A spinner has three sections which are coloured red, green and blue. Chris spun the spinner 100 times in total. The frequency of spins that landed on green was 35. The ratio of the frequency of red to the frequency of green was 4:7. What is the estimated probability of the spinner landing on blue? Give your answer as a decimal.​

Answer:

\(x = \frac{10}{\tan(52^o)}\)

Step-by-step explanation:

Given

See attachment for illustration

Required

Equation to find x

The relationship between angle \(52^o\) and side lengths x and 10 inches is by tangent formula which is given by:

\(\tan(\theta) = \frac{Opposite}{Adjacent}\)

So, we have:

\(\tan(52^o) = \frac{10}{x}\)

Make x the subject

\(x = \frac{10}{\tan(52^o)}\)

Answer:

1000

Step-by-step explanation!

The formula for the amount accrued [ƒ(x)] on an investment earning compound interest is f(t) = P(1 + r)^t where:

P = the amount of money invested (the principal)

r = the interest rate per payment period expressed as a decimal fraction

t = the number of periods

Your formula is

f(x) = 1000(1 + 0.05)^x

In comparison, we can see that the term that represents the amount of money originally invested is 1000.

Answer:

(A) 1,000

Step-by-step explanation:

i just took the test

The area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

Double integration is an important tool in calculus that allow us to calculate the area of irregular shapes in the Cartesian coordinate system. In particular, they are useful when we are dealing with shapes that are defined in polar coordinates.

To find the area inside this curve, we can use a double integral in polar coordinates. The general form of a double integral over a region R in the xy-plane is given by:

∬R f(x,y) dA

where dA represents the infinitesimal area element, and f(x,y) is the function that we want to integrate over the region R.

In polar coordinates, we can express dA as r dr dθ, where r is the distance from the origin to a point in the region R, and θ is the angle that this point makes with the positive x-axis. Using this expression, we can write the double integral in polar coordinates as:

∬R f(x,y) dA = ∫θ₁θ₂ ∫r₁r₂ f(r,θ) r dr dθ

where r₁ and r₂ are the minimum and maximum values of r over the region R, and θ₁ and θ₂ are the minimum and maximum values of θ.

To find the area inside the curve r = 3 + sin(θ), we can set f(r,θ) = 1, since we are interested in calculating the area and not some other function. The limits of integration can be determined by finding the values of r and θ that define the region enclosed by the curve.

To do this, we first note that the curve r = 3 + sin(θ) represents a cardioid, which is a type of curve that is symmetric about the x-axis. Therefore, we only need to consider the region in the first quadrant, where 0 ≤ θ ≤ π/2.

To find the limits of integration for r, we note that the curve intersects the x-axis when r = 0. Therefore, the minimum value of r is 0. The maximum value of r can be found by setting θ = π/2 and solving for r:

r = 3 + sin(π/2) = 4

Therefore, the limits of integration for r are r₁ = 0 and r₂ = 4.

The limits of integration for θ are simply θ₁ = 0 and θ₂ = π/2, since we are only considering the region in the first quadrant.

Putting it all together, we have:

Area = ∬R 1 dA

        = ∫\(0^{\pi /2}\) ∫0⁴ 1 r dr dθ

Evaluating this integral gives us:

Area = π(3² - 2²)/2 = (5π)/2

Therefore, the area inside the curve r = 3 + sin(θ) is (5π)/2 square units.

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Using double integrals, the area inside the curve r = 3 + sin(θ) is 0 units².

For the area inside the curve r = 3 + sin(θ), we can use a double integral in polar coordinates. The area can be expressed as:

A = ∬R r dr dθ

where R represents the region enclosed by the curve.

In this case, the curve r = 3 + sin(θ) represents a cardioid shape. To determine the limits of integration for r and θ, we need to find the bounds where the curve intersects.

To find the bounds for θ, we set the expression inside sin(θ) equal to zero:

3 + sin(θ) = 0

sin(θ) = -3

However, sin(θ) cannot be less than -1 or greater than 1. Therefore, there are no solutions for θ in this case.

Since there are no intersections, the region R is empty, and the area inside the curve r = 3 + sin(θ) is zero.

Hence, the area inside the curve r = 3 + sin(θ) is 0 units².

