Eliot's backpack weigh 4,200 grams
kilogram is 1,000 grams. How many
kilograms does Eliot's back weigh?
​

Answer:

B.) [tex]1\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{4} -\frac{2}{3}

Then multiply 4 by 2, then add 1.

frac{9}{4} - \frac{2}{3} \\[/tex]

Then find the Least Common Denominator(LCD); simply just multiply 4 by 3 to get 12; then multiply using the opposite number.

[tex]\frac{3}{3} *\frac{9}{4} - \frac{4}{4} * \frac{2}{3}[/tex]

to get: [tex]\frac{27}{12} - \frac{8}{12}[/tex].

now the denominators is the same on both sides, just subtract the numerator.

27 - 8 = 19

Now simply: [tex]\frac{19}{12} = 1\frac{7}{12}[/tex].

Your final answer is 1\frac{7}{12}[/tex].

Answer:

Step-by-step explanation:

That 7 in the 4th position of the given decimal is greater than 5 and thus indicates that we must round that 4 up:

25.0347 → 25.035.  This is "to 3 decimal places" accuracy.

The number 25.0347 rounded to 3 decimal places is 25.035.

The question is asking to round the number 25.0347 to 3 decimal places. As it is, the number 25.0347 already has 4 decimal places. Rounding it to 3 decimal places means you should retain up to the thousands place (3 digits after the decimal point) and adjust the last digit based on the digit that comes after it. If the 4th digit after the decimal point is 5 or more, you round up. If not, you just drop it.

In the number 25.0347, the fourth digit after the decimal point is 7, which is greater than 5. Therefore, we round up the third digit (4) by 1. So, the number 25.0347 rounded to 3 decimal places is 25.035.

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Answer:

5a

Step-by-step explanation:

Just use the reflexive property / reflexive angles, 5a = x and 4a equals the remaining side.

Answer:

100

Step-by-step explanation:

5a+4a=9a

180/9=a

20=a

4a+x=180

(4 times 20)+x=180

80+x=180

x=100

The answer is

x=10+2y

Steps:

2(x-2y)=20

x-2y=20/2 (in fraction form 20/2)

x-2y=10

X=10+2y

2x-4y=20

Add both sides by -4y

2x=20+4y

Then divide both sides by 2 and you get your answer

x=2y+10

Answer:

B

Step-by-step explanation:

Using the law of sines, we can make a proportion.

But first, we'll need to solve for the unknown angle.

We add up the two known angles and subtract that by 180.

90 + 41 = 131

180 - 131 = 49

So the unknown angles is 49.

Then, we can use the law of sines.

Make the equation.

sin(90)/55 = sin(49)/x

Simplify this using a calculator and you get around 41.51 or option B.

The correct option is B. [tex]41.51[/tex] The value of [tex]\( x \)[/tex] to the nearest hundredth

To find the value of [tex]\( x \)[/tex] to the nearest hundredth, we need to use the trigonometric functions for the right triangle given.

We are given:

The hypotenuse [tex](\( 55 \))[/tex]

An angle [tex](\( 41^\circ \))[/tex]

We need to find the adjacent side[tex](\( x \))[/tex]

We can use the cosine function, which is defined as:

[tex]\[\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\][/tex]

Substituting the given values:

[tex]\[\cos(41^\circ) = \frac{x}{55}\][/tex]

Solving for \( x \)

[tex]\[x = 55 \times \cos(41^\circ)\][/tex]

Using a calculator to find \(\cos(41^\circ)\)

[tex]\[\cos(41^\circ) = 0.7547\][/tex]

Now, multiplying:

[tex]\[x = 55 \times 0.7547 = 41.5085\][/tex]

To the nearest hundredth, \( x \) is:

[tex]\[x = 41.51\][/tex]

The complete Question is

To the nearest hundredth, what is the value of x?

