a contractor hired 150 men to pave a road in 30 days how many men would he hire to do the same work in 10 days​

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

Answer:

c

Step-by-step explanation:

.......,..............

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer: 3448.15

Step-by-step explanation:

The formula is

A=p ((1+(r/n))^(tn)

A future value ?

P present value 2410

R interest rate 0.12

N compounded monthly 12

T time 3 years

A=2,410×((1+(0.12÷12))^(3×12)

A=3448.15

Answer: y-9 = 17(x+7)

Step-by-step explanation:

We will use the second coordinate point to use in the equation and the first coordinate (-8, -8) to figure out the slope of this line.

Answer:

y-9=17x+119

Step-by-step explanation:

given points (-8,-8) & (-7,9)

let's take (-7,9) as (x1,y1) and (-8,-8) as (x2,y2)  

now for finding out equation through two points, we use

\( \frac{x-x_{1} }{x_{1}-x_{2}  } =\frac{y-y_{1} }{y_{1}-y_{2}  } \)

So accordingly, we input the values

\( \frac{x-(-7) }{-7-(-8)}  } =\frac{y-9 }{9-(-8)  } \)

\( \frac{x+7 }{-7+8}  } =\frac{y-9 }{9+8  } \)

\( \frac{x+7 }{1}  } =\frac{y-9 }{17 } \)

\( 17(x+7) = y-9 \)

\( 17x+119 = y-9 \)

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))

To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.

The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.

The total number of possible arrangements is given by the factorial of the total number of letters:

Total arrangements = 10!

However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:

Total arrangements = 10! / (2!)

To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.

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A linear recurrence relation is homogeneous if f(n) = 0. The order of the recurrence relation is determined by k. We say a recurrence relation is of order k if an = f(an−1,...,an−k).

Given: a)  an = 3an-1 + 4an-2 +5an-3

We note that the given recurrence relation is linear, because the right-hand side is a linear combination of previous terms. We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms. The degree of the recurrence relation is the largest value k for which are occurs in the recurrence relation.

k=3

Given: b) an = 2nan-1 + an-2

We note that the given recurrence relation is not linear, because the right-hand side is not a linear combination of previous terms (due to the

fact that 2n is not a constant). We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms.

Given: c) an = an-1 + an-4

Because the right-hand side is a linear combination of the prior terms, we observe that the provided recurrence relation is linear. Given that there are no constant terms in the recurrence relation, it is important to observe that it is homogenous. The biggest value k for which are k appears in the recurrence relation is the recurrence relation's degree.

Degree of linear homogeneous recurrence are k=3 .

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you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

24.

Step-by-step explanation:

The hypotenuse of a triangle is simply the slanted side of a triangle and it is always the longest side of any triangle.

Mathematically, the hypotenuse of a triangle is calculated using the Pythagorean theorem;

C² = A² + B²

Where;

C is the hypotenuse i.e the longest side.

A is the opposite side of the triangle.

B is the adjacent side of the triangle.

Answer:

16,000

Step-by-step explanation:

11,319 rounded to the nearest thousand is 11,000.

4,895 rounded to the nearest thousand is 5,000.

11,000 + 5,000 is equal to 16,000.

The screenshot you sent us didn't not require it to be a fraction, so i will make it a decimal

47/100*70=

0.47*70=

4.7*7=

32.9

Answer:

32.9 = x

47% of 70 = 32.9/70

or, if rounded, = 33/70

Step-by-step explanation:

Two ways:

A. 47/100 = x/70

47 = 100x/70

3290 = 100x

32.9 = x

47% of 70 = 32.9

B. 70 * 47% = x

70 * .47 = x

32.9 = x

Answer:

Just do 60 divided by 10

Step-by-step explanation:

60=10 x  10 times 6 = 60 so x=6

Answer: \(x=6\)

Divide both sides by 10

\(10x=10=60/10\\x=6\)

Percent of change of price is 59%.

The percentage change calculator will measure the difference between two numbers and specify whether the difference is an increase or decrease.

A % change calculator like this one. The number of apples has increased (changed) by 100% from 10 to 20.

When there is a "old" and "new" number or a "initial" and "final" value, this calculator will be utilized most frequently. While a negative change is expressed as a decrease in the absolute value of the percentage value, a positive change is expressed as an increase in the percentage value.

Percentage Change=\(\frac{V2-V1}{V1} *100\);

Given,

V1=34,V2=54;

⇒Percentage change=\(\frac{54-34}{34} *100\)=59%

Percent of change of price is 59%.

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Answer:

  B.

Step-by-step explanation:

The instructions to connect points WYXZ to make the square mean that WX and YZ are diagonals of the square. They must be mutual perpendicular bisectors. Their point of intersection is necessarily the center of the circle. That is, WX must be a diameter.

The calculated measure of t from the given equation is 15 degrees

From the question, we have the following parameters that can be used in our computation:

10

to

25°

When expressed properly, we have

10° + t° = 25°

Evaluate the like terms

So, we have

t° = 15°

Hence, the value of t° is 25°

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a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Reaction rate and reaction time are inversely proportional to each other.

Reaction rate and reaction time are two intertwined concepts. Reaction rate refers to how quickly or slowly a reaction occurs while reaction rate refers to the time taken for a particular reaction to occur.

If the reaction rate increases, the reaction time decreases, if the reaction rate decreases, the reaction time increases hence the both quantities are inversely proportional to each other.

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The percentile of the top students will be 88%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state.

The percentile of the top student is given as,

⇒ 100% - 12%

⇒ 88%

The percentile of the top students will be 88%.

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Answer:

V=11858.98

Step-by-step explanation:

V=r^2*pi*h

first find r

r=d/2

d=1.4(19.75)

d=27.65

r=27.65/2

r=13.825 ft

plug into volume equation

V=13.825^2*pi*19.75

V=11858.97771

V=11858.98 ft^3

The radius is 5.316 cm, height is 10.362 cm and Maximum volume is  

60.583 cm³.

We have,

Surface area of sphere = 36 cm²

4πr² = 36

πr² = 9

r = 3√π

r= 5.316

Now, Volume spherical cap

= 1/3 πh² (3R- h)

= 1/3π (10.362) (3 (5.316) - 10.362)

= 1/3 π (57.882132)

= 60.583 cm³

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Answer:

x is -1/b yw

Step-by-step explanation:

Answer:

The answer is 49.! :)

Step-by-step explanation:

If you look at the table, it shows 3;7. If you look at the 21 in the 2 row, and look under it in the other orange row its 49. So the answer would be 49! :)

Answer:

49

Step-by-step explanation:

Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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Answer:

-0.0625

Step-by-step explanation:

Answer:

$73,000

$43,000 + $5,000 x t

Step-by-step explanation:

Every year increase $5,000, after 6 years increase $5000 x 6 = $30,000

Her salary will be $43,000 + $30,000 = $73,000

After t years, her salary will be

$43,000 + $5,000 x t

Answer:

Line UM.

Step-by-step explanation: you can name a line by naming at least two points on it.

Line l can be called line UM, line LM, and line UL because line l is contained in plane S.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

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

m is the ratio of the line,

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases.

It is given that:

A plane S contains a line l.

It is possible to give a name for line l in different ways.

The line l can be called:

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

Thus, line l can be called line UM, line LM, and line UL because line l is contained in plane S.

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