Malcom and his sister ran 3 races. Their distances are shown below.
Race Malcom's / Sister Distance
1. 10 yards 300 inches
2. 18 feet 180 inches
3. 120 inches 5 feet

Who can run the farthest? How do you know? Use the lines and space below to
prove your answer.

Answer:

No

Step-by-step explanation:

\(7^{-1}\) is a fraction

using the rule of exponents

• \(a^{-m}\) = \(\frac{1}{a^{m} }\)

then

\(7^{-1}\) = \(\frac{1}{7^{1} }\) = \(\frac{1}{7}\) ← that is a fraction

a) 625

b) 120

=============================================

Explanation:

If we select with replacement, then the first battery chosen is put back or we put a cloned copy in the bag. The contents of the bag have not changed. This means the second selection has the exact same identical situation as the first selection. By extension, any future selection has the same idea.

We have 5 batteries for any given selection, and we select 4 batteries. That gives 5*5*5*5 = 5^4 = 625 different outcomes in the sample space.

---------------

Now consider a situation where we don't apply replacement. Whatever is selected is not put back, and we don't put in a cloned copy. We go from 5 choices in the first selection, then 5-1 = 4 choices for the second,  5-2 = 3 choices for the third, and 5-3 = 2 choices for the fourth.

Overall there are 5*4*3*2 = 120 different outcomes in the sample space this time.

Another way to calculate this value is to plug n = 5 and r = 4 into the nPr permutation formula below

\(nPr = \frac{n!}{(n-r)!}\)

The exclamation marks represent factorials.

Answer:

\(=-6w^2-31w-35\)

Step-by-step explanation:

Apply Foil.
\(\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)\)
\(=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)\)
\(=-6w^2-31w-35\)

Answer:

m=-25

Step-by-step explanation:

m=Δh/Δt

(Im choosing for the difference in height and time (Δh and Δt) to be the difference between the data in the first two rows)

m=(4500-5000)/(20-0)

m=-500/20

m=-25

Answer:

169.65

Step-by-step explanation:

Answer:

9x^3y^4

Step-by-step explanation:

18x^3y^4

/

2

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer: Section formula

Step-by-step explanation:

Given

The line segment AB with endpoints \(A(2,2)\) and \(B(14,14)\) is divided by a point X in the ratio 1:2

To verify that X divides the line segment in the ratio 1:2, we will use section formula. Section formula tells the coordinates of the point which divide the line segment in the certain ratio or vice-versa.

We will assume that X divides AB in k:1 and insert the values in the section formula. If the ratio k:1 comes out to be 1:2, then it verifies the claim.

Answer:

Answer choice B was correct

Step-by-step explanation:

Line segment EB is congruent to line segment CB. I took the test.

Answer:

((1+2)x3) + (4x5) = 29

Step-by-step explanation:

Since 4x5 = 20 and 3x3 = 9, and 9 + 20 = 29, we put parenthesis around 1+2,

we get,

((1+2)x3) + (4x5) = 29

This is true because,

(3x3) + (4x5) = 29

(9) + (20) = 29

29 = 29

Answer: 200ft

Step-by-step explanation:

43+43+57+57=200

Answer:

A

Step-by-step explanation:

A is the answer because the origin is located at point (0,0)

Answer:

$3.85 per gallon.

Step-by-step explanation:

48.51 / 12.6 = 3.85

Answer: The answer would be 1 gallon=$3.85

Step-by-step explanation:

Answer:

Step-by-step explanation:

\( \mathsf{ \frac{x}{4} = 2}\)

Apply cross product property

\( \mathsf{x \times 1 = 2 \times 4}\)

Calculate

\( \mathsf{x = 8}\)

Hope I helped!

Best regards!

