Each day Mike drives to his job from his home. Sometimes he goes along two roads, the long route shown by the solid lines. Other times he takes the shortcut indicated by the dotted lines. How many kilometers shorter is the shortcut than the long route? Show work.

Answer:

the amount of soup that I can make in my crockpot

Step-by-step explanation:

A) is an area. the foil would be cut into a square or circle, making it an area.

B) is the soup in the pot. the amount is given by the cross-sectional area of the pot (if circular Area of circle = π r ²) multiplied by the depth of the pot. since we have r ² (which is r X r) multiplied by a length (depth of pot) , it is a volume.

C) like A) this would be a two-dimensional item. so it is an area.

D) this will just be a number

Answer:

FG is y = -0.5x - 5.5. circle is (x - 1)² + (y + 1)² = 20. Length FA = 7

Step-by-step explanation:

please see attached

only 5 attachments/pics allowed

so FA² = (√69)² - (√20)²

            = 69 - 20

           = 49

FA = √49 = 7

Null hypothesis: µ = 162 lbs (mean weight of male nurses is equal to 162 lbs)

Alternative hypothesis: µ ≠ 162 lbs (mean weight of male nurses is not equal to 162 lbs)

Hypothesis testing is a method of making decisions about a population based on sample data.

The null hypothesis (H₀) represents the default position that there is no significant difference between specified populations, or that there is no effect of a particular treatment.

On the other hand, the alternative hypothesis (H₁) represents the opposite of the null hypothesis, which is that there is a significant difference between the populations or that there is an effect of the treatment being tested.

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Space is used in art Area around an object​. Therefore, the correct option is option D.

The term "art" refers to a wide range of human endeavours and the resulting works that reflect technical mastery, aesthetic beauty, emotional heft, or mental concepts. No single definition of what makes art exists, and different cultures and historical periods have interpreted it very differently. Space is used in art Area around an object​.

Therefore, the correct option is option D.

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The statements that are true about the area of the figure is that the area can be found by multiplying 3 by 2 1/2 and adding the product of 1/2 and 1/2 .

Recall that In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle

Also, the area of a rectangle can be found by multiplying the length of the rectangle by its width and using the formula, where is the base and is the height of the triangle.

Area of the rectangle - LB

Area = (1/2 * 1/2) + (7/2*7/2)

Area = 1/4 + 35/4

Simplifying the fraction to get

36/4

Area of the figure is 9 square units

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To solve the equation [tex]2\cos(\theta) - \sqrt{2} = 0\\[/tex] and express the answer in radians in terms of π, we can follow these steps:

Step 1: Add [tex]\sqrt{2}\\[/tex] to both sides of the equation:

[tex]2\cos(\theta) = \sqrt{2}\\[/tex]

Step 2: Divide both sides of the equation by 2:

[tex]\cos(\theta) = \frac{\sqrt{2}}{2}\\[/tex]

Step 3: Recall the special values of cosine in the first quadrant:

[tex]\cos(\theta) = \frac{\sqrt{2}}{2}\\[/tex]¥ corresponds to [tex]\\ \theta = \frac{\pi}{4}\\[/tex] in radians.

Therefore, the solution to the equation in radians in terms of π is [tex]\theta = \frac{\pi}{4}\\[/tex].

Johnny stopped running for the first time after 15 minutes.

From the graph, we can see that Johnny ran for the first 15 minutes without stopping. During this time, he covered a distance of around 1.5 miles. After 15 minutes, he stopped running for a short time, and then continued running. Therefore, Johnny stopped running for the first time after 15 minutes.

Answer:

Step-by-step explanation:

The answer is 360.

Explanation: each pillow is $3 and you have $960.

You need to figure out how many times $3 can go into $960 and you do that by dividing.

960 divided by 3 is 360.

The hotel can buy 360 pillows.

0.0007% of students in Class 7 spent less than 15 minutes on homework.

Total students = 100

Number of students spent less than 7 minutes are: 0.7

Now, the percentage of students less than 15 minute

= 0.7/100 x 100

= 7/1000 x 100

= 0.0007 x 100

= 0.0007%

Thus, 0.0007% of students in Class 7 spent less than 15 minutes on homework.