A.36.08

B. 41.51

C. 47.81

D. 72.88

Answer: 1/3 or 33.3% (rounded to nearest tenth)

Step-by-step explanation:

3 and 6 are multiples of 3

6 sides of a dice

2/6= 33%

Answer:

1/3

Step-by-step explanation:

there are 2 multiples of 3 in a die, 6, 3 so you have a 2/6 chance or 1/3

Answer:

20

Step-by-step explanation:

Let t represent the number of toddlers in the class.  Then 15% of t = 3.

In other terms, 0.15t = 3, and t = 3/0.15 = 20.

There are 20 toddlers in the class.

A percent equation representing the problem is 0.15x = 3. Solving this equation reveals that there are 20 toddlers in the total class.

This problem can be solved by expressing the information given in mathematical form.

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Answer:

130.07 Watts

Step-by-step explanation:

hope this helps

Answer:

130.1 W

Step-by-step explanation:

Power is work or energy divided by time, so power has the units of joules/second, which is called the watt.

Power = gravitational potential energy / time

Gravitational potential energy = m g h

here m = mass

        g = gravity die to acceleration = 9.81 m/s²

        h = height

1 Ib = 0.453592 kg

32 Ib = 14.5 kg

1 feet = 0.3048 m

12 feet = 3.6576 m

Plug value in the formula

(14.5) (9.81) (3.6576)

520.3 J

520.3 / 4

130.1 W

Answer:

214

Step-by-step explanation:

set bc = to cd and solve for x

then substitute x into one of the equations and solve --> you should get 73

multiply 73 by 2 and then subtract that from 360

you should get 214

Answer:

Vertical asymptotes: x=-9 and x=3

Slant asymptote: y=5x-1

Step-by-step explanation:

Given

f(x)=(5x^3+29x^2-140x+21)/(x^2+6x-27)

For vertical asymptote, the denominator is put equal to zero,so

x^2+6x-27=0

Factorizing

x^2+9x-3x-27=0

x(x+9)-3(x+9)=0

(x+9)(x-3)=0

So,

x=-9 ;x=3

As the degree of the numerator is greater than the denominator the function will not have horizontal asymptote but it will have a slant asymptote which will be calculated by long division.

After dividing 5x^3+29x^2-140x+21  by x^2+6x-27  we get

Quotient: 5x-1

Remainder: x-6

We only need the quotient for the slant asymptote,

So the slant asymptote is y = 5x -1  ..

Answer:

Vertical asymptotes: x=-9 and x=3

Slant asymptote: y=5x-1

Step-by-step explanation:

Answer: I predict 460.

Step-by-step explanation:

Answer:

C. 460

Step-by-step explanation:

We are given a dot graph which shows the number of Hybrid cars sold over the years.

The x-axis represents the years and y-axis represents the number of cars sold.

By looking at the graph, we can infer the following information.

In 2003, the number of cars sold was 120

In 2004, the number of cars sold was 160.

In 2005, the number of cars sold was 260.

In 2006, the number of cars sold was 360.

If you look at the last 3 years, the number of cars sold was increase by 100 by each year.

So, we can predict that in 2007, the number of cars sold was 460.

C. 460

Answer:

[tex]y=2.5x-1[/tex]

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem we have

[tex]15x-6y=6[/tex] ---> equation of the line in standard form

Convert to slope intercept form

Isolate the variable y

Subtract 15x both sides

[tex]-6y=-15x+6[/tex]

Divide by -6 both sides

[tex]y=(15/6)x-1[/tex]

[tex]y=2.5x-1[/tex] ----> equation of the line into slope intercept form

Answer:

The lighthouse is 424 feet away.

Step-by-step explanation:

There is no other way to do this but to use one of the 6 trigonometry functions.

Drawing

Draw a dotted horizontal line.

judge an angle that could be 23o. Let it slant downward from the left side of the dotted line.

Draw another horizontal line that represents sea level.

Join the left side of the dotted line to the last line you drew. The angle on your right is also 23o.

