The radius of a dog's collar

should be at least 0.5 inch larger than

the radius of the dog's neck. A dog collar

adjusts to a circumference of 10 to

14 inches. Should the collar be worn

by a dog with a neck circumference of

12.5 inches? Explain.

Answer:

(2, [tex]\frac{13}{3}[/tex] )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 17 → (1)

3y = 15 - x → (2)

Substitute 3y = 15 - x into (1)

2x + 15 - x = 17, that is

x + 15 = 17 ( subtract 15 from both sides )

x = 2

Substitute x = 2 into either of the 2 equations for corresponding value of y

Substituting in (1)

2(2) + 3y = 17

4 + 3y = 17 ( subtract 4 from both sides )

3y = 13 ( divide both sides by 3 )

y = [tex]\frac{13}{3}[/tex]

Solution is (2, [tex]\frac{13}{3}[/tex] )

Rearranging...

3y + x = 15

3y + 2x = 17

Using elimination method

2x - x = -15 + 17

X = 2

From equation.... 2

3y + 2 = 15

3y = 15 - 2

3y = 13

Y = 13/3

::x = 2 while y = 13/3

Answer:

7.5 quarts of soda

Step-by-step explanation:

Kindly refer to the attached image for explanations

Answer:

12.152

Step-by-step explanation:

Step-by-step explanation:

Given

{ 11 , 2 , 5 , 10 , 25 , 30 , 36}

No of sample space, n(s) = 7

Even numbers = 2 , 10 , 30 ,36

No of favourable cases, n(e) = 4

Now

Probability that an even number will be selected is, P(even) = n (e) / n(s)

= 4/ 7

Hope it will help you :)

1,205.76 units^3 or 384 π

Here is why:

The formula for the volume of a cone is:

[tex]V=\frac{1}{3}\pi r^2 h[/tex]

We can plug in.

[tex]V=\frac{1}{3}*3.14*8*8*18[/tex]

= 1,205.76 units^3

~

If you are looking for the exact answer, we will leave π.

[tex]V=\frac{1}{3}*\pi*8*8*18[/tex]

= 384 π

Answer:

B) f(x) = -3/5x +5

Step-by-step explanation:

There are several ways you can write the equation of a line from a list of points. When you look through the list and see that one of them is the y-intercept, then the problem can be easier. When you look through the list of answers and see that the required answer is in slope-intercept form, then you know all you need to do is find the slope to go with the intercept you've located. The point (x, f(x)) = (0, 5) tells you the y-intercept is 5.The slope, the change in y divided by the change in x for two points, is ...... (-1 -2)/(10 -5) = -3/5This is the slope and the coefficient of x in the linear equation.Now, we know the y-intercept (b=5) and the slope (m=-3/5), so we can fill in the slope-intercept form of the equation of a line:... y = mx + b... y = (-3/5)x + 5

Answer: The length of the beetle in the drawing is 9 cm.

Step-by-step explanation:

Hi, since is a scaling up scale, we have to multiply the original length of the beetle (1.8 cm) by 5 to obtain the length of the beetle in the drawing.

Mathematically speaking

5 x 1.8 = 9 cm

The length of the beetle in the drawing is 9 cm.

This type of scale is used to increase in size.

Feel free to ask for more if needed or if you did not understand something.

Answer:

[tex]\frac{13}{5}[/tex]

Step-by-step explanation:

Remember this??- [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Now substitue the points on that! It should look like this!- [tex]\frac{6-(-7)}{2-(-3)}[/tex]

Now SOLVE!! You should get- [tex]\frac{13}{5}[/tex]

There ya go!! Stay Safe, Stay at Home!! =)

Answer:

848.81

Step-by-step explanation:

find 14 percent of 744.57 then add that to 744.57

The original price of the video camera was $866.50.

To find the original price of the video camera, we can use the following equation:

Original price - (14% of original price) = Sale price

Let's assign the variable x to represent the original price. We can set up the equation:

x - 0.14x = $744.57

Simplifying the equation, we get:

0.86x = $744.57

Dividing both sides of the equation by 0.86, we find that:

x = $866.50

So, the original price of the video camera was $866.50.

