The addition of w, 9 and 4 is (w+13).
According to the question,
We have the following information:
We need to add w, 9 and 4.
We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.
So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.
Now, the whole numbers can be easily added.
So, we have the following expression:
w+9+4
w+13
Hence, the addition of w, 9 and 4 is (w+13).
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How to find x here if the perimeter, diagonal, and length is given?
Answer:
see explanation
Step-by-step explanation:
(a)
perimeter (P) is calculated as
P = 2(l + b) ← l is the length and b the breadth
given l = x and P = 20 , then
2(x + b) = 20 ( divide both sides by 2 )
x + b = 10 ( subtract x from both sides )
b = 10 - x
Using Pythagoras' identity in the right triangle
x² + (10 - x)² = 8²
x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )
2x² - 20x + 36 = 0 ( divide through by 2 )
x² - 10x + 18 = 0 ← as required
(b)
solve using the method of completing the square
x² - 10x + 18 = 0 ( subtract 18 from both sides )
x² - 10x = - 18
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 18 + 25
(x - 5)² = 7 ( take square root of both sides )
x - 5 = ± [tex]\sqrt{7}[/tex] ( add 5 to both sides )
x = 5 ± [tex]\sqrt{7}[/tex]
Then
x = 5 - [tex]\sqrt{7}[/tex] ≈ 2.35 ( to 3 significant figures )
x = 5 + [tex]\sqrt{7}[/tex] ≈ 7.65 ( to 3 significant figures )
A bottle maker assumes that 24% of his bottles are defective. If the bottle maker is right, what is the probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.
What is the probability that the population proportion will be greater than 4%?To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.
Here is the formula:
z = (x-μ)/σ
First population proportion = 0.24
The sample proportion, hat p = 0.04
Z score =
[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]
So, the Z score will
= -10.9469
So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469, is = 10.9069
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there are three consecutive odd integers such that if the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. find the sum of the first and second
The sum of the first and second integer is 44.
How to illustrate the information?Let the numbers be x, x+2 and x+4.
If the second is subtracted from twice the sum of the first and third,the result is 52 more than the first. This will be:
2(x + 2 + x + 4) - (x + 2) = x + 52
2(2x + 6) - (x + 2) = x + 52
4x + 12 - x - 2 = x + 52
Collect like terms
4x - x - x = 52 - 12 + 2
2x = 42
Divide
x = 42/2
x = 21
Second Integer = x + 2 = 21 + 2 = 23
Third integer = x + 4 = 21 + 4 = 25
Sum = 21 + 23 = 44
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WHat is 5/1 x 4/5 This is a hard one
4
Step-by-step explanation:
[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]
[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]
[tex]{ \tt{ = \frac{20}{5}}} [/tex]
[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]
Question 6
The functions g is defined on the real numbers by g (x) = (x² + 1) (3x - 5). What is the value
of g(4) ?
-51
63
119
175
Answer: 119
Step-by-step explanation:
(4^2+1)(3*4-5)
=(16+1)(12-5)
=17*7
=119
Answer:
g(4) = 119
Step-by-step explanation:
g(x) = (x² + 1) (3x - 5)
Substitute x for 4 in the equation
g(4) = (4² + 1) (3(4) - 5)
g(4) = (16 + 1) (12 - 5)
g(4) = (17) (7)
g(4) = 119
Hence, the value of g(4) is 119
Gabriel has a stack of nickels that is 2 inches tall. The thickness of a nickel is
0.08 inch. How many nickels does Gabriel have?
Show your work.
Answer: Gabriel has
nickels.
Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
As given in the question,
Gabriel has 2 inches tall stack of nickel
Thickness of each nickel = 0.08inch.
Let 'n' be the number of nickels Gabriel has .
Required equation to get the number of nickel is equal to :
0.08 × n = 2
⇒ n = 2 / 0.08
⇒ n = 200/ 8
⇒ n = 25
Therefore, Gabriel owns a stack of nickels which is 2 inches tall and thickness of each nickel is 0.08 inch then number of nickels with Gabriel is equal to 25.
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Answer 0.04
Step-by-step explanation:
because 0.08 divided by two is 0.04
Evergreen Landscaping bought 7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270. The next week the firm bought 5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015. Pea gravel costs $28 less per ton than topsoil. Find the cost per ton for each item.
The cost of topsoil per ton would be $48.
The cost of pea gravel per ton is $20.
The cost of mulch per ton is $479.
What is the linear equations in two variable?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.
We have,
7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.
5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.
Let,
cost of topsoil per ton = x
cost of pea gravel per ton = x - 28
cost of mulch per ton = m
7x + 6m + 3(x - 28) = 3270
7x + 6m + 3x - 84 = 3270
10x + 6m = 3270 + 84
10x + 6m = 3354 -------------(i)
5x + 5m + 5(x - 28) = 3015
5x + 5m + 5(x - 28) = 3015
10x + 5m = 3015 - 140
10x + 5m = 2875 -----------(II)
Subtracting equation (II) from (I), we get
10x + 6m = 3354
- 10x + 5m = 2875
Solving we get
m = 479
Put m = 479 in equation(I), we get
10x + 6m = 3354
10x + 6(479) = 3354
10x = 480
x = 480/10
x = 48
Hence,
The cost of topsoil per ton would be = x = $48.
The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.
The cost of mulch per ton = m = $479.
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What is the image of (12,-12) after a dilation by a scale factor of 1/4 centered at the origin?
The image of (12, -12) after a dilation by a scale factor of 1/4 centered at the origin would have these coordinates (3, -3).
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object based on the scale factor applied, but not its shape.
Next, we would dilate the coordinates of the preimage (12, -12) by using a scale factor of 1/4 centered at the origin (0, 0) as follows:
Coordinate A (12, -12) → Coordinate A' (12 × 1/4, -12 × 1/4) = Coordinate A' (3, -3).
In conclusion, the coordinates of the image after a dilation by using a scale factor of 1/4 are (3, -3).
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Please help ASAP will mark brainliest
Plot the points ( -3, 7 ) and ( 9, 0)
Find the distance between the points and the midpoint of the line segment joining the points.
Answer: 13.89 units
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
India's hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Step-by-step explanation:
10 hours per week: $10.50 x 10 = $105.00
20 hours per week: $105.00 x 2 = $210.00
40 hours per week: $210.00 x 2 = $420.00
From ratio proportion for the following using
2 different way
45 members of Glee Club to 30 members of Dance
Club
Answer:
see explanation
Step-by-step explanation:
this can be expressed in ratio form and fractional form , that is
45 : 30 ( divide each part by 15 )
= 3 : 2 ← in simplest form
= [tex]\frac{3}{2}[/tex]
For which equation would x = 5 be a solution?
3x+6=21
12-2x = 13
7+ 6 x = 27
4x-7=27
A chemist is mixing a 30% salt solution with a 15% salt solution to make 60 L of a new solution that will contain 20% salt. How much of the 30% solution
should the chemist use?
20 amount of 30% salt solution
How to find the salt solution percentage?
Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.
Let x be the amount of 30% salt solution
Then, 60-x = amount of 15% salt solution
Salt content of the first solution + salt content of second solution = salt content of the mixture
∴ 0.30x + 0.15(60-x) = 0.20*60
0.30x + 9 - 0.15x = 12
0.15x = 3
x = 20
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Identify the values of the variables. Give your answers in simplest radical form. Help!
Considering the right angle triangle given the values of the variables are
n = 2√3k = 4√3How to determine the values of the variablesInformation from the question
right angle triangle
The values of the variables is worked using SOH CAH TOA
The right angle triangle of sides as described below
hypotenuse = k
opposite = n
adjacent = 6
The variable n is solved using tan, TOA, the angle is 30
tan 30 = Opposite / Adjacent
tan 30 = n / 6
tan 30 * 6 = n
n = 2√3
The variable k is solved using cos, CAH, the angle is 30
cos 30 = Adjacent / Hypotenuse
cos 30 = 6 / k
k = 6 / cos 30
k = 4√3
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ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)
The missing side length of triangle XYZ is 7.
