a 300-acre farm produced 20,000 bushels of corn last year. what is the minimum rate of production, in bushels per acre, that is needed this year, so the farm's two-year production total will be at least 49,100 bushels of corn?

The expression of v = (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0) is [tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

To express v= (2,1,5) as a linear combination of (1,2,1), (1,0,2) and (1,1,0), it will be written as:

[tex](2,1,5)=x(1,2,1)+y(1,0,2)+z(1,1,0)[/tex]

This will yield the following equations:

x + y + z = 2........(1)

2x + z = 1..........(2)

x + 2y = 5........(3)

The solution to the system of equations above is:

x = 1, y = 2, z = -1

Therefore, the linear combination is:

[tex](2,1,5)=1(1,2,1)+2(1,0,2)+-1(1,1,0)[/tex]

Learn more on linear combinations here:https://brainly.com/question/17407318

#SPJ1

Answer:Rules for rotating points about the origin

1. The point (a,b) rotated 90° counterclockwise about the origin

becomes (-b,a).

A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)

A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)

B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)

C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)

D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)

Step-by-step explanation:

Answer:

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

Learn more about limiting factor from here brainly.com/question/18415071.

#SPJ1

The equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]

The expression is given as:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex]

Divide 128 by 2

[tex]\sqrt{\frac{64x^5y^6}{x^7y^5}}[/tex]

Apply the law of indices to the variables

[tex]\sqrt{\frac{64y^{6-5}}{x^{7-5}}}[/tex]

Evaluate the differences

[tex]\sqrt{\frac{64y}{x^2}}[/tex]

Take the square root of 64

[tex]8\sqrt{\frac{y}{x^2}}[/tex]

Take the square root of x^2

[tex]\frac{8\sqrt y}{x}[/tex]

Hence, the equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ1

The transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis

The complete question is added as an attachment

From the graph, we have the following highlights:

This means that parallelogram LMNO is reflected across the x-axis to get parallelogram L'M'N'O'

Hence, the transformation from parallelogram LMNO to parallelogram L'M'N'O' is a reflection across the x-axis

Read more about transformation at:

https://brainly.com/question/11709244

#SPJ1

Answer:

D.  -11

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]

[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]

[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]

f(-4) means to substitute x = -4 into the function.

As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:

[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]

Learn more about piecewise functions here:

https://brainly.com/question/28186577

https://brainly.com/question/28151925

Answer is D. -11

Answer:

Solution Given:

f(-4) depends on the condition x≤-4,

so

f(-4)=2*-4-3=-8-3=-11

The attached graph represents the piecewise function.

The piecewise function is given as:

f(x) = 3x - 5, x ≤ -1

      = -2x + 3, -1 < x < 4

      = 2, x ≥ 4

To plot the graph, we simply plot the equations together with their domains

i.e.

3x - 5 with the domain of x ≤ -1,  -2x + 3 with the domain of -1 < x < 4 and 2 with the domain of x ≥ 4

See attachment for the graph of the function

Read more about piecewise functions at:

https://brainly.com/question/12561612

#SPJ1

The secant in the diagram is [tex]\overline{AD}[/tex]

Segment AD intersect the circle at two points. So it can be a secant.

We have been given that a circle of center O. We have to find the segment that is secant.

Secant : If a line which intersect the circle at two points.Then the line segment  is called  secant.

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)

Segment OB intersect the circle at one point B only. so OB cannot be a Secant.

Segment AD intersect the circle at two points. So it can be a secant.

Learn more about secant here;

https://brainly.com/question/7513459

#SPJ2

Part A

1) (5, -1)

2) (1, -3)

3) (-2, -2)

4) (-5, -4)

Part B

1) (-5, 1)

2) (-1, 3)

3) (2, 2)

4) (5, 4)

The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex]  the result of the division is [tex]30.8666667[/tex] in decimal form.

When a large number is distributed into small numbers of equal parts is called division.

The number [tex]1.5[/tex] is not a factor of [tex]46.3[/tex] ,  on dividing them the remainder is not zero.

Therefore,  first convert [tex]1.5[/tex] it into a whole number by multiplying it  [tex]10[/tex] so it becomes [tex]15[/tex] .

Then convert [tex]46.3[/tex]  it into a whole number by multiplying it by [tex]10[/tex] so it becomes [tex]463[/tex]

Here,  [tex]\dfrac{463 \times 10}{15 \times 10}[/tex] which results in [tex]\dfrac{463}{15}[/tex].

Now, divide [tex]\dfrac{463}{15}[/tex] ,  the result will be [tex]30.8666667[/tex].

