a farmer finds that if she plants 95 trees per acre, each tree will yield 80 bushels of fruit. she estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. how many trees should she plant per acre to maximize her harvest?

Answer:

Step-by-step explanation:

The probability that Steve chooses two different types of biscuits is 5/11 (or approximately 0.4545).

To calculate this, we need to consider the different combinations of two biscuits that Steve can take from the tin. There are two digestive biscuits, three chocolate biscuits, and seven ginger biscuits, so the total number of possible combinations is 12.

The number of combinations where he chooses two different types of biscuits is 5 (2 digestive and 1 chocolate, 2 digestive and 1 ginger, 1 chocolate and 1 ginger).

Therefore, the probability of choosing two different types of biscuits is 5/12, which is 0.4545.

Answer:

I think it's 3

Step-by-step explanation:

becuse if he has 12 biscuits and u take away 2 which is 10. then its says there are 3 chocolate but it might just be chocolate not a biscuit. then u take away 7 and u get 3.

The cost of each table is $110.

Given:

Total Amount spent = $900

Cost of bookshelf = $50

By dividing the entire amount paid by 70%, you may calculate the cost of the chair and desk.

Cost of chair and desk = 900 x 0.70 = $60

Now, subtract that cost from the total amount spent:

900 - 630 = $270 was spent on the rest three items.

Next, subtract the cost of the bookshelf:

270 - 50 = $220

The cost of two tables is $220.

So, the price of one table can be calculated by dividing this cost by 2:

220/2 = $110

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The total number of squares that can be formed with 4 of the 200 points as vertices is 39,600.

The equation for calculating the total number of squares that can be formed with 4 of the 200 points as vertices are:

Number of squares = (200 Choose 4) x (4!/2) = (200!/196! x 4!) x (4!/2)

Using the factorial notation, this simplifies to:

Number of squares = (200 x 199 x 198 x 197) x (2) / (4 x 3 x 2 x 1)

The number of squares = 39,600.

Solving the equation, the total number of squares that can be formed is 39,600.

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Answer:

3x + 2

Step-by-step explanation:

this is an algebraic equation.

Answer:

Step-by-step explanation:

3*x+2

The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.

The absolute value (or modulus) |x| of a real number x is the non-negative value of x without regard to its sign.

It is represented as |a|, which defines the magnitude of any integer ‘a’.

it defines removing any negative sign in front of a number and thinking of all numbers as positive.

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.

When x itself is negative (x<0), then its absolute value is necessarily positive

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Answer:

x-intercept is (-16,0) and y-intercept is (0,2)

Step-by-step explanation:

To find the x-intercept of the equation 1/2x = -4y - 8, we need to set y to 0 and solve for x.

1/2x = -4(0) - 8

1/2x = -8

x = -8*2

x = -16

So the x-intercept of the equation is (-16,0)

To find the y-intercept of the equation 1/2x = -4y - 8, we need to set x to 0 and solve for y.

1/2(0) = -4y - 8

-8 = -4y

y = 8/4

y = 2

So the y-intercept of the equation is (0,2)

Answer:

the x-intercept of the equation is (-16, 0).
the y-intercept of the equation is (0, 2).

Step-by-step explanation:

To find the x-intercept and y-intercept of the equation 1/2x = -4y - 8, we can set one of the variables to zero and solve for the other variable.

For the x-intercept, we set y = 0 and solve for x:

1/2x = -4(0) - 8

1/2x = -8

x = -8 * 2

x = -16

So the x-intercept of the equation is (-16, 0).

For the y-intercept, we set x = 0 and solve for y:

1/2(0) = -4y - 8

-4y = -8

y = 2

So the y-intercept of the equation is (0, 2).

Using factorization, the zeros of the polynomial y = 3p³ - 8p² + 4p are 0, 2/3 and 2.

The values of the independent variable (x) for which the function equals zero are referred to as the zeros of a function, also known as the roots or solutions. They are, in other words, the x-coordinates of the spots where the function's graph crosses the x-axis. You can set a function's value to zero and then work out the value(s) of x that the equation requires in order to identify the zeros of the function.

If the function, for instance, is f(x), then you would set f(x) to 0 and then solve for x:

f(x) = x^2 + 2x - 3 = 0

This can be simplified as

(x-3)(x+1) = 0

Taking the x - values

x - 3 = 3

or

x + 1 = -1

hence;

x^2 + 2x - 3 = -1, 3

Therefore, -1 and 3 are the zeros of the function f(x) = x2 + 2x - 3.

