If Logan's family can drive 23 1/8 miles on 1 gallon of gas,how far can they drive on 17 gallons

You can see that each term is twice the previous one, with inverted sign.

You double a number by multiplying it by two, and you change its sign by multiplying it by -1.

So, you multiply each term by 2 and by -1, which results in a multiplication by -2.

Since we start with 3, the terms are

[tex]a_1 = 3[/tex]

[tex]a_2 = 3\cdot (-2) = -6[/tex]

[tex]a_3 = -6\cdot (-2) = 12[/tex]

and so on. So, the general term is

[tex]a_n = 3\cdot(-2)^{n-1}[/tex]

Answer:

Markup rate = 0.512 or 51.2%

Step-by-step explanation:

Mark up rate is the increase amount added to the original price.

Sales Price = $95.98

Original Price= $63.45

Gross profit margin = Sales Price - Original cost

                                = $95.98 - $63.45

                                = $ 32.53

Mark up Rate = Gross profit margin/ original price

                                  = 32.53 / 63. 45

                                  = 0.51

converting into percentage by multiplying with 100

Mark up Percentage = 0.512 * 100

                                  = 51.2 %

Answer:

44444444444444444444444444444444444444444444467

Step-by-step explanation:

Answer:

[tex]0.5\ days[/tex]

Step-by-step explanation:

we know that

Using proportion

[tex]\frac{4}{8}\frac{days}{necklaces} =\frac{x}{1}\frac{days}{necklace} \\ \\x=4/8\\ \\x=0.5\ days[/tex]

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[tex]\frac{48}{1369}[/tex]

Step-by-step explanation:

A bag contains 4 green marbles, 6 red marbles, 14 orange marbles, 5 brown marbles, and 8 blue marbles. You choose a marble, replace it, and choose again. Total marbles = 37 marbles

Probability (choosing red) = number of red marbles / total marbles

= 6/37

Red is replaces so total marbles again becomes 37

P( choosing blue)= 8/37

P(red, then blue)= [tex]\frac{6}{37} * \frac{8}{37} = \frac{48}{1369}[/tex]

Answer:

a

Step-by-step explanation:

0=3x²+20x+12

0=(3x+2)(x+6)

0=3x+2 0=x+6

-2=3x -6=x

-2/3=x

x + x +1 + x +2 + x + 3 >= 244

=》 4x + 6 >= 244

=》 4x >= 238

=》 x >= 238/4 >= 59.5

since x is an integer...least value of x is 60

The least possible even integer is 58

Let's let x be an even integer. The next three would be shown by x+2, x+4 x+6 so now we can add all these to equal 244. Shown with an equation would look like:

x + x+2 + x+4 + x+6 = 244

Combine like terms will be:

4x+12=244

Subtract 12 from both sides we will get

4x=232

Now Divide each side by 4

x=58

So now put x in the above equation and we get  the numbers

x=58,

x+2= 60

X+4 =62

x+6= 64

The least one is 58

Answer:

C

Step-by-step explanation:

The surface are of the prism will be the area of a each side added together. The work would look like this:

SA = 2[(l×h)+(l×b)+(b×h)]

SA = 2(lh+lb+bh)

But if you multiply each dimension by 5, the area becomes

SA = 2[(5l×5h)+(5l×5b)+(5b×5h)]

SA = 2(5²lh+5²lb+5²bh)

SA = 5²×2(lh+lb+bh)

SA = 5²area

Since 5² = 25, then the the surface area is multiplied in size by 25.

1/2 is .5

and knowing this, just make a fraction out of the numbers before .5 .

2/5 is .4

3/10 is .3

1/5 is .2

1/10 is .1

and there are your fractions less than 1/2

The three fractions that are not greater than 1/2 will be 1/3, 1/4, and 1/5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The three fractions that are not greater than 1/2. If the denominator increases then the value gets decreases. Then the three fractions are given as,

1/3, 1/4, 1/5

The three fractions that are not greater than 1/2 will be 1/3, 1/4, and 1/5.

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Answer:

∠BAM=30°

Step-by-step explanation:

Points A and B split the circle into two arcs. If the measure of minor arc AB is 150°, then the measure of the major arc AB is 360°-150°=210°.

If point M splits major arc with the ratio 2:5, then

Angles BOM and AOM together form angle with the measure 210°, thus

2x+5x=210,

7x=210,

x=30°

and ∠BOM=60°, ∠AOM=150°.

Consider isosceles triangle BOM. In this triangle,

∠OBM=1/2(180°-60°)=60°.

Consider isosceles triangle AOB. In this triangle,

∠OAB=1/2(180°-150°)=15°.

Consider isosceles triangle AOM. In this triangle,

∠OAM=1/2(180°-150°)=15°.

