Students observing a caterpillar crawl on a tree noticed that the caterpillar crawled upwards 38 of an inch every minute. The caterpillar was already 4.5 feet off the ground when the students began observing.

Which function represents the total number of inches the caterpillar crawls after x minutes?

f(x) = 4.5x + 3/8

f(x) = 54x + 3/8

f(x( = 3/8x + 54

f(x) = 3/8x + 4.5

Answer:

See below.

Step-by-stepexplanation:

The slope = rise/run

= (7- -5)/(-3-1)

=  12/-4

= -3

In point slope form:

y - y1 = -3(x - x1)

y - (-5) = -3(x - 1)

y + 5 = -3(x - 1) <--------- Point slope form.

y + 5 = -3x + 3

y = -3x - 2. <----------Slope-intercept form.

Answer:

y = -3x - 2

Step-by-step explanation:

If a line passes through (1.-5) and (-3, 7), the appropriate equation for the line in point-slope form is, y = -3x - 2.

Answer:

d

Step-by-step explanation:

Definitely choose the point-slope form y - k = m(x - h) (Answer d)

Final answer:

To write the equation of a line when you have the slope and a single point on the line, the D) point-slope form is the most suitable formula to use.

Explanation:

When you know the slope of a line and a point on the line, the best form to use is the point-slope form. The point-slope formula is expressed as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the known point. This formula allows you to plug in the slope and the coordinates of the point directly to form the equation of the line.

The slope-intercept form y = mx + b is used when you know the slope and the y-intercept, while the point-slope form is specifically designed to formulate an equation given a point and the slope of the line. A horizontal line, which has a slope of zero, nor a vertical line, which has an undefined slope, would not apply to this particular situation.

Answer:

[tex]8.33\%[/tex]

Step-by-step explanation:

we know that

The total removed by milling is equal to (3.00"-2.75")=0.25"

In this problem 3.00" represent the 100%

so

using proportion

Find out how much percentage represent the total removed by milling

[tex]\frac{3.00}{100}=\frac{0.25}{x}\\\\x=100*0.25/3.00\\\\x=8.33\%[/tex]

Final answer:

To find the percentage of the block removed by milling, subtract the final size from the original size, divide by the original size, and multiply by 100. A 0.25" reduction from a 3.00" block represents an 8.33% decrease.

Explanation:

The question asks us to calculate the percentage of material removed from a block through the milling process. To find the percentage reduction, we start by determining the difference in size before and after the milling, which is 3.00" - 2.75" = 0.25". The next step is to divide the amount removed by the original size and then multiply by 100 to get the percentage. The calculation is as follows:

Find the difference: 3.00" - 2.75" = 0.25" (amount removed)

Calculate the percentage: (0.25" / 3.00") × 100 = 8.33%

Therefore, 8.33% of the original block is removed by milling.

Answer:

0.1056

Step-by-step explanation:

Given from the question;

Mean=125cm

Standard deviation =12cm

You should find the z* value from  mean and standard deviation

The formula to apply is;

z=(wingspan in question - mean)÷standard deviation

[tex]z=\frac{140-125}{12} =\frac{15}{12} =1.25[/tex]

Using the Z score table read the value of proportion that corresponds to 1.25

From the table, the proportion is 0.1056

Answer:

The average absolute deviation (or mean absolute deviation (MAD)) about any certain point (or 'avg. absolute deviation' only) of a data set is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values). It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be the mean, median, mode, or the result of any other measure of central tendency or any random data point related to the given data set. The absolute values of the difference, between the data points and their central tendency, are totaled and divided by the number of data points.

Measures of dispersion

Edit

Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, the statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since in general, they may have values considerably different from each other.

Mean absolute deviation around a central point

Edit

For arbitrary differences (not around a central point), see Mean absolute difference.

The mean absolute deviation of a set {x1, x2, ..., xn} is

{\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}|x_{i}-m(X)|.} \frac{1}{n}\sum_{i=1}^n |x_i-m(X)|.

The choice of measure of central tendency, {\displaystyle m(X)} m(X), has a marked effect on the value of the mean deviation. For example, for the data set {2, 2, 3, 4, 14}:

Mean Absolute Deviation (MAD) is a measure of the average distance between each data point and the mean of the dataset. It is calculated by finding the absolute value of the difference between each data point and the mean, and then averaging those differences. MAD is a robust statistic, less sensitive to outliers compared to standard deviation.

