question 1 options: what is the common difference in the sequence 7, 12, 17, 22, 27, ...? put the just the number in the blank.

Answer:

D. [tex]y=\dfrac{-2}{3}x + 2[/tex]

Step-by-step explanation:

All of these answer choices are in slope intercept form:

[tex]y=mx+b[/tex]

where [tex]m[/tex] is the line's slope and [tex]b[/tex] is its y-intercept.

First, we'll find the line's slope using the points [tex](-3,4)[/tex] and [tex](0, 2)[/tex].

[tex]m=\dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{2-4}{0-(-3)} = \dfrac{-2}{3}[/tex]

Then, plug that [tex]m[/tex]-value into the slope intercept form equation:

[tex]y = \dfrac{-3}{2} + b[/tex]

Next, find the y-value at which the line crosses the y-axis:

[tex]b=2[/tex]

Finally, plug that [tex]b[/tex]-value into the slope intercept form equation and look at which answer choice the equation we solved for matches.

D. [tex]y=\dfrac{-2}{3}x + 2[/tex]

To the nearest of tenth hour kwan has driven total 234 miles.

Speed is the pace at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Speed= distance/time

Based on his speed and the distance driven within that time, Kwan will have driven 234 miles

First find out Kwan's speed per hour:

Speed = Distance / Time

Convert the time to decimals:

= 1 + 1/10 hours

= 1 + 0.1

= 1.1 hours

Speed:

= 234 / 1.1

= 212 miles per hour

In tenth of an hours therefore, Kwan would have gone:

= 212*1.1 hours

= 234 miles

Therefore,Kwan would have driven 234 miles.

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Answer:he drives 234 in 1.1 miles

Step-by-step explanation:

i jus know

The relation that is displayed by the given table is: B. {(1,2), (3,4), (5,6), (8,7)}

A relation can be described as a set of ordered pairs which contain one object from each sets, of which one pair is represented as (x, y). So, in a table, a relation can be represented by having all the set of x-values one column, and their corresponding y-values on another column.

Given the table below:

x   |  y

1      2

8     7

5     6

3     4

We can list out the set of ordered pairs as follows:

(1, 2), (8, 7), (5, 6), and (3, 4).

Ordering the pairs of values, we would have the following relation of the table, which is expressed as: B. {(1,2), (3,4), (5,6), (8,7)}

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Answer:

(4x^2 +7x + 2)

Step-by-step explanation:

(8x³ +26x² + 25x + 6)/( 2x + 3)

(8x³ +26x² + 25x + 6) = (4x^2 +7x + 2)(2x + 3)

(4x^2 +7x + 2)(2x + 3)/(2x+3) = (4x^2 +7x + 2)

The expression that represents the number of football cards that Frankie has is given as follows:

F = J + 65.

The situation can be modeled by a system of equations, in which the variables are given as follows:

Frankie has sixty-five more football cards than his friend John, hence the expression that represents the number of football cards that Frankie has is given as follows:

F = J + 65.

As the term sixty-five more means that the number 65 is added to the amount of cards that John has, which is symbolized by J, to obtain the amount F, which is the number of football cards that Frankie has.

The problem asks for the expression of the number of cards that Frankie has.

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The price of the winter coats is going to be $17.325.

The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price.

given,

Marked Price of winter coats = $57.75 and  discount = 70%

Discount = 70%

57.75 × 70/100

5.775 × 7

40.425

Selling Price = M.P - Discount

57.750 - 40.425

17.325

therefore ,

The price of the winter coats is going to be $17.325.

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The expression is - 2xz⁴

An exponent is a method of expressing large numbers in terms of power. So, exponent means how many times a number is multiplied by itself. For example, 5 is multiplied by itself 3 times i,e 5 *5*5. It can be written as 5³.

Here, 3 is the exponent, and 5 is the base. We can read it as 5 is raised to power 3. The symbol '^' is used to represent the exponents. It is called a carrot.

