Select the correct answer from each drop-down menu. Simplify. √63

In the 5th year

For the first year, the salary is 1.2million = 1,200,000

For the second year, the salary is 1.2million + 75000 = 1,200,000 + 75,000 = 1,275,000

.

.

.

For the last year, the salary is 1.5million = 1,500,000

This gives the following sequence...

1,200,000 1,275,000  .   .   . 1,500,000

This follows an arithmetic progression with an increment of 75,000.

Remember that,

The last term, L, of an arithmetic progression is given by;

L = a + (n - 1)d           ---------------(i)

Where;

a = first term of the sequence

n = number of terms in the sequence (which is the number of years)

d = the common difference or increment of the sequence

From the given sequence,

a = 1,200,000                          [which is the first salary]

d = 75,000                               [which is the increment in salary]

L = 1,500,000                          [which is the maximum salary]

Substitute these values into equation (i) as follows;

1,500,000 = 1,200,00 + (n - 1) 75,000

1,500,000 - 1,200,000 = 75,000(n-1)

300,000 = 75,000(n - 1)

[tex]\frac{300,000}{75,000} = n - 1[/tex]

4 = n - 1

n = 5

Therefore, in the 5th year the maximum salary will be reached.

Answer:she earned 196$ in a week in which she worked 28 hours. she earned 784$ in a month which she worked 112 hours.

196$ and 784$ are your answers

Step-by-step explanation:

Answer:

A,and C

Step-by-step explanation:

A and C have the same level precision , they have three significant digit

Answer:

4 is the answer to your question

Step-by-step explanation:

Answer:

Rs216.98

Step-by-step explanation:

If Rs230 is including the 6% tax then 230 = 106%

230 / 106 = 1% = 2.1698

2.1698 X 100 = 100% = 216.98

The original price of a packet of biscuits will be Rs216.98.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the original price of a packet of biscuits bought for Rs230 including 6% tax.

The original price will be calculated as below:-

If Rs230 is including the 6% tax then 230 will be equal to 106 percent as below:-

230 = 106%

Then 1 percent will be equal to the ratio of 230 and 106 as below,

1% = 230 / 106= 2.1698

Divide 230 by 106 and to calculate the original price multiply by 100.

2.1698 X 100 = 100% = Rs216.98

Therefore, the original price of a packet of biscuits will be Rs216.98.

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Answer:

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Step-by-step explanation:

Given;

Initial position y1= 80 ft below the surface of water = -80ft

Final Position y2 = 15 ft above the surface = +15ft

The vertical distance travelled by the shark is;

∆y = y2 - y1 = 15 - (-80) ft

∆y = 15 +80 ft

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Answer:

29

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

3x + 22 = 0 or x - 7 = 0

3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

3x + 1 = 3(7) + 1 = 22

The greater integer is 22.

The sum of the integers is 7 + 22 = 29

Answer: 29

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To determine if a point lies on the curve, substitute the x- coordinate into the equation. If the value obtained is equal to the y- coordinate then the point lies on the curve, that is

A

y = ([tex]\frac{3}{2}[/tex] )² = [tex]\frac{9}{4}[/tex] ≠ [tex]\frac{9}{2}[/tex] ← not on line

B

y = (- 1)² = 1 ← lies on line

C

y = 4² = 16 ← lies on line

D

y = ([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] ← lies on line

Answer:

See below.

Step-by-step explanation:

[tex](5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}[/tex]

First, note that everything to the zeroth power is 1. Thus:

[tex]=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}[/tex]

Distribute using Power of a Power property:

[tex]=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}[/tex]

Make the exponents positive by putting them to the numerator:

[tex]=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}[/tex]

[tex]=\frac{4x^{-6}y^{10}}{1}[/tex]

Make the exponent positive by this time putting it to the denominator:

[tex]=\frac{4y^{10}}{x^6}[/tex]

Answer:

[tex]62.4$ cm^2[/tex]

Step-by-step explanation:

The net of the triangular pyramid is attached below.

Since each of the faces is an equilateral triangle of side 6cm, the base of the pyramid will also be an equilateral triangle of side lengths 6cm .

