A fish bowl contains blue, green and red plastic fish. When a fish is picked out at random, the probability of it being blue is 0.7 and the probability of it being green is 0.2. A prize is given if a red fish is picked out. What is the probability of Matt picking a red fish? (Give your answer as a decimal.) There are 60 fish in the fish bowl. How many of the fish are red?

Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

2500

Step-by-step explanation:

The perimeter is given by the formula :

P = 4L  (L is length)

We rearrange the equation to get L as the subject:

L = P÷4

L = 200÷4

L = 50

The area of a square is given by the formula :

A = L²

A = 50²

A = 2500

Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.

1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.

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Answer:

Value of slope is -2 and y-intercept is 1

Step-by-step explanation:

We can see that the values in the table have a linear relationship.

A linear function is a straight line written as:

y = mx+b

Here,

m is the slope and b is the y-intercept

The slope is calculated by:

\(m = \frac{y_2-y_1}{x_2-x_1}\)

We can take any two consecutive pairs in the table to calculate the slope.

Taking first two input-output pairs.

(x1,y1) = (-3, 7)

(x2,y2) = (-2, 5)

Putting the values

\(m = \frac{5-7}{-2+3}\\m= -2\)

Putting the value of m in the general form

\(y = -2x+b\)

To find the value of b, we will put any pair of input-output (x,y) in the equation

Putting the first pair

\(7 = -2(-3) +b\\7 = 6 + b\\b = 7-6\\b = 1\)

Hence,

Value of slope is -2 and y-intercept is 1

Answer:

x/3 -3= 18 (add three to both sides)

x/3= 21

x/3(*3) =21(*3) (multiply by 3 on each side to cancel out the division)

x= 63

63/3-3=18

21-3=18

18= 18 (checking answers)

Step-by-step explanation:

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

It comes out to around 127

Step-by-step explanation:

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Answer:

3 years: $27691.30

7 years: $23359.70

Step-by-step explanation:

3.5% of 30,940 = 1082.9

for each year there is interest, we multiply it by that amount of years.

equation: 1082.9x

3 years: 3248.7  

7 years: 7580.3

since interest is subtracted, we will subtract the multiplied interests from above.

equation: 30940 - 1082.9x = answer

3 years: $27691.3

7 years: $23359.7

Answer:

Step-by-step explanation:

The possible dimensions of the cereal box to ensure that it has a volume of 4, 000 cm ³ are :

To find the possible dimensions that would give a volume of 4000 cm^3 for the cereal box, we can use the formula for the volume of a rectangular prism:

= Length x width x height

Since we know that the volume of the cereal box is 4000 cm^3, we can set up an equation:

4, 000 = l x w x h

We can try out different combinations of dimensions. For example, we could have:

l = 20 cm, w = 10 cm, h = 20 cm

l = 16 cm, w = 25 cm, h = 10 cm

l = 40 cm, w = 5 cm, h = 20 cm

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Answer:

3rd option

Step-by-step explanation:

One of our exponent rules tells us that \((\frac{x}{y} )^{z}\) =  \(\frac{x^{z} }{y^{z} }\). So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?

We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.

Let me know if you have any questions!

a) For two distinct real roots: x > 0 or x > m

b) For two distinct real roots: x > 0 or x > 2m

c) For two distinct real roots: x > 0 or x > 4

This is based on the quadratic equation.

Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.

a) Quadratic equation: x² - 4x + m = 0

The discriminant: Δ = b² - 4ac

Δ = (2x)² - 4.x.(m)

Δ = 4x² - 4mx

Δ = 4x (x - m)

For two distinct real roots: Δ > 0

4x (x - m) > 0

x > 0 or x > m

For two real roots: Δ ≥ 0

4x (x - m) ≥ 0

x ≥ 0 or x ≥ m

For a repeated root: Δ = 0

4x (x - m) = 0

x = 0 or x = m

(b) Quadratic equation: mx² + 3x + 2 = 0

The discriminant: Δ = b² - 4ac

Δ = (3x)² - 4.mx.(2)

Δ = 4x² - 8mx

Δ = 4x (x - 2m)

For two distinct real roots: Δ > 0

4x (x - 2m) > 0

x > 0 or x > 2m

For two real roots: Δ ≥ 0

4x (x - 2m) ≥ 0

x ≥ 0 or x ≥ 2m

For a repeated root: Δ = 0

4x (x - 2m) = 0

x = 0 or x = 2m

(c) Quadratic equation: x² - mx + 1 = 0

The discriminant: Δ = b² - 4ac

Δ = (x)² - 4.x.(1)

Δ = x² - 4x

Δ = x (x - 4)

For two distinct real roots: Δ > 0

x (x - 4) > 0

x > 0 or x > 4

For two real roots: Δ ≥ 0

x (x - 4) ≥ 0

x ≥ 0 or x ≥ 4

For a repeated root: Δ = 0

x (x - 4) = 0

x = 0 or x = 4

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Answer:

1/2 of an answer is zero answer.

Step-by-step explanation:

1/2 of an answer is zero answer.

ANSWER

EXPLANATION

A standard deck of 52 cards has 4 suits which are; heart, club, spades and diamonds.

