A bag contains 2 red marbles, and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Give the answer as a fraction in simplest form.

To find the width of the rectangle, we need to use the formula for the perimeter of a rectangle, which is:

Perimeter = 2(length + width)

We can set this equal to the given expression for the perimeter:

14x^3 + 12x^2 - 10x + 10 = 2[(x^4 - x^3 + x^2 - x + 1) + width]

Simplifying the right-hand side, we get:

14x^3 + 12x^2 - 10x + 10 = 2x^4 - 2x^3 + 2x^2 + (-2x + 2) + 2width

Combining like terms, we have:

2width = 2x^4 - 2x^3 + 16x^2 - 8x + 8

Dividing both sides by 2, we get:

width = x^4 - x^3 + 8x^2 - 4x + 4

Therefore, the width of the rectangle is x^4 - x^3 + 8x^2 - 4x + 4.

The formula for finding the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width of the rectangle.

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Answer:

ROTATION

Step-by-step explanation:

Answer:

2x=10

divide by 2

x=5

1-2x

1-2(5)

1-10

answer is -9

Answer:

-9

Step-by-step explanation:

First solve the equation, 2x=10 to get the value of x

2x = 10

x = 10÷ 2

x= 5

now, put this value of x in the expression 1-2x

1 - 2x

= 1- 2(5)

= 1- 10

= -9

Answer:

3

Step-by-step explanation:

Answer:

  155 miles

Step-by-step explanation:

The sum of n terms of an arithmetic series is given by the formula ...

  Sn = (2·a1 +d(n -1))(n/2)

__

The number of miles Ryan ran in July is described by the arithmetic series ...

  0.5 +0.8 +1.1 +... (a total of 31 terms)

The first term is a1=0.5, and the common difference is d=0.3.

The total number of miles Ryan ran in July is ...

  S31 = (2(0.5) +0.3(31 -1))(31/2) = (1 +9)(31/2) = 155

Ryan ran 155 miles in July.

The probability of drawing at least 7 hearts is 0.0567.

A card is randomly drawn from a deck of cards.

Total number of cards in a deck = 52

The number of times the process is repeated, n = 15

Number of hearts in a deck = 13

The probability of getting a spade is:

p = 13/52 = 1/4

The formula for probability is given as:

P( E ) = favorable cases / total number of cases

The probability of getting no heart is:

q = 1 - p = 1 - 1/4 = 3/4

Using the binomial theorem of probability,

P( X = x ) = \(_{n}C_{r} \times p^{r} \times q^{n-r}\)

So, the probability of drawing at least 7 hearts will be:

P = P( 7 ) + P( 8 ) + .....P( 15 )

Now,

P( 7 ) = 15!/( 15 - 7 )! × (0.25)⁷ × (0.75)⁶ =  0.03932

P(8) = 15!/(15 - 8)! × (0.25)⁸ × (0.75)⁷ = 0.0131

P(9) = 15!/(15 - 9)! × (0.25)⁹ × (0.75)⁶ = 0.003398

P(10) = 15!/(15 - 10)! × (0.25)¹⁰ × (0.75)⁵ = 0.00068

P(11) = 15!/(15 - 11)! × (0.25)¹¹ × (0.75)⁴ = 0.000103

P(12) = 15!/(15 - 12)! × (0.25)¹² × (0.75)³ = 0.000102

P(13) = 15!/(15 - 13)! × (0.25)¹³ × (0.75)² = 8.80099833e-7

P(14) = 15!/(15 - 14)! × (0.25)¹⁴ × (0.75)¹ = 4.19095159e-8

P(15) = 15!/(15 - 15)! × (0.25)¹⁵ × (0.75)⁰ = 9.3132257e-10

So, the probability is:

P = P( 7 ) + P( 8 ) +......P( 15 )

P = 9.3132257e-10 + 4.19095159e-8 + 8.80099833e-7 + 0.000102 + 0.000103 + 0.00068 + 0.003398 +  0.0131 + 0.03932

P = 0.0567

Therefore, the probability of drawing at least 7 hearts is 0.0567

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The coterminal angle of -15x is given by -15x + 2πn, where n is an integer. The solution is as follows:

To find the coterminal angle of -15x, we need to add or subtract multiples of 2π until we reach an angle that is greater than or equal to 0 and less than 2π.

The coterminal angle can be found by adding or subtracting multiples of 2π to -15x.

To simplify the expression further, we need to consider the properties of the tangent function.

We know that tan(π + θ) = tan(θ) and tan(2π + θ) = tan(θ), where θ is any angle.

Therefore, the coterminal angle can be expressed as:

-15x + 2πn, where n is an integer.

Hence, the coterminal angle of -15x is given by -15x + 2πn, where n is an integer.