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Answer:

Step-by-step explanation:

Sure! Here’s how you can solve the equation 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=9 for x:

First, let’s rewrite the equation in terms of a common base. Since 9 can be written as 3², we can rewrite the equation as 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=3².

Now, let’s isolate the exponential terms on one side of the equation by adding 8.3ˣ⁺¹ to both sides: 3²⁽ˣ⁺¹⁾=3²+8.3ˣ⁺¹.

Next, let’s take the logarithm of both sides with base 3: log₃(3²⁽ˣ⁺¹⁾)=log₃(3²+8.3ˣ⁺¹).

Using the properties of logarithms, we can simplify the left side of the equation: 2(x+1)=log₃(3²+8.3ˣ⁺¹).

Now, let’s solve for x by isolating it on one side of the equation: x=log₃(3²+8.3ˣ⁺¹)/2-1.

This is an approximate solution for x. To find a more precise value for x, you can use a numerical method such as Newton’s method or a calculator.

I hope this helps!

The graph of y = 3(3/5)^x is an exponential growth curve that starts at the point (0, 3) and approaches the x-axis and y = 3 asymptotically.

We have,

The graph of the exponential function y = 3(3/5)^x is an upward curve that approaches but never touches the x-axis, as the base of the exponential term (3/5) is between 0 and 1.

As x approaches negative infinity, the function rapidly approaches the y-axis, which is the vertical asymptote.

As x increases, the value of the function increases rapidly, but at a decreasing rate, as the base of the exponential term is less than 1.

As x approaches infinity, the function approaches but never touches the horizontal line y = 3, which is the horizontal asymptote.

Therefore,

The graph of y = 3(3/5)^x is an exponential growth curve that starts at the point (0, 3) and approaches the x-axis and y = 3 asymptotically.

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Susan's gross capital loss on the sale of the stock was $127.62.

We have,

Susan's initial investment in the stock.

= 24.87 shares x $33.12/share

= $823.98

Four years later, she sold the shares.

= 24.87 shares x $28/share

= $696.36

To calculate the capital loss, we need to subtract the sale price from the purchase price:

= $823.98 - $696.36

= $127.62

Therefore,

Susan's gross capital loss on the sale of the stock was $127.62.

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Answer:

25

Step-by-step explanation:

Given from the question,

125 cubed = [tex]125^3[/tex]

Therefore square root of 125 cubed is:

[tex]\sqrt{125^3} \\ =125^\frac{2}{3} \\ \\=25[/tex]

Hello!

4.9 × 10⁻¹

= 4.9 × 0.1

= 0.49

The area of the shaded which is obtained using the composite figure formed the shaded region and the area under the curve of the specified function is; (2·π - 3·√3)/2 square units

A composite figure is one that is composed of two or more simpler figures.

The area can be considered of comprising of a composite figure of the area under the curve of the function and the area of the shaded region

The function representing the curve under the shaded region can be presented as follows;

y = 3·cos(x) + 1

The interval specified under the curve can be expressed as follows;

0 ≤ x ≤ π/3

Therefore, the area under the curve can be found as follows;

[tex]\int\limits^\frac{\pi}{3} _3 {3\cdot cos(x) + 1} \, dx = [3\cdot sin(x) + x]^{\frac{\pi}{3} }_0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3} - 0 = 3\cdot sin(\frac{\pi}{3} ) + \frac{\pi}{3}[/tex]

sin(π/3) = (√3)/2

Therefore; 3·sin(π/3) + π/3 = 3·(√3)/2 + π/3 = (2·π + 9·√3)/6

The area of the rectangle = (4 - 0) × (π/3 - 0) = 4·π/3

The area of the shaded region = Area of the rectangle - Area under the curve of the specified function

Therefore, area of the shaded region = 4·π/3 - (2·π + 9·√3)/6 = (2·π - 3·√3)/2

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Given statement solution is :- The Sketch Graph is a straight line with a negative slope. It passes through the points (-3, 2.5), (-2, -2.5), (-1, -2.5), and (0, -5). The line is interrupted at x = 1 .

