what is the smallest even consecutive number such that their sum is at most 90?


SOLVE PLEASE

The measure of the smallest possible sector angle possible is 8°.

Let [tex]$a_1$[/tex] be the first term of the arithmetic progression and [tex]$a_{12}$[/tex] be the last term of the arithmetic progression.

From the formula of the sum of an arithmetic progression, we have -

[tex]$12*\frac{a_1+a_{12}}{2}=360$[/tex]

simplifying we get,

[tex]$a_1 + a_{12} = 60$[/tex]

[tex]$a_{12}$[/tex]  is the largest term of the progression and it can also be expressed as-

[tex]a_{12} = $a_1+11d$[/tex]

where d is a common difference.

Since each angle measure must be an integer, d should also be an integer.

[tex]$a_{12}-a_1=a_1+11d-a_1=11d$[/tex]

Since d is an integer, the difference between the first and last terms, 11d, must be divisible by 11.

Since the total difference should be less than 60, let's start checking multiples of 11 less than 60 for the total difference between [tex]$a_1$[/tex] and [tex]$a_{12}$[/tex].

Let us take the largest multiple because the maximum difference will give us the minimum value of the first term.

If the difference is 55, [tex]$a_1=\frac{60-55}{2}=2.5$[/tex], is not an integer.

If the difference is 44, [tex]$a_1=\frac{60-44}{2}= 8[/tex] . It satisfies the given conditions.

Hence, the measure of the smallest possible sector angle possible = 8°.

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Answer:

6000

Step-by-step explanation:

Interest of 3% a year of principal of 200,000 = 6000

monthly payment of 843 also includes a portion of amortization of the principal itself, which you can ignore cause the question only asked for the interest portion.

this is an unclear question cause it didn't say PER YEAR interest paid.  you only need to remember interest% * principal = ANNUAL interest payment $.  Then you can divide that over 12 months, which is 500$ per month.

[tex]7+2^3[/tex]

[tex]7+(2^3)[/tex]

[tex]7+8[/tex]

[tex]=\fbox{15}[/tex]

Sum to the correct number of significant figures is 6.43

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.

Significant figures are used to establish the number which is presented in the form of digits. These digits carry a meaningful representation of numbers. The term significant digits are also used often instead of figures. We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.

Since the least precise measurement 1.67 is correct to only two decimal place.

  2.0800

+ 2.677

+  1.67          

  6.427

Therefore, the final result should be rounded off to 6.43 where Significant Figures: 3, Decimals: 2.

The arithmetic addition of given numbers to the correct number of significant figures is 6.43.

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Neither of the ordered pairs is a solution of the equation 6x + 3y = 15.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Given linear equation is 6x + 3y = 15

Substitute each of the point given in the options.

A : (3, -2)

6x + 3y = (6 × 3) + (3 × -2) = 18 - 6 = 12 ≠ 15

B : (2, 2)

6x + 3y = (6 × 2) + (3 × 2) = 12 + 6 = 18 ≠ 15

Neither (3, -2) nor (2, 2) are the solutions of the equation.

Hence neither is the solution of the given linear equation.

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Answer:

b

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

2x + 1 + 5x + 5 + 90 = 180

7x + 96 = 180 ( subtract 96 from both sides )

7x = 84 ( divide both sides by 7 )

x = 12

Answer: An inequality for the expected population, p, next year can be written using the information provided. Since the population is expected to grow between 5% and 8% per year, we can represent that as a range of growth rates: 0.05 <= growth rate <= 0.08

To find the expected population next year, we can use the formula:

p = population * (1 + growth rate)

where "population" is the current population of 50,000 and "growth rate" is the percentage increase. Since the growth rate is expected to be between 0.05 and 0.08, we can write the inequality as:

50,000 * (1 + 0.05) <= p <= 50,000 * (1 + 0.08)

This inequality represents the expected range of population next year, with the lower bound being the population if it grows by 5% and the upper bound being the population if it grows by 8%.

Simplifying the inequality:

52,500 <= p <= 54,000

So the expected population next year, p, is between 52,500 and 54,000.

