please help me with this problem everything is on the image

Answer:

Let's call the number of soldiers that should leave the group as x.

We know that the group of 30 soldiers has enough food for 40 days. And we want to find the number of soldiers that should leave the group so that the food is enough for 100 days for remaining soldiers.

We can use the proportion of soldiers to days of food to find the number of soldiers needed for 100 days of food.

30/40 = (30-x) / 100

We can cross-multiply and then solve for x:

1200 = 30x - x^2

x^2 + 30x -1200 = 0

x = 20 or x = -40

20 is the valid solution, so 20 soldiers should leave the group.

So, 20 soldiers should leave the group so that the food is enough for 100 days for remaining soldiers.

The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration.

If the pH level is 2.5, we can calculate the hydronium ion concentration by rearranging the equation:

H+ = 10^(-pH)

H+ = 10^(-2.5)

H+ = 3.162 x 10^-3 (Option A)

Therefore, the hydronium ion concentration of the vinegar is 3.162 x 10^-3.

Answer:

The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration. To find the hydronium ion concentration of a particular vinegar if the pH level is 2.5, we can rearrange this equation to solve for H+:

H+ = 10^-pH

So, if the pH level is 2.5, we can plug in this value into the equation to find the hydronium ion concentration:

H+ = 10^-2.5

H+ = 3.162 x 10^-3

So the hydronium ion concentration of the vinegar is 3.162 x 10^-3.

Option 3.162 x 10^-3 is correct.

The value of the variables 'x' and 'y' will be 7 and 4, respectively.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔMAS is congruent to the triangle ΔNER. Then the corresponding sides and angles are equal to each other. Then we have

∠NER = ∠MAS

(16x)° = 112°

x = 7

Then the other equation is given as,

NR = MS

3x + 5y = 41

3(7) + 5y = 41

21 + 5y = 41

5y = 20

y = 4

The value of the variables 'x' and 'y' will be 7 and 4, respectively.

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When a population which grows exponentially at the rate of 1.55%, will take 44.7 years become double.

Exponential growth function is defined as a function that shows an increase within a population that occurs at the same rate over time. When populations experience doubling or tripling in numbers, can assume the data increases exponentially. We have, a population grows exponentially.

The growth rate of population = 1.55%

Let us assume initial population be "P₀". We have to determine the time ( in years ) will it take the population to double, i.e., excepted value = 2P₀.

As we know, exponential population growth function is, P = P₀ eʳᵗ

where, P ---> total expected population

P₀ --> initial population

r --> population growth rate

t --> time period (in years)

P = 2P₀ , r = 1.55% = 0.0155 , substituting all known values in above formula,

2P₀ = P₀e⁰.⁰¹⁵⁵ᵗ

=> 2 = e⁰.⁰¹⁵⁵ᵗ

Taking natrual logarithm both sides

=> ln 2 = ln (e⁰.⁰¹⁵⁵ᵗ )

=> ln 2 = 0.0155 ×t ln e

=> 0.6931 = 0.0155 ×t ( since ln e = 1)

=> t = 0.6931/0.0155

=> t = 44.719 ~ 44.7

So, required value of t is 44.7 years.

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The decimal number 0.875 to a percentage will be 87.5%. Then the correct option is A.

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 to 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 decimal number is given below.

⇒ 0.875

To convert the decimal number to percent, just multiply the decimal number by 100. Then we have

⇒ 0.875 x 100

⇒ 87.5%

The decimal number 0.875 to a percentage will be 87.5%. Then the correct option is A.

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Answer:

1/3

Step-by-step explanation:

1/3

The graph of a logarithmic function is first distinguished by the fact that it passes through (1,0).

In the 17th century, Scottish mathematician John Napier (1550-1617) developed logarithms as a tool for computing. From the Greek terms for ratio (logos) and number, he constructed the phrase (arithmos).

A logarithmic function is an exponential function's inverse. Recall that switching the x and y positions yields the inverse of a function. This corresponds to the graph's y=x line. The exponential curve reflects the logarithmic curve, as shown in the graph to the right.