To sketch the graph of the equation 2y + 5x + 10 = 0 within the given range of x, we first need to rearrange the equation to solve for y:

2y = -5x - 10

Dividing both sides by 2:

y = (-5/2)x - 5

Now, let's plot the graph:

Choose some x-values within the range [-3, 1) to find their corresponding y-values.

Let's choose x = -3, -2, -1, 0.

For x = -3:

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

= (15/2) - 5

= 7.5 - 5

= 2.5

For x = -2:

y = (-5/2)(-2) - 5

= 5/2 - 5

= 2.5 - 5

= -2.5

For x = -1:

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

= 5/2 - 5

= 2.5 - 5

= -2.5

For x = 0:

y = (-5/2)(0) - 5

= 0 - 5

= -5

Plot the points (-3, 2.5), (-2, -2.5), (-1, -2.5), and (0, -5) on the graph.

Draw a straight line passing through these points. Since the range for x is (-3, 1), the line should be dotted or interrupted at x = 1.

The resulting graph should look like this:

yaml

Copy code

       |    

   *   |    

       |   *  

       |      

-------+-------

       |      

       |

Note: The Sketch Graph is a straight line with a negative slope. It passes through the points (-3, 2.5), (-2, -2.5), (-1, -2.5), and (0, -5). The line is interrupted at x = 1 since it is not included in the given range.

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-2x≤6 and 2x≥-6 is the inequalities represented by the number line

The visual representation of the real numbers on a straight lineis known as number line

On a number line each  point of  is assumed to correspond to a real number, and every real number to a point.

As we observe the graph the red line is directed towards left side which means the values are decreasing and line has solid point  at 6 so it is included

Hence, the number line shows that -2x≤6 and 2x≥-6

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Answer:

they're pronounced different

Answer:

mass= 563 grams

Step-by-step explanation:

Volume = 7cm * 6cm * 2cm

Volume = 84 cm³

Density = mass / volume

6.7 grs/cm³ = mass / 84cm³

84cm³ * (6.7grs/cm³) = mass

mass = 562.8 gr

To the nearest gram:

mass = 563 gr

The pair of possible coordinates of point D are (0, 8), (0, -8), (8, 0) and (-8, 0)

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

D = 8 units away from the origin.

using the above as a guide, we have the following:

The possible coordinates of point D are

(0, ±8), (±8, 0)

When expanded, we have

(0, 8), (0, -8), (8, 0) and (-8, 0)

Hence, the pair of possible coordinates of point D are (0, 8), (0, -8), (8, 0) and (-8, 0)

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A non-example of mean, mode, median and range are as follows;

1. A non example of a mode in the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is other numbers except 7.  7 is the mode because it is repeated more frequently.

2. Non-example of median is 9 because it is not the middle value of the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 when arranged orderly.

The mean is the average of all the values in a dataset. And therefore a non-example of mean in the data set 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is 70. Which is gotten by adding all the numbers together.

The mean can be found by saying 7 + 8 + 9 + 7 + 5 + 9 + 7 + 4 + 3 + 7 divided by 10. this should be 7.

The non-example of range in the dataset 7, 8, 9, 7, 5, 9, 7, 4, 3, 7 is choosing the lowest value of the set 3.

The range is the difference between the highest and lowest values in a dataset. which is 9-3 = 6

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Answer:

3 and 4 both SAS (Side-Angle-Side) axiom.

Step-by-step explanation:

Note:

There are four basic conditions for two triangles to be congruent. These are:

One of the conditions should be needed to fulfill to determine whether the two triangles are congruent.

Over here:

3.

In ΔOMT and ΔOGE

MT=GE Given Side

∡MOT=∡GOE Vertically Opposite angle Angle

MO=OE Given Side

It fulfills the condition of the SAS (Side-Angle-Side) axiom.

ΔOMT ≅  ΔOGE by SAS (Side-Angle-Side) axiom.

4.

In ΔKJL and ΔIJH

JL=JH Given Side

∡KJL=∡HJI Vertically Opposite angle Angle

IJ=JK Given Side

It fulfills the condition of the SAS (Side-Angle-Side) axiom.

