Find f(5) for f(x)=1/4(2)^x
A. 2
B. 4
C. 32
D. 8

The best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex]

What is a Fraction ?

A fraction is written as p/q , where q [tex]\rm \ne[/tex] 0

It is asked to determine the sum of the fraction

31/4 + 17/3 + 8/18

Taking the LCM of 4 , 3 , 18

LCM of 4 , 3 ,18 is 36

Therefore

[tex]\rm \dfrac{ 31 *9 + 17 *12 + 8 *2}{36 }[/tex]

(279+204+16) /36

499 / 36

[tex]\rm 13 \dfrac {31}{26}[/tex]

Therefore the best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex].

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Answer:3x+4=28

Step-by-step explanation:

the second one would equal 3x=32

And the third one would equal 3x+12=28 which isn’t right either

Answer:

a

Step-by-step explanation:

The midline is at y=2.

Eliminate c, d, e

Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.

This means the answer is a.

The form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]

The fraction is given as:

[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2}[/tex]

To decompose the above, we make use of the following rule:

[tex]\frac{px^n + qx^m +....+ r}{(x^2 + a)(x^2 + b)^2} = \frac{Ax + B}{(x^2 + a)} + \frac{Cx + D}{(x^2 + b)} + \frac{Ex + F}{(x^2 + b)^2}[/tex]

So, we have:

[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2} = \frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]

Hence, the form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]

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TheThe smallest diameter of wrapper that will fit the candy bar is 5cm.

Given:

AD = DC

AC = AD + DC

Segment AD = 2.5cm

Hence:

AC = AD + AD (AD = DC)

AC = 2AD

Where:

AD=2.5

So,

AC = 2(2.5cm)

AC = 5cm

Therefore the smallest diameter of wrapper that will fit the candy bar is 5cm.

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Answer: 5cm.

Step-by-step explanation:

Answer:

The answer would be A: -15

Answer:

no solution

Step-by-step explanation:

use grouping method:

f(x) = x^2 - 4x + 2

factor it:

when we try to factor the above equation, we see that there is no ordered pair in which the numbers multiple to -4 and add to 2, so there is no solution

Answer:

no man you should reconsider the question again

try typing again i guess its wrong

Step-by-step explanation:

no man you should reconsider the question again

try typing again i guess its wrong

winning a lottery would be correct one i guess

The solution using correct step of substitution in the equation y=2x-1 4x+y=2 is x = 1/2 and y = 0

y = 2x - 1

4x + y = 2

4x + y = 2

4x + (2x - 1) = 2

4x + 2x - 1 = 2

6x - 1 = 2

6x = 2 + 1

6x = 3

x = 3/6

x = 1/2

y = 2x - 1

y = 2(1/2) - 1

= 2/2 - 1

= 1 - 1

y = 0

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Answer:

67.5

Step-by-step explanation:

I'm assuming this is simple interest.

1500x0.03x1.5=67.5

By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.

For polynomials of the form a · x² + b · x + c = 0, the two roots can be found analytically by quadratic formula, whose expression is described below:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]    

If we know that a = 2, b = - 7 and c = 1, then the roots of the polynomial are:

x = 7/4 ± (1/4) · √41

x = (7 ± √41) / 4

By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.

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5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the amount of 45% copper and y represent the amount of 66% copper needed to make 42 pounds of a third alloy containing 66% copper. Hence:

x + y = 42   (1)

Also:

0.45x + 0.69y = 42(0.66)   (2)

This gives:

x = 5.25, y = 36.75

5.25 pounds of one alloy containing 45% copper and 36.75 pounds of 69% copper is used to make 42 pounds of 66% copper

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Both the options that Nadia gives are wrong about the length of hypotenuse.

Given length of hypotenuse is 73 and options which are :

1) Because the pythagoras theorem states that [tex]28^{2} +45^{2}[/tex] squared = 73 squared.

2) 3 squares are positioned to form a right triangle.

We have to choose the correct option which shows the calculation of length of hypotenuse.

Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to sum of the square of base and square of perpendicular.

[tex]H^{2} =P^{2} +B^{2}[/tex]

First option says that [tex]28^{2} +45^{2} =73^{2}[/tex]

784+2025=5329

2809≠5329

so it is wrong.

Second option says that the length  of hypotenuse is the sum of three squares but we have seen that the square of the length of hypotenuse is equal to sum of two square one is the square of base and the square of perpendicular.

