Which of the following are solutions to the inequality 2y+3<7? Mark all that are solutions.

[_] 2

[_] 0

[_] -1

[_] 1

The union of the sets P and Q does not have the integer 5 since it is neither a multiple of 3 or a multiple of 4.

P is the set of integers between 1 and 10 and multiple of 3.

∴P = {3,6,9}

Q is the set of positive integers less than 15 and multiple of 4.

∴Q = {4,8,12}

Now the union of the sets P and Q is given by :

P∪Q = {3,4,6,8,9,12}

Now the union of the sets does not contain the integer 5.

Any collection of items, including a set of raw materials, the seven days of the week, several car types, etc., can be categorized as a set.

Any set component counts as an element of the set. Curly brackets are used to write a set. A very basic set would resemble something like this:

Q = {4,8,12}.

Therefore the integer 5 does not belong to the union of P and Q .

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The solution of the system of equations is (2, 4, 5)

The given equations are :

3x+10y-12z = 40    equation(1)

x-5y = 0     equation (2)

x-4z = 0      equation(3)

From 2nd equation, x -5y = 0, 5y = x, y = x/5

From 3rd equation, x -4z = 0, 4z = x, z = x/4

Putting the values of y and z in equation (1), we get :

[tex]3x +10y -12z = 40\\\\3x +10*\frac{x}{5} -12*\frac{x}{4} = 40\\\\3x +2x -3x =40\\\\2x = 40\\\\x = \frac{40}{2} = 20[/tex]

Now, putting the value of x = 20 to evaluate y and z, we have,

y = 20/5 = 4

and z = 20/4 = 5

Hence, the solution of the system of equations is (2, 4, 5)

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Answer: $1338.96

Step-by-step explanation:

The wholesale cost means the cost that the store buys the table from the supplier. To find the price that the store sells it, it is a 20% markup.

The orginal price is $1,115.80. What is 20% of $1,115.80?

$1,115.80 * .20 = $223.16

Lets add the original price to the markup.

$1,115.80 + $223.16 = $1338.96


Hope this helps <3

The following are the characteristics of the graph of the linear parent function:

B. It has a slope of 1.

C. It is a parabola.

D. It is a straight line.

Lets explain the meaning of linear parent function

- A linear parent function is the equation y = x or f(x) = x

- A parent function is the simplest equation of a function

- It represented by a straight line passing through the origin point O

- The x-coordinate and the y-coordinate of any points lie on it are equal

- The slope of the line is 1 because the slope is the change of Δy/Δx

and Δy = Δx

The characteristics of the graph of the linear parent  function are

∵ Linear parent function is f(x) = x and f(x) = y

∴ x = y

∵ The slope = Δy/Δx

∵ Δx = Δy because x = y

∴ The slope of it is 1

B. It has a slope of 1

∵ y = 0

∵ If x = 0 then y must = 0

∴ It goes through the origin

C. It goes through the origin

∵ It is a linear function

∵ All linear function represented by a straight line

∴ The graph of the linear parent function is a straight line

D. It is a straight line

Hence we get the right answers.

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The rate that the house's value decrease in dollars, that is the current value of the house in terms of:

A stock's price rises if there is a greater demand (buyers) than supply (sellers) for it. On the other hand, if there was a bigger supply than there was a demand for a stock, the price would drop. It's simple to comprehend supply and demand.

The price decreases by:

= $447, 000 * (0.17)

=$75,990.

The current value is:

= 447, 000  - 75,990

= $371,010.

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Step-by-step explanation:

w = t/7

at the beginning we 0 inches of water.

after 56 minutes we have 8 inches of water.

that is a ratio of 56 minutes / 8 inches = 7/1 = 1 / 1/7.

so, in 1 minute we get 1/7 inch of water.

in 2 minutes 2×1/7 = 2/7.

in 3 minutes 3×1/7 = 3/7.

...

hence the equation.

Answer:

Step-by-step explanation:

Find the value of m and b in the equation y = mx + b.

The value of b = 0, since there is no level in the bucket initially.

Find the value of m, the slope:

So the equation is:

or

The linear equation that represents the hours Yuson has left after x days is (A) y = -2x + 30

Given in question,

Hours she should complete = 30 hours

Hours she complete each day = 2 hours

Hours completed in x days = 2x

Hours left after x days = 30 -2x

Hence, the linear equation that represents the hours Yuson has left after x days is y = -2x + 30.

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Answer:

y = (24/5)x + 24

Step-by-step explanation:

Knowing that the parent equation for linear functions is "y = mx+b", where "m = slope" and "b = y-intercept", we can create an equation for the line of best fit.

We also need to know the formula for using two points to find the slope is  "(y2 - y1)/(x2 - x1)", where (x2, y2) is a point on the graph and (x1, y1) is a point on the graph.

Finding the slope:

I will be using points (5, 48) and (0, 24).

