Tasty Treats Baking Company asked all students in the senior class at Ridgemont High School the question, “Do you prefer chocolate or butterscotch Tasty Treats?” Everyone surveyed had to pick one of the two answers, and 42%, percent said they preferred chocolate.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:


(Choice A)
A
42%, percent of all students at Ridgemont High prefer chocolate.

(Choice B)
B
42%, percent of all students in the senior class at Ridgemont High prefer chocolate.
(Choice C)
C
42%, percent of the male students in the senior class at Ridgemont High prefer chocolate, but we cannot conclude anything about the population.

Answer:

B) x + 1/y times h/g+1

Step-by-step explanation:

We need to divide [tex]\frac{x+1}{y}[/tex] by [tex]\frac{g+1}{h}[/tex] then match with given choices to find the correct equivalent result.

where given choices are:

A) x/y times h/g

B) x + 1/y times h/g+1

C) x+ 1/y divided h/g+1

D) y/x+1 divided g+1/h

So let's divide  [tex]\frac{x+1}{y}[/tex] by [tex]\frac{g+1}{h}[/tex]

[tex]\frac{\left(\frac{x+1}{y}\right)}{\left(\frac{g+1}{h}\right)}[/tex]

we are allowed to flip the bottom fraction and change division sign into multiplication. So we get:

[tex]=\left(\frac{x+1}{y}\right)\cdot\left(\frac{h}{g+1}\right)[/tex]

Hence correct choice is: B) x + 1/y times h/g+1

Let's start by simplifying the given expression step-by-step:
\[ \text{Given Expression:} \quad \frac{x + \frac{1}{y}}{g + \frac{1}{h}} \]
Firstly, we will find a common denominator for the numerator and denominator of the given fraction.
For the numerator, we already have a single term x and a fraction \( \frac{1}{y} \), which can be combined without altering the denominator.
For the denominator, we have term g and a fraction \( \frac{1}{h} \). To combine these, we need to multiply both terms by h to get a common denominator.
So, the expression becomes:
\[ \frac{x + \frac{1}{y}}{g + \frac{1}{h}} = \frac{xy + 1}{y} \cdot \frac{h}{gh + 1} \]
Next, we will multiply the separated fractions across the numerator and the denominator:
\[ \frac{xy + 1}{y} \cdot \frac{h}{gh + 1} = \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \]
Now, let's consider the given options and check which one is equivalent to our simplified expression:
Option A) \( \frac{x}{y} \times \frac{h}{g} \)
This option simplifies to \( \frac{xh}{yg} \), which is not equivalent to the expression we have because we have \( xy + 1 \) in the numerator, not just \( xh \).
Option B) \( (x + \frac{1}{y}) \times \frac{h}{g+1} \)
For this option, if we simplify, we do not obtain a single fraction with the term \( xy + 1 \) in the numerator and \( y(gh + 1) \) in the denominator, instead, this option gives us \( xh + \frac{h}{y(g+1)} \), which is different from our simplified expression.
Option C) \( \frac{x + \frac{1}{y}}{h/(g + 1)} \)
To simplify this option, we take the reciprocal of the denominator and multiply it with the numerator:
\[ \frac{x + \frac{1}{y}}{h/(g + 1)} = (x + \frac{1}{y}) \times \frac{g + 1}{h} \]
\[ = \frac{(x + \frac{1}{y})(g + 1)}{h} \]
\[ = \frac{xg + x + \frac{g}{y} + \frac{1}{y}}{h} \]
\[ = \frac{xg + x + \frac{g + 1}{y}}{h} \]
This is not equivalent to our simplified expression either because it involves terms like \( xg \) and \( x \), which do not appear in our expression and does not fit the form \( \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \).
Option D) \( \frac{y/(x+1)}{g + \frac{1}{h}} \)
To simplify this option, we multiply by the reciprocal of the denominator:
\[ \frac{y/(x+1)}{g + \frac{1}{h}} = \frac{y}{x+1} \times \frac{h}{gh + 1} \]
\[ = \frac{yh}{(x+1)(gh + 1)} \]
Again, this is not equivalent to our simplified expression, since the expressions \( y/(x+1) \) and \( (xy + 1)/y \) are different.
None of the options (A, B, C, or D) match the simplified form:
\[ \frac{(xy + 1) \cdot h}{y \cdot (gh + 1)} \]
Therefore, none of the given options are equivalent to the original expression \( \frac{x + \frac{1}{y}}{g + \frac{1}{h}} \).