Hence both the options are incorrect about the length of hypotenuse.

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Answer:

C

Step-by-step explanation:

Answer:

x < -4

Step-by-step explanation:

add 8 to both sides

Simplify

Subtract 3x from both sides

Simplify, again

Multiply both sides by -1 ( reverse inequality)

Simplify, again

Divide both sides by 5

And vwola x < -4

HOPE THAT HELPS! :)

Answer:

Step-by-step explanation:

The sequence of required answers provides a step-by-step solution to the problem.

In the given trinomial, we identify the coefficients as ...

  ax² +bx +c = 25x² -20x -12   ⇒   a=25; b=-20; c=-12

Then the ac product is ...

  ac = (25)(-12) = -300

The factor pairs that make this product can be listed as ...

  -300 = (-300)(1) = (-150)(2) = (-100)(3) = (-75)(4) = (-60)(5) = (-50)(6) = (-30)(10) = (-25)(12) = (-20)(15) . . . . (only pairs with a negative sum are listed)

The sums of these pairs are -299, -148, -97, -71, -55, -44, -20, -13, -5.

The factors of the ac product that add to -20 are -30 and 10.

These factors are used to rewrite the -20x term as a sum.

  25x² -20x -12 = 25x² -30x +10x -12

Grouping these terms in pairs, we can identify common factors:

  = (25x² -30x) +(10x -12)

  = 5x(5x -6) +2(5x -6)

  = (5x +2)(5x +(-6))

There are 138 female patients in the hospital.

The solution to the word problem involving ratios in the given problem can be determined as follows.

From the given information:

The total number of people in the hospital = male + female

= 184 + x(unknown)

The ratio of males in the hospital is:

[tex]\mathbf{184= \dfrac{4}{7} \times x }[/tex]

[tex]\mathbf{184\times 7= 4 x }[/tex]

x = 322

The number of female patients in the hospital can now be computed as:

[tex]\mathbf{=\dfrac{3}{7}\times 322}[/tex]

= 138 female patients

Check:

The total number of people in the hospital is:

= 184 + 138

= 322 patients

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Answer: 1

Step-by-step explanation:

If [tex]x > -7[/tex], then [tex]x+7 > 0 \implies |x+7|=x+7[/tex]

So, we have the original fraction is equal to

[tex]\frac{x+7}{x+7}=\boxed{1}[/tex]

Answer:

A

Step-by-step explanation:

You are given one angle and one side are similar

 for  Angle-Side-Angle     you obviously need one more angle attached to the given side

A  angle r = ~ angle c

The resistance measured in ohms according to the given task is; 3.75 ohms.

Since it follows that the three quantities are related by the formula; V = √P. R can be used to estimate the required resistance.

Hence, when V = 130 and P = 1200; we have;

130 = √1200 × R

R = 3.75 ohm

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[tex]\frac{2}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\=\frac{2\sqrt{13}-2\sqrt{11}}{13-11}\\\\=\boxed{\sqrt{13}-\sqrt{11}}[/tex]

The solution is: our final quotient is:  (√13 - √11).

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation

Since we have radicals in the denominator, we need to rationalize our expression.

To do it we just need to multiply both numerator and denominator by the conjugate of the denominator.

Remember that the conjugate of a binomial is the same binomial with the sing in between changed.

given that,

2/ (√13 + √11)

Now, we can simplify the denominator:

multiplying by  (√13 - √11)

we get,

2 *  (√13 - √11) / (√13 + √11)*  (√13 - √11)

The only radical that we can simplify in the numerator is , which simplifies to:

2 (√13 - √11) / 13 - 11

=  2(√13 - √11) /2

= (√13 - √11)

So, our final quotient is:  (√13 - √11)

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Answer:

to find this radius you need to square the area and divide it by pi or 3.14 if your using Alex

M + T in standard form polynomial is -15r² + 2r + 8

Polynomial in standard is when all its terms are arranged by decreasing order of degree.

Therefore,

M = - 8r²+ 11r - 6

T = -7r² - 9r + 14

M + T =  - 8r²+ 11r - 6 + (-7r² - 9r + 14)

M + T =  - 8r²+ 11r - 6 - 7r² - 9r + 14

combine like terms

M + T = - 8r² - 7r² + 11r - 9r  - 6  + 14

In standard form, the polynomial is represented as follows;

M + T = -15r² + 2r + 8

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The p value is less, therefore one should reject the null hypothesis.

