G is inversely proportional to the square of a. If a = -3 when g = 9, find two values for a, which will make g equal 25.

The scale factor from the map to the actual hiking trails can be found to be 50, 000.

To find the scale factor, we first need to look at the scale which is :

3 cm : 1. 5 km

This scale needs to have the same units of measurement so we can convert the  1.5 km to centimeters.

This becomes :

= 1. 5 x 100, 000 cm per km

= 150, 000 cm

The scale factor for the map to the actual hiking trails is :

= 150, 000  / 3

= 50, 000

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Answer:

Step-by-step explanation:

8×-4

Answer:

3,200 kK

Step-by-step explanation:

Typically, only about 10% of the energy available at one trophic level is transferred to the next trophic level. This is known as the 10% rule, and it means that herbivores will only be able to incorporate about 10% of the energy available in the big bluestem grasses.

Therefore:

32,000 kJ x 0.10 = 3,200 kJ

B' is 11 right and 3 down from B.

A shape is translated when it is moved up, down, left, or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

Here, we have

Given: Point B​′​​(6,−5) is the image of B(−5,−2) under a translation.

The translation is from (-5, -2) to (6, -5). That is the values (h, k) was added to the coordinates where ...

-5 +h = 6

h = 11 . . . . . . . a translation of 11 to the right

and

-2 +k = -5

k = -3 . . . . . . . a translation of -3 upward is a translation of 3 downward.

Hence, B' is 11 units to the right and 3 units down from B.

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Stacy's age is 3 less than 4 times what her age was 6 years ago. The  algebraic equation to express this is x = 4(x - 6) - 3. A pair of pants was originally selling for $135, and discounted by 25% before an 9% tax was applied. The cost of the item after the discount and tax is $110.36.

1) Let's begin by defining a variable for Stacy's age. We'll use x to represent her current age.
According to the question, Stacy's age is 3 less than 4 times what her age was 6 years ago. We can write this as an algebraic equation:
x = 4(x - 6) - 3
Now, we'll solve for x by simplifying and isolating the variable on one side of the equation:
x = 4x - 24 - 3
x = 4x - 27
27 = 3x
x = 9
So, Stacy's current age is 9.

2) To find the cost of the item after the discount and tax, we'll first calculate the discount amount and then the tax amount.
The discount amount is 25% of the original price, so we'll multiply the original price by 0.25:
$135 * 0.25 = $33.75
Now, we'll subtract the discount amount from the original price to find the discounted price:
$135 - $33.75 = $101.25
Next, we'll calculate the tax amount by multiplying the discounted price by the tax rate of 9%:
$101.25 * 0.09 = $9.11
Finally, we'll add the tax amount to the discounted price to find the final cost of the item:
$101.25 + $9.11 = $110.36
So, the cost of the item after the discount and tax is $110.36.

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The 99.5% confidence interval for the population mean μ is (23.140, 38.260), accurate to 3 decimal places.

The 99.5% confidence interval for a sample of size 54 with a mean of 30.7 and a standard deviation of 19.8 can be calculated as follows:

1. Find the critical value for the 99.5% confidence level using a z-table or a t-table. For a 99.5% confidence level, the critical value is 2.807.
2. Calculate the standard error of the mean by dividing the standard deviation by the square root of the sample size:
SE = 19.8 / √54 = 2.694
3. Multiply the critical value by the standard error to find the margin of error:
ME = 2.807 * 2.694 = 7.560
4. Subtract the margin of error from the sample mean to find the lower bound of the confidence interval:
LB = 30.7 - 7.560 = 23.140
5. Add the margin of error to the sample mean to find the upper bound of the confidence interval:
UB = 30.7 + 7.560 = 38.260
6. Write the confidence interval as an open-interval using parentheses:
(23.140, 38.260)

Therefore, the 99.5% confidence interval for the population mean μ is (23.140, 38.260), accurate to 3 decimal places.

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a. The variables for this problem is x + y = 140

b. a system of equations that represents this situation is 20x + 10y = 2270

An attribute οr phenοmenοn that may be quantified as a variable and that changes in value οver time. As a result, a variable is a quantity that can be calculated and is subject tο change.