Given,
Triangle ABC and triangle XYZ are similar.
Triangle ABC;Length of AB = 4
Length of BC = 8
Length of AC = x
Triangle XYZ;Length of XY = 24
Length of YZ = 48
Length of XZ = 42
We have to find the missing length x.
Here,
Triangle ABC and triangle XYZ are similar.
So,
AB : XY = BC : YZ = AC : XZ
Then,
Take AB : XY = AC : XZ
= 4 : 24 = x : 42
= 4 × 42 = 24x
x = 4 × 42 / 24
x = 42/6
x = 7
That is,
The missing side length of triangle XYZ is 7.
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ASAPPPPP PLEASE HELPPP!!!!!!!!!!
Between 50 and 100 books are stored on a shelf. Exactly 20 percent of them are textbooks. Exactly one-seventh of them are novels. Can the exact number of books on the shelf now be determined? Why or why not?
Answer:
no
Step-by-step explanation:
the percentage has nothing to do with how many of them there are, forgive me if im wrong
The exact number of books on the shelf cannot be determined based on the information given.
What is an expression?An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.
We know that between 50 and 100 books are stored on a shelf, so let's assume the number of books is some integer value between 50 and 100, inclusive. Let's call this value "n".
Exactly 20% of the books are textbooks, which means there are 0.2n textbooks on the shelf.
Exactly one-seventh of the books are novels, which means there are (1/7)n novels on the shelf.
We know that n, 0.2n, and (1/7)n are all integers because they represent whole numbers of books. We can write this as:
n = a
0.2n = b
(1/7)n = c
where a, b, and c are integers.
From the second equation, we know that 0.2n is a multiple of 1/10. From the third equation, we know that n is a multiple of 7. Therefore, we can rewrite these equations as:
n = 10b
n = 7c
Since n is equal to both 10b and 7c, we know that n must be a multiple of the least common multiple of 10 and 7, which is 70.
So, n must be a multiple of 70, and therefore must be one of the integers 50, 70, or 90. However, we cannot determine which of these three values is the correct one based on the information given, because all three satisfy the conditions in the problem:
If n=50, then 20% of the books (i.e., 10 books) are textbooks, and 1/7 of the books (i.e., 7.14 books, which we round down to 7) are novels.
If n=70, then 20% of the books (i.e., 14 books) are textbooks, and 1/7 of the books (i.e., 10 books) are novels.
If n=90, then 20% of the books (i.e., 18 books) are textbooks, and 1/7 of the books (i.e., 12.86 books, which we round down to 12) are novels.
Therefore, the exact number of books on the shelf cannot be determined based on the information given.
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12. Use the coordinate grid below to answer the question.
What are the coordinates of Point A?
Answer: (7, 12)
Step-by-step explanation:
The x-coordinate is 7.
The y-coordinate is 12.
Thus, the coordinates are (7, 12).
Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.
Total: 499.75
Step-by-step explanation:
4 × 110.5 = 442
3 × 19.25 = 57.75
442 + 57.75 = 499.75
Keala is making a new book cover before giving their favorite picture book to their little brother. The cover is 22 1 4 cm 22 4 1 cm22, start fraction, 1, divided by, 4, end fraction, start text, c, m, end text tall. It has a rectangular shape and an area of 890 cm 2 890cm 2 890, start text, c, m, end text, squared. How wide across is Keala's book cover? cm
The width across Keala book cover is 40cm
What is a rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees
From the question,
The length of the cover
= 22 1/4
= 89/4
The area of the cover
=890 cm²
From the formula
Area of a Rectangle = Length x Breadth
890=89/4×Breadth
Breadth = 890×4/89
Breadth=40cm
Hence, the width of the book cover is 40cm
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Barbara borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year payment is
The actual end-of-year payment or present value of this ordinary annuity is equal to $1,482.
