500 soldiers in a fort had enough food for 30 days if 125 more soldiers joined them then for how many days will the food last​

A total of 30 golf balls are there in the bag that weighs 1110 grams.

A total of 69 golf balls weights 2553 grams in a bag.

It is asked that how much golf balls does make 1110 grams of weight.

Let us say that the weight of one ball is X.

So, Using unitary method,

We can write,

69 times mass of one golf ball = 2553 grams.

69X = 2553

X = 2553/69

X = 37 grams.

Hence, the weight of one ball is 37 grams.

Now, let us say that Y balls weights 1110 grams,

So, we can write,

Y time weight of one ball = 1110

37Y = 1110

Y = 1110/37

Y = 30.

Hence, 30 golf balls will weight 1110 grams.

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Answer:

30

Step-by-step explanation:

Prior to placing an order to buy ABCD stock at a lower price, the investment adviser must conduct thorough research and analysis, set a target price, and determine an appropriate entry point for the purchase.

The investment adviser's primary responsibility is to act in the best interest of their client and make informed investment decisions. In this case, where the adviser believes ABCD stock is appropriate only if the price falls to $35 per share, several steps need to be taken before placing an order.

Firstly, the adviser should conduct comprehensive research on ABCD stock to understand its historical performance, financial health, industry trends, and any relevant news or events that might impact its future prospects. This research will help validate the adviser's belief that the stock is worth considering at a lower price.

Secondly, the adviser should establish a target price of $35 per share based on their analysis and the client's investment objectives. This target price serves as a reference point and provides a clear criterion for initiating the purchase.

Lastly, the adviser needs to identify an appropriate entry point for the purchase. This involves monitoring the stock's price movements and market conditions closely. The adviser may choose to set a limit order at $35 per share or implement a strategy to take advantage of potential price declines, such as dollar-cost averaging.

By following these steps, the investment adviser ensures that they have thoroughly evaluated the investment opportunity and have a plan in place before placing an order to buy ABCD stock for the client's account.

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Answer:

(x,y)=(-10/3+8r/3,4r t 1)

Step-by-step explanation:

乁( •_• )ㄏMe da wuebo escribir todo la explicación

The most accurate statement regarding the risk tolerance parameter is:

The risk tolerance parameter influences the relationship between a payoff and the utility of the payoff.

The risk tolerance parameter is a measure of an individual's or firm's willingness to accept risk in exchange for potential reward. It influences the utility function, which maps payoffs to the utility they provide.

A higher risk tolerance parameter implies a greater willingness to accept risk, and a lower risk tolerance parameter implies a lesser willingness to accept risk. The parameter can be any positive number, not just between 0 and 1. Statements 1, 2, and 3 are incorrect.

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The statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:

A. measure of angle FEB + measure of angle HGD = 180°

By definition, supplementary angles are two angles that have a sum of 180 degrees when added together, that is, one is a supplement of the other.

Given the image below, we know the following:

Since angle FEA is supplementary to angle FEA would be congruent to angle HGC, and angle HGD is congruent to angle FEB. This is because, the supplement of angle

angle FEA + angle FEB - angle FEA + angle HGD = 180° - 180°. Therefore,

angle FEB = angle HGD.

In summary, from the options given, the statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:

A. measure of angle FEB + measure of angle HGD = 180°

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For a single game, the mean and the standard deviation of the number of hits is given as follows:

For 25 games, the mean and the standard deviation are:

For 50 games, the mean and the standard deviation are:

This shows that as the number of trials increase, the standard error reduces.

The mean is given by the sum of each outcome multiplied by it's respective probability, hence:

E(X) = 0 x 0.1666 + 1 x 0.3275 + 2 x 0.2875 + 3 x 0.1489 + 4 x 0.0382 + 5 x 0.0313 = 1.659 hits.