Bοth discrete and cοntinuοus variables are pοssible.

a. Tο sοlve this questiοn we will need twο variables x and y.

Let number οf adults be x and number οf kids be y then we get,

x + y = 140

b. Tο write a system fοr sοlving this questiοn we are given the price οf tickets.

20x + 10y = 2270

and, x + y = 140

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Laura's net proceeds were -$94.43. This means that she lost $94.43 on the transaction.

What is the commission?

A commission is a fee or percentage of a sale that is paid to a person or organization for their services in facilitating or completing a transaction. Commissions are commonly used in sales or business settings, where an individual or organization acts as a middleman between a buyer and a seller.

Laura's total cost for buying the stock was:

55 shares x $3.50/share = $192.50

Her broker's commission was 1% of $192.50, which is:

$192.50 x 0.01 = $1.93

So, her total cost including commission was:

$192.50 + $1.93 = $194.43

Her total revenue from selling the stock was:

55 shares x $2/share = $110

Her broker's fee for selling the stock was $10.

So, her total cost for selling the stock was:

$10

Therefore, Laura's net proceeds were:

$110 - $194.43 - $10 = -$94.43

This means that Laura lost money on the transaction.

Hence, Laura's net proceeds were -$94.43. This means that she lost $94.43 on the transaction.

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Answer:

Without more information about the diagram, it is impossible to determine the term that describes GI. The terms median, angle bisector, perpendicular bisector, and altitude are all related to different types of lines and segments in triangles. Depending on the context and information given in the diagram, GI could be any of these.

Step-by-step explanation:

wag na pa delete nito na bweweset ako ang bob0 ng admin

The perimeter of the triangle PQR is 309 units

The figure represented in the question is a triangle

Given that the triangle side lengths are 92, 107 and 110

The total length of all sides of the triangle is equal to the perimeter of the triangle.

So, we have

Perimeter = 92 + 107 + 110

Evalyate the sum

Perimeter = 309

Hence, the perimeter is 309 units

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The proportion of observations in a standard Normal distribution that satisfies each of the given statements are:

1) P(z > -1.66) = 0.95154

2) P(-1.66 < z <2.85​) = 0.94936

Z table or z-score table is defined as a mathematical table that provides the values of cumulative density function for standard normal variates. It is used to determine the probability of a standard normal variate lying in a given interval.

We have to find the proportion of observations from a standard normal distribution that has a z-score between -1.66 and 2.85.

1) z > -1.66

From normal probability distribution table, we have that:

P(z > -1.66) = 0.95154

2) -1.66 < z <2.85​

From normal probability distribution table, we have that:

P(-1.66 < z <2.85​) = 0.94936

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The smallest three positive solutions are 0.31, 1.88, and 3.45, accurate to at least two decimal places.

To solve 6 cos(4x) = 2 for the smallest three positive solutions, we need to first isolate the cosine function:
6 cos(4x) = 2
cos(4x) = 2/6
cos(4x) = 1/3
Next, we can use the inverse cosine function to find the angle:
4x = 1.23 (rounded to two decimal places)
Now we can solve for x:
x = 1.23/4
x = 0.31 (rounded to two decimal places)
Since cosine is a periodic function, we can find the next two positive solutions by adding the period of the function (2π) to the previous solution:
x = 0.31 + (2π/4)
x = 1.88 (rounded to two decimal places)
x = 1.88 + (2π/4)
x = 3.45 (rounded to two decimal places)
The final answer is: 0.31, 1.88, 3.45

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The smaller solution for the equation is - 1 and the larger solution is 2/14.

The values of the unknown variable x that fulfil the quadratic equation are the solutions to the problem. Quadratic equations' roots or zeros are known as these solutions. The answers to the given problem are the roots of any polynomial.

The given equation is:

14x² + 12x - 2 = 0

Splitting the middle term:

14x² + 14x - 2x - 2 = 0

14x (x + 1) - 2(x + 1) = 0

(14x - 2) (x + 1) = 0

x = 2/14 and x = -1

Hence, the smaller solution for the equation is - 1 and the larger solution is 2/14.

