231. At noon, my odometer read 6852 miles. At 3:30 pm, it read 7034 miles.
(a) What was my average rate of change during these three and a half hours?
(b) Let t represent the number of hours I have been driving since noon and y represent my
odometer reading. Write an equation that relates y and t. Assume constant speed.
(c) Graph your equation.
(d) Show that the point (5,7112) is on your line, and then interpret this point in the context
of this problem.

Answer:

Question 4:

Question 5:

Question 6:

Step-by-step explanation:

Given vertices of the pre-image:

If the pre-image is reflected in the line x = -1, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 180° about the origin, the transformation rule is:

Therefore the vertices of the image are:

Given vertices of the pre-image:

If the pre-image is rotated 270° about the origin, the transformation rule is:

If the direction of a rotation is not specified, then it is counterclockwise.

Therefore the vertices of the image are:

The values are;

1. 35/3 days - Direct proportion

2. 4254 - Direct proportion

3. 120 teachers - Indirect proportion

Proportion can be described as an equation that has two ratios set equal to each other.

It is also seen as a mathematical comparison of numbers, terms, or variables.

The different types of proportion are;

From the information given, we have;

1. If 3 men completes the project in 7 days

Then 5 men would finish it in x days

cross multiply

x = 5(7)/3

x = 35/3 days

2. If 25kg of rice cost 1130

Then 100kg would cost x

cross mutiply

x = 1130(100)/25

x =  4,254

3. If there are 90 teachers = 1500 students

Then x teachers = 2000 students

x = 2000(90)/1500

x = 120 teachers

Hence, the values are 35/3 days, 4, 254 and 120 teachers.

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The geom_ jitter () method creates a scatter plot and then it adds a small amount of random noise to every point in the plot to make the points easier to find.

Therefore, the geom_jitter is shortcut that creates a scatterplot and add random variation in each point.

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Answer: 3

Hope this helps :)

Step-by-step explanation:

1+2+3+4+5=15

15/5=3

Answer:

2 miles

Step-by-step explanation:

Distance = speed x time

= 10mph x 1/5

= 2 miles

Answer: The area of the floor of the store room is 1080 m^2

Step-by-step explanation:

We can begin by using the information provided about the ratios of the dimensions of the store room to set up a system of equations.

Let's call the height of the store room h, the length l, and the breadth b.

From the first ratio given, we know that:

h/l = 5/4

From the second ratio given, we know that:

h/b = 2/3

We can also use the information about the total area of the four walls to set up another equation.

The total area of the four walls is the sum of the area of the top and bottom walls (length x height) and the area of the two side walls (breadth x height).

So we have:

2lh + 2bh = 2760

We can now use the first two equations to solve for one of the variables in terms of the other two.

We can cross-multiply and simplify the first equation:

l = (4/5)h

We can cross-multiply and simplify the second equation:

b = (3/2)h

We can now substitute these expressions for l and b into the equation for the total area of the four walls:

2(4/5)h^2 + 2(3/2)h^2 = 2760

Solving for h, we get:

h = 30

Now that we know the value of h, we can use the equations l = (4/5)h and b = (3/2)h to find the values of l and b.

l = (4/5)h = (4/5)(30) = 24

b = (3/2)h = (3/2)(30) = 45

Now we have all the information we need to find the area of the floor, which is the product of the length and breadth of the store room

Area of floor = lb = 2445 = 1080 m^2

Explanation: By using the information about the ratios of the dimensions of the store room and the total area of the four walls, we set up a system of equations and used algebra to solve for the height, length and breadth of the store room. With this information, we were able to find the area of the floor of the store room.

Answer:

10

Step-by-step explanation:

The given series is a geometric series with the first term a = 8, and the common ratio r = 1/5. To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

So, in this case, the sum of the series is:

S = 8 / (1 - 1/5) = 8 / (4/5) = 8 * (5/4) = 40/4 = 10.

Therefore, the sum of the series is 10.

Answer:

10

Step-by-step explanation:

A geometric series is the sum of the terms of a geometric sequence.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric series:

The ellipsis means to "continue in this pattern".  Therefore, find the sum to infinity of the given geometric series.

From inspection of the sequence, the first term is 8:

[tex]\implies a=8[/tex]

To find the common ratio, divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{1.6}{8}=0.2[/tex]

Substitute the found values of a and r into the geometric series formula:

[tex]\implies S_{\infty}=\dfrac{8}{1-0.2}=\dfrac{8}{0.8}=10[/tex]

Therefore, the sum of the given geometric series is 10.

Answer:

2y+x=7

Step-by-step explanation:

The equation of a line is in the form:

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

where m is the gradient and c is the y-intercept.

