1. The average annual pay of 4 construction workers is $46,800. Three of the workers earned these annual announcements of pay: $44,200; $47,450; $45,900. What was the annual pay of the fourth worker?

Please answer fast! Thx!

The perimeter of the equilateral triangle which has sides of length (3x+7) is 9x+21.

A triangle's three sides and angles must be equal for it to be considered an equilateral triangle.

An equilateral triangle is also referred to as an equiangular triangle because it has angles that are each 60 degrees in length. Because its sides and angles are equal, the equilateral triangle is regarded as a regular polygon or triangle.

Depending on how many sides a triangle has, there are three different types. These triangles are equilateral, isosceles, and scalene.

In an equilateral triangles all sides are equal

so,

perimeter = 3x+7 + 3x+7 + 3x+7

perimeter = 9x+21

Thus, perimeter of the equilateral trinagle which has sides of lenght (3x+7) is 9x+21.

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By distributive property, the polynomial (3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v² is equivalent to polynomial (1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²).

In this problem we find a polynomial that must be simplified by means of algebra properties, especially by distributive property.  First, write the entire polynomial:

(3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v²

Second, use distributive property to simplify the polynomial thrice:

(1 / 2) · (3 · u² · v⁴ - 2 · u³ · v⁵ + u⁴ · v²)

(1 / 2) · u² · (3 · v⁴ - 2 · u · v³ + u² · v²)

(1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²)

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Answer:

The exponential model representing the amount of Iodine-125 remaining in the tumor after t days would be:

Iodine-125(t) = 0.6 * e^(-0.0115t)

To find the amount of Iodine-125 that would remain in the tumor after 60 days, we would plug in t = 60 into the model:

Iodine-125(60) = 0.6 * e^(-0.0115(60))

= 0.6 * e^(-0.69)

= 0.6 * 0.5032

= 0.3019

So after 60 days, there would be approximately 0.3019 grams of Iodine-125 remaining in the tumor.

If I helped you, could you please make my answer best?

The solved for x round to the nearest tenth is x≈ 14.

What is meant by round ?

Remember Sine of an angle is = opposite side /hypotenuse

So let the hypotenuse be  x :

sin(54°) = opposite side / x

sin(54°) = 12 / x

To solve for x, divide sin(54°) by 12:

x = 12 / sin(54°)

x≈14

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The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories.

a. The weighted average total return for the mutual funds covered by Morningstar is 9.20%.

This is calculated by taking the sum of the products of the total return and the number of funds for each of the four categories:

(4.65 * 9191) + (18.15 * 2621) + (11.36 * 1419) + (6.75 * 2900) / (9191 + 2621 + 1419 + 2900) = 9.20%

b. Yes, there is a difficulty associated with using the number of funds as the weights in computing the weighted average total return for Morningstar. This is because the number of mutual funds in each category can fluctuate over time, and thus, the weights used to calculate the average total return may not accurately reflect the true performance of the mutual funds.

An alternative to using the number of funds as weights would be to use the dollar amount invested in each type of mutual fund as the weight. This would give a more accurate representation of the performance of the mutual funds.

c. The expected return on the portfolio is 9.63%.

This is calculated by taking the sum of the products of the total return and the amount invested in each of the four categories:

(4.65 * 2000) + (18.15 * 4000) + (11.36 * 3000) + (6.75 * 1000) / (2000 + 4000 + 3000 + 1000) = 9.63%

The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories. However, using the number of funds as weights may not accurately reflect the true performance of the mutual funds, and an alternative would be to use the dollar amount invested in each type of mutual fund as the weight. The expected return on the portfolio is 9.63%, calculated by taking the sum of the products of the total return and the amount invested in each of the four categories.

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Answer:

-2

Step-by-step explanation:

The rate at which the candle burns is 1.5 inches per hour.

We know that the proportional relation between the number of inches that the candle has burned away, b, and the time in hours, t, is:

b = 1.5*t

The rate at which the candle burns is the amount burned in one unit of time, in this case, hours, then:

So, after t = 1 (one hour)

b = 1.5

In one hour, the candle burns 1.5 inches.

That is the rate at which the candle burns, it should be written as:

rate = 1.5 inches burned per hour.

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The result of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex] is[tex]$-56\frac{13}{20}$[/tex]

A mixed number is a combination of a whole number and a fraction, like [tex]3\frac{1}{2}[/tex], expressing numbers greater than one whole unit. It can be converted to an improper fraction.

To find the solution of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex]

We can first simplify the inner parenthesis

[tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right)=53\cdot(-1\frac{1}{10})=-53\frac{11}{10}$[/tex]

Then simplify the denominator, The denominator is the bottom part of a fraction, which represents the total number of parts in the whole. It is used to indicate the size of the fraction's unit or whole. It is also used to divide the numerator (top part of a fraction) by in order to determine the fraction's value.

[tex]$2\frac{3}{4} - 1\frac{2}{3} = \frac{11}{4} - \frac{5}{3} = \frac{44}{12} - \frac{20}{12} = \frac{24}{12} = 2$[/tex]

Now we can divide -53 and 11/10 by 2

[tex]$-53\frac{11}{10} \div 2 = -53\frac{11}{20} = -\frac{1133}{20} = -56\frac{13}{20}$[/tex]

So, the answer is [tex]$-56\frac{13}{20}$[/tex]

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Answer:

what to find in this question ?

Answer:

a.x (x + 1)

b. 3x (1 - 3x)

c. 7x (x² - 5)

d. 4x² (x + 6).

Answer:

$24.50

Step-by-step explanation:

hourly rate on Sunday is 1.75 times his normal hourly rate, that is

1.75 × $14 = $24.50

hourly rate on a Sunday is $24.50

According to the information, the probability that the next pice of fruit out of the bag will be an apple is 0.66.

To calculate the probability that the next piece of fruit out of the bag will be an apple we have to perform the following mathematical operation:

We have to calculate how many fruits there are in the bag.

So, we have 4 apples and 2 peaches, so we have 6 fruits in total. Now, we have to divide the number each fruit in the bag by the total number of fruits as shown.

4 / 6 = 0.66

2 / 6 = 0.33

According to the above, the probability that the next pice of fruit out of the bag will be an apple is 0.66.

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Answer:

Step-by-step explanation:

0.25 L = 250 mL

12 000mL = 12 L

5 L 400mL = 5400mL

[tex] \tt \: 4x + y = 10 ---- eqⁿ[/tex]

[tex] \: [/tex]

-6 is already given ,

[tex] \: [/tex]

so , put the value of y = -6 in the given eqⁿ ~

[tex] \: [/tex]

[tex] \tt \: 4x + y = 10[/tex]

[tex] \: [/tex]

[tex] \tt \: 4x + (-6) = 10[/tex]

[tex] \: [/tex]

[tex] \tt \: 4x = 10 + 6[/tex]

[tex] \: [/tex]

[tex] \tt \: 4x = 16[/tex]

[tex] \: [/tex]

[tex] \tt \:x = \cancel \frac{16}{4} [/tex]

[tex] \: [/tex]

[tex] \underline{\boxed { \red{\tt \large \: x = 4}} { \green✓}}[/tex]

[tex] \: [/tex]

missing value is 4!

hope it helps! :)

A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.

A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.

A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.

Given that sin theta = √3/√7

Opposite = √3

Hypotenuse = √7

Get the adjacent

Adj² = (√7)²-(√3)²

simplifying the above equation, we get

Adj² = 7-3

Adj² = 4

Adj = √4

Adj = 2

Cos theta = adj/hyp = 2/√7

csc theta = 1/sin theta = 1/(√3/√7) = √7/√3

sec theta = 1/cos theta = 1/(2/√7) = √7/2

tan theta = opp./adj = √3/2

cot theta = 1/tan theta = 1/(√3/2) = 2/√3

= 2√3/3

The complete question is:

Find the exact value of each of the remaining trigonometric functions of theta. Rationalize denominators when applicable.

sin theta [tex]$=\sqrt{\frac{3}{7}}$[/tex] given that theta is in quadrant I.

cos theta=

csc theta =

sec theta =

tan theta =

cot theta =

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The value of x = 19 and the value of z = 70° in the figure given above.

In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown.

" x is a variable in x + 2 = 7, but we can figure out its value if we try! A variable can be any letter, name, or symbol; it doesn't have to be "x"; examples include "y" and "w." Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation.

The z-score is simply the raw score less the population mean, divided by the population standard deviation, as the calculation demonstrates. A raw score's position relative to its distance from the mean is described by the z-score.

Using The property Vertically opposite angles are equal

110° = 9x - 61

⇒ 9x = 110 +61

⇒ 9x = 171

⇒ x = 171/9

⇒ x = 19

As all angles equal 360°

110° + 110° + 2z = 360°

⇒ 2z = 360° - (110° + 110°)

⇒ 2z = 140

⇒ z = 140/2

⇒ z = 140/2

⇒ z = 70°

Thus, The value of x = 19 and the value of z = 70° in the figure given above.

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The range is not likely to vary, which is one of the claims regarding the new salary distribution that is supported.

Therefore,

Given that a small company's salary distribution of 27 employees has a mean of $35,000 and a standard deviation of $2,000,

When a highly unusual value, such as 120000, is taken into account for the 28th employee, we discover that the mean increases.

The new median would be the average of items 14 and 15, as the prior median was the 14th item. Thus, the median may alter.

Because the maximum has been raised up to 120000, the range will undoubtedly vary.

so that we can say

Range changes, median changes, and mean increases.

Thus, we determine that Option B is correct.

The complete question is:

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th

28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?

The median is not likely to change. I

The range is not likely to change. II

The mean is likely to increase. III

A) I only

B) III only

C) I and II only

D) I and III only

E) I, II, and III

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Using multiplication operation, the number of ounces of Isabella's spray fixative contained in the economy size is 9¹/₃ ounces.

Multiplication operation is one of the four basic mathematical operations, including addition, division, and subtraction.