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a) The annual simple interest rate for this transaction is 16%.

b) Wolfgang paid $3,000 for the loan.

The annual simple interest rate is the percentage of the principal amount that is charged as interest for one year. It can be calculated using the formula I = P*R*T, where I is the interest, P is the principal amount, R is the annual interest rate, and T is the time in years.

(a) In this case, the principal amount is $2,500, the interest is $2,700 - $2,500 = $200, and the time is 180/360 = 0.5 years. We can plug these values into the formula and solve for R:

$200 = $2,500*R*0.5

$200 = $1,250*R

R = $200/$1,250

R = 0.16

The annual simple interest rate for this transaction is 16%.

(b) To find out how much Wolfgang paid for the loan, we can use the same formula and solve for P. The interest is $2,700 - $2,500 = $200, the annual interest rate is 20%, and the time is 120/360 = 0.3333 years:

$200 = P*0.20*0.3333

$200 = 0.06666*P

P = $200/0.06666

P = $3,000

Wolfgang paid $3,000 for the loan.

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The inequality representing s is: s ≥ 50.

An inequality is a mathematical statement that compares the values of two expressions using inequality symbols such as <, >, ≤, or ≥.

For example, 3x + 2 < 8 is an inequality that means "three times x plus two is less than eight."

The minimum number of glasses needed is 637 and there are already 343 glasses, so Mason needs to buy (637 - 343) = 294 more glasses. Since each set contains 6 glasses, the number of sets Mason should buy is s = 294/6 = 49.

However, since s represents the number of sets he should buy, we need to round up to the next integer since he can't buy a fraction of a set.

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The common ratio is equal to 3.

The tenth term of this geometric sequence is -78,732.

The explicit-formula of this geometric sequence is aₙ = -4(3)ⁿ⁻¹.

The three terms in the sequence after the last one given are -324, -972, and -2916.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -12/-4

Common ratio, r = 3.

For the explicit formula, we have:

aₙ = a₁rⁿ⁻¹ = -4(3)ⁿ⁻¹

Now, we can determine three terms in the sequence after the last one given;

a₅ = a₁r⁵⁻¹ = -4(3)⁴ = -324.

a₆ = a₁r⁶⁻¹ = -4(3)⁵ = -972.

a₇ = a₁r⁷⁻¹ = -4(3)⁶ = -2916.

f(10) = a₁₀ = a₁r¹⁰⁻¹ = -4(3)⁹ = -78,732.

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The exponential function is y = 5*(∛2)^x and the value after 10 days is 50.4

Here we can see an exponential function of the form y = a*b^x

First, notice that it passes through (0, 5), then:

5 = a*b^0 = a

5 = a

So we got the initial value, so we can write the equaton like:

y = 5*b^x

And now we need to find the value of b.

We also can see that it passes through (3, 10), then:

10 = 5*b^3

10/5 = b^3

2 = b^3

∛2 = b

So the function is:

y = 5*(∛2)^x

b) The value after 10 days is what wet when we evaluate the function above in x = 10, then we will get:

y = 5*(∛2)^10  = 50.4

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Answer:

3/700

Step-by-step explanation:

hope this helps :))

Statistically significant means that the relationship between two variables is likely to be real and not due to chance. If the p-value is lower than the predetermined threshold, usually 0.05, then the correlation is said to be statistically significant.

When a correlation between two variables is said to be statistically significant, it means that the relationship between the two variables is not due to chance or random error. In other words, the relationship is likely to be a real one and not just a coincidence.

Statistical significance is often determined by calculating a p-value, which is the probability of observing a relationship as strong as the one observed if there was no actual relationship between the variables. If the p-value is less than a predetermined threshold, usually 0.05, the relationship is considered to be statistically significant. This means that there is less than a 5% chance that the relationship observed is due to random error.

Therefore, It is usually determined by calculating a p-value, which measures the probability that the relationship between two variables is due to random chance.

