Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum. Select all that apply:
a. f(x)=In( 1-x) over [0.2] b. g(x)=ln(1+1) over 10, 2] c. 11(x)=VF-1 over [ 1.4] d. k(x)=マ over [1,4]

Answer:

35.03 inches

Step-by-step explanation:

We Know

A tablecloth has a circumference of 220 inches.

Circumference of circle = 2 · r · π

C = 220 inches

π = 3.14

What is the radius of the tablecloth?

We Take

220 = 2 · r · 3.14

110 = r · 3.14

r ≈ 35.03 inches

So, the radius of the tablecloth is about 35.03 inches.

Answer:

Option (1)

Step-by-step explanation:

\(\text{log}_4(x + 3)=\text{log}_2(2 + x)\)

\(\text{log}_4(x + 3)=\frac{\text{log}_{10}(x+3)}{\text{log}_{10}4}\)

\(\text{log}_2(2 + x)=\frac{\text{log}_{10}(2+x)}{\text{log}_{10}2}\)

System of equations can be written as,

\(y_1=\text{log}_4(x + 3)=\frac{\text{log}_{10}(x+3)}{\text{log}_{10}4}\)

\(y_2=\text{log}_2(2 + x)=\frac{\text{log}_{10}(2+x)}{\text{log}_{10}2}\)

Therefore, system of equations given in Option (1) is the correct option.

Answer:

Option (A)

Step-by-step explanation:

Good Luck on your test

Given: The trigonometry shown in the image

To Determine: The exact values of the six trogonometric functions of each angle shown

Solution

It can be observed that

Therefore

Answer:

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

Step-by-step explanation:

The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:

\(t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}\)

The sum of these times must be equal to the total time of the trip, therefore:

\(t_{stage1} + t_{stage2} = 5\)

\(\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10\)

Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.

If the population density for the area is 18.8 residents per square mile, to the nearest hundred, approximately 34,000 residents would be infected.

When a virus is accidentally released from a CDC lab, and it infects everyone within a 24-mile radius from the CDC lab, then if the population density for the area is 18.8 residents per square mile, to the nearest hundred, how many people were infected.

The number of people infected within the 24-mile radius from the CDC lab is calculated as follows:

The area of a circle with a radius of 24 miles is A = πr²,

which is A = π(24²) = 1,809.56 square miles, and the population density for the area is 18.8 residents per square mile.

Therefore, the number of people infected is calculated by multiplying the area by the population density:

Residents infected = area x population density

= 1,809.56 x 18.8 ≈ 34,037.

Approximating to the nearest hundred yields 34,000.

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Answer:

7238 units^3

Step-by-step explanation:

The formula for the volume of a sphere of radius 12 units is

V = (4/3)(pi)r^3.  

Here, with r = 12 units,

V = (4/3)(pi)(12 units)^3 = 7238 units^3

Answer:

V = 2304π units³

Step-by-step explanation:

V = (4/3)πr^3

V = (4/3)π(12)^3

V = (4/3)π(1728)

V = 2304π units³

Answer:

x = -1.33333333333

Step-by-step explanation:

\(\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\)

\(-2x+1-1=4x+9-1\)

\(\mathrm{Simplify}\)

\(-2x=4x+8\)

\(\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\)

\(-2x-4x=4x+8-4x\)

\(\mathrm{Simplify}\)

\(-6x=8\)

\(\mathrm{Divide\:both\:sides\:by\:}-6\)

\(\frac{-6x}{-6}=\frac{8}{-6}\)

\(x=-\frac{4}{3}\)

\(x=-1.33333333333\)

~Lenvy~

The number of cups of sugar will be 11²/₃.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Donna's recipe calls for 2¹/₃ cups of sugar for each cake. Donna wants to make 5 cakes.

The number of cups of sugar will be,

Number = 2¹/₃ x 5

Number = (7/3) x 5

Number = 35 / 3

Number = 11²/₃.

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The number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

In this case, the coefficient is 3.23, and the power of 10 is 6. To convert this number into standard decimal notation, we need to multiply the coefficient by the corresponding power of 10. The power of 10, in this case, is 10^6, which means 10 raised to the power of 6. This is equivalent to 1 followed by six zeros: 1,000,000. To obtain the standard decimal notation, we multiply the coefficient, 3.23, by 1,000,000.

Calculating the multiplication, we have:

3.23 × 1,000,000 = 3,230,000.

Hence, the number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. This means that the number is equal to 3.23 million.

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Answer:

p = 8

Step-by-step explanation:

Let one root of the eqn. be alpha . Other root is 1/alpha .

We know that product of both roots of an quadratic eqn. is c/a where "c" is the co-efficient of the constant  & "a" is the co-efficient of x^2.

Here "c" is p-4 & "a" is 4. And the product of roots is 1 ( ∵ prdouct of a number and its reciprocal is 1 )

\(\frac{c}{a} = 1\\=> \frac{p - 4}{4} = 1\\=> p - 4 = 4\\=> p = 4 + 4 = 8\)

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

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Answer:

1

Step-by-step explanation:

because no number Is beside it except 1 because 1 x anything will give it back

The coefficient of the second term of the expression 3x⁴ + x² will be 1. Then the correct option is B.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The expression is given below.

⇒ 3x⁴ + x²

The number which is associated with the variable is known as the coefficient of that variable.

In the expression 3x⁴ + x², the coefficient of x⁴ is 3 and the coefficient of x² is 1.

The coefficient of the second term of the expression 3x⁴ + x² will be 1. Then the correct option is B.