ΔKJL≅ ΔIJH by the SAS (Side-Angle-Side) axiom.

what you mean but heres the points on the map u were talking about

Answer: The slope m = 3/5

Step-by-step explanation:

The slope can be found by using the formula: m = y2 - y1 / x2-x1

Where m is the slope and (x1, y1) and (x2, y2) are the two points on the line.

x1 = 2  , y1 = 1

x2 = -3 , y2 = -2

Substituting the values from the points in the problem gives :

m = -2-1 / -3-2

m = 3/5

Hence, the slope that passes through (2, 1) and (-3, -2) is 3/5.

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Answer:

Step-by-step explanation:

You want an equation and its solution to tell you the number of $5 books that were purchased for $58 with a $7 discount coupon.

The cost of b books at $5 each is 5b.

After a $7 discount is subtracted, the cost is 5b -7.

That cost is said to be $58, so an appropriate equation is ...

  5b -7 = 58

Adding 7 gives ...

  5b = 65

Dividing by 5 tells the number of books:

  b = 13

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Answer:

a) 2nd form: 5b-7=58

b) 13 books

Step-by-step explanation:

Equation:

5b-7=58

b) 5b=65

b=13

The ways to elect the candidates from the total is 462

From the question, we have

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 11 and r = 6

Substitute the known values in the above equation

Total = ¹¹C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 11!/5!6!

Evaluate

Total = 462

Hence, the number of ways is 462

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Based on the calculations, the measure of angle M is -15°.

The given diagram, it appears that we have a triangle MNL with an angle measure of 88° at point L and an angle measure of 107° at point K.

We are asked to find the measure of angle M, denoted by m∠MLK.

The measure of angle M, we can use the fact that the sum of the angles in a triangle is always 180°.

We can subtract the measures of angles L and K from 180° to find the measure of angle M.

m∠M = 180° - m∠L - m∠K

Substituting the given values:

m∠M = 180° - 88° - 107°

m∠M = 180° - 195°

m∠M = -15°

This result is not physically possible since angles cannot have negative measures.

It is likely that there was an error in the given information or in the calculations.

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The equivalent value of the expression is xy² = 18

Given data ,

Let the equation be represented as A

Now , the value of A is

A = xy²

where the value of the first variable x = 2

And , the value of the second variable y = -3

Now , the expression is solved as

A = xy²

On simplifying the equation , we get

A = ( 2 ) ( -3 )²

A = 2 ( 9 )

On further simplification , we get

A = 18

Therefore , the value of A is 18

Hence , the expression is A = 18

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Answer:

  an infinitely long time

Step-by-step explanation:

You want to know the time it takes for a kitten running 20 ft/s to catch a puppy running 25 ft/s when they start 180 ft apart and the puppy runs away from the kitten.

The kitten runs slower than the puppy, so can never catch up to it.

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We can use the property of Multiplication  5x8=40 to determine the product of 5x800, which is 4000.

To find the product of 5x800 using the basic fact 5x8=40, we can use the property of multiplication that states that multiplying a number by 10 increases its value by one place value. Therefore, we can rewrite 800 as 80x10 and multiply it by 5 as shown below:

5x800 = 5x(80x10)   (replacing 800 with 80x10)

     = (5x80)x10   (associative property of multiplication)

     = 400x10      (using the basic fact 5x8=40)

     = 4000

Thus, we can use the basic fact 5x8=40 to determine the product of 5x800, which is 4000.

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Area of small sector is,

⇒ A = 3.28π cm²

And,. Area of large sector is,

⇒ A = 5.73π  cm²

We have to given that;

Angle ACB = 131°

And, radius = 3 cm

Since, We know that;

⇒ Area of sector = θ/360 × πr²

Hence, For θ = 131°

So, Area of small sector is,

⇒ A = 131/360 × π × 3²

⇒ A = 1179/360π

⇒ A = 3.28π cm²

For large sector,

Angle = 360 - 131

          = 229°

Hence, Area of large sector is,

⇒ A = 229/360 × π × 3²

⇒ A = 2061/360π

⇒ A = 5.73π  cm²

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