Jillian exercises 5 times a week. She runs 3 miles each morning and bikes in the evening. If she exercises a total of 30 miles over 5 days, how many miles does she bike each evening?



Do not include units (miles) in your answer.

Graph: a.

The graph had to represent each of the data given,

. starting with 3 rows or branches for the 3 types of bread: white, wheat and rye

. followed by 2 branches coming out of each of the former bread branches to represent the 2 types of meat available for each type of bread: turkey and roast beef

. ending with the 2 types of each available for each type of bread and meat: American and Swill

The only graph with all the data represented is graph a.

The equation of the line containing coordinates (5, 3) that is perpendicular to the line y + 11 = 1/2(4x + 6) is y = (-1/2)x - 1/2.

What are coordinates of a line segment?

A line segment is a part of a line that is joined by two different endpoints. Each endpoint has its own coordinates, which are usually represented as an ordered pair (x,y).

For example, if one endpoint of a line segment has the coordinates (1,2) and the other endpoint has the coordinates (5,6), we can represent the line segment as the pair of points: {(1,2), (5,6)}.

Now,

To find the equation of a line that is perpendicular to the given line, we first need to find the slope of the given line.

Starting with the equation given:

y + 11 = 1/2 (4x + 6)

We can simplify it to slope-intercept form:

y = 2x - 5

So the slope of the given line is 2.

Since the line we want is perpendicular to the given line, its slope will be the negative reciprocal of 2, which is -1/2.

Using the point-slope form of a line

y - y1 = m(x - x1)

where (x1, y1) is the point (5, 3) and m is the slope we just found (-1/2).

Substituting in the values, we get:

y - 3 = (-1/2)(x - 5)

Simplifying and rearranging to slope-intercept form, we get:

y = (-1/2)x + 5/2 - 3

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

Therefore, the equation of the line containing (5, 3) that is perpendicular to the line y + 11 = 1/2(4x + 6) is y = (-1/2)x - 1/2.

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The domain of the function is (-∝, -3) ∪ (-3, +∝)

The range is (-∝, 3) ∪ (3, +∝) and the asymptotes are x = -3 and y = 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 2/(x + 3) + 3

Set the denominator to not equal to 0

So, we have

x + 3 ≠ 0

So, we have

x ≠ -3

As an interval notation, we have

(-∝, -3) ∪ (-3, +∝)

Here, we have

f(x) = 2/(x + 3) + 3

When x = -3, we have

f(-3) = undefined + 3

This means that

f(x) ≠ -3

As an interval notation, we have

(-∝, 3) ∪ (3, +∝)

In (a), we have

x ≠ -3

This means that

Vertical asymptote: x = -3

In (b), we have

f(x) ≠ -3

This means that

Horizontal asymptote: y = 3

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Answer:

  $50,000

Step-by-step explanation:

The given relations can be used to write and solve an equation for the amount invested in stocks.

Let s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...

  0.18s +0.12(120,000 -s) = 17,400

Simplifying the equation, we have ...

  0.06s +14,400 = 17,400

  0.06s = 3000 . . . . . . . . . . subtract 14,400

  s = 50,000 . . . . . . . . . . . . divide by 0.06

Neal invested $50,000 in stocks.

__

Additional comment

The amount invested in bonds was 70,000. The profit earned was ...

  0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

Answer:

x+3

Step-by-step explanation:

Kofi is 3 years older than Ama, so the answer is "x+3".

The probability of failure on the trial 9 for the given binomial experiment is 0.15.

An experiment with a set number of independent trials and just two results is referred to as a binomial experiment. The results of these experiments can be classified as either successes or failures. Due to the nature of the experiment's subject, results may only be categorised as successes or failures.

Due to the set number of outcomes that might occur in each experiment's trial, binomial experiments are unique from other types of studies. Binomial experiments, in particular, can only ever produce one of two outcomes.

The probability of success and failure of a trial is same for every number of trials.

Given that,

n = 12 trials

Success = 0.85

The failure is given as:

failure = 1 - success of trial

failure = 1 - 0.85

failure = 0.15

Hence, the probability of failure on the trial 9 for the given binomial experiment is 0.15.

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Answer:

Volume of pentagon = 27.52 yd² (Approx.)

Step-by-step explanation:

Given:

Length of base of pentagon = 2 yd

Height of pentagon = 4 yd

Find:

Volume of given figure

Computation:

Volume of given figure = Volume of pentagon

Volume of pentagon = (1/4)(a²)(h)√5(5+2√5)

Volume of pentagon = (1/4)(2²)(4)√5(5+2√5)

Volume of pentagon = (4)√5(5+2√5)

Volume of pentagon = (4)√5[5+2(2.236)]

Volume of pentagon = (4)√5[5+4.472]

Volume of pentagon = (4)√5[9.472]

Volume of pentagon = (4)√47.36

Volume of pentagon = 4[6.8818]

Volume of pentagon = 27.52 yd² (Approx.)

Answer: 12 games

Step-by-step explanation:

45/30*8 = 12

For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.

