Solve the equation of exponential decay. Hugo sold his car after one year for $25,000. He bought it new for $29,400. What was the rate of depreciation?

Answer:

It reduces the distance from the plotted points to the function curve.

Step-by-step explanation:

The goodness of fit of a model is measured by the "residuals", the differences between the given points and the modeled points. The smaller the residuals, the better the model. Any change to the model that will put it closer to the plotted points makes it a better model. The change proposed in your problem statement does that.

Answer:

[tex]b=\frac{g}{x} + \frac{5}{x^{3} } +\frac{1}{x^{2} }[/tex]

Step-by-step explanation:

[tex]10=\frac{5}{-2}-b(-2)^{2} +1\\\\\\9=\frac{5}{-2} -b(4)\\\\-18=5-b(4)\\\\-23=-b(4)\\\\\frac{-23}{4} =-b\\\\\frac{23}{4}=b\\\\\\b=\frac{23}{4}[/tex]

Answer:

(P, Q) = (-75, 57)

Step-by-step explanation:

The equation will have infinitely many solutions when it is a tautology.

Subtract the right side from the equation:

Px +57 -(-75x +Q) = 0

x(P+75) +(57 -Q) = 0

This will be a tautology (0=0) when ...

P+75 = 0

P = -75

and

57-Q = 0

57 = Q

_____

These values in the original equation make it ...

-75x +57 = -75x +57 . . . . . a tautology, always true

Answer:

Step-by-step explanation:

Givens

V = 58 in^3

h = 5 inches

pi = 3.14

Formula

V = pi * r^2 * h

Solution

58 = 3.14 * r^2 * 5

58 = 15.7 * r^2

58/15.7 = r^2

3.6942 = r^2

sqrt(r^2) = sqrt(3.6942)

r = 1.922 which when rounded is

r = 1.92

Answer: r=1.92

given what we know about the equation i can determine what steps are needed to solve this :)

volume

1) V = 58 in^3

we know that h=5inches

2) h = 5 inches

heres what pi equals

3) pi = 3.14

then we use pi in the equation

4)= pi * r^2 * h

heres the solution steps

1)58 = 3.14 * r^2 * 5

2)58 = 15.7 * r^2

3)58/15.7 = r^2

4)3.6942 = r^2

5)sqrt(r^2) = sqrt(3.6942)

6)r = 1.922 then we round and get  r = 1.92

so final solution is r = 1.92

×║hope this helps║×

the answer is C. move the decimal place to the left 4 times since it is positive to the 4th power

Answer:

26 terms

Step-by-step explanation:

The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...

an = -2 +5(n -1)

The sum of the first n terms is ...

(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573

n(5n -9) = 3146

5n^2 -9n -3146 = 0 . . . . . quadratic in standard form

Using the quadratic formula, we can find the positive solution for n to be ...

n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26

26 terms must be added to give the desired sum.

_____

Relevant formulas are ...

Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d

x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0

Answer: x=14

Step-by-step explanation:

1. Simplify 1/5(x−4) to (x−4)/5​​.

(−x−4)/5=−2

2. Multiply both sides by 5.

−x+4=−2×5

3. Simplify 2×5 to 10.

−x+4=−10

4. Regroup terms.

4−x=−10

5. Subtract 4 from both sides.

−x=−10−4

6. Simplify −10−4 to −14.

−x=−14

7. Multiply both sides by −1.

x=14

Answer:

The volume of the pyramid is [tex]6.125\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of the pyramid

h is the height of the pyramid

Find the area of the base B

[tex]B=3.5^{2}= 12.25\ cm^{2}[/tex]

we have

[tex]h=1.5\ cm[/tex]

substitute

[tex]V=\frac{1}{3}(12.25)(1.5)[/tex]

[tex]V=6.125\ cm^{3}[/tex]

All you have to do is treat the inequality like an equation and multiply both sides by 2.

[tex]-x<2 \\ \\ x>-2[/tex]

Answer: x> -2

Step-by-step explanation:

step 1 :take 2 to the other side ,and 1 will multiply by 2 which will give you 2

step 2 : take the negative or -1 to the other side ( you will divide 2 by -1 ) which will result to a -2

step 3: most important thing to remember once you multiply or divide by a negative number you will have to change the inequality sign ( in this case the smaller than sign changes to bigger than because you divided by -1 in step 3 )

hope this helped

Answer:

m∠1 = 92°

Step-by-step explanation:

∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that

m∠2 + m∠3 = 73° +107° = 180°

so, the angles are supplementary and lines a and b are parallel.

Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.

m∠1 = m∠4 = 92°

Answer:

Step-by-step explanation:

55 LRD = 1 USD

100 LRD = 1 CHD

[tex]1 LRD = \frac{1}{55} USD\\\\100 LRD = \frac{100}{55} USD = 1\frac{45}{55} USD=1\frac{9}{11} USD\\1 CHD = \frac{100}{55} USD\\1 USD = \frac{55}{100} CHD = 0.55CHD[/tex]

there are 4,500 of 4 digit multiples of 2

Answer:

4500

Step-by-step explanation:

Answer:

y = 1/2x -8

Step-by-step explanation:

The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...

rise/run = 1/2

The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...

y = slope·x + y-intercept

y = 1/2x -8

Answer:

B(5,2)

Explanation:

AC=8 units

AB must equal 2 units.

If line AC is y=x-3, and x values are -1<x<7 in AC, then B is located in x= 5. Plug x in equation.

y=5-3

y=2

B(5,2)

Final answer:

To solve the system of equations x + y = 6 and 12x + y = 5, substitute 6 - y for x in 12x + y = 5 and solve for y.

Explanation:

To solve the given system of equations x + y = 6 and 12x + y = 5, we need to substitute the value of x or y into the second equation. In this case, substituting 6 - y for x in 12x + y = 5 will allow us to solve for y.

Let's substitute 6 - y for x:

12(6 - y) + y = 5

After simplifying, we get:

72 - 12y + y = 5

Combining like terms:

-11y = -67

Dividing both sides by -11, we find that y = 67/11 or approximately 6.09.

So, option 1: 6 - y for x in 12x + y = 5 is the correct expression to substitute.

Answer:

C

Step-by-step explanation:

Use such properties of logarithms:

[tex]\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa[/tex]

Thus,

[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]

Answer:

The answer is C

Step-by-step explanation:

Use such properties of logarithms:

\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa

Thus,

\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).

Answer:

3 : 36 10: 120 6:72

Step-by-step explanation:

60 divided by 5 is 12

3 x 12 = 36

10 x 12 = 120

72/12= 6

3-36

5-60

6-72

10-120

One month equals 12$ saved

Answer:

[tex]7.5m^2[/tex]

Step-by-step explanation:

Divide the composite shape into two shapes, a rectangle and a triangle.

We can see that the rectangle has dimensions of 3 x 2.

We can use the area formula.

[tex]A=b*h[/tex]

[tex]A=3*2[/tex]

[tex]A=6[/tex]

We can also see that the triangle has a height of 3 and a base of 1 (3 - 2).

We can use the area formula.

[tex]A=\frac{1}{2}(b*h)[/tex]

[tex]A=\frac{1}{2}(3)[/tex]

[tex]A=1.5[/tex]

Now we can add these areas together.

[tex]1.5 +6=7.5[/tex]

A)

Prime numbers and numbers with a multiple of four that are between 1 and 14 include: 1, 2, 3, 4, 5, 7, 8, 12, 13.

There are 9 numbers listed.

9/14 = ~0.64285... or roghly 65.3%

B) Numbers between 1 and 14 with the multiples of 2 or 3 include: 2, 4, 6, 8, 9, 10, 12, 14.

There are 8 numbers listed.

8/14 = ~0.5714... or, about 57.14%

C) 3 and 4 is a list of two numbers.

2/14 = 1/7 = ~0.1429, or about 14.9%

D) There is a total of  numbers equal to or less than 8 in a list of 1 and 14.

8/14 = ~0.5714... or, about 57.14%

Answer:

50,000

Step-by-step explanation:

Set up a proportion:

6/1500 = 200/x

Cross multiply and solve for x:

200x1500 = 6x

300000 = 6x

50000 = x

Answer:

50000

Step-by-step explanation:

Find the "unit rate" for occupancy:  

1500 ft²

------------- = 250 ft²/person

6 people

Now multiply this unit rate by 200 people.  "people" drops out, and you are left with

250 ft²

--------------- * 200 people = 50,000 ft²

1 person

Enter 50000.  200 people will need 50000 ft² of housing.

Answer: upon itself

Step-by-step explanation: apex

[tex]\frac{4z^2-16z+15}{2z^2-11z+15}[/tex]   Factor the numerator and the denominator

[ax² + bx + c]

4z² - 16z + 15     Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.

