A boy is n years old. His sister is four times as old. The sister's age is

The last digit of 73 factorial (73!) is 0 because any factorial of a number greater than 4 ends in 0 due to the multiplication with 2 and 5.

The last digit in a factor of an integer is dependent upon the pattern of the last digits in its individual factors. We know that factorial of any number greater than 4 ends in 0 because factorial operation involves multiplication by 2 and 5. Since 2 and 5 are factors of any number greater than 4, and the multiplying them results in 10, the final digit will always be 0.

In our case, the student wants to find out the last digit in 73!, which is far greater than 4. So, the last digit of 73! is 0.

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Answer:

1:5.25

2:10.5

10:52.5

x:5.25x

Step-by-step explanation:

Basically, you do 42 divided by 8 to get the cost of $5.25 which is the cost of one ticket. Then you multiply that for each number of ticket.

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ h(x)=x^2+x-6 \qquad \begin{cases} x_1=0\\ x_2=3 \end{cases}\implies \cfrac{h(3)-h(0)}{3-0} \\\\\\ \cfrac{(3^2+3-6)~~-~~(0^2+0-6)}{3}\implies \cfrac{(6)-(-6)}{3} \\\\\\ \cfrac{6+6}{3}\implies \cfrac{12}{3}\implies 4[/tex]

Answer:

22.5°

Step-by-step explanation:

The inscribed angle theorem tells us that the measure of an inscribed angle is half of the central angle swept out by the same arc. Here, the arc BD sweeps out a central angle of 45°, so the measure of angle BAD must be half that, or 45/2 = 22.5°

Answer:

2 quart ///////////////////// I think

The radius of the circle is 17 uints and the point (-15,-16) or (-15,14) lies on the circle.

step by step explanation is here,

centre of circle(h,k)=(-7,-1)

if the circle passes through the point (8,7)

then the distance between (8,7) and (-7,-1) represents the radius.

so, r^2= (x2-x1)^2 + (y2-y1)^2

or, r^2=(-7-8)^2 +(-1-7)^2

or, r^2=(-15)^2 +(-8)^2

or, r^2=225+64

or, r^2=289

or, r=17 units

now the equation of circle is

(x-h)^2 +(y-k)^2 =r^2

or, (x+7)^2 +(y+1)^2 =289

or, x^2 +14x +49 + y^2 + 2y+ 1=289

or, x^2 + y^2 + 14x +2y-239=0

puttimg x=-15,

or, (-15)^2 + y^2 +14×(-15) + 2y -239=0

or, y^2 + 2y -239+225-210=0

or, y^2 + 2y -224=0

If you slove y, then you will get 14 and -16.

The radius of the circle is 17.

The point (-15, 14) lies on the circle.

Given that:

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

That is:

Center of the circle = (-7, -1)

A point on the circle = (8, 7)

The equation of the circle is:

(x - a)² + (y - b)² = r²

Here (a, b) is the center and r is the radius.

Substituting the given center.

(x - -7)² + (y - -1)² = r²

(x + 7)² + (y + 1)² = r²

Substitute points (8, 7).

(8 + 7)² + (7 + 1)² = r²

r² = 289

r = 17

So, the radius of the circle is 17.

So, the equation of the circle is:

(x + 7)² + (y + 1)² = 289

Substitute x = -15.

(-15 + 7)² + (y + 1)² = 289

(y + 1)² = 225

y + 1 = 15

y = 14

Hence the radius is 17 and the point is (-15, 14).

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Answer:

A

Step-by-step explanation:

If you reflect figure P over the x-axis, it will be below the axis, below where figure P is. Then you need to move it 7 units right.

Answer: A

Answer:

It's x = -4 ,  2.

Step-by-step explanation:

x^2 + 2x - 8 = 0

The left side will factor to the form (x + a)(x + b).

We need 2 numbers  (a and b)  whose  product = -8 and whose sum = +2.

