Theresa commutes to work 16 days
each month. She travels 56 miles
round trip. Carl commutes to work
20 days each month; he also travels
56 miles round trip. Theresa works
12 months of the year, and Carl works
11 months. Who travels more in one
year?

Answer:

Depending on where the 5) is supposed to be, if it is multiplying the 9 x 1000, then total answer is 45280. If however the equation is 80 + 200 + 45000 then multiply by 5 it is 46400

The worth of the investment is $1.51 * 10^39

The given parameters are

Principal, P = $500

Rate, r - 4%

Time, t = 7 years

Number of times, n = 12

So, we have:

A(t)=P*e^nt

This gives

A(12) =  500 *e^(12 * 7)

Evaluate

A(12) = 1.51 * 10^39

Hence, the worth of the investment is $1.51 * 10^39

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The set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} belong to a function

[y = f(x)] considering the pairs are in the order of (x, y).

As per the question statement, we are provided with a set of ordered pairs: {(-2, 4), (0, 2), (-1, 3), (4, -2)}.

We are required to determine if the pairs in the set satisfy a function or not.

To solve this question, let us consider each pair in the form of (x, y) and then, we will have to find out a relation between x and y that will satisfy all the ordered pairs. If we are able to find out one such common relation or pattern, we will determine our ordered pairs as inputs and outputs of the same function, otherwise not.

We can say that, [tex][(-2)(-1)+2]=4,[/tex]

[tex][(0)(-1)+2]=(0+2)=2,[(-1)(-1)+3]=1+2)=3,\\[/tex]

And, [tex][4*(-1)]+2=[(-4)+2]=(-2)[/tex]

That is, all our ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} satisfy the function [y = f(x) = {x(-1) + 2}], being in the order of (x, y).

Therefore, the set of ordered pairs {(-2, 4), (0, 2), (-1, 3), (4, -2)} are the inputs and outputs of the function [y = f(x) = {x(-1) + 2}].

       (b = q).

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Answer:

-X < -2x

3x>2x

Step-by-step explanation:

Answer:

-19/2

Step-by-step explanation:

If you want the reciprocal you need to change the sign to the opposite and flip the numbers.

Answer:

27

Step-by-step explanation:

=4(3)^2-3(3)

=4(9)-9

=3(9)

=27

Answer:

here is the answer for your question 4500=3200(1+R/100)^4, hope it helps

Answer:

19 + 0.06

taking out the whole number leaves you with 0.06

or you could do 10 + 9 +0.06

if you want to split it up more

The expanded form of the number 19.06 is 1×10 + 9×1 + 0/10 + 6/100.

Numerology can be expressed in a variety of ways. Word form is a means of expressing numbers verbally. Numbers can be written in expanded form by indicating the value of each digit. The digits 0 through 9 are used to write numerals in standard form, and each digit has a place value.

Given, A number in a decimal form which is 19.06.

This can be written as,

1×10¹ + 9×10⁰ + 0/10¹ + 6/10².

1×10 + 9×1 + 0/10 + 6/100.

Each digit has a face value and a place value.

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It will take 44 minutes for the car to pass the truck.

Relative speed is the net speed difference between two objects when they are on the same direction we subtract and when they are on different direction we add.

According to the given question A truck enters a highway driving 60 mph which is (60/60) miles per minute = 1 mile per minute.

The car is going at a speed of 71 miles hour or (71/60) mile per minute = 1.183 miles per minute.

∴ Their relative speed difference is ( 1.183 - 1 ) = 0.183 miles.

Given the car enters the highway 8 minutes later on that time the truck will cover the distance of (1×8) = 8 miles.

so, the time needed for the car to pass the truck is (8/0.183) minutes which is = 43.7 minutes or 44 minutes.

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the value of the function is zero, then the correct option is the first one.

g(x)=0

We know that the given function:

g(x) = -3*(x - 3)^2 + 4

Crosses the x-axis at x = 1.845

Now, remember that the x-axis is located at y = 0, to for the function:

y = g(x)

We should have that g(1.845) = 0

Then what we can conclude about the value of g(x) at x = 1.845 is that the value of the function is zero, then the correct option is the first one.

g(x)=0

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The answers are:

a) The domain is the set of all real numbers.

b) The range is R:  (-∞, -2]

c) there are not any x-intercept.

d) The y-intercept is y = -5

e) f(0) = -5

   f(4) = -4

For a function f(x) =y, we define the domain as the set of the inputs and the range as the set of the outputs.

To identify the domain we need to look at the horizontal axis, and there we can see that the function covers it completely, then the domain is the set of all real numbers.

For the range, we look at the vertical axis. Here we can see that the function has a maximum at y = -2 and then goes down, then the range is:

R: (-∞, -2]

c) Now we want to get the xintercepts. As you can see in the graph, it never intercepts the x-axis (the horizontal one). Thus, there are not any x-intercept.

d) The y-intercept is when the graph intercepts the vertical axis, in this case the y-intercept is at y = -5

e) f(0) is the value of the y-intercept, which we already know is y = -5

for f(4) we need to find x = 4 in the horizontal axis and then find the correspondent value of the graph.

We can see that f(4) = -4.

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The value of the given function is given as follows f(-5) ,g(2),f(4m)  are 25,-3,-12m+10.

The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope. The vertex of a quadratic function is calculated by rearranging the equation to its general form, f(x) = a(x – h)2 + k; where (h, k) is the vertex.

The notation y=f(x) defines a function named f. This is read as “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable

F(x) is the notation for a function which is essentially the thing that does your operation to your input. You can think of a function as a little machine. You put in your input, it changes it around and gives you output in return. F(x) means it's a function f with respect to x.

f(x) = -3x+10

f(-5) = -3*-5 +10

= 15+10=25

g(x) = x^2-7

g(2)= 2^2-7

= 4-7

=-3

f(4m) = -3x+10

= -3*4m+10

=-12m +10

= -12m +10

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The values of the above functions are 25, 3, and 12m+10 for f(-5) and g(2) and f(4m), respectively.

By rearranging the equation to take on its general form, f(x) = mx + c, where m is the slope, one can determine the slope of a linear function. By rearranging the equation to its general form, f(x) = a(x - h)2 + k, where (h, k) is the vertex, one can determine the location of a quadratic function's vertex.

A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value or independent variable is denoted by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).

A function is essentially the item that applies your operation to your input, and its notation is F(x). A function can be compared to a tiny machine. You provide your input, which is altered and converted into output. F(x) denotes that a function is one that has respect to x.

f(x) = -3x+10

f(-5) = -3*-5 +10

= 15+10=25

g(x) = x^2-7

g(2)= 2^2-7

= 4-7

=-3

f(4m) = -3x+10

= -3*4m+10

=-12m +10

= -12m +10

Step-by-step explanation:

Answer:

The final temperature is 10.1 degrees Fahrenheit

Using the t-distribution, the limits of the 95% confidence interval are given as follows:

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 16 - 1 = 15 df, is t = 2.1315.

The other parameters are given as follows:

[tex]\overline{x} = 33, s = 4, n = 16[/tex]

Hence the bounds of the interval are given as follos:

Which are the lower and the upper bound, respectively.

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Answer:

261 stairs

Step-by-step explanation:

If David trips twice every 9 stairs and he has tripped 58 times. We can multiply 9 by 58.

58*9=522

Since David trips twice in 9 stairs, then to find how many stairs he has climbed we need to divide 522 by 2.

522/2=261

David has climbed 261 stairs.

Answer:

77

Step-by-step explanation:

2(4)^2+9(5)

2(16)+45

32+45

=77

Answer:

109

Step-by-step explanation:

First, you substitute x with 4 and y with 5

so your equation should be 2(4)squared +9(5)

PEMDAS

Parrentisies first so 2x4=8 and 9x5=45

then exponents so 8squared = 64

Addition next so 64 + 45 =?

? = 109

Answer: 6 days

Divide 30 by 5

Answer:

Neither

Step-by-step explanation:

MN: slope = 4/5

PQ: slope = -4/5

Two lines are parallel when their slopes are equal but their y-intercepts are different.

Two lines are perpendicular when their slopes are negative reciprocals of each other.