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Answer:

no solution

Step-by-step explanation:

Answer:

  there is no greatest load

Step-by-step explanation:

Let x and y represent the load capacities of my truck and my neighbor's truck, respectively. We are given two relations:

  x ≥ y +600 . . . . . my truck can carry at least 600 pounds more

  x ≤ (1/3)(4y) . . . . . my truck carries no more than all 4 of hers

Combining these two inequalities, we have ...

  4/3y ≥ x ≥ y +600

  1/3y ≥ 600 . . . . . . . subtract y

  y ≥ 1800 . . . . . . . . multiply by 3

My truck's capacity is greater than 1800 +600 = 2400 pounds. This is a lower limit. The question asks for an upper limit. The given conditions do not place any upper limit on truck capacity.

Answer:

[tex]\large \boxed{\text{2400 lb}}[/tex]

Step-by-step explanation:

We have two condition:

    Let x = the load of your truck

   and y = load of their trucks Then

(1)       x ≥ y + 600  

       4y = the total load of their four trucks

⅓ × 4y = the load  of load of your truck

(2)  ⁴/₃x ≤ y

Calculations:  

[tex]\begin{array}{lrcll}(1) & x & = & y+ 600\\(2)& x & =&\dfrac{4}{3}y\\\\(3)& x - 600 & =&y&\text{Subtracted 600 from each side of (1)}\\& x & = & \dfrac{4}{3}(x - 600)&\text{Substituted (3) into (2)}\\\\&3x & = & 4(x - 600)&\text{Multiplied each side by 3}\\\end{array}[/tex]

[tex]\begin{array}{lrcll}&3x & = & 4x - 2400&\text{Distributed the 4}\\&3x + 2400 & = & 4x&\text{Added 2400 to each side}\\ & x & = & \mathbf{2400}&\text{Subtracted 3x from each side}\\\end{array}\\\text{The greatest load my truck can carry is $\large \boxed{\textbf{2400 lb}}$}}[/tex]

Hi there! Hopefully this helps!

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The Answer: a decline in prices.

Given:

Given that the graph of the triangle ABC.

The coordinates of the triangle are A(2,-1), B(-1,1) and C(1,-2)

We need to determine the coordinates of the point A after the dilation with a scale factor of 3 centered at the origin.

Coordinates of the point A after dilation:

The general rule for a coordinate to dilate a factor of c from the origin is given by

[tex](x, y) \rightarrow (cx, cy)[/tex]

Thus, applying the above rule, the coordinate A(2,-1) is dilated by a scale factor of 3 about the origin, we get;

[tex](2,-1)\rightarrow (3(2), 3(-1))[/tex]

Simplifying, we get;

[tex](2,-1)\rightarrow (6,-3)[/tex]

Thus, the coordinates of point A after dilation with a scale factor of 3 centered at the origin is (6,-3)

Answer:

Exact percentage  = 87.5%

Explanation:

We need to find out the percent of the women in the village.

So the percent of one unit is represented by 56/64.

we want 56 out of 64 as a percentage

we multiply by the 100 .

=0.875*100

=87.5 %

So, final answer is 87.5%

Answer:

6 or 7

Step-by-step explanation:

if he does not take any himself, the answer is 7 as

35/5=7

if he takes 5 himself, the answer is 6 because

35-5=30

30/5=6

Todd will be able to give candy to 7 friends.

To find out how many friends Todd will be able to give candy to, we need to divide the total number of candy pieces he has (35) by the number of candy pieces he wants to give to each friend (5).

35 ÷ 5 = 7

Todd will be able to give candy to 7 friends.

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Answer:

7/12

Step-by-step explanation:

4/12 + 3/12

Multiply the 2/6 by 2 and the 1/4 by 3

Answer:

Step-by-step explanation:

LCM of 6, 4 = 12

[tex]\frac{2}{6}+\frac{1}{4}=\frac{2*2}{6*2}+\frac{1*3}{4*3}\\\\=\frac{4}{12}+\frac{3}{12}\\\\=\frac{7}{12}[/tex]

Answer:

Minimum 7 buckets of water is needed to completely fill spherical storage tank.

Step-by-step explanation:

We are given the following in the question:

Cylindrical bucket:

Radius, r = 6 inches

Height = 18 inches

Volume of bucket = Volume of cylinder

[tex]V = \pir^2 h \\V = 3.14\times (6)^2\times 18\\V =2034.72\text{ cubic inches}[/tex]

Spherical storage tank:

Radius, r = 15 inches

Volume of tank = Volume of sphere =

[tex]V =\dfrac{4}{3}\pi r^3\\\\\V = \dfrac{4}{3}\times 3.14\times (15)^3\\\\V = 14130\text{ cubic inches}[/tex]

Number of baskets required =

[tex]n = \dfrac{\text{Volume of tank}}{\text{Volume of bucket}}\\\\n =\dfrac{14130}{2034.72} = 6.94 \approx 7[/tex]

Thus, minimum 7 buckets of water is needed to completely fill spherical storage tank.

Answer:

Step-by-step explanation:

Factors :  (x - 8) (x- 1/2)  or

(x - 8 ) (2x - 1)

Equation: (x - 8)(2x - 1) = x*2x + x*(-1) -8*2x -8*(-1)

= 2x² -x -16x + 8

=2x² -17x + 8

Answer:

Area of a 30-inch circular mirror is greater than area of a 18-inch circular mirror by 452.16 square inches.

Step-by-step explanation:

We are given the following in the question:

Mirror 1:

[tex]d_1 = 30\text{ inches}\\\\\Rightaroow r_1 = \dfrac{30}{2}=15\text{ inches}[/tex]

Area of mirror 1 = Area of circle

[tex]A_1 = \pi r_1^2[/tex]

Putting values, we get,

[tex]A_1 = 3.14\times (15)^2=706.5\text{ square inches}[/tex]

Mirror 2:

[tex]d_1 = 18\text{ inches}\\\\\Rightaroow r = \dfrac{18}{2}=9\text{ inches}[/tex]

Area of mirror 1 = Area of circle

[tex]A_2 = \pi r_2^2[/tex]

Putting values, we get,

[tex]A_2 = 3.14\times (9)^2=254.34\text{ square inches}[/tex]

Difference between area =

[tex]=A_1-A_2\\=706.5-254.34\\=452.16\text{ square inches}[/tex]

Thus, area of a 30-inch circular mirror is greater than area of a 18-inch circular mirror by 452.16 square inches.

Answer:

c

Step-by-step explanation:

beacuse in the question it says mary is more likley to draw a green ball after a red ball

Answer:

F and I

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.  

Through which points should a line of rotation be placed to create a cylinder with a radius of 3 units?

E and J

F and I

J and G

G and E

My answer:

From the photo, we can see that:

the point F is in the middle of the length EG => EF = FG = 3 units

the point I is in the middle of the length JH and because this is a rectangle so EG = JH

=> JI = JH = 3 units

So the points should a line of rotation be placed to create a cylinder with a radius of 3 units is: F and I  where F and I are the center points of the two bases in the cylinder

Answer:

A

Step-by-step explanation:

they are both -

Answer: I think It is B) because it's definitely not C). But it could also be A like the answer above said. (I'm very very sorry if it's not correct!)

B) -6÷3 ?

Answer:

Step-by-step explanation:

Sounds like "continuous compounding."

Here, A = Pe(0.068t), where t is the number of years.

Final answer:

Subsidized Stafford Loans are for undergraduates with financial need and the government pays the interest while in school. Unsubsidized Stafford Loans are for all students and accrue interest immediately. Private loans often have variable interest rates and are less advantageous than federal loans.

Explanation:

Subsidized Stafford Loans are offered to undergraduate students with financial need, and the interest is paid by the government while the student is in school, during deferment periods, and for six months after graduation, commonly referred to as the grace period. The interest rate is fixed and typically lower than that of unsubsidized loans. The maximum loan amount varies, but it can go up to $12,500 per year of schooling.

