A forest covers 78,000 acres. A survey finds that 0. 4% of the forest is old-growth trees. How many

acres of old-growth trees are there?

There are

acres of old-growth trees.

It will take Emily 12.1 hours to mow 5 acres

Variation is the relation between a set of values of one variable and a set of values of other variables

Let T and A represent the time and area respectively

Since the time it takes Emily to mow a lawn is proportional to its area. We can write:

T α A

T = kA (where k is constant of proportionality)

It takes her about 30 minutes to mow 1,000 square yards. That is:

T = 30 and A = 1,000

T = kA

30 = 1000k

k = 30/1000

k = 0.03

Time for 5 acres:

5 acres = 5 × 4840 = 24200 square yards   (1 acre = 4840 square yards)

T = kA

T = 0.03 × 24200

T = 726 minutes     (divide by 60 to get time in hours)

T = 12.1 hours

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The required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

What is system of equations?

A set or group of equations that are solved together is referred to as a system of equations. Both algebraic and graphic solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.

If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.

Then the total hours she can work = t + r

Since she can work up to 25 hours.

Thus  t + r ≤ 25

If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .

Then her total earning = $25t + 12r

Since she must earn $200.

Then 25t + 12r ≥ 200

Hence, the required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

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The concentration in the new mixture will be 11.1 grams.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Stefanie has 18 grams of 20% sugar syrup.

And, john has 30 grams of 25%.

Here,

Stefanie has 18 grams of 20% sugar syrup.

Hence, The amount of sugar = 18 × 0.2

                                             = 3.6 grams

And, john has 30 grams of 25%.

Hence, The amount of sugar = 30 × 0.25

                                             = 7.5 grams

Thus, The concentration in the new mixture = 3.6 + 7.5 grams

                                                                     = 11.1 grams

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The graph of the linear function f(x) = 2/(x + 5) is attached.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the linear function as -

f(x) = 5/(2x + 5)

Refer to the graph of the linear function attached. This graph represents the function f(x).

Therefore, the graph of the linear function f(x) = 2/(x + 5) is attached.

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The equation of the line in fully simplified intersect is y = mx + b

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Answer:

(2x+10°) + (x°) +(2x-20°) = 540°

540 is the sum angle of the polygon

collect like terms

2x+x+2x+10°-20°=540°

5x-10°=540°

5x=540°+10°

5x=550°

x=550°/5

x=110°

(2(110)+10)+(110)+(2(110)-20)=540°

The general solution of the given differential equation is y(x) = C₁e^-x + 4xe^-x. The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution.

The differential equation given can be rearranged into the form dy/dx + (x + 2)/(x + 1)y = 8xe^-x, which is a linear first order differential equation. Using the integrating factor method, an integrating factor of e^(x + 1) can be used to obtain the general solution y(x) = C₁e^-x + 4xe^-x.

The integration constant C₁ can be determined by supplying the appropriate initial conditions. As the equation is a linear first order differential equation, the general solution is valid over the entire domain of x, which is (-∞, ∞). As the equation does not involve any terms that provide a particular value for y at any point in the domain, there are no transient terms in the general solution.

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The finding is significant at both α = 0.05 and α = 0.01.

What is hypothesis ?

A hypothesis (plural: hypotheses), in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

Have given ,

H0: p = 0. 65 ,  Ha: p < 0. 65 and  the z test statistic is found to be -2. 35.

From the test statistic value, we can obtain the p value of the test ,

To determine if the claim is significant at both α = 0.05 and α = 0.01

We compare the Z statistic and Z critical values

If Z statistic < Z critical ; then we reject H0; if otherwise, we fail to reject H0

Z critical at 95% one tailed = - 1.645 (left tail)

Z critical at 95% one tailed = -2.326 (left tail)

- 2.35 < - 1.645

-2. 35 < 2.326

Since, Z statistic < Z critical;

The finding is significant at both α = 0.05 and α = 0.01.

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Step-by-step explanation:

what do you not understand ? please let me know where you need more instructions.

the basic rule : every term of one side has to be multiplied with every term of the other side, and the results are added (by using the correct signs of the products).

remember :

+ × + = +

- × - = +

+ × - = -

- × + = -

(3x - 3)(5x - 4) = 3x × 5x + 3x × -4 + -3 × 5x + -3 × -4 =

= 15x² - 12x - 15x + 12 = 15x² - 27x + 12

Rounded to the nearest tenth, the measure of side ST is 8.0.

In order to find the measure of side ST, you will need to use the concept of similarity. If two triangles are similar, then their corresponding sides are in proportion. If we let x be the measure of side ST, then we can set up a proportion using the given information:

[tex]OP/PQ = ST/RQ[/tex]

We also know that

[tex]OP/PQ = 2/3[/tex]

and

[tex]RQ = 12[/tex]

So we can substitute these values into the proportion and solve for x:

[tex](2/3) = ST/12[/tex]

[tex]ST = (2/3) * 12[/tex]

[tex]ST = 8[/tex]

Rounded to the nearest tenth, the measure of side ST is 8.0.

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The linear expression that is not equivalent to the other three is D) (-5x-1)+(6x + 7).

A linear expression is an algebraic expression which is composed of constants, variables, and coefficients that are related by only addition and multiplication operations. It usually takes the form of ax + b, where 'a' and 'b' are constants and 'x' is a variable. Linear expressions can be used to describe various mathematical and physical phenomena, such as the slope of a line or the volume of a cylinder.

This linear expression is not equivalent to the other three because it does not have the same coefficient for the x terms and the constant terms. The other three expressions all have the same coefficients for the x terms and the constant terms, making them equivalent.

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The coefficient of the variable x  in the expression 4a+3x +a is 3

Given that,

The expression is 4a+3x +a which can be simplified as 4a+3x +a

To find : The coefficient of the variable x in the expression

The coefficient of x in 4a+3x +a is 3

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

Coefficient is the number that is beside the variable in the equation.

As we can see that the term that is in multiplication with x is 3

Hence, the coefficient of x in the equation  is 3

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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{4}}} \implies \cfrac{3 +6}{-6} \implies \cfrac{ 9 }{ -6 } \implies - \cfrac{3 }{ 2 }[/tex]

Answer:

9/-6 or -1.5

Step-by-step explanation:

Follow the steps in the image

-Hope this Helped

A triangle is a polygon with 3 sides, and the sum of its interior angles is 180 degrees.

The properties of a triangle are:

There are several types of triangles, including:

Equilateral triangle: This is a triangle with three sides of equal length and three angles of 60 degrees.

Isosceles triangle: This is a triangle with two sides of equal length and two angles of equal measure.

Scalene triangle: This is a triangle with three sides of different lengths and three angles of different measure.

Right triangle: This is a triangle with one 90-degree angle.

Acute triangle: This is a triangle with three angles that are all less than 90 degrees.

Obtuse triangle: This is a triangle with one angle that is greater than 90 degrees.

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By working together, they can make the work done in two hours and forty-six minutes.

Given data :

Think of these work rates as "greenhouses per hour", not "hours per greenhouse". Then Steve's work rate is one fourth of a greenhouse per hour, and his son's is one ninth of a greenhouse per hour. Now, multiply each rate by the time t to get the portion of the greenhouse each paints, and add the products up to get one greenhouse. The work equation becomes:

1 / 4 t + 1 / 9 t = 1

9 / 36 . t + 4 / 36 t = 1

13 / 36 t = 1

36 / 13. 13 / 36 t  = 36 / 13 .1

t = 36 / 13 hrs

or 36 / 13. 60 = 166 min

This is two hours and forty-six minutes.

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[tex](69)(5.6\times 10^{5})\implies (69)(560000)\implies 3\underset{\leftarrow 7\to }{\underline{8640000}}\implies 3.864\times 10^{7}[/tex]

The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent

What is probability ?

Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.

Given ,

X ∼ Geom(p) and Y ∼ Geom(r) are independent.

P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})

=∑1≤k<n,n∈NP(X=k,Y=n)

=∑n=1∞∑k=1n−1P(X=k)P(Y=n)

=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1

=pq∑n=1∞(1−q)n−11−(1−p)n−1p

=q∑n=1∞(1−q)n−1(1−(1−p)n−1)

=1−q / ∑n=1∞[(1−q)(1−p)]n−1

=1−q / 1−(1−p)(1−q)

=1−(1−p)(1−q)−q / 1−(1−p)(1−q)

=p(1−q) / p+q−pq.

Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if  X ∼ Geom(p) and Y ∼ Geom(r) are independent.

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Example of an undecidable problem is given by the problems in the system created by computer viruses.

According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.

A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.

whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.

If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.

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The price of the sales tax on the elephant could be 0.75$

What is percentage ?

percentage can be defined as the product of ratio of given value and total value and hundred.

Given

he sells a stuffed elephant for $14.95,

the sales tax is 5% of the sale price .

So,

as the tax is 5% of the given value.

so we are here multiplying the given value to the 5/100

we get,

The amount of the tax could be

 = 14.95*5/100

 = 0.7475

≈ 0.75 (rounded)

Hence the  price of the sales tax on the elephant could be 0.75$

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The water level is rising at a rate of 0.5tf² /min*ft². This is in cubic feet per minute per square feet, if you want to express this in terms of height, you will have to convert the units

To find out how fast the water level is rising, we need to use the concept of volume flow rate. Volume flow rate is the volume of fluid that passes through a given surface per unit of time. In this case, the volume flow rate is given as 3tf^3/min.

Since the base of the tank is a rectangle with dimensions 2x3 ft, we can find the area of the base by multiplying the length and width:

2 ft * 3 ft = 6 ft^2

To find the rate of change of the water level, we need to divide the volume flow rate by the area of the base.

3tf^3/min / 6 ft^2 = 0.5tf^3/min*ft^2

So the water level is rising at a rate of 0.5tf^3/min*ft^2

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Answer:

decreasing is the answer

By translating, stretching and contracting, or reflecting, two functions from the same function family can become one another. Any function from a function family can be obtained by applying one or more transformations to a parent function.

By altering the graph of the parent absolute value function, many other absolute value functions can be created. The resulting absolute value functions take the following form:

[tex]y = |x-h| + k[/tex], where h and k are real numbers.

Absolute value functions can be created using the same kinds of operations that produce new linear functions. They also have a similar impact on absolute value functions. The transformations may, however, appear differently graphically due to some important discrepancies between linear functions and absolute value functions.

Here are some of the transformations:

Vertical Transformations

Horizontal Transformations

This is how we graph the transformation of an absolute value function.

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The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH

What is Quadrilateral ?

Quadrilateral can be defined as the type of the polygon in which it contains four sides.

Given ,

JKLM ~ EFGH

Since , JKLM ~ EFGH

3/30 = 11/z

 z = 30*11/3

z =110

3 / 30 = 8/ x

3 * x = 8 * 30

x = 80

3 / 30 = y/ 20

y = 20 * 3 / 30

y = 2

Hence the values of x , y and z are 80,2,110 respectively.

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The function Formula is, f(t) = 6t + 8.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.  The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.

Given:

Carolina charges an initial fee plus $6 for each hour of work

Her total fee for a 4-hour job = $32

So, if she work for 't' hours then linear equation will be of the form

f(t) = mt + b

Here m is the constant rate = 6

Now we plug in the values and find out b, m=6

f(t) = mt + b

32 = 6(4) + b

32= 24 + b

8 = b

So, the function is f(t) = 6 t+8.

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The probability of Greg being late again, along with the type of probability, is given as follows:

1/7, experimental probability.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

In the context of this problem, the outcomes are given as follows:

The probability of Greg being late is then calculated as follows:

3/21 = 1/7.

Which is an experimental probability, as the number of outcomes are taken from previous "experiments".

The other type of probability is theoretical, for example, a fair coin has a 50% chance of falling heads and 50% change of falling tails.

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The solution of given triangle is 32°.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal.

Given,

∠BAC=52°

since, ΔBAC is isosceles triangle hence opposite angle will be equal.

∠BAC+∠ABC+∠ACB=180°

2∠BCA=180°-52°

∠BCA=128/2

∠BCA=64°

also,

∠BCA+∠DCA=180°

∠ACD=180°-64°

∠ACD=116°

since,

ΔACD is isosceles triangle, hence opposite angle is equal

∠ACD+∠CAD∠ADC=180°

2∠CAD=180°-116°

∠CAD=64/2

∠CAD=32°

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Answer:

2800

Step-by-step explanation:

20% of 14,000 is 2800

Multiply both sides by 14,000, then divide the left side to get the result.

Answer:

2800

is what the calculator says

Answer:

x=4

Step-by-step explanation:

2x-(x+5)=-1

Solve for x

Distribute the minus sign

2x-x-5=-1

Combine like terms

x -5 = -1

Add 5 to each side

x-5+5 = -1+5

x=4

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

Distribute negative sign:

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

[tex]2x+-x+-5=-1[/tex]

Combine Like Terms:

[tex](2x+-x)+(-5)=-11[/tex]

[tex]x-5=-1[/tex]

Add 5 to both sides:

[tex]x-5+5=-1+5[/tex]

[tex]\fbox{x = 4}[/tex]

Answer:

1/ 0.8 kilograms

2/ 800 grams

Step-by-step explanation:

We know

1/

Baseball bat = 28 ounces

1 kilogram = 35 ounces

To find weight in kg we take

28 / 35 = 0.8 kg

2/

We know

1 kg = 1000 g

0.8 kg = 800 grams

So, the baseball bat weights 0.8kg or 800 grams

Answer:

The fourth one could not represent the three sides of a triangle

Step-by-step explanation:

because the two sides of the triangle must be larger together than the third side and 7+16=23<24, so the fourth one could not represent the three sides of a triangle.

Answer:

C

Step-by-step explanation: The third one down. There are two ways you know this.

1. If you had two boards that where 6 cm and 20 cm and tried to make a triangle with the third side = 27, the two little boards would lie flat on the 27 cm board.

2. The other three answers all make the smaller two sides larger than the third larger side.