How to calculate the actual end-of-year payment?For the rate of interest, we have:
Rate of interest, r = APR/12
Rate of interest, r = 0.12/12
Rate of interest, r = 0.01
Next, we would calculate the present value of this ordinary annuity by using this formula:
Present value, PV = [P ÷ [1 - (1 + r)^{-n}]/r]
Where:
r is the interest rate.P is the principal.n is the number of times compounded.Substituting the given parameters into the formula, we have;
Present value, PV = 4,500 ÷ ((1 - (1 + 0.12)^(-4))/(0.12))
Present value, PV = 4,500 ÷ ((1 - (1.12)^(-4))/(0.12))
Present value, PV = 4,500 ÷ ((1 - 0.635518078)/(0.12))
Present value, PV = 4,500 ÷ ((0.364481922)/(0.12))
Present value, PV = 4,500/3.0373
Present value, PV = $1,481.58 ≈ $1,482.
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carolina and her friends are training for a kayaking competition. the average distance and time traveled by each is shown in the table below. if the distance kayaked in the competition is 3 miles, predict who will win based on the rates shown. predict how long it will take the winner to complete the race if their rate remains constant
Carolina, 7/8 mi in 1/2 hr
Leslie, 1 mi in 1/3 hr
Bryan 3/4 mi in 3/4 hr
Javier 1 mi in 2/3 hr
The winner of the race among the friends would be Leslie.
Who would win the race?The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.
Average speed = total distance / total time
Carolina's average speed = 7/8 ÷ 1/2
7/8 x 2 = 7/4 = 1 3/4 miles per hour
Leslie's average speed = 1 ÷ 1/3
1 x 3 = 3 miles per hour
Bryan's average speed = 3/4 ÷ 3/4
3/4 x 4/3 = 1 mile per hour
Javier's average speed = 1 ÷ 2/3
1 x 3/2 = 1 1/2 miles per hour
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Can someone please help me solve this, I’m so stressed
Answer:
3a. $8493.42
3b. 139.0 months
4a. 10
4b. 10.2 years
Step-by-step explanation:
Given exponential equations, you want values for specific times, and you want times for specific values.
In part (a), the value is found by substituting an appropriate value for t and doing the arithmetic.
In part (b), logarithms will be involved in solving for t.
3. Investment(a) Use t=12, the number of months in one year. You want the value of ...
S = 8000·1.005^12 ≈ 8493.42
The amount after 1 year is $8493.42.
(b) The time it takes to double the investment is the value of t such that ...
16000 = 8000·1.005^t
2 = 1.005^t . . . . . . divide by 8000
log(2) = t·log(1.005) . . . . . take logarithms
t = log(2)/log(1.005) ≈ 138.976
The investment will double in about 139.0 months.
4. Otters(a) Use t=0 and evaluate.
y = 2500 -2490e^(-0.1·0) = 2500 -2490 = 10
The population of otters was 10 when they were reintroduced.
(b) The time it takes for the population to reach 1600 is the value of t such that ...
1600 = 2500 -2490e^(-0.1t) . . . . use 1600 for y
-900 = -2490e^(-0.1t) . . . . . . . . . subtract 2500
900/2490 = e^(-0.1t) . . . . . . . . . divide by -2490
ln(900/2490) = -0.1t . . . . . . . . . take natural logs
t = ln(900/2490)/-0.1 . . . . . . . . divide by the coefficient of t
t ≈ 10.176 ≈ 10.2
It will be 10.2 years before the otter population reaches 1600.
parallel lines, traversal, and algebra
need help!
The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;
x = 4°, y = 10°
11. x = 9°, y = 12°
12. x = 14°, y = 5°
13. x = 8°, y = 11°
14. x = 16°, y = 23°
15. x = 9°, y = 13°
What are parallel lines?Parallel lines are lines that maintain the same distance from each other along their lengths.
From the figure, we get;
(29·x - 3) and (15·x + 7) are linear pair angles, therefore;
(29·x - 3) + (15·x + 7) = 180°
44·x + 4 = 180
x = (180 - 4)/44 = 4
x = 4°
(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;
(15·x + 7) + (13·y - 17) = 180°
(15×4 + 7) + (13·y - 17) = 180°
67 + 13·y - 17 = 180°
50 + 13·y = 180
13·y = 180 - 50 = 130
y = 130 ÷ 13 = 10
y = 10°
11. (18·x - 44)° and (8·x - 10)° are same side exterior angles, therefore;
(18·x - 44)° + (8·x - 10)° = 180°
26·x - 54 = 180
x = (180 + 54)/26 = 9
x = 9°
(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;
(8·x - 10)° + (13·y - 38)° = 180°
(8 × 9 - 10)° + (13·y - 38)° = 180°
62 - 38 + 13·y = 180
13·y = 180 - (62 - 38) = 156
y = 156 ÷ 13 = 12
y = 12°
12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;
(9·x - 2)° = (5·x + 54)°
(9·x - 2)° = (5·x + 54)°
9·x - 5·x = 54 + 2 = 56°
4·x = 56°
x = 56° ÷ 4 = 14°
x = 14°
(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;
(9·x - 2)° + (10·y + 6)° = 180°
(9 × 14 - 2)° + (10·y + 6)° = 180°
124 + 6 + 10·y = 180
10·y = 180 - 130 = 50
y = 50 ÷ 10 = 5
y = 5°
13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;
(8·x - 1)° is congruent to angle (11·x - 25)°
(8·x - 1)° = (11·x - 25)°
11·x - 8·x = 25 - 1 = 24
3·x = 24
x = 24 ÷ 4 = 8
x = 8°
Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;
(15·y - 48)° + (8·x - 1)° = 180°
(15·y - 48)° + (8 × 8 - 1)° = 180°
(15·y - 48)° + 63° = 180°
15·y + 15° = 180°
15·y = 180° - 15° = 165°
y = 165° ÷ 15 = 11°
y = 11°
14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;
(4·x + 4)° = (7·x - 44)°
7·x - 4·x = 44° + 4° = 48°
3·x = 48°
x = 48° ÷ 3 = 16°
x = 16°
The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°
Therefore;
39 + 8·y - 43 = 180°
8·y = 180 + 43 - 39 = 184
y = 184 ÷ 8 = 23
y = 23°
15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;
(15·x - 26) = (12·x + 1)
(15·x - 12·x) = (26 + 1)
3·x = 27
x = 27 ÷ 3 = 9
x = 9°
The vertical angle to (2·x + 1) is therefore;
12·x + 1 = 12 × 9 + 1 = 109
The angle sum property indicates that we have;
28° + 109° + (4·y - 9)° = 180°
(4·y - 9)° = 180° - (28° + 109°) = 43°
(4·y - 9)° = 43°
(4·y)° = 43° + 9° = 52°
y = 52°/4 = 13°
y = 13°
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Im giving 20 points for this
Answer:
(B)={8,10,15,18,20}
Step-by-step explanation:
1. Which expression has a whole-number product?
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
C (-6+ i)(3- i)
D(-4+3i)(4-3i)
Option (B) (3 + 2i) (3 - 2i) is the expression that has the whole number product.
Whole number:
Whole number refers the numbers without fractions and it is a collection of positive integers and zero and represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.
Given,
Here we have the following expression:
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
(C) (-6+ i)(3- i)
(D) (-4+3i)(4-3i)
Now, we need to find the whole number product.
In order to find the solution we have to perform the multiplication on the given expression,
First expression will gives the following,
(A) (4 - 2i) (4 - 2i)
When we apply the (a-b)² formula in it then we get,
=> 4²+ (2i)² - (2 x 4 x 2i)
=> 16 - 4 - 16i
=> 12 - 16i
Which is not a whole number product.
