Answer:
First of all you will start by saying 2-4=-2.
-2(-8b+1)=3b+6.
16b-2=3b+6.
13b=8.
b=8/13.
b=0.6153~0.62.
Find the distance between the points (-3,1) and (1,-4)
Answer:
[tex]\sqrt{41} \: \: or \: 6.4 \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-3,1) and (1,-4)
The distance between them is
[tex]d = \sqrt{ ({ - 3 - 1})^{2} + ({1 + 4})^{2} } \\ = \sqrt{ ({ - 4})^{2} + {5}^{2} } \\ = \sqrt{16 + 25} \\ [/tex]We have the final answer as
[tex] \sqrt{41} \: \: or \: 6.4 \: \: units[/tex]Hope this helps you
I have no idea what I’m doing
Answer : The polynomial in standard form is [tex]1a^2+9a+20[/tex]
Step-by-step explanation :
The polynomial in standard form means that the terms are ordered from highest exponent to lowest exponent.
Given: Subtract [tex]9a^2-6a+5[/tex] from [tex]10a^2+3a+25[/tex]
The expression will be :
[tex](10a^2+3a+25)-(9a^2-6a+5)[/tex]
Now open the bracket and change the sign.
[tex]=10a^2+3a+25-9a^2+6a-5[/tex]
Now we are adding or subtracting the like terms, we get:
[tex]=1a^2+9a+20[/tex]
Thus, the polynomial in standard form is [tex]1a^2+9a+20[/tex]
Find two consecutive whole numbers that \sqrt(48)
lies between.
Answer:
6 and 7
Step-by-step explanation:
Step 1: Find 2 perfect square roots
√36 = 6
√49 = 7
√36 < √48 < √49
6 < √48 < 7
So, between 6 and 7
2.5 tons = how many pounds
Answer:
5000 pounds
Step-by-step explanation:
1 ton = 2000 pounds so 2.5 = 2000 + 2000 + 1000 = 5000
Answer:
5,000 pounds
Step-by-step explanation:
just subtract 2.5 by 1,000 5 times
what is 0.1 as a fraction
Answer:
1/10
Step-by-step explanation:
divide the numerator by the denominator. For example, 1/2 is equal to 1 divided by 2, which is equal to 0.5.
Answer:
1/10
Hoped I helped
Question Help
A particular country has so total states in the areas of all 50 states are added and the sum is divided by 50, the result is 188,461 square kilometers Determine whether
This result is a statistic or parameter
Answer:parameter
Step-by-step explanation:
0.72 is ten times as much as ________. *
Answer:
0.072 or .072
Step-by-step explanation:
0.72 is ten times as much as 0.072.
0.072 times 10 is .72.
0.72 / 10 = 0.072 .
Answer:
0.072 or .072
Both is right
Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
1. Let W{1} be the set of all polynomials of the form p(t) = at^{2}, where a is in {R}.
2. Let W{2} be the set of all polynomials of the form p(t) = t^{2} + a, where a is in {R}.
3. Let W{3} be the set of all polynomials of the form p(t) = at^{2} + at, where a is in {R}.
Answer:
1) W₁ is a subspace of Pₙ (R)
2) W₂ is not a subspace of Pₙ (R)
4) W₃ is a subspace of Pₙ (R)
Step-by-step explanation:
Given that;
1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R
2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R
3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R
so
1)
let W₁ = { at² ║ a∈ R }
let ∝ = a₁t² and β = a₂t² ∈W₁
let c₁, c₂ be two scalars
c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)
= c₁a₁t² + c²a₂t²
= (c₁a₁ + c²a₂)t² ∈ W₁
Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁ and scalars c₁, c₂
Thus, W₁ is a subspace of Pₙ (R)
2)
let W₂ = { t² + a ║ a∈ R }
the zero polynomial 0t² + 0 ∉ W₂
because the coefficient of t² is 0 but not 1
Thus W₂ is not a subspace of Pₙ (R)
3)
let W₃ = { at² + a ║ a∈ R }
let ∝ = a₁t² +a₁t and β = a₂t² + a₂t ∈ W₃
let c₁, c₂ be two scalars
c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)
= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t
= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃
Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂
Thus, W₃ is a subspace of Pₙ (R)
The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is normally distributed.
