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The mass percentage of Cesium in the sample is 25.0 %. (Correct choice: C)

Herein we find the case of a mixture of two elements: Cesium, Iodine, whose Cesium mass percentage can be determined by the following formula:

%m = [mCs / (mCs + mI)] × 100 %

Where:

If we know that mCs = 100 g and mI = 300 g, then the Cesium mass percentage is:

%m = [100 g / 400 g] × 100 %

%m = 25 %  

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Using the Pythagoras theorem, the value of line segment RQ denoted as x is option C: 20 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

According to the diagram given -

ST = 9 units and TQ = 16 units.

Δ SRQ and Δ STR are equal and congruent as RT is perpendicular to hypotenuse SQ.

From similar triangles,

Δ SRQ ⩭ Δ STR ------(1)

{∵ RT 丄 Hypotenuse SQ}

Similarly, Δ SRQ and Δ RTQ are equal and congruent Δ SRQ, Δ STR and Δ RTQ  are similar right-angled triangles.

Δ SRQ ⩭ Δ RTQ ------(2)

{∵ Δ SRQ, Δ STR and Δ RTQ are similar triangles}

So, this gives that the sides -

SR/ST = SQ/SR = RQ/TR

SR/9 = 25/SR = x/TR

SR² = 25 × 9

SR = 5 × 3 = 15

Now, applying the Pythagoras theorem -

SR² + RQ² = SQ²

RQ² = SQ² - SR²

RQ² = 25² - 15²

RQ = √(625 - 225)

x = RQ = √400

RQ = 20 units

Therefore, the value of x is obtained as 20 units.

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With a video tutorial and in-depth explanations, learn how to properly measure baking ingredients and why measuring is so crucial in baking.

12 grams/cake × 3 cakes = 36 grams.

That is 500 ml of milk per cake times 3 cakes, giving 1500 ml of milk for three cakes.

two cups per cake multiplied by three cakes is equal to 6 cups.

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Answer:

see explanation

Step-by-step explanation:

(a)

the radius r of a circle is half the diameter , so

r = 10 ÷ 2 = 5

(b)

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r the radius

here (h, k ) = (3, - 8 ) and r = 5 , then

(x - 3)² + (y - (- 8) )² = 5² , that is

(x - 3)² + (y + 8)² = 25 ← equation of circle

Answer:

8. Missing side = 50

9. Missing side = 8

Step-by-step explanation:

In order to find the hypotenuse, we have to use the Pythagorean Theorem which states:

[tex]a^{2} +b^{2} = c^{2}[/tex]

Where a and b are sides and c is the hypotenuse.

[tex]14^{2} +48^{2} = c^{2}[/tex]

196 + 2304 = [tex]c^{2}[/tex]

2500 = [tex]c^{2}[/tex]

[tex]c[/tex] = [tex]\sqrt{2500}[/tex]

[tex]c = 50[/tex]

[tex]15^{2} +b^{2} = 17^{2}[/tex]

225 + [tex]b^{2}[/tex] = 289

[tex]b^{2}[/tex] = 64

[tex]b[/tex] = [tex]\sqrt{64}[/tex]

[tex]b=8[/tex]

Answer:

To divide 3 4/7 by 2/5, you will need to convert the mixed number 3 4/7 to an improper fraction. To do this, you will multiply the whole number (3) by the denominator of the fraction (7) and add the numerator (4) to get an improper fraction of 25/7.

Next, you will divide the numerator of the first fraction (25) by the numerator of the second fraction (2) and divide the denominator of the first fraction (7) by the denominator of the second fraction (5). So the answer is 25/2 divided by 7/5 which is equivalent to 25/2 * 5/7 = 25/14 which can be simplified further to 5/2

You can use the law of sines along with the angle of elevation given to find out the length of the distance of the vertical beam from the lower end of the support beam(horizontally).

The distance between lower end of the support beam from the vertical beam along the horizontal floor is given by

Option A: 3.0 meters

What is law of sines?

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}[/tex]

Remember that we took

[tex]\frac{sin(angle)}{Length Of The Side Opposite To That Angle}[/tex]

Using the law of sines, as referring in the figure attached below, we get:

[tex]\frac{sinC}{|AB|} = \frac{sinA}{|BC|}[/tex]

Since in a triangle, the sum of its angle is 180 degrees, thus,

∠A + ∠B + ∠C = 180°

∠A = 180°- 28° - 90° = 62°

Using the fact that |AB| = 1.6 meters and that angle C is of 28°, we get

[tex]\frac{sinC}{|AB|} = \frac{sinA}{|BC|}\\\frac{sin28}{1.6} = \frac{sin62}{|BC|}[/tex]

Using the sin calculator

[tex]\frac{0.469}{1.6} = \frac{0.8829}{|BC|}\\ |BC| = \frac{0.0029*1.6}{0.469} = 3.012[/tex]

|BC| ≈ 3 meters

Thus,

As length of BC = |BC| = 3 meters denote the horizontal length from the vertical beam and the lower end of the support beam, thus,

The distance between lower end of the support beam from the vertical beam along the horizontal floor is given by 3 meters.