Mean Absolute Deviation (MAD) is a statistical measure used to quantify the average deviation of data points from the mean or average of the dataset. To calculate MAD, you follow these steps:

The mean is the sum of all data divided by the number of data points, while the median is the middle value of an ordered dataset. MAD is more robust than standard deviation as it is not affected as much by extreme values. For example, if we have a dataset of exam scores, the standard deviation tells us how scores are spread out from the mean, which could be influenced by extremely high or low scores. On the other hand, MAD gives us a measure of spread that is more resilient to outliers in the data.

Relative Average Deviation (RAD) is similar to MAD, but it expresses the deviation as a percentage of the mean and hence provides a relative measure of spread.

For this case we have that[tex]\frac {1} {4}[/tex]of the songs are jazz.

The total songs are 100.

So:

[tex]\frac {1} {4} = 0.25\\\frac {3} {4} = 0.75[/tex]

This tells us that 25% of the songs are jazz and 75% of the songs are pop.

[tex]\frac {1} {4} + \frac {3} {4} = \frac {4} {4} = 1[/tex]

So, the correct option is option D.

Answer:

Option D

Answer:

The process below should work.

Step-by-step explanation:

Let's pretend we have these two points we are trying to find an exponential equation for:  (-2,6) and (2,1).

Exponential equations are of the form [tex]y=a \cdot b^x[/tex] where we must find [tex]a[/tex] and [tex]b[/tex].

So you enter both points into that equation giving you:

[tex]6=a \cdot b^{-2}[/tex]

[tex]1=a \cdot b^{2}[/tex]

I'm going to divide equation 1 by 2 because if I do the a's will cancel and I could solve or b.

[tex]\frac{6}{1}=\frac{a \cdot b^{-2}}{a \cdot b^2}[/tex]

[tex]6=\frac{b^{-2}}{b^2}[/tex]

By law of exponent, I can rewrite the right hand side:

[tex]6=b^{-2-2}[/tex]

[tex]6=b^{-4}[/tex]

Now do ^(-1/4) on both sides to solve for b:

[tex]6^\frac{-1}{4}=b[/tex]

Now we use one of the equations along with our value for b to find a:

[tex]1=a \cdot b^2[/tex] with [tex]b=6^{\frac{-1}{4}}[/tex]

[tex]1=a \cdot (6^{\frac{-1}{4}})^2[/tex]

Simplify using law of exponents:

[tex]1=a \cdot 6^{-\frac{1}{2}}[/tex]

Multiply both sides by 6^(1/2) to solve for a:

[tex]6^{\frac{1}{2}}=a[/tex]

[tex]y=a \cdot b^x[/tex] with [tex]a=6^{\frac{1}{2}} \text{ and } b=6^{\frac{-1}{4}}[/tex] is:

[tex]y=6^\frac{1}{2} \cdot (6^{\frac{-1}{4})^x[/tex]

We can simplify a smidgen:

[tex]y=6^\frac{1}{2} \cdot (6)^\frac{-x}{4}[/tex]

Answer:

C.

Step-by-step explanation:

The remote exterior angles are angle x and y

The sum of two  interior angles (x +y) is equal to the value of exterior angle (z)

m∠x=(5n-19)°

m∠y=(n+7)°

m∠z=(144-6n)°

Equate as

∠x+∠y=∠z

(5n-19)° +(n+7)°=(144-6n)°

5n-19+n+7=144-6n----------------------collect like terms

5n+n+6n=144+19-7

12n=156---------------------divide both sides by 12 to get value of n

n=156/12= 13°

substitute value of n is equations

∠x=(5n-19)° =(5×13)-19 =65-19=46°

∠y=(n+7)°= (13+7)=20°

Measure of remote exterior angle will be 20°+46°=66° (From the theorem of interior angles and exterior angles)

Answer:

c

Step-by-step explanation:

Answer:

2(x - 3) = 7

Step-by-step explanation:

Set up the difference part first.

x - 3

Now deal with the "Twice."

2(x - 3)

Next equals

2(x - 3) =

And finally what it equals

2(x - 3) = 7

Answer:

2(x-3)=7

Step-by-step explanation:

Dont take my word for it double check with someone else.

Answer: [tex]15.5\ mm^2[/tex]

Step-by-step explanation:

You can calculate the area of a kite with the following formula:

[tex]A=\frac{d_1d_2 }{2}[/tex]

Where [tex]d_1[/tex] is the length of a diagonal and [tex]d_2[/tex] is the length of the other diagonal.

In this case, you can identify that:

[tex]d_1=6.2\ mm\\d_2=5\ mm[/tex]

Therefore, the final step is to substitute the values into the formula.

Then, the area is:

 [tex]A=\frac{(6.2\ mm)(5\ mm)}{2}\\\\A=15.5\ mm^2[/tex]

Answer:

x+3y=14

Step-by-step explanation:

Standard form for an equation of a line is ax+by=c . Some books have restrictions on a,b, and c.

So first thing I'm going to do is state the equation I'm going to use to get there.

I'm going to use the point-slope form because we are given a point (2 really) and we can find the slope using two points (we have).

Line up points and subtract. You will then put second difference over the first difference.  This will give you the slope. You could just use (y2-y1)/(x2-x1).

( -1 , 5)

-(  2, 4)

-----------

-3     1

So the slope is 1/-3 or -1/3 .

So the equation in point-slope form, y-y1=m(x-x1), is y-4=-1/3 (x-2) .

y-4=-1/3 (x-2)

First step: I'm going to get rid of the fraction by multiplying both sides by 3.

3y-12=-1(x-2)

Second step: Distribute

3y-12=-x+2

Third step: add x on both sidfes

x+3y-12=2

Fourth step: add 12 on both sides

x+3y=14.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+5y=10\\3x+y=1&\text{multiply both sides by (-5)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x+5y=10\\-15x-5y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-14x=5\qquad\text{divide both sides by (-14)}\\.\qquad x=-\dfrac{5}{14}\to x\approx-0.357\\\\\text{Put it to the equation}\ 3x+y=1:\\\\3(-0.357)+y=1\\-1.071+y=1\qquad\text{add 1.071 to both sides}\\y=2.071[/tex]

Answer: option b

on edg guys:))

Step-by-step explanation:

y ^2/3

Answer:

25,095238095 = 25 2⁄21

Step-by-step explanation:

Just multiply each denominator and numerator straight across and convert to a mixed number, decimal, or whatever you want.

I am joyous to assist you anytime.

Answer:

4names: z3, zt, zstu, zuts

So, the inequality in slope-intercept form is [tex]\( y \geq 2x - 15 \).[/tex]

To write the given inequality in slope-intercept form [tex](y = mx + b)[/tex], let's first isolate the y term:

[tex]-6x + 3y \geq -45[/tex]

Add 6x to both sides:

[tex]3y \geq 6x - 45[/tex]

Now, divide both sides by 3:

[tex]y \geq 2x - 15[/tex]

[tex]\[\begin{align*}\frac{3y}{3} & \geq \frac{6x}{3} - \frac{45}{3} \\y & \geq 2x - 15\end{align*}\][/tex]

Answer:$96.75

Step-by-step explanation:

Answer: $64.5

Step-by-step explanation:

First let’s do 40% of 150 (40%=4/10): 4/10*150=60

The price of the bike is $60

7.5%=7.5/100, however we cannot have a decimal in a fraction so we multiply by 2/2 and get 15/200.

Next let’s multiply 60 by 15/200: 6*15/200=4.5

Then we add 60 which is the price of the bike, with 4.5, which is the tax to get the total of $64.5

Answer:

B., D., E.

Step-by-step explanation:

[tex] \sqrt{9} \cdot \sqrt{100} = [/tex]

[tex] = \sqrt{9 \cdot 100} [/tex]      This is choice B.

[tex] = \sqrt{900} [/tex]          This is choice E.

[tex] = 30 [/tex]              This is choice D.

Answer:

Infinitely Many

Step-by-step explanation:

Equations:

y = 5 - 2x

4x + 2y = 10

There are multiple ways to solve this, but I'm going to use substitution.

Since y = 5 - 2x, I will input this y value into the second equation.

4x + 2(5 - 2x) = 10

From here, it's simple algebra.

4x + 10 - 4x = 10

     - 10         - 10

4x - 4x = 0

0x = 0

Because we essentially have the solution 0 = 0, this means that the system has an infinite amount of solutions.

Why?

Well, they're the same line. (Put both into slope intercept form.)

y = 5 - 2x OR y = -2x + 5

4x + 2y = 10

2y = -4x +10

=                     y = -2x + 5

Answer:

INFINITE  SOLUTIONS.

Step-by-step explanation:

y = 5 - 2x

4x + 2y = 10

From the first equation:

2x + y = 5         Multiply this equation by -2:

-4x - 2y = -10

Adding the above to the second equation:

0 = 0   So the 2 equations are identical and  there are Infinite  SOLUTIONS>

Answer:

6.

Step-by-step explanation:

14x=84

x=84÷14

x=6

Hope this helps!

Answer:

x=6

Step-by-step explanation:

14x = 84

Divide each side by 14

14x/14 = 84/14

x =6

Answer:

Step-by-step explanation:

The equation is in vertex form ...

  y = a(x -h)² +k . . . . . . . . vertex (h, k) and vertical scale factor "a"

  y = (x +2)² -1

so, you can read the vertex coordinates directly from the equation:

  (h, k) = (-2, -1)

__

The line of symmetry is the vertical line through the vertex, so has equation ...

  x = h

  x = -2 . . . . for this parabola

__

The vertex is always a point on the graph.

At x-values ±1 either side of the vertex, the vertical distance from the vertex is "a". Here, that is 1 unit, so the points (-3, 0) and (-1, 0) are on the graph.

At x-values ±2 either side of the vertex, the vertical distance from the vertex is a·2². Here that is 4 units, so the points (-4, 3) and (0, 3) are on the graph.

This is basically what the vertex form of the equation is telling you.

Answer:

-10 is the answer

Step-by-step explanation:

Diving 10 feet below sea level increases the pressure by 1 atmosphere (ATA), causing the body's air pockets to compress. Divers must equalize the pressure by adding air to these airspaces on the descent.

When diving 10 feet below sea level, the pressure increases by 1 atmosphere (ATA). According to Boyle's law, the volume of gases decreases as pressure increases. The increase in pressure can compress the body's air pockets, such as those in the ears and lungs, which can cause discomfort or injury. Divers must equalize the pressure by adding air to these airspaces on the descent.

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Answer:

12 hours

Step-by-step explanation:

If you divide 168 by 8, you get 21 which is the rate that Austin receives for every hour of work. Then divide 252 by 21 to find how many hours he worked and you get the answer, 12.

The Inverse of the function f(x) = (1/3)^x is derived by swapping x and y and solving for y, resulting in f^-1(x) = log base (1/3) of x.

To find the Inverse of a function in the form f(x) = (1/3)^x, you need to interchange x and y and solve for y.

So, the Inverse of the function f(x) = (1/3)^x is first represented as x = (1/3)^y. However, we need to isolate y. We can do this by taking a logarithmic function on both sides. It turns out that y = log base (1/3) of x.

In other words, the inverse of f(x) = (1/3)^x is f^-1(x) = log base (1/3) of x.

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Answer:

Yes. These outcomes are mutually exclusive; they cannot occur simultaneously in one spin of the wheel.

Step-by-step explanation:

It's the answer trust

Answer:

[tex]M=-\frac{d^2F}{kn}[/tex]

Please look at what I assumed your equation was:  [tex]F=-\frac{kMn}{d^2}[/tex].

Step-by-step explanation:

I'm going to pretend that says:

[tex]F=-\frac{kMn}{d^2}[/tex].

Please correct me if I'm wrong.

We want to solve for M.

The very first thing I'm going to do is multiply both sides by [tex]d^2[/tex].

[tex]d^2F=-kMn[/tex]

Now I'm going to divide both sides by -kn:

[tex]\frac{d^2F}{-kn}=\frac{-kMn}{-kn}[/tex]

Simplifying:

[tex]\frac{d^2F}{-kn}=M[/tex]

Sometimes people don't like the negative on bottom; just move it to the center:

[tex]-\frac{d^2F}{kn}=M[/tex]

[tex]M=-\frac{d^2F}{kn}[/tex]

Answer:

[tex]\large\boxed{(f-g)(x)=4^x+x+5}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=4^x+3x,\ g(x)=2x-5\\\\(f-g)(x)=(4^x+3x)-(2x-5)=4^x+3x-2x+5=4^x+x+5[/tex]

Answer:

6 and x

Step-by-step explanation:

h(-4)

=|-4-2|

=|-6|

=6

.

h(-x+2)

=|-x+2-2|

=|-x|

=x