In our given problem;

y = 3p³ - 8p² + 4p

y = p(3p - 2)(p - 2)

Taking the zeros

0 = p(3p - 2)(p - 2)

p = 0

3p - 2 = 0

p = 2 / 3

p - 2 = 0

p = 2

The zeros or roots of the polynomial are (0, 2/3 and 2)

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Answer:

not a function

Step-by-step explanation:

for the mapping to be a function, each value of x (input ) must map to exactly one unique value of y ( output )

here 1 → 2 and 1 → - 2

- 5 → 4 and 5 → - 4

since the input for these values maps to 2 output values

Then the mapping is not a function

Answer:

0.3, 0.323, 0.333

Step-by-step explanation:

Answer:

0.3,0.323,0.333

Hope it helps!

A semicircle with diameter AB is constructed inside the square ABCD which has side length 2. CE is a tangent of the semicircle that intercepts side AD. The length of CE is 2.5 unit.

Information available from the problem:

- ABCD is a square with side length of 2

- A semicircle with diameter AB is constructed inside the square

- The semicircle's tangent from C intersects AD at point E.

The situation can be depicted in the attached picture.

Refer to the attached picture,

FG = FB = radius of semicircle = 1

Since EC is a tangent of the semicircle, then.

∠CBF = ∠CGF = 90⁰

CF is a common sides of triangle CBF and triangle CGF.

Since there are 2 equal sides and 1 equal angle, using SAS rule, triangle CBF and triangle CGF are congruent.

Hence,

CG = CB = 2

FG² = CG x GE

1² = 2 x GE

Hence,

GE = 1/2

CE = CG + GE

CE = 2 + 1/2 = 2.5

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Answer:

Step-by-step explanation:

a) The probability of obtaining 2 heads when a coin is thrown twice is (2/5) * (2/5) = 4/25.

b) To find the probability of obtaining at least one head, we can find the probability of obtaining no heads (0 heads) and subtract that from 1. The probability of obtaining 0 heads is (3/5) * (3/5) = 9/25. The probability of obtaining at least one head is 1 - (9/25) = 16/25.

The savings plan balance after 18 months will be 15,028.63 dollars.

So the answer is a) $15,028.63

What is the annuity problem?

An annuity is a series of equal payments made at regular intervals.

APR (Annual Percentage Rate) = 6%

Monthly payments = $800

Number of months = 18

We can use the formula for the future value of an annuity (FV) to find the savings plan balance after 18 months. The formula for the future value of an ordinary annuity is:

FV = PMT x (((1 + r)^n - 1) / r)

Where:

FV = future value of the annuity

PMT = the regular payment made

r = the interest rate per period (in this case, the monthly interest rate)

n = the number of payments or periods

The interest rate is given as an annual percentage rate (APR), so we need to divide it by the number of periods per year to find the interest rate per period. In this case, 6% / 12 months/year = 0.5% per month.

FV = 800 x (((1 + 0.005)^18 - 1) / 0.005)

FV = $15,028.63

Hence, the savings plan balance after 18 months will be 15,028.63 dollars.

So the answer is a) $15,028.63

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Answer:

A

Step-by-step explanation:

Answer:

259 miles

Step-by-step explanation:

To find this, we need to multiply his 8 gallons by [tex]\frac{7}{8}[/tex] since he only uses 7 gallons of gas. In turn, we also need to multiply 296 by [tex]\frac{7}{8}[/tex]. We get:

[tex]296 * \frac{7}{8} = 37 * 7 = 259[/tex]

So, Ian drove 259 miles last weekend.

Hope this helped!

The angular speed of the wheel, in radians per second is equal to 52.37 rad/sec.

In Mathematics, an angular speed can be defined as the rate of change of angular displacement of a physical object with respect to time. This ultimately implies that, angular speed is a measure of how fast and quickly a physical object revolves or rotates relative to another point or how its angular position changes with respect to time.

Mathematically, the angular speed of a physical object can be calculated by using this formula:

ω = 2πF or ω = Δθ/Δt

Where:

Substituting the given parameters into the angular speed formula, we have;

Angular speed of the wheel, ω = 2 × 3.142 × 500

Angular speed of the wheel, ω = 3142 rad/min

In rad/sec, we would divide by 60;

Angular speed of the wheel, ω = 3142/60

Angular speed of the wheel, ω = 52.37 rad/sec.