All logarithmic function graphs will exhibit the following traits: The graph of the logarithmic function travels across points (1,0). If the base of a logarithmic function exceeds 1, the graph will become steeper.

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A) f(0) = 2(0)-5 = -5

B) f(3) = 2(3) -5 = 6-5 = 1

C) f(-3) = 2(-3)-5 = -6-5 = -11

D) f(4) = 2(4) -5 = 8-5 = 3

E) f(-1) = 2(-1) -5 = -2-5 = -7

Answer:

height of tank = 104 cm

Step-by-step explanation:

the volume (V) of a rectangular tank is

V = Ah ( A is the area of the base and h the height )

here A = 50 × 40 = 2000 cm²

all units must be the same, so

note that 1 litre = 1000 cm³

then 52L = 52 × 1000 = 52000 cm³

height of water in tank is then

2000h = 52000 ( divide both sides by 2000 )

h = 26 cm

this h is [tex]\frac{1}{4}[/tex] of the height of the tank, thus

height of tank = 4 × 26 cm = 104 cm

Answer:

3/22

Step-by-step explanation:

4 sides + 5 sides + 12 sides = 22 sides

and all three types have 1 6 on them so it would be 3/22= 13.63%

The second graph  shows the greatest integer function.

Integer function is a type of mathematical function whose range and domain are both sets of integers. The integer function is defined such that all the values in the domain, when plugged into the function, will result in an integer value. Integer functions are useful in many applications, such as cryptography and number theory. Integer functions are also used in computer science to represent discrete values. Integer functions are typically defined using a set of rules that dictate the relationship between the integers in the domain and the integers in the range.

y = [x]

У returns the largest integer less than or equal to X, In essence it round down a real number to the nearest integer.

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The expected value to the nearest dollar is 4895.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given that Amount of Claim $0 $2000 $4000 $6000 $8000 $10000

Probability 0.70 0.15 0.08 0.05 0.01 0.01

Therefore, Expected value E(x) = Σx * p(x)

E(x) = - 5(0.999999) + 4899999995(0.000001)

E(x) = - 4.999995 + 4899.999995

E(x) = 4895

Hence, expected value is 4895

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Answer:

Step-by-step explanation:

To find the value of y at the point where x=1, we can substitute x=1 into the equation:

x^2+xy+y^3=1

1+y+y^3=1

y+y^3=0

y(y^2+1)=0

y=0 or y=-1 or y=1

To find the value of y' at the point where x=1, we need to take the derivative of the equation with respect to x:

2x + y + xy' + 3y^2y' = 0

y' = -(2x+y)/(3y^2+x)

When x = 1, y' = -(2(1)+y)/(3y^2+1)

To find the value of y'' at the point where x=1, we need to take the derivative of the equation with respect to x again:

2 + y' + xy'' + 3(2y)(y') = 0

y'' = -(2+y')/(3(2y)+(x))

When x = 1, y'' = -(2+y')/(3(2y)+(1))

To find the value of y''' at the point where x=1, we need to take the derivative of the equation with respect to x one more time:

y'' + xy''' + 3(2y')(y') + 3y(3y)(y') = 0

y''' = -(y'' + 3(2y')(y') + 3y(3y)(y'))/(x)

When x = 1, y''' = -(y'' + 3(2y')(y') + 3y(3y)(y'))/(1)

It is important to note that to find the exact value of y, y', y'', y''' we need to find the value of y in the equation x^2+xy+y^3=1 and substitute it into the derivative equations, but without the equation solved we can't find the exact values.

The end behavior of the graph of f(x) is,

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.

A data set is a collection of organized data. Data is a collection of information that has been obtained by observations, measurements, study, or analysis, as we are all aware. It could contain names, numbers, facts, and even straightforward descriptions of items. For our study, data can be arranged in the form of graphs, charts, or tables.

Given the data,

x           -5     -4     -3     -2      -1       0      1         2         3

f(x)         -6     -2     0       4      4       0     -2      -6      -10

the graph moves towards the negative side for negative values of x,

so from the data, we observed that,

if x tends to -∞ then f(x) will be -∞,

and the value of f(x) again moves towards the negative side for all positive values of x.

so  x tends to ∞ then f(x)  will again -∞.