Function

You have 6 trig functions to choose from. You have the lighthouse height (180 feet) the angle on your right, and the length on the horizontal representing the distance from the lighthouse base to the boat.

You have an angle

You have an opposite side

You have a horizontal line (the adjacent side)

You want to use the tangent function.

Tan(23) = opposite / ad

Tan(23) = 180 / adjacent     Multiply both sides by the adjacent

adjacent*Tan(23)= 180        Divide by Tan(23)

adjacent = 180/Tan(23)

adjacent = 180 / 0.42447

adjacent = 424 feet.

Answer:

Step-by-step explanation:

In order for these lengths to form a right triangle they need to satisfy the equation:

[tex]a^2 + b^2 = c^2[/tex], where c is always the highest value as it represents the length of the hypotenuse.

So plugging in:

10, 24, 26.

a = 10, b = 24, c = 26

[tex]10^2 + 24^2 = ?[/tex]

100 + 576 = 676

[tex]\sqrt{676} = 26[/tex]

So, this is a right triangle.

Now do this operation on all of the values.

Tip: a = random number smaller than the biggest, b = smaller than the biggest and not the same as 'a', c = always the biggest.

If [tex]a^2 + b^2 = c^2[/tex] then it is a right triangle

Answer:

12 cm^3

Step-by-step explanation:

The volume of a pyramid with a square base is V = 1/3(l*w*h). Substitute l = 3, w = 3 and h = 3.

V = 1/3(3*3*4) = 1/3(36) = 12

Answer:

F. $28 for jeans; $32 for shirt

Step-by-step explanation:

The two hand written equations are correct.

Multiply both sides of the first equation by -3.

-3j - 3s = -180

The second equation is

4j + 3s = 208

Add these two equations.

j = 28

The only choice that has $28 for a pair of jeans is choice F, so that is the correct answer.

Step-by-step explanation:

A triangular prism has five faces in total. There are two triangular bases and three rectangular lateral faces. Few examples of triangular prism are - a camping tent, Toblerone chocolate shape. The base of a prism is also a face.

Here the given prism is a triangular prism which has triangular bases.

Therefore, the answer is option C triangle.

By critically observing the triangular prism shown in the image attached above, the base shape of this triangular prism is a: C. triangle.

A triangular prism can be defined as a geometric shape (figure) with five (5) faces in total. Generally, a triangular prism comprises two (2) triangular bases and three (3) rectangular lateral faces.

By critically observing the triangular prism shown in the image attached above, we can logically deduce that the base shape of this prism is a triangle.

In conclusion, the base shape of this triangular prism is a triangle.

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Answer: z = -3 , y = 2 , x = 2

The solution to the system of equations is: x - y + 9z = -27 , 2x - 4y - z = -1 , 3x + 6y - 3z = 27 is

x = 2

y = 2

z = -3

Given the system of equations:

1. x - y + 9z = -27

2. 2x - 4y - z = -1

3. 3x + 6y - 3z = 27

We'll use the method of elimination to solve this system.

Step 1: Eliminate y from equations (1) and (2):

Adding equations (1) and (2):

(x - y + 9z) + (2x - 4y - z) = -27 + (-1)

x + 2x - y - 4y + 9z - z = -27 - 1

3x - 5y + 8z = -28

Step 2: Eliminate y from equations (2) and (3):

Multiplying equation (2) by (3) and equation (3) by (2):

6x - 12y - 3z = -3  (from equation 2)

6x + 12y - 6z = 54 (from equation 3, after multiplying by 2)

Adding these two equations:

(6x - 12y - 3z) + (6x + 12y - 6z) = -3 + 54

6x + 6x - 12y + 12y - 3z - 6z = 51

12x - 9z = 51

Now, we have two equations:

1. 3x - 5y + 8z = -28

2. 12x - 9z = 51

From equation (2), let's solve for (x):

