The distance formula states that distance (d) is equal to the product of rate (r) and time (t).

Which equation could be used to solve the problem?
John ran at a constant rate of 200 mph. How many minutes did it take john to run 500 m?

A. t=500/200

B. t=500d/200

C. t=200/500

D. t=200r/500

Answer: 60°, 72°, 90°, 120° and 180°

Step-by-step explanation:

To calculate the angle of rotational symmetry of a shape or polygon, you make use of this formula

[tex]\frac{360}{n}  where n is the number of sides of the shape[/tex]

example for a Square with 4 sides. the angle of rotational symmetry is 360/4 =90°.

The question is missing the figure. So, it is attached below.

Answer:

Area of the shaded sector is 144π units squared.

Step-by-step explanation:

Given:

Central angle of the sector is, [tex]\theta=\frac{8\pi}{9}\ rad[/tex]

Radius of the circle is, [tex]R=18\ units[/tex]

We know that, area of a sector of a circle of radius 'R' and central angle [tex]\theta[/tex] is given as:

[tex]A=\frac{1}{2}R^2\theta[/tex]

Plug in [tex]\theta=\frac{8\pi}{9},R=18[/tex]. This gives,

[tex]A=\frac{1}{2}\times (18)^2\times \frac{8\pi}{9}\\\\A=(\frac{324\times 4}{9})\pi\\\\A=(36\times 4)\pi\\\\A=144\pi\ units^2[/tex]

Therefore, the area of the shaded sector is 144π units squared.

Answer: 144Pi units squared

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

P(B) = 1/2

Now we are considering that the three children are all boys. This means we are considering that the first is a boy, the second is a boy and the third too is a boy. This brings us to the situation BBB

That is a boy and a boy and another boy. In probability, the word and means we multiply the three.

Hence:

P(BBB) = P(B1) * P(B2) * P(B3) = 1/2 * 1/2 * 1/2 = 1/8 or 0.125

The probability of a three-child family having all boys, given that each birth is independently a boy with a probability of one half, is 1/8 or 0.125 (12.5%).

The subject of your question is based in

probability

, a key concept in mathematics. Specifically, you're asking about the

probability of a family having three boys

, with the probability of any birth resulting in a boy being given as one half. As the question indicates that all births are independent, we're dealing with independent events in probability. The probability of independent events is calculated by multiplying the probabilities of each individual event. In this case, the probability of having a boy is one half (or 0.5), and we have three independent events (the births of the three children). Therefore, the probability of all three children being boys is (1/2) * (1/2) * (1/2), which simplifies to 1/8 or 0.125. So, assuming that all births are equally likely to result in a boy or a girl, the probability of a three-child family having all boys is 0.125, or 12.5%.

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This is a vertical line that goes through all points with an x-coordinate of -9.

To graph it, I can give you a couple of points this line goes through so you can draw it more easily.

Points that are on line: (-9,0) and (-9,1)

Answer:

C. $29.20

Step-by-step explanation:

The difference between using an electric stove and a gas stove everyday is 13 cents - 5 cents= 8 cents.

Saving 8 cents everyday.

Therefore for a year, Bryce will save 8 cents × 365days = 2920 cents

Then 2920 cents = $(2920÷100)

=$29.20

Answer:

C. $29.20

Step-by-step explanation:

Answer:

1. [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]

2. [tex]E_d=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

The given demand equation is

[tex]p=\dfrac{45}{q^{1.5}}[/tex]

where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.

Part 1 :

We need to Express q as a function of p.

The given equation can be rewritten as

[tex]q^{1.5}=\dfrac{45}{p}[/tex]

Using the properties of exponent, we get

[tex]q=(\dfrac{45}{p})^{\frac{1}{1.5}}[/tex]      [tex][\because x^n=a\Rightarrow x=a^{\frac{1}{n}}][/tex]

[tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]

Therefore, the required equation is [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex].

Part 2 :

[tex]q=(45)^{\frac{2}{3}}p^{-\frac{2}{3}}[/tex]

Differentiate q with respect to p.

[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{2}{3}-1}})[/tex]

[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{5}{3}})[/tex]

[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})[/tex]

Formula for price elasticity of demand is

[tex]E_d=\dfrac{dq}{dp}\times \dfrac{p}{q}[/tex]

[tex]E_d=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{(45)^{\frac{2}{3}}p^{-\frac{2}{3}}}[/tex]

Cancel out common factors.

