This shape is a polygon.
O True
O False

We have to pull 9 marbles from the box to label the box correctly.

Given, three boxes with 10 marbles each can be black or white.

1 box has 10 black marbles, 1 box has 10 white marbles, and 1 box has mixed marbles, could be 1:9 or 5:5, 4:6, etc.

also all the boxes are labeled incorrectly.

we have to find the number of marbles we have to pull to correctly determine the proper labelling for the boxes.

as the box contain 10 marbles, and box contains mixed marbles

so, we have to pull 9 marbles to correctly label the box.

as, we have to check the 9 marbles.

Hence, we have to pull 9 marbles from the box to label the box correctly.

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The leading coefficient determines the shape of the graphs, such as how

the characteristic of a function are directed.

Correct response:

The graphs that represents functions that have a negative leading

coefficient are;

Graph A:

The function in graph A is x³

When the coefficient of x³ is negative, the value of the function rises as x decreases from 0 to -∞, and decreases as x increases from 0 to ∞

Therefore;

Graph B:

The value of the graph decreases as the magnitude of x increases

therefore, the graph is similar to a quadratic function, such that the leading

coefficient is negative, which inverts the function to give increasing output

with negative value as the value of x increases.

Therefore;

Graph C:

The given function in graph C is a linear function having a negative slope,

therefore;

Graph D:

The function of the graph in Graph D, that have y values that increases

exponentially as x increases is a quadratic function.

Given that y increases as the value of x increases, the leading coefficient

(coefficient of x²) is positive.

Therefore;

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Answer:

3 teaspoons.

Step-by-step explanation:

500/2=250 grams per teaspoon

750/250=3

3 teaspoons

Answer:

The 1st one

Step-by-step explanation:

I would explain but you said u need help fast

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer: C

Step-by-step explanation:

Using the substitution U = (2x + 1) is correct, and the statement is True.

We can set U = (2x + 1) by applying the substitution rule. We obtain dU = 2dx by dividing both sides with regard to x. When we solve for dx, we get dx = (1/2)dU.

Now, we substitute these values in the integral:

∫4(2x + 1)² dx = ∫4U² (1/2)dU

Simplifying the expression, we have:

(1/2)∫4U² dU

Now we can integrate with respect to U:

(1/2) * (4/3)U³ + C

(2/3)U³ + C

Finally, substituting back U = (2x + 1), we get:

(2/3)(2x + 1)³ + C

Therefore, using the substitution U = (2x + 1) is correct, and the statement is True.

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Answer:

Step-by-step explanation:

You want an inequality relating the number of 250 lb refrigerators (x) and the number of 425 lb pianos (y) a truck with a 5900 lb load limit can carry. And you want to know if 12 refrigerators and 8 pianos will overload the truck.

The weight of x refrigerators will be 250x. The weight of y pianos will be 425y. Then the restriction on the total weight is ...

  250x +425y ≤ 5900 . . . . . . the load limit of the truck

The weight of 12 refrigerators and 8 pianos will be ...

  250·12 +425·8 = 3000 +3400 = 6400 . . . . pounds

This weight will overload the truck.

__

Additional comment

The graph shows the point (12, 8) is not in the solution space of the inequality. Hence the truck will be overloaded with that load.

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Answer:

13)ignorance

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

8 1/2 x 4

Answer:

47.45754235

31.46697634

Hey do you need to show your work for these? I found an answer key

Step-by-step explanation:

We need to use law of cosines

c²=a²+b²-2abcos(C)

let x= angle xzy

plugging in what we have the equation looks like

17²=22²+20²-2*22*20*cos(x)

289=484+400-880cos(x)

.676136364=cos(x)

x=47.45754235

b.)

The smallest angle should be opposite to the smallest side

Using the law of cosines again we get

9²=13²+17²-2*13*17*cos(x)

81=458-442cos(x)

.852941176=cos(x)

x=31.46697634

Answer:

negative slope

Step-by-step explanation:

using the slope equation you can see that the slope is -53

Answer:

(X+6)(x-5) + (X-5)(X+6)

Answer:

\(2x ^{2} - 22x + 60\)

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Number of tosses / trials = 20

Number of heads = 5

The experimental probability = the actual output of am event when an experiment or test is carried out :

Experimental probability = number of occuences / number of trials

That is :

P(head) = 5 / 20 = 1/4

Theoretical probability could be regarded as the expected output of an event based on the mathematical calculation :

Required outcome / Total possible outcomes

Theoretical probability P(head) in a toss = 1/2

Answer:

-2/3x + -4

Step-by-step explanation:

to get the equation of any straight line, we only need two points off of it, let's use those two on the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}}\implies \cfrac{6}{2}\implies 3\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{3}(x-\stackrel{x_1}{2}) \\\\\\ y-2=3x-6\implies y=3x-4\)

Given:

The system of equation is

\(y=-8x-3\)

\(x+y=7\)

To find:

Whether (3,4) is a solution of the given system or not.

Solution:

We have,

\(y=-8x-3\)          ...(i)

\(x+y=7\)            ...(ii)

Putting the value of y in (ii) from (i), we get

\(x+(-8x-3)=7\)

\(x-8x-3=7\)

\(-7x=7+3\)

\(-7x=10\)

Divide both sides by -7.

\(x=\dfrac{10}{-7}\)

\(x=-\dfrac{10}{7}\)

Putting \(x=-\dfrac{10}{7}\) in (i), we get

\(y=-8\times (\dfrac{-10}{7})-3\)

\(y=\dfrac{80}{7}-3\)

\(y=\dfrac{80-21}{7}\)

\(y=\dfrac{59}{7}\)

So, the only solution of the given system is \(\left(-\dfrac{10}{7},\dfrac{59}{7}\right)\).

Hence, (3,4) cannot be a solution of given system, Hence the correct option is B.

Answer: B I got it right in khan academy

Step-by-step explanation:

Answer:

\(\displaystyle x = \frac{\pi}{4} + k\, \pi\) for integer \(k\) (including negative numbers.)

Step-by-step explanation:

Pythagorean Identity: \(\sin^{2}(x) + \cos^{2}(x) = 1\). Equivalently, \(\cos^{2}(x) = 1 - \sin^{2}(x)\).

Rewrite the original equation and apply this substitution to eliminate \(\cos(x)\):

\(\displaystyle \sin^{6}(x) + \cos^{6}(x) = \frac{1}{4}\).

\(\displaystyle (\sin^{2}(x))^{3} + (\cos^{2}(x))^{3} = \frac{1}{4}\).

\(\displaystyle (\sin^{2}(x))^{3} + (1 - \sin^{2}(x))^{3} = \frac{1}{4}\).

Let \(y = \sin(x)\) (\(-1 \le y \le 1\).) The original equation is equivalent to the following equation about \(y\):

\(\displaystyle y^{6} + (1 - y^{2})^{3} = \frac{1}{4}\).

Expand the cubic binomial in the equation:

\(\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, (y^{2})^{2} - (y^{2})^{3} = \frac{1}{4}\).

\(\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, y^{4} - y^{6} = \frac{1}{4}\).

Simplify to obtain:

\(\displaystyle 1 - 3\, y^{2} + 3\, y^{4} = \frac{1}{4}\).

Rearrange and simplify:

\(12\, y^{4} - 12\, y^{2} + 3 = 0\).

\(3\, (2\, y^{2} - 1)^{2} = 0\).

\(2\, y^{2} - 1 = 0\).

\(\displaystyle y^{2} - \frac{1}{2} = 0\).

Solve for \(y\):

Either \(\displaystyle y = \frac{1}{\sqrt{2}}\) or \(\displaystyle y = -\frac{1}{\sqrt{2}}\).

If \(\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}\), then \(\displaystyle x = \frac{\pi}{4} + 2\, k\,\pi\) for all \(k\in \mathbb{Z}\).

On the other hand, if \(\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}\), then \(\displaystyle x = \frac{3\, \pi}{4} + 2\, k\,\pi = \frac{\pi}{4} + (2\, k + 1) \, \pi\) for all \(k\in \mathbb{Z}\).

Combine both situations to obtain:

\(\displaystyle x = \frac{\pi}{4} + 2\, k\, \pi\) for all \(k \in \mathbb{Z}\).

The value of angle SJP is determined as 270⁰.

The value of angle SJN is determined as 90⁰.

The value of angle SJP is calculated by applying intersecting chord theorem as follows;

From the diagram, the value arc SAJ is equal to the value of angle SJP.

Thus, angle SJP = 270⁰

The value of angle SJN is calculated as follows;

angle SJN = 360 - angle SJP (sum of angles in a circle)

angle SJN = 360 - 270

angle SJN = 90⁰

Thus, the values of angle SJP and SJN are calculated by applying chord angles theorem.

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Solution a needed 70 ounces and solution b needed 50 ounces

What does "1 ounce" mean?

One ounce weighs 437.5 grains or 28.349 grams and is a sixteenth of a pound (avoirdupois) of weight.

One ounce, abbreviated "oz," equals 480 grains, or 31.103 grams, and is one-twelfth of a Troy or Apothecaries' pound in weight. abbreviation for fluid ounce. a tiny amount or percentage.

So, let x=the of ounces of the 50% acid solution. The total volume after both are mixed is 100 ounces so the amount of the 20% solution will be 120-X. The equation will therefore be:

50% * x + 20% * (100-x) = 41% * 100

Dropping the ‘%’ we get

50x + 2000 - 20x = 4100

30x = 2100

x = 2100/30 = 70

Hence 70 ounces will be needed

Solution a = 70 ounces

Solution b = 50 ounces

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According to the statement Jones's new time compared with the old time was \(\frac{1}{5}\) or one-fifth of the original time.

Jones covered a distance of 50 miles on his first trip.

On a later trip, he traveled 300 miles while going three times as fast.

To find out how the new time compared with the old time, we can use the formula:
\(speed=\frac{distance}{time}\).
On the first trip, Jones covered a distance of 50 miles.

Let's assume his speed was x miles per hour.

Therefore, his time would be \(\frac{50}{x}\).
On the later trip, Jones traveled 300 miles, which is three times the distance of the first trip.

Since he was going three times as fast, his speed on the later trip would be 3x miles per hour.

Thus, his time would be \(\frac{300}{3x}\)).
To compare the new time with the old time, we can divide the new time by the old time:
\(\frac{300}{3x} / \frac{50}{x}\).
Simplifying the expression, we get:
\(\frac{300}{3x} * \frac{x}{50}\).
Canceling out the x terms, the final expression becomes:
\(\frac{10}{50}\).
This simplifies to:
\(\frac{1}{5}\).
Therefore, Jones's new time compared with the old time was \(\frac{1}{5}\) or one-fifth of the original time.

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Jones traveled three times as fast on his later trip compared to his first trip. Jones covered a distance of 50 miles on his first trip. On a later trip, he traveled 300 miles while going three times as fast.

To compare the new time with the old time, we need to consider the speed and distance.

Let's start by calculating the speed of Jones on his first trip. We know that distance = speed × time. Given that distance is 50 miles and time is unknown, we can write the equation as 50 = speed × time.

On the later trip, Jones traveled three times as fast, so his speed would be 3 times the speed on his first trip. Therefore, the speed on the later trip would be 3 × speed.

Next, we can calculate the time on the later trip using the equation distance = speed × time. Given that the distance is 300 miles and the speed is 3 times the speed on the first trip, the equation becomes 300 = (3 × speed) × time.

Now, we can compare the times. Let's call the old time \(t_1\) and the new time \(t_2\). From the equations, we have 50 = speed × \(t_1\) and 300 = (3 × speed) × \(t_2\).

By rearranging the first equation, we can solve for \(t_1\): \(t_1\) = 50 / speed.

Substituting this value into the second equation, we get 300 = (3 × speed) × (50 / speed).

Simplifying, we find 300 = 3 × 50, which gives us \(t_2\) = 3.

Therefore, the new time (\(t_2\)) compared with the old time (\(t_1\)) is 3 times faster.

In conclusion, Jones traveled three times as fast on his later trip compared to his first trip.

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Answer:

1) \(\frac{1}{2^7}\) ; 2) \(11^7\)

Step-by-step explanation:

1) Using the Power of a Fraction Rule \((\frac{a}{b} )^x = (\frac{a^x}{b^x} )\),

\((\frac{1}{2} )^7 = (\frac{1^7}{2^7} )\), which can just be simplified to \(\frac{1}{2^7}\).

2) Using the Negative Exponent Rule, \(a^{-x} = \frac{1}{a^{x}}\),

\((\frac{1}{11} )^{-7} = \frac{1}{\frac{1}{11^7}}\), which can be simplified to \(11^7\).

The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.

First find out the selling price of the clarinet:

= Discounted price / ( 1 - discount rate)

= 93.60 / ( 1 - 20%)

= $117

This selling price is 30% more than what the store paid so the price the store paid was:

= Selling price / ( 1 + rate of increase)

= 117 / ( 1 + 30%)

= $90

In conclusion, the amount the store paid was $90.

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Complete question

A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.

How much did the store pay for the clarinet?

Answer:

f(n+1) = f(n)+5

Step-by-step explanation:

So lets say

f(1)=5

f(2)=10

1+1=2 so

f(2)=f(1+1)

therefor

f(n+1)=f(n)+5 since the difference of the functions is 5

the answer is A f(n+1)=f(n)+5

we know that

An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term

In this problem

the sequence of numbers increase by a constant amount equal to

5

each term

so

f(2)=f(1)+5

f(3)=f(2)+5

f(4)=f(3)+5

.

.

f(n+1) = f (n) + 5

therefore

the answer is the option

f(n + 1) = f(n) + 5

Answer:

A

Step-by-step explanation:

Answer:

\(y - 3 = - 4(x + 2)\)

The equilibrium price is the price at which the quantity demanded equals the quantity supplied.

Looking at the graph, we can see that the demand curve intersects the supply curve at a quantity of approximately 200 million boxes. To find the corresponding equilibrium price, we need to find the price level at this quantity.

From the graph, we can observe that the price axis ranges from $20 to $40. Since the graph is not accurately scaled, we can estimate the equilibrium price to be around $30 per box based on the midpoint of the price range.

Therefore, the equilibrium price in this market is approximately $30 per box.

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The value of state price λ(2,0) is 0.18.

In a two-step model with R = 1.2, if one state price is λ(2,2) = 0.18, the state price λ(2,0) can be determined as follows: State prices are the measure of the cost of different future states of the economy. In terms of probabilities, they express the likelihood that the economy will experience different future states. The state price λ is defined as follows:

λ = (1 + R) / R^(n+1)

where R is the gross risk-free interest rate,

n is the number of periods to maturity and

λ is the state price for that maturity.

λ(2,2) = 0.18 can be rewritten as follows: 0.18 = (1 + 1.2) / 1.2^(2+1)

Simplifying:0.18 = 2.64 / 1.728

Thus, λ(2,2) = 0.18 means that λ = 0.06 for the first period and λ = 0.12 for the second period.

Using the two-state model, the state price λ(2,0) can be determined as follows:

λ(2,0) = λ(2,2) x (1 + R)^(n-2) = λ(2,0) = 0.18 x (1 + 1.2)^(2-2) = λ(2,0) = 0.18 x 2.2^0 = λ(2,0) = 0.18 x 1

λ(2,0) = 0.18

Thus, the value of state price λ(2,0) is 0.18.

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The equation which can be used to represent each situation, in terms of x, is;

A = 80 + 2x

B = 45 + 3x

The interval of miles driven, x, for which Company A is cheaper than Company B is when x = 35 miles

Let

Company A:

A = 80 + 2x

Company B:

B = 45 + 3x

Company B > Company A:

45 + 3x > 80 + 2x

collect like terms

3x - 2x > 80 - 45

x > 35

In conclusion, the interval of miles driven, x, for which Company A is cheaper than Company B is 35 miles.

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Length of x:

21:  x  =  6.05

22: x  =  6.66

23:  x  =  5.87

24:   x  =  16.24

For 21 :

Since the given triangle inside the circle is right angle triangle

Therefore,

We can apply Pythagorean theorem:

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

And the diameter intersects a chord into two equal parts

There3fore,

Now put value which is given in the figure,

(16)²= (x)² + (14.8)²

  x² = 36.96

   x  =  6.05

For 22 :

Since the given triangle inside the circle is right angle triangle

Therefore,

We can apply Pythagorean theorem:

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

And we know a diameter intersects chord into two equal parts.

Therefore,

Now put value which is given in the figure,

(10.8)²= (x)² + (8.5)²

  x² = 44.39

   x  =  6.66

For 23 :

Since the given triangle inside the circle is right angle triangle

Therefore,

We can apply Pythagorean theorem:

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

Now put value which is given in the figure,

(10.5)²= (x)² + (8.7)²

  x² = 34.56

   x  =  5.87

For 24 :

Since the given triangle inside the circle is right angle triangle

Therefore,

We can apply Pythagorean theorem:

We know that the Pythagoras theorem for a right angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

Now put value which is given in the figure,

(17.5)²= (x)² + (6.5)²

  x² = 264

   x  =  16.24

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Answer:

-4

Step-by-step explanation:

Wehn dealing with order of operations, we can remember the expression PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction.

So, our first step in the above problem is the parentheses:

\(2(3-5)^3+4(-4+7)\\2(-2)^3+4(3)\)

The second step is exponents:

\(2(-2)^3+4(3)\\2(-8)+4(3)\)

The third step is multiplication:

\(2(-8)+4(3)\\-16+12\)

The fourth and final step is addition:

\(-16+12\\-4\)

Answer:

x = -4 and x = 5

Step-by-step explanation:

Since \(x^2 + 2x\) and \(3x + 20\) both equal to y, we know that the expressions equal to each other. We can write a new equation base on that.

\(x^2 + 2x = 3x + 20\)

Now we solve the equation.

\(x^2 + 2x = 3x + 20\)

\(x^2 - x = 20\)

\(x^2 - x - 20 = 0\)

\((x + 4) (x - 5) = 0\)

\(x + 4 = 0 ; x -5 = 0\)

\(x = -4 ; x = 5\)