Second expression,
(B) (3 + 2i) (3 - 2i)
Apply the (a + b)(a - b) formula in it,
Then we get,
=> 3² - (2i)²
=> 9 + 4
=> 13
Therefore, this one is the whole number product.
Third expression,
(C) (-6 + i) (3 - i)
When we perform the multiplication on it, then we get,
=> -18 + 6i +3i -i²
=> -18 + 9i + 1
=> -17 + 9i
his one is not a whole number product.
Final expression,
(D) (-4 + 3i) (4 - 3i)
When we perform the multiplication on it, then we get,
=> -16 + 12i + 12i - (3i)²
=> -16 + 24i + 9
=> -7 + 24i
This one is also no the whole number product.
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A doll sold for $209 in 1977 and was sold again in 1989 for $467. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V0=209
b) Find the Exponential growth function in terms of t, where t is the number of years since 1977
c) Estimate the value of the doll in 2009.
d) What is the doubling time for the value of the doll to the nearest tenth of a year?
e) Find the amount of time after which the value of the doll with be $2221
Step-by-step explanation:
the exponential growth function is
f(t) = v0 × (1 + k)^t
1977 to 1989 is 12 years (t).
a)
so, we have
467 = 209 × (1 + k)¹²
467/209 = (1 + k)¹²
12th root(467/209) = 1 + k = 1.069295033...
k = 0.069295033...
b)
f(t) = 209 × 1.069295033...^t
c)
2009 = 32 years after 1977
f(32) = 209 × 1.069295033...³² = $1,783.478472... ≈
≈ $1,783.48
d)
double the value of 209 is 418.
418 = 209 × 1.069295033...^t
2 = 1.069295033...^t
t = log1.069295033...(2) =
= log(2)/log(1.069295033...) = 10.34554457... ≈
≈ 10.3 years
e)
2221 = 209 × 1.069295033...^t
2221/209 = 1.069295033...^t
t = log1.069295033...(2221/209) =
= log(2221/209)/log(1.069295033...) =
= 35.27452616... years ≈
≈ 35.3 years
35 years would mean end of 2012. so, 35.3 years would be early 2013.
Chang will run at least 21 miles this week. So far, he has run 12 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
Using an inequality to represent the problem, Chang must run at least an additional 9 miles or greater than 9 miles
What is an InequalityIn Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
To find the number of additional miles he will run, let's set the unknown number equals t
12 + t > 21
t > 21 - 12
t >9
Chang will need to run at least 9 miles
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Many Texas cities have experienced substantial growth in population over the last 20 years. The growth of Houston, Texas, since 2015 is shown in the scatterplot. A least-squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by Population = 0.025 (year) + 2.01.
Based on the residual plot, is a linear model suitable for modeling the population growth of Houston?
A linear model is suitable because a pattern is evident in the residual plot.
A linear model is not suitable because the residuals do not cluster around zero.
A linear model is not suitable because the residual plot shows a curved pattern.
A linear model is suitable because the residuals seem to be randomly scattered.
Based on the given residual plot, as regards the linear model, we can say that; A linear model is not suitable because the residual plot shows a curved pattern.
What is a residual Plot?
A residual plot is a plot that shows the difference between the observed response and the fitted response values.
The ideal residual plot is usually called the null residual plot, and it shows a random scatter of points that form an approximately constant width band around the identity line.
When it comes to finding out if a linear model will be suitable, we can say that the points will form a pattern when the model function is not correct.
Now, you might be able to transform variables or even add polynomial and interaction terms in order to remove the pattern.
Now, looking at the given graph, we can say that a linear model is not suitable because from the definitions above, we can see that the residual plot shows a curved pattern.
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I’m doing my geometry homework and don’t remember the formula or way to solve the lengths of a triangle side with graph points. How do I solve both parts of #1?
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]
11/7 Thursday Math Math Hw. Fractions
Answer:
96, $ 144
Step-by-step explanation:
