A mouse scurries across your kitchen floor at 2.0 feet per second. How many miles can the mouse travel in 1.5 hours (rounded to the nearest tenth)?

let's firstly, convert the mixed fractions to improper, and then multiply.

[tex]\bf \stackrel{mixed}{3\frac{2}{5}}\implies \cfrac{3\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{17}{5}}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{17}{5}\cdot \cfrac{7}{3}\implies \cfrac{17\cdot 7}{5\cdot 3}\implies \cfrac{119}{15}\implies 7\frac{14}{15}[/tex]

This is a procedure to multiply mixed numbers. Then multiply the fractions and simplify the resulting fraction into a mixed number.

The problem asked here is a multiplication problem with mixed numbers. First, let's convert 3 2/5 and 2 1/3 to improper fractions. For 3 2/5, multiply 5 (the denominator) and 3 (the whole number), then add 2 (the numerator). We get 17/5. For 2 1/3, multiply 3 (the denominator) and 2 (the whole number), then add 1 (the numerator). We get 7/3.

Now let's multiply the fractions. The resulting fraction is (17/5) x (7/3) = 119/15. This simplifies to 7 14/15.

So, 3 2/5 multiplied by 2 1/3 equals 7 14/15.

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The answer is B. 2

Hope it helps

The two of the given numbers 54.045 and 54.405 can be compared using the inequality as 54.045 < 54.405.

Given two numbers 54.045 and 54.405. If the two numbers are plotted on the graph as shown below, it can be clearly seen that 54.045 comes before 54.405 on positive axis.

Therefore, 54.045 is smaller than 54.405. So ‘<’ smaller than inequality symbol will be used in between  54.045 and  54.405.

Hence, the correct representation of the comparison is 54.045 < 54.405.

Learn more about Inequality here:
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x= -2 hope this help do you need to show your steps?

Step 1. Separate terms with roots from terms without roots

[tex]\sqrt{x+3}=5 - 4[/tex]

Step 2. Simplify 5 - 4 to 1

[tex]\sqrt{x+3} =1[/tex]

Step 3. Square both sides

[tex]x + 3 = 1[/tex]

Step 4. Subtract 3 from both side

[tex]x = 1 - 3[/tex]

Step 5. Simplify 1 - 3 to -2

[tex]x = -2[/tex]

y = 8/5( x - 9 ) + 16

8/5 = 1.6

y = 1.6x - 14.4 + 16

y = 1.6x + 1.6

The slope is therefore 1.6 and

The y-intercept is 1.6

The coordinates of the other endpoint L are (-19, 13).

If K is the midpoint of segment HL, we can use the midpoint formula to find the coordinates of point L.

The midpoint formula states that if you have the coordinates of two endpoints of a line segment and the coordinates of the midpoint, you can find the missing endpoint.

Let's denote the coordinates of point L as (x, y).

The midpoint formula is:

Midpoint =[tex]\(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\)[/tex]

Given:

Coordinates of K = (-9, 3)

Coordinates of H = (1, -7)

Let (x, y) be the coordinates of point L.

Using the midpoint formula for x-coordinates:

[tex]\(\frac{{1 + x}}{2} = -9\)[/tex]

Solving for x:

[tex]\(1 + x = -18\)[/tex]

[tex]\(x = -19\)[/tex]

Using the midpoint formula for y-coordinates:

[tex]\(\frac{{-7 + y}}{2} = 3\)[/tex]

Solving for y:

[tex]\(-7 + y = 6\)[/tex]

[tex]\(y = 13\)[/tex]

Therefore, the coordinates of the other endpoint L are (-19, 13).

The answer is 3.88888888889

The answer is 35/9

You first would remove the parentheses

Next you see that there is a subtraction symbol and a negative symbol right beside each other. You cant have 2 negatives side by side, so you change the symbol to addition

The problem then looks like this: 5/9 + 3 1/3

To make the problem easier you change the mixed number (3 1/3) to an improper fraction which is 10/3

Because its 5/9 + 10/3 you multiply 10 and 3 and get 30, and you keep the LCD (least common denominator) which is 9

Finally you add 5 + 30 = 35 and have 9 as your denominator

35/9 or 3 8/9

[tex]\frac{3}{2}x[/tex] - 4 = 16

[tex]\frac{3}{2}x[/tex]  = 20    added 4 to both sides

3x = 40       multiplied both sides by 2

x = [tex]\frac{40}{3}[/tex]     divided both sides by 3

Answer: x = [tex]\frac{40}{3}[/tex]

[tex]y = e^{-sin(x)}[/tex]

[tex]y' = -e^{-sin(x)}(cos(x))[/tex]

[tex]0 = -e^{-sin(x)}(cos(x))[/tex]

When is cos (x) = 0?  at 90° (aka π/2)

Answer: [tex]\frac{\pi}{2}[/tex]

Answer: Hello there!

We have the function f(x) = exp(-sin(x)) and we want to see in wich point the slope is 0.

