The new merry go round can hold a total weight of 500 pounds. Susie weighs 45.67 pounds, Johnny weighs 76.9 pounds, Grace weighs 66.72 pounds, and Max weighs 89.3 pounds. Can the merry go round hold all of the children? Show and explain your answer.

Final answer:

To determine which negative number is greater between -4.03 and -4.3, compare their standard forms with the same exponent, concluding that -4.03 is larger due to its higher coefficient.

Explanation:

To determine which number is larger between -4.03 and -4.3, we can compare them in standard form:

-4.03 = -4.03 × 100

-4.3 = -4.3 × 100

Since both numbers have the same power of 10 (exponent), we compare the coefficient: -4.03 is larger than -4.3 because 0.03 is greater than 0. Therefore, -4.03 is larger than -4.3.

Answer:

{x∈Z+ | x is an even, 2≤x≤12}

Step-by-step explanation:

∈ = elememt of

Z+ = +ve integer

even = even no.

≤ = smaller than or equal to

The set builder notation is  {x : x =  2n where n ∈ N and n < 6}.

A set is a group or collection of objects or numbers, considered as an entity unto itself.  

Now the given set is,

Let S = {2,4,6,8,10,12}

Now, Set-builder notation describe a set by saying what properties its members have.

It uses curly brackets called "braces".

The first part after the first curly bracket tells you what set of numbers x belongs to.  

The ∈ symbol means "is an element of".  

Now,  x = 2n where n ∈ N

and n < 6

Therefore, the required set builder notation is,

S = {x : x =  2n where n ∈ N and n < 6}

Thus, the set builder notation is  {x : x =  2n where n ∈ N and n < 6}

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Answer:

The Area of rectangle A is  576 feet²  .

Step-by-step explanation:

Given as :

The width of rectangle A = 16 feet

The Length of rectangle A = 8 feet + The length of rectangle B

The width of rectangle B = 14 feet

Let The length of rectangle B = L feet

So, The Length of rectangle A = 8 feet + L feet

The perimeter of rectangle A + The perimeter of rectangle B = 156 feet

So, 2 × ( Length A + width A ) +  2 × ( Length B + width B ) = 156 feet

Or,  2 × ( 8 + L + 16 ) +  2 × ( L + 14 ) = 156 feet

Or,  2 ×( 24 + L ) +  2 × ( L + 14 ) = 156 feet

Or, 48 + 2 L + 2 L + 28 = 156

Or, 76 L + 4 L = 156

So, 4 L = 156 - 76

Or, 4 L = 80

∴  L = [tex]\frac{80}{4}[/tex] = 20 feet

So , The Length of rectangle A = 8 feet + 28 feet = 36 feet

And The width of rectangle A = 16 feet

So, Area of rectangle A = Length of rectangle A × width of rectangle A

I.e  Area of rectangle A = 36 × 16 = 576 feet²

Hence The Area of rectangle A is  576 feet²  . Answer

425 g for the 15 ounce box of cereal?

Answer:

$215.94

Step-by-step explanation:

You do 20% × $179.95 to get $35.99

Since the 20% is being added to your bill, you add it to your base price

$179.95 + $35.99 = $215.94

Answer:

[tex]\large\boxed{W=\dfrac{A}{L}}[/tex]

Step-by-step explanation:

[tex]A=LW\qquad\text{divide both sides by}\ L\neq0\\\\\dfrac{A}{L}=\dfrac{LW}{L}\\\\\dfrac{A}{L}=W[/tex]

Answer:

x = 1

Step-by-step explanation:

-2x - 16 = -14 - 4x

-2x + 4x = -14 + 16

2x = 2

x = 1

Answer: 7 pizzas

Step-by-step explanation:

Answer:

60/8 = 7.5 = 7 pizzas (round down to the nearest integer)

Step-by-step explanation:

You can only buy a whole pizza, not slices of it.

Answer:s

Step-by-step explanation:

Answer:

$13.20

Step-by-step explanation:

so add the prices up 1.25+0.40 should be

$1.65 now multiply it by the 8 postcards he will send

so 1.65•8= $13.20

Answer:

A power of 10 is the number 10 multiplied by itself by the number of times indicated by the exponent.When the exponent is greater than o it is followed by zeros

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of the number with a power 10 is a multiplication of that number 10 times.