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Answer:

I think it might be C or B

Step-by-step explanation:

Hope this helped have a nice day :)

Answer:

I didn't understand the question well is it 1.8meter in 1h24m if so then here is my answer

Step-by-step explanation:

so basically to make things easy for me I convert hours to minutes 4h is 4×60=240minutes 1h24min= 84min right

so if I baby walks 1.8m in a 84min then in a 240min they gonna walk X meter

84min-->1.8m

240min--> X

so 240×1.8÷84=5.14

So a baby will walk 5.14m in 4H

The vertices of the hyperbola are the x-intercepts of the hyperbola

The equation of the hyperbola is \(\frac{y^2}{400} -\frac{x^2}{81} = 1\)

The equation of a hyperbola is represented as:

\(\frac{(y - k)^2}{a^2} -\frac{(x - h)^2}{b^2} = 1\)

The vertices are (20,0) and (-20,0).

So, the center of the hyperbola is:

(h,k) = (0,0).

Also, we have:

a = 20

This gives

\(\frac{(y - 0)^2}{a^2} -\frac{(x - 0)^2}{b^2} = 1\)

Evaluate

\(\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1\)

Substitute 20 for a

\(\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1\)

\(\frac{y^2}{400} -\frac{x^2}{b^2} = 1\)

The length of the conjugate axis is:

l = 18 units

So, we have:

\(b = \frac{18}2 = 9\)

The equation becomes:

\(\frac{y^2}{400} -\frac{x^2}{9^2} = 1\)

\(\frac{y^2}{400} -\frac{x^2}{81} = 1\)

Hence, the equation of the hyperbola is \(\frac{y^2}{400} -\frac{x^2}{81} = 1\)

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It is 35.15. Hope it helps

Answer:

3:6

Step-by-step explanation:

8:24 and 24:72 reduce down to 1:3. 3:6 is 1:2.

Answer:

x9y5+3x2

Step-by-step explanation:

3x2+y4x2x6yx

=3x2+x9y5

Answer:

50 and 150

Step-by-step explanation:

Raheem- (2x+50)

Usman- x

(2x+50)+x=200

3x+50=200

3x=150

x=50

plug in the numbers

Answer:

V = 904.78

Step-by-step explanation:

Volume of a Sphere = 4π\(\frac{r^3}{3}\)

=> V = 4π\(\frac{6^3}{3}\)

=> V = 4π\(\frac{216}{3}\)

=> V = 4π(72)

=> V = 904.78

Hope this helps!

Answer:

\(\dfrac{9}{25}\)

Step-by-step explanation:

Given that the bag contains black and red marbles.

Number of black marbles in the bag = 2

Number of red marbles in the bag = 3

Total number of marbles in the bag = Number of black marbles + Number of red marbles = 2 + 3 = 5

Let us have a look at the formula for probability of an event E, which can be observed as:

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)

\(P(\text{First red marble}) = \dfrac{\text{Number of red marbles}}{\text{Total number of marbles}} = \dfrac{3}{5 }\)

Now, the marble chosen at first is replaced.

Therefore, the count remains the same.

\(P(\text{Second red marble}) = \dfrac{\text{Number of red marbles}}{\text{Total number of marbles}} = \dfrac{3}{5}\)

Now, the required probability can be found as:

\(P(\text{First red marble})\times P(\text{Second red marble}) = \dfrac{3}{5}\times \dfrac{3}{5} = \bold{\dfrac{9}{25} }\)

14/2 = 7

7/2 = 3.5

3.5/2 = 1.75

1.75/2 = 0.875

9514 1404 393

Answer:

  15 meters

Step-by-step explanation:

Zeno's last jump was 2 meters, so another jump half as far adds 1 meter to the 14 m total.

After 4 jumps, Zeno would have jumped 15 meters from his starting place.

__

Comment on the question

The given distances give a total "after 3 jumps." The question asks for a total "after 4 jumps." It is not clear whether that is 4 jumps total, or 4 more jumps. In the above, we have assumed it is 4 jumps total.

\((-1,\infty)\cap (-2,2) ---- > (-1,2)\)

Generally, the equation for the function is mathematically given as

f(x) = -5x + 11 + 10

Therefore

When x >= -1, the function decreases because f(x) = -5(x+1)+10.

This means that the function is dropping throughout this range\((-1,\infty).\)

b)

A look at the graph reveals a decreasing trend in the function over the timeframe (-2,2).