These  are a = 4 and b = -2,  so the factors are

(x + 4)(x - 2) = 0

Now either x + 4 = 0 or x - 2 = 0,

giving x = -4, x = 2 (answer).

Answer:

-2 , 4

Step-by-step explanation:

Their are 4 ways you can solve this but I am going to factorise to solve

x² + 2x − 8 = 0

Factors = 4 , -2

Sum = 2

Product = -8

x ( x + 4 ) - 2 ( x + 4 ) = 0

( x - 2 ) ( x + 4 ) = 0

x = - 2 , 4

Answer:

right triangle

Step-by-step explanation:

We know that the total angles of the triangle are 180 degrees:

(x) + (4x-10) + (2x+15) = 180

7x - 10 + 15 =180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175÷ 5 = 25

Now we calculate each angle

x=25

4x-10= (4*25) -10=100-10=90

2x+15=(2*25)+15=50+15=65

Because we have a right angle, then the triangle is right triangle

Answer:

right angle

Step-by-step explanation:

dont let the look of the triangle fool you

Answer: -125p12z18u3

Reason:

Square negative five twice, so: -5 x -5 x -5 = -125

The first squaring is -5 x -5, which is 25. The second squaring is 25 x (-5), which is - 125.

When it comes to the letters, they act like they are being multiplied.

(p4)3 = p12

(z6)3 = z18

(u)3 = u3

So the answer is -125p12z18u3.

Hope this helps! :)

First you have to know the "power rule." This is when there is an exponent outside the parentheses and some/all of the variables/numbers in the parentheses have exponents as well. What you do is multiply the outer exponent with each of the exponents inside the parentheses.

[tex]((-5)^{1*3} p^{4*3} z^{6*3} u^{1*3} )[/tex]

[tex](-5)^{3}p^{12}z^{18}u^{3}[/tex]

[tex]-125p^{12}z^{18}u^{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: B.

Step-by-step explanation:

Diameter = Radius divided by 2.

The volume formula of a sphere is V = 4/3 π r^3.

Radius of this problem = 7.5.

So, V = 4/3 π (7.5) ^3.

Once you "plug in" the radius and solve the equation, you get an answer of 1,766.3, rounded to the nearest tenth.

Don't forget the inches cubed!

The answer is B. 1766.3

using pythagoras theorem the height ladder reaches above the wall can be found as in picture the answer would be 12ft

Answer:

Because the answer is found as

5/2(s) - 5/2(s) = 0,

S can actually be anything since the above results to 0(s)=0 and anything multiplied by 0 just gives you 0 Hence, the value of S can be anything

Answer:

5/2(s) - 5/2(s) = 0

Step-by-step explanation:

Answer:

5 pencils can be bought with 45 cents

Step-by-step explanation:

hope my handwriting is readable.

Answer:

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

therefore

|-4.5| = -(-4.5) = 4.5

Answer:

4.5

Step-by-step explanation:

usually if you are finding absolute value for a negative number, it is usually the opposite of that negative number.

If I am trying to find absolute value for -7 it would be 7.

Answer:

B

Step-by-step explanation:

You may have a different calculator than me, but what I did is I pressed the statistics button on my calculator, then I went to the option that said "Edit" which brought me to a table where I could type the given values in. Then I pressed the statistics button again but this time I went to the page that said "CALC" and I scrolled down to the option that said "LinReg(ax+b), then I went all the way down to where it says "Calculate" and I pressed the enter button. And then it told me what the slope and y-intercept values are for the line of regression (a is the slope, and b is the y-intercept or starting value).