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The variable or factors that the unknown function depends on are referred to as the independent variables.

Everything that track in the study and what is impacted by it are both considered dependent variables. Depending on the independent variable, the dependent variable will change. Because it "depends" on the independent variable, it is known as a dependent variable. The dependent variable on other measurable variables As a result of an experimental modification of the independent variable or variables, these variables should change.

The amount of study one did, how much sleep one got the night before the test, or even how hungry he or she were can all affect your test result, which makes it a dependent variable. As an example, the test score might be a dependent variable.

Differential equations that have a constant power of one are known as linear differential equations.

A linear ordinary differential equation is what the given differential equation is.

The highest derivative that appears in the connection determines the order of a differential equation.

Consequently, the differential equation has an order of 1.

The variable or factors that the unknown function depends on are referred to as the independent variables.

As a result, in the above differential equation, t is independent and p is dependent variable.

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The complete question is as follows:

Alternate interior angles are supplementary when transversal on parallel lines is perpendicular.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles.

Given,

To prove alternate interior angles are supplementary.

In the figure

EF is a transversal intersecting the two line AB and CD at 90°.

AB||CD

∠3 and ∠6, ∠4 and ∠5 are alternate interior angles.

∵ EF⊥ AB and EF⊥CD

∴ ∠3 = ∠6 = ∠4 = ∠5 = 90°

Thus sum of alternate interior angles,

∠3 + ∠6 = 90° + 90° = 180°

∠4 + ∠5 = 90° + 90° = 180°

For supplementary angles sum of angles should be 180° .

Hence, when transversal is perpendicular to the parallel lines, the alternate interior angles are supplementary.

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Answer: in a triangle if all its angle measure less than 90 degree is called an acute triangle.

Step-by-step explanation: In equilateral triangle all of its 3 angle measure equally and are less than 90 degree thus making it an acute triangle.

On solving the provided question, we can say that by using N= 2X + 1 or  N = 2X-1  will do the job for composite numbers.

By multiplying two small positive integers, you can create a composite number, which is a positive integer. Likewise, any positive integer that has at least one divisor besides itself and 1. Positive whole numbers make up composite numbers. It lacks prime (that is, it has divisors other than 1 and itself). The first several composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, and are frequently referred to simply as "composites." In other words, composite odd numbers encompass all non-prime odd numbers. for illustration: 9, 15, 21, etc. No. As a result, 2 only possesses the divisors 1 and 2. To put it another way, since 2 only has two divisors, it is not a composite number.

by using N= 2X + 1

or

N = 2X-1

will do the job for composite numbers.

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Answer:

x = 2, -6

Step-by-step explanation:

3x + 6 = ±12
=> If 3x + 6 = 12
3x = 6
x = 2
=> If 3x + 6 = -12
3x = - 18
x = -6

Answer: 2

Step-by-step explanation: To find the value of x, we need to use the order of inverse operations. Inverse operation(s) means to do the opposite of the operations used. So, instead of adding, we subtract, instead of multiplying, we'll divide. So, the opposite of 6 + 12 is 12 - 6. So, that's 6. Now, instead of multiplying 6 by 3, we need to divide 6 by 3. That's 2. Therefore x = 2. Now, to check our answer, we plug 2 in for 6. So, | 3(2) + 6 | is the positive value of 3(2) + 6, which is 6 + 6.

12 = 12

So, therefore the absolute value of |3x+6|=12 is 2. I hope this helped!

A line would be drawn on the graph for x 324 and tinted also on left side of the line until x = 0.

Social justice theories are based on the concept of unequal, namely the notion that individuals are not similar, particularly in terms of position, rights, and showed that the type. It is susceptible to misinterpretation in public conversation, nevertheless, as it typically has distinct meanings to different people. However, some characteristics apply to everyone.

54 total pages

Football card pages = 18

Pages remaining = 54 - 18 Equals 36

As a result, the remaining 36 pages may each hold 9 cards.

Therefore, the remaining spaces are 36 * 9 = 324.

Inequality: 324 spots available

A line would be drawn on the graph for x 324 and tinted also on left side of the line until x = 0.

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The length in order for the quadrilateral JKLM to be a parallelogram are:

i. JK = 10

ii. JL = 7

A quadrilateral is a family of shapes or figures which has four straight sides, and four measures of internal angles. Examples are: trapezium, rhombus, kite, square, parallelogram etc.