Based on the power there are different laws of exponents, such as :

So, The expression is - 2xz⁴

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The division represented by the model is:

B:1/6÷2

First, we can see a square that is divided into 6 strips, and one of these strips (actually half of it) is shaded, so we can start by writing:

1/6

Now, notice that only half of the strip is shaded, so we need to divide again by 2, then we will get the division:

(1/6)/2

That is the division represented by the model. So the correct option is B

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Answer:  The correct answer is x = 19 / 5

Step-by-step explanation:

Solve the equation

5x + 3 = 22

Subtract 3 from both sides

5x + 3 − 3 = 22 − 3

5x = 19

Divide both sides by 5

5x/5 = 19/5

x = 19 / 5

On the 19th day, the lily pad covered half the pond.

The reason behind this is, If the lily pad doubles in size every day, then on the 20th day it will be twice as large as it was on the 19th day. That means it was already covering half the pond on the 19th day.

In this puzzle, the water lily is described as doubling in size every day. This means that on the first day, the lily pad is small, but by the second day, it has doubled in size. On the third day, it doubled in size again, and so on. By the 20th day, the lily pad has grown so large that it covers the entire pond.

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Answer: B. 6

Step-by-step explanation:

I think 6 because it says seven liked football and 10 liked basketball, so 1 didn't pick.

We also know that 5 like both and 1 didn't pick, so 1 + 5 = 6 students

The equation of the line passing through (3, 4) and perpendicular to the line  y=1/9x + 8 in slope-intercept form is y = -9x + 31

Suppose we have two lines with slope m₁ and m₂ respectively, then those lines are perpendicular to each other if

m₁ x m₂ = -1

In the given problem, the line is perpendicular to a line whose equation is:

y = 1/9 x + 8

Hence,

m₁ x m₂ = -1

1/9 x  m₂ = -1

m₂ = -9

Therefore, the equation of the second line is:

y = -9x + b

To find the value of b, we use the fact that the line passing through (3,4)

Substitute x = 3, and y = 4

4 = -9 (3) + b

b = 4 + 27 = 31

Thus, the equation of the line is:

y = -9x + 31

Your question is incomplete, but most probably your question was:

Find the equation of the line passing through (3, 4) and perpendicular to the line whose equation is y=1/9x + 8 in slope-intercept form.

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Answer:

22

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −22 and 0 is 22 .

Using the FOIL method, the products are:

1.  x² + 6x - 16

2. x² - 6x - 72

3. x² + 13x + 36

4. x² + 8x + 12

5. x² + 15x + 54

6. x² + x - 20

7. x² - 9

8. x² + 20x + 100

9. x² + 9x - 36

10. x² + x - 12

11. x² + 7x + 10

12. x² - 7x + 12

The FOIL method is an acronym that stands for "First, Outside, Inside, and Last". This method simply describes the order you use in multiplying the terms of a given expression, that is, you have to multiply first terms, then outside terms, then inside terms, then last terms. The final step is to combine like terms together to arrive at your final answer.

Therefore, using the FOIL method, we have the following products:

1.  (x - 2)(x + 8)

x² + 8x -2x - 16

Combine like terms

x² + 6x - 16

2. (x + 6)(x - 12)

x² - 12x + 6x - 72

Combine like terms

x² - 6x - 72

3. (x + 9)(x + 4)

x² + 4x + 9x + 36

x² + 13x + 36

4. (x + 6)(x + 2)

x² + 2x + 6x + 12

Combine like terms

x² + 8x + 12

5. (x + 6)(x + 9)

x² + 9x + 6x + 54

Combine like terms

x² + 15x + 54

6. (x - 4)(x + 5)

x² + 5x - 4x - 20

x² + x - 20

7. (x + 3)(x - 3)

x² - 3x + 3x - 9

x² - 9

8. (x + 10)(x + 10)

x² + 10x + 10x + 100

x² + 20x + 100

9. (x - 3)(x + 12)

x² + 12x - 3x - 36

x² + 9x - 36

10. (x + 4)(x - 3)

x² - 3x + 4x - 12

x² + x - 12

11. (x + 5)(x + 2)

x² + 2x + 5x + 10

x² + 7x + 10

12. (x - 3)(x - 4)

x² - 4x - 3x + 12

x² - 7x + 12

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Answer:

y-int. is (0,7) and slope is 2/3

just repeat the points 3 times

The number of cabinets of large size Lee should pack is equal to 40 and that of small size is equal to 25.

