A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).

What is the percent by mass of Cs in the sample?

A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%​​​​

Answer: 6

Step-by-step explanation:

Since M is the midpoint of LN, M divides LN by exactly half.

This means that LM and MN have the same length.

Using this, we can set up the equation:

3x=2x+2

x=2

Since we now know the value of x, let's use it to find LM.

LM = 3x = 6

So the answer is 6.

A graph which shows the relationship given in the table is: B. graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 56 through the point 1 comma 54.

In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 56

Therefore, the y-intercept is equal to (0, 56).

In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days (x) and total amount of sunglasses (y).

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The expression (5/3x+4)^2 in simplest trinomial form is (25x^2+36x+96)/6.

An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions utilise separators like +, -, ×, and ÷ that are symbols or operations. This algebraic statement encompasses polynomials, monomials, binomials, and trinomials.

The given expression is -

(5/3x+4)^2

Solve it to get the trinomial -

= (5/3x+4)^2

= 25/(3x+4)^2

= 25/(6x^2+6x+16)

= (25x^2/6) + 6x + 16

= (25x^2+36x+96)/6

Therefore, the trinomial obtained is (25x^2+36x+96)/6.

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Answer:

Increases by 71% to the nearest whole number

Step-by-step explanation:

=((12-7) /7 )x100

=57×100

=0.714286×100

=71.4286%change

=71.4286%increase

Answer:

-455

Step-by-step explanation:

First lets find what is. -1037 + 582.

With negative number such at the one that you are asking, since it says that you need to add when you found out the real solution it looks like subtracting. Because your adding “ 582 “ to -1037. Your bringing the value UP so now lets figure it out -1037 + 582 = -455.

How did we get that??

Remember like I said on the top /\. It is like subtracting so we can make the problem easier by just making it 1037 - 582. The reason why we are doing minutes because like I said on the top it was a negative number, now lets subtract them:

1037-582=455

Since “ 1037 “ is actually negative we make the number negative. 455

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Answer = -455

Answer:

$15 per hour

Step-by-step explanation:

270/18= 15, if you take the total which is 270 and divide that by the number of hours she works each week it equals 15

Answer: 4

Step-by-step explanation:

The cost of 650 bricks which are right rectangular prisms is $1774.5.

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

The dimensions of the right rectangular prism brick is -

width, w = 7 in

length, l = 3 in

height, h = 3(1/4) in = 3.25 in

Find the volume of the brick -

Volume = w × l × h

Volume = 7 × 3 × 3.25

Volume = 68.25 in³

The volume occupied by 650 bricks is -

V650 = 68.25 × 650

V650 = 44362.5 in³

The cost of cubic inch of brick is $0.04.

The cost of 650 bricks is -

Total cost = 44362.5 in³ × $0.04

Total cost = $1774.5

Therefore, the total cost is obtained as $1774.5.

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The value of the discount that will be give for the doll is $54.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, it should be noted that there's a 15% discount. The value of the discount will be:

= 15% × $360

= $54

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A Barbie doll costs $360 and has a 15% discount. How much is the discount?

Answer:

7

Step-by-step explanation:

f(30)=-11

f(30)=-3/5(30)+k

-11=-18+k

+18 +18

7=k

Answer:

The sum of the exterior angles of a quadrilateral is 360 degrees. This is because the exterior angle of a polygon is supplementary to the interior angle (the angle formed by two adjacent sides). The sum of the interior angles in a quadrilateral is 360 degrees (180 x 2) and since the exterior angles are supplementary to the interior angles, the sum of the exterior angles is also 360 degrees.

Uday Tahlan

The number of the students that prefer documentaries is 120.

We know that in this case, we are dealing with the pie chart and that it is a representation of the preferences of each of the students that we have in the data set that is given.

We can see that;

Number that prefer documentaries = 22 %

Total number of the students = 500

We then have;

Number that prefer documentaries = 22/100 * 500

= 120

Hence, we have 120 students that prefer documentaries.

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Answer:

D

Step-by-step explanation:

add -2 to the other side of the equation to isolate y

Answer: 6x+28

Step-by-step explanation:

The perimeter of the triangle is the distance around the triangle.

We need to apply our ability to convert word problems in to mathematical expressions.

we were told that the bottom of the triangle is [tex]x[/tex] units.

From the diagram perimeter

The length of the bottom of the triangle is [tex]x[/tex]

14 more than 4 times the bottom will be [tex]4x+14[/tex]

14 more than the bottom of the triangle will be [tex]x+14[/tex]

So, [tex]x+4x+14+x+14[/tex][tex]=6x+28[/tex]

Answer:

6x+28

Step-by-step explanation:

The 1 ordinary horse can pull the 17 dan of supplies. The 1 military horse can pull the 23 dan of supplies.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that There are 3 military horses and 4 ordinary horses. Together 1 military horse and 1 ordinary horse can pull 40 dan of supplies. The team of horses can pull 137 dan of supplies.

Let x = military horses

y = ordinary horses

So, 3x + 4y = 137

x + y = 40

Solving;

x + y = 40

x = 40 -y

Thus, 3(40 -y) + 4y = 137

120 - 3y +  4y = 137

y = 17

x =23

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The best explanation for determining 40% of 50 is A. Find 10% of 50 by dividing 50 by 10. Then multiply the result by 4.

The percentage is a way of expressing one value in relative terms or as a ratio to another.