5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68
1) Determine a point estimate for the population mean.
2) Construct and Interpret a 95% confidence interval for the mean pH of rainwater.
a) if repeated samoles are taken, 95% of them will have a sample pH of rain water between [ ] & [ ].
b) there is a 95% chance that the true mean pH of rain water is between [ ] & [ ].
c) there is 95% confidence that the population mean pH of rain water is between [ ] & [ ].
3) Construct and interpret a 99% confidence interval for the mean pH of rainwater.
a) there is 99% confidence that the population mean pH of rain water is between [ ] & [ ].
b) there is a 99% chance that the true mean pH of rain water is between [ ] & [ ].
c) if repeated samoles are taken, 99% of them will have a sample pH of rain water between [ ] & [ ].
4) What happens to the interval as the level of confidence is changed? Explain why is a logical result.
As the level of confidence increases l, the width of the interval_____this makes sense since the_____,______.
Answer:
(1) The point estimate for the population mean is 4.925.
(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .
(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .
(4) As the level of confidence increases, the width of the interval increases.
Step-by-step explanation:
We are given that the following data represent the pH of rain for a random sample of 12 rain dates.
X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.
(1) The point estimate for the population mean is given by;
Point estimate, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}[/tex]
= [tex]\frac{59.1}{12}[/tex] = 4.925
(2) Let [tex]\mu[/tex] = mean pH of rainwater
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 4.925
s = sample standard deviation = 0.33
n = sample of rain dates = 12
[tex]\mu[/tex] = population mean pH of rainwater
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.201 < [tex]t_1_1[/tex] < 2.201) = 0.95 {As the critical value of t at 11 degrees of
freedom are -2.201 & 2.201 with P = 2.5%}
P(-2.201 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.201) = 0.95
P( [tex]-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }[/tex] , [tex]4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }[/tex] ]
= [4.715, 5.135]
Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .
The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.
(3) Now, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-3.106 < [tex]t_1_1[/tex] < 3.106) = 0.99 {As the critical value of t at 11 degrees of
freedom are -3.106 & 3.106 with P = 0.5%}
P(-3.106 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 3.106) = 0.99
P( [tex]-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.99
P( [tex]\bar X-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.99
99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }[/tex] , [tex]4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }[/tex] ]
= [4.629, 5.221]
Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .
The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.
(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.
how do you determine when a counting problem involves a permutation or a combination?
solve using Substitution y = 6x - 11 -2x - 3y = -7
Answer:
(2, 1)
Step-by-step explanation:
To solve by substitution, we solve one equation for one of its variables and then substitute the solved value for that variable into the other equation. Because this system of equations already has one solved for the variable, this makes our job much easier. We only need to implement the solved value for y into the other equation and solve for x.
y = 6x - 11
-2x - 3(6x - 11) = -7 Distribute.
-2x - 18x + 33 = -7 Combine like terms.
-20x + 33 = -7 Subtract 33 from both sides of the equation.
-20x = -40 Divide by -20 on both sides of the equation.
x = 2
Then, with this value, we will place it into the equation that was already solved for y in order to get a definite value for y.
y = 6(2) - 11
y = 12 - 11
y = 1
Using this information, the coordinate pair for this equation (the point of intersection between the two lines) is (2, 1).
Name the missing coordinate(s) of the triangle
Answer:
R(7a, 0 )
Step-by-step explanation:
R is on the vertical line RQ so will have the same x- coordinate as Q
R is on the horizontal line OR so will have the same y- coordinate as O
Thus coordinates of R = (7a, 0 )
Payton leaves to go on an 85 minute bike ride at 3:27 p.m.Payton's family eats dinner at 5:45 p.m How much time will Payton have between finishing her bike ride and eating dinner?