To determine the length of each sides, we have;

opposite sides of a parallelogram are equal, so that;

3x - 2 = x - 6

collect like terms

3x - x =  2 + 6

2x = 8

x = 4

Thus,

i. JK = 3x - 2

       = 3(4) - 2

       = 12 - 2

JK = 10

ii. JL = 2x - 1

         = 2(4) - 1

         = 8 - 1

JL = 7

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The percent error of Alex's measurement is 5.714%.

Percent error is a measure of how accurate a measurement is compared to the true value. It is calculated by taking the absolute value of the difference between the measured value and the true value, divided by the true value, and then multiplying by 100%.

In this case, the measured value is 3.7 cm and the true value is 3.5 cm.

To calculate the percent error, we can use the following formula:

Percent error = |(measured value - true value) / true value| x 100%

Plugging in the given values, we get:

Percent error = |(3.7 - 3.5) / 3.5| x 100%

= |0.2 / 3.5| x 100%

= 0.05714 x 100%

= 5.714%

This means that Alex's measurement is off by 5.714% from the true value, indicating that the measurement has a low accuracy.

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The solution will remain the system since the same two inequalities still make up the system.

Answer:

Step-by-step explanation:

add the 2 equations:

3x+18+4x+15

simplify:

7x+33

we know that all angles on a straight line is 180 degrees.

7x+33=180

solve that equation:

7x=147

x=21

from here substitute x=21 into both equations.

3x+18

3x=63

63+18=81

left angle is 81 degrees

4x+15

4x=84

84+15=99

right angle is 99 degrees

we can check this by adding them both: 99+81=180

its right as all angles on a straight line add to 180, which these do.

hope this helped

By increasing the mass of an object , the Elastic Potential Energy (EPE) is increased

Elastic potential energy ( EPE) is energy stored as a result of applying a force to deform an elastic object. The energy is stored until the force is removed and the object springs back to its original shape, doing work in the process. The deformation could involve compressing, stretching or twisting the object.

The effect of doubling mass on potential energy is similar to doubling the height. By doubling the mass, the potential energy is also doubled, which becomes the reason to begin the work.

This means that adding more mass to an object will increase the elastic potential energy.

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Answer:

1200

Step-by-step explanation:

step 1: Locate and underline the hundreds place (2) then look at the digit to the right (1): 1212

Step 2: The digit to the right (1) is 4 or below. So, we replace it with a 0 (zero) to get 1200 as the answer.

In short: 1212 rounded to the nearest hundred is 1200.

Answer:

71

Step-by-step explanation:

There are two types of relative extremas for a function, described as follows:

On the graph, these relative extremas of a function are the turning points of the function.

The function for this problem is defined as follows:

f(x) = 2x³ - 39x² + 180x + 4.

For the function defined in this problem, the graph is given by the image presented at the end of the answer, with the points representing the relative extremas marked.

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The volume of the parallelepiped with adjacent edges PQ, PR, and PS     is V=16  

Let the parallelepiped be PQRS.

The vertices of parallelepiped are P(3, 0, 1), Q(-1, 2, 5), R(5, 1, -1), S(0, 4, 2).

Given three vectors, there is a product, called scalar triple product, that gives (the absolute value of it), the volume of the parallelepiped that has the three vectors as dimensions.

So

PQ=(3+1,0-2,1-5)=(-4,-2,-4)

PR=(-2-1,-1-4,0+1)=(-2,-1,2)

PS=(-2-3,1-6,0-1)=(3,-4,-1)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

|-4 -2 -4|

|-2 -1 +2|

|3 -4 -1|

and the determinant is given for example with the Laplace rule choosing the first row:

a(ad-bc)-b(ad-bc)+c(ad-bc)

=4⋅[(−1)(−1)−(2)(−4)]−(−2)[(−2)(−1)−(2)⋅(3)+(−4)[(−2)(−4)−(−1)(3)]

=4(1+8)+2(2−6)−4(8+3)

=36−8−44=−16

So the volume is: V=|−16|=16

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0.000004% is the probability that four aces appear together when a pack.

What in mathematics is probability?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.  

                                    Statistics describes the examination of events subject to probability.

The first ace is a  4 aces and 52 cards =  4/52 chance

there are three aces left and 51 cards in total.

The second ace is 3/51,

since,

The third ace = 2/50 (1/25)

the fourth is 1/49.

          = 4/52 * 3/51 * 1/25 * 1/49  

          =  1/270725

          =  0.000004%.

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