The solution to the problem when [tex]46.3[/tex] divided by  [tex]1.5[/tex] the result is [tex]30.8666667[/tex].

Learn more about division here:

https://brainly.com/question/8969674

#SPJ6

Answer:

Step-by-step explanation:

If (x, 68, 85) form a Pythagorean Triple, what is the value of x?

to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse

x = √(85²- 68²)

x = (7225 - 4624)

x = √2601

x = 51

Answer:

  x = 51

Step-by-step explanation:

The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.

A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:

  a² +b² = c²

The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}

There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.

The given values of the triple have the ratio ...

  68/85 = (4·17)/(5·17) = 4/5

Only the values in the {3, 4, 5} triple and its multiples will have this ratio.

The value of x is 3·17 = 51, so the triple is {51, 68, 85}.

  x = 51

__

Additional comments

Any primitive triple will have two odd numbers.

The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.

For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.

__

The above triple can be verified using the Pythagorean theorem:

  51² +68² = 2601 +4624 = 7225 = 85²

Answer:

the third option, x = –3, –1, 3

Step-by-step explanation:

Answer:

C. 0.12

Step-by-step explanation:

Let's use a sample number of 100

Out of 100 members, 50 are in the brass section

Out of those 50, 24% play the trombone. This means that 12 people total play the trombone.

12/100 is .12.. That is the final answer

A function which could represent the graph is: C. f(x) = x⁴(x - a)(x - b)².

The nature of the intercept on a polynomial graph highlights the nature of its multiplicity. Also, the polynomial graph has no single zero (factor) but bounced off the x-axis at three (3) different locations.

This ultimately implies that the polynomial graph has an even multiplicity at these three (3) points:

x⁴

x - a

(x - b)²

In conclusion, a function which could represent the graph is f(x) = x⁴(x - a)(x - b)².

Read more on multiplicity here:

brainly.com/question/3791218

#SPJ1

The previous tax rate was 20%

What is tax rate?

Tax rate is the percentage of the earnings tax payers would pay to the government from their earnings as taxes.

It should be borne in mind that the new tax rate is 25% which has increased by 25% compared to the previous tax rate, which is the unknown.

The mathematical relationship between the current and prior tax rates is as shown below:

Current tax rate=previous tax rate*(1+% increase in tax rate)

Current tax rate=25%

previous tax rate=X

% increase in tax rate=25%

25%=X*(1+25%)

25%=X*1.25

X=25%/1.25

X=previous tax rate=20%

Technically speaking, an increase of 25% in 20% is 5%(i.e. 20%*25%=5%), which when added to the original 20% would give a tax rate of 25%.That the shortcut to affirming that the new tax rate of 25% is correct

Find out more about tax rate on:https://brainly.com/question/25791968

#SPJ1

Using the z-distribution, the observed test statistic is given as follows:

z = 3.69.

At the null hypothesis, it is tested if older students have the same mean as the general population, that is:

[tex]H_0: \mu = 115[/tex]

At the alternative hypothesis, it is tested if they have a greater mean, that is:

[tex]H_0: \mu > 115[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}[/tex]

z = 3.69.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

they are the same line

Step-by-step explanation:

if you divide the first line by 2 you'll get:

2(3x)+2y=2(23)===> 3x+y=23

answer : 2 1/2

divide y by x

divide  2 1/2 by 1

its 2 1/2

10 divided by 4 is also

2 1/2

17 1/2 divided by 7 is also

2 1/2

Answer: Choice B

[tex]2 = \log_{8}(64)[/tex]

======================================================

Explanation:

The original equation is [tex]8^2 = 64[/tex] with 8 as the base. That is also the base of the log when we get the final answer shown above. Logs are useful to isolate the exponent.

The general rule is that [tex]\text{y} = b^{\text{x}}[/tex] is equivalent to the log form of [tex]\text{x} = \log_{b}(\text{y})[/tex] where b is the base of each.

2 = log Subscript 64 Baseline 8 is the  logarithmic equation which is equivalent to 82 = 64.

Two or more expressions with an Equal sign is called as Equation.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

The logarithmic equation equivalent to 82 = 64 is:

2 = log Subscript 64 Baseline 8

This is because the logarithmic equation relates the base (64) to the result of the exponentiation (8), which in this case is 2.

Hence, 2 = log Subscript 64 Baseline 8 is the  logarithmic equation which is equivalent to 82 = 64.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Step-by-step explanation:

b1) Any line parallel to the x-axis is horizontal. If we look at the graph of a horizontal line, we see that for any x-value you give, the y-value will be the same. In this case, the y-value is -1. Hence, the equation for the line is [tex]y=-1[/tex], as y will be -1 no matter the x.