12x - 9z = 51

12x = 51 + 9z

x = (51 + 9z) ÷ 12

Now, we'll substitute this expression for (x) into equation (1) to solve for (z):

3x - 5y + 8z = -28

[tex]\[ 3\left(\frac{51 + 9z}{12}\right) - 5y + 8z = -28 \][/tex]

[tex]\[ \frac{153 + 27z}{12} - 5y + 8z = -28 \][/tex]

Next, we'll isolate (z):

153 + 27z - 60y + 96z = -336

249z - 60y = -489

Now, let's solve for (z):

249z = -489 + 60y

z = (-489 + 60y) ÷ 249

Now, we'll substitute the expression for (z) back into equation (2) to solve for (y):

[tex]\[ 12x - 9\left(\frac{-489 + 60y}{249}\right) = 51 \][/tex]

[tex]\[ 12x - \frac{-489 + 60y}{27} = 51 \][/tex]

[tex]\[ 12x = 51 + \frac{-489 + 60y}{27} \][/tex]

[tex]\[ x = \frac{51 + \frac{-489 + 60y}{27}}{12} \][/tex]

[tex]\[ x = \frac{51\times27 + -489 + 60y}{12\times27} \][/tex]

[tex]\[ x = \frac{1377 - 489 + 60y}{324} \][/tex]

[tex]\[ x = \frac{888 + 60y}{324} \][/tex]

[tex]\[ x = \frac{148 + 10y}{54} \][/tex]

Now, we'll substitute the expressions for (x) and (z) into equation (1) to solve for (y):

x - y + 9z = -27

[tex]\[ \frac{148 + 10y}{54} - y + 9\left(\frac{-489 + 60y}{249}\right) = -27 \][/tex]

The least common multiple of (54) and (249) is (54 × 249).

⇒ (148 + 10y) × 249 - 54 × 249 × y + 9 × 54 × (-489 + 60y)  = -27 × 54 × 249

⇒ 36752 + 2490y - 133146y - 233640 + 29160y = -1458 × 249

⇒  2490y - 133146y + 29160y + 36752 - 233640 = -1458 × 249

⇒ -106496y - 197888 = -362682

⇒ -106496y = -164794

⇒ y = (-164794) ÷ (-106496)

y ≈ 1.547

y ≈ 2

Now that we have found (y = 2), we can substitute this value back into the expressions for (x) and (z) to find their values.

For (x):

[tex]\[ x = \frac{148 + 10(2)}{54} = \frac{168}{54} = 2 \][/tex]

For (z):

[tex]\[ z = \frac{-489 + 60(2)}{249} = \frac{-369}{249} = -\frac{3}{1} = -3 \][/tex]

So, the solution to the system of equations is:

x = 2

y = 2

z = -3

Im gonna have to say its c

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

f -----> the number of pounds of fertilizer

s ----> the number of pounds of seeds

we know that

The inequality that represent the situation is

[tex]2f+20s\leq 4,000[/tex]

using a graphing tool

see the attached figure

The solution is the triangular shaded area

Answer:

top right :D

Step-by-step explanation:

Answer:

(-a,b)

Step-by-step explanation:

You use midpoint formula which is (x1+x2/2),(y1+y2/2)

Answer:

d may cause f

Step-by-step explanation:

Apex

The true statement is that the d may cause f. Correlation is a statistical measure used to measure the relationship that exists between two variables.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Here are the options

d must not cause f.

f must cause d.

d must cause f.

d may cause f.

1. Positive correlation: it means that the two variables move in the same direction. If one variable increases, the other variable also increases.

For example, there should be a positive correlation between quantity supplied and price

When there is a positive correlation, the graph of the variables is upward sloping

2. Negative correlation:  it means that the two variables move in a different direction. If one variable increases, the other variable decreases.