(24 - 48)/(0 - 5)

(-24)/(-5)

24/5      is the slope so "m = 24/5"

We can tell from the graph (0, 24) is the y-intercept, so "b = 24"

Final equation:

y = (24/5)x + 24

Answer:

Convergence

Step-by-step explanation:

Use the Squeeze Theorem,

I know that

[tex] \frac{k \sin {}^{2} (k) }{1 + k {}^{3} } [/tex]

lies between 0 and 1 so

[tex]0 \leqslant \frac{k \sin {}^{2} (k) }{1 + {k}^{3} } \leqslant \frac{k}{1 + k {}^{3} } [/tex]

The final series behaves like

[tex] \frac{1}{k {}^{2} } [/tex]

Using the p series, since p is 2, the series

[tex] \frac{k}{1 + k {}^{3} } \: converges[/tex]

Since the 0 and k/1+k^3 converges, the series converge.

Convergence

Answer:

30

Step-by-step explanation:

Divide each term in 6 w = 180 by 6 and simplify. w = 30

Answer:

w = 30

Step-by-step explanation:

Given equation,

→ 6w = 180

Now the value of w will be,

→ 6w = 180

→ w = 180/6

→ [ w = 30 ]

Hence, the value of w is 30.

The portion of the original price that has been deducted to get the clearance price is D. 0.85

Given that the the prices on a clearance rack of merchandise are 0.62 of the original price and that the sign on the clearance rack states that an additional 23% of the original price will be taken off at checkout.

Therefore, the prices deducted will be:

= 0.62 + 23%

= 0.62 + 0.23

= 0.85

In conclusion, the correct option is D.

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(MAKE BRAINLIEST IF I HELPED)

Answer:

x=10

Step-by-step explanation::

We can use Triangle angle bisector theorem and proportions to solve this problem.  We put the small triangle side over the large triangle side

8           x+4

------ = ------------

12          2x+1

Using cross products

8(2x+1) = 12(x+4)

16x+8 =12x+48

Subtract 12x from each side

16x-12x +8 = 12x-12x+48

4x+8 = 48

Subtract 8 from each side

4x+8-8 = 48-8

4x = 40

Divide by 4

4x/4 = 40/4

x = 10

Answer:

x=10

Step-by-step explanation:

The domain of the function f(x) = 16.4·x + 2, where x is the distance from the office, which is (always) a positive number is the set of all real numbers but the reasonable domain differs from the mathematical domain in that; The reasonable domain is the set of positive real numbers

The domain is the set of the possible inputs while the range is the set of the possible outputs of the function.

The mathematical domain is the set of the inputs that the function accepts

The function, f(x) = 16.4·x + 2, mathematically, is continuous for all real number value of x. that is the function has an output when the input, x, is a member of the set of real numbers which includes negative number.

The number of miles from the office, which is the distance from the office is (always) a positive number, because it is the distance between two places, and therefore is not a negative number.

The values of x are therefore positive numbers and the reasonable values of the variable, x, which is the distance from the office is the set of positive real numbers.

The option that indicates how the reasonable domain differ from the mathematical domain is therefore;

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The required value of the given expression : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100 = 5.3

The Bodmas rule is based on the BODMAS acronym, which stands for Brackets, Order of Powers or Roots, Division, and Multiplication. Subtraction is represented by the letter S, while addition is represented by the letters A and S. According to the BODMAS rule, mathematical expressions with multiple operators must be resolved in the order of BODMAS, starting from the left. As with addition and subtraction, division and multiplication are interchangeable and depend on which comes first in the expression.

Given : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100

on calculating it further

we get :

[tex]\frac{4}{75}[/tex] × 100

0.0533 X 100

=> 5.3

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Triangle C forms a right angle triangle.

Given:

Triangle A : 8 cm , 13 cm , 5 cm

Triangle B : 14 cm , 30 cm , 17 cm

Triangle C : 26 cm , 10 cm , 24 cm

To form a right angled triangle the longest side square is equal to the sum of squares of other sides.

In triangle A :

[tex]13^{2} = 8^{2} +5^{2}[/tex]

169 = 64 + 25

169 ≠ 89.

This is not a right angle triangle.

In triangle B:

[tex]30^{2} =17^{2} +14^{2}[/tex]

900 =  289 + 196

900 ≠ 485

This is not a right angle triangle.

In triangle C:

[tex]26^{2} = 10^{2} +24^{2}[/tex]

676 = 100 + 576

676 = 676

so it is a right angle triangle.

Therefore Triangle C forms a right angle triangle.

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An amount of $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, one part of $2600 was invested at a rate of 7.5% and the other part was invested at a rate of 5%, and the total yield was $175 simple interest.

Let $x was invested at 7.5%, then $(2600-x) was invested at 5%.

Since the yield is $175, it follows,

7.5% of x + 5% of (2600-x) = 175

7.5x/100 + 5(2600-x)/100 = 175

7.5x + 13000 - 5x = 17500

2.5x = 17500-13000

2.5x = 4500

x = 1800

Now, the value of (2600-x) is,

2600-1800

=800

Hence, $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.