Step-by-step explanation:

We can write the measurements as -

a = 7.8

b = 9.24

(B) = 50°

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that two triangles in the map below are similar.

We can write -

{ 1 } -

sin (A) = a/c

a = c sin(A)

a = 12 sin(40°)

a = 12 x 0.65

a = 7.8

{ 2 } -

cos (A) = b/c

b = c cos(A)

b = c cos(40°)

b = 12 x 0.77

b = 9.24

{ 3 } -

tan (B) = b/a

tan (B) = 9.24/7.8

tan (B) = 1.19

(B) = 50°

Therefore, we can write the measurements as -

a = 7.8

b = 9.24

(B) = 50°

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An equation of a circle which represents the picture include the following: A. (x)² + (y)² = 25.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

From the information provided above, we have the following points on this circle:

Substituting the given points into the equation of a circle, we have the following;

(x - 0)² + (y - 0)² = 5²  

(x)² + (y)² = 25.

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For the given case the Null hypothesis is The mean mpg of the 91 cars tested is equal to the manufacturer's mpg rating of 55.7 and the  Alternative hypothesis is The mean mpg of the 91 cars tested is less than the manufacturer's mpg rating of 55.7.

In order to determine whether the cars underperform the manufacturer's mpg rating, the independent testing firm would need to perform a hypothesis test. To do this, they would need to compare their sample mean of 55.2 mpg with the manufacturer's mpg rating of 55.7. They would also need to know the standard deviation of the sample, which is 3.24.

The independent testing firm would then calculate the z-score by subtracting the manufacturer's rating from the sample mean, and dividing it by the standard deviation. If the z-score is greater than the critical value for a 0.05 level of significance, then there is sufficient evidence to reject the null hypothesis.

In this case, the z-score is -1.51. Since the critical value for a 0.05 level of significance is 1.96, the z-score is less than the critical value. Therefore, there is not sufficient evidence to reject the null hypothesis, and we cannot conclude that the cars underperform the manufacturer's mpg rating.

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Answer:

x = 11

Step-by-step explanation:

We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)

Answer:  We can use the concept of rates to solve this problem.

A rate is a ratio of the amount of work done to the amount of time it takes to do the work. We can find the rate of work for the 4 painters by dividing the number of rooms they painted by the number of hours it took them:

Rate = Rooms painted / Hours

Rate = 12 rooms / 8 hours = 1.5 rooms per hour

Now we can use this rate to find out how long it will take 7 painters to paint 21 rooms. To do this, we'll use the formula:

Time = Rooms / Rate

Time = 21 rooms / 1.5 rooms per hour = 14 hours

So it would take 7 painters working at the same efficiency as the 4 painters 14 hours to paint 21 rooms.

Step-by-step explanation:

The time needed until there are 82 bacteria is given as follows:

23.8 hours.

An exponential function is defined as follows:

[tex]y = a(b)^{\frac{x}{n}}[/tex]

In which:

The parameters for this problem are given as follows:

a = 40, b = 2, n = 23.

Hence the function is:

[tex]y = 40(2)^{\frac{x}{23}}[/tex]

There will be 82 bacteria at a time x when y = 82, hence:

[tex]82 = 40(2)^{\frac{x}{23}}[/tex]

[tex](2)^{\frac{x}{23}} = 2.05[/tex]

Applying the logarithm of base 2 to each side, we have that:

x/23 = log2(2.05)

x = 23 x log2(2.05)

x = 23.8 hours.

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Answer:

AAA similarity

Step-by-step explanation:

      In ΔECD,

            ∠E + ∠D + ∠ECD = 180°   {Angle sum property}

            ∠E + 36 + 123       = 180°

                      ∠E + 159     = 180

                                   ∠E = 180 - 159

                                  ∠E = 21°

In ΔACB,

           ∠A + ∠B + ∠ACB = 180°   {Angle sum property}

            ∠ACB + 36 + 21       = 180°

                      ∠ACB + 57    = 180

                                   ∠ACB = 180 - 57

                                  ∠ACB= 123°

    In ΔECD & ΔBCA,

               ∠A ≅ ∠D

              ∠B ≅ ∠A

           ∠BCA ≅ ∠ECA

ΔECD ~ ΔBCA by Angle Angle Angle similarity.

Her monthly finance charge will be: $1.80

Now, According to the question:

Gabriela has an average daily balance of $232. 94 on her credit card.

and, Her card charges 9. 25% annual interest.

Based on the given condition:

$232.94 × 9.25%

232.94 × 9.25/100

Calculate the product or quotient:

232.94 × 9.25/100 = 21.54694

21.54694 rounds up to 21.55

Her monthly finance charge will be:

21.55/12 = 1.7958333333

1.7958333333 round up 1.80

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To find the balance of the account after 3 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial principal is $2,600, the interest rate is 4.2% (expressed as a decimal), the number of times the interest is compounded per year is 12 (monthly), and the number of years is 3.

So, we can plug these values into the formula:

A = 2600(1 + 0.042/12)^(12*3)

A = 2600(1.0035)^36

A = 2600 * 3.876

A = 10,049.6

The balance of the account after 3 years is $10,049.6.

The slope of the relationship is equal to; C. 4.

In Mathematics, the slope of any straight line can be calculated by using this mathematical expression;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points on the line:

Substituting the given points into the slope formula, we have;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-9 + 13)/(-1 - (-2))

Slope (m) = 4/1

Slope (m) = 4

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Answer:

--------------------------

If we put the number of sticks in a sequence we get:

As we see the difference of the terms is common and is 4, and the first term is 6. It is therefore an arithmetic progression with:

Use the nth term equation:

Substitute n = 6 to find the number of sticks of the 6th term:

Find the nth term:

We can write the coordinates after reflection as -

A (x₁, y₁) → A" (x₁, - y₁)

B (x₂, y₂) → B" (x₂, - y₂)

C (x₃, y₃) → C" (x₃, - y₃)

Given is that to describe a sequence of transformation that maps triangle ΔABC onto triangle ΔA”B”C” a student starts with a reflection over x - axis.

Assume the coordinates of a triangle are -

A (x₁, y₁)

B (x₂, y₂)

C (x₃, y₃)

So after the reflection over the {x} axis, we can write the coordinates as -

A" (x₁, - y₁)

B" (x₂, - y₂)

C" (x₃, - y₃)

Therefore, we can write the coordinates after reflection as -

A (x₁, y₁) → A" (x₁, - y₁)

B (x₂, y₂) → B" (x₂, - y₂)

C (x₃, y₃) → C" (x₃, - y₃)

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The length of diagonal of a parallelogram is 2546 inches.

A quadrilateral with equal pairs of opposing sides and angles is referred to as a parallelogram. It has a pair of opposing sides that are parallel to one another. The inner angles are supplementary in nature, meaning that the sum of them equals 180 degrees. A parallelogram's diagonals are bisected by one another, or divided into two equal portions. A parallelogram's internal angles add up to 360 degrees.

The diagonals of parallelogram are given by:

x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)

Given the two sides are 35 and 75 inches.

We also know that the adjacent angles of parallelogram are supplementary:

∠A + ∠B = 180

140 + ∠B = 180

∠B = 40

Substitute the value of sides and angle in the equation:

x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)

x = √((35)^2 + (72)^2 + 2(35)(72) cos 140)

x = 1225 + 5184 + (5040)(-0.766)

x = 1225 + 5184 - 3860

x = 2546 inches

Hence, the length of diagonal is 2546 inches.

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Answer:

Sal previously earned $61640.

Answer:

$62,000.00

Step-by-step explanation:

x + .08x = 66960  Combine like terms

1.08 x = 66960  Divide both sides by 1.08

[tex]\frac{1.08x}{1.08}[/tex] = [tex]\frac{66960}{1.08}[/tex]

x = 62000

Answer:

0.2

Step-by-step explanation:

8 is bigger than 5 so we will make 8 zero and will will add 1 to the next number

Answer:

0.2

Step-by-step explanation:

Hope this helps

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If Lilyana runs a cake decorating business for which 10% of her orders come over telephone , then probability that it takes fewer than 5 orders for Lilyana to get her first telephone is 0.3439  .