For example, there should be a negative correlation between quantity demanded and price

When there is a negative correlation, the graph of the variables is downward sloping

3. Zero correlation: there is no relationship between the variables

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Answer:It is 100

Step-by-step explanation:

0.75x = 60

You can also make it easier by using fractions:

3x/4 = 60

Multiply both sides by 4:

3x = 240

x = 80

Answer:

13ft

Step-by-step explanation:

V= 1/3 x B x h

507=1/3 x B x 9

B= 169ft²

B= b x b

169= b x b

b = 13ft

The length of each side of the base of the pyramid is, 13 feet

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

A square pyramid is 9 ft tall and has a volume of 507 cubic feet.

Since, We know that;

Volume of square pyramid is,

V= 1/3 x B x h

Substitute all the values, we get;

507=1/3 x B x 9

B = 169ft²

B = 13ft

Thus, The length of each side of the base of the pyramid is, 13 feet

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For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have the following points:[tex](x1, y1) :( 5,6)\\(x2, y2) :( 4,8)[/tex]

Substituting:

[tex]m = \frac {8-6} {4-5}\\m = \frac {2} {- 1}\\m = -2[/tex]

Then, the equation is:

[tex]y = -2x + b[/tex]

To find "b" we substitute one of the points:

[tex]8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16[/tex]

Finally, the equation is:

[tex]y = -2x + 16[/tex]

Answer:

Option B

Answer:

I believe the answer is B.

Step-by-step explanation:

Because a proportional relationship is one where x is proportional (equal) to y, and Graph A does not fall into that category, and Graph B does, the answer should be B.

Answer:

The answer A

Step-by-step explanation:

Only graph A represents a proportional relationship.

Two quantities are proportional to each other if the graph is a straight line through the origin.

Answer:

the answer is b

Step-by-step explanation:

Answer:

The solution in the attached figure

Step-by-step explanation:

case 1) we have

[tex]\frac{7}{4}x+3[/tex]

Classify

a) Name using degree ---> Is a linear polynomial (the power of the largest term is 1)

b) Name using Number of Terms ----> Monomial (the number of terms is 1)

case 2)

we have

[tex]5.2x^{2}-4x+2.5[/tex]

Classify

a) Name using degree ---> Is a quadratic polynomial (the power of the largest term is 2)

b) Name using Number of Terms ----> Trinomial (the number of terms is 3)

case 3)

we have

[tex]3/5[/tex]

Classify

a) Name using degree ---> Is a constant (the power of the largest term is 0)

b) Name using Number of Terms ----> Monomial (the number of terms is 1)

case 4)

we have

[tex]0.75x^{2}[/tex]

Classify

a) Name using degree ---> Is a quadratic polynomial (the power of the largest term is 2)

b) Name using Number of Terms ----> Monomial (the number of terms is 1)

A polynomial is said to be:

1) Constant if it is of degree 0 i.e. in general it is represented by: a

2) Linear if it is of degree one i.e. in general it is represented by: ax+b

3) Quadratic if it is of degree two i.e. in general it is represented by: [tex]ax^2+bx+c[/tex]

4) cubic if it is of degree 3 i.e. in general it is represented by: [tex]ax^3+bx^2+cx+d[/tex]

Also,

1) Monomial-- is a polynomial with one term.

2) Binomial-- is a polynomial with two terms.

3) Trinomial-- is a polynomial with three terms.

Answer:

2250$ thats the answer

Answer:

56

Step-by-step explanation:

First, do you know what a CD is? ;-)

Since you will pick 3 CDs out of 8, and the order of the CDs don't import (1,2,4 is the same as 2,1,4 and 4,2,1 for example),we'll calculate the Combinations (and not the permutations). The formula for Combinations is:

[tex]C(n,r) = \frac{n!}{(r!(n-r)!)}[/tex]

Where n is the number of elements (8 in our case) an n is the sample (3 in our case).

[tex]C(8,3) = \frac{8!}{(3!(8-3)!)} = \frac{40320}{6 * 120} = 56[/tex]

So, there are 56 random groups of 3 you can pick from your potential 8 CDs.