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Answer:

If the family has $800 for sit-down restaurant meals and fast food and they budgeted all of it for fast food, then they can buy $800/$20 = 40 fast food meals.

Step-by-step explanation:

yw;)

Answer:

40

Step-by-step explanation:

No. Of Meal=Budget/price of Meal

=800/ 20

=40

First, we write out the probability formula:

Total number of tickets = 13

Pr(both Ashley and Matt win) = Pr(Ashley wins) x Pr(Matt wins)

The final answer is 1/169

In order to express our answer as a percentage, we multiply by a 100%

= 1/169 x 100% = 0.592% ( to 3 significant figures)

Answer:

18

Step-by-step explanation:

3*6=18

a. To write a system of equations, let's assign variables to the unknowns. Let's use m for the cost of one mango and k for the cost of one kiwi.

For the first basket, the cost is $9.00, and it contains 2 mangos and 3 kiwis. So, the equation can be written as:

2m + 3k = 9

For the second basket, the cost is $14.25, and it contains 5 mangos and 2 kiwis. So, the equation can be written as:

5m + 2k = 14.25

b. Writing the system of equations as a matrix, we have:

[[2, 3], [5, 2]] * [m, k] = [9, 14.25]

c. To find the identity and inverse matrices for the coefficient matrix [[2, 3], [5, 2]], we perform row operations until we reach the identity matrix [[1, 0], [0, 1]]. The inverse matrix is [[-0.1538, 0.2308], [0.3846, -0.0769]].

d. Using the inverse matrix, we can solve the system by multiplying both sides of the equation by the inverse matrix:

[[2, 3], [5, 2]]^-1 * [[2, 3], [5, 2]] * [m, k] = [[-0.1538, 0.2308], [0.3846, -0.0769]] * [9, 14.25]

After performing the calculations, we find [m, k] = [1.5, 2].

e. The solution [m, k] = [1.5, 2] tells us that each mango costs $1.50 and each kiwi costs $2.00. This means that the cost of the fruit is consistent with the given information, satisfying both the number of fruit in each basket and their respective prices.

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The area of the parallelogram is the product of length and height. Then the area of the parallelogram will be 51 square cm.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.

A parallelogram has a base that is 10.2 centimeters long and a height that measures 5 centimeters.

Then the area of the parallelogram will be

Area = bh

Area = 10.2 x 5

Area = 51 square cm

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The measurement of angle X in ∆WXY is 75.7

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC.

The sum of angle in a triangle is 180°. i.e

X+Y+Z = 180°

W = Y-5

X = Y+21

therefore

Y+21+Y-5+Y = 180

3Y +16 = 180

3Y = 180-16

3Y = 164

Y = 164/3

Y = 54.7°

X = 54.7° + 21

X = 75.7°

therefore the measurement of angle X is 75.7°

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Amber earns more than Svetlana.

The wages of Amber and Svetlana must be contrasted in order to discover who makes more money.

Let's determine each person's earnings:

Amber:

13 necklaces are created per hour.

Each necklace costs £0.58.

Earnings per hour = Number of necklaces made per hour × Cost of each necklace

= 13 × £0.58

= £7.54 (rounded to two decimal places)

Svetlana:

Worked 38 hours; earned £285 for 38 hours.

Let's compare their salaries now:

While Svetlana receives a set payment of £285 for 38 hours of labour, Amber is paid £7.54 per hour.

We must compare their hourly rates to ascertain who makes more money. We'll split each person's profits by the number of hours they each put in:

£7.54 is Amber's hourly wage.

The hourly wage for Svetlana is £285 / 38 = £7.50.

We can tell that Amber makes more money per hour (£7.54) than Svetlana does (£7.50) by comparing the hourly rates.

Hence, Amber makes more money than Svetlana.

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The complete question is =

Amber makes pearls necklaces. She makes at least 13 necklaces per hour. She is paid 58p for each necklace she makes.

Svetlana is a personal assistant. She works 38 hours and is paid £285

Which of Amber or Svetlana has the highest hourly rate of pay?

Answer:

169 cm or 1.69 m

Step-by-step explanation:

the area of the square=length of any side^2

Answer:

Step-by-step explanation:

Precision is defined as the ratio of true positives (TP) to the total predicted positives (TP + FP). In this case, the confusion matrix shows 46 TP and 4 FP, so the precision can be calculated as:

precision = TP / (TP + FP) = 46 / (46 + 4) = 0.92

Rounding to 2 decimal places, the precision ratio is 0.92.

Answer:

420 minutes

Step-by-step explanation:

first I subtracted 30 from 59.4 and got 29.4

then I divided 29.4 by .07 and got 420

so there you go hope it helped

hmm...let me think a little bit

Step-by-step explanation:

hmmm ..... i dont know so sorry

i am very very sory

The null hypothesis is rejected at the significance level of 5%. (Round the t-statistic to the second decimal place.)- t-statistic is 2.5, so the null hypothesis is rejected.

Hypothesis

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population.

It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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Answer:

not sure if the answer requested is 5 or 5.00

The range of c for which the optimal solution does not change is c = 2.

To determine the range of c for which the optimal solution does not change, we need to identify the values of c for which the objective function remains parallel to the original objective function 2x1 + 5x2.

In the original problem, the objective function is Z = 2x1 + 5x2.

If we change the coefficient of x1 to c, the new objective function becomes Z = cx1 + 5x2.

To keep the optimal solution unchanged, we need the direction of the objective function to remain the same. This means that the slope of the new objective function should be the same as the original objective function (2x1 + 5x2).

The slope of the new objective function is equal to the coefficient of x1, which is c. Therefore, for the optimal solution to remain the same, the value of c must be equal to 2.

So, the range of c for which the optimal solution does not change is c = 2.

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Answer:

108 degrees

Step-by-step explanation:

hope that works

Answer:

256/5=51.2

Step-by-step explanation:

Answer:

51 with a remainder of one, or 51.2

Step-by-step explanation:

She has 256 donuts and 5 friends. I assume this is for long division practice, so I will do long division.

5 | 256

Look at the first term. Does 5 go into 2? No. Bring down the next term.

5|256

  25

Does 5 go into 25? Yes! How many times? 5. The first digit of our answer will be 5.

5|256 = 5

  25

Now to get rid of the 25, we multiply the number we took for our answer by the divisor. 5x5 = 25. Subtract this from 25 and bring down the next (and last term).

5|256 = 5

  25

 -25

     06

Does 5 go into 6? Yes. One time. Repeat what we did just now with this term now.

5|256 = 51

  06

   -5

     1

Does 5 go into 1? No, it is smaller. Therefore we have a remainder of one donut.

If we are trying to divide ALL of the donuts equally, we will have to cut up the donut into 5 equal pieces. They would each be 1/5 of the donut, or 0.2.

So adding this, each friend would get 51 donuts, with an extra donut for Mrs Rivas, or each friend would get 51.2/51 and 1/5 donuts.

Answer:

15√15−15√5+15√3−15

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form: 15√15−15√5+15√3−15

Decimal Form: 35.53449264…

The range of values of x which satisifies both of the inequalities is:

(-3, 2)

Here we have two inequalities:

3 + x < 5

8 + x > 5

And we want to see which range of values of x satisfie both of these inequalities.

If we isolate x on both inequalities, we will get:

3 + x < 5

x < 5 - 3

x < 2

And the other one is:

8 + x > 5

x > 5 - 8

x > -3

Then we havethe compound inequality:

x < 2

x > -3

Then the range of values that satisfies both inequalities is (-3, 2)

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Answer:

0.94

Step-by-step explanation:

You just divide 47 by 50 and you get 0.94 bam!

We can use the principle of conservation of energy and the specific heat capacities of water. The correct answer is (b) 344 kg.

We can use the principle of conservation of energy to solve this problem. The heat gained by the cold water will be equal to the heat lost by the hot water when they reach thermal equilibrium.

The heat gained by the cold water can be calculated using the formula:

Q_cold = m_cold * c_cold * ΔT_cold

where:

m_cold is the mass of cold water (125 kg),

c_cold is the specific heat capacity of water (4.18 J/g°C),

and ΔT_cold is the change in temperature (38.0°C - 13.0°C).

The heat lost by the hot water can be calculated using the same formula:

Q_hot = m_hot * c_hot * ΔT_hot

where:

m_hot is the mass of hot water,

c_hot is the specific heat capacity of water,

and ΔT_hot is the change in temperature (38.0°C - 50.0°C).

Since the heat gained by the cold water is equal to the heat lost by the hot water, we can set up the equation:

m_cold * c_cold * ΔT_cold = m_hot * c_hot * ΔT_hot

Simplifying the equation, we can solve for m_hot:

m_hot = (m_cold * c_cold * ΔT_cold) / (c_hot * ΔT_hot)

Substituting the given values into the equation, we find:

m_hot = (125 kg * 4.18 J/g°C * (38.0°C - 13.0°C)) / (4.18 J/g°C * (38.0°C - 50.0°C))

Calculating the expression, we get m_hot ≈ 344 kg. Therefore, the correct answer is (b) 344 kg.

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Answer:

20, 18, 14, and 24 are all not perfect squares

Step-by-step explanation:

Answer:

Step-by-step explanation:

99