The multiplication operation involves the multiplicand multiplied by the multiplier, resulting in a product.

The multiplication operand is depicted using (x), (*), or (of).

The normal spray fixative purchased by Isabella = 6²/₃ = 6.667 ounces

The relative size of the economy can = 1²/₅ of 6²/₃ ounces

The number of ounces in the economy can = 9¹/₃ ounces (1²/₅ x 6²/₃)

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Answer: C(n)=24n+5 =24

(A)=A/6 =0

Step-by-step explanation:

The point on the unit circle that corresponds to the real number t = 7/4 is given as follows:

(-0.1782, 0.9840).

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

With parameter t, the coordinates of the point are given as follows:

(cos(t), sin(t)).

Hence the x-coordinate when t = 7/4 is given as follows:

cos(7/4) = -0.1782.

The y-coordinate when t = 7/4 is given as follows:

sin(7/4) = 0.9840.

Meaning that the coordinates are:

(-0.1782, 0.9840).

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The correct order of bond lengths P, Q, and R in the above diagram is P > Q > R. The correct option is A.

The bond length is the distance between the centers of two bound atoms. Consider the fact that a homonuclear diatomic molecule's bonded atoms are separated by half their element's atomic radius (sometimes referred to as the covalent or bonding atomic radius).

Less percentage of s character in a bond means the length of orbitals of the molecule is more, and also the bond length is more.

Therefore, the correct option is A. P > Q > R.

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The question is incomplete. Your most probably complete question is given below:

Which is the correct order of bond lengths P, Q, and R in the above diagram?

P > Q > R

R > Q > P

Q > P > R

Q > R > P

In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.

1976: Republican: 43 states, District of Columbia; Democrat: 6 states

2012: Republican: 24 states, District of Columbia; Democrat: 26 states

In 1976, 43/49 (including the District of Columbia) states voted Republican, which is 87.76%. This is a relative frequency.

1. Calculating the total number of states and District of Columbia in 1976: 43 + 6 + 1 = 50.

2. Calculating the percentage of states voting Republican in 1976: 43/50 (including the District of Columbia) = 0.87 or 87.76%.

3. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.

In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency.

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The total monthly revenue when 200 units were sold is $28800 and the monthly revenue when 800 units were sold is $52800.

Given,

 The equation for monthly revenue, [tex]R(x)= 170x - 0.13x^{2}[/tex]      [tex](0 < x < 800)[/tex]

      where [tex]x[/tex] is the number of units sold

(a)  Total number of units sold, [tex]x = 200[/tex]

                Monthly revenue, [tex]R(200)= 170x- 0.13x^{2}[/tex]

                                                           [tex]= 170*200 - 0.13*200^{2}[/tex]

                                                           [tex]= 34000 - 0.13* 40000[/tex]

                                                           [tex]= 34000 - 5200[/tex]

                                                           [tex]= 28800[/tex]

         Hence , monthly revenue = $28800

(b)   Total number of units sold, [tex]x = 800[/tex]

                    Monthly revenue, [tex]R(800)= 170x- 0.13x^{2}[/tex]

                                                               [tex]= 170*800 - 0.13*800^{2}[/tex]

                                                               [tex]= 136000 - 0.13*640000[/tex]

                                                               [tex]= 136000- 83200[/tex]

                                                               [tex]= 52800[/tex]

         Hence , monthly revenue = $52800

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In repeated sampling from the S distribution, the mean of the values will be close to 4.66, which is the appropriate interpretation of the mean.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a set of findings from a survey, experiment, or observational study. The average of a group of values is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Here,

The average of the values will be close to 4.66 in repeated sampling from the S distribution, which is the correct interpretation of the mean.

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If 3 inches on the map represents 1.25 miles, we can use that proportion to find how many inches represents 10 miles.

3 inches / 1.25 miles = x inches / 10 miles

We can cross multiply and divide to find x:

x = (3 inches * 10 miles) / 1.25 miles

x = 24 inches

So on the map, 24 inches represent 10 actual miles.

Answer:

y intercepts : (0, -5)

Step-by-step explanation:

Answer:

(0,-5)

Step-by-step explanation:

Answer: X = 17

Step-by-step explanation:

8.75 + 1.95x = 41.9

1.95x = 41.9 - 8.75

1.95x = 33.15

x = 33.15/1.95

x = 17

Answer:

Diameter is 8

Circumference is 8pi ~= 25.13

Step-by-step explanation:



The diameter is double the radius. So the given radius is 4 and double is 8.

The Circumference is given by C = pi•d or C = 2pi•r

Both of these equations will give the circumference.

C = pi•d

= pi•8

= 8pi ~= 25.13

OR

C = 2pi•r

= 2pi•4

= 8pi ~= 25.13

For finding the diameter, I multiply the radius by 2:

Diameter = 2 × radius

                = 2 × 4

                = 8

So the diameter is 8. As for the circumference, we can use two ways : either multiply pi times the diameter, or multiply 2 times pi times the radius.

The formulas are

C = πd              and C = 2πr

To find the circumference, stick in 8 for d:

C = π × 8

C = 25.13 units