The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values, hence:

S(X) = sqrt((0-1.659)² x 0.1666 + (1-1.659)² x 0.3275 + (2-1.659)² x 0.2875 + (3-1.659)² x 0.1489 + (4-1.659)² x 0.0382 + (5-1.659)² x 0.0313) = 1.209.

For the repetition of n experiments, we have that the mean remains constant, while the standard deviation is given as follows:

s = S(X)/sqrt(n).

Meaning that it is divided by the square root of the sample size.

Hence, for 25 games, the standard deviation is:

S(X) = 1.209/sqrt(25) = 0.242.

For 50 games, the standard deviation is:

S(X) = 1.209/sqrt(50) = 0.171.

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Answer:

24

Step-by-step explanation:

Two negatives make a positive.

11 + 13 = 24

Answer:

24

Step-by-step explanation:

= 11 - ( -13 )

According to sign conventions, - ( - ) = +

= 11 + 13

= 24

\(\rule[225]{225}{2}\)

Hope this helped!

do you need the equations solved? i'll answer in the comments after you lmk what i need to do with the equations lol

Usando conceptos de funciones lineales, se encuentra que hizo 5 cortes.

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

Una funcion lineale tiene el seguiente formato:

\(y(x) = ax + b\)

En que:

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

Entonces, la funcion de su recibimiento y, como funcion de su numero de cortes x, es da por:

\(y(x) = 25 + 50x\)

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

Entonces, el numero de cortes es:

\(y(x) = 25 + 50x\)

\(25 + 50x = 275\)

\(50x = 250\)

\(x = \frac{250}{50}\)

\(x = 5\)

Realizó 5 cortes.

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Queremos encontrar y resolver una ecuación lineal que representa el problema dado.

Veremos que el miércoles Rocío realizó 5 cortes.

La información que se nos da es:

Rocío recive $50 por corte.

Adicionalmente, recibe $25 por día (esto se paga una sola vez)

Entonces si Rocío realiza x cortes, la cantidad de dinero que recibirá es:

C(x) = $25 + $50*x

Ahora sabemos que un dado día ella recibe $275, queremos ver cuantos cortes realizo ese día, entonces debemos resolver la ecuación lineal:

C(x) = $275 = $25 + $50*x

         $275 - $25 = $50*x

         $250 = $50*x

         $250/$50 = x = 5

Así podemos concluir que Rocío realizó 5 cortes.

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Answer:

No

Step-by-step explanation:

The angles of a triangle have to add up to 180°.

Answer:

no

Step-by-step explanation:

the interior of the triangle cannot be over 180 degrees added up this exceeds 180

To solve for the Marshallian demands x1(p1, p2, m) and x2(p1, p2, m) in the consumer problem with utility function U(x1, x2) = min{x1, ax2}, we need to maximize the utility subject to the budget constraint p1x1 + p2x2 ≤ m, where p1 and p2 are the prices of goods 1 and 2 respectively, and m is the consumer's income.

To find the Marshallian demands, we need to solve the consumer's optimization problem. The objective is to maximize the utility function U(x1, x2) = min{x1, ax2} subject to the budget constraint p1x1 + p2x2 ≤ m.

The first step is to set up the Lagrangian function:

L(x1, x2, λ) = min{x1, ax2} + λ(m - p1x1 - p2x2)

Next, we take the first-order conditions by differentiating the Lagrangian with respect to x1, x2, and λ, and setting the derivatives equal to zero. This will give us the equations for the optimal values of x1, x2, and the Lagrange multiplier λ.

By solving these equations, we can find the specific values for x1(p1, p2, m) and x2(p1, p2, m) that maximize the utility function while satisfying the budget constraint. The resulting demands will depend on the prices (p1, p2) and the consumer's income (m).

Note that the specific calculations involved in solving the optimization problem can be quite involved and may require further mathematical manipulation.