Answer:

The length of the rectangular pen is [tex]40\ ft[/tex]

The width of the rectangular pen is [tex]20\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangular pen

y----> the width of the rectangular pen

we know that

The perimeter of the rectangular pen in this problem is equal to

[tex]P=x+2y[/tex] ---> remember that one side of the rectangle won’t need a fence

[tex]P=80\ ft[/tex]

so

[tex]80=x+2y[/tex]

[tex]y=(80-x)/2[/tex] -----> equation A

The area of the rectangular pen is equal to

[tex]A=xy[/tex] -----> equation B

Substitute equation A in equation B

[tex]A=x*(80-x)/2\\ \\A=-0.5x^{2}+40x[/tex]

The quadratic equation is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex is the length of the rectangular pen that maximize the area of the pen

The y-coordinate of the vertex is the maximum area of the pen

using a graphing tool

The vertex is the point (40,800)

see the attached figure

so

[tex]x=40\ ft[/tex]

Find the value of y

[tex]y=(80-x)/2[/tex] ----> [tex]y=(80-40)/2=20\ ft[/tex]

therefore

The length of the rectangular pen is [tex]40\ ft[/tex]

The width of the rectangular pen is [tex]20\ ft[/tex]

Answer:

length is 40

Width is 20

Step-by-Step explanation:

Answer:

The measure of the central angle is 35° to the nearest degree

The area of the triangle formed is 28.7 inches²

Step-by-step explanation:

* Lets revise the cosine rule to solve the question

- In Δ ABC:

# AB² = BC² + AC² - 2(BC)(AC) cos∠C

- If you want to find m∠C, we can rearrange the rule

# cos∠C = BC² + AC² - AB²/2(BC)(AC)

* Now lets solve the problem

- The length of the radius of the circle is 10 inches

- The length of the chord is 6 inches

- The chord and the two radii drawn to the endpoints of the chord

 formed an isosceles triangle and the angle between the two radii

 is the central angle

- Lets use the cosine rule to find the measure of the central angle

- Let the name of the central angle is Ф

∵ cos Ф = r² + r² - (chord)²/2(r)(r)

∵ r = 10 inches and the chord = 6 inches

∴ cos Ф = (10)² + (10)² - (6)²/2(10)(10)

∴ cos Ф = (100+ 100 - 36)/200

∴ cos Ф = 164/200 = 41/50

- Find the measure of the Ф by using cos^-1 Ф

∴ m∠Ф = cos^-1 (41/50) ≅ 35°

* The measure of the central angle is 35° to the nearest degree

- To find the area of the triangle we will use the sine rule

# Area of any triangle by using the sine rule is

  A = 1/2 × (s1 × s2) × sin the included angle between them

∵ s1 = r , s2 = r and the angle between them is the central angle Ф

∴ Area of the triangle = 1/2 (r × r) × sin Ф

∵ r = 10 and Ф = 35°

∴ Area of the triangle = 1/2 × (10 × 10) × sin 35°

∴ Area of the triangle = 50(sin 35°) ≅ 28.7 inches²

* The area of the triangle formed is 28.7 inches²

there are 36 possible outcomes

Answer:

0.8

Step-by-step explanation:

You are given the equation

[tex]\left(\dfrac{1}{64}\right)^{0.5x-3}=8^{9x-2}[/tex]

First note that

[tex]\dfrac{1}{64}=\dfrac{1}{2^6}=2^{-6}\\ \\\left(\dfrac{1}{64}\right)^{0.5x-3}=(2^{-6})^{0.5x-3}=2^{-6\cdot (0.5x-3)}=2^{-3x+18}\\ \\8=2^3\\ \\8^{9x-2}=(2^3)^{9x-2}=2^{3\cdot (9x-2)}=2^{27x-6}[/tex]

Now

[tex]2^{-3x+18}=2^{27x-6}\\ \\-3x+18=27x-6\\ \\-3x-27x=-6-18\\ \\-30x=-24\\ \\x=\dfrac{24}{30}=\dfrac{8}{10}=0.8[/tex]

Final answer:

To solve the given equation, we convert both sides to a common base and equate the exponents. After simplifying, we find that the solution is x = 8/11.

Explanation:

We are asked to solve the equation (1/64)^0.5x-3 = 8^9x-2. To begin, we will express both sides of the equation with the same base since 64 is 2^6 and 8 is 2^3. This transformation will allow us to use the property of exponents that states when the bases are equal, the exponents must also be equal.

First, let's rewrite the equation using base 2:

Now, since the bases are the same, we can equate the exponents:

The solution to the equation is x = 8/11. Always remember to check for extraneous solutions when dealing with exponents and roots.

Answer:

b. closed circles on 1 and 4 with arrows pointing outward

Step-by-step explanation:

Which of the following describes the graph of {x | x < = 1} u {x | x > = 4},

We have been given the following set;

x < = 1

This set comprises of real numbers that are less than or equal to 1;

(1, 0, -1, -2, -3, -4, .......... -∞)

On the other hand, the set x > = 4 comprises of real numbers that are greater than or equal to 4;

(4, 5, 6, 7, 8, 9, ........∞)

The symbol ∪ means a union of sets. That is the set of numbers that belong in either or both sets;

{x | x < = 1} u {x | x > = 4} is same as writing;

(1, 0, -1, -2, -3, -4, .......... -∞) ∪ (4, 5, 6, 7, 8, 9, ........∞)

Therefore, the solution set will be closed circles on 1 and 4 with arrows pointing outward

Answer:

Closed circles on 1 and 4 with arrows pointing outward ⇒ answer b

Step-by-step explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

 grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

 grater than or equal b

* Now lets solve the problem

∵ {x I x ≤ 1}

∴ x is smaller than or equal 1

∵ {x I x ≥ 4}

∴ x is greater than or equal 4

∵ {x I x ≤1} ∪ {x I x ≥ 4}

- The meaning of ∪ is all numbers smaller than or equal 1 and all

  the numbers greater than or equal 4

∴ {x I x ≤ 1} ∪ {x I x ≥ 4} = (-∞ , 1] ∪ [4 , ∞)

- This solution represented graphically by closed circles on 1 and

 4 with arrows pointing outward

The terminal side of an angle measuring -7x/6 radians lies in the second quadrant, considering the angle implies a clockwise rotation from the positive x-axis and one complete rotation is 2π radians.

One complete revolution is equal to 2π radians, which is approximately 6.28 radians. Negative angles imply a clockwise rotation from the positive x-axis. The given angle, -7x/6 radians, would place the terminal side in a clockwise rotation from the positive x-axis.

Angles that measure between 0 to -π/2 radians lie in the fourth quadrant, while angles between -π/2 to -π radians lie in the third quadrant, angles between -π to -3π/2 radians lie in the second quadrant, and angles between -3π/2 to -2π radians lie in the first quadrant.

Assuming the variable x represents any positive real number, the angle -7x/6 would likely be between -π and -3π/2 (or -1.57 and -4.71), and therefore, the terminal side of this angle would lie in the second quadrant.

Answer:

115°

Step-by-step explanation:

A triangle always has 3 angles, and thew sum of the angles is always 180°. Therefore,

38° + 27° + x° = 180°

65° + x° = 180°

x° = 115°

Answer:

Step-by-step explanation:

Box 1: contains 4 items, two of which are pens. the probability of choosing a pen is 2/4

Box 2: contains 7 crayons and 3 colored pencils for a total of 10. The probability of choosing 1 crayon out of that box is 7/10

Event Probability = 2/4 * 7/10 = 14/40   = 7 / 20

Answer:

B. y = tan x  and  C. y = cot x

Step-by-step explanation:

Range:

range is defined as the set of values that any given function y=f(x), can take for which the x values are defined. It is the value that y can take for the values of x.

Given:

From the given options

the range of tanx and cotx are all real numbers

as the period of tanx and cotx are π

where as range of secx is all real numbers except π/2 + n*π i.e.

(-∞ , -1] U [1 , + ∞)

And range of cscx is all real numbers except n*π i.e.

(-∞ , -1] U [1 , + ∞)

So from the given option:

option B and C are correct while A and D are not !

The answer is:  The correct options are B. Tan(x) and C. Cot(x)

The range is the output of a function when we evaluate the function with inputs (domain), not all functions have a range of all real numbers, however it's more common to find functions without range or domain restrictions.

Both options B. Tan(x) and C. Cot(x) have a range of all real numbers while the functions Sec(x) and Csc (x) have a restricted range.

Sec(x) and Csc(x):

Domain, all real numbers.

Range, from -1 to 1 or  [-1,1]

Tan(x) and Cot(x):

Domain, all real numbers except [tex]\frac{\pi }{2}+-n\pi[/tex]

Range, all real numbers.

Hence, the correct options are B. Tan(x) and C. Cot(x)

Have a nice day!

[tex]\bf \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\[1em] [\log(3)-\log(4)]-\log(2)\implies \log\left( \cfrac{3}{4} \right)-\log(2)\implies \log\left( \cfrac{\frac{3}{4}}{~~2~~} \right) \\\\\\ \log\left( \cfrac{\frac{3}{4}}{~~\frac{2}{1}~~} \right)\implies \log\left( \cfrac{3}{4}\cdot \cfrac{1}{2} \right)\implies \log\left( \cfrac{3}{8} \right)[/tex]

To write the expression as a single logarithm, we'll use the properties of logarithms to combine them. The given expression is:
(log3 - log4) - log2
We start by combining the first two logarithms inside the parenthesis using the difference of logarithms property:
log(a) - log(b) = log(a/b)
Applying this property to (log3 - log4), we get:
log(3/4)
Now, our expression looks like this:
log(3/4) - log2
We can use the same property to combine this with the remaining logarithm:
log(a) - log(b) = log(a/b)
So we apply it with a = 3/4 and b = 2:
log((3/4)/2)
When dividing by 2, we are effectively multiplying by 1/2, so we have:
log(3/4 * 1/2)
Now we perform the multiplication inside the logarithm:
log(3/8)
And that is the expression written as a single logarithm:
log(3/8)

Answer:

Step-by-step explanation:

[tex]\text{The zeros is for}\ f(x)=0.\\\\f(x)=3x^3-3x^2-6x\\\\f(x)=0\iff3x^3-3x^2-6x=0\qquad\text{divide both sides by 3}\\\\x^3-x^2-2x=0\qquad\text{distributive}\\\\x(x^2-x-2)=0\\\\x(x^2+x-2x-2)=0\\\\x\bigg(x(x+1)-2(x+1)\bigg)=0\\\\x(x+1)(x-2)=0\\\\\text{The product is equal to 0, when one of the factors is equal to 0.}\\\text{Therefore:}[/tex]

[tex]x(x+1)(x-2)=0\iff x=0\ \vee\ x+1=0\ \vee\ x-2=0\\\\x=0\ \vee\ x=-1\ \vee\ x=2[/tex]

Answer:

c. the empty set

Step-by-step explanation:

set of {x | x < - 5} n {x | x > 5}

The set x < - 5 comprises of real numbers that are less than -5;

(-6, -7, -8, -9, -10, -11, ......)

On the other hand, the set x > 5 comprises of real numbers greater than 5;

(6, 7, 8, 9, 10, 11, ......)

Clearly, the intersection of the above sets is empty, in that the intersection has no elements.

Therefore, {x | x < - 5} n {x | x > 5} is an empty or null set

Answer:

The solution set empty set or null set ⇒ answer c

Step-by-step explanation:

* Lets study the meaning of the inequality

- If a < x < b, that means the value of x is between a and b

- If a ≤ x ≤ b, that means the value of x is from a to b

- If x < a and x > b, that means the value of x is smaller than a and

 grater than b

- If x ≤ a and x ≥ b, that means the value of x is smaller than or equal a and

 grater than or equal b

* Now lets solve the problem

∵ {x I x < -5}

∴ x is smaller than -5

∵ {x I x > 5}

∴ x is greater than 5

∵ {x I x < -5} ∩ {x I x > 5}

- The meaning of ∩ is the common numbers between the

 two sets, but there is no common numbers between the

 two sets

∴ {x I x < -5} ∩ {x I x > 5} = { }

∴ The solution set empty set or null set

the easiest to solve for is y in the first equation

Answer:

the easiest to  for y in the first equation

Step-by-step explanation: -3

Answer:

0=0

Step-by-step explanation:

When you  combine both expressions  you multiply the first one  by -3

As result all the terms in the second expression are cancelled when both expressions are added

-3x -6y = -30

3x  + 6y =30

0   +  0  = 0

Answer:

Step-by-step explanation:

Put x = -3 to the equation of the function h(x) = x² - 2:

h(-3) = (-3)² - 2 = 9 - 2 = 7

Answer:

-3

Step-by-step explanation:

Expression: |-4| - |7|

1. Absolute value (positive distance from zero; found by removing negative sign unless positive): 4 - 7

2. Subtract: -3

The simplified expression is given by -3.

The absolute value of a number is the positive value of that number. The number, if it is negative, will become positive and a positive number will remain positive.

It is given that the expression is: |-4|-|+7|​

We can now simplify the expression.

The expression can be simplified as follows:

|-4|-|+7|​ = 4 - 7

= -3

The given expression was simplified.

The simplified value of the given expression |-4|-|+7|​ is found to be -3.

Therefore, we have found that the simplified expression is given by -3.

Learn more about absolute values here: https://brainly.com/question/1301718

#SPJ2

Answer:

465.3 = 16.5x

Step-by-step explanation:

We can determine the miles per gallon  by taking the number of miles driven and dividing by the gallons

465.3 /16.5 =x

Rewriting by multiplying each side by 16.5

465.3 = 16.5x

Answer:

A

Step-by-step explanation:

Answer:

easy, it traveled/swam 75.6 miles

Step-by-step explanation:

16.8 x 4.5= 75.6

hope this helps

Answer:

1. 1/4

2. 1/2

Step-by-step explanation:

If there are equal numbers of males and females, we can simplify that by saying there's one male and one female for each coat color.

1. What's the probability that both are males?

Well, there's a 1/2 chances the light-colored coat bear is a male and there's also a 1/2 chances the dark-colored coat bear is a male.  So, we can make this reference table:

Light             Dark

Male             Male

Male             Female

Female         Male

Female         Female

As you can see, the probability that both of the spotted bears are males is 1/4 (1/2 * 1/2).

2. If the light-colored bear, what are the odds both are males?

If we know for sure the light-one is male, then there's 1/2 chances the other is too, refer to the table above to verify.

Answer:yes that is the right answer

Step-by-step explanation:

For this case we must indicate an algebraic expression corresponding to the following:

"6 to the square root of 3"

Then, we must indicate an expression of the form:

[tex]a ^ n[/tex]

Where:

[tex]a = 6\\n = \sqrt {3}[/tex]

Thus, the expression is:

[tex]6 ^ {\sqrt {3}}[/tex]

ANswer:

[tex]6 ^ {\sqrt {3}}[/tex]

Select the equations of the lines that are parallel to the line whose equation is y = 3x + 5

Answer:

6x+2y=12

and

3y=9x

Answer:

The correct answer option is f(x) = 3^(x+3).

Step-by-step explanation:

We are to determine whether which of the given answer options represent the given graph.

A graph which has a similar shape like that of the given graph here (big on the left and crawling along the x-axis on the right) represents the exponential growth or decay.

Therefore, the only correct option we have here is f(x) = 3^(x+3).

.140 I think it's that

Answer:

Step-by-step explanation:

Total number of marbles = 6 + 3 + 5 = 14

You want to draw out 3 marbles -- all of them red. In solving this, you have to assume that none are put back.

The answer is

P(Red) = 6/14 * 5/13 * 4/12

P(Red) = 3/7 + 5/13 + 1/3

numerator = 3*5*1 = 15

denominator = 7 * 13 * 3

denominator = 273

P(red) = 15 / 273

P(red) = 0.0549

Answer:

It is 2, 4, & 5.

Step-by-step explanation:

just got it right on edge.

1. 1/3 to get a red ball.

2. 4/13 to get a blue ball.

3. 3/7 to get a green ball.

Hope this helps!

Answer:

the answer is the green bin

Step-by-step explanation:

12•5•4 is 240

10•6•5 is 300

so, the answer is the green bin

hope this helps!

have a blessed day!

please give brainliest!

Answer:

The length of NO is [tex]14\ ft[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

The Kite  has two pairs of equal-length adjacent (next to each other) sides.

so

The perimeter is equal to

[tex]P=2[MN+NO][/tex]

[tex]P=80\ ft[/tex]

so

[tex]80=2[MN+NO][/tex]

[tex]40=[MN+NO][/tex]

substitute the values and solve for x

[tex]40=[(3x+5)+(x-7)][/tex]

[tex]40=[4x-2][/tex]

[tex]4x=42[/tex]

[tex]x=21\ ft[/tex]

step 2

Find the length of NO

[tex]NO=(21-7)=14\ ft[/tex]

Answer:

Step-by-step explanation:

We know that the diagonals of the parallelogram intersect in half.

Therefore we hawe the equation:

x - 30 = -9 - 6x              add 30 to both sides

x = 21 - 6x              add 6x to both sides

7x = 21            divide both sides by 7

x = 3

X=3 hope this helps sorry if I’m wrong