Answer:

it is y=-8.583x+475.215

Step-by-step explanation:

[tex]\bf \cfrac{1}{x-10}\div\cfrac{9x}{x^2-9x-10}\implies \cfrac{1}{x-10}\cdot \cfrac{x^2-9x-10}{9x} \\\\\\ \cfrac{1}{\begin{matrix} x-10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \cfrac{\begin{matrix} (x-10) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+1)}{9x}\implies \cfrac{x+1}{9x}[/tex]

A. The distance between the library and the park is equal to [tex]2\sqrt{10}[/tex] miles.

B. The distance between the park and the football field is [tex]2\sqrt{35}[/tex] miles.

Therefore, the correct answer option is D. [tex]2\sqrt{10}[/tex] miles and [tex]2\sqrt{35}[/tex] miles.

According to the geometric mean (leg) theorem, the length of the leg of a right-angled triangle is the geometric mean between its hypotenuse and the segment of the hypotenuse which is adjacent to that leg;

Hypotenuse/leg = leg/part or altitude/left = right/altitude

where;

left = 10 miles

right = 4 miles

Part A.

By applying geometric mean (leg) theorem, the distance between the library and the park (x) can be calculated as follows;

[tex]x^{2} =10 \times 4\\\\x=\sqrt{40} \\\\x=2\sqrt{10} \;miles.[/tex]

By applying geometric mean (leg) theorem, the distance between the park and the football field (y) can be calculated as follows;

(10 + 4)/y = y/10

14/y = y/10

[tex]y^2=\sqrt{140} \\\\y=2\sqrt{35}\;miles[/tex]

(180-30)/2 would be the equation and the answer is 150/2

The value of x (the perpendicular side) in the given right triangle is approximately 21.2137.

In a right triangle with a 45° angle, we can use the trigonometric function sine (sin) to find the value of the perpendicular side (x) when the hypotenuse is given.

sin(angle) = opposite / hypotenuse

Here the angle is 45°, and the hypotenuse is 30.

Therefore, we can write the equation as:

sin(45°) = x / 30

To solve for x, we can rearrange the equation:

x = sin(45°) × 30

Using the value of sin(45°) = 0.7071 (approximately), we can calculate x:

x = 0.7071 × 30

x = 21.2137

Therefore, the value of x (the perpendicular side) in the given right triangle is approximately 21.2137.

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Step-by-step explanation:

8*8=64

4S=64

S=16

white = 6S = 96 ft²

Blue = 6S = 96 ft²

Turkeyy :))

The area of the figure will be 96 square feet.  Then the correct option is A.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A composite figure has three congruent triangles removed from it.

Then the area of the figure will be

Area = 3 x area of square + 3 x area of triangle

Area = 3 x 8 x 8 - 3 x 1/2 x 8 x 8

Area = 192 - 96

Area = 96 square feet

The area of the figure will be 96 square feet.

Then the correct option is A.

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Answer:15 pi

Step-by-step explanation:

The scope is 10(r)*2*pi

XPY is 3 quarters of the slope, which equals to 0.75*20*pi=15pi

Answer:

$ 4.50

Step-by-step explanation:

Given:

Charges of shipping package up to 1 ounce= $0.57

charges of shipping package of 224  grams=?

Converting grams into ounces

1 gram = 0.035274 ounces

224 grams = x ounces

By cross-multiplication we get

224(0.035274)= x ounces

7.90137= x

224 grams= 7.90137 ounces

Now finding charges of shipping package of 7.90137 ounces

Charges of shipping package up to 1 ounce= $0.57

charges of shipping package of 7.90137 ounces= $ x

By cross-multiplication we get

$x= 7.90(0.57)

   = 4.50

Hence the cost to ship the package in dollar and cents is $4.50

i.e. 4 dollars and 50 cents!

The answer is:

She will need 9 tins to cover all the panels.

To find how many tins will she need to cover the 30 panels for her allotment and her garden, we need to calculate the total area of the panels and then, calculate how many tins will she need knowing that each liter of tin, covers 12 square meters.