From the information given, the test statistic will be:

t = (10 - 0)/(6.733/✓7)

t = 3.930.

The degree of freedom will be:

= 7 - 1 = 6

Using the table, the p value will be 0.0039.

Since the p value is less than 0.05 one should reject the null hypothesis.

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The truth table for implication of the equations is F F ⇒ T

A truth table is a mathematical logic table that shows the truth values of different logic statements combined by a given logic rule.

Analysis:

P: 7 +1 is not equal to 0 making P to be false(F)

q: 2+2  is not equal to 5 making q to be false(F)

so for conditional or implication, F F⇒ T

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The slope and the y-intercept of the function are: A. Slope = -2/5; y-intercept = -1/3.

Slope (m) = change in y / change in x.

Using two pairs of points form the table value, (1/4, -13/30) and (2/3, -3/5)"

Slope (m) = (-13/30 - (-3/5))/(1/4 - 2/3)

Slope (m) = (-13/30 + 3/5))/(1/4 - 2/3)

Slope (m) = (1/6)/(-5/12)

Slope (m) = (1/6)(12/-5) = 12/-30

Slope (m) = -2/5

Plug in m = -2/5 and (x, y) = (2/3, -3/5) into y = mx + b to find the y-intercept (b).

-3/5 = -2/5(2/3) + b

-3/5 = -4/15 + b

-3/5 + 4/15 = b

-1/3 = b

b = -1/3

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Answer:

A. Slope = -2/5; y-intercept = -1/3.

Step-by-step explanation:

Hope this helps!!

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{What is addition \& subtraction?}[/tex]

[tex]\huge\textbf{What is addition?}[/tex]

[tex]\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}[/tex]

[tex]\huge\textbf{Random notes}[/tex]

[tex]\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}[/tex]

[tex]\huge\textbf{Example:}[/tex]

[tex]\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}[/tex]

[tex]\huge\textbf{What is subtraction?}[/tex]

[tex]\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}[/tex]

[tex]\huge\textbf{Random notes:}[/tex]

[tex]\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}[/tex]

[tex]\huge\textbf{Example:}[/tex]

[tex]\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}[/tex]

[tex]\huge\textsf{KEEP IN MIND:}[/tex]

[tex]\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitirite1040:)}[/tex]

Answer: Option (2)

Step-by-step explanation:

[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].

Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].

So, the answer is Option (2).

The total surface area of the tomato ketchup given in the diagram can be determined as follows:

The total surface area of a shape is the addition of the areas of its individual surface.

So that the questions can be answered as thus:

A. To find the area of the given circle;

i. Area of a circle = [tex]\pi r^{2}[/tex]

where r is the radius of the circle.

area of the circle = π[tex](2.5)^{2}[/tex]

                            = 6.25[tex]\pi[/tex]

ii. There are two identical circles in the cylinder.

iii. The total area of all circles = 2(6.25[tex]\pi[/tex])

                                                 = 12.5[tex]\pi[/tex] square inches

B. To find the area of the rectangle;

i. one side of the rectangle is 5 inches.

ii. The other side of the rectangle = 2[tex]\pi[/tex]r

                                     = 2(2.5)[tex]\pi[/tex]

                                     = 5[tex]\pi[/tex] inches

iii. The area of the rectangle = l x b

                             = 5[tex]\pi[/tex] x 5

                             = 25[tex]\pi[/tex] square inches

C. Total surfce area of the cylinder = 5[tex]\pi[/tex] + 25[tex]\pi[/tex]

                                         = 30[tex]\pi[/tex] square inches

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Answer:

Step-by-step explanation:

First box

6.25

2

12.5

------

Second box

------

5

5

25

------

Last box

------

37.5

The probability he will get at least 2 hits in the game is 0.470

The batting average is 0.229

In one game he gets 5 at bat

To find the probability he will get at least 2 hits we use binomial distribution.

The binomial distribution is also a Frequency distribution used for the possible no. of successful outcomes in a given no. of trials in each of which there is the same probability of success.

So we have

n = 5

p = 0.299

q = 1 - p

   = 0.701

[tex]P(X) = nC_{x} p^x q^(n-x)[/tex]

P(at least 2 hits in the game) = 1 - P(less than 2 hits)

= 1 - P(0) - P(1)

[tex]= 1 - 0.701^5 - 5C1 x 0.299 x 0.701^4[/tex]

= 1 - 0.169 - 0.361

= 0.470

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