Unsubsidized Stafford Loans do not require demonstrating financial need and are available to both undergraduate and graduate students. Interest accrues from the time the loan is disbursed, and the student is responsible for all of it, including while they are in school. Like subsidized loans, they also have a fixed interest rate and a maximum loan amount of up to $12,500 per year for undergraduates and $20,500 per year for graduate students.

Private loans are provided by banks, credit unions, or other financial institutions and can have variable interest rates, which means the rate may increase or decrease over time. Private loans are less favorable compared to federal loans due to higher interest rates and less flexible repayment options.

Other options like Direct PLUS Loans and Direct Consolidation Loans are also available for specific student populations and situations. PLUS Loans are for graduate or professional students and parents, whereas Consolidation Loans allow combining federal loans into one.

Since federal loans offer lower interest rates and more flexible repayment terms than private loans, they are generally the preferred choice for students. Aid offices often guide students to preferred lenders, but it's essential to understand all options and choose loans wisely.

Answer: The square shield would equal to 18.0625 because base x height and the base and height is both 4.25 so times that by 4.25 and you get 18.0625 ft and the rectangular shield would equal 27 ft because base: 6.75 and height: 4 You will times those and get 27 ft and the circular shield is and the circular one is 28.26 ft you use pie 3.14 times it by 3 squared well first you square 3 which gives you 9 = 3x3=9. So then its left to 3.14x9 and that gives you 28.26 so the best shield is the circlular shield

Step-by-step explanation:

I explaned on top

Answer:

sdfghjkl

Step-by-step explanation:

Answer: 19,200 years

Step-by-step explanation:

Answer: 32 cm

Step-by-step explanation:

Hi, the options of the questions are •

32 cm  

87 cm  

54 cm  

167 cm

The formula for the volume of a sphere is  

V = 4/3 πr³

Where r is the radius.

Since the radius is equal to the diameter divided by 2:

r = d/2= 4 /2 = 2 cm  

Replacing in the formula

V = 4/3 π 2³

Solving

V = 4/3 π 8= 33.51 cm

So, the correct option is 32 cm, which  closest to the value.

Feel free to ask for more if needed or if you did not understand something.

Answer:

1. 25 times larger

2. The scale factor is 25:1

Step-by-step explanation:

Given

Let A represent the area of your swimming pool

Let a represents the area of your neighbour's swimming pool.

From the question, we understand that the area of your swimming pool is 25 times larger than the area of you neighbour's. This can be represented as follows;

A = 25 * a. --- divide through by a

A/a = 25 * a/a

A/a = 25

This means that your pool is 25 times larger than your neighbour's.

To get the scale factor, we have to convert the expression above to ratio

A/a = 25

This can be rewritten as

A/a = 25/1

By comparison the position of constraints at the left hand side to those at the right hand side of the equation

A = 25

a = 1

So,

A : a = 25 : 1

Hence, the scale factor is 25 : 1

Answer: 3

Step-by-step explanation: 3x3 is 9, and one side is 3 and we have square centimeters so 3 squared  or 3x3 is 9 which makes my answer correct, sorry if it was bad explanation this was the easiest question ive answered, plz follow me at twitch, at InfernoEliteGamingYT21

Answer:

Step-by-step explanation:

look at the examples below~

Final answer:

To solve special right triangles, utilize the mnemonic SOHCAHTOA and apply the Pythagorean theorem along with trigonometric functions to find side lengths and angles.

Explanation:

To solve a special right triangle, you'll need to use various relationships between the sides and the angles. A popular mnemonic for remembering these relationships is "SOHCAHTOA", which stands for Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent. It's useful for finding the values of the sides and angles of a right triangle.

For problems involving right triangles, if you have the length of one side (x) and the hypotenuse (r), you can use the Pythagorean theorem to find the length of the other side. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Moreover, you can find the angles aside from the right angle by applying trigonometric functions such as sine, cosine, or tangent, which relate the angles to the lengths of the sides. For example, the sine of an acute angle would be the length of the opposite side divided by the length of the hypotenuse. The cosine would be the adjacent side divided by the hypotenuse, and the tangent would be the opposite side divided by the adjacent side.