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Answer: the answer might be D. The slopes of the two triangles are the same

Step-by-step explanation:

The estimate of the given fraction, 15 9/10 + 5 3/7, is 21

From the question, we are to estimate the answer of the given expression

From the given information, we have a fraction expression.

The given expression is

15 9/10 + 5 3/7

To estimate the answer, we will add the fractions

First,

Convert the fractions from mixed to improper fractions

159/10 + 38/7

Find the LCM of 10 and 7

LCM of 10 and 7 = 70

Using the LCM, add the fractions

[7(159) + 10(38)]/70

(1113 + 380)/70

1493/70

= 21 23/70

≈ 21

Hence,

The estimate is 21

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aₙ = 0.20aₙ₋₁ + 200 is the recursive formula for the above sequence.

Therefore, choice A is the right one.

Given:

A holiday tree farm is owned by Mahek.

Currently, the site has 800 trees.

200 saplings are planted together with the 20% of the trees that are harvested and sold each year.

a₁ = 800

The recursive formula is,

aₙ = 0.20aₙ₋₁ + 200

Hence, the correct formula is aₙ = 0.20aₙ₋₁ + 200

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Step-by-step explanation:

The given inequalities are :

\(y\le x^{2}-1\ .....(1)\)

And

\(x>y^{2}-3\ .....(2)\)

We need to draw the graphs for inequalities (1) and (2).

Put the value of y from (1) in (2).

\(x>(x^2-1)^{2}-3\)

The attached figure shows the required graph.

The unshaded portion of the graph represent the solution.

y ≤ x2 – 1 and x > y2 – 3

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

\(y\leq x^2-1\)
and \(x < y^2-3\)
putting y in second equation
\(x < \left(\left(x^{2}-1\right)^{2}-3\right)\)
now plotting the graph of the equation attached below

Thus The required graph represent the solution is unshaded portion of the graph

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We are increasing every professor's salary by 4000, let this new salary be Yi for every professor then mean of new salary Y will be

Y = 1/n∑Yi

Y  = 1/n∑(Xi + 4000)

Y  = 1/n(∑Xi + ∑4000/n)

Y  = X + 4000

Median Xm is the middle most value of the Professor's old salary, since new salary is

            Yi = Xi + 4000

then new median salary Ym will be

            Ym = Xm + 4000

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Answer:

Step-by-step explanation:The mean and Median salary would increase by $4,000.

Let sum of the salaries be n1+n2+n3+.......... +n30

   Mean = sum of observation / no. of observation

Thus,

   Initial mean, M1 = n1+n2+n3+.......... +n30 / 30

When $4,000 is added to every salary 4000 is added 30 times to the sum.

Thus,

  New mean, M2 = n1+n2+n3+.......... +n30 +( 4000 * 30)

                                                30

                           = M1 + ( 4000 * 30)

                                              30

  Thus,         M2 = M1+ 4000

Therefore, The mean salary increase by $4,000.

We know Median of even number of observation =  [(n/2)th term + ((n/2) + 1)th term]/2

Here n/2th term is n15 and (n/2 +1)th term is n16

Thus,

    Initial Median, Median 1 = n15 + n16  

                                                     2

When $4,000 is increased in each salary

    New Median, Median 2 = n15 + 4000 + n16 + 4000

                                                                 2

                                         = Median 1 + 2 * 4000

                                                                    2

Thus,                  Median 2= Median 1 + 4000

Therefore, The median salary increases by $4,000

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The value of x shown in the right angled triangle is 15.9 units

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Pythagoras theorem shows the relationship for the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, substituting:

17² = x² + 6²

x² = 17² - 6²

x² = 253

x = 15.9 units

The value of x is 15.9 units

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part a.   the total bus fare cost for Mrs Themba's family per week is R337.

part b. The cost per bus trip per child is found to be around R9.50.

Cost is described as an amount that has to be paid or spent to buy or obtain something.

The cost of a weekly bus pass from Blue Downs to Rondebosch =  R109.