In the equation y=2x+3 the gradient is 2, so to find the perpendicular gradient, it is the negative reciprocal, or in other words, flip the number upside down and make it negative:

[tex]2 = \frac{2}{1} [/tex]

[tex] \frac{2}{1} \: flipped \: upside \: down = \frac{1}{2} [/tex]

[tex] make \: \frac{1}{2} \: negative = - \frac{1}{2} [/tex]

So the gradient for the point (1, 3) is -1/2

Using y=mx+c to find c (the y-intercept) where y=1, m=-1/2, x=1, substitute these values in:

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

[tex]3 = - \frac{1}{2} (1) + c[/tex]

[tex]3 = - \frac{1}{2} + c[/tex]

[tex]3 + \frac{1}{2} = c[/tex]

[tex]c = \frac{7}{2} [/tex]

So the equation is:

[tex]y = - \frac{1}{2} x + \frac{7}{2} [/tex]

We need to write this in the form ax+by=c, so multiply everything by 2 to get rid of the fractions on the right:

[tex]2y = - x + 7[/tex]

Bring x to the left side by adding it:

[tex]2y + x = 7[/tex]

This is now in the form ax+by=c

Answer: r <= -24.32
CMIIW :))

Step-by-step explanation:

Answer:

B)  x + y ≤ 30,000

     x ≥ 8,000

     x ≥ 3y

Step-by-step explanation:

Definition of the variables:

If Tamara has $30,000 and part or all of which she wants to invest into a combination of corporate bonds and municipal bonds, then the sum of the investments in the two bonds will be less than or equal to $30,000:

If Tamara wants to invest no less than $8,000 into corporate bonds, then the amount invested in corporate bonds (x) will be greater than or equal to $8,000:

If Tamara wants to invest at least three times as much into corporate bonds than into municipal bonds, then the amount invested in corporate bonds (x) will be greater than or equal to 3 times the amount invested in municipal bonds (y):

The list of all sets which are subsets of the given set; {Lennon, McCartney} as required is; { }, {Lennon}, {McCartney}, {Lennon, McCartney}.

It follows from the task content that the list of all subsets of the given set is to be determined.

It is noteworthy to know that the empty set, {} is a subset of all sets.

Also, if all the elements of a set A are present in another set B; it can be inferred that the set A is a subset of set B.

On this note, the list of all sets which are subsets of the given set; {Lennon, McCartney} is; { }, { Lennon }, { McCartney }, { Lennon, McCartney }.

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Plot the given coordinates of the polygon in the coordinate plane and connect it with a smooth curve.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end.

A coordinate plane is a two-dimensional plane created by the intersection of two number lines. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two of these number lines.

Plot the points on the graph according to the given coordinates. Connect all the points. The polygon is triangle.

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√25  is the greatest value of the expressions .

What is an expression in maths ?

A number, a variable, or a mix of both plus certain operation symbols make up an expression. Two expressions are combined to form an equation, which is joined by the equal sign.

                         The combination of 8 and 3 is an example of a word. Example sentence: The result of adding 8 and 3 is 11. An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

√25   = 5

√5  =   2.2360

√8  =   2.8284

√10 =    3.1622

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Answer:

A= 110 degrees AND B= 140 degrees.

Y= 112 degrees and X= 157 degrees.

Step-by-step explanation:

Triangle XYZ is an isocoles triangle, because it has two congruent sides. 70 degrees is a measurement of an angle opposite of one of those congruent sides, so angle YXZ is also 70 degrees. By the triangle angle sum theorem, we can say that the measurement of angle YZX is 40 degrees. So, for the first triangle, by the linear pairs theorem, we can find the two missing angles.

A= 110 degrees AND B=140 degrees.

For the triangle on the right, we can use the triangle angle sum theorem to say that angle BDC is 68 degrees. Then, we can say that by the by the linear pairs theorem that angle ADE is 112 degrees.  From there, we need to look at the 23 degree measurement on the lower right triangle. We can see that the angle steadily rises on that line and then we can take 180-23 by the linear pairs theorem to conclude than angle BEA is 157 degrees. This can be confirmed by looking at the two innermost angles in the top right triangle. If you take 180-23-112, you will get 45. If you add 45 to 112, you will get 157.

Y= 112 degrees and X= 157 degrees.

The interest paid at the term end will be $5400.

What is interest and its types(Simple and compound interest)?

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for the loan. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period. Simple interest is calculated only on the principal amount of a loan or deposit, so it is easier to determine than compound interest.

​The formula for these are

Simple Interest= P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

Compound Interest=P×(1+r)^t−P

where:

P=Principal amount

r=Annual interest rate

t=Number of years interest is applied

Here,

Interest rate will be risk percentage + LIBOR

i.e.4.8%

Hence,  the interest can be found by using formula for simple interest

Therefore,

SI=P*r*t

=$450000*0.048*0.25               (Time is 3 month or  0.25 years.)