In conclusion, The number line will represent

Using the point where the intervals with decreasing functions overlap

\((-1,\infty)\cap (-2,2) ---- > (-1,2)\)

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Answer:

see photos

Step-by-step explanation:

Plato/Edmentum

For n = 10: -3.8981

For n = 100: -398.4496

For n = 1000: -38886.3254

For n = 10000: -388823.2811.

The given expression in summation notation is:

S(n) = Sum[6k(k-1) / (k+1), {k,1,n}]

We can use the summation formula for k(k-1) and write it as \(k^2 - k\), and the summation formula for 1/(k+1) and write it as ln(k+1). Substituting these in the expression above, we get:

\(S(n) = Sum[6k^2/(k+1) - 6k/(k+1), {k,1,n}]\\ = Sum[6k^2/(k+1), {k,1,n}] - Sum[6k/(k+1), {k,1,n}]\\ = Sum[6k^2/(k+1), {k,1,n}] - Sum[6/(1+1/k), {k,1,n}]\\ = Sum[6k^2/(k+1), {k,1,n}] - 6Sum[1+1/(k+1), {k,1,n}]\\ = Sum[6k^2/(k+1), {k,1,n}] - 6Sum[1, {k,1,n}] - 6Sum[1/(k+1), {k,1,n}]\\ = Sum[6k^2/(k+1), {k,1,n}] - 6n - 6Sum[1/(k+1), {k,1,n}]\\ = Sum[6k^2/(k+1), {k,1,n}] - 6n - 6(ln(n+1) - ln(2))\)

Now, we can use this formula to find the values of S(n) for different values of n.

For n = 10:

\(S(10) = (6\times 1^{2/2} + 6\times 2^{2/3} + ... + 6\times 10^{2/11}) - 6\times 10 - 6(ln(11) - ln(2))= -3.8981\)

For n = 100:

\(S(100) = (6\times 1^{2/2 }+ 6\times 2^{2/3} + ... + 6\times 100^{2/101}) - 6\times 100 - 6(ln(101) - ln(2))= -389.4496\)

For n = 1000:

\(S(1000) = (6\times 1^{2/2} + 6\times 2^{2/3 }+ ... + 6\times 1000^{2/1001}) - 6\times 1000 - 6(ln(1001) - ln(2))= -38886.3254\)

For n = 10000:

\(S(10000) = (6\times 1^{2/2} + 6\times 2^{2/3} + ... + 6\times 10000^2/10001) - 6\times 10000 - 6(ln(10001) - ln(2))= -388823.2811\)

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Answer:

-6.05+(-3.611)=-9.661

Step-by-step explanation:

If the machinist makes 500 of these parts, the cost of the steel is 1170 dirham ( rounds to the nearest dirham).

We have, A machinist creates a solid steel part for a wind turbine engine. Let us consider volume, mass and density of steel part be "V", "M", "D" respectively.

Density of a material is defined as mass of material per unit volume of material,

D = M/V .

Volume of steel part, V = 1015 cm³

The cost of steel part = 29 fils per kg

Density of steel part, D = 7. 95 g/cm³

Number of steel part used by machinist

= 500

So, Denssity = Mass of steel part/ Volume of steel part

=> 7. 95 g/cm³ = M/1015 cm³

=> M = 7.95× 1015 g

=> M = 8,069.25 g

Now, Convert the mass of steel part from grams to kilograms using conversion units.

Mass of steel part, M = 8,069.25/1000 g

=> M = 8.07 kg

So, cost of one steel part = 29 fils/kg × 8.07 kg = 234.008 ~ 234 fils

If the machinist makes 500 of these parts, the cost of the steel = 500× 234

= 117,000 fils.

But we wants the cost of steel in dirham so we have to convert the fils units into dirham units,

One dirham is divided into 100 fils.

So, 117,000 fils = 117,000/100 dirham

= 1170 dirham.

Thus, required cost of steel is 1170 dirham.

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Answer:

The number is 270

Step-by-step explanation:

Let the number be 'x'

3/5 of x = 162

\(\frac{3}{5}*x = 162\\\\x=162*\frac{5}{3}\\\\x=54 * 5\\\\x = 270\)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{270}}}}}\)

Step-by-step explanation:

Let the number be 'x'

\( \sf{ \frac{3}{5 } \: \: of \: x \: = 162}\)

⇒\( \sf{ \frac{3x}{5} = 162}\)

Apply cross product property

⇒\( \sf{3x = 162 \times 5}\)

Multiply the numbers

⇒\( \sf{3x = 810}\)

Divide both sides of the equation by 3

⇒\( \sf{ \frac{3x}{3} = \frac{810}{3} }\)

Calculate

⇒\( \sf{x = 270}\)

Hope I helped!

Best regards!!

Step-by-step explanation:

Given:

To find:

Solution:

(multiplication of digits give a larger number compared to addition, subtraction and division)

= (12 × 7) × (4 + 1)

∴ The biggest number Tony can make is 420.

Answer:

10 small boxes and 12 large boxes

Step-by-step explanation:

Let x = number of large boxes

Let y = number of small boxes

We are told that;

volume of each small box = 6 cubic feet

volume of each large box = 22 cubic feet.

Total volume = 324 ft³

Thus;

6x + 22y = 324 - - - (eq 1)

We are told that 22 boxes of paper were shipped.

Thus; x + y = 22 - - - (eq 2)

Making x the subject in eq 2 gives;

x = 22 - y

Put 22 - y for x in eq 1;

6(22 - y) + 22y = 324

132 - 6y + 22y = 324

16y = 324 - 132

16y = 192

y = 192/16

y = 12

So, x = 22 - 12 = 10

Answer:

138.....................

Answer:

888

Step-by-step explanation:

C equals 5 so u do 6 times 5. Then you have to do that by the exponent of 2 which equals 900. Because d equals 4 u do 5 times 4 which equals 20. So 900 minus 20 equals 880 plus 8 equals 888

ANSWER

C. 12

EXPLANATION

1/3 of the pizzas is:

Therefore, 6 pizzas were cheese and the rest were pepperoni:

There were 12 pepperoni pizzas.

An equation that relates T to N can be written as T = 750 + 560N.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).

Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:

T = A + B

Substituting the given parameters into the formula, we have;

T = (750 + 165N) + 395N

T = 750 + 165N + 395N

T = 750 + 560N.

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Complete Question:

Ann and her husband are each starting a saving plan. Ann will initially set aside $750 and then add $165 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+165N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $395 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=395N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.

Simplify your answer as much as possible.

The contour plot shows that the probability that θ > 0.5 increases as θ0 increases and n0 increases. This means that if we believe that θ is close to 0.5, and we have a lot of data, then we are more likely to believe that θ is actually greater than 0.5.

The contour plot is a graphical representation of the probability that θ > 0.5, as a function of θ0 and n0. The darker the shading, the higher the probability. The plot shows that the probability increases as θ0 increases and n0 increases. This is because a higher value of θ0 means that we believe that θ is more likely to be close to 0.5, and a higher value of n0 means that we have more data, which makes it more likely that θ is actually greater than 0.5.

The plot can be used to explain to someone whether or not they should believe that θ > 0.5, based on the data that ∑i=1100Yi=57. If we believe that θ is close to 0.5, and we have a lot of data, then we should be more likely to believe that θ is actually greater than 0.5. However, if we believe that θ is far from 0.5, or if we don't have much data, then we should be less likely to believe that θ is actually greater than 0.5.

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Answer:

We conclude that when we put x = 11, it does not satisfy the inequality.

Hence, option (A) is correct.

Step-by-step explanation:

Given the inequality

x - 7 > 12

Any value which makes the inequality FALSE would be the value that not satisfy the inequality.

Putting x = 11 in the inequality

x - 7 > 12

11 - 7 > 12

4 > 12

FALSE!

Reason: 4 can not be greater than 12

Putting x = 33 in the inequality

x - 7 > 12

33 - 7  > 12

26 > 12

TRUE!

Reason: 26 is indeed greater than 12

Putting x = 22 in the inequality

x - 7 > 12

22 - 7 > 12

15 > 12

TRUE!

Reason: 15 is indeed greater than 12

Putting x = 44 in the inequality

x - 7 > 12

44 - 7 > 12

37 > 12

TRUE!

Reason: 37 is indeed greater than 12

Therefore, we conclude that when we put x = 11, it does not satisfy the inequality.

Hence, option (A) is correct.

Answer:

11

Step-by-step explanation:

The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Answer: ) (2a+7)(3b- 4)

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation: