Rasberry Crazy Ants, a species found in wall sockets, cellphones, and television sets are
slowly spreading across Texas and are poised to spread across the entire South. Named for
Texas exterminator Tom Rasberry, who spotted ants moving in an erratic swarm in 2002,
the destructive ants are now in 23 counties in Texas, the Austin American-Statesman
recently reported. Although their march in impossible to stop, it is also quite slow. They travel at an average speed of 1.8 feet per day.
a. At that rate, how long will the swarm that is presently centered in Austin, Texas, take to reach your home? Express your answer in the timeframe that is most appropriate.
b. Do you need to be worried about these ants infesting your cellphone or television? Do you need to worry for your children? For your grandchildren? Explain why or why
not.

Numerical Expression

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

find the common denominator and thin combine the numerators over the common denominator trhin simplify each term thin simplify by adding subtracing  thin the result can be shown in multiple forms

exact form 19/2

decimal form 9.5

mixed number form 9 1/2

The composite function is given as follows:

[tex](f \circ g)(x) = \frac{2x + 6}{3x + 22}[/tex]

The domain of the composite function is: [tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

The composite function is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, the functions are:

Hence the composite function is:

[tex](f \circ g)(x) = f\left(\frac{13}{x + 3}\right) = \frac{2}{\frac{13}{x + 3} + 3} = \frac{2(x + 3)}{13 + 3(x + 3)} = \frac{2x + 6}{3x + 22}[/tex]

For the domain, we have to remove the points outside the domain of both the primitive and the composite functions, that is, the zeroes of the denominators, hence:

[tex]x + 3 \neq 0 \rightarrow x \neq 3[/tex]

[tex]3x + 22 \neq 0 \rightarrow x \neq -\frac{22}{3}[/tex]

Hence the domain is:

[tex]\mathbb{R} - \left\{-\frac{22}{3}, 3\right\}[/tex]

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Step-by-step explanation:

sin(x/2) = sqrt((1 - cos(x))/2)

cos(x/2) = sqrt((1 + cos(x))/2)

tan(x/2) = sin(x/2)/cos(x/2)

sin(x) = 15/17

so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.

via Pythagoras we get the 3rd, horizontal side :

17² = 15² + side²

289 = 225 + side²

64 = side²

side = 8

cos(x) = 8/17

sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =

= 0.514495755...

cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =

= 0.857492926...

tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =

= 3/5 = 0.6

Answer:

x = 31.5, y = 41.7, z = 48

Step-by-step explanation:

use the rule that cos (x)  = adjacent/hypotenuse:

you know that x (the angle) = 42 and the adjacent side = 35, so:

cos (42) = 35/y

y = 35/cos(42)

y = 47.1

then, to find x:

use the fact that tan (x) = opposite side/adjacent side

so tan (42) = x/35

x = 35tan(42)

x = 31.5

finally, you know all 3 angles of the triangle have to add up to 180, so to find z you can do:

z + 90 + 42 = 180

z + 132 = 180

z = 48

Answer:

[tex]-\frac13[/tex]

Step-by-step explanation:

Just the slope, so we can simply apply the definition, as variation in y over the variation in x

[tex]m= \frac{\Delta y}{\Delta x} = \frac{1-4}{2-(-7)} = \frac {-3}{9} = -\frac13[/tex]

Answer:

0.222

Step-by-step explanation:

Y2-Y1 ÷ X2-X1

4-2 ÷ -7-2

2÷-9

0.222

Answer: 18x+24

Step-by-step explanation:

[tex]f(x+3)=3(x+3)^2 + 5\\\\f(x+3)=3(x^2 + 6x+9)+5\\\\f(x+3)=3x^2+18x+27+5\\\\f(x+3)=3x^2 + 18x+32[/tex]

[tex]\therefore f(x+3)-[f(x)+3]=(3x^2 +18x+32)-[3x^2 +5+3]\\ \\=3x^2 +18x+32-3x^2 - 8\\\\=\boxed{18x+24}[/tex]

If function f(x) = 3x² + 5 then the value of f(x + 3) - [f(x) + 3] is 18x + 24.

Given the function f(x) = 3x² + 5.

We have to find the value of f(x + 3) - [f(x) + 3]

First we have to find the value of f(x + 3) - [f(x) + 3]

f(x + 3) = 3  (x + 3) ² + 5f(x + 3)

           = 3(x ² + 6x + 9) + 5f(x + 3)

           = 3x ² + 18x + 27 + 5f(x + 3)

           = 3x ² + 18x + 32

Now substitute these values and find the value of f(x + 3) - [f(x) + 3].

f(x + 3) - [f(x) + 3] = (3x² + 18x + 32) - [3x ^ 2 + 5 + 3]

                           =3x ²  + 18x + 32 - 3x ² - 8

                           =18x + 24

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The number of students is 33.2 million

Percent decrease refers to the percent change in the value when it is decreased over a period of time. Percentage decrease expresses the decrease in the given value with respect to its initial value in the form of a percentage.

Given:

In 2019= 16.6 million

% decrease = 5%

So,

% decrease= x - 16.6/ x

5% = x- 16.6/x

0.05= (x-16.6)/x

0.05x = x-16.6

-0.05 x = -16.6

x= 16.6/0.05

x= 16600000/0.05

x= 332,000,000

x= 33.2 million.

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Answer:

1400 units

$26,600

1700 units

$32,300

Step-by-step explanation:

yw :))

Step-by-step explanation:

Answer:

AB : y=1/5x+12

CB : y=-3x+10

CD : y=1/2x-1

DA : y=-2x+1

Using the Poisson distribution, it is found that:

a) The mean is of 15.63.

b) The probability is of 0.0911 = 9.11%.

c) The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The mean is given by:

[tex]\mu = \frac{5705}{365} = 15.63[/tex]

Item b:

The probability is P(X = 17), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 17) = \frac{e^{-15.63}(15.63)^{17}}{(17)!} = 0.0911[/tex]

The probability is of 0.0911 = 9.11%.

Item c:

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-15.63}(15.63)^{0}}{(0)!} = e^{-15.63}[/tex]

The probability is [tex]e^{-15.63}[/tex], which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

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Using the Poisson distribution, it is found that

a) The mean is 15.63.

b) The probability is[tex]e^{-15.63}[/tex] of 0.0911 = 9.11%.

c) The probability is, which is less than 0.05, hence 0 births in a single day would be a significantly low number of​ births.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P\left(X=x\right)=\frac{e^{-\mu }\mu ^x}{x!}[/tex]

The parameters are

x is the number of successes.

e = 2.71828 is the Euler number.

[tex]\mu[/tex] is the mean in the given interval.

Item a:The mean is given by:

[tex]\:\mu =\frac{5705}{365}[/tex]

Item b: The probability is P(X = 17), hence:

[tex]P\left(X=17\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{17}}{17!}=0.0911[/tex]

The probability is of 0.0911 = 9.11%.

Item c:The probability is P(X = 0), hence:

[tex]P\left(X=0\right)=\frac{e^{-15.63\:}\left(15.63\right)\:^{0}}{0!}=e^{-15.63}[/tex]

The probability is,[tex]e^{-15.63}[/tex] which is less than 0.05,

hence 0 births in a single day would be a significantly low number of​ births.

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Answer:

wrong question please place correctly thanks

Answer:

[tex]\boxed{\bf x=7}[/tex]

[tex]\boxed{\bf GH= 52}[/tex]

Step-by-step explanation:

In the line segment..

[tex]\bf 7x+3+3x-5=9x+5[/tex]

Combine like terms.

Add -2 to both sides.

Subtract 9x from both sides.

[tex]\bf GH=7x+3[/tex]

The simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

Simplify the expression: (x³ + (-y)³) / (x - y)

Do not include parentheses in your answer.

The expression is given as:

[tex]\frac{x^3 + (-y)^3}{(x - y}[/tex]

Open the inner bracket

[tex]\frac{x^3 -y^3}{(x - y}[/tex]

Apply the difference of two cubes to the numerator

[tex]\frac{(x-y)(x^2+xy+y^2)}{(x - y}[/tex]

Cancel out the common factors

[tex]x^2+xy+y^2[/tex]

Hence, the simplified expression of [tex]\frac{x^3 + (-y)^3}{(x - y}[/tex] is [tex]x^2+xy+y^2[/tex]

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Answer:

Relation 3 is not a function, as s has two outputs: tree and desk. Relation 4 is not a function for the same reason. -1 has three outputs: -2, -4, and -7.

Answer:

48 cm²

Explanation:

Let the breadth be b, then the length is 3b

P = 2(Length + Breadth)

32 = 2(3b + b)

32 = 2(4b)

8b = 32

b = 4

Breadth is 4 cm

Length: 3b = 3(4) = 12 cm

Area of rectangle:

Length × Breadth

12 × 4

48 cm²

Given :-

To Find :-

Solution :-

Using formula;

Where;

We have;

By putting all values in formula we get;

→ 2(3x + x) = 32

→ 2(4x) = 32

→ 2 × 4x = 32

→ 8x = 32

→ x = 32/8

After dividing 32 with 8, we get;

→ x = 4

Hence;

Now, using formula;

Where;

We have;

By putting all values in formula we get;

→ Area of rectangle = 12 × 4

By multiplying 12 with 4, we get;

→ Area of rectangle = 48 cm²

Answer:

The answer is 1.5.