(a·c) --> (4 · 15) = 60

Factors of 60:

1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10  

[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z

4z² - 6z - 10z + 15   Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15

2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:

(2z - 3)(2z - 5)

Do the same for the denominator, and you should get (z - 3)(2z - 5)

Now you have:

[tex]\frac{(2z - 3)(2z-5)}{(z-3)(2z - 5)}[/tex]   You can cancel out (2z - 5)

[tex]\frac{2z - 3}{z-3}[/tex]

ANSWER

[tex]\frac{(2z-3)}{(z-3)} [/tex]

EXPLANATION

The given expression is:

[tex] \frac{4z^2-16z+15}{2z^2-11z+15} [/tex]

Let us split the middle terms to get,

[tex]\frac{4z^2-6z - 10z+15}{2z^2-6z - 5z+15} [/tex]

Factor by grouping:

[tex]\frac{2z(2z-3) - 5(2z - 3)}{2z(z-3) - 5(z - 3)} [/tex]

Factor further:

[tex]\frac{(2z - 5)(2z-3)}{(2z - 5)(z-3)} [/tex]

We cancel the common factors,

[tex]\frac{(2z-3)}{(z-3)} [/tex]

where

[tex]z \ne \frac{5}{2} \: or \: z \ne3[/tex]

Answer:

25

Step-by-step explanation:

You can get that the common difference for all of the terms if four by finding the difference between -3 and 5, which gives us four. Using this, we can calculate the last term by doing 5+4*5 which is 25.

Answer: Third and fifth option

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Step-by-step explanation:

Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.

For example, for the following set of 7 data:

2, 3, [5], 8, 13

the median is 5.

If the data number is even, for example 10 data:

3, 5, 9, 12, [19, 21], 33, 35, 40, 69

The median is the average between the two data that are in the middle

[tex]\frac{19 +21}{2} = \frac{40}{2} = 20[/tex]

Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example

2, 4, 4.5, 4.8, 5          Median = 4.5

2, 4, 4.5, 67, 1506     Median = 4.5

The median does not represent the difference between the highest and the lowest data.

Therefore the correct affirmations are:

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Answer:

$1214.19

Step-by-step explanation:

Let c and p represent the cost of the sofa and the original selling price, respectively. The original markup was 0.69·p, so we have ...

c + 0.69p = p . . . . . based on selling price, the original markup was 69%

c = p(1 -0.69) = 0.31p . . . . subtract the markup

p = c/0.31 . . . . . . . . . . . . . divide by the coefficient of c

So, the original selling price was ...

520/0.31 ≈ 1677.42

The first markdown decreased the selling price to ...

1677.42 - 0.13·1677.42 = 0.87·1677.42 ≈ 1459.36

The markup increased the selling price to ...

1459.36 +0.30·1459.36 ≈ 1897.17

And the final markdown decreased the selling price to ...

1897.17 -0.36·1897.17 ≈ 1214.19

The final sale price was $1214.19.

ANSWER

Y-intercept: 3000

Slope:-275

Linear equation:y=-275x+3000

EXPLANATION

The straight line touches the y-axis at

(0,3000).

The y-intercept is b=3000

The line also passes through (2,2450).

The slope is calculated using the formula,

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

[tex] = \frac{3000 - 2450}{0 - 2} [/tex]

[tex] = \frac{550}{ - 2} = - 275[/tex]

The slope is -275.

The linear equation is given by:

[tex]y = mx + b[/tex]

[tex]y = - 275x + 3000[/tex]

Answer: OPTION A

Step-by-step explanation:

You can convert  30 kilograms to grams ([tex]1\ kilogram= 1,000\ grams[/tex]), then:

[tex](30\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=30,000\ grams[/tex]

Then, if a book in the bookcase has a mass of 400 grams and you need to find the number of books of the same mass that would take to equal the mass of the bookcase, you can divide the weight of the bookcase (in grams) by the weigth of one of these books.

Therefore:

[tex]books=\frac{30,000\ grams}{400\ grams}\\\\books=75[/tex]

Answer:

20%

Step-by-step explanation:

So, 40 is the dependent and 8 is the independent

40% divided by 8% equals 5%

100% divided by 20% equals 5%

Answer:

The product of [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{3}[/tex] is [tex]\frac{5}{9}[/tex] .

Step-by-step explanation:

Multiply both numerators and denominators.

[tex]\frac{5*2}{6*3}[/tex]

[tex]\frac{10}{18}[/tex]

Simplify this by dividing both the numerator and denominator by 2.

[tex]\frac{10/2}{18/2}[/tex]

[tex]\frac{5}{9}[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{The word product means multiply}[/tex]

[tex]\dfrac{5}{6}\times\dfrac{2}{3}=\ ?\\\\\\\dfrac{5(2)}{6(3)}=\dfrac{5\times2}{6\times3}\\\\\bf{5\times2=10}\\\\\bf{6\times3=18}\\\\\\=\dfrac{10}{18}\\\\\\\text{Both numbers foes into two so we can DIIVIDE it by two}\\\\\\\dfrac{10\div2}{18\div2}=?[/tex]

[tex]10\div2=5\\\\\18\div2= 9\\\\\\\boxed{\boxed{\bf{Answer:\dfrac{5}{9}}}}\checkmark[/tex]

[tex]\text{Good luck on your asignment and enjoy your day!}\\\\\\\frak{LoveYourselfFirst:)}[/tex]

Answer:

12.5

Step-by-step explanation:i did that problem before