1024 can be a number with power 10

i.e [tex]2^{10}[/tex]

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A number with power 10.

This means,

The value of the number with a power 10 is a multiplication of that number 10 times.

i.e

[tex]2^{10}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

[tex]2^{10}[/tex] = 2³ x 2³ x 2³ x 2 = 8 x 8 x 8 x 2 = 1024

Similarly,

1024 can be a number with power 10

Thus,

The value of the number with a power 10 is a multiplication of that number 10 times.

1024 can be a number with power 10

i.e [tex]2^{10}[/tex]

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Answer:

I am going to assume you mean the relationship between x and y.

If the y-intercept is 0, that means the point is on the origin.

So x and y are equal to each other. they are both zero

Answer:

The proof is written below.

Step-by-step explanation:

Given:

[tex]DF \cong EF\\FG\ \textrm {bisects}\ \angle DFE[/tex]

Prove :

[tex]\triangle DFG \cong \triangle EFG[/tex]

Proof:

[tex]DF \cong EF \ \textrm{Given}\\FG\ \textrm{bisects}\ \angle DFE\ \textrm{Given}\\[/tex]

[tex]\angle 1 \cong \angle 2[/tex] Definition of angle bisector

[tex]\overline{FG} \cong \overline{FG}\ \textrm{Reflexive Property}\\\triangle DFG \cong \triangle EFG\ \textrm {SAS Congruence}[/tex]

Answer:

[tex]\displaystyle \boxed{3\frac{1}{4}}[/tex]

Step-by-step explanation:

7n - 8 = 3n + 5

- 7n - 5 - 7n - 5

____________

[tex]\displaystyle \frac{-13}{-4} = \frac{-4n}{-4} \\ \\ 3\frac{1}{4} = n[/tex]

I am joyous to assist you anytime.

Answer:

2.5 x 13.7 = 34.25

4.9 + 1.6 = 6.5

Step-by-step explanation:

Here we are multiplying 2 decimals we can just write it as

[tex]25 * 10^{-1} * 137 * 10^{-1}[/tex]

= [tex]25*137*10^{-2}[/tex]

= [tex]3425 *10^{-2}[/tex]

= 34.25

Here we are just performing simple addition

4.9 + 1.6

= [tex]49 *10^{-1} +16*10^{-1}[/tex]

= [tex](49+16)*10^{-1}[/tex]

=[tex]65 * 10^{-1}[/tex]

= 6.5

Answer:− 1 x (small)2  y + 39 x(small)  2 + 30 x

Step-by-step explanation:

5x + 3x + 7x = 180

15x = 180

x = 12

I = 5(12) = 60

M = 3(12) = 36

S = 7(12) = 84

Check: 60 + 36 + 84 = 180

Answer:

∠I=75° , ∠M=45° ,∠S=105°, ∠E=173.5°

Step-by-step explanation:

given ∠I=5X,∠M=3X,∠S=7X, ∠E=128.5+3X

IN TRIANGLE IMS

∠I+∠M+∠S=180°

5X+3X+7X=180°

12X=180°

X=15°

HENCE ∠I=5X=[tex]5\times15°[/tex]

            ∠I=75°

      ∠M=3X=[tex]3\times15°[/tex]

     ∠M=45°

∠S=7X=∠[tex]7\times15°[/tex]

∠s=105°

∠E=128.5+3X=128.5+45=173.5°

∠E=173.5°

Answer:

The equations that represent the situation are:

2y+x=5

5x-y=3

Answer:

2y+x=5

5x-y-3

Step-by-step explanation:

Two times of the larger number which is y is 2y added to the smaller number x is equal to 5 . Which is 2y+x=5

The difference of five times the smaller number and larger number is 5x-y

And the resulting answer is 3

ie..5x-y=3 , when the 3 crosses to the other side it becomes 5x-y-3=0

hence,the equation 5x-y-3

Answer:

The number of once is 9.1  

The number of hundreds is 8.9

Step-by-step explanation:

Given as :

The total of digits having ones and hundreds = 900

The sum of digits = 18

Let The number of ones digit = O

And The number of hundreds digit = H

So, According to question

H + O = 18             .........1

100 × H + 1 × O = 900          ........2

Solving the equation

( 100 × H - H ) + ( O - O ) = 900 - 18

Or, 99 H + 0 = 882

Or , 99 H = 882

∴   H = [tex]\frac{882}{99}[/tex]

I.e H = 8.9

Put the value of H in eq 1

So, O = 18 - H

I.e  O = 18 - 8.9

∴    O = 9.1

So, number of once = 9.1

number of hundreds = 8.9

Hence The number of once is 9.1  and The number of hundreds is 8.9

Answer

Final answer:

The number that fits the criteria of rounding to 900, having twice as many hundreds as ones, having all different digits, and the sum of its digits being 18, is 864.