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Answer: 8 cubic inches

Step-by-step explanation:

Answer:

Volume of cube = length x width x height

V = 2x2x2

V = 8

Therefore, the volume of the box is 8 inches long.

According to the properties of quadrilaterals:

If a shape is a Parallelogram than it is a Square: False.

If a shape is a Square than it is a Rectangle: True.

If a shape is a Rhombus than it is a Quadrilateral: True.

If a shape is a Trapezoid than it is a Parallelogram: False.

If a shape is a Quadrilateral than it is a Rectangle: False.

Explain about quadrilaterals ?

Quadrilaterals are closed two-dimensional shapes with four straight sides and four angles. The word "quadrilateral" comes from the Latin words "quadric" which means "four" and "latus" which means "side". Some common examples of quadrilaterals include squares, rectangles, parallelograms, rhombuses, and trapezoids.

Each type of quadrilateral has its own unique set of properties and characteristics. For example, a rectangle has four right angles and opposite sides that are parallel and congruent. A parallelogram has opposite sides that are parallel and congruent, and opposite angles that are congruent. A rhombus has four congruent sides and opposite angles that are congruent.

According to the question:
Here are the answers to the true or false questions:

1. If a shape is a Parallelogram than it is a Square.

False. A parallelogram can have any angle measure as long as the opposite sides are parallel. A square is a specific type of parallelogram with four congruent sides and four right angles.

2. If a shape is a Square than it is a Rectangle.

True. A square is a special type of rectangle where all four sides are congruent.

3. If a shape is a Rhombus than it is a Quadrilateral.

True. A rhombus is a type of quadrilateral with four congruent sides.

4. If a shape is a Trapezoid than it is a Parallelogram.

False. A trapezoid has only one pair of parallel sides, while a parallelogram has two pairs of parallel sides.

5. If a shape is a Quadrilateral than it is a Rectangle.

False. A quadrilateral is a broad category of four-sided shapes that includes rectangles, but it also includes many other types of shapes, such as trapezoids, parallelograms, rhombuses, and kites.

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We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:

8 individuals per boat times 1,254 passengers is 156.75 boats.

We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.

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The maximum and minimum values for the corn and grain constraints for which the current constraint value does not change are 0.15 and 0.20.

a) To develop the model in Excel, define the decision variables and objective function as follows:

Let x1, x2, x3, and x4 represent the amount of each feed in thousands of kilograms. The objective function is to minimize the total cost, given by:

Minimize: 0.15x1 + 0.2x2 + 0.18x3 + 0.25x4

Subject to:

x1 + x2 + x3 + x4 = 8  (total feed = 8,000 kg)

0.1x1 + 0.15x2 + 0.2x3 + 0.2x4 ≥ 0.8  (minimum 10% corn)

0.2x1 + 0.3x2 + 0.25x3 + 0.25x4 ≥ 2  (minimum 25% grain)

0.2x1 + 0.2x2 + 0.2x3 + 0.3x4 ≥ 1.6  (minimum 20% minerals)

x1, x2, x3, x4 ≥ 0 (non-negativity constraints)

b) Solving the problem using Excel Solver gives the following least-cost feed mix: x1 = 5, x2 = 0, x3 = 3, and x4 = 0. This mix will cost $2.35 per kilogram, or $18,800 in total.

c) The nutritional elements with a surplus are corn and grain, in amounts of 0.5 and 0.2 thousand kilograms, respectively.

d)i) The objective function's value would decrease to $17,400 if Feed 3 is forced to be in the solution.

ii) The shadow prices for the grain and minerals constraints mean the maximum amount of extra cost per kilogram increase in the corresponding constraint value. The maximum and minimum values for the corn and grain constraints for which the current constraint value does not change are 0.15 and 0.20, respectively.

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For the system of linear equations

[tex]\[ \begin{aligned} h x_{1}-3 x_{2}-6 x_{3} & =-3 \\ x_{1}+3 x_{2}+x_{3} & =1 \\ -4 x_{1}-9 x_{2}+2 x_{3} & =-1 \end{aligned} \][/tex],  

the value of [tex]\( h \)[/tex] is [tex](15/4)x_2 + (30/4)x_3[/tex].