Thus, ∠BAM=15°+15°=30°

Answer:

arc BAM =  300°

Step-by-step explanation:

Refer to the figure attached.

arc AB = 150°

then:

arc AMB = 360° - 150° = 210°

arc AMB can be decomposed as:  

arc AM + arc MB = arc AMB (eq. 1)

From data:

arc MB/arc AM = 2/5

arc MB*(5/2) = arc AM (eq. 2)

Replacing equation 2 into equation 1:

arc MB*(5/2) + arc MB = 210°

arc MB*(7/2) =  210°

arc MB = (2/7)*210° = 60°

On the other hand:

arc MB + arc BAM = 360°

arc BAM = 360° - 60° =  300°

Answer:

Well it would come out to 2x-3y=-9

Step-by-step explanation:

Here's how you solve this problem:

1) Multiply the first equation by 2 (result:2x+2y=8).

2) Add both equations together (result:2x+x+2y-2y=8-5)

3) Simplify (result:3x=3)

The answer is 3x=3.

This could be simplified more, however, to equal x=1, since both sides are divisible by 3.

p.s. Have a good day!

Answer:

Option b

Step-by-step explanation:

To solve this problem we must test if the function is even.

If f(-x) = f(x) then the function is even and is symmetric with respect to the y-axis.

If f(-x) = -f(x) then the function is odd and has symmetry with respect to the origin.

We have the function:

[tex]f(x) = \frac{e^x + e^{-x}}{2}[/tex]

We make:

[tex]f(-x) = \frac{e^{-x} + e^{-(-x)}}{2}[/tex]

Rewriting the function we have

[tex]f(-x) = \frac{e^{-x} + e^{x}}{2} = \frac{e^{x} + e^{-x}}{2}\\\\f(-x) = f(x)[/tex]

Finally, the function has symmetry with respect to the y axis.

Answer:

b

Step-by-step explanation:

Answer:

Choice D is correct

Step-by-step explanation:

The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.

Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.

Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;

k = 1*4 = 4

This polar equation is given by alternative D.

Answer:

D

Step-by-step explanation:

it's right on edge, i just took the test :)

Answer:

651 and 3/25 is 651.12 as a mixed number.

651.12 can be written as the mixed number 651 3/25.

To convert hundredths to a fraction, we write the decimal as the numerator and the place value as the denominator. T

Therefore, .12 can be written as 12/100.

651 + 12/100

= 651 12/100

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:

651 12/100 = 651 3/25

Therefore, 651.12 can be written as the mixed number 651 3/25.

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Answer:

for the orange juice it's 6/24

for the apple juice it's 4/24

Step-by-step explanation:

since there are 24 juices you need to put the denominator as 24 at all time no matter the juice choice and then you find how many there are of that specific juice and put it as the top number because that is the probability of you getting that specific juice.

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Answer:

Option A

Step-by-step explanation:

A relation can be defined as a function if there is only one output for each input.

In this case, the output is the cost of the fabric and the input is the number of yards of fabric.

Then, for each number of yards of fabric there will be a cost. But there will not be two different costs (outputs) for the same number of fabric yards (entrance)

Then the answer is the Option A: Yes, because one imput (number of yards of fabric) will always have the same output (costs)

Answer:

f is not  defined at x = 3 ⇒ answer (b)

Step-by-step explanation:

∵ f(x) = x² - x - 6/x² - 9 is a rational function

∴ It will be undefined at the values of x of the denominator

∵ The denominator is x² - 9

∵ x² - 9 = 0 ⇒ x² = 9 ⇒ x = ±√9

∴ x = ± 3

∴ f(x) can not be defined at x = 3

∴ The f(x) can not be continuous at x = 3

∴ The answer is (b)

Answer:

b. f is not defined at x=3

Step-by-step explanation:

The given function is

[tex]f(x)=\frac{x^2-x-6}{x^2-9}[/tex]

One of the conditions for continuity is that; the function must be defined at [tex]x=a[/tex]

If we plug in [tex]x=3[/tex], we obtain;

[tex]f(x)=\frac{3^2-3-6}{3^2-9}[/tex]

[tex]f(x)=\frac{9-3-6}{9-9}[/tex]

[tex]f(x)=\frac{0}{0}[/tex]

Since the function is not defined at x=3, it is not also continuous at x=3

The correct choice is B

Answer:

multiply the radius by 2π

Step-by-step explanation:

The formulas for circumference of a circle is

C = πD     where D is the diameter,

or

C = 2πr    where r is the radius.

Either formula is correct, but we will work with the second one since the question is asking about radius.

We see that 2π(r) = the circumference, so multiply r by 2π to get the circumference

Hello there! How are you doing? I am doing fine! I'll answer the question now.  

So basically when wanting to find the circumference of a circle you simply use the formula, C = 2 times PI times R. PI is the infamous number known for 3.1415912654... and the R represents the radius. You would multiply 2 times PI  and then after getting that you would basically multiply it by the radius. And then that would be the circumference and be the answer to any problem you face like this. Know that diameter is 2 times the radius and that all.