We then find the , the total cost per week for Mrs. Theba's family

1 x R109+ 2 x R114  = R337

part b.

The cost of a weekly bus pass from Bellville to Cape Town =  R95.

We find the cost per bus trip per child as:

R95 /  10 = R9.50

So in conclusion,  the cost per bus trip per child is R9.50.

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Answer: A

Step-by-step explanation:

Gradual, long-term movement in time-series values is called temporal variation. Therefore, the correct option is (a) temporal variation.

Temporal variation is one of the components of a time series, along with seasonal variation, cyclical movement, and irregular or random variation. Temporal variation refers to the long-term trend or pattern of movement in the time series, which can be increasing, decreasing, or remaining constant over time. It is often caused by underlying factors such as population growth, economic changes, or technological advancements.

Cyclical movement refers to the regular, repeating up and down patterns in the time series, which are usually longer than a year and can be caused by factors such as business cycles or political cycles. Exponential smoothing and linear regression are statistical methods used to forecast or model time series data, but they do not describe the components of the time series themselves.

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The area of the water's surface is approximately 981.25 square units.

Since the water depth is 10, the water fills up half of the hemispheric bowl. Therefore, we need to find the surface area of a circle with radius 25 (the base of the hemisphere) and divide it by 2.

The surface area of a circle with radius r is given by A = πr^2. So, the surface area of the circle with radius 25 is:

A = π(25)^2 = 625π

Dividing by 2, we get

625π/2

So the surface area of the water's surface is 625π/2 square units.

Approximating the value of π as 3.14, we get:

625π/2 ≈ 625(3.14)/2 ≈ 981.25

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The length of the curve is 2sqrt(10).

The length of the curve given by r(t) = (t, 3sin(t), 3cos(t)) for -1 < t < 1 is given by the formula:

L = ∫_a^b |r'(t)| dt

where r'(t) is the derivative of r(t) with respect to t, and |r'(t)| is the magnitude of the derivative.

We have:

r'(t) = (1, 3cos(t), -3sin(t))

|r'(t)| = sqrt(1^2 + (3cos(t))^2 + (-3sin(t))^2) = sqrt(1 + 9cos^2(t) + 9sin^2(t)) = sqrt(10)

So, the length of the curve is:

L = ∫_{-1}^1 |r'(t)| dt = ∫_{-1}^1 sqrt(10) dt = sqrt(10) * ∫_{-1}^1 dt = 2sqrt(10).

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When rotated about its center, a regular hexagon has 6 rotational symmetries. in addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

When a regular hexagon is rotated about its center, it has 6 rotational symmetries, one for each angle of 60 degrees.

In addition to rotational symmetry, a regular hexagon also has 6 lines of reflectional symmetry. Each line of symmetry passes through the center of the hexagon and two opposite vertices, dividing the hexagon into two congruent halves.

Hence, when rotated about its center, a regular hexagon has 6 rotational symmetries. in addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

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The ordered pair that lies on the inverse of the function is (-1, -3)

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

g(x)=^3√x+2

Rewrite as

g(x) = ∛(x + 2)

Next, we test the options

Set x = -3

So, we have the following representation

g(-3) = ∛(-3 + 2)

Evaluate the expression

g(-3) = -1

As an ordered pair, we have (-1, -3)

So, the ordered pair of teh inverse is (-1, -3)

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Answer: -1,-3

Step-by-step explanation:

To find the distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, we need to consider the ranges of numbers that can appear in each column.

The first column can have any 5 numbers from the set 1-15. There are 15 numbers in this range, so there are "15 choose 5" possibilities for the numbers in the first column.

The second column can have any 5 numbers from the set 16-30. Again, there are 15 numbers in this range, so there are "15 choose 5" possibilities for the numbers in the second column.

The third column has a Wild square in the middle, so we need to skip it and consider the remaining 4 squares. The numbers in the third column can come from the set 31-45, which has 15 numbers. Therefore, there are "15 choose 4" possibilities for the numbers in the third column.