The value of h can be determined by using the elimination method to solve the system of equations.

First, multiply the second equation by 4 and the third equation by -1 to eliminate the x1 term: [tex]\[ \begin{aligned} 4 h x_{1}-12 x_{2}-24 x_{3} & =-12 \\ -4 x_{1}-12 x_{2}-4 x_{3} & =-4 \\ 4 x_{1}+9 x_{2}-2 x_{3} & =1 \end{aligned} \][/tex]

Next, add the second and third equations to the first equation: [tex]\[ \begin{aligned} 4 h x_{1}-15 x_{2}-30 x_{3} & =-15 \\ \end{aligned} \][/tex]

Now, divide the equation by 4 to solve for h: [tex]\[ \begin{aligned} h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =-\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4} & =0 \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4}-\frac{15}{4} & =-\frac{15}{4}+\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =0 \\ h & =\frac{15}{4} x_{2}+\frac{30}{4} x_{3} \end{aligned} \][/tex]

Therefore, the value of h is dependent on the values of x2 and x3 and can be expressed as h = [tex](15/4)x_2 + (30/4)x_3[/tex].

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Answer:

400

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 400 because you have to solve from left to right because of PEMDAS. So first you mutlipy 5x8 which is 40, and then you do 40x10 which is 400.

Answer:

66y + 33

Step-by-step explanation:

Open up the parenthesis, then simplify

-11 (-2y - 3 - 4y)

22y + 33 + 44y

66y + 33

If you need it simplified, take 33 common

33 (2y + 1)

Answer:

66y+33

Step-by-step explanation:

22y+33+44y

66y+33

The first 3 iterates of the function f(x) = 3x when x0=2 are,

⇒ 6, 18, 54

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The function is,

⇒ f (x) = 3x

At x₀ = 2

Now, We get;

The first iterate is,

⇒ f (x₁) = 3x₀ = 3 × 2 = 6

Second iterate is,

⇒ f (x₂) = 3x₁ = 3 x 6 = 18

Third iterate is,

⇒ f (x₃) = 3x₂ = 3 x 18 = 54

Thus, The first 3 iterates of the function f(x) = 3x when x0=2 are,

⇒ 6, 18, 54

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Answer:

  3-4-5 right triangle is scalene

Step-by-step explanation:

You want to show the triangle defined by points P(3,2),Q(6,2) and R(6,6) is a scalene triangle.

We observe that points P and Q have the same y-coordinate, so lie on the horizontal line y=2. The length PQ is 6 -3 = 3 units.

Points Q and R have the same x-coordinate, so lie on the vertical line x=6. The length QR is 6 -2 = 4 units.

These legs are different lengths and are at right angles to each other. The third leg, the hypotenuse, will be longer than either of them.

The triangle's sides are unequal, so the triangle is a scalene triangle.

the solution is: population in 2015 will be 40,115,896

The exponential function is an illustration of a mathematical function that may be used to identify if something is increasing or decreasing exponentially. An exponential function employs exponents, as suggested by its name.

But, you should be aware that an exponential function does not have a constant base and a variable exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

the median population change in California from 2000 to 2009 in percentage terms.

Given that there are 9 years, add up all the percentages, and then divide by 9.

1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9 = 1.3567%

From 2009 through 2015, there were six different time periods.

In the future, 37,000,000 x (1 + 0.013567) x 6 = 40,115,896.06

Hence, the solution is: population in 2015 will be 40,115,896

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There are 70 ways to assign 4 runners from a group of 8 to run the legs of the race.

Permutation and combination are two fundamental concepts in mathematics that deal with counting and arranging objects.

This is a combination problem. The formula for calculating the number of combinations of r items from a set of n items is:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n, or the product of all positive integers up to and including n.

In this problem, we want to choose 4 runners from a group of 8, without regard to order. So we can use the combination formula as follows:

8C4 = 8! / (4! * (8-4)!)

= (8765) / (4321)

= 70

Therefore, there are 70 ways to assign 4 runners from a group of 8 to run the legs of the race.

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