To determine how many of each size of cabinet Lee should pack in the truck, you can set up a system of equations. Let X be the number of large cabinets and Y be the number of small cabinets.

The total weight of the large cabinets is 30X pounds, and the total weight of the small cabinets is 20Y pounds. The total weight of all the cabinets is 1550 pounds, so the equation to represent this is:

30X + 20Y = 1550

The total number of cabinets is the sum of the number of large cabinets and the number of small cabinets, so the equation to represent this is:

X + Y = 65

To solve this system of equations, you can use the substitution method. First, solve for X in the second equation by substituting 65 - Y for X:

X = 65 - Y

Then, substitute 65 - Y for X in the first equation:

30(65 - Y) + 20Y = 1550

Solving this equation for Y, you get:

Y = 25

Substituting this value for Y in the second equation, you get:

X = 65 - 25 = 40

So, Lee should pack 40 large cabinets and 25 small cabinets in the truck.

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In a lottery game, if a player picks 6 numbers then the total 9366819 different choices player have if order doesn't matter.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items, regardless of the order of selection. Formula is

ⁿCᵣ = n! /r!(n-r)!

where n is total number of objects

r is total number of choosing objects

We have given that,

In a lottery game total number = 46 = { 1,2,...., 46}

A player can pick total number = 6 numbers

We have to calculate different choices does the player have if order doesn't matter.

Using Combination formula,

we have , n = 46 , r = 6

⁴⁶C₆ = 46!/6!(40!)

=> ⁴⁶C₆ = 46×45×44×43×42×41×40!/40!(6!)

= 46×45×44×43×42×41 /(6×5×4×3×2×1)

= 23×3×7×11×43×41

= 9366819

Hence, the required ways are 9366819..

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If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

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We will discover that the probability that you will at random wind up with an orange hat is as follows: P = 1/12

Observe how we arrived at that now:

4 pieces of clothing (shirt, pants, socks, or hat)

three hues (purple, blue, or orange)

The color of only one item of clothing will change. The likelihood that you will receive an orange hat is what we are looking for.

We must first determine the likelihood that you will choose a hat at random. The likelihood of picking your hat at random is if all the apparel has the same probability of being chosen, just one more than the number of options (4). p = 1/4

The color is now chosen at random using the same methodology as before, with the likelihood that orange will be chosen at random being: q = 1/3.

When we multiply the individual probabilities by the joint probability, we obtain:

P = q*p = (1/4)*(1/3) = 1/12

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Check the picture below, so the parabola looks more or less like so.

keeping in mind the vertex is half-way between the focus point and the directrix, this one lands as you see it in the picture, with a negative "p" distance.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-5\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=( ~~ x-(-5) ~~ )^2\implies -8y=(x+5)^2 \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{8}(x+5)^2 \end{array}} ~\hfill[/tex]

Answer:

yes

Step-by-step explanation:

for a relation to be a function then each value of x can only map to one unique value of y.

This is the case here, then the relation is a function

The solutions to the quadratic equation 8x² - 3x = 5 are x = 1 and x = -5/8

From the question, we have the following parameters that can be used in our computation:

8 x squared - 3 x = 5

Express properly

So, we have

8x² - 3x = 5

This gives

8x² - 3x - 5 = 0

The quadratic formula is represented as

x = (-b ± √[b² - 4ac])/2a

Substitute the known values in the above equation, so, we have the following representation

x = (3 ± √[(-3)² - 4 * 8 * -5])/(2 * 8)

Evaluate

x = (3 ± √169)/16

So, we have

x = (3 ± 13)/16

Expand

x = (3 + 13)/16 and x = (3- 13)/16

Evaluate

x = 1 and x = -5/8

Hence, the solution is x = 1 and x = -5/8

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The equation x²/3 + y²/3 = 4 represents an ellipse in the shown graph below and the length of the given ellipse is 8 units.