This is equivalent to see when f'(x) = 0

where f'(x) is the derivative of f(x)

Then the first step is derivate the function f(x)

if we have a function of the form g(h(x)), his derivate is:

g'(h(x))*h'(x)

In our case, g(x) = exp(x) and h(x) = - sin(x)

then f'(x) = exp(-sin(x))*(-cos(x))

Now we know that exp(-sin(x)) is never equal to 0, then we need to se when the cosine is equal to zero.

cos(90°) = 0, and 90° is equivalent to pi/2

Then f'(pi/2) = exp(-sin(pi/2))*(-cos(pi/2)) = 0

this means that the function f(x) has a slope of 0 in the point x = pi/2

[tex]-7k < 63\qquad|\text{change the signs}\\\\7k > -63\qquad|\text{divide both sides by 7}\\\\k >-9\\\\Answer:\ c)\ k > -9.[/tex]

If you consider the logarithm base 3 of both sides, you have

[tex] \log_3(3^c) = \log_3(27) [/tex]

You can use a rule of logarithms that allow you to turn exponents into multiplicative factors:

[tex] \log_a(b^c) = c\log_a(b) [/tex]

So the equation becomes

[tex] c\log_3(3)=\log_3(27) [/tex]

Now, by definition, you have

[tex] \log_a(b)=c \iff a^c=b [/tex]

So, you have

[tex] \log_3(3)=x \iff 3^x=3 \iff x = 1,\quad \log_3(27)=y \iff 3^y=27\iff y=3 [/tex]

So, the equation becomes

[tex] 1\cdot c = 3 \iff c=3 [/tex]

[tex]log_{3}[/tex]27 = c

using the law of logs : [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

given [tex]3^{c}[/tex] = 27 then

[tex]log_{3}[/tex] 27 = c

D. y = 50x + 200 is your answer

The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.

The expression shown is an exponential expression.  An exponential expression usually takes the form [tex]ab^{x}[/tex], as this one does.  A represents the initial value, in this case-the initial number of bacteria.  B represents the growth rate.  When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion.  In this case, a=57, and b=0.31.

Hope this makes sense!

Answer:

$35

Step-by-step explanation:

Rounding to the nearest dollar which would be 4 so in that case you would use the 5 in .57 and because 5 is a large number it would make the 4 into a five thus making it $35. Hope this helped :)

A. y = -x³   leading coefficient is negative

B. y = x³ + 1   leading coefficient is positive

C. y = x²    leading coefficient is positive

D. y = (x-1)³    leading coefficient is positive

Answer: B, C, D

The answer to your problem is Substitution (A) due to y being 4.

Answers:

The domain of the graph is {-3, -1, 1, 4}. The range of the graph is {-4, -1, 1, 4}

The domain of the set of ordered pairs is {-4, -3, 1}. The range of the set of ordered pairs is {1, 3, 4}

====================================================

Recall that the domain is the set of allowed x values. All we do is list the unique x coordinates of each point which are -3, -1, 1 and 4. The range is the set of y values so we just list the unique y coordinates of each point which are -4, -1, 1 and 4.

The same will happen with the other problem as well. The set of points listed is pretty much identical to the first problem, but the points haven't been graphed, but instead their coordinates have been listed out. The first coordinate is the x coordinate. The second coordinate is the y coordinate. Each point is in the form (x,y).

The domain of the graph is {-3, -1, 1, 4}. The range of the graph is {-4, -1, 1, 4}

The domain of the set of ordered pairs is {-4, -3, 1}. The range of the set of ordered pairs is {1, 3, 4}

====================================================

Recall that the domain is the set of allowed x values. All we do is list the unique x coordinates of each point which are -3, -1, 1 and 4. The range is the set of y values so we just list the unique y coordinates of each point which are -4, -1, 1 and 4.

The same will happen with the other problem as well. The set of points listed is pretty much identical to the first problem, but the points haven't been graphed, but instead their coordinates have been listed out. The first coordinate is the x coordinate. The second coordinate is the y coordinate. Each point is in the form (x,y

ANSWER

The correct answer is A

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

EXPLANATION

Given [tex]f(x)=ax-b[/tex].

We can find the inverse by taking the steps.

1. Let  [tex]y=ax-b[/tex]

2. Interchange x and y

[tex]x=ay-b[/tex]

3. Make y the subject

[tex]x+b=ay[/tex]

[tex]\frac{x+b}{a}=y[/tex]

The new function we got now is the inverse of f(x)

[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]

x + b/a Replace f(x) with y, interchange x and y and solve for y.

Solve for x by simplifying both sides of the equation, then isolating the variable.

x = 5

To solve the equation 5(2x-1)/3 - 4 = 11 for x, you need to isolate the term containing x on one side and perform basic algebraic operations to find that x = 5.

The mathematical equation in question is 5(2x-1)/3 - 4 = 11, which you can solve to find the value of x. First off, you should isolate the term including x on one side to simplify the equation. Multiply both sides by 3 to get rid of the division by 3. The equation then becomes: 5(2x-1) - 4*3 = 11*3, which simplifies to 5(2x-1) - 12 = 33. Then, add 12 to both sides to isolate the term containing x on one side: 5(2x-1) = 45. Next, divide both side by 5 so the equation becomes: 2x-1 = 9. Finally, add 1 then divide by 2 to solve for x, and you get x = 5.

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i looked it up and i may be wrong but i think its 45

Answer:

I think it is 55 because it said how many people were at least 60 so i added the last two columns together.

Step-by-step explanation:

Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.

If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.

Divide total miles between airports by the airplane's speed to find the time it took to travel by plane:

1450 miles / 350 mph = 4.142 hours = 4 hours 9 minutes

Then add the time the bus traveled:

4 hours 9 minutes  + 20 minutes = 4 hours 29 minutes

Answer:

4 hours and 29 mins

Step-by-step explanation:

For this question, you simply take the x value from the given chart and plug it into the equation, then if the outcome makes sense based on the chart then you use another value of x and plug the second value in and if that also makes sense then you continue plugging in all the x values from the chart until all of them match. There is only one chart which contain the correct table of values.

To start of, let’s plug in the x values from graph 1, the first two values seems to be correct. However, in the third value, it does not match, therefore the first option is in correct.

Moving on to the second option, we could already determine that this table of values is incorrect because the very first x value does not match.

Moving onto the third table of values, we determine that all of the x values are in accordance with the y-values, therefore this option is correct.

Answer: Third option