In the equilateral triangles

Therefore, the surface area of the pyramid formed from the net shown

= 4 X Area of One Triangular Face

[tex]=4 (\frac12 \times bh)\\=4 (\frac12 \times 6\times 5.2)\\=4(15.6)\\=62.4$ cm^2[/tex]

Answer:

[tex]c.\hspace{3}x=12[/tex]

Step-by-step explanation:

Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.

You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached.  As you can see:

[tex]x=2a[/tex]

And we can find a easily using pythagorean theorem:

[tex](\sqrt{45} )^{2} =3^{2} +a^{2}[/tex]

Solving for a:

[tex]a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\[/tex]

[tex]a^{2} =36\\\\a=\sqrt{36} \\\\a=6[/tex]

Therefore:

[tex]x=2a\\\\x=2(6)\\\\x=12[/tex]

Answer:

Lies in the shaded regions of both the top and bottom inequalities.

Step-by-step explanation:

The point of solution for BOTH systems of inequalities must work for both equations. Therefore, the point has to lie in both top and bottom shaded regions or it won't work for both, but just one.

Answer:

C: Lies in the shaded regions of both the top and bottom inequalities.

Step-by-step explanation:

Hope this helps!

Answer:

[tex]-7[/tex]

Step-by-step explanation:

[tex]5(x+9) = 10[/tex]

[tex]5x+45=10[/tex]

[tex]5x = -35[/tex]

[tex]x=-7[/tex]

Hope this helps.

Answer:

-7

Step-by-step explanation:

5(x + 9) = 10

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is your order of operation.

First, divide 5 from both sides:

(5(x + 9))/5 = (10)/5

x + 9 = 10/5

x + 9 = 2

Next, isolate the variable x, by subtracting 9 from both sides:

x + 9 (-9) = 2 (-9)

x = 2 - 9

x = -7

x = -7 is your answer.

~

Answer:

4x - 4

Step-by-step explanation:

4 × x = 4x

4 × -1 = -4

4x - 4

Answer:

4x-4

Step-by-step explanation:

Answer:

The matched pairs are:

(A, 4), (B, 1), (C, 2) and (D, 3)

Step-by-step explanation:

The complete question is:

Match each description of an algebraic expression with the symbolic form of that expression :

A. 2 terms; variables = x and y

B. 3 terms; variables = x and y; constant = 3

C. 2 terms; variable = x; constant = 4.5

D. 3 terms; variables = x and y; constant = 2

1. x - 2y + 3

2. 4.5 - 2x

3. 4.5x + 2 - 3y

4. 4.5y - 2x

Solution:

A. 2 terms; variables = x and y  ⇒ 4. 4.5y - 2x

B. 3 terms; variables = x and y; constant = 3  ⇒ 1. x - 2y + 3

C. 2 terms; variable = x; constant = 4.5  ⇒ 2. 4.5 - 2x

D. 3 terms; variables = x and y; constant = 2 ⇒ 3. 4.5x + 2 - 3y

Answer:

B. f(x) = 1 - x²

Step-by-step explanation:

Since we are dealing with only vertical movement, all we change is the constant. Since the red graph is up one from the reflected parent graph, we know our graph is f(x) = -x² + 1 or f(x) = 1 - x².

Answer:

B. F(x) = 1 - x^2

Step-by-step explanation:

The red graph is the blue graph translated 3 units down. It has a vertical translation of -3 units.

F(x) = G(x) - 3

F(x) = 4 - x^2 - 3

F(x) = 1 - x^2

Answer:

We can call the supplementary angle of x as (180 - x)°. Since the lines are parallel, 61° and (180 - x)° are congruent because they are alternate interior angles. We can write:

61 = 180 - x

-119 = -x

x = 119°

Answer:

[tex]Vol=883.6875\,\, cm^3\\[/tex]

Step-by-step explanation:

Recall that the volume of a whole sphere is given by the formula:

[tex]Vol_{sphere}=\frac{4}{3} \pi\,R^3[/tex]

then, the volume of a semi-sphere would be half of the formula above:

[tex]Vol=\frac{2}{3}\, \pi\,R^3[/tex]

Now, the radius R is given by half of the semi-sphere diameter: 15/2 = 7.5 cm.

which makes our calculation:

[tex]Vol=\frac{2}{3}\, \pi\,R^3=\frac{2}{3}\, \pi\,(7.5\,cm)^3=883.6875\,\, cm^3\\[/tex]

Answer: 50 grams of fat

Step-by-step explanation:

From the question, we are informed that one serving of pretzels contains 1.5 grams of fat which is 3% of the daily amount recommended for a 2,000 calorie diet.

This means that we are expected to find the grams of fat for 100%. Since one serving of pretzels contains 1.5 grams of fat which is 3%, this means 1% will contain (1.5/3) = 0.5 grams of fat.

Therefore the grams of fat that are recommended will be:

= 100 × 0.5

= 50 grams of fat

Answer:

50 grams of fat

1.5 / 3 = 0.5

0.5 x 100 = 50

Step-by-step explanation:

Answer:

37.57 + 1.95x

Step-by-step explanation:

The cost of the shoes is a constant, and we don't know how many socks she bought, but we know that for every pair of socks she bought, they cost would be 1.95. Since we haven't been given the total cost of the purchase, meaning how much the total was, this will be an expression. We will multiply an x against the amount (1.95), which will calculate the price for how many socks were purchased. This means the answer will be 37.57 + 1.95x.

I will clarify a little bit more on why the other answers are incorrect. The first option is 37.57x + 1.95. This is incorrect because the question is not asking how many shoes were bought, but it is questioning how many socks were bought. Option number two states 37.57x + 1.95x. This means that the number of socks and shoes are both unknown, and the question does not state that. Also, another point to make would be that we could also add these variables together, and we do not want that. Option number three states 37.57 + 1.95 + x. X cannot be a separate variable, because by stating that, it means that there would be one more object that was bought that is unknown. I hope this helps you understand my explanation a bit more.

Have a great day, and best of luck for your math problem!

Answer:

[tex]Area = 336\ m^2[/tex]

Step-by-step explanation:

If the ratio of the sides is 13:14:15, we can say that the length of each side is 13x, 14x and 15x.

Then, if the perimeter is 84 m, we have:

[tex]P = 13x + 14x + 15x = 84[/tex]

[tex]42x = 84[/tex]

[tex]x = 2[/tex]

The length of each side is:

[tex]13x = 26\ m[/tex]

[tex]14x = 28\ m[/tex]

[tex]15x = 30\ m[/tex]

Now, to find the area of the field, we can use the following formula:

[tex]Area = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides and p is the semi perimeter:

[tex]p = P/2 = 42\ m[/tex]

So we have that:

[tex]Area = \sqrt{42(42-26)(42-28)(42-30)}[/tex]

[tex]Area = 336\ m^2[/tex]

Answer:

The function f(x) = 4e* when evaluated for f(2) is:

Step-by-step explanation:

Its slope must be m= f'(0).

f'(x) = 8e2x ⇒ m = f'(0) = 8

y - y1 = m(x - x1)

m = 8

y1 = 10

x1 = 0

cause

Answer:

D,xy=-12

Step-by-step explanation:

y=x²+x-2

x+y=1

or x+x²+x-2=1

x²+2x-3=0

x²+3x-x-3=0

x(x+3)-1(x+3)=0

(x+3)(x-1)=0

either x=-3

or x=1

when x=-3

x+y=1

-3+y=1

y=1+3=4

one solution is (-3,4)

xy=-3×4=-12

if x=1

1+y=1

y=0

second solution is (1,0)

xy=1×0=0

Answer:

[tex]Y\approx 84^\circ $(to the nearest angle)[/tex]

Step-by-step explanation:

The lengths of the sides of the scalene triangle are 6, 11, and 12.

We want to use the law of cosines to find the largest angle.

Note that the largest angle is always opposite the largest side.

Therefore:

[tex]1. 12^2 = 11^2 + 6^2-2(11)(6)\cos(Y) \\\\2. 144 = 121 + 36-(132)\cos(Y) \\\\3. 144 = 157 - (132)\cos(Y) \\\\4. -13 = -(132)\cos(Y)\\\\\\5. \cos(Y) = \dfrac{-13}{-132} \\\\6. Y = \arccos \left ( \dfrac{13}{132}\right)\\\\7. Y=84.35^\circ\\\\8. Y\approx 84^\circ $(to the nearest angle)[/tex]

The largest angle is 84 degrees to the nearest angle.