Each suit comprise equal number of cards which is 13

Hence, the number of club in the cards is 13.

Therefore, the probability of being dealt a club is;

By fraction method, 55/16 pounds of rice Belle purchased.

In math, what is a fraction?

Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                 Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

  = 2 3/4 * 5/4

   = 5/4 * 2 + 5/4 *  3/4

   = 5/2 + 5/4 * 3/4

  = 5/2 + 15/ 4 * 4

  = 5/2 + 15/16

  common denominator and write the numerators above common denominator   =   5 *8/16 + 15/16

         = 40/16 + 15/16

         = 40 + 15/16

          = 55/16

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Answer:

2

Step-by-step explanation:

Answer:=2

Step-by-step explanation:

20x.1=2

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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The distribution of the sample mean for all possible simple random samples of size 15 from the population of net worth in the US will be approximately normal, with a mean of μ and a standard deviation of σ/√15.

Courtney's estimate of the net worth of all people in the US is strongly skewed to the right. This means that the majority of the population has a net worth that is lower than the average net worth. When Courtney selects an SRS of size n = 15 from this population and calculates the sample mean, the shape of the distribution of the sample mean for all possible simple random samples of size 15 from this population will be approximately normal.

The Central Limit Theorem states that if a population has a mean of μ and a standard deviation of σ, then the sampling distribution of the sample mean will be approximately normal, no matter what the shape of the population distribution is, as long as the sample size is large enough. Since Courtney's sample size of 15 is large enough, the sampling distribution of the sample mean will be approximately normal.

The sample mean will have a mean of μ, which is the population mean, and a standard deviation of σ/√n, where n is the sample size. Since Courtney's sample size is 15, the standard deviation of the sample mean will be σ/√15. This means that the sample mean will be normally distributed with a mean of μ and a standard deviation of σ/√15.

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Answer:

7.5 days

Step-by-step explanation:

7.5 days because it is 30 percent off then the the sale decreases 20 percent making it 10% off and if the price is 75 you'd have to divide it by 10 and you would get 7.5 days

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

do you have a pic

Step-by-step explanation:

Step-by-step explanation:

To find the value of x for which f(x) = g(x), we can equate the two functions:

f(x) = g(x)

x^2 - 1 = 3x

Bringing all the terms to one side, we get:

x^2 - 3x - 1 = 0

Using the quadratic formula, we can solve for x:

x = [ -(-3) ± sqrt((-3)^2 - 4(1)(-1))] / 2(1)

Simplifying the expression:

x = [3 ± sqrt(13)] / 2

Therefore, the values of x for which f(x) = g(x) are (3 + sqrt(13))/2 and (3 - sqrt(13))/2.

Answer:

.26 * 2900= 754 dollars

Step-by-step explanation:

I'm not sure if it's right.

Answer:

y=9

Step-by-step explanation:

Answer:

A.  $762.94

B.  $896.81

C.  $133.87

Step-by-step explanation:

Given function modelling Lisa's saving account:

\(\boxed{f(x)=250(1.25)^x}\)

where x is the number of years.

Given table modelling Xavier's savings account:

\(\begin{array}{|c|c|c|c|c|}\cline{1-5} x & 0 & 1 & 2 & 3\\\cline{1-5} g(x) & 200 & 270 & 364.5 & 492.08\\\cline{1-5}\end{array}\)

To find the amount in Lisa's savings account after 5 years, substitute x=5 into the function:

\(\begin{aligned}\implies f(5)&=250(1.25)^5\\&=250(3.051757...)\\&=762.939453...\end{aligned}\)

Therefore, the amount in Lisa's savings account after 5 years is $762.94 (nearest cent).

First, create an exponential function to model Xavier's savings account.

General form of an exponential function:

\(y=ab^x\)

where:

From inspection of the given table, the initial value (a) is 200.

\(\implies g(x)=200b^x\)

To find the value of b, substitute point (1, 270) into the function:

\(\begin{aligned}\implies g(1)=200b&=270\\b&=\dfrac{270}{200}\\b&=1.35\end{aligned}\)

Therefore. the function that models Xavier's savings account is:

\(\boxed{g(x)=200(1.35)^x}\)

To find the amount in Xavier's savings account after 5 years, substitute x=5 into the found function:

\(\begin{aligned}\implies g(5)&=200(1.35)^5\\&=200(4.4840334...)\\&=896.806687...\end{aligned}\)

Therefore, the amount in Xavier's savings account after 5 years is $896.81 (nearest cent).

To find the positive difference in their accounts after 5 years, subtract Lisa's balance from Xavier's balance:

\(\implies 896.81-762.94 =133.87\)

The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

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This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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Answer:

Step-by-step explanation:

2:3:4= 9

2/9 x 180= 40 degrees

3/9 x 180= 60 degrees

4/9 x 180= 80 degrees

~~~Inuola1234

Because both of the components of the point are negative, we conclude that it is on the third quadrant.

For a point with coordinates (x, y) we have the following rule:

In this case, we have the point (−9.73, −3.32), where both components are negative, then we can conclude that it must be on the third quadrant.

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Answer:

12km/h

Step-by-step explanation:

10*6=60min=1hr

2*6=12km