[tex]E_d=(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{p^{-\frac{2}{3}}}[/tex]

Using the properties of exponents we get

[tex]E_d=-\dfrac{2}{3}(p^{-\frac{5}{3}+1-(-\frac{2}{3})})[/tex]

[tex]E_d=-\dfrac{2}{3}(p^{0})[/tex]

[tex]E_d=-\dfrac{2}{3}[/tex]

Therefore, the price elasticity of demand is -2/3.

To address the question, q as a function of p is q = (45/p)^(2/3), and the price elasticity of demand when p is $4 can be found by taking the derivative of q with respect to p and substituting the given values in the elasticity formula.

The student has asked to express q as a function of p and to find the price elasticity of demand when the price is set at $4.00 per serving for a new roast chicken product. The given equation is p = 45 / q1.5.

The derivative of q with respect to p is dq/dp = -2/3 × (45/p4/3). Substituting p=4, we get the quantity q = (45/4)2/3. Plugging these values into our elasticity formula gives us the price elasticity of demand at p=$4.00.

Answer:

Deduct/subtract

Step-by-step explanation:

Federal Reserve board uses different methods to increase or decrease the currency in circulation. This methods are known as Monetary policy. The Central bank, at its discretion, can print more currency to increase the flow of currency in circulation

The Federal Reserve Board, which is the governing body that manages the Federal Reserve System, oversees all domestic monetary policy. The Fed"s job is to increase and decrease paper currency in circulation. This effort is to curb inflation and hyperinflation, stabilize the economy and create room for ease of doing business with the international community

The Fed can increase the money supply by lowering the reserve requirements for banks, which allows them to lend more money.

Also, by raising the banks' reserve requirements, the Fed can decrease the size of the money supply.

The Central bank modify short-term interest rates by lowering or increasing the discount rate that banks pay on short-term loans from the Fed.

Modifying Reserve Requirements : they can moderate the amount of money banks can hold.

Answer:

D

Step-by-step explanation:

Joe already has $40 and can save $20 each week. the total amount he can save in a given number of weeks is $20 multiplied by the that number of weeks which in this case is w so 20w. To find the total T of the amount he has after w weeks, you add the amount he already has to the amount saved. So the equation would be T=40+20w

Answer:

D) T = 40 + 20w

Step-by-step explanation:

Trust me! i had this on my test/ exam, and it was correct!!

i really hoped this helped! Have a wonderful day!

Answer:

It is C

Step-by-step explanation:

(3x-2)(x+2)

3x(x)+3x(2)-2(x)-2(2)

3x^2+6x-2x-4

3x^2+4x-4 <----------

(Im bad at explaining but that is right trust me :P)

Answer:

104°

Step-by-step explanation:

Thinking process:

Let the triangle be:

ΔMNO

The angle be: ∠LMN.

From the description, NOP is 104°

If, segment MN and NO are marked congruent then the corresponding angle,  ∠LMN is 104°

This property of congruency applies since the segments are equal.

Isn't this Anatomy and Physiology?

Answer:

[tex]\frac{13}{2}[/tex] square units

Step-by-step explanation:

We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).

We have to find the area of triangle.

We know that area of triangle=[tex]\frac{1}{2}\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid [/tex]

[tex]x_1=3,x_2=5,x_3=6[/tex]

[tex]y_1=1,y_2=4,y_3=-1[/tex]

Substitute the values in the formula then we get

Area of right triangle =[tex]\frac{1}{2}\mid (3(4+1)+5(-1-1)+6(1-4))\mid [/tex]

Area of right triangle =[tex]\frac{1}{2}\mid (15-10-18)\mid [/tex]

Area of right triangle =[tex]\frac{1}{2}\times 13=\frac{13}{2}[/tex] square units

Answer:

Every point in the line would get reflected about the x axis and we would get a new line.

Step-by-step explanation:

When you reflect a point about the x-axis , the x-coordinate of the image remains the same but the y - coordinate changes to its negative value.

Now a line is a collection of points and we have to find out what happens when we reflect a line about the x-axis.

Reflecting a line about the line is same as keeping a mirror along the x-axis and the image we see in the mirror is the same as the image we obtain in the mirror.

So every point in the line would get reflected about the x axis and we would get a new line.

Final answer:

Reflecting a line across the x-axis inverts the y-coordinates of all points on the line, while the x-coordinates remain unchanged; the reflected line appears flipped over the x-axis, preserving distance but potentially changing orientation.

Explanation:

When a line is reflected across the x-axis, each point on the original line is flipped vertically to a new position on the opposite side of the x-axis, maintaining the same distance from the x-axis. Essentially, every point's y-coordinate is multiplied by -1, causing the line to appear as a mirror image of itself with respect to the x-axis. This transformation preserves the shape and size of the original line but changes its orientation relative to the x-axis.

If it's 4 o'clock, the hour hand will be on the 4 and the minute hand will be on the 12.

This takes 4 partitions/pieces of the clock, and there are 12 different partitions. That's 4/12, or 1/3 of the entire clock.

The total clock is a 360 degree angle.

360 * (1/3) = 120

1/3 of 360 degrees is 120 degrees.

Since the angle between the minute and hour hand takes up 1/3 of the clock, the angle is 120 degrees.

Let me know if you need any clarifications, thanks!

Answer:

[tex](1.5,2.85)[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

we have the endpoints:

Q(0.3, 1.8), R(2.7, 3.9)

substitute in the formula

[tex]M(\frac{0.3+2.7}{2},\frac{1.8+3.9}{2})[/tex]

[tex]M(\frac{3}{2},\frac{5.7}{2})[/tex]

[tex]M(1.5,2.85)[/tex]

Answer:

The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.

Step-by-step explanation:

Let the amount of Strawberry juice in ounces be 'j'

Let the amount of water in ounce be 'w'

Given:

For each ounce of strawberry juice she uses three times as many ounces of water.

It means that amount of water in ounce is 3 times of amount of strawberry juice in ounce.

framing the equation we get;

[tex]w=3j[/tex]

Now we need how many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water.

We know that Total Strawberry infused water is equal to sum of amount of Strawberry juice in ounces and the amount of water in ounces

Framing in equation form we get;

[tex]j+w=64[/tex]

But we know [tex]w=3j[/tex]

hence,

[tex]j+3j= 64\\\\4j=64\\\\j=\frac{64}{4} = 16 \ ounces[/tex]

Hence amount of Strawberry juice = 16 ounces

Amount of water = [tex]3j = 3\times16 =48 \ ounces[/tex]

Hence The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.

Answer:

The Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

Step-by-step explanation:

Given:

Number of skaters = 30

Area for each skater = 40 sq ft

We need to find the dimension of rectangular ring the are going to build.

Now we know that they building the skating ring such that they all can use at same time.

Hence if the all use at same time then we will find the total area first.

Total area can be calculated by multiplying Number of skaters with area required for each skaters.

Framing the equation we get;

Total area = [tex]30\times 40 = 1200 \ ft^2[/tex]

Hence The total area of the rectangular ring would be 1200 sq. ft.

Now we know that Total area is equal to product of length and width.

[tex]length\times width =1200ft^2[/tex]

1200 can be written as = 20 × 60, 25 × 48, 30 × 40,60 × 20,48 × 25,40 × 30

Hence the Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

Answer:

The y intercept of the equation is 10.

Answer:

  28 in²

Step-by-step explanation:

Without constraining the problem unduly, we can make the assumption that AB = 2 inches. Then the altitude from AB to D is h in ...

  Area ABD = (1/2)(AB)h

  16 in² = (1/2)(2 in)(h)

  16 in = h . . . . . . . . . . . divide by 1 in

__

The altitude D to AB is the sum of the heights from D to EC (h1) and from AB to EC (h2). That is ...

  16 = h1 + h2

We also know that the height from FG to EC is 1/2 the height from D to EC, hence (1/2)h1. Likewise, the height to midsegment HI from either EC or AB is half the height from EC to AB, hence (1/2)h2. This means the total height of the quadrilateral HFGI is (1/2)h1 + (1/2)h2 = (1/2)(h1 +h2) = 8.

__

We are given that FG is 50% longer than AB, so its length will be ...

  FG = AB×(1 + .5) = (2 in)(1.5) = 3 in

Since FG is the mid-segment of triangle CDE, base EC is twice its length, or ...

  EC = 2×FG = 2(3 in) = 6 in

__

Mid-segment HI is the average of the base lengths of trapezoid ABCE, so is ...

  HI = (EC +AB)/2 = (6 + 2)/2 = 4

__

Now, we know the height and base lengths of trapezoid HFGI, so we can find its area as ...

  A = (1/2)(b1 +b2)h = (1/2)(3 in + 4 in)(8 in) = 28 in²

The area of quadrilateral HFGI is 28 square inches.

_____

You can make any assumption you like about the dimension of AB, and the rest of the dimensions scale accordingly. The result is still the same.

Answer: interest at the end of 3 years is $495.72

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 3 years

P = $3,672

R = 4.5%

Therefore

I = (3672 × 4.5 × 3)/100

I = 49572/100

I = 495.72

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as [tex](-1)^{k+1}(\frac{1}{2^{k}})[/tex].

where k is from 1 to 10.

By the given expression sequence will be [tex]\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......[/tex]

In this sequence first term "a" = [tex]\frac{1}{2}[/tex]

and common ratio in each successive term to the previous term is 'r' = [tex]\frac{\frac{(-1)}{4}}{\frac{1}{2} }[/tex]

r = [tex]-\frac{1}{2}[/tex]

Since the sequence is infinite and the formula to calculate the sum is represented by

[tex]S=\frac{a}{1-r}[/tex] [Here r is less than 1]

[tex]S=\frac{\frac{1}{2} }{1+\frac{1}{2}}[/tex]

[tex]S=\frac{\frac{1}{2}}{\frac{3}{2} }[/tex]

S = [tex]\frac{1}{3}[/tex]

Now we are sure that the sum of infinite terms is [tex]\frac{1}{3}[/tex].

Therefore, sum of 10 terms will not exceed [tex]\frac{1}{3}[/tex]

Now sum of first two terms = [tex]\frac{1}{2}-\frac{1}{4}=\frac{1}{4}[/tex]

Now we are sure that sum of first 10 terms lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{3}[/tex]

Since [tex]\frac{1}{2}>\frac{1}{3}[/tex]

Therefore, Sum of first 10 terms will lie between [tex]\frac{1}{4}[/tex] and [tex]\frac{1}{2}[/tex].

Option D will be the answer.

Answer:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

Step-by-step explanation:

We presume you're starting with ...

  y = ax^2 +bx +c

As you would with numbers, factor the first two terms:

  y = a(x^2 +b/a·x) +c

Add half the square of the x term inside and its opposite outside parentheses:

  y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2

  y = a(x +b/(2a))^2 +c -b^2/(4a)

You can combine the last two terms to a more familiar fraction:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

To write a quadratic function in vertex form, use the values of a, b, and c. Find the coordinates of the vertex using h = -b/2a and k = f(h).

Substitute the values into the vertex form.

To write a quadratic function in vertex form, you can use the values of a, b, and c.

The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k,

where (h, k) represents the coordinates of the vertex.

To find h and k, you can use the formulas h = -b/2a and k = f(h).

Once you have the values of h and k, you can substitute them into the vertex form to obtain the quadratic function in vertex form.

Learn more about quadratic function in vertex form here:

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Answer:

If the question is single answer correct then the answer is [tex]\frac{1}{3}[/tex] and if it's multiple options correct than the answer is [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

There is a little ambiguity in the question, that whether one answer is correct or multiple options are correct, but let;s deal with both the cases.

Probability = [tex]\frac{TotalNo.OfFavourableOutcomes}{TotalOfNoOfOutcomes}[/tex]

Probability when one option is right=[tex]\frac{1}{3}[/tex]

If this is a question , where multiple options are right then the total no. of cases for it will be = TTT, TFF, FTF, FFT, TTF, TFT, FTT  (FFF is not a valid case, because the question has to have at least one valid answer.)

Probability when more than one option can be right=[tex]\frac{1}{7}[/tex]

Answer:

76

Step-by-step explanation:

Answer:

The 8th term of geometric sequence is -8748

ie., [tex]a_{8}=-8748[/tex]

Step-by-step explanation:

Given geometric sequence is 4,-12,36,...