Option A: 3.0 meters.

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Complete question:

A support beam needs to be placed at a 28° angle of elevation so that the top meets a vertical beam 1.6 meters above the horizontal floor. The vertical beam meets the floor at a 90° angle.

Law of sines:

Approximately how far from the vertical beam should the lower end of the support beam be placed along the horizontal floor?

3.0 meters

3.4 meters

3.9 meters

4.4 meters

Answer: a) 3.0

Step-by-step explanation:

just did it

Answer: 53 degrees

Step-by-step explanation:

X = 360 - 307 = 53 degrees

Answer:

53

Step-by-step explanation:

subtract 307 from 360

The cost of paper for the reports is $21.48.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A long year-end status report for work is 160 pages long.

You need to print 18 copies for a meeting next week.

So, the number of pages

= 160 x 18

= 2880 pages.

Now, the cost for those reports

= 2880 / 500 x 3.73

= 5.73

= $21.48

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Using a graphing tool, the y-intercept is located at (0,-5) Plot the intercepts and join them to graph the line.

5x - 2y = 10.

Discover the x-intercept.

Keep in mind that the value of x when the value of y is equal to zero is the x-intercept.

5x - 2(0) Equals 10 for y = 0 and x = 2.

5x = 10

The point is the x-intercept (2,0)

Discover the y-intercept.

Keep in mind that the value of y when the value of x is zero is the y-intercept.

y = - 5 for x = 0 5(0) - 2y = 10 - 2y = 10

Using a graphing tool, the y-intercept is located at (0,-5) Plot the intercepts and join them to graph the line.

danielle plans to graph the linear equation 5x-2y=10 is  (0,-5).

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The formula for finding the total measure of all interior angles in a polygon is: (n – 2) x 180. In this case, n is the number of sides the polygon has.

Describe an angle. An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The study of shapes and their measurements falls under the umbrella of geometry, a subfield of mathematics. It also emphasises how the shapes are arranged in relation to one another and their spatial characteristics.

We are aware that geometry is divided into 2D and 3D categories. All geometrical shapes are first created by the intersection of points, lines, rays, and plane surfaces.

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D/ If x=10, √√2x=32 is not true. The correct result would be √√2x = √√20 = √4 = 2.

What is the square root?

There are many kinds of roots

etc

square=2D so it means 2 identical numbers that multiply to get that number

The square root of a number is a value that, when multiplied by itself, gives the original number.

The double square root of a number is the square root of the square root of that number. For example, the double square root of 20 is the square root of the square root of 20, which is the square root of √20 = √4 = 2.

In the statement "If x=10, √√2x=32", the value of x is set to 10, so the statement is asking to find the double square root of 2x when x = 10. So it would be √√2(10) = √√20 = √4 = 2 which is not equal to 32.

Hence, D/ If x=10, √√2x=32 is not true. The correct result would be √√2x = √√20 = √4 = 2.

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The equation that can be used to determine the cost price of the book is y = x- 45x/100

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

Let represent the original value by x

the cost of the book is 45% original price = 45/100 × x = 45x /100 = 9x/20

therefore if we represent the new cost by y

Therefore the new cost of the book = x - 45x/100

Therefore the equation the could be used to determine the selling price is y = x -45x/100

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Answer:I think its

12.

Step-by-step explanation:

The number of atoms could be laid end-to-end on a meterstick which is 100 cm in length will be 10^6.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the atom is 10^8 centimeters in length, the number of atoms could be laid end-to-end on a meterstick which is 100 cm in length will be:

= 10^8 / 10^2

= 10^6

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Complete question

One atom is 10^8 centimeters in length. How many atoms could be laid end-to-end on a meterstick (which is 100 cm in length)? Leave the answer in scientific notation. Round

We can write that -

An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.

Given are the numbers to be verified as rational or irrational.

Therefore, we can write that -

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The tree has been growing for 5 months according to the task content.

A tree in Teresa's backyard grows 0.7 meters each month. If the tree is 3.43 meters tall,the tree has been growing,

Since the tree is presently 3.43 m high and grows 0.7 m every month, the task's requirements are supported by this information.

Consequently, the equation for the number of months may be expressed as follows;

3.43  = 0 . 7x -6

3.43  = 0.7 x

x = 4.9 0r 5 months.

The tree has been growing for 5 months according to the task content.

5 months has the tree been growing.

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This looks like a test. I'm sorry, I can't help you. But if this is homework, I'll be happy to help!

About 463 minutes would take them to complete the whole thing

The area of Rectangle is length times of width.

Given that Mr. Elliot's class created a mural about Martin Luther King in their school.

The mural was 4.75 feet long by 3.25 feet wide.

Length=4.75

Width=3.25

Area=4.75×3.25

=15.43

it took the class 30 minutes to paint 1 square foot of the mural

We have to find the time taken to paint the whole thing

Let x be the time.

30/1=x/15.43

Apply cross multiplication

30×15.43=x

462.9=463

Hence, about 463 minutes would take them to complete the whole thing

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The model of the growth of the quantity is A(t) = 350(1.10)^t.  The expression for the size of the quantity after 50 years is A(50) = 350(1.10)⁵⁰.

What is a function?

A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.

Given that a quantity starts with a size of 350 and grows by 10% per year.

The growth of the object can be calculated by using the exponential function:

A = P(1+r)^t

A = final amount

P =  initial size

r = rate of increasing

Here P = 350, r = 10% = 0.10

The model becomes:

A(t) = 350(1+0.10)^t

A(t) = 350(1.10)^t

To find the quantity after 50 years, put t = 50 in A(t) = 350(1.10)^t:

A(50) = 350(1.10)⁵⁰.

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Answer:

7^3/4

Step-by-step explanation:

use the formula below to solve your problem

There are 67 more baseballs than basketballs.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a coach buys 125 more soccer balls than basketballs He buys 58 fewer baseballs than soccer balls.

Let the number of soccer balls be x, and that of basketballs and baseballs be y and z respectively.

Therefore, according questions,

x-y = 125

x = 125 + y...(i)

x-z = 58

x = 58 + z...(ii)

Now, since, LHS of both equations are equal,

125 + y = 58 + z

z - y = 67

Since, y is being subtracted by z and result is positive, therefore, number of baseball is greater than number of basket balls,

Hence, there are 67 more baseballs than basketballs.

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The vertical cross section of the prism is equal to a triangle.

In Mathematics and Engineering, a section view can be defined as a type of drawing which is used to reveal the inner part of a geometric object (figure) that is remaining after a portion have been cut and removed.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

By critically the cross section of the prism, we can reasonably infer and logically deduce that the resulting geometric object has three (3) sides and as such, it represents a triangle.

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Answer:

(10x + 2) + (3x + 9) = 180

x= 13

I think this is the right answer.

Step-by-step explanation:

The point where Alex can place point H so that he does not have to buy more fencing is D.  (0, 3)

The length of fence already used is:

EF +FG = 3 + √((9-6)² +(5-1)²) = 3 +5 = 8

So, the remaining segments of fence must total less than 22 -8 = 14 units.

A plot of the points shows you that D(0, 3) is closest to the other three. An estimate* of the distance from the next-closest point, A(0, 0), shows it must be greater than 5+9 = 14, so only D is a possible location.

In the attached we have shown an ellipse that is the set of all points such that their total distances to E and G is 14. Any point that is a solution to the problem must lie on or in that ellipse.

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Answer:

Step-by-step explanation:

Using the distance formula with points E, F, and G - he has used 8 units of fencing.  22 - 8 = 14 units.

Point H must use no more than 14 units meaning the distance from point G to H and then H back to E has to be 14 or less units.

Only choice D (0, 3) is less than 14 units.

GH has a distance of approximately 9.21

EH has a distance of approximately 3.60.

Total of 12.61 which is less than 14.

All other options use more than 14 units.

The number of outcomes available in Boulder and Sarasota will be 4 and 6. Then the total number of outcomes available in Boulder and Sarasota will be 10.

What are permutation and combination?

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

Angelica is comparing vacation prices in Boulder, Colorado, and Sarasota, Florida. In Boulder, she can choose a 1- or 2-week stay in a 1- or 2-bedroom suite. In Sarasota, she can choose a 1-, 2-, or 3-week stay in a 2- or 3-bedroom suite, on the beach or not.

The number of outcomes is available in Boulder will be

→ 2 x 2

→ 4

The number of outcomes is available in Sarasota will be

→ 3 x 2

→ 6

The number of outcomes is available in Boulder and Sarasota will be

→ 4 + 6

→ 10

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The area of the garden is calculated from the area of the rectangle which has a value of 15x + 19.5

The area of a rectangle is calculated by multiplying the length of the rectangle by its width. The formula is:

Area = length x width

In the given question, we can simply calculate the area of the walkway by subtracting one variable from the other.

Area of walk way = area (walkway + garden) + area (garden)

Area of walk way = (5x + 7) + (10x + 12.5)

Area of walk way = 5x + 7 + 10x + 12.5

Area of walk way = 15x + 19.5

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Down payment = down payment percent times purchase price.

The down payment is computed as down payment Equals down payment % times purchase price. For this computation, the down payment percentage must be converted to a decimal. Divide your annual interest rate by the amount of payments you’ll make. If your interest rate is 6% and you make monthly payments, divide 0.06 by 12 to get 0.005. Multiply that figure by your remaining loan balance to get how much interest you’ll pay that month.

The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The acronym “PMT” refers for “payment” hence the function’s name.

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