Step-by-step explanation:

I don't have one

Substituting into point-slope form,

[tex]y+5=-\frac{5}{3}(x-15)\\\\y+5=-\frac{5}{3}x+25\\\\\boxed{y=-\frac{5}{3}x+20}[/tex]

The expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

Expression is a mathematical statement consisting of variables , constants and mathematical operators .

It is given in the question to solve the expression

[tex]\rm \dfrac{4x}{7} + \dfrac{5}{4x^2}[/tex]

Taking LCM , LCM = 28x²

[tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

Therefore the expression given can be written as [tex]\rm \dfrac{(16x^2 + 35 )}{28x^2}[/tex]

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Answer:

x = 9/2

Step-by-step explanation:

√2x + √2x = 6

2√2x = 6

2√2x/2 = 6/2

√2x = 3

(√2x)² =( 3)²

2x = 9

x = 9/2

Answer:

x = 4.5

Explanation:

[tex]\rightarrow \sf \sqrt{2x} + \sqrt{2x} = 6[/tex]

add following

[tex]\rightarrow \sf 2\sqrt{2x} = 6[/tex]

divide both sides by 2

[tex]\rightarrow \sf \sqrt{2x} = 3[/tex]

square both sides

[tex]\rightarrow \sf 2x = 3^2[/tex]

simplify the following

[tex]\rightarrow \sf 2x = 9[/tex]

divide both sides by 2

[tex]\rightarrow \sf x = 4.5[/tex]

The conclusion about the relationship is

The complete question is:

Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.

The functions have the same base.

The functions have the same range.

The functions have the same exponent.

The functions have the same domain.

g(x) is a translation left 1 unit.

g(x) is a translation right 2 units.

g(x) is a translation up 2 units.

Given function is:

f(x) = [tex]3^{x}[/tex]

g(x) = [tex]3^{x+1}[/tex]

Firstly, the functions have the same base i.e., base 3.

second, the functions have the same range.

As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.

third, both functions have the same domain as x = {0,1,2,3}.

Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.

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Answer:

B) 8cm, 15cm, 17cm

Step-by-step explanation:

We will use angle sum property for this question. (Angle sum property means the addition of the 2 smallest sides have to be larger or equal to the biggest side)

We will try it with all the options.

Option A) 5+8=13. Which is not greater then 17 so it cant be a right triangle.

Option B) 8+15=23. Which is greater then 17 so it can be a right triangle

Hope I helped

Answer:

My guess would be D

Step-by-step explanation:

Answer:

B AND E

Step-by-step explanation:

hope that helpsndbwbe

The baby is 111.3 ounces or 6.96 pounds lighter than an average baby.

Weight is the measurement of Gravitational force on an object.

It can be zero as in the space.

It is given in the question that

A baby weighed only 8.7 ounces at birth

weight of an average baby is 7lb 8 ounces

1 lb = 16 ounce

an average baby weight = 7 * 16 +8 = 120 ounces

The baby weight is just 8.7 ounces

so the baby is 120-8.7 = 111.3 ounces lighter than an average baby.

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Answer:

A pentagon has 5 sides.

Sum of the interior angles = ( n - 2) x 180

Sum of the interior angles = ( 5 - 2) x 180

Sum of the interior angles = 540°

STEP 2: Find one interior angle:

one interior angle = 540 ÷ 5 = 108°

STEP 3: Find the sum of interior angles of a decagon

A decagon has 10 sides

Sum of the interior angles = ( n - 2) x 180

Sum of the interior angles = ( 10 - 2) x 180

Sum of the interior angles = 1440°

STEP 4: Find one interior angle:

one interior angle = 1440 ÷ 10 = 144°

STEP 5: Find the ratio:

Pentagon : Decagon = 108 : 144

Simplify:

Pentagon : Decagon = 3 : 4

Answer: The ratio is 3 : 4

Answer:

  D.  330.6

Step-by-step explanation:

To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.

__

T(x) = x +0.14x . . . . . given function definition

T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x

T(290) = 330.6

The value of T(290) will be 330.6.The relation between them is shown as T(x)  is dependent and x is the independent variable. Option D s correct.

A connection between independent variables and the dependent variable is defined by the function.

Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.

Given relation;

T(x) = x +0.14x

Substitute the value of x we get;

T(290) = 290 +0.14×290

T(290) = 330.6

Hence, option D s correct.

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