Answer:

\( \frac{x}{4} = 2\)

X=2

Step-by-step explanation:

4•x/4=2•4

X=8

Check the picture below.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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Answer:

1/(e - 1)  

Step-by-step explanation:

ln (1 + x) = 1 + ln (x)

ln (1 + x) - ln (x) = 1

ln ((1 + x)/x) = 1

(1 + x)/x = e = 1 + 1/x

x = 1/(e - 1)

Answer:

22 in.

Step-by-step explanation:

Perimeter = Length + Length + Breadth + Breadth

Perimeter = 7 in. + 7 in. + 4 in. + 4 in.

Perimeter = 22 in.

As a result, whereas the latter two expressions are not polynomials, the first two and last one are polynomial.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or any expression . For instance, the first two terms of the polynomial with the variables x and y have coefficients of 7 and -3, respectively. The constant coefficient is the third term of 1.5.

An expression made up of variables and coefficients and utilizing solely the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables is referred to as a polynomial.

Let's examine each phrase separately:

Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "3X² -5x⁴+2x-12" is a polynomial.

Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x⁵-5x⁴+4x³-3x²+2x-1" is a polynomial.

- Since it contains negative exponents of variables, which are not permitted in polynomials, "x⁻⁵-5x⁻⁴+4x⁻³+2x⁻¹ - 1" is not a polynomial.

- Because it contains division, which is not permitted in polynomials, "4/x⁴+3/x³-2/x²-1" is not a polynomial.

-Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x³-7x²+9x-5x⁴-20" is a polynomial.

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The length of segment CM is equal to the square root of 10. This is determined by dividing the area of the square ABCD, which has sides of length 3, into three equal parts, resulting in a segment of length √10.

The area of square ABCD can be calculated by squaring the length of one side, which is 3, to get 9. To divide this area into three equal parts, each part must have an area of 3. To find the length of segment CM, the square root of this area, 3, must be taken, resulting in a length of √10.

To find the length of segment CM in square ABCD, the area of the square must first be determined. This can be done by squaring the length of one side, which is 3, resulting in an area of 9. To divide this area into three equal parts, each part must have an area of 3. This means the length of segment CM must be the square root of 3, which is equal to √10. Therefore, the length of segment CM is equal to √10. This is the result of dividing the area of the square ABCD into three equal parts.  This process can be used to determine the length of any segment dividing an area into equal parts

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The value of x is 4.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

In ΔCDB and ΔEAB

<CDB = <ABE    (alternate interior angle)

<DBC = <EAB    (alternate interior angle)

By AA similarity criteria

ΔCBD ~ ΔEAB

Now,

EB/ CD= EA/CB

6/x-1 = 4/x-2

6X-12= 4X-4

2x= 8

x=4

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Answer:

2,4 3,5

Step-by-step explanation:

Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

Step-by-step explanation:

a)

g(3) = 9

b)

g(-1) = 1

c)

g(-x) = x²

d)

g(2y) = 4y²

e)

g(1 + h) = 1 + h² + 2h

using the identity (a +b)² = a² + b² + 2ab

Answer:

c

Step-by-step explanation:

Answer:

y=8x-34

Step-by-step explanation:

Answer:

(0,0)

Step-by-step explanation:

Hi there!

We are given the line segment AB, with endpoints A and B and we want to find the midpoint of it.

We can use the midpoint formula to do that, which states that the value of the midpoint can be found using the formula \((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\), where the coordinates \((x_1, y_1)\) and \((x_2, y_2)\) are the endpoints of the line segment

As stated above, the endpoints are A and B

So let's find the values of A and B

The point A is (-1, 2)

The point B is (1, -2)

Although we have the endpoints, let's label the values of the points to avoid confusion for when we calculate.

\(x_1=-1\\y_1=2\\x_2=1\\y_2=-2\)

Now substitute those values into the formula to solve for the midpoint.

\((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\)

\((\frac{-1+ 1}{2}, \frac{ -2+ 2}{2})\)

Simplify the numerators:

\((\frac{0}{2}, \frac{ 0}{2})\)

Divide

(0, 0)

The midpoint of AB is (0,0)

Hope this helps!