Here,

a. No for every 4 beef cattle there is 3 dairy cattle.

b. 4/3=x/24

x=4*24/3

x=32 beef cattle

There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.

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Answer:

To solve this I would multiply both sides by 3

Step-by-step explanation:

i would use the multiplication property of equality

The property that justifies that action x/3=12 is a linear question using reciprocal law.

A linear equation has one or two variables.

explanation:-

x/3= 12

x = 12*3 ( using reciprocal)

hence x = 36

solving this we will get the valve of Y if x is given.

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Solution:

The slope of a line gives the steepness of the line.

It is evaluated as

The higher the slope value, the steeper the slope.

Thus, a slope of 999 will have a nearly vertical line.

Today Isabella is having her 5th birthday and her parents want to make one single deposit now so they can collect a total of 50000 Brazilian Real when she is 18.

The investment is thought to be for n=13 years.

The present value (PV) and the future value (FV) of the investment can be calculated by using the compound interest's formula:

Where r is the interest rate (APR) offered by the bank, m is the number of compounding periods by each year. Since the compounding period is monthly, then m=12.

If we are given the final value and we want to calculate the present value, then the formula is:

Substituting:

Calculating:

Isabella's parents should deposit near 24500 Brazilian Reals today

Step-by-step explanation:

200 + 100 + 150 + 200 +150 = 800 m in total

8 min in total

you are going 100 m a minute or 6000 m an hour

Answer:

1,3

Step-by-step explanation:

Answer:

B. $8,631.96

Step-by-step explanation:

Create an equation where x is the number of years and y is the car's value

y = 48500(0.75)^x

Plug in 6 as x, since the question asks for the value in 6 years, and simplify:

y = 48500(0.75)^6

y = 8631.96

So, in 6 years, the car will be worth $8,631.96

The correct answer is B. $8,631.96

Answer:

B. $8,631.96

Step-by-step explanation:

Because it is the "Correct Answer"

The representation that is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time is a Line Plot

A line plot, or dot plot/strip plot, is a simple visual method of displaying data that shows the spread of values on a horizontal scale. A frequent application of it is to graphically display the occurrence or spread of a solitary factor.

A line plot generally displays individual data points as a small dot or short line segment along a specific axis, usually the horizontal axis. The location of the dot or line segment indicates the numerical value of the data point. Usually, the up and down axis showcases the frequency or the number of times a particular value occurs.

With this type of Table, the top is always X and the bottom is always Y.

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Answer:

the person who bought it saved 40 dollars and the percentage saved was 12.50 i just used a discount calculator on google

Step-by-step explanation:

Answer:

12.5%

Step-by-step explanation:

Answer:

D reorder the terms using communitive  properties

because there is nothing else to do with this problem

Step-by-step explanation:

8 3√25 k

I checked the other problems and K was 12

Hope this helps ?

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.

What is an Agreement?

This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.

Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.

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The linear equation obtained is y = 0.3X + 18.3

A linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x represents an unknown variable. The solutions of linear equations are often graphed on a coordinate plane, forming a straight line. Linear equations can be used to model many real-world situations, such as population growth, the rate of change of a physical quantity, or the total cost of an item. Linear equations can also be used to solve systems of equations, where several equations must be solved simultaneously.

Given that data :
x = year ;
y = trunk diameter, in inches
Year ________trunk diameter
1 __ 18.6
3 __ 19.2

5 __ 19.8
7 __ 20.4
9 ___21.0
11 __ 21.6
13 __ 22.2
Using the linear regression calculator :
The linear equation obtained is :
y = 0.3X + 18.3
Where ;
Slope = 0.3 ; intercept, c = 18.3

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Answer:

1 chain = 12 pounds

4 inches = x

4×12=49

= 50

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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Answer:

The maximum possible error of in measurement of the angle is  \(d\theta_1 =(14.36p)^o\)

Step-by-step explanation:

From the question we are told that

    The angle of elevation  is  \(\theta_1 = 15 ^o = \frac{\pi}{12}\)

     The height of the tree is  h

      The distance from the base is  D

h is mathematically represented as

            \(h = D tan \theta\)       Note : this evaluated using SOHCAHTOA i,e

                                               \(tan\theta = \frac{h}{D}\)

Generally for small angles the series approximation of  \(tan \theta \ is\)

          \(tan \theta = \theta + \frac{\theta ^3 }{3}\)

So given that \(\theta = 15 \ which \ is \ small\)

       \(h = D (\theta + \frac{\theta^3}{3} )\)

       \(dh = D (1 + \theta^2) d\theta\)

=>        \(\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta\)

Now from the question the relative error of height should be at  most

        \(\pm p\)%

=>    \(\frac{dh}{h} = \pm p\)

=>    \(\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p\)

=>      \(d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p\)

 So  for   \(\theta_1\)

            \(d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p\)

substituting values  

          \(d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p\)

 =>       \(d\theta_1 = 0.25 p\)

Converting to degree

           \(d\theta_1 = (0.25* 57.29) p\)

            \(d\theta_1 =(14.36p)^o\)

Answer:

A.

Step-by-step explanation:

Answer:

0.1875 miles

Step-by-step explanation: