If the reclusive rule for a geometric sequence is a1 = 6 an = 2an-1.
What would be the explicit rule?

Answer:

69.75

Step-by-step explanation:

6.5%  = 0.065

So the cost of the textbook = 65.49 + 0.065*65.49

=  69.75  to nearest hundredth

Answer:

168 = x

Step-by-step explanation:

mean  = u=132

standard deviation =sigma = 20

z score =z=1.8

The formula is

z = (x-u)/ sigma

Substituting what we know

1.8 = (x-132)/20

Multiply by 20

1.8*20 = (x-132)/20 *20

36 = x-132

Add 132 to each side

36+132 = x-132+132

168 = x

Multiply the standard deviation by the z-score and add that to the mean:

Value = 132 + (20*1.8) = 132 + 36 = 168

The value would be 168.

Answer:

[tex]3m^2+5n^2+8mn[/tex]

[tex]x^2-11x+17[/tex];0

Step-by-step explanation:

We have been given [tex]m^2+3mn−n^2 [/tex] and [tex]4m^2+5mn+6n^2[/tex]

for (1) we will subtract [tex]4m^2+5mn+6n^2[/tex]  from [tex]m^2+3mn−n^2 [/tex]  that is:

[tex]4m^2+5mn+6n^2-m^2+3mn-n^2[/tex]

Now, simplify the like terms we get:

[tex]4m^2-m^2+6n^2-n^2+5mn+3mn[/tex]

After simplification we get:

[tex]3m^2+5n^2+8mn[/tex]

Hence, [tex]3m^2+5n^2+8mn[/tex] is the required result.

(2) Now, we need to find how much less than [tex]3x^2-7x+9[/tex] is [tex]2x^2+4x-8[/tex]

Subtract [tex]3x^2-7x+9[/tex] from [tex]2x^2+4x-8[/tex] we get:

[tex]3x^2-7x+9-2x^2-4x+8[/tex]

After simplifying like terms

[tex]x^2-11x+17[/tex]

When x=2 the the above  expression becomes:

[tex](2)^2-11(2)+17[/tex]

[tex]4-22+17=0[/tex]

For the first question, 4m^2+5mn+6n^2 is 3m^2+2mn+7n^2 greater than m^2+3mn-n^2. For the second question, 3x^2-7x+9 is x^2 -11x + 17 less than 2x^2+4x−8 and the value of the result when x=2 is 12.

For the first question, begin by subtracting the given expressions (m^2 + 3mn - n^2) from (4m^2+5mn+6n^2). This equates to:

(4m^2 + 5mn + 6n^2) - (m^2 + 3mn - n^2) = 3m^2 + 2mn + 7n^2

For the second question, we subtract (2x^2+4x−8) from (3x^2−7x+9). This is equal to:

(3x^2−7x+9) - (2x^2+4x−8) = x^2 -11x + 17

To find the value of the result when x=2, simple plug in '2' wherever x is in the equation, giving the result 17 - 22 + 17 = 12

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Find the volume of the rectangle:

8 x 2 x 4 = 64 cubic inches.

This means the square can have a volume of 64 cubic inches.

The formula for the volume of a square is V = S^# where S is the length of the side.

Replace V with 64 to solve for S:

64 = S^3

To find S, take the cubic root of 64:

S = ∛64

S = 4

The length of a side is 4 inches.

Answer:

79

Step-by-step explanation:

Since the triangles are similar, the sides that are the same length have angles that are the same size at the top.

Answer:

ABCD must be a paralellogram

Step-by-step explanation:

In parallelogram, rectangle, square and rhombus the diagonals bisect each other. Since angle ABC=91°, then this quadrilateral cannot be rectangle and cannot be square, because rectangle and square have all right angles (90°).

If diagonals of a quadrilateral bisect each other, then quadrilateral is parallelogram. A rhombus is a parallelogram with all congruent sides.

You know nothing about any lengths in the diagram, then you can state that this quadrilateral is parallelogram (always) and can be rhombus (sometimes).

Answer:

<A =21

<B = 84

<c = 75

Step-by-step explanation:

<A =x

<B = 4x

<C =5x-30

The sum of A+B+C = 180

 x+ 4x + 5x-30 = 180

Combine like terms

10x -30 = 180

Add 30 to each side

10x-30+30 = 180+30

10x = 210

Divide by 10

10x/10 = 210/10

x= 21

Since x =21 we can find the value of the angles

Substituting x into the equations for angles A, B and C

<A =21

<B = 4x = 4*21 = 84

<C = 5x-30 = 5*21-30 = 105-30 = 75

Answer

a,b,c

Step-by-step explanation:

21

84

75

Answer: choice C) 60 degrees

smaller angle = 3*x; larger angle = 6*x

The two angles are supplementary, so they add to 180

6x+3x = 180

9x = 180

x = 180/9

x = 20

If x = 20, then,

smaller angle = 3*x = 3*20 = 60 degrees

(the other angle being 6*x = 6*20 = 120; note how 60+120 = 180)

Answer:

try going with C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

Caroline can make 804 full pastrami sandwiches with 201 1/4 pounds of pastrami, using 3/8 of a pound for each sandwich.

To find out how many pastrami sandwiches Caroline can make with 201 1/4 pounds of pastrami, we first need to determine the total number of sandwiches that can be made from a single pound of pastrami. As each sandwich uses 3/8 of a pound, we can calculate this as follows:

1 pound / (3/8 pound per sandwich) = 8/3 sandwiches per pound.

Next, we multiply the number of sandwiches that can be made per pound by the total pounds of pastrami:

201 1/4 pounds * 8/3 sandwiches/pound = 804 sandwiches + 2/3 of a sandwich.

Since Caroline can't make 2/3 of a sandwich, she can make a total of 804 full sandwiches with the pastrami she has.

Answer:

The store will sell it for $58.50

Step-by-step explanation:

To find this amount, start by multiplying the cost by the mark up percentage.

$45 * 30% = $13.50

Now that we have the markup amount, we can add it to the original cost to get the store price.

$45.00 + $13.50 = $58.50

Step 1.

Calculate measure of angle α:

[tex]47^o-38^o=9^o[/tex]

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]

Step 3.

Calculate the circumference of the Earth (circle):

[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]

Step 4.

The length of arc is equal 1/40 of the circumference:

[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]

[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]

The distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is approximately 628 miles, calculated using the formula for arc length of a sphere, considering the Earth's radius and the difference in degrees of latitude.

The question revolves around the concept of calculating the arc length in degrees, which is a topic in mathematics, specifically trigonometry.  

The formula for calculating the arc length of a sphere is arc length = radius x angle (in radians).

We already know the radius of the earth (4000 miles) and the difference in latitude between Seattle and San Francisco (47°-38°=9°).

However, in the formula, we need the angle to be in radians. To convert degrees to radians, we use the formula 1 degree = π/180 radians.

So, 9° equals 9*(π/180) = 0.157 radians.

Now, we substitute the values into the formula: arc length = 4000 miles * 0.157 radians. This gives an answer of approximately 628 miles.

Therefore, the distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is about 628 miles.

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Answer:

Minimum 15 bracelets to be sold to meet the break even.

Step-by-step explanation:

The cost price of bracelets is represented by C(x) =180+8x

The revenue earned (selling price) is represented by R(x) =20x

In these two functions x represents number of bracelets.

If P represents the profit then P = 20x-(180+8x)

P = 20x-180-8x = (12x-180)

For break even profit P = 0

12x-180 =0

12x = 180

x = 180÷12

x = 15

So minimum quantity of bracelets to be sold is 15 for the break even.

Answer:

The answer is 5

Answer:

[tex]\frac{1}{2}[/tex] of the pie.

Step-by-step explanation:  

We have been given that Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave leftovers to his friends.

Let us find out pie given to friends by subtracting amount of pie eaten by Christine and her brother from 1 pie, that will be 6/6.

[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{1}{3})[/tex]

[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{2*1}{2*3})[/tex]

[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{2}{6})[/tex]

[tex]\text{The pie given to friends}=\frac{6}{6}-\frac{3}{6}[/tex]

[tex]\text{The pie given to friends}=\frac{6-3}{6}[/tex]

[tex]\text{The pie given to friends}=\frac{3}{6}[/tex]

[tex]\text{The pie given to friends}=\frac{1}{2}[/tex]

Therefore, he gave [tex]\frac{1}{2}[/tex] of the pie to his friends.

Answer:

sinB = 8/17

Step-by-step explanation:

sinB = Opposite/Hypotenuse

Here we have to find the opposite side using the Pythagorean theorem.

AB^2 = AC^2 + BC^2

17^2 = AC^2 + 15^2

AC^2 = 17^2 - 15^2

AC^2 = 289-225

AC^2 = 64

Taking the square root on both sides, we get

AC = 8

Opposite side = 8

SinB = 8/17

Answer:

sin B = 8/17

Step-by-step explanation:

sin B can be expressed as the opposite over the hypotenuse in a right triangle.  But we don't know the opposite yet.  We can use the Pythagorean theorem to solve for it

a^2 + b^2 = c^2

15^2 +b^2 = 17^2

225+b^2 = 289

Subtract 225 on each side

225-225 +b^2 = 289-225

b^2 = 64

Take the square root of each side

b=8

The opposite side is 8

sin B = opp/hyp

sin B = 8/17

Answer:

8*5^n-1 / 2^n-1 = n

This is the function for your sequence

8*5^n-1 / 2^n-1 = n

The Sequence Calculator finds a equation of the sequence or also allows you to view the next terms in a sequence. Arithmetic Sequence Formula: an = a1 +d(n −1) a n = a 1 + d (n - 1) Geometric Sequence Formula: an = a1rn−1 a n = a 1 r n - 1

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Answer:  $ 16.96      

Step-by-step explanation:

Here, the present value of the loan, PV = $695.20

Annual Interest rate = 17.9%

⇒ Monthly interest rate = 17.9/12 = 1.41666666667

Thus, the monthly interest rate (decimal ) , r = 0.014167 ( approx)

Monthly payment, P = $ 325

Let the time period of the loan = n.

Since, [tex]P= \frac{r(PV)}{1-(1+r)^{-n}}[/tex]

⇒ [tex]325= \frac{0.014167(695.20)}{1-(1+0.014167)^{-n}}[/tex]

⇒  [tex]1-(1+0.014167)^{-n}= \frac{10.37008984}{325}[/tex]

⇒ [tex]1-(1+0.014167)^{-n}= 0.03190796873 [/tex]

⇒  n = 2.19

Thus, her total payment = 2.19 × 325 =  711.75

⇒ Her total interest = 711.75 - 695.20 = $16.55

Since only 16.96 is near to 16.55

Thus, second option is correct.

Answer:

1

Step-by-step explanation:

[tex]A.\\\\\dfrac{y}{a}-b=\dfrac{y}{b}-a\qquad\text{multiply both sides by }\ ab\neq0\\\\by-ab^2=ay-a^2b\qquad\text{add}\ ab^2\ \text{to both sides}\\\\by=ay+ab^2-a^2b\qquad\text{subtract}\ ay\ \text{from both sides}\\\\by-ay=ab^2-a^2b\qquad\text{distributive}\\\\(b-a)y=ab^2-a^2b\qquad\text{divide both sides by}\ (b-a)\\\\\boxed{y=\dfrac{ab^2-a^2b}{b-a}}\to y=\dfrac{ab(b-a)}{b-a}\to\boxed{y=ab}[/tex]

[tex]B.\\t+\dfrac{b^2}{a}=\dfrac{bt}{a}+a\qquad\text{multiply both sides by}\ a\neq0\\\\at+b^2=bt+a^2\qquad\text{subtract}\ b^2\ \text{from both sides}\\\\at=bt+a^2-b^2\qquad\text{subtract}\ bt\ \text{from both sides}\\\\at-bt=a^2-b^2\qquad\text{distributive}\\\\(a-b)t=a^2-b^2\qquad\text{divide both sides by}\ (a-b)\neq0\\\\\boxed{t=\dfrac{a^2-b^2}{a-b}}\to t=\dfrac{(a-b)(a+b)}{a-b}\to\boxed{t=a+b}[/tex]

Answer:

Where are y and t?

Step-by-step explanation:

There might be a simpler way to do this, if there is, sorry.

If you look at the graph, x is greater than 3 but less than 5.

So: x > 3 and x < 5

I would simplify each solution set and get "x" by itself (until I get the right answer):

A.) 2x - 4 > 6 or 3x < 9

2x - 4 > 6    Add 4 on both sides

2x > 10      Divide 2 on both sides

x > 5        (you could stop here and go to the next choice since you know this does not match the graph)

3x < 9     Divide 3 on both sides

x < 3

x > 5 and x < 3

B.)   2x - 4 < 6 and 3x > 9

x < 5   and    x > 3

Your answer is B or the 2nd option

[C and D would have given a negative number]

The compound sentence that has its solution set shown on the graph is 3x + 8 > -7 and -4x < 12.

The solution set for the given compound inequalities is represented by the graph where the shaded region includes the points -1, 0, 1, 2, 3, 4, and 5. The compound sentence that has this solution set is:

3x + 8 > -7 and -4x < 12

Let's break down the compound sentence step by step:

Solve the first inequality: 3x + 8 > -7. Subtract 8 from both sides to get 3x > -15. Divide both sides by 3 to get x > -5.

Solve the second inequality: -4x < 12. Divide both sides by -4 and flip the inequality sign to get x > -3.

Combine the two inequalities by using the word 'and': x > -5 and x > -3.

The solution to this compound sentence is the values of x that satisfy both inequalities, which is x > -3.

Therefore, the compound sentence 3x + 8 > -7 and -4x < 12 has its solution set shown on the given graph.

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Answer:

3.5

Step-by-step explanation:

The speed difference is 40 mph

then divide the distance by the speed difference and you get 3.5

Answer:

they will be 140 miles apart in 2 hours

Step-by-step explanation:

in one hour they will be 70 miles apart since 15 + 55 = 70 and then they get 70 more miles apart in the second hour and 70 + 70 = 140 so 2 hours

Answer:

Question 1 is A.

Answer:

i just did the quiz and its  FALSE  i got it wrong so i thought you should have a right answer

Step-by-step explanation:

The order of operations in mathematics ensures that the result of a numerical expression is the same regardless of the order in which the operations are performed. - True

In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. Following these rules ensures that you always get the same result, regardless of the order in which the operations are performed.

The order of operations, also known as PEMDAS, stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). For example, in the expression 4 + 5 × 2, according to the order of operations, you would perform the multiplication first and then the addition. So, the correct way to evaluate this expression would be 4 + (5 × 2) = 4 + 10 = 14.

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Complete Question:

You will always get the same result in a numerical expression no matter the order in which you perform the operations. True/False ?

Answer:

512

Step-by-step explanation:

64 / 2 = 32

32 * 16 = 512

64 / 2 * 16 = 512

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[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{62 \div 2 \times 16}\\\\\mathsf{= \dfrac{62}{2} \times 16}\\\\\mathsf{= \bold{32}\times16}\\\\\mathsf{= \bf 512}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{512}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

40% of the pieces of fruit in the Bowl are apples.    

Step-by-step explanation:

Given the statement:- There are 15 pieces of fruit in a bowl and six of them are apples.

⇒ Total number of pieces of fruit  in a bowl = 15 pieces

and  

Number of pieces of apple in a bowl = 6 pieces.

To find the percentage of the pieces of fruit in the Bowl are apples.

[tex]Percentage = \frac{Number of pieces of apple in bowl}{Total number of pieces of fruit in Bowl} \times 100[/tex]

                           = [tex]\frac{6}{15} \times 100 = 40\%[/tex]

Therefore, 40% of the pieces of fruit in the Bowl are apples.

The percentage of apples present in the bowl is [tex]40\%[/tex].

According to the question, there are 15 pieces of fruit in a bowl and 6 of them are apples.

So, the percentage of apples present in the bowl is evaluated as-

[tex]Percentage\;of\;apples=\dfrac{Apples}{Total\;number\;of\;fruits}\times 100\%\\Percentage\;of\;apples=\dfrac{6}{15}\times 100\%\\Percentage\;of\;apples=40\%[/tex]

Hence, the percentage of apples present in the bowl is [tex]40\%[/tex].

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Answer:

RX = 12 and XU = 6

Step-by-step explanation:

Given :  In ΔTRV , TW ,RU and VS are the medians .

             X is the centroid

To Find : RX and XU

Solution:

Since we know that the centroid divides each median in a ratio of 2:1.

Since X is the centroid so RX : XU = 2:1

So, let RX = 2x and XU = x

And we are given that RU = 18

⇒RX +XU=18

⇒2x+x=18

⇒3x=18

⇒[tex]x=\frac{18}{3}[/tex]

⇒[tex]x=6[/tex]

Thus,  RX = 2x = 2*6 =12

          XU = x =6

Hence length of RX = 12 and XU = 6