Hence option D is correct.

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Answer:29

Step-by-step explanation: a right angle is 90 degrease so (90-32)divided by 2 =29

-

Answer:

29⁰

Step-by-step explanation:

2x⁰+ 32 ⁰= 90⁰

2x= 90⁰ - 328⁰

2x= 58⁰

x=29⁰

Answer:

201.7 m^3

Step-by-step explanation:

The formula for the volume of a right circular cone is:

V = (1/3) * π * r^2 * h

where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.

Given the height of 18 m and radius of 5.8 m, we can plug these values into the formula:

V = (1/3) * π * (5.8 m)^2 * 18 m

V = (1/3) * 3.14 * 33.64 * 18

V = (1/3) * 605.112

V = 201.704 m^3

Rounding to the nearest tenth of a cubic meter we get 201.7 m^3

So, the volume of a right circular cone that has a height of 18 m and a base with a radius of 5.8 m is 201.7 m^3.

The line segment that externally divides the locations ( 4, 5) and ( 6, 3 ) in the ratio 3 : 2 is at the point ( 6, 3).

An area or portion of a line with two endpoints is known as a line segment.

A line segment has a set length as opposed to a line.

Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment Symbol.

Example:

Let A = ( 6, 3 ) and B = ( 4, 5) be the two points, and let P = ( x, y ) be the necessary point that externally splits the line segment in the ratio of 3 : 2.

We have a division for external affairs.

x = 3 ( − 4 ) − 2 ( 6) /3 − 2

y = 3 ( 5 ) − 2 ( 3 ) / 3 − 2

⇒ x =  − 24

y = 9

Because of this, the necessary coordinates are ( 24, 9 ).

The Complete Question.

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The value of x is 14 and the angles of Q and R are 58 and 92 degrees respectively .

What is triangle ?

triangle can be defined in which it consists of three sides  , three angles and sum of three angles is always 180 degrees .

Given in the triangle,

we have to solve for x .

so ,

P = 30 degrees

Q = 4x+2 degrees

R = 8+6x degrees

In a triangle the sum of all angles is always 180 degrees

so ,

P+Q+R = 180

30+4x+2+8+6x = 180

10x + 40 = 180

10x = 180 - 40

10x = 140

x = 14

Q = 4*14+2

Q = 58 degrees

R = 8+6*14

R = 92 degrees.

Hence, the value of x is 14 and the angles of Q and R are 58 and 92 degrees respectively .

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Answer:

The perimeter of the square base is 12 cm, so the length of each side of the base is 12/4=3cm.

The volume of the pyramid can be found using the formula:

V = (1/3)Bh

where B is the area of the base and h is the height.

The area of the base is the length of one side squared, so B = 3^2 = 9.

So, the volume of the pyramid is:

V = (1/3) * 9 * 5 = 15 cubic centimeters.

They rented the small car $39/day for 3 days after they lost their insurance coupon

Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge against the risk of a contingent or uncertain loss.

Given here: The available car rents as

small car rental fee-( seats 4 passengers):$39/day

full car rental fee:$49/day

Insurance : $21/day

Now total cost = $75×3

                          =$225

Now insurance fee=$21×5

                               =$105

Thus the required sum before insurance =$120

Hence,  They rented the small car $39/day for 3 days after they lost their insurance coupon

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The object has been rotated to -180° from quadrant 3 to 1.

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given an object is in 3rd quadrant and rotated clockwise to 1st quadrant,

Rotating anticlockwise with the angle indicates that the angle is positive.

Rotating anticlockwise with an angle indicates that the angle is negative.

In the first quadrant, a figure is sketched.

When is turned 90 degrees (-270 degrees), the second quadrant contains its image.

Its image is located in the third quadrant if is turned 180 degrees (-180 degrees).

if turned by 270 degrees (-90 degrees), its picture will be in the fourth quadrant.

object is in 3rd quadrant and moved to1st quadrant clockwise, which is degree change is negative,

so it changed -180°.