We are given the dimensions of the panels:

[tex]Long=1.8m\\Hight=2m[/tex]

Now, calculating the area of one (1) panel, we have:

[tex]Area=long*height=1.8m*2m=3.6m^{2}[/tex]

So , the total area of all 30 panels is:

[tex]TotalArea=30*3.6m^{2}=108m^{2}[/tex]

Then, calculating how many tins will she need to paint all the panels, we have:

[tex]NeededTins=\frac{TotalArea}{AreaToCoverWithOneTin}\\\\NeededTins=\frac{108m^{2}}{12m^{2} }=9[/tex]

Hence, we have that she will need 9 tins to cover all the panels.

Have a nice day!

To treat 30 panels, Nancy will need 9 tins of wood preservative.

The total area of 30 panels:

Each panel is 1.8m * 2m = 3.6m²

Total area for 30 panels = 30 panels * 3.6m²/panel = 108m²

Calculate the number of tins needed:

1 litre of preservative covers 12m²

Number of tins needed = Total area / Area covered by 1 tin = 108m² / 12m² = 9 tins

Answer:

(f * g)(2) =  -11√2 +66

Step-by-step explanation:

Points to remember

Let f(x) and g(x) be the two functions, then (f * g) can be written as,

(f * g) = [f(x)][g(x)]

To find the value of (f * g)(2)

we have,

f(x) = -5x - 1 and g(x) =√x - 6

f(2) = -5*2 - 1 = -11

g(2) = √x - 6 = √2 - 6

(f * g)(2) = [f(2)][g(2)]

 = -11 (√2 - 6)

= -11√2 +66

Therefore (f * g)(2) =  -11√2 +66

Answer:

420

Step-by-step explanation:

420 I think that’s what you wanna

Answer:

6

Step-by-step explanation:

first subtract 29 from 35, then you get the difference, which is 6!

Hello There!

We have an equation “35 - x = 29”

To solve this we can use addition.

29 plus some number = 35.

29+5 = 34 so add 1 more and you get 35.

X=6

8+5+15+12+10= 50 / 5 = 10

Answer:

A) 5 + 2 =7 x 4= 28

B) 8

Step-by-step explanation:

A) 5 x 4 = 20 and 2 x 4 = 8 so you add 20 + 8 and you get 28

B)  so 5 x 4 is 20 and there is 8 left over and if you do 2 x 4 you get 8

To determine the number of egg salad sandwiches served, we set up an equation 5x + 2x = 28, where x is the number of egg salad sandwiches, and solve for x to find that 4 sandwiches were egg salad sandwiches.

To solve for the number of egg salad sandwiches served at the restaurant, we set up the following equation based on the proportion given: let x be the number of egg salad sandwiches, and 5 times x will be the number of tuna sandwiches since there are 5 tuna sandwiches for every 2 egg salad sandwiches.

The total number of sandwiches is 28, which gives us the following equation:

5x + 2x = 28

We then combine like terms:

7x = 28

Next, we divide both sides of the equation by 7 to solve for x:

x = 28 / 7

x = 4

This means that 4 sandwiches were egg salad sandwiches.

Final answer:

The volume of Kathy's stacks is 24 cm³ greater than Marco's stacks. Each cube has a volume of 8 cm³, and after multiplying by the number of cubes each person has and subtracting, we find the difference in volume.

Explanation:

To calculate how much greater the volume of Kathy's stack of cubes is compared to Marco's, we need to determine the volume of both sets of cubes and then subtract the smaller volume from the larger one. Each cube has a volume of 2 cm × 2 cm × 2 cm, which equals 8 cm³.

Kathy has 8 cubes, so her total volume is:

8 cubes × 8 cm³ per cube = 64 cm³.

Marco has 5 cubes, so his total volume is:

5 cubes × 8 cm³ per cube = 40 cm³.

To find out how much greater Kathy's volume is:

Kathy's volume – Marco's volume = 64 cm³ – 40 cm³ = 24 cm³.

Therefore, the volume of Kathy's stacks is 24 cm³ greater than Marco's stacks.