He starts to ride at 3:27 p.m.
85 minutes -> hours = 1 h 25 minutes (85/60 = 1 with 25 of rest)
3:27 + 1 h 25 min = h. 4:52
between 4:52 and 5:45 =>
5 hours 45 min - 4 hours 52 minutes =
4h 105 min ( 1h = 60min ) - 4h 52 min =
0h 53min
Payton has 53 minutes
Answer:
53 minutes
Step-by-step explanation:
Payton leaves at 3:27 p.m. and rides for 85 minutes. When she has finished, the time will be 3:27 + 0:85, or
3:27 + 1:25, since 1 hr = 60 min
4:52 p.m.
Dinner will be at 5:45 p.m. That means Payton will have (5:45 - 4:52) hours until dinner: Borrowing 60 minutes from 5:45, we get
4:105 - 4:52 = 0:53. That's 53 minutes to while away before dinner.
a 2 day automobile trip of 880 miles is planned. half of the distance is to be traveled each day at 55 miles per hour. how many hours will be driven each day
Answer:
Time travelled each day = 8 hours
Step-by-step explanation:
total distance of 2-day trip = 880 miles
half the distance each day = 880 ÷ 2 = 440 miles
velocity travelled each day = 55 miles per hour
time travelled each day = ???
velocity = (distance trvaelled) ÷ (Time)
55 = 440 ÷ Time
[tex]55=\frac{440}{Time} \\cross-multiplying\\55\ \times\ Time = 440\\Time = \frac{440}{55} \\Time = 8\ hours[/tex]
∴ Time travelled each day = 8 hours
Answer:
9 hours
Step-by-step explanation:
Total distance for the two days = 880 miles
If half of the distance is to be traveled each day, then;
distance each day = 440 miles
speed of the automobile = 55 miles per hour.
Now, let's calculate the number of hours that will be driven each day.
Remember that;
speed = distance / time
=> time = distance / speed [substitute the values of distance and speed]
=> time = (440 miles) / (55 miles/hour)
=> time = 9 hours.
Therefore, the number of hours that will be driven each day is 9
[tex]6 = \frac{m}{8} [/tex]
what does m equal?
Answer:
m = 48
Step-by-step explanation:
Isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Multiply 8 to both sides:
6 = m/8
(6) * 8 = (m/8) * 8
6 * 8 = m
m = 6 * 8
m = 48
48 is your answer for m.
~
The function h(x) = 12x + 49 is an even function. Which transformation of h(x) would result in a function that is neither
even nor odd?
Answer:
A reflection over x - axis
Step-by-step explanation:
If f(-x) = f (x), (ie all the signs are the same), then the function is even
also, if f(-x) = -f (x), (ie all the signs are switched), then the function is odd.
Given;
h(x) = 12x + 49
Then test for h(-x);
h(-x) = 12(-x) + 49
h(-x) = -12x + 49,
Thus h(-x) ≠ h(x) and also h(-x) ≠ -h(x)
The function is neither odd nor even.
Therefore, a reflection over x - axis would result in a function that is neither even nor odd.
If a polygon is a kite, then it is a quadrilateral. Write the inverse of the conditional statement and determine whether it is true or false. A) If a polygon is a quadrilateral, then it is a kite. TRUE B) If a polygon is a quadrilateral, then it is a kite. FALSE C) If a polygon is not a kite, then it is not a quadrilateral. TRUE D) If a polygon is not a kite, then it is not a quadrilateral. FALSE
The correct answer is D) If a polygon is not a kite, then it is not a quadrilateral. FALSE
Explanation:
The statement "If a polygon is a kite, then it is a quadrilateral" as other statements is composed of two parts: the if statement or hypothesis and the conclusion. Additionally, to create the inverse of this statement it is necessary to negate both statements, this means the inverse is "If a polygon is not a kite, then it is not a quadrilateral" because this negates the hypothesis and the conclusion. Besides this, it can be concluded this inverse statement is false because the word "quadrilateral" describes all shapes with four sides, which include not only kites but squares, rectangles, trapezoids, etc. Therefore, a polygon can be quadrilateral without being a kite.
Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.
What is the standard error?
Answer:
The standard error is 0.033.
Step-by-step explanation:
We are given that Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.
Let [tex]\hat p[/tex] = proportion of employees who planned to take an extended vacation next year
[tex]\hat p[/tex] = [tex]\frac{X}{n}[/tex] = [tex]\frac{21}{125}[/tex] = 0.168
n = number of employees at her company = 125
Now, the standard error is calculated by the following formula;
Standard error, S.E. = [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
= [tex]\sqrt{\frac{0.168(1-0.168)}{125} }[/tex]
= [tex]\sqrt{\frac{0.168 \times 0.832}{125} }[/tex] = 0.033
Hence, the standard error is 0.033.
Answer:
.10 - .23
Step-by-step explanation:
.168 +/- 1.96 ( sqrt ((.168 * .832)/125))
Mark borrowed $5,500 at 11.5 percent for five years. What is the amount of Mark's total payment? $8,520 $8,160 $7,410 $7,257
Answer:
7,257
Step-by-step explanation:
use the formula of: M = amount/discount factor
1. Write 206 in base 7 2. The number 3, 956, 427, 8ab is divisible by 72. Calculate a and b.
Answer:
k
Step-by-step explanation:
What are the values of x & y?
Answer:
X= 60°
Y= 30°
Step-by-step explanation:
In triangle ABD, we have:
AB = BD = AD
Then triangle ABD is equilateral triangle.
Then, all its angles are equal to 60°.
=> X = 60°
____________________________________
ADC is right triangle at D.
So, X and Y are congruent angles (their sum is equal to 90°)
So, X + Y =90°
60° + Y = 90°
Y = 90 - 60
Y= 30°
[tex]hope \: this \: helps[/tex]
n ΔABC, AB = 10 and BC = 5. Which expression is always true? A. 5 < AC < 10 B. AC = 5 C. 5 < AC < 15 D. AC = 10
Answer:
A. 5 < AC < 10
Step-by-step explanation:
We are given the ∆ABC
To solve for the sides of ∆ABC , we make use of Pythagoras Theorem
Pythagoras Theorem states that:
AB² = AC² + BC²
Where AB = Longest side, hence its length is always more that AC and BC.
In the above Question, we are given the values of AB and BC
AB = 10
BC = 5
Inputting these values into the Pythagoras Theorem,
10² = AC² + 5²
100 = AC² + 25
AC² = 100 - 25
AC² = 75
AC = √75
AC = 8.6602540378
According to the above calculation, we can see that the expression that is always true = Option A "5 < AC < 10"
Factor by grouping x3 - 3x2 + 4x -12 Group of answer choices
A( x - 3 ) (x2 + 4 )
B(x3 - 3x2) ( 4x -12)
C( x +4 ) (x2 - 3 )
D( x - 4 ) (x2 + 3 )
Answer:
(x² + 4)(x - 3)
or
A
Step-by-step explanation:
Step 1: Write out expression
x³ - 3x² + 4x - 12
Step 2: Factor by grouping
x³ - 3x²
x²(x - 3)
4x - 12
4(x - 3)
Step 3: Combine
(x² + 4)(x - 3)
Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
∫ (x + 8x) dx
Step-by-step explanation:
Given
[tex]\int\limits {(x+8x)} \, dx[/tex]
to integrate we use
[tex]\frac{dy}{dx} =\int\limits {ax^n} \, dx \\[/tex]
we have
[tex]y= \frac{ax^n^+^1}{n+1}[/tex]
[tex]y= \frac{x^1^+^1}{1+1}+ \frac{8x^1^+^1}{1+1}+c\\\\y= \frac{x^2}{2}+ \frac{8x^2}{2}+c\\\\y= \frac{x^2}{2}+ 4x^2+c\\\\y= \frac{x^2+8x^2}{2}+c\\\\y= \frac{9x^2}{2}+c[/tex]
in order to verify using differentiation we use
[tex]y= ax^n\\\\ \frac{dy}{dx} = nax^n^-1[/tex]
[tex]y= \frac{9x^2}{2}+c\\\\ \frac{dy}{dx} =2* \frac{9x^2^-^1}{2}\\\\ \frac{dy}{dx} =2* \frac{9x}{2}\\\\ \frac{dy}{dx} =9x\\\\9x= x+8x\\\\ \frac{dy}{dx}= x+8x[/tex]
A landowner has some land on which he wants to plant trees. He can plant 1,357 trees on landl if he already has 1,289 trees. How many does he have left to purchase?