SI (Interest paid)=$5400

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The total interest paid for the period of three months will be $5225 on the loan amount of $450000.

What is interest?

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $450000

R=2.2%+2.8%=5%

T=1/4 years or three months

So from the simple interest formula

SI= PNR/100

SI=15000×5×1/`100×4

SI=$5625

Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.

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Answer: 844000

Step-by-step explanation:

843857 = 844000 because you round up

Answer:

Step-by-step explanation:

Love these kinda problems.

Alr,

d/dx of lnx = 1/x

let 3x³ + 12x = t

dt/dx = 9x² + 12 ( d/dx of xⁿ = n[tex]x^{n-1}[/tex])

then, d/dx of ln t= 1/t x dt/dx  = 1/(3x³+12x) x (9x² + 12) = (3x² + 4)/(x³ + 4x)

Pls mark as brainliest if possible. Cheers

Answer:

Step-by-step explanation:

If you used good technique, you would expect the range of measurements to be small. Good technique would include using a measuring instrument that is calibrated correctly, measuring in the same position and at the same time of day, and being consistent in how you position your body during the measurement. All of these factors would help to reduce the amount of measurement error and therefore lead to a smaller range of measurements.

Answer:

A=4.2 P=9.2

Step-by-step explanation:

Did this also and used mathaway

Answer:

6

Step-by-step explanation:

85 +12.5*x visits =155

12.5x≥70

x must be greater than 5.6 so she need to go 6 times & then she'll get her free ticket

Answer:

  (-20x -25)/(x^2-x-30)

Step-by-step explanation:

You want to simplify the rational expression (3x²)/(x²-x-30) -(3x+5)/(x-6).

Usually these problems are constructed so that the higher-degree polynomial denominator has the lower degree denominator as a factor. That is the case here.

  [tex]\dfrac{3x^2}{x^2-x-30}-\dfrac{3x+5}{x-6}=\dfrac{3x^2}{(x+5)(x-6)}-\dfrac{(x+5)(3x+5)}{(x+5)(x-6)}\\\\=\dfrac{3x^2-(3x^2+20x+25)}{x^2-x-30}[/tex]

  [tex]=\boxed{\dfrac{-20x-25}{x^2-x-30}}[/tex]

The time it takes until the deposit amounts to $6,000 is 2.6 years

From the question, we are to calculate how long it takes until the deposit amounts to $6000

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $5,000

r = 7%= 0.07

n = 12

t = ?

A = $6,000

Putting the parameters into the formula

A = P(1 + r/n)^nt

6000 = 5000(1 + 0.07/12)^(12×t)

6000/5000 = (1 + 0.0058333)^12t

1.2 = (1.0058333)^12t

Take log1.0058333 of both sides

31.346375 = 12t

31.346375/12 = t

t = 2.6 years

Hence, the time it takes is 2.6 years

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A relative maximum is a highest point in that little area.  Think of it as a top to a mountain in a mountain range.  It's a peak, but it might not be the tallest peak.

A relative minimum is the lowest point in that little area.  Think of it as a the bottom of a valley in some area.  It's possibly one of many valleys, so might not be the deepest valley.

When we talk about where these things happen, we describe them based on their x-values.  They happen at the x-value of that peak or valley.

There's a little peak on the left side and the x-value of that peak is x = -1.2.

There's a little valley on the right side and the x-value of that valley is x = 1.2.

The answer is A.

On solving the provided question, we can say that the value of the quadratic equation would be x = 0.18

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

The roots of a quadratic equation ax^2 + bx + c = 0 can be found using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

The given equation is 2x² + 5x - 1 = 0

Hence, the larger root of the given quadratic equation would be x = 0.18.

[tex]x = \frac{-5 + \sqrt{5^2 - 4(2)(-1)} }{2(2)} \\x = 0.18\\or \\x = -2.68\\[/tex]

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well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

[tex]~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}[/tex]

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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Answer: 96 Euros each month

Step-by-step explanation: 2400 * 0.2 = 480 -> 2400-480 = 1920(this is the amount of money needed to pay each month) 1920 / 20 = 96

The graph that represents a geometric sequence is Graph A.

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding one by a fixed, non-zero number called the common ratio.

Examples of geometric sequences include:

2, 4, 8, 16, 32, ... (common ratio of 2)

1/3, 2/3, 4/3, 8/3, ... (common ratio of 2/3)

5, -25, 125, -625, ... (common ratio of -5)

Geometric sequences have the property that the ratio of any two consecutive terms is always the same, and the quotient of any two consecutive terms is the common ratio.

This is shown only in the first graph so Graph A shows the geometric sequence.

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Answer:

0.65 and 13/20

Step-by-step explanation: