
Answer:
x = 6 and y = 2
Step-by-step explanation:
2x + 3y = 18 .......... Eqn 1
3x - 3y = 12 ........... Eqn 2
Add both Equations to eliminate y
we have
2x + 3x + 3y - 3y = 18 + 12
5x = 30
Divide both sides by 5
5x / 5 = 30/5
x = 6
Substitute x = 6 into any of the Equations
Using equation 1
we have
2(6) + 3y = 18
3y = 18 - 12
3y = 6
Divide both sides by 3
That's
3y/3 = 6/3
y = 2
Therefore x = 6 and y = 2
Hope this helps
A bread recipe calls for 2 1/2 cups of whole wheat flour 2/3 cups of rice flour 2 1/4 cups of white flour how many total cups of flour are needed write your answer as a simplified mixed number
Answer:
5 5/12
Step-by-step explanation:
you find the common denominator which is 12
2 6/12
8/12
2 3/12
now u add them all
hope this helps
Answer:
5 5/12 cups
Step-by-step explanation:
What is the value of 45-0.023
The value is 44.977
Feel pleasure to help u
Answer:
44.977
Step-by-step explanation:
4 builders are building some new classrooms at Trinity. It takes them 5 months to build the classrooms. How long will it take 10 builders?
Answer:
it takes
[tex]\boxed {\red {2 \: \: months}}[/tex]
for 10 builders
Step-by-step explanation:
[tex]4 \: \: \: builders = 5 \: month \\ 10 \: builders = x[/tex]
Let us solve
[tex]4 = 5 \\ 10 = x[/tex]
so
[tex]4 = x \\ 10 = 5[/tex]
use cross multiplication
[tex]5 \times 4 = 10 \times x \\ 20 = 10x \\ \frac{20}{10} = \frac{10x}{10} \\ \green {x = 2}[/tex]
Answer:
[tex]\boxed{2months}[/tex]
Step-by-step explanation:
B1 = 4
M1 = 5
B2 = 10
M2 = x (we have to find this)
Since it is an inverse proportion (more builders will take less time and vive versa), we'll write it in the order of
=> B1 : B2 = M2 : M1
=> 4:10 = x : 5
Product of Means = Product of Extremes
=> 10*x = 4*5
=> 10x = 20
Dividing both sides by 10
=> x = 2 months
So, it will take 2 months to build classrooms by 10 builders.
What are the divisors of 60?
Answer:
Step-by-step explanation:
The divisors of a number are the numbers that divide it exactly.
60/2
2/30
3/3
5/5
one
divisors = 1,2,3,, 4,5,6,10,12,15,20,30,60.
answer:
1, 2, 3, 6, 10, 30, 60
Step-by-step explanation:
i am pretty sure!
Which best describes the relationship between the line that passes through the points (-9, 2) and (-5, 4) and the line that passes through the points (-3, 4) and (1, 6)?
Answer:
Parallel!
Step-by-step explanation:
If you put these points on a graph and connect the dots to be two lines, they are perfectly side to side :)