Geometric sequence can be written as

[tex]a_{1},a_{2},a_{3},..,[/tex]

[tex]a_{1}=4=a[/tex]

[tex]a_{2}=-12=ar[/tex]

[tex]a_{3}=36=ar^2[/tex]

and so on.

common ratio is [tex]r=\frac{a_{2}}{a_{1}}[/tex]

[tex]r=\frac{-12}{4}[/tex]

[tex]r=-3[/tex]

[tex]r=\frac{a_{3}}{a_{2}}[/tex]

[tex]r=\frac{36}{-12}[/tex]

[tex]r=-3[/tex]

Therefore [tex]r=-3[/tex]

Geometric sequence of nth term is [tex]a_{n}=ar^{n-1}[/tex]

To find the 8th term:

[tex]a_{8}=ar^{8-1}[/tex]

[tex]a_{8}=ar^{7}[/tex]

here a=4 and r=-3

[tex]a_{8}=ar^{7}[/tex]

[tex]=4\times (-3)^7[/tex]

[tex]=4\times (-2187) [/tex]

[tex]=-8748[/tex]

[tex]a_{8}=-8748[/tex]

Therefore the 8th term of geometric sequence is -8748

Answer:

1/12,000

Step-by-step explanation:

Data provided in the question:

Size of a population of mustard plants = 6,000

Now,

According to genetic drift theory

The probability that a newly-arisen mutation will become fixed is given using the formula

⇒ 1 ÷ [ 2 × Size of a population of mustard plants ]

⇒ 1 ÷ [ 2 ×6,000 ]

⇒ [ 1 ÷ 12,000 ]

Hence,

probability that a newly-arisen mutation will become fixed in this population is 1/12,000

Answer:

[tex]1217+(4.1\times 10^3)=5.317\times 10^3[/tex]

Step-by-step explanation:

Given : Expression [tex]1217+(4.1\times 10^3)[/tex]

To find : After converting the following numbers into scientific notation, solve the problem ?

Solution :

Expression [tex]1217+(4.1\times 10^3)[/tex]

Re-write 1217 by multiplying and divide by 1000 to convert into decimal,

[tex]=\frac{1217\times 1000}{1000}+(4.1\times 10^3)[/tex]

[tex]=1.217\times 10^3+(4.1\times 10^3)[/tex]

[tex]=(1.217+4.1)\times 10^3[/tex]

[tex]=5.317\times 10^3[/tex]

Therefore, in scientific notation [tex]1217+(4.1\times 10^3)=5.317\times 10^3[/tex]

Answer:

The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].

Step-by-step explanation:

Let 's' represents the number of guest small tier can serve.

Let 'm' represents the number of guest medium tier can serve.

Now Given:

For First cake:

Number of small tiers = 3

Number of medium tier = 1

Total serving guest = 100

Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.

Framing in equation form we get;

[tex]3s+m=100[/tex]

For Second cake:

Number of small tiers = 3

Number of medium tier = 2

Total serving guest = 140

Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.

Framing in equation form we get;

[tex]3s+2m=140[/tex]

Hence The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].

Answer: it will need 40 cups of lemonade to break even

Step-by-step explanation:

Break even represents the point at which there is neither profit nor loss.

It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. Assuming that she made x cups of lemonade, the total cost of making x cups would be

30 + 0.5x

She sells each cup of the lemonade for $1.25 . Assuming that she sold x cups of lemonade, therefore, the total amount would be 1.25×x = 1.25x

To break even,

30 + 0.5x = 1.25x

1.25x - 0.5x = 30

0.75x = 30

x = 30/0.75

x = 40

Answer:

The Total of Charlie's will be $7.16.

Step-by-step explanation:

Given:

Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.

Price of regular ticket = $9.00.

tax = 6%.

We need to find Charlie’s total.

So we will first find the price of regular ticket with 25% off.

25% percent of regular ticket  = [tex]\frac{25}{100}\times 9 = \$2.25[/tex]

Discounted Price of regular ticket will be equal to Price of regular ticket minus Discounted amount.

Discounted Price of regular ticket = 9 - 2.25 = $6.75

Now, including tax :

Tax paid will be on discounted amount.

Hence Amount paid in tax = [tex]6\% \times 6.75= \frac{6}{100}\times 6.75 = \$0.405[/tex]

Total amount paid by charlie is equal to sum of Discounted Price of regular ticket and Amount paid in tax

Total Amount paid by charlie = [tex]6.75+0.405 =\$7.155 \approx \$7.16[/tex]

Therefore, the total of Charlie's will be $7.16.