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William invested $1800 at 7.5% and $800 at 5% on his both accounts.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, William opened two investment accounts. In the first​ year, these​ investments, which totaled ​$2600​,

Assuming he invested $x at 7.5% on the first account and $(2600 - x) at 5% in the second account and yielded ​$175 in simple interest.

∴ (x×7.5×1)/100 + {(2600 - x)×5×1}/100 = 175.

7.5x/100 + (13000 - 5x)/100 = 175.

7.5x + 13000 - 5x = 17500.

2.5x = 4500.

x = 1800. And (2600 - x) = (2600 - 1800) = 800.

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The table of values for the function  ƒ(x) = –2 ∛x is

x   y

-8  4

-4   3.175

0    0

4    3.175

8     4

The correct graph option is attached

Using the given expression, the table of values is calculated with the input values as

x = -8, -4, 0, 4, 8

for x = -8

ƒ(x) = –2 ∛-8 = 4

for x = -4

ƒ(x) = –2 ∛-8 = 3.175

for x = 0

ƒ(x) = –2 ∛-8 = 0

for x = 4

ƒ(x) = –2 ∛-8 = -3.175

for x = 8

ƒ(x) = –2 ∛8 = -4

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Expression is equal to = 2.35 x 10^7.

Given,

In the question:

Wendy solved a problem with her calculator, and she got this answer:

2.35E7

To find the which expressions are equivalent to the answer she got?

Now, According to the question;

The number is given as:

2.35E7

Expression is equal to = 2.35 x 10^7

Hence, Expression is equal to = 2.35 x 10^7.

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Check the picture below.

The rate at which Bart read is 24/7 book/day.

Given, Bart read 4/7 of comic book in 1/6 of a day.

We have to find the rate at which he read the book in a day.

Now, Bart read 4/7th of a comic book = 1/6th of a day

4/7 comic book = 1/6 day

1 day = (4 × 6)/7 comic book

1 day = 24/7 comic book

So, the rate at which Bart read is 24/7 book/day.

Hence, the rate at which Bart read is 24/7 book/day.

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The different possibilities available for selecting an executive board in Student Council in election is 990 ways

In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6

The problem is a permutation problem trying to select 3 from 11 where order matters. The order include choosing the president the ramainig position is left 2 for 10. and so on.

This is shown in permutation as follows

₁₁P₃  = 11! / (11 - 3)!

= 11! / 8!

= 990 ways

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The equation that can be used to find the length of the afternoon practice is B. 4(h + 3) = 20

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, during the summer the team practices 4 days per week and each of those days, they practice for 3 hours in the morning and practice again in the afternoon.

Let the afternoon practice be h.

Therefore, the equation will be:

4(h + 3) = 20

In conclusion, the correct option is B.

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To complete the given series 9, 70 , 499, 2488, 7469 the next number is given by 7466.

As given in the question,

Given series is equal to :

9, 70 , 499, 2488, 7469

Simplify the given series to get the next sequence number we have:

Pattern of the given series is given by:

9  

70 = 9 × 9 -11

    = 70

499 = 70 × ( 9 -2 ) + ( 11 - 2 )

      = 70 × 7 + 9

      = 499

2488 = 499 × ( 7 - 2 ) - ( 9 - 2 )

         = 499 × 5 - 7

         = 2488

7469 = 2488 × ( 5 - 2 ) + ( 7 -2 )

        = 2488 × 3 + 5

        = 7469

Next number is :

7469 × ( 3 - 2 ) - ( 5- 2 )

= 7469 × 1 -3

= 7466

Therefore, to complete the given series 9, 70 , 499, 2488, 7469 the next number is given by 7466.

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The probability that the person is between 67.1 and 68.3 inches, using the normal distribution, is of:

0.1056 = 10.56%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the heights of UCB students are given as follows:

[tex]\mu = 65, \sigma = 2.4[/tex]

The probability that the person is between 67.1 and 68.3 inches is the p-value of Z when X = 68.3 subtracted by the p-value of Z when X = 67.1, hence:

X = 68.3:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (68.3 - 65)/2.4

Z = 1.38.

Z = 1.38 has a p-value of 0.9162.

X = 67.1:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (67.1 - 65)/2.4

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

0.9162 - 0.8106 = 0.1056 = 10.56%.

The problem asks for the probability that the person is between 67.1 and 68.3 inches.

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Answer:

X=3

Step-by-step explanation:

I'm not sure what statements below you want me to confirm that X=Y, Y=3

Jimmy has to write 369 words per day for the next 6 days to finish the paper.

The total number of words in the paper has to be 3000

Jimmy has already written = 786 words.

3000-786 = 2214

So, Jimmy still has to write 2214 words.

He has 6 days to write the paper and he wants to write the same number of words per day.

With this in mind to find out how many words he has to write per day we can divide 2214 by 6.

2214/6 = 369 words

So, Jimmy has to write 369 words per day for the next 6 days to finish the paper.

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Answer:

B, C

Step-by-step explanation:

A is incorrect, it should be seventy-six hundredths.

D is incorrect, the place value for the third term is wrong - it should be 0.06.