The gradient for a horizontal line is 0, as the "rise" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would have 0 on the top, which makes the whole fraction 0.

b2) Any line parallel to the y-axis is vertical. If we look at the graph of a vertical line, we see that for any y-value, the x-value will be the same. In this case, the x-value is -1. Hence, the equation for the line is [tex]x=-1[/tex], as x will be -1 no matter the y.

The gradient for a vertical line is undefined, as the "run" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would be dividing by 0, which is undefined.

Answer:

68

Step-by-step explanation:

Lets first find the quantity of tape the computing center is purchasing/month.

3/5 Of their 1600 dollar spending is on the heavy duty tapes, meaning they are spending 960 dollars/month on heavy duty tape, if we divide that by the original price, 40, it will give us the original quantity of heavy tape they are purchasing, 24/month.

The other 2/5 of their money, 640 dollars, are spent on regular tape, meaning they purchase 20 rolls of regular tape/month.

Given they are purchasing 24 rolls of heavy tape and 20 rolls of regular tape every month, we can simply multiple those by the new prices and sum the results.

24*38=912

20*31=620

912+620=1532

Then to find the money they are saving we subtract the new price from the original price.

1600-1532=68

Answer:

1 - 100 primes numbers

Step-by-step explanation:

2,3,5,7,11,13,17,19,23,29,31,37,41,47,57,59,61,67,71,79,83,8797

The volumes of the right prisms are listed below:

In this problem we have six cases of right prisms with rectangular bases, the volume of right prisms (V), in cubic length units, is equal to the product of the area of the base (A), in square length units, and the height (h), in length units. The equation of the volume of the right prism is shown below:

V = w · l · h     (1)

Where:

Now we proceed to calculate each volume:

Prism 1 (w = 2 / 3 ft, l = 1 / 3 ft, h = 1 / 2 ft)

V = (2 / 3 ft) · (1 / 3 ft) · (1 / 2 ft)

V = 1 / 9 ft³

Prism 2 (w = 1 / 8 in, l = 3 / 4 in, h = 13 / 16 in)

V = (1 / 8 in) · (3 / 4 in) · (13 / 16 in)

V = 39 / 512 in ³

Prism 3 (w = 7 / 8 cm, l = 1 / 4 cm, h = 1 / 12 cm)

V = (7 / 8 cm) · (1 / 4 cm) · (1 / 12 cm)

V = 7 / 384 cm³

Prism 4 (w = 1 / 7 cm, l = 7 / 8 cm, h = 2 / 3 cm)

V = (1 / 7 cm) · (7 / 8 cm) · (2 / 3 cm)

V = 1 / 12 cm³

Prism 5 (w = 9 / 10 m, l = 2 / 3 m, h = 1 / 5 m)

V = (9 / 10 m) · (2 / 3 m) · (1 / 5 m)

V = 3 / 25 m³

Prism 6 (w = 7 / 8 yd, l = 6 / 7 yd, h = 1 / 2 yd)

V = (7 / 8 yd) · (6 / 7 yd) · (1 / 2 yd)

V = 3 / 8 yd³

To learn more on prisms: https://brainly.com/question/12649592

#SPJ1

Answer: The graph of f(x) is horizontally stretched

Answer:

70

Step-by-step explanation:

45+90=135

180-45=45

q=45

45+65=110

180-110=70

70-45=25

p=25

45+25=70

Answer: 70°

Step-by-step explanation:

We know that the sum of all 3 angles in a triangle is 180°. Hence, we can just set all measures to be equal to 180° and solve for the variables.

[tex]p+65+90=180\\p+155=180\\p=25[/tex]

[tex]45+90+q=180\\135+q=180\\q=45[/tex]

[tex]p+q=25+45=70[/tex]

The sum of p and q is 70°.

The maximum value of the objective function is 26 and the minimum is -10

The objective function is given as:

z=−3x+5y

The constraints are

x+y≥−2

3x−y≤2

x−y≥−4

Start by plotting the constraints on a graph (see attachment)

From the attached graph, the vertices of the feasible region are

(3, 7), (0, -2), (-3, 1)

Substitute these values in the objective function

So, we have

z= −3 * 3 + 5 * 7 = 26

z= −3 * 0 + 5 * -2 = -10

z= −3 * -3 + 5 * 1 =14

Using the above values, we have:

The maximum value of the objective function is 26 and the minimum is -10

Read more about linear programming at:

https://brainly.com/question/15417573

#SPJ1

Please see the graph below

Answer:

20

Step-by-step explanation:

20+20=40