The negative reciprocal of 4/5 (MN) is -5/4

PQ -4/5

-5/4 [tex]\neq[/tex] -4/5

therefore the lines are Neither

Answer:

8.5 square feet

Step-by-step explanation:

(3.4x5)/2

=8.5

Answer:

y = 4x + 45

Step-by-step explanation:

The slope for the equation y = -1/4x + 9 would be the number before the x.  In this case, that number is -1/4.  A perpendicular slope would be the opposite inverse to this number which would be  4.    We know have the slope.  We need the y- intercept.  

To find the y-intercept we would need and x and y value that is on the line and the slope.  We are given this information.  From above, we see that the slope is 4.  We can use the x and y from the ordered pair given (-9,9)  The x value is -9 and the y value is 9.

y = mx + b  Substitute in what we know.

9 = 4(-9) + b  We are soling for b  

9 = -36 + b  Add 36 to both sides of the equation

45 = b  We now know the y-intercept

The equation will be:

y = mx + b

y = 4x + 45

Answer:

  C = 16

Step-by-step explanation:

Given point M=2 and J=18 on a number line, you want the coordinate of point C that is 7/8 of the distance from M to J.

The distance from M to J is the difference of their coordinates:

  J -M = 18 -2 = 16

7/8 of that distance is ...

  (7/8)(16) = 7(16/8) = 7(2) = 14

You are being asked for the coordinate of the point that is 14 units from M in the direction of J.

To find the coordinate of C, we add the desired distance to the coordinate of M:

  C = M +14

  C = 2 +14 = 16

The coordinate of point C is 16.

Answer:

  3

Step-by-step explanation:

You want to know the appropriate number of significant digits in the quotient of measurements 2.09×10^9 and 4.053×10^-4.

The number of significant digits in a number written in scientific notation is the count of digits in the mantissa. Numbers with more significant digits are considered to be more precise.

  2.09×10^9 . . . . has 3 significant digits

  4.053×10^-4 . . . . has 4 significant digits

When imprecise numbers are multiplied or divided, the resulting product or quotient cannot be more precise than the least precise number used. The quotient of numbers with 3 and 4 significant digits will only have 3 significant digits.

Answer: g(-2) = 17

Step-by-step explanation:

         When finding g(-2), we will substitute all values of x for -2 in the function. First, we will substitute values in. Then, we will simplify by squaring, multiplying, and adding.

g(x) = 3x² -2x + 1

g(-2) = 3(-2)² -2(-2) + 1

g(-2) = 3(4) + 4 + 1

g(-2) = 12 + 4 + 1

g(-2) = 17

Answer:

7(n + 4) or 7×(n + 4)

Step by step explanation:

Answer:

Yes, there were people on more than 70% of the seats.

Step-by-step explanation:

Let's start with the children. We know that 2/3 of the children had seats in the Stalls, which means that the other 1/3 of the children had seats in the Circle. We know that 114 children had seats in the Circle. Therefore, we can calculate that there were 342 children total, since 114 (1/3 of the children) times 3 is 342.

In order to find how many adults there were, we can use the ratio of adults to children, 4:3. We're basically going to undo our math from the previous part. We divide 342 by 3 to determine how much 1 is. This gives us 114, which we multiply by 4 to find how many adults there were.

There were 456 adults.

There were 342 children.

456 + 342 = 798

There were 798 people in the theatre total.

To find what 70% of 1100 is, we multiply 0.7 x 1100. This gives us 770. Because 798 is more than 770, we know that there were people on more than 70% of the seats.

Answer: C

Step-by-step explanation:

Answer:

[tex](\sqrt[12]{8} )^x[/tex]

Step-by-step explanation:

[tex](\sqrt[3]{8} ) \frac{1}{4} x = 8\frac{1}{3} \frac{1}{4} x = 8\frac{1}{12} x = (\sqrt[12]{8} )^x[/tex]

The cost of the baker's shelf is $1,448.94

The length of the bakery is 12 meters

The width of the bakery is 19 meters

The wooden shelf costs £23.37 per meter

The cost can be calculated as follows

2(12+19) × 23.37

= 2(31) × 23.37

= 62 × 23.37

= 1,448.94

Hence the cost of the baker's shelf is $1,448.94

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