16 - x + x + 19 - x = 31

The equivalent expression of 6a/(2a²) is 3/a.

And none of the given option is correct.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

6a/(2a²)

Simplifying,

6a/(2a²),

= 6a /(2a×a)

= 3/a is the equivalent expression.

Therefore, 3/a is the equivalent expression.

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The scatter plot for the randomly selects 12 students is illustrated below.

The term called scatter plot in math is defined as a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

Here we have know that the statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade.

Here we know that the number of samples is 12.

And here we have each student's total is recorded along with their final grade.

Then the scatter plot for the following table of data is illustrated on the diagram.

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The correct result for the expression 3x + 10/2 + 4(x + 3/2) is solved to be

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= 3x + 10/2 + 4(x + 3/2)

parenthesis

= 3x + 10/2 + 4x + 6

division

= 3x + 5 + 4x + 6

addition

= 3x + 4x + 6 + 5

= 7x + 11

solving for x

7x = -11

x = -11/7

x = -1 4/7

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Actor Albert Brook changed his surname to Albert Einstein to avoid sharing it with another well-known Al. Option C

In 1921, Albert Einstein received the Physics Nobel Prize in honor of his contributions to theoretical physics, particularly the creation of the law of the photoelectric effect. Despite moving to Switzerland in 1895 and giving up his German nationality the following year to become a citizen of the County of Württemberg, Einstein was born within the boundaries of the German Empire.

He enrolled in the program for teaching diplomas in physics and mathematics at the Swiss Federal University of Technology School in Zürich in 1897 as a 17-year-old, and he completed it in 1900.

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If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.

Compound interest is simply interest that is earned over prior interest. You receive interest on the initial principal as well as the interest that builds up over time when you open a savings account that pays compound interest.

When you deposit funds into a savings account or other type of account, you will earn interest on the amount you deposited. For instance, after a year, if you deposited $1,000 in an account with 1% annual interest, you would have received $10 in interest.

Compound interest formula is

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here,

P = $10000

r = 5%

n = 12

t = 10

A = to find

Lets solve,

[tex]$\text A = 10000(1 + \frac{0.05}{12})^{12\times 10}[/tex]

A = 16470

Thus, If you invested $10000 in a stock with 5% compounded monthly you will have $16470 in 10 years.

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Given the above function:

a) Note that the number of people that need to sign up for a tour in order for the profit to be at least $108 is:

b) The number of people that need to sign up for a tour in order for the profit to be more than $144 is:

c) Yes, it is possible to make a negative profit on the tour in which case they would have made a loss.

a) To find out the number of people that need to sign up for the profit to be at least $108 where the function y = - x7 + 24x, models profit in y,

we must equate the function to $108 and solve for x.

Thus:

- x7 + 24x = 108

resolve like terms

17x = 108

x = 108/17

x = 6.35294117647

x [tex]\approx[/tex] 6. 4

Plug x back into the formula, and we have:

-(6.4) * 7 + 24 (6.4) = 108.8 this shows that our calculation is correct. Since you can have 6.4 persons, the best number to aim for is 7.

b) The number of people that need to sign up for the project to turn a profit of $144 is:

- x7 + 24x = 144

resolve like terms

17x = 144

x = 144/17

x = 8.4705882353

Let's impute back 8.5 into the equation:

-(8.5)7 + 24(8.5)

= 144.5.

This shows that our calculation is correct. However since you cannot have 8.5 persons, the number to budget for would be 9 persons.

c) for the tour guide to lose money, the amount made, that is revenue, would have to be less than the amount invested.

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Answer:

100%

Step-by-step explanation:

The mark-up percentage is the amount by which the cost price of a product is increased to arrive at the selling price. To calculate the mark-up percentage, you can use the formula:

Mark-up percentage = (selling price - cost price) / cost price x 100

In this case:

Cost price = $450

Selling price = $900

Mark-up percentage = ($900 - $450) / $450 x 100 = 100%

So the specialty shop has a mark-up of 100% on each painting.

It means that the shop is charging twice as much as the price they procured the paintings.

Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.