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Explanation:

Start with the first equation. We'll plug in y = 2x+2

3x - y = 3

3x - ( y ) = 3

3x - ( 2x+2 ) = 3 ..... replace y with 2x+2

3x - 2x - 2 = 3 ..... distribute the negative through to all terms inside

x-2 = 3  ............ combine like terms

x-2+2 = 3+2 .... add 2 to both sides

x = 5

Use this x value to find the value of y. The easiest equation to use is the one in which y is already isolated for us

y = 2x+2

y = 2*5+2 ..... replace x with 5

y = 10+2

y = 12

Though we can use the other equation as well

3x-y = 3

3*5-y = 3 .... replace x with 5

15 - y = 3

15-y-15 = 3-15 ..... subtract 15 from both sides

-y = -12

y = 12 ..... multiply both sides by -1, or change the signs of both sides

We get the same result for y.

The solution is (x,y) = (5,12) meaning that the graphs of the two original equations cross at this point.

It’s 5 & 12. Just substitute them in and boom!

Well you didn't include a direct question but she traveled 7.5 miles on the bus and she walked .5 miles home.

Answer: 45 kilometers

Step-by-step explanation:

The equation to solve this problem is:

$165 = 1.4x + 102

The variable x represents the number of kilometers he travels.

To solve the equation:

Subtract 102 from each side-

63 = 1.4x

Next divide each side by 1.4-

45 = x

Teague needs to run 45 kilometers in order to raise $165.

165=1.40x+102 (equation) x = amount run and final answer is x=45

Final answer:

The factory takes 18 hours to produce 180 cars.

Explanation:

To find out how many hours the factory takes to produce 180 cars, we need to set up a proportion. Since the factory takes 6 hours to produce 60 cars, we can set up the proportion:

6 hours / 60 cars = x hours / 180 cars

Cross-multiplying, we get:

6(180) = 60(x)

Simplifying, we have:

1080 = 60x

Dividing both sides by 60, we find:

x = 18

So, the factory takes 18 hours to produce 180 cars.

The answer is 50%.

Divide 2.25 by 1.50. That equals 1.5. That’s the equivalent to 50% because if you subtract 1 from 1.5 and multiply by 100. You get the same answer. Only do that for numbers greater than one, otherwise it won’t work

volume of the cylinder= pi r^2 h

=22/7*3*3*5=141.428

nearest hundredth =141.420

volume of the given cylinder= 141.42 cubic feet

Answer:

The volume of the cylinder is 141.43 ft³.

Step-by-step explanation:

Since, the volume of a cylinder is,

[tex]V=\pi (r)^2 h[/tex]

Where, r is the radius of the cylinder,

And, h is the height of the cylinder,

Here, r = 3 feet,

h = 5 feet,

Hence, the volume of the given cylinder is,

[tex]V=\pi (3)^2 (5)[/tex]

[tex]=\frac{22}{7}\times 9\times 5[/tex]     (  [tex]\pi =\frac{22}{7}[/tex] )

[tex]=\frac{990}{7}[/tex]

[tex]=141.428571429\text{ cube feet}=141.43\text{ cube feet}[/tex]

Answer: The rate is 7.5%.

Step-by-step explanation: The formula to calculate simple interest is:

Interest = Principal x Rate x Time

So, we need to plug our information into the formula:

$562.50 = $1,500 x R x 5

Now, perform the multiplication that you can:

$562.50 - $7,500R

Next, divide both sides by $7,500:

.075 = R

Therefore, the rate is 7.5%.

Answer:

62.5

Step-by-step explanation:

By dividing 50 by 10 and 10 by 2 we can find that r, or the common ratio is 1/5, meaning that this series converges, so it is solvable. The formula for a convergent series is [tex]\frac{a_{1}}{1-r}[/tex]. By plugging in 1/5 for r and 50 for  [tex]a_{1}[/tex] we can find that the sum of this infinite series is 62.5

Answer:

Option c

Step-by-step explanation:

We have two matrices, matrix A and matrix B.

Before doing the addition of matrices, we must multiply the matrix A by the scalar -7 and then multiply the matrix B by the scalar -6.

The multiplication of a matrix A by a scalar c, is done by multiplying all the elements of matrix A by the value c.

So

[tex]-7A = \left[\begin{array}{ccc}70&-70&-56\\14&7&-35\\28&-56&42\end{array}\right]\\\\\\-6B =\left[\begin{array}{ccc}-30&-36&24\\-60&36&60\\54&-6&-60\end{array}\right][/tex]

Now we add both matrices.

The sum of the matrices is done by adding each term [tex]a_{mn}[/tex] with each term [tex]b_{mn}[/tex]

For example: (70 - 40) , (-70 + (-36)), ...,    

Then:

[tex]-7A + (-6B) = \left[\begin{array}{ccc}40&-106&-32\\-46&43&25\\82&-62&-18\end{array}\right][/tex]

D is the answer hope it helps

We will need to picture for this.