Hence the degree change is -180°.

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Answer:

Julie's

Step-by-step explanation:

because she used 2 scoops of choclate and 4 scoops of vanilla

Answer: 4/15

Step-by-step explanation:

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function. Domain→ Function →Range. If there exists a function f: A →B such that every element of A is mapped to elements in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is given by 'b', where (a,b) ∈ R. The range of the function is the set of images. The domain and range of a function is denoted in general as follows: Domain(f) = {x ∈ R} and range(f)={f(x) : x ∈ domain(f)}.

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The value of p that makes the equation true is p = 1/24

An equation is a mathematical function that show the relationship between two variables.

Given the equation -3p + 1/8 = -1/4, we desire to find the value of p which will make the equation true.

So, to find the value of p which will make the equation true, we solve the equation for p.

So, we have that -3p + 1/8 = -1/4

-3p + 1/8 = -1/4

Subtracting 1/8 from both sides, we have that

-3p + 1/8 - 1/8 = 1/4 - 1/8

-3p + 0 = (2 - 1)/8

-3p = 1/8

Now, dividing both sides by 3, we have that

-3p = 1/8

p = 1/8 ÷ 3

p = 1/24

So, the value of p is p = 1/24

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The probability that 2 or fewer students in a class of 30 will be overweight, P(X < 2) is 0.33.

Probability is defined as the ratio of the possible outcomes to the total outcomes of an event. We have, 20% of children are considered overweight.

Total students in a class = 30

We have to determine the probability that 2 or fewer students in a class will be overweight. Using the exponential probability distribution,

P( X= x ) = me⁻ᵐˣ

where, m --> parameter

e --> special math constant and e = 2.73

Now, the probability for X is less than x

P( X < x ) = 1 - e⁻ᵐˣ

here, m = 0.20 , x = 2

The required probability, P(X < 2)

= 1 - e⁻⁽⁰·²⁰⁾²

= 1 - e⁻⁰·⁴⁰

= 1 - 0.670

= 0.33

So, required probability is 0.33.

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Common logarithms, also known as base 10 logarithms, are logarithms in which the base of the exponential function is 10.

1. Common logarithms (base 10)

2. Natural logarithms (base e)

3. Binary logarithms (base 2)

Common logarithms, also known as base 10 logarithms, are logarithms in which the base of the exponential function is 10. This means that the logarithm of a number is the exponent to which 10 must be raised to produce that number. Natural logarithms, also known as base e logarithms, are logarithms in which the base of the exponential function is e, which is an irrational number approximately equal to 2.718. This means that the logarithm of a number is the exponent to which e must be raised to produce that number. Binary logarithms, also known as base 2 logarithms, are logarithms in which the base of the exponential function is 2. This means that the logarithm of a number is the exponent to which 2 must be raised to produce that number. All three types of logarithms are used in mathematics, science, and engineering to simplify complicated calculations.

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The ordered pairs are {(0, 2), (2, 6), (4, 10)}, option A is correct.

A set of ordered pairs (x, y) that have x in set A and y in set B make up a function f from set A to set B.

An ordered pair in f is (x, y).

where there is precisely one y ∈ B, for every x ∈ A.

Given that an arrow goes from 0 to 2, 2 to 6, and 4 to 10,

to write the ordered pairs,

the relation of the arrow is 0 to 2, 2 to 6, and 4 to 10

the pairs are (0, 2)

(2, 6)

(4, 10)

pairs are  {(0, 2), (2, 6), (4, 10)}

Hence option A is correct.

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Solving a formula for a variable means rewriting the formula so that the variable is isolated on one side of the equation. This is useful in algebraic equations when trying to solve for a certain variable in order to find the value of that variable.

This means that all of the other terms in the equation will be on the opposite side of the equation, and the variable will be alone with no other terms. r example, if you have the equation 2x + 5 = 15, you would want to solve for x. To do this, you would need to move the 5 to the other side of the equation, and then divide both sides by 2. This would leave you with x = 5, which is the solution for the equation.

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