The equation x²/3 + y²/3 = 4 represents an ellipse centered at the origin with a major axis along the x-axis and a minor axis along the y-axis.

The equation can be rewritten as x²/4 + y²/12 = 1 to highlight the lengths of the semi-major and semi-minor axes.

The semi-major axis length is given by the square root of the denominator of the x-term, which is 4, so the semi-major axis length is 2.

The semi-minor axis length is given by the square root of the denominator of the y-term, which is 12, so the semi-minor axis length is 2√3.

Based on the symmetry of the ellipse, we can determine that it is symmetric with respect to both the x-axis and the y-axis.

This means that the length of the entire ellipse can be found by multiplying the semi-major axis length by 4, since there are 4 identical sections due to symmetry.

Length of the ellipse = 4 * semi-major axis length

= 4 * 2

= 8.

Therefore, the length of the given ellipse is 8 units.

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The correct question is as follows:

Sketch the curve with the equation x²/3 + y²/3 = 4 and use symmetry to find its length.

The total number of possibilities for matching up players, assuming that in each game it does matter who has the white pieces, is 670442572800.

A permutation is a mathematical way of an arrangement of objects in a particular way or order. We have, there is total 20 people at chess club on a particular day. Now, these 20 people divided into two groups each find opponents and start playing. There are 10 games in total. Let's say the first player in line plays with the white pieces in the first game. The second person in line plays with the black pieces in the first game. The third person plays with the white pieces in game two. The fourth person plays with the black pieces in game two, and so on. There are 20 of them! ways to do it. But we have to remember that the order of the games doesn't matter, so we have to divide this number by 10! , i.e, number of game permutations . Therefore, the total number of possible arrangement is,

20!/10! = 20×19×---×10!/10! = 20× 19×--× 11

= 670442572800.

Hence, required possibilities is 670442572800.

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Complete question:

There are 20 people at a chess club on a certain day. They each find opponents and start playing. How many possibilities are there for how they are matched up, assuming that in each game it does matter who has the white pieces (in a chess game, one player has the white pieces and the other player has the black pieces)?

The subtotal is $20, Savings is $ 1, New Subtotal is $19, Sales tax is $1.14 and the Total is $20.14

A sales discount is a reduced price offered by a business on a product or service

Given:

1 bottle of lotion = $5

1 t-shirt = $12

1 birthday card = $3

Subtotal = $5 + $12 + $3 = $20

If you use your Target RedCard and save 5%, savings will be:

Savings = 5% of Subtotal

Savings = 5/100 × $20 = $1

New Subtotal: $20 - $1 = $19

Sales tax is 6%: 6/100 × $19 = $1.14

Total: New Subtotal + Sales tax = $19 + $1.14 =$20.14

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A continuous quantitative variable is a measure of a quantity that can take any value within a certain range. An example of this is the number of gallons of paint purchased.

A continuous quantitative variable is a type of data that is measured on a continuous scale. This type of data is typically used to measure quantities that can take any value within a certain range. Examples of continuous quantitative variables include the number of gallons of paint purchased, the number of miles of interstate highways, or the population of a city. Continuous quantitative variables differ from discrete quantitative variables, which are used to measure counts of items or events. For example, the number of quarts of milk purchased or the number of times you sharpen your pencil while working on statistics problems would be discrete quantitative variables. Continuous quantitative variables can be measured with precise accuracy, while discrete quantitative variables can only be measured in whole numbers, since they are counts of items or events.

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Answer:

L = 12ft

W = 13ft

Step-by-step explanation:

Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).

The length and width are consecutive integers

L+1=W

The area of the rectangle is 156 square feet.

L*W=156

We know that W=L+1 from our first equation, so substituting that information into our second equation we get

L*(L+1)=156

Let's distribute that L

L^2 + L = 156

and subtract 156 from both sides

L^2 + L - 156 = 0

Now we can use the quadratic formula to find L. L cannot be negative, so

L = 12

using our very first equation we know L, so we can solve for W.

L+1=W

12+1=W

W = 13