Regular Lemonade: 9

Strawberry Lemonade: 21

Regular Lemonade:

Price of Regular Lemonade = 1.50

Total earnings from Regular Lemonade = 9 x 1.50 = 13.50

Strawberry Lemonade:

Price of Strawberry Lemonade = 2

Total earnings from Strawberry Lemonade = 45 - 13.50 = 31.50

Number of Strawberry Lemonade sold = 31.50 / 2 = 15.75

Number of Regular Lemonade sold = 15.75 - 12 = 3.75

Rounded to nearest whole number,

Number of Regular Lemonade sold = 4

Number of Strawberry Lemonade sold = 16

Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.

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The roots of the quadratic function f(b) = b² - 75 are Ob=5√3 and Ob=-5√3.

A quadratic function is a polynomial function of degree two, which means it is a function that can be expressed as an equation with the second-degree degree of the highest exponent of the unknown variable. It is typically expressed as ax^2 + bx + c, where a, b and c are constants, and x is an unknown variable. Quadratic functions can be used to model many real-world situations, such as the height of a projectile in motion or the area of a circle.

The Quadratic Formula can be used to solve for the roots of a quadratic function. The Quadratic Formula states that for a quadratic equation of the form ax² + bx + c = 0, the two roots are given by x = [-b ± √(b² - 4ac)]/2a.

In this case, a = 1, b = 0, and c = -75. Therefore, the two roots are given by x = [-0 ± √(0² - 4(1)(-75)]/2(1). This simplifies to x = [0 ± √(75)]/2, or x = ±5√3/2. The two roots are thus Ob=5√3 and Ob=-5√3.

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What Meg needs to find is the whole and what Steve needs to find is the part.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

a/b * 100

(in percentage)

Since Meg already knows the part and the percent which is 10 and 33% respectively, then it means that what she needs to find is the whole which is the total number of dogs she saw.

Steve already knows the whole which is 12 dogs and the percent which is 50% and as such what he will need to do now is to find the part that makes up the percentage part.

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The domain and the range of the relation shown to the right are given as follows:

The graph is not a function, as a vertical line for x > -5 would cross a function in multiple points.

The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, thus the domain is of:

x >= -5.

The range of a function is the set that contains all the output values of the function, hence on the graph it is the values of y, thus the domain is of:

All real values.

As there are inputs that are mapped to multiple outputs, the graph does not represent a function.

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Students who are proficient in math begin by defining a problem for themselves and searching for possible solutions.

They examine assumptions, limitations, connections, and objectives. Instead of just launching into a solution attempt, they formulate hypotheses regarding the structure and significance of the solution and outline a solution pathway. In order to get insight into the problem's solution, they take into account similar difficulties, try specific situations, and take the original problem in simpler forms. They track and assess their development, and if necessary, they alter their direction. A good puzzle not only involves more of the "real world" for a child than, instance, calculating the amount of paint required.

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Answer:

Answer in image

Step-by-step explanation:

Using the y-intercept, we can graph our first point at (0,5) the y-intercept. Then from there we can use the slope to continue to plot points. (This is a negative graph by the way based off of the slope -3/4).

-Hope this helped

The simplified exponential expression for this problem is given as follows:

(3² x 5)³ = 3^6 x 5³.

The exponential expression for this problem is defined as follows:

(3² x 5)³.

As we have a product applied to the exponent, the exponent can be applied to each factor of the exponent, as follows:

(3²)³ x 5³.

Applying the power of power rule, we have that:

(3²)³ = 3^(2 x 3) = 3^6.

Hence the simplified exponential expression for this problem is given as follows:

(3² x 5)³ = 3^6 x 5³.

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Answer:

There are only 6 factors of the number 44 which are 1, 2, 4, 11, 22 and 44.

From this list, the factors of 44 are:

1) 22

2) 44

3) 1

4) 4

5) 11

6) 2

Answer:

1,2,4,11,22,44

Step-by-step explanation:

Let's work our way up.