The geometric distribution is used to calculate the required probability ,

In this case, the success is a telephone order, and

the failure is an order placed in some other way.

Let probability of success is ⇒ p , and

let the number of orders needed to get the first telephone order be = x . Then, X follows a geometric distribution with parameter p, so we have:

Probability of P(X = k) is = (1-p)^(k-1) × p ;

where k is the number of orders needed.

the probability of success (p) is  = 10% = 0.1

we have to find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.

that means : P(X<5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)

Substituting the values of p = 0.1 ,

we get ;

= (1-0.1)⁰ × 0.1 + (1-0.1)¹ × 0.1 + (1-0.1)² × 0.1 + (1-0.1)³ × 0.1

Simplifying further ,

we get ;

= 0.1 + 0.09 + 0.081 + 0.0729

Adding all the terms ,

we have ;

= 0.3439

Therefore , the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month is 0.3439.

The given question is incomplete , the complete question is

Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the method of placing each cake order is independent.

Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.

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The solutions to the system of equations f(x) = g(x) are given as follows:

x = 0 and x = 1.

The reason for these solutions is that f(x) and g(x) have the same numeric value at x = 0 and at x = 1.

A system of equations is composed by multiple equations.

The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.

The x-values for which the numeric values of f(x) and g(x) are the same are given as follows:

x = 0 and x = 1.

Which are the solutions to the system of equations.

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If on Wednesday evening sonto spent one ½ doing doing homework 45 minutes doing housework 1 hour visiting friends and 1 hour ½ watching television .This  information in a ratio is: 2: 3 : 4 :6.

We need to first analyze the details  before determining the ratio.

​1 hour = 60 minutes

1/2 h = 30 minutes

1 1/2 = 90 minutes

So,

30 : 45 = 60 :90

Reduce the above minutes  to ratio

2: 3 : 4 :6

Therefore the ratio of the information is 2: 3 : 4 :6.

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Answer:

If you get 7 tokens a minute and you work for 9 hours, or 540 minutes, then you would have:

7 tokens/minute * 540 minutes = 3780 tokens

You would have 3780 tokens in total.

Answer:

3,780

Step-by-step explanation:

7* 540= 3780

because you get 7 every minute and there are 540 minutes

The table which matches the equation and includes only viable solutions is the third table.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

Given that equation is,

c = 3.5b

Here b is the number of loaves of bread and c is the total cost of the bread.

All the table values matches the equation when we substitute the value of b and c in the equation.

But number of loaves of bread cannot be fractions or negative numbers.

So the most viable solution is the third table consisting of values of b as  0, 3, 6, 9 and corresponding value of c as 0, 10.5, 21, 31.5.

Hence the 2-column table with the first column labeled loaves (b) with entries 0, 3, 6, 9 and the second column labeled cost (c) with entries 0, 10.5, 21, 31.5 is the correct one.

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Answer:

The third one

Step-by-step explanation:

The length of Jane's shadow is approximately 2.85 feet

To find the length of Jane's shadow, we can use the principle of similar triangles.

The ratio of the shadow length to the object height is the same for both King Neptune and Jane, then we can set up a proportion:

(shadow length of King Neptune) / (height of King Neptune) = (shadow length of Jane) / (height of Jane)

Given that King Neptune's shadow is 3 13 5 feet and the statue is 34 feet tall.

By substituting these values into the proportion:

(3 13 5 feet) / (34 feet) = (shadow length of Jane) / (5' 9")

To find the shadow length of Jane, we can cross-multiply and solve for the shadow length:

(3 13 5 feet) * (5' 9") = (shadow length of Jane) * (34 feet)

Converting Jane's height into feet: 5'9" = 5*12 +9 = 69 inches = 5.75 ft

(3 13 5 feet) * (5.75 ft) = (shadow length of Jane) * (34 feet)

shadow length of Jane = (313.5*5.75) / 34 = 2.85 ft

So, The length of Jane's shadow is approximately 2.85 feet.

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