60÷3[150÷2{6+3(17-14)}]
Answer:
plz mark as BRAINLIEST....
Step-by-step explanation:
60÷3[150÷2{6+3(17-14)}]
= 60÷3[150÷2{9-3}]
=60÷3[75-6]
=20-69
=49
8x - 6(x + 1) < 4(2x - 9)
Answer:
x > 5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
8x - 6(x + 1) < 4(2x - 9)
Step 2: Distribute parenthesis
8x - 6x - 6 < 8x - 36
Step 3: Combine like terms
2x - 6 < 8x - 36
Step 4: Subtract 2x on both sides
-6 < 6x - 36
Step 5: Add 36 on both sides
30 < 6x
Step 6: Divide both sides by 6
5 < x
Step 7: Rewrite
x > 5
Order these from least to greatest: -3/4, 0.5, 2/3, -7/3, 1.2 Thank you
Answer:
-7/3
-3/4
0.5
2/3
1.2
You can get these numbers by sorting in your head. Think of a number line and that'll make things easier :)
Answer:
-7/3, -3/4, 0.5, 2/3, 1.2
Step-by-step explanation:
The larger the negative number is the smaller it's value is and its the complete opposite for positive numbers
If m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17X-16)°, find each measure
Answer: m∠ TUW = 38°
m∠WUV = 12°
m∠TUV = 103°
Step-by-step explanation:
Given: m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17x-16)°
Since, m∠TUV = m∠ TUW + m∠WUV
So, 17X-16 = (5x + 3) + (10x-5)
⇒ 17X-16 = 5x + 3 + 10x-5 [open parenthesis]
⇒ 17X-16 =5x + 10x +3 -5 [combine like trems]
⇒ 17X-16 =15x -2
⇒ 17X -15x = -2+16 [subtract 15x and add 16 on both sides]
⇒ 2x = 14
⇒ x= 7 [divide both sides by 2]
Now, m∠ TUW = (5(7) + 3)°= 38°
m∠WUV=(10(7)-5)° = 12°
m∠TUV=(17(7)-16)° = 103°
Hence, m∠ TUW = 38°
m∠WUV = 12°
m∠TUV = 103°
A=1/2bh solve for b.
Answer:
2A /h = b
Step-by-step explanation:
A=1/2bh
Multiply each side by 2
2A = 2*1/2bh
2A = bh
Divide each side by h
2A/h = bh/h
2A /h = b
Step-by-step explanation: First, get rid of the fraction by
multiplying both sides of the equation by 2.
That gives us 2A = bh.
Don't be thrown off by the capital A in this problem.
Just treat it like any other variable.
To get b by itself on the right side of the equation, we now simply
divide both side of the equation by h and our answer is 2A/h = b.
Take a look back at the formula now in the original problem.
Does it look familiar?
It's the formula for the area of a triangle.
Take a look at the image I have provided below.
I have made the "b" purple so you
can see that we are solving for it.