Percentages are quotients of the numerator divided by the denominator, multiplied by 100.

Percentages represent ratios of one variable or value compared to another, like other fractional values.

40% of 50 = 20

10% of 50 = 5 (50/10)

5 x 4 = 20

Thus, among the given options, Option A is the best way to determine 40% of 50.

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Answer:

D

Step-by-step explanation:

rise over run

from the points you go up 3, then 2 to the right

3/2

The value of x for the expression in form of fractions is, 7. So Option D is correct

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

First fraction ,

32/8

Second Fraction,

28/x

The value of x = ?

According to given condition,

32/8 = 28/x

Here, the rules of algebra can be used

1. If a number is in division operation then when it goes to another side of equal to, it will be in multiplication operation or vice-versa.

2. If a number is in addition  operation then when it goes to another side of equal to, it will be in subtraction operation or vice-versa.

Now, applying rules of algebra in the expression,

⇒ 32/8  = 28/x

⇒  4   =  28/x

⇒  x   =  28/4

⇒  x   =  7

Therefore, the value of x is 7

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Answer:

I believe it is D. (Sorry if I'm wrong!)

Explanation:

Since a flat line would be 180°, you just need to add the answers to the top obtuse angle (138°) until you get 180°, and since they are the same angles on the top and bottom, angle 7 would be the same as angle 6

Answer:

Step-by-step explanation:

hcg

The correct answers are X=76.5 and Perimeter= 210.9.

Perimeter is the distance around the outside of a shape. It is a measurement of length and is calculated by adding up the lengths of all the sides of a shape. Perimeter is often used to measure the size of outdoor areas such as a garden, park, or pool, or to find the length of fencing needed for a yard.

To solve for x, use the formula x = (P + Q - R)/2 where P, Q, and R are the lengths of the sides of the triangle. Thus, x = (AST + APQ - APR)/2 = (176 + 140 - 126)/2 = 76.5. To find the perimeter of the triangle STU, use the formula Perimeter = ST + SU + TU = 176 + 28 + 6 = 210.9.

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On solving the provided question we cans ay that equation will be => x *(x+1) = 12 => x = 6, -2

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

a pack of pencils, a pack of pens, and a notebook for = $12.

the pack of pens cost = $1 more than the pack of pencils,

let,

x = cost of pen

y = cost of note book

equation will be

x *(x+1) = 12

x^2 + x = 12

(x+2)(x-6) = 0

x = 6, -2

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Therefore , the solution of the given problem of range comes out to be option b is y ≤ -5 .

The variable range is calculated by determining its maximum observed value and deducting its minimum observed value (minimum). Possible range or variational bounds: different pricing for steel; different designs; The breadth or scope of a process or action: insight a weapon's projectile's maximum or anticipated range. A list or set's range is the integer between its lowest and maximum. Aligning all the numbers will help you find the region. The lowest number should then be subtracted from the greatest number.

Here,

Given :

=> y = -3x² - 12x -17 or

=> f(x) =  -3x² - 12x -17

To find the range :

=> If a < 0 the range of f(x) ≤ y

=> If a > 0 the range of f(x) ≥ y

As a =-3

So ,  vertex(xv ,yv ) = (-2 , -5)

=> y ≤ -5

Therefore , the solution of the given problem of range comes out to be option b is y ≤ -5 .

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The value which is not defined is h(3).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given expression of function is, h(y) = [tex]\frac{4-y^2}{3-y}[/tex]

The function will not be defined when the value of the denominator equals zero.

That is,

3 - y = 0

or y = 3

Hence the function is not defined for when the value of y is 3.

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The complete question is :

If h(y)=4−y^2/3−y , which of the following is not defined?

(a) h(0)

(b) h(3)

(c) h(-3)

(d) h(2)

(e) h(-2)

Answer:

about 100 feet

Step-by-step explanation:

Answer:

16052.47m²

Step-by-step explanation:

area of a circle=πr²

π=314

3.14×71.5×71.5=16052.465m²

=16052.47m²

Answer:

16,060.61 m² (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a circle}\\\\$A=\pi r^2 $\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Given:

Substitute the given radius into the area of a circle formula and solve for A:

[tex]\implies A= \pi \cdot 71.5^2[/tex]

[tex]\implies A= 5112.25 \pi[/tex]

[tex]\implies A= 16060.6070...[/tex]

[tex]\implies A= 16060.61\; \sf m^2\;(2 \; d.p.)[/tex]

Therefore, the area of the circle is 16,060.61 m² (2 d.p.).

The angle N is 56 degrees.

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. This theorem can be expressed mathematically as follows:

Exterior Angle = Interior Angle 1 + Interior Angle 2

This theorem is useful for finding the measure of an unknown exterior angle when the measures of the two remote interior angles are known.

This problem  can be determined by using the exterior angle theorem,

In this case, the measure of angle N is equal to the sum of the measures of angles M and 138°,

which is

56° + 138° = 194°.

Thus, the measure of angle N is 56°.

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Since Amy is determining the difference between the number of butterflies she saw in the past 4 months (figure A) and this month (figure B), her next step is to subtract figure A from figure B.

The difference between the two figures or numbers is the result of a subtraction operation.

A subtraction operation, which is one of the four basic mathematical operations, involves the minuend, subtrahend, and difference, using the minus sign (-) and the equal symbol (=).

Thus, Amy's next step is a subtraction operation to find the difference.

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