5 gummy worms. 4 are red, 1 is blue. Two gummy worms are chosen at random and not replaced. What is probability of two red gummy worms.

Answer: 1

Step-by-step explanation:

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Answer:

20° and 70°

Step-by-step explanation:

complimentary angle sum to 90°

let x be the compliment then the angle is 3x + 10 , so

x + 3x + 10 = 90 , that is

4x + 10 = 90 ( subtract 10 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

3x + 10 = 3(20) + 10 = 60 + 10 = 70

the 2 angle measures are 20° and 70°

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

-4;  -3;   -2;   0;  1;   3;

Step-by-step explanation:

Answer:

Confidence interval variance [21.297 ; 64.493]

Confidence interval standard deviation;

4.615, 8.031

Step-by-step explanation:

Given :

Variance, s² = 34.34

Standard deviation, s = 5.86

Sample size, n = 27

Degree of freedom, df = 27 - 1 = 26

Using the relation for the confidence interval :

[s²(n - 1) / X²α/2, n-1] ; [s²(n - 1) / X²1-α/2, n-1]

From the chi distribition table :

X²α/2, n-1 = 41.923 ; X²1-α/2, n-1 = 13.844

Hence,

[34.34*26 / 41.923] ; [34.34*26 / 13.844]

[21.297 ; 64.493]

The 95% confidence interval for the population variance is :

21.297 < σ² < 64.493

Standard deviation is the square root of variance, hence,

The 95% confidence interval for the population standard deviation is :

4.615 < σ < 8.031

The population variance of 95% confidence interval is \(4.615<\sigma<8.031\) and this can be determined by using the given data.

Given :

First, determine the degree of freedom.

\(df = 27-1=26\)

The determine the confidence interval using the below formula:

\(\left(\dfrac{s^2(n-1)}{X^2_{\alpha/2,(n-1) }}\right);\left(\dfrac{s^2(n-1)}{X^2_{(1-\alpha)/2,(n-1) }}\right)\)

Now, using the chi distribution the above expression becomes:

\(\left(\dfrac{34.34\times 26}{41.923 }}\right);\left(\dfrac{34.34\times 26}{13.844 }}\right)\)

Simplify the above expression.

(21.297 ) ; (64.493)

So, the population variance of 95% confidence interval is:

\(\begin{aligned}\\21.297&<\sigma^2<64.493\\4.615&<\sigma<8.031\\\end{alingned}\)

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Both figures have an area of 4 units squared, so yea, the area is the same.

The area of a square of side length S is equal to S squared, for the square, we can see that:

S = 2 units.

Then the area is:

A = (2 units)² = 4 square units.

For the triangle, we know that the area is equal to:

A = B*H/2

Where B = base, H = height.

We can see that:

B = 2 units.

H = 4 units.

Then:

A = (2 units)*(4 units)/2= 4 square units.

So yea, both have the same area.

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Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

<95141404393>

Answer

25/1 and 43/125

Step-by-step explanation:

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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A bottle of orange juice contains 64 fluid ounces. The percent of bottle of orange juice is water is 75% and there are 48 cups of orange juice are there in bottles.

Percentage:

In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Using this formula

Percentage = Ounces of water/Ounce bottle of orange juice

Where:

Ounces of water = 48 ounces

Ounce bottle of orange juice = 64 ounce

Let plug in the formula

Percentage = 48/64

Percentage = 0.75×100

Percentage = 75%

Therefore,

the percent of bottle of orange juice is water is 75%.

Complete Question:

A bottle of orange juice contains 64 fluid ounces. how many cups of orange juice are in three bottles. What percent of bottle of orange juice is water

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Answer:

the percent of bottle of orange juice is water is 75%.

Step-by-step explanation:

Answer:

I believe that u are right with the answer A: 302 in.²

The t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (df) is 1.753050356.

We have to determine the t-value.

The area in the right tail is 0.10 with 32 degrees of freedom(df).

The t-test is a test that is used as an alternative to the z-test in statistics. If the data are normally distributed but the sample size is small and the population standard deviation is unknown, the t-test is utilized.

A value that appears on the t distribution is the critical t value. The area under the curve and the degrees of freedom can be used to determine the t statistic value.

Using Excel Formula,

The t-value = (=TINV(0.1,15))  

The t-value = 1.753050356

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The solution to the algebraic problem is \(x^{2}\)

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Solution:

(\(x^{3}\) – 1) = (x+2)

On dividing (\(x^{3} - 1\)) by (x+2)

The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.

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Answer:

663/20

Step-by-step explanation:

if you want simplist form its 33 3/20 or decimal its 33.15

Given statement solution is :-

1) Gather your electricity bills from the period before the summer break.

2) Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

3) Research or locate the power consumption information for each appliance.

4) Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

5) After the summer break, collect your electricity bill for the corresponding period.

6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:

Examine your electricity bills of pre-summer break:

Gather your electricity bills from the period before the summer break.

Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.

List the various electrical appliances used in your home:

Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

Find out the power consumption and duration for each device in use:

Research or locate the power consumption information for each appliance.

This information is typically provided on the appliance itself or in the user manual.

Note down the power rating of each device in watts (W) or kilowatts (kW).

Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).

Calculate the estimated electricity consumption and cost:

Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).

Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.

Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.

Sum up the estimated costs for all appliances to get the total estimated electricity bill.

Make an energy reduction plan and determine implementation:

Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

Unplugging devices when not in use.

Determine the feasibility of implementing these energy reduction measures in your home.

Re-examine your electricity bill of post-summer break:

After the summer break, collect your electricity bill for the corresponding period.

Calculate the actual energy consumption and cost using the same method as in step 4.

Compare the actual post-summer break bill with the estimated pre-summer break bill.

Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.

Document your reduction plan and changes in the bill:

Write a report summarizing your findings and observations.

Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.

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Using the mathematical induction, proved that when n is an exact power of 2, T ( n ) = n log n is the solution of the recurrence relation.

Let, n = 2

T(2) = 2 log(2)

= 2(1)

This satisfies the recurrence relation T(n) = 2T(n/2) + n,

so the base case holds.

Assume that the statement is true for all k where k is an exact power of 2 and k <= n.

n = 2m,

where m is an integer.

Using the recurrence relation,

T(2m) = 2T(2m/2) + 2m

T(2m) = 2T(2m-1) + 2m

Substitute the value of T(2m-1)

T(2m) = 2[ T(2(m-1)) + 2(m-1) ] + 2m

T(2m) = 2T(2(m-1)) + 2m + 2m - 2

T(2m) = 2T(2(m-1)) + 2(2m - 1)

Using the induction hypothesis, we can replace T(2(m-1)) with its value

T(2m) = 2[ T(2(m-2)) + 2(m-2) ] + 2(2m - 1)

T(2m) = 2T(2(m-2)) + 2(2m - 2) + 2(2m - 1)

T(2m) = 2T(2(m-2)) + 2(2m - 1)

Continue this process until we reach the base case of T(2)

T(2m) = 2T(2) + 2(2m-1)log(2m-1) + 2(2m-2)log(2m-2) + ... + 2(2)log(2)

T(2m) = 4 + 2(2m-1)log(2m-1) + 2(2m-2)log(2m-2) + ... + 4

T(2m) = 2m log(2m) (by the identity 1 + 2 + 2^2 + ... + 2^(k-1) = 2^k - 1)

Therefore, T(n) = n log(n) is the solution of the recurrence relation when n is an exact power of 2.

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Answer:

A. x <= 2

Step-by-step explanation:

The domain of a real function should be all real numbers. In

f(x) = sqrt(2-x)

we need 2-x to be non-negative, therefore

2-x >= 0

which implies

x <= 2

Answer:

\(\Huge \boxed{{x\leq 2}}\)

Step-by-step explanation:

The function is given,

\(f(x)=\sqrt{2-x}\)

The domain of a function are all possible values of x.

There are restrictions for the value of x.

2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.

\(2-x\geq 0\)

\(-x\geq -2\)

\(x\leq 2\)

The domain of the function is x ≤ 2.

Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

The value of the variable is 1. 40

we need to know that algebraic expressions are described as expressions that are made up of term, variables, constants, factors and coefficients.

these algebraic expressions are also made up of arithmetic operations.

These arithmetic operations are listed as;

From the information given, we have that;

7.5x/11=4.8/5

cross multiply the values, we get;

7.5x(5) = 4.8(11)

multiply the values

37. 5x = 52. 8

Divide both sides by the coefficient of x, we get;

x = 1. 40

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Answer:

θ = 61.927

Step-by-step explanation:

Sinθ = 30/34

θ  = ArcSin(30/34)

θ = 61.927

Therefore , the solution of the given problem of matrix comes out to be matrix A's (3,4)th place is -1.

A matrix is a group of numbers arranged in rows and columns to form a rectangular array. The numbers make up the matrix's constituents or parts. Matrix algebra is widely used in many branches of mathematics, as well as in the sciences of architecture, physics, economics, and statistics.

Here,

Given that matrix A has 4 rows and 5 columns,

=> it has a dimension of 4 x 6.

=> -1, 2, 3, 4, and 5 are the values in the fourth row of matrix A.

=> 2, 0, 6, and -3 are the values in matrix A's third column.

The entry in matrix A's (3,4)th place is -1.

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Explanation:

We have 8 choices for the first slot, 7 for the second, and so on. We count our way down until we have 1 choice left for the eighth slot.

We'll get 8*7*6*5*4*3*2*1 = 40,320 different permutations.

You could use the nPr formula

\(_nP_r = \frac{n!}{(n-r)!}\)

with n = 8 and r = 8 to get the same result. The exclamation marks indicate factorials.

The 8 violinists can be seated in 40,320 ways.

A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given In the orchestra, there are eight violinists in the front row,

the sitting arrangement of violinists is done with the help of permutation,

ⁿPₓ = n!/(n - x)!

here n = 8 and x = 8

(n - x)! = (8 - 8)!

(n - x)! = = 0! = 1

⁸P₈ = 8!/1

⁸P₈ = 8 x 7 x 6 x 5 x 4 x 3 x 2 x1

⁸P₈ = 40,320

Hence they can be seated in 40,320 ways.

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The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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Answer:

4x -8 +4y

Step-by-step explanation:

Distribute

4(x – 2 + y)

4*x -4*2 +4*y

4x -8 +4y

The magnitude of the resultant force is approximately 9.07 lb.

We have,

To use the parallelogram rule to find the magnitude of the resultant force for the two forces, we first draw a diagram:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb)  |

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

where A and B are the magnitudes of the given forces, and θ is the angle between them.

Using the parallelogram rule, we draw a parallelogram with sides AB and BC:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb) D

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

The diagonal BD represents the magnitude and direction of the resultant force.

To find its magnitude, we use the Law of Cosines:

BD^2 = AB^2 + BC^2 - 2(AB)(BC)cos(θ)

BD^2 = (7 lb)^2 + (11 lb)^2 - 2(7 lb)(11 lb)cos(133 degrees)

BD^2 = 49 + 121 - 2(77)cos(133 degrees)

BD^2 = 170 - 154cos(133 degrees)

BD ≈ 9.07 lb (rounded to two decimal places)

Therefore,

The magnitude of the resultant force is approximately 9.07 lb.

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