Explanation:

The question involves finding a number that meets a set of criteria: it rounds to 900, has twice as many hundreds as ones, all its digits are different, and the sum of its digits equals 18. To solve the problem, we can break down the clues and use them to narrow down the possibilities.

Since the number rounds to 900, we know it must be in the range of 850 to 949. The clue that it has twice as many hundreds as ones implies that the number of hundreds is a digit that is double the digit in the ones place. And since all digits must be different, we are looking for a number that does not repeat any digit.

Given the criteria, let's assume the hundreds digit is '8' (since it's in the 800 series), and therefore the ones digit would be '4'. The only digit left to assign is the tens place, which cannot be the same as the other two and must ensure the sum of all three digits equals 18. The digit for the tens place should then be 18 - 8 - 4 = 6, making the number 864, which satisfies all conditions.

So, the number we are looking for is 864: it rounds to 900, has twice as many hundreds (8 hundreds) as ones (4 ones), all digits are different, and the sum of the digits (8+6+4) equals 18.

a) The total amount the Bells will pay for their house is $187,488. b) The interest paid, including the 3 points, is $97,488. c) The exact amount applied to the principal in the first payment is unknown without additional information.

a) To determine the total amount the Bells will pay for their house, we need to calculate the total amount paid over 20 years. The monthly mortgage payment is $781.20, so the annual payment would be $781.20 x 12 = $9374.40. Therefore, over 20 years, the Bells will pay $9374.40 x 20 = $187,488.

b) The interest paid over the 20-year mortgage period can be calculated by subtracting the total mortgage amount from the total amount paid. The total mortgage amount is $90,000, so the interest paid is $187,488 - $90,000 = $97,488, including the 3 points.

c) The first payment on the mortgage is typically applied mostly to the interest. However, to determine the exact amount applied to the principal, we need more information about the breakdown of the monthly mortgage payment between interest and principal.

Answer:

The time after which the rocket hit the ground is 5 seconds

Step-by-step explanation:

Given as :

The distance of the cover by rocket at the height h = - 16 t² + 160 t

Let the time after which rocket hit the ground = T seconds

Now, When the rocket hits the ground, then at that time, the velocity of the rocket becomes zero.

I.e velocity = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Or, v = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Now, v = [tex]\frac{\partial h}{\partial t}[/tex]

Or, v = [tex]\frac{\partial (-16t^{2}+160t)}{\partial t}[/tex]

or, v = - 32 t + 160

Now, ∵ velocity of rocket after reaching the ground becomes zero

So, v = - 32 t + 160 = 0

Or, 32 t = 160

Or, t = [tex]\frac{160}{32}[/tex]

∴ t = 5 sec

So, The time after which the rocket hit the ground = 5 sec

Hence The time after which the rocket hit the ground is 5 seconds answer

To find when the rocket will hit the ground using the quadratic equation h = -16t² + 160t, solve for t when h=0; the rocket will hit the ground after 10 seconds.

To determine when the rocket will hit the ground given the equation h = -16t² + 160t, we need to find the value of t at which the height h is zero. The equation represents a quadratic equation, where t is the time in seconds after the rocket was fired, and h is the height of the rocket at any time t.

To solve for the time when the rocket hits the ground, we set h to zero and solve for t:

We discard the t = 0 since it represents the initial time at launch. Thus, the rocket will hit the ground after 10 seconds.

During this entire period, while the rocket is ascending and descending, it is important to consider the horizontal motion if analyzing its trajectory in more detail, but for this problem, we are only concerned with the vertical motion.

Answer:

x=841/68

Step-by-step explanation:

-68(x-11)=1+(-94)

-68(x-11)=-93

-68x+748=-93

-68x=-93-748

-68x=-841

68x=841

x=841/68

Final answer:

To solve this problem, set up an equation by representing the unknown number as x. Distribute -68 to the terms inside the parentheses and solve for x by isolating it on one side of the equation.