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Answer:

27

Step-by-step explanation:

75 % of 36 is 27. The place kicker expects he that will make 27 field goals. 36 − 27 = 9 The place kicker expects that he will miss 9 field goals.

Answer:

x/7 + 9 = 6

Step-by-step explanation:

Hope this helps! Please give brainliest!

Answer:

3 + 9x = 11x - 7

simplify

9x + 3 = 11x - 7

subtract 11x from both sides

-11x             -11x

-2x + 3 = -7

get rid of constants first by subtracting by 3 from both sides

-3            -3

-2x = -10

divide both sides by -2 since that is the inverse operation of multiplication

/-2    /-2

X = 5

Answer:

x=5

Step-by-step explanation:

Hi, first the thing to do here is simple,

step 1, collecting like terms

3+9x=11x-7

11x-9x=3+7

2x=10

then divide both by 2.

x= 5

Answer: 157.5

Step-by-step explanation:

I would add 45 % again and you'd get 90 % or

150.00 the find 10 % of 75 which is 10*75/100 or 7.5

then add 150.00+ 7.5 = 157.5

Answer:

(1, -1)

Step-by-step explanation:

we isolate y in the first equation

2x+y=1

-2x.  -2x

y=1-2x

and now we fill y into second equation

4x-2(1-2x)=6

4x-2+4x=6

8x-2=6

   +2 +2

8x=8

/8 /8

x=1

and now to find y we insert x

2(1)+y=1

2+y=1

-2.   -2

y= -1

hopes this helps

Answer:

292° 24' 36"

Step-by-step explanation:

d = int(292.41°) = 292°

m = int((292.41° - 292°) × 60) = 24'

s = (292.41° - 292° - 24'/60) × 3600 = 36"

292.41°

= 292° 24' 36"

Answer:

292 degrees 24 minutes and 36 seconds:

292° 24' 36"

Step-by-step explanation:

There are 60 minutes in a degree and 60 seconds in a minute.

so 0.41 degrees = 0.41 * 60 = 24.6 minutes

and 0.6 of a minute = 0.6 * 60 = 36 seconds.

Answer:

8/19

Step-by-step explanation:

Answer:

8/19

Step-by-step explanation:

2 3/8 = 19/8, reciprical =8/19

he initial number of trees was 204.

The first step to finding the initial number of trees is to write an equation that represents the situation.

This number can be rounded as 204.

Note: This question is incomplete; here is the missing section:

Find the initial number of trees.

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Answer:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Step-by-step explanation:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.

Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.

Given the following:

Length of arc = 6.47 cm

Radius (r) = 2.9 cm

θ = m∠DAB

Plug in the values into the arc length formula:

6.47 = θ × 2.9

6.47/2.9 = θ

θ = 2.23 radians

m∠DAB = 2.23 radians

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Answer:

DAB = 2.23 radians

Hope this helps!

Step-by-step explanation:

The total number of the outcomes will be 12. The table is shown below with all the outcomes.

A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.

Julie went to visit her aunt and uncle for the weekend.

She took the following clothes:

two pairs of slacks – one brown, one black;

three sweaters – one tan, one red and one white;

two shirts – one white and one gray.

Then the total number of the outcomes will be

Total outcomes = 2 x 3 x 2

Total outcomes = 12

The table is shown below with all the outcomes.

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I'm sorry the photo is on a side. I'm too lazy to text it on here lol

The solution is : The equation of the circle is (x - 4)^2 + y^2 = 100

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

we know that

The general equation of the circle into center-radius form is equal to

(x - h)^2 + (y-k)^2 = r^2

where

(h,k) is the center of the circle

In this problem

(h,k) = (4,0)

substitute

(x - 4)^2 + (y-0)^2 = r^2

or, (x - 4)^2 + y^2 = r^2

Find the radius:

we know that

The distance between the points (-2,8) and (4,0) is equal to the radius

Applying the distance 's formula

Formula: distance= √(x_2-x_1)²+(y_2-y_1)²

we get,

d = 10

so

the radius is equal to 10 units

substitute

(x - 4)^2 + y^2 = 10^2

(x - 4)^2 + y^2 = 100

hence, The solution is : The equation of the circle is (x - 4)^2 + y^2 = 100

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#2

Reflexive sides

#3

Already given in question

#4

Given in the question

#5

By bisector definition

#6

Third angle therom

#7

Angle-Side-Angle

Done

Step-by-step explanation:

Missing reasons:

Answer:

8+4+2=14

Step-by-step explanation:

Sorry if this did not help! I give away points!

Answer:
Midpoint = (-0.5, 1)

Step-by-step explanation:

Midpoint formula is (x1 + x2)/2, (y1 + y2)

Lets plug that into the formula.

-4 + 3 = -1

x = -1/2 or -0.5


-1 + 3 = 2

2/2 = 1

y = 1

Final Answer: (-0.5, 1) or (-1/2, 1)

This is true, so we have shown that the solution x = 4 is indeed of the form x. To solve an equation that has only one solution, we need to first identify the equation. Let's say the equation is given as:

x + 3 = 7

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 3 from both sides:

x + 3 - 3 = 7 - 3

This simplifies to:

x = 4

So the solution to this equation is x = 4.

Now, to show that the solution is of the form x, we can substitute the value of x into the original equation and see if it satisfies the equation.

In this case, we have:

4 + 3 = 7

This is true, so we have shown that the solution x = 4 is indeed of the form x.

Overall, the steps to solve an equation with one solution are:

1. Identify the equation
2. Isolate x on one side of the equation
3. Simplify the equation to find the value of x
4. Substitute the value of x into the original equation to check that it satisfies the equation
5. If the substituted value satisfies the equation, the solution is of the form x.

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