You can start with 1, cause every number has a factor of 1. Then you can find that 44, cause every number is divisible by itself. and 1 × 44 = 44. Since 44 ends with a 4, it has to be divisible by 2. So to find the number that multiplies with 2 to get 44, divide 44 by 2 which equals 22. So 2×22=44. 44 is not divisible by 3. But it is divisible by 4. 4×11=44. No other number is a factor of 44. Therefore; 1,2,4,11,22,44

Hope that helps. Let me know if you have any further questions!

Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

The null hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is less than or equal to 57%. The alternative hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is greater than 57%.

To test this, you would use a one-sample proportion test. The test statistic is calculated using the sample proportion (60%) and the hypothesized proportion (57%) and the sample size (800).

You would then compare the calculated test statistic to the critical value from a z-table (using a two-tailed test and a 0.02 level of significance) to determine whether or not to reject the null hypothesis.

Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

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An equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15 is y=-2x+19.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx +c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

Given;

Line is  passing through the point (-10,1)

Parallel to the line 10x+5y=15.

So, the slope of the line is equal to the line parallel to it

Slope of given line

5y=-10x+15

y=-10x/5+15

m=-2

Equation; 1=-2x+c

c=-2*-10-1

c=19

Therefore, the equation will be y=-2x+19.

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For the given normally distributed data, the number of children have height greater than 116 is given by 79.

Using normally distribution we have,

Z = ( X - µ ) / σ

Here,

Mean 'µ' = 110

Standard deviation 'σ' = 6 cm

n = 500

Number of children with height greater than 116 cm

P (x > 116) = 1 - P (x < 116)

For,

P( X < 116 )  

⇒ P[ (X - μ) / σ > (116 - 110)/ 6 )

⇒ P( Z < 6 / 6 )

⇒ P( Z < 1 )

Using the value from normal distribution table we have:

P (Z< 1) = 0.8413

⇒P (x > 116) = 1 - 0.8413

⇒P (x > 116) = 0.1587

Number of children with height greater than 116 is :

= 0.1587 × 500

= 79.35

= 79 ( approximately )

Therefore, the number of children have the height greater than 116 cm is equal to 79.

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The number of customers when there are 576 towers will be 12.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Based on the information, it should be noted that the number of phone is proportional to the number of customers

The constant of proportionality will be:

= 252 / 5.25

= 48

Therefore, the customers when there are 576 towers will be:

= 576 / 48

= 12

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Answer:

see below

Step-by-step explanation:

make x = 7

Answer:

Subtract 5 from both sides

x = 7

Step-by-step explanation:

x + 5 = 12  Subtract 5 from both sides

x + 5 - 5 = 12 - 5

x = 7

The unknown side BC is 2.33 units.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

A right triangle ABC.

∠ACB is a right angle.

∠ABC is twenty-five degrees.

The side AC is unknown.

Side BC is five units.

Now,

AC = x

BC = 5 units

Tan 25° = AC/BC

Tan 25° = x/5

0.47 = x/5

x = 5 x 0.47

x = 2.33

Thus,

Side BC is 2.33 units.

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Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

The null hypothesis is that the proportion of Americans supporting the new health policy is less than or equal to 0.5 (p <= 0.5). The alternative hypothesis is that the proportion of Americans supporting the new health policy is greater than 0.5 (p > 0.5).

The test statistic for a one-sample proportion test is:

z = (p^ - p) / sqrt((p * (1-p)) / n)

where p^ is the sample proportion (117/200 = 0.585), p is the hypothesized proportion of Americans supporting the new health policy (0.5), and n is the sample size (200).

Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.

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The required inequality to show how many refrigerators and how many pianos the truck could carry is  300x + 425y ≤ 7300.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have,

A truck that can carry no more than 7300 lb is being used to transport refrigerators and upright pianos.

Let x be the number of refrigerators in the truck and y be the number of pianos in the truck.

Then

300x + 425y = 7300

At x = 11 and y = 9

300(11) + 425(9)

= 7125 ib

So, the truck will not overload.

Inequality will we

300x + 425y ≤ 7300

Thus, required inequality is 300x + 425y ≤ 7300.

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Answer:

212

Step-by-step explanation:

277 - 68 ( I would give further explantion but it ez )

=

209

I’m so dum sorreh

Answer:

212

Step-by-step explanation:

277 - 65 =

212

The number of miles that a person walks at this speed to use at least 250 ​calories will be 2.49 miles.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

A​ 150-pound person uses 6.7 calories per minute when walking at a speed of 4 mph.  If the number of calories burnt is 250. Then the number of minutes the person is given as,

T = 250 / 6.7

T = 37.313 minutes

T = 0.62 hours

Then the distance is given as,

D = 4 x 0.62

D = 2.49 miles

The number of miles that a person walks at this speed to use at least 250 ​calories will be 2.49 miles.

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If horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F , then normal range of body temperature of a horse as an inequality 99 ≤ T ≤ 100.8  .

If the temperature of the horse denoted by "T" , is within at least 0.9 °F of 99.9 °F , then it is considered as Normal ;

To express this as an inequality, we can use the following:

⇒ 99.9 - 0.9 ≤ T ≤ 99.9 + 0.9  ;

Simplifying further , this inequality can also be written as:

⇒ 99 ≤ T ≤ 100.8

Therefore , the normal range of body temperature of a horse is 99 ≤ T ≤ 100.8 .

The given question is incomplete , the complete question is

A horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F. Write the normal range of body temperature of a horse as an inequality .

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The amount of each item, pizza and chicken wings that should be bought are 7 and 4 respectively. For an additional member the additional number of pizzas is 0 and chicken wings are 10.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

A: X is the quantity of pizzas, while Y is the quantity of bags of chicken wings.

1 pizza cost x, thus 6 cost = 6 x

1 bag of chicken wings costs y dollars, thus 7 cost = 7 y.

Given: Total cost = 6x + 7y = 70

Total servings are now equal to (24)(2) for a total of 48.

One pizza includes four portions, thus 1 x 4 = 4

Servings in a bag of chicken wings are 5y.

Servings total: 4x + 5y = 48

The set of linear equations is hence 1.

6x + 7y = 70 .....(I)

4x + 5y = 48 ......(II)

Having solved (I) and (II), we obtain x = 7 and y = 4.

B:

One more guest brings the total to 25.

Total portions are therefore 4x + 5y = 2.25 = 50.

The total cost of 6x + 7y stays at 70.

The set of linear equations is hence 1.

6x + 7y = 70 .....(I)

4x + 5y = 50 ......(II)

We obtain x = 0 and y = 10 by solving for (I) and (II).

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By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given Equation,

y = 5x and y = 45 - 10x

So,

use the slope form is

y= mx+b , where m is slope and b is the y-intercept.

find the valued of m an b using the form y = mx+b

m = 10 and b=0

The slope of line is the value of m and y-intercept the value of b

slope = 10

y-intercept = (0,0)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.

create a table for x and y values.

x    y

0    0

1      10

and soon

Similarly for y = 45-10x

x    y

0   45

1     35

2    25

and soon

And Hence plot the points in the graph.

Therefore, By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.

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The scatter plot shows data points that do not follow a trend, thus it shows a: nonlinear association.

A nonlinear association is a relationship between two variables, whereby a change in one does not correspond to a change in another.

Thus, on a scatter plot showing a nonlinear association, the data points do not follow a trend line and are scattered, therefore, predictions cannot be made using the scatter plot.

Thus, the scatter plot that is given shows: nonlinear association.

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A varied group of volunteers is frequently better able to function as a team since having a variety of viewpoints and personalities helps facilitate collaboration.

Diversity in volunteering refers to both the individuals participating and the opportunities offered. Regardless of ethnicity, gender, religion, sexual orientation, or other characteristics, volunteering should be a process that welcomes participation from people with a variety of backgrounds and talents.

People can learn from one another as a result of diversity, which introduces new ideas and experiences. Better problem-solving results from incorporating many ideas and perspectives. Working in diverse teams fosters innovation and encourages dialogue. Our culture benefits from variety as well.

Any employee, regardless of gender, race, age, ethnicity, physical ability, sexual orientation, religion, or other characteristic, has the same rights and opportunities in a diverse workplace.

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