Answer:

i.) (-0.25, 0), (1.25, 0)

ii.) (0.5, 2), (1.5, 2)

Step-by-step explanation:

For i, it is asking for the roots of the quadratic, or where the graph crosses the x-axis.

For ii, it is asking for the x-values when y = 2.

*The box plots are shown in the attachment

Answer/Step-by-step explanation:

Range is the difference between the largest value of a data set and the lowest value in that data set.

In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.

For Crackers, the range = 100-70 = 30

For Cookies, the range = 115-70 = 45

Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).

Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

I hope this helps you

Sphere Surface Area Formula is

4.pi.r^2

4.pi.13^2

4.pi.169

676.pi

The surface area of the sphere with radius 13 units is S = 676π units²

A sphere is a three-dimensional geometrical object that is perfectly round in shape. A sphere is a fully spherical, three-dimensional geometrical object. Every point on its closed surface is equally spaced from the centre, which is the only point on the surface.The distance from the center to any point on the surface of the sphere is known as the radius of the sphere..

Surface Area of a Sphere = 4πr²

Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

They are used to represent many natural and man-made objects such as planets, basketballs, and molecules.

Let the data be ,

Let r = 13 units be the sphere's radius.

Let S be the sphere's surface area.

And , Surface Area of a Sphere = 4πr²

On simplifying , we get

S = 4π ( 13 )²

S = 4π ( 169 )

S = 676π units²

Thus, the sphere's surface area is S = 676 units2.

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━━━━━━━☆☆━━━━━━━

▹ Answer

[tex]\frac{3}{10}[/tex]

▹ Step-by-Step Explanation

2 + 1 = 3

Written as → [tex]\frac{3}{10}[/tex]

Hope this helps!

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Brainliest is greatly appreciated!

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Answer:

Step-by-step explanation:

Total pencils that Lisa had = 10 pencils

Total pencils that Lisa had given to Anna and Ben:

=2+1

= 3

Now,

Fraction of her pencils that she gave away:

[tex] \frac{3}{10} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

3 and 5/12

Step-by-step explanation:

To find how much flour you need, subtract how much sugar you need from how much total you need of sugar and flower. To do this, turn both numbers into improper fractions. This means 3 and 2/3 turns into 11/3 as there are 3 thirds per whole, and there are three wholes plus the 2 thirds, equaling 11/3. The 1/4 is already an improper fraction, so you can move on.

Now you just covert them to have the same denominator by multiply 11/3 by 4 on top and bottom and 1/4 by 3 on both the top and bottom to get 44/12 and 3/12. Now you just subtract 44/12-3/12 and get 41/12. Made into a mixed number that is 3 and 5/12.

The recipe will require three and five-twelfths (3 5/12) fraction cups of flour.

A fraction is a portion of a whole or, more broadly, any number of equal pieces.

It is written in the form p/q, read as "p by q", where p is called the numerator and q is called the denominator, and the fraction p/q represents p number of equal parts from q number of equal parts.

Fractions are of two types:

In the question, we are informed that a recipe calls for a total of 3 and two-thirds cups of flour and sugar.

We are asked if the recipe calls for One-fourth cup of sugar, then how much flour is needed.

We suppose the quantity of flour required to be x cups.

We know the quantity of sugar required = One-fourth cup.

This can be written as a fraction = 1/4 cup.

We know the total sugar and flour is three and two-thirds cups.

This can be written as a fraction = 3 2/3 cup = 11/3 cup.

Now, we know quantity of sugar + quantity of flour = total quantity

or, 1/4 + x = 11/3

or, x = 11/3 - 1/4 = (44 - 3)/12 = 41/12 = 3 5/12.

Therefore, the recipe will require three and five-twelfths (3 5/12) fraction cups of flour.

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Answer:

6 granite, 3 marble, 14 sandstone, 1 slate

ratio of sandstone to marble

how many sandstone does she have .....14

how many marble does she have......3

so the ratio would be 14:3

Answer:

C. 14:3

Step-by-step explanation:

Dana has 14 pieces of sandstone.

Dana has 3 pieces of marble.

The ratio of pieces of sandstone to pieces of marble is 14:3.

The ratio cannot be simplified further.