Tell whether x and y show direct variation.Explain your reasoning.If so, find k #3

[tex]\dfrac{25}{35}=\dfrac{25:5}{35:5}=\dfrac{5}{7}\to\boxed{D)}[/tex]

Answer:   $ 22

Step-by-step explanation:

[tex]\boxed{\$ 22}[/tex] of sales tax should be paidon the new price.

Further Explanation:

Calculation:

The given listed price of furniture in the month of May is [tex]\$550.[/tex]

The sales tax is of [tex]3\%[/tex] on the listed price of the furniture.

The price of the month May is increased by [tex]33\dfrac{1}{3}\%.[/tex]

The increased price of the furniture can be obtained as follows,

[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\%  \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32 \\\end{aligned}[/tex]

The new price of the furniture in dollars is [tex]\$ 733.32.[/tex]

The sales tax is of  [tex]3\%[/tex] on the listed price.

The sales tax on the new price can be obtained as follows,

[tex]\begin{aligned}{\text{Sales tax}}&= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]

[tex]\boxed{\$ 22}[/tex] of sales tax should be paid in dollars on the new price.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Sales Tax

Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month, 33 1/3%, paid, dollars, new price.

The given lines 'x=-2' and 'y=8' are indeed perpendicular as they intersect at a right angle of 90 degrees, which defines perpendicularity.

In the context of coordinate geometry, the equations 'x=-2' and 'y=8' represent two lines in a 2D space. The line x=-2 is a vertical line that passes through -2 on the x-axis, while y=8 is a horizontal line that passes through 8 on the y-axis.

These lines are indeed perpendicular because they intersect at a right angle, which is a primary characteristic of perpendicular lines. Perpendicularity in 2D space is defined by a 90-degree angle between two lines, and in this case, the vertical line (x=-2) and horizontal line (y=8) do, indeed, intersect perpendicularly.

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Answer:

x = 91.5

Step-by-step explanation:

for 30.5 miles travelled gas used is 1 gallon ← unit rate

To calculate distance travelled multiply gas used by 30.5

For 3 gallons used

distance travelled = 3 × 30.5 = 91.5 miles

⇒ x = 91.5

Answer:

8.3 * 10 ^5

Step-by-step explanation:

830000

To change this to scientific notation, we move the decimal 5 places to the left.  The exponent will be positive 5 because we moved it to the left

8.3 * 10^ +5

8.3 * 10 ^5

Answer:

(x-3, y+4) hope this helps.

Answer:

The correct answer option is (x + 3, y - 4).

Step-by-step explanation:

If we are talking about the translation rule with respect to the origin (0, 0), then the correct option will be (x + 3, y - 4).

Since moving to the right on the x axis means a positive addition so moving three units right will mean 'plus 3'.

While moving down means that the value of y is going in negative so it will be (y - 4)

Kevin needs to answer at least 26 questions correctly out of 32 to exceed an 80% success rate, which means he needs to get 2 more questions right than he previously did.

Kevin correctly answered 75% of his 32 test questions, which is 24 questions. To achieve more than an 80% correct rate, Kevin needs to answer more than 80% of 32, which is more than 25.6 questions. Since Kevin can't answer a fraction of a question, he must answer at least 26 questions correctly. To find the number of additional questions he needs to answer correctly to exceed 80% when he has already answered 24 correctly, we subtract 24 from 26, resulting in 2 more questions that Kevin needs to answer correctly to exceed an 80% success rate.

Answer:

[tex]\dfrac{9}{100}=0.09\ or\ \dfrac{9}{10}=0.9[/tex]

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\text{We have}\ \sqrt{81}:\\\\\sqrt{81}=9\ because\ 9^2=81.\ \text{Therefore}\\\\\dfrac{\sqrt{81}}{100}=\dfrac{9}{100}\\\\\text{If is}\ \sqrt{\dfrac{81}{100}},\text{then:}\\\\ \text{Use}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{\dfrac{81}{100}}=\dfrac{\sqrt{81}}{\sqrt{100}}=\dfrac{9}{10}=0.9\\\\\sqrt{81}=9\ because\ 9^2=81\\\sqrt{100}=10\ because\ 10^2=100[/tex]

900 = 2 · 2 · 3 · 3 · 5 · 5

Next numbers:

2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 5 = 900 · 15 = 13,500

2 · 2 · 2 · 2 · 3 · 3 · 3 · 3 · 5 · 5 · 5 · 5 = 13,500 · 15 = 202,500

202,500 · 15 = 3,037,500

3,037,500 · 15 = 45,562,500

....

Answer:

Solving the system of equations using the substitution method, the solution is: x=2 and y=-2

Step-by-step explanation:

(1) y=7x-16

(2) y=2(2x-5)

Substituting "y" of the equation (1) in the equation (2)

(2) 7x-16=2(2x-5)

Applying the distributive property to eliminate the parentheses on the right side of the equation:

7x-16=2(2x)-2(5)

Multiplying:

7x-16=4x-10

Solving for x: Subtracting 4x and adding 16 both sides of the equation:

7x-16-4x+16=4x-10-4x+16

3x=6

Adding like terms:

Dividing by 3 both sides of the equation:

3x/3=6/3

x=2

Replacing x by 2 in the equation (1):

(1) y=7(2)-16

y=14-16

y=-2

Solution: x=2 and y=-2

Answer:

Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution? (, )Step-by-step explanation:

Answer:

117 Girls

Step-by-step explanation:

If 64% of the kids are boys, then 36% are girls   64% + 36% = 100%

.36 x 325 = 117  girls

Proof

.64 x 325 = 208 boys

208 + 117 = 325

There are 117 girls at the zoo.

To determine how many children at the zoo are girls, we start by understanding that 64% of the 325 children are boys. Let's go through the steps to find out the number of girls.

Calculate the number of boys by multiplying 64% by 325.

Percentage to decimal conversion: 64% = 0.64. So, 0.64 × 325 = 208 boys.

Subtract the number of boys from the total number of children to find the number of girls: 325 - 208 = 117 girls.

Therefore, there are 117 girls at the zoo.

Given : Water Level in the Pool decreases by 6.35 × 10⁻¹ cm each Day

⇒ In One Day : The Level decreases by 6.35 × 10⁻¹ cm

⇒ In [8.64 × 10⁻⁴] Seconds : The Level decreases by 6.35 × 10⁻¹ cm

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = (\frac{6.35 \times 10^-^1}{8.64 \times 10^4})}[/tex]

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 0.73 \times 10^-^5}[/tex]

[tex]\mathsf{\implies In\;One\;Second : The\;Level\;Decreases\;by = 7.3 \times 10^-^6}[/tex]

First Blank : 7.3

Second Blank : 10⁻⁶

Answer:

The two equations are [tex]y=\frac{1}{2}x+5[/tex]    and  [tex]y=\frac{1}{2}x[/tex]                                                                                                                                                                            

Step-by-step explanation:

we have given that : Part I=  [tex]y=\frac{1}{2}x+5[/tex] equation of line

slope intercept form is y=mx+c

the slope of the line Part I is m=1/2

taken another equation of line Part II= [tex]y=\frac{1}{2}x[/tex]

whose slope of line Part II is m=1/2

since, both equation have same slope therefore these two equation  Part II and Part I are parallel

It is also shown by the graph attached.

Answer:

4.7

Step-by-step explanation:

Multiply 15 by 2.2. And get 33

Divide 33 by 7 and get 4.7

Hope it helps!

Final answer:

To accommodate 15 people, the elevator must be approximately 4.7 feet wide.

Explanation:

The question is asking us to calculate the width of the elevator box that can legally accommodate 15 people, given that the elevator building code requires at least 2.2 square feet per person and the depth of the elevator is 7 feet.

First, we need to find out the total area required for 15 people:

Total area = Number of people × Area per person = 15 × 2.2 square feet

Total area = 33 square feet

As we have the depth of the elevator, we can now calculate the width:

Total area = Width × Depth

Width = Total area / Depth

Width = 33 sq ft / 7 ft

Width ≈ 4.7 feet

Therefore, the elevator must be approximately 4.7 feet wide to accommodate 15 people as per the building code's requirements.

Answer:

C

Step-by-step explanation:

The general functional notation is:

[tex]f(x)=A[/tex]

Where it means that [tex]f[/tex] is a function of [tex]x[/tex], and the answer is [tex]A[/tex].

From the problem, we know that the depth is a function of distance, and at that specific distance, the depth is 30 ft.

So we see that depth is a function of distance from shore, and the answer is 30 ft.

Matching this to our explanation of functional notation above, we can say that:

Depth(distance from shore) = 30 ft

Answer C is right.

Answer:

Depth distance from shore equals 30 ft

Step-by-step explanation:

Confirmed from pretest

[tex]\bf \stackrel{\textit{solving for \underline{y}}}{3y+12=2x}\implies 3y=2x-12\implies y=\cfrac{2x-12}{3}\implies y=\cfrac{2x}{3}-\cfrac{12}{3} \\\\\\ y=\cfrac{2}{3}x-4\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

Symbols (or letters) in an equation can be important.

Step-by-Step Explanation:

The symbol [or letter (x, m, n, etc.)] is usually not important because the symbol represents a number. Sometimes it is important because each symbol (or letter) can represent another number.

for example: n+3 = 4-m (the symbol/ letters are different because they represent a different number).

for another example: n+3 = 4 (the symbol/ letter is only one letter).

The choice of letter or symbol to represent an unknown number in mathematics is arbitrary. It doesn't impact the mathematical operation or relationships, as the fundamental principles of algebra apply universally to any symbol.

It doesn't matter what letter or symbol is used to represent an unknown number because the essence of algebra and mathematical expressions is based on abstraction and generality. Mathematical symbols are placeholders for values and can be interchanged without changing the underlying mathematical relationships. Here's why it doesn't matter:

1. Universality of Symbols: Mathematical symbols and variables are universally understood and follow consistent rules. Whether you use "x," "y," "a," "b," or any other symbol, the principles of mathematics remain the same.

2. Abstraction: Algebra allows us to work with general concepts rather than specific numbers. The choice of symbols is arbitrary and doesn't affect the mathematical operations. The symbols represent placeholders for any number that satisfies the given conditions.

3. Flexibility: Different symbols can be used for different contexts or problems. For example, "x" is often used for unknowns in equations, "a" for constants, and "y" for dependent variables in functions. However, this is a convention, and other symbols can be used interchangeably.

4. Consistency: The rules of algebra, such as the commutative, associative, and distributive properties, hold true regardless of the symbols used. Algebraic manipulations and equations remain valid irrespective of the choice of symbols.

In summary, mathematical symbols are versatile and interchangeable because they serve as placeholders for values. The principles of algebra and mathematics are symbol-independent, allowing for flexibility in representation while maintaining the same underlying mathematical relationships.

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Answer:

Option D is correct.

Explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]

Step-by-step explanation:

Geometric sequence states that a sequence of numbers in which the ratio between consecutive terms is constant,

we can write a formula for the nth geometric sequence in the form of:

[tex]a_n = a_1r^{n-1}[/tex] .....[1] where [tex]a_1[/tex] is the first term and  r is the common ratio between successive term.

Given the sequence: 64, 32, 16 , 8......

Here, first term ([tex]a_1[/tex]) = 64.

Common ratio(r) = 0.5

Since,

[tex]\frac{32}{64} =0.5[/tex]

[tex]\frac{16}{32} = 0.5[/tex] ,

[tex]\frac{8}{16} = 0.5[/tex] ......

Substitute the value of a and r in [1] we get;

[tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]

therefore, the explicit formula for the geometric sequence is, [tex]a_n = 64 \cdot (0.5)^{n-1}[/tex]

The bolt with a diameter of 0.52 inch has a percent error of approximately 5.45% from the advertised 0.55 inch, which is within the acceptable margin of less than 6%. Therefore, it should be included in the package.

The question revolves around determining if a bolt with a diameter of 0.52 inch should be packaged given that the labeled diameter is 0.55 inch and the allowable percent error is less than 6%. To calculate the percent error, we use the formula: Percent Error = (|Actual Value - Theoretical Value| / Theoretical Value) × 100%. Applying the numbers: Percent Error = (|0.52 - 0.55| / 0.55) × 100% = (0.03 / 0.55) × 100% ≈ 5.45%.

Since the percent error of 5.45% is less than 6%, the bolt with a diameter of 0.52 inch should be included in the package. This decision is based on the calculated percent error being within the accepted tolerance level.

Answer:

The median of the histogram is scores ranging from 70-80

Step-by-step explanation:

Median of a histogram is always the "class interval" in which the MIDDLE NUMBER falls in.

If we add up all the bars (y-axis), we see HOW MANY NUMBERS in total there are. So we have:

[tex]1+2+1+2+6+9+13+5=39[/tex] numbers in total

What is the middle number out of 39 numbers?

It is: [tex]\frac{n+1}{2}[/tex] th number where [tex]n=39[/tex] for this problem

So, the middle number is : [tex]\frac{39+1}{2}=\frac{40}{2}=20[/tex]th number

Which class interval does the 20th number fall into?

So, definitely, 20th number falls into the sixth class interval which is "70-80".

Hence, the median of the histogram is scores ranging from 70-80.

Let the Length of River D be : P

Given : River C is 100 Miles Longer than River D

⇒ Length of River C = P + 100

Given : The Sum of Both Rivers is 5570 Miles

⇒ P + (P + 100) = 5570

⇒ 2P + 100 = 5570

⇒ 2P = 5570 - 100

⇒ 2P = 5470

⇒ P = 2735

⇒ Length of River D is : 2735 Miles

⇒ Length of River C is : (P + 100) = (2735 + 100) = 2835 Miles

Answer:

Step-by-step explanation:

OK... You have to use this formula: Y2 - Y1

                                                          X2 - X1

Y2 - Y1

X2 - X1

-5 - 7

2 - - 2

-12

-2

Simplify by dividing both -12 & -2 by 2: -6

                                                                 -1

It's either -6 or it's just -6 by itself... Really sorry if I'm wrong...

                -1  

Well, a linear equation should look like this: y = ax + b.

So if the slope is 0, then y = a*0 + b = b.

If y = b, then the line is a horizontal line like this:    ______________

Now, we look at the points that were given in the question: (-2, 7), (2, -5)

If the slope is 0, then the value of y, should not change, but the value of x will constantly be changing. So it means that as x increases, y is always the same.

If we look at the y place on the points: The y values are the bold numbers:

(-2, 7), (2, -5)

As you can see, 7 is not the same as -5. So the line's slope is not 0. The slope would be a negative number. Why? Well, 7 is above the x-axis and -5 is below the x-axis. For the x values, -2 is smaller than 2, so the point (-2, 7) is located at the top left quadrant and the point (2, -5) is located at the bottom right quadrant.

So to answer your question, the slope is not zero. The slope is negative.

Answer:

Step-by-step explanation:

Find x

Find y

Answer:

75 weeks

Step-by-step explanation:

Let the number of weeks be x

10x + 45 = 789          Subtract 45 from both sides

10x = 789 - 45           Combine

10x = 744                   Divide by 10

x = 744/10                  Divide

x= 74.4 weeks.          It will not hurt her to save the extra week to get the phone

Answer:

22 days  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

Nonmember:

swim: $5

exercise: $9

Per day:  9 + 5 = $14

Member:

$300 per year plus $4 per day for an exercise class.  $0 for swimming

300 ÷ 14 = 21.428      21 days x $14 = $294     22 days x $14 = $308

So.... if he goes to the gym at least 22 days he will save money with the membership.

Answer:

The answer is D.) 5d+9d = 300 + 4d

Step-by-step explanation:

The equation states that for each day he attends to the gym to swim and exercise without a membership he has to pay for both, which is $5 and $9 respectively. This is each day that he attends.

However, if he HAS a membership, he only has to pay the $300 yearly fee once, and then $4 everyday he attends afterwards to do both swimming and exercising.

Now, in order to find out when the membership is worth it you need to find out when the membership cost and the non-membership cost is equal. so on one side of the equation you'll need the non-membership costs, and on the other side we'll put the membership cost.

So, for the non-membership cost, every day he goes it'll cost him $5 to swim and $9 to exercise, meaning that one side of the equation is 5d (d represents days) + 9d

And for the membership side we have the $300 initial, one-time fee, and then the $4 a day he has to pay to attend. This is equivalent to 300+4d

Finally, we put both equations together in a way to show that we want both sides to be equal, i.e

5d+9d = 300+4d

Thus our answer is D

Answer:

a. opens: upward

b. a.o.s.: x = 1

c. vertex: (1, -4)

d. x-intercepts: (-1, 0), (3, 0); y-intercept: (0, -3)

Step-by-step explanation:

By looking at the graph, we can see that the parabola opens upward. This means that its a-value is positive.

The axis of symmetry is the line that passes exactly through the center of the parabola. It always starts with x = __, because it is a vertical line.

The center of this parabola is at the x-value of 1, so we can say that the equation of the axis of symmetry is x = 1.

The vertex is at the highest or lowest point of the parabola, also known as the maximum or minimum point. Since this graph opens up, the vertex is at the minimum point.

Look at the graph and find the point where the parabola opens upwards. This point is at the x-value of 1 and the y-value of -4, so the vertex of the parabola is at (1, -4).

Again, look at the graph provided to find the x and y-intercepts. On the x-axis, the parabola crosses through at the x-values of -1 and 3, so the x-intercepts are (-1, 0) and (3, 0).

The parabola crosses the y-axis at the y-value of -3, so the y-intercept of the parabola is (0, -3).

Unable to determine the subject of the question due to lack of information.

The arithmetic operations described pertain to the addition and multiplication of numbers and the result of their signs. For instance:

When two positive numbers add or multiply, the result is also positive (e.g., 3 + 2 = 5 and 2 x 3 = 6).

When two negative numbers add or multiply, the result is negative when adding and positive when multiplying (e.g., -4 + (-2) = -6 and (-4) x (-3) = 12).

For numbers with opposite signs, in addition, subtract the smaller number from the larger number and give the result the sign of the larger number, while in multiplication, the result will have a negative sign (e.g., -5 + 3 = -2 and (-3) x 2 = -6).

Regarding quantum numbers, the sets of quantum numbers provide information about the state of an electron in an atom. Each set of numbers must follow specific rules:

The principal quantum number n must be a positive integer.

The azimuthal quantum number l must be an integer ranging from 0 up to n - 1.

The magnetic quantum number mē must range from -l to +l.

The spin quantum number ms must be either +1/2 or -1/2.

Therefore, for the given quantum numbers a. {4, 2, -2, 1} is not an allowed set because the spin quantum number must be either +1/2 or -1/2, not 1. Similarly, set b. {3, 1, 0, -1/2} is a possible set because it follows all the designated rules for quantum numbers.

Answer:

1. 2x-3

2.-4x+12

3.9x+3

4.-15x-12

5.2x-5

6.-11x

7.23x+42

8.-21x

9.-2x-12

10.4x-8

Step-by-step explanation:

The recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.

To determine how many grams of carbohydrates are recommended per day based on a daily value of 12%, you can use the following calculation:

First, calculate what 1% of the daily value would be:

1% of daily value = 36 grams / 12% = 3 grams

Now, to find the recommended daily intake, simply multiply this by 100 since you want to find the recommended intake for 100% of the daily value:

Recommended daily intake = 3 grams/1% * 100% = 300 grams

So, the recommended daily intake of carbohydrates is 300 grams per day based on a daily value of 12%.

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Answer:

C) y + 1 = -2/3(x - 4)

Step-by-step explanation:

The given line passes through the points A (4, -1) and B (-2, 3)

Let's find the slope now.

Slope (m) = (y2 - y1)/(x2 - x1)

= (3 - (-1)) / (-2 - 4)

= (3 + 1)/-6

= 4/-6

Slope (m) = -2/3

The equation of line y - y1 = m (x - x1)

y - (-1) = -2/3(x - 4)

y + 1 = -2/3(x - 4)

Answer:  C) y + 1 = -2/3(x - 4)

Thank you.

Answer:

answer is c)

Step-by-step explanation:

:)