Explanation:

To find the answer to this problem, we can set up an equation. Let's let the unknown number be represented by x. The difference between a number and 11 can be written as (x - 11). The problem states that -68 times this difference is equal to the number one plus -94, which can be written as -68(x - 11) = -94 + 1.

To solve this equation, we can distribute -68 to the terms inside the parentheses: -68x + 748 = -93. Then, we can subtract 748 from both sides to get -68x = -841. Finally, we divide both sides by -68 to find that x = 12.38.

Therefore, the solution to this problem is x = 12.38.

Answer:

t = 1/2

Step-by-step explanation:

4(t+1/4)=3

First, distribute:

4(t)+4(1/4)=3

4t+1=3

Then isolate the variable:

4t+1-1=3-1

4t=2

4t/4=2/4

t=2/4

t=1/2

The equation is solved first by distributing the 4, then by subtracting 1 from both sides to isolate the variable term, and finally by dividing both sides by 4 to solve for 't', which gives the solution t = 0.5.

To solve the equation 4(t+1/4) = 3, we start by distributing the 4 inside the parentheses, so we get 4t + 1 = 3.

Then, we subtract 1 from both sides of the equation to isolate the variable term, and this gives us 4t = 2.

Finally, to solve for 't', we divide both sides of the equation by 4, and we find that t = 0.5.

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Answer:

5n-28

Step-by-step explanation:

28-6n+7(2n-8)-3n

28-6n+14n-56-3n

28+8n-56-3n

28-56+8n-3n

-28+5n

5n-28

Answer:

f(3) = g(3)

Step-by-step explanation:

we know that

When solve a system of linear equations by graphing, the solution of the system is the intersection point both lines

The intersection point is common point for bot lines

In this problem

we have the system of equations

f(x)

g(x)

The intersection point is (3,6)

That means that the solution for the system is the point (3,6)

so

For x=3

The value of f(3)=6 and the value of g(3)=3

therefore

f(3)=g(3)

Verify the statements

Find the equation of the blue line f(x)

(0,-3) and (1,0)

the slope is

[tex]m=(0+3)/(1-0)=3[/tex]

The equation  in slope intercept form is equal to

[tex]f(x)=3x-3[/tex]

Find the equation of the red line g(x)

(-3,0) and (0,3)

the slope is

[tex]m=(3-0)/(0+3)=1[/tex]

The equation  in slope intercept form is equal to

[tex]g(x)=x+3[/tex]

case 1) f(6) = g(3)

The statement is false

Because

For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]

For x=3 ----> [tex]g(3)=3+3=6[/tex]

therefore

[tex]f(6) \neq g(3)[/tex]

case 2) f(3) = g(3)

The statement is true

Because

For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]

For x=3 ----> [tex]g(3)=3+3=6[/tex]

therefore

[tex]f(3)=g(3)[/tex]

case 3) f(3) = g(6)

The statement is false

Because

For x=3 -----> [tex]f(3)=3(3)-3=6[/tex]

For x=6 ----> [tex]g(6)=6+3=9[/tex]

therefore

[tex]f(3) \neq g(6)[/tex]

case 4) f(6) = g(6)

The statement is false

Because

For x=6 -----> [tex]f(6)=3(6)-3=15[/tex]

For x=6 ----> [tex]g(6)=6+3=9[/tex]

therefore

[tex]f(6) \neq g(6)[/tex]

Answer:

f(3)=g(3)

Step-by-step explanation:

Edge 2021

Answer:

17/4

Step-by-step explanation:

2 5/6=17/6

4/6=2/3

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

(17/6)/(2/3)=(17/6)(3/2)=51/12=17/4

Answer:

0.5 891 7,800

Step-by-step explanation:

is because least always go first

To order from least to greatest, convert all measurements to grams: 7,800 mg becomes 7.8 g, and 0.5 kg becomes 500 g. The order is 7.8 g, 500 g, and 891 g.

To order the weights 891 g, 7,800 mg, and 0.5 kg from least to greatest, we first convert them all to the same unit. Given that there are 1,000 mg in a gram (g) and 1,000 g in a kilogram (kg), we can convert as follows:

Now that we have all the weights in grams, we can easily compare them:

Ordering these from least to greatest, we get: 7.8 g < 500 g < 891 g.