The fourth column can have any 5 numbers from the set 46-60, which has 15 numbers. So there are "15 choose 5" possibilities for the numbers in the fourth column.

The last column can have any 5 numbers from the set 61-75, which again has 15 numbers. So there are "15 choose 5" possibilities for the numbers in the last column.

To find the total number of distinct possibilities for the diagonal, we multiply the number of possibilities for each column together:

"15 choose 5" "15 choose 5"  "15 choose 4"  "15 choose 5"  "15 choose 5".

Evaluating this expression, we find:

(3003)  (3003)  (1365)  (3003)  (3003) = 13,601,464,112,541,695.

Therefore, there are 13,601,464,112,541,695 distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, in order.

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A situation can have more than one sample space when there are multiple possible outcomes or events that can occur. A sample space is a set of all possible outcomes of an experiment or situation.

For example, let's consider the situation of flipping a coin. The sample space for this situation can be defined as {heads, tails}. In this case, there are two possible outcomes: either the coin lands on heads or it lands on tails.

However, we can also consider a situation where we are interested in the number of times the coin lands on heads in three consecutive flips. In this case, the sample space would be {0, 1, 2, 3}. Each outcome represents the number of times the coin lands on heads in three flips. So, we can have zero heads, one head, two heads, or three heads.

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Answer: Use a calculator sorry for being toxic that’s just who I am

Step-by-step explanation:

Answer:

∠ VWU and ∠ VUW are correct

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ VUP is an exterior angle of the triangle, so

17x + 6 = 56 + 8x + 4

17x + 6 = 60 + 8x ( subtract 8x from both sides )

9x + 6 = 60 ( subtract 6 from both sides )

9x = 54 ( divide both sides by 9 )

x = 6

Then

∠ VWU = 8x + 4 = 8(6) + 4 = 48 + 4 = 52° ← correct

∠ VUP = 17x + 6 = 17(6) + 6 = 102 + 6 = 108°

∠ VUW = 180° - 108° ( adjacent angles sum to 180° )

∠ VUW = 72° ← correct

Answer:

1) \(10\sqrt{10\)

3) \(15\)

5) \(9\sqrt3\)

7) \(35\sqrt7\)

Step-by-step explanation:

We can simplify these values by factoring the value underneath the square root sign.

1) We can factor 1000 as:

\(1000 = 10 \cdot 10 \cdot 10\)

From this factorization, we can see that there is a pair of 10s. So, we can represent this as one 10 outside the square root.

\(\sqrt{1000}\)

\(= \sqrt{10 \cdot 10 \cdot 10}\)

\(= \boxed{10\sqrt{10}}\)

3) We can factor 225 as:

\(225 = 5 \cdot 5 \cdot 3 \cdot 3\)

We can see that there is a pair of 5s and a pair of 3s. So, we have one 5 and one 3 outside the square root.

\(\sqrt{225}\)

\(= \sqrt{5\cdot 5 \cdot 3 \cdot 3}\)

\(= 5 \cdot 3 \sqrt{1}\)

\(= \boxed{15}\)

5) We can factor 243 as:

\(243 = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\)

We can see that there are two pairs of 3s. So, there will be two 3s outside the square root.

\(\sqrt{243\)

\(= \sqrt{3 \cdot 3 \cdot3 \cdot 3\cdot 3\)

\(= 3 \cdot 3\sqrt3\)

\(=\boxed{9\sqrt3}\)

7) We can factor 175 as:

\(175 = 5 \cdot 5 \cdot 7\)

We can see that there is a pair of 5s. So, there will be one 5 outside the square root multiplied by the 7 that is already there.

\(7\sqrt{175\)

\(= 7\sqrt{ 5 \cdot 5 \cdot 7}\)

\(= 7 \cdot 5\sqrt7\)

\(= \boxed{35\sqrt7}\)