Family
es of
cost
6 Mrs. Baker uses 7.5 cups of sugar to make
14 dozen cookies. To the nearest hundredth,
what is the rate of cups of sugar per cookie?
© 22.4 cups
s?
@ 0.45 cup
Ⓡ 0.04 cup
☺ 0.54 cup



What is the answer

Answer:

Only Elijah's model is correct

Step-by-step explanation:

The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play

This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play

Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.

Elijah's model is correct .

Elijah and Jonathan play on the same soccer team. They have played 3 of their 15 games.  

x is the number of games that are left to be played.

Elijah and Jonathan have 12 games left on their soccer team.

Elijah  and Jonathan  both try to simulate the situation which are shown in figure.

Creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance.

On the other side Elijah placed 15 cubes.

The value of each cube = 1

so  15 [tex]\times 1 = 15[/tex] which are equal to total number of games.  

Since 3 games are already played so on the left hand side

3 boxes of magnitude 1 each are placed.

[tex]x[/tex] is the number of  games that are left.

Jonathan uses a table  with  three x values  in a row and a 15 is the total number of games to be played are represented in the second row trying to model the same situation.

This table doesn't show the number of games left to play.

Which are 12 in number

According to Jonathan's model

[tex]3x = 15 \\x =5[/tex]

This does not model the number of games left which are 12 in number and hence

Jonathan's model  does not explains the situation

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Answer:

(-3, 3).

Step-by-step explanation:

4x^2-36= 0

4x^2 = 36    Taking square roots of both sides:

2x = +/- 6

x = +/- 3.

Answer:

(-3, 3)

Step-by-step explanation:

The equation is:

[tex]4x^2-36=0[/tex]

to clear for x, first we move the -36 to the right as a +36 (or you can also say that we add 36 to both sides):

[tex]4x^2=36[/tex]

dividing by 4:

[tex]x^2=36/4\\x^2=9[/tex]

taking the square root:

[tex]x=[/tex] ± [tex]\sqrt{9}[/tex]

we add the ±  because a square root has two solutions, a positive one, and a negative one.

Then we get:

[tex]x=[/tex] ± 3

The solutions are -3 and +3

which is represented in the option (-3, 3)

Answer:

not 100% sure of this but I think its a4=192

Answer:

[tex]d=8.9\ units[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(-3, 2) and (5, -2)

substitute the values in the formula

[tex]d=\sqrt{(-2-2)^{2}+(5+3)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(8)^{2}}[/tex]

[tex]d=\sqrt{80}\ units[/tex]

[tex]d=8.94\ units[/tex]

Round to the nearest tenth

[tex]d=8.9\ units[/tex]

Answer: B & D

Step-by-step explanation:

The system is consistent.

The system is independent.

Answer:

Step-by-step explanation:

L= 6.47 units is the answer for APEX

Answer:

B. 6.4

Step-by-step explanation:

We need to recall the theory of  the chord distance to the center which tells that the two congruent chords are equidistant from the center of the circle.

In this situation, A is the center point, CR and  BE are congruent with the length of 5,27. So, the distance from A to CR must be equal to the distance from A to BE. Hence, the length of the blue segment in A below is 6.4

Hope it will find you well.

Answer: see the explanation

Step-by-step explanation:

Add the price of the item and the tax on the item, or just multiply the price of the item by the tax rate plus 1 (to include the price of the item)

Let's say the cost of an item is

100 dollars and the tax rate is 5% or 0.05. To get the amount of tax that has to be paid on

the $100 item, multiply 100 by 0.05 to get 5 .

Add the amount of the tax ( $5 ) to the price of the item ( $100) to get a total cost of $100.

Or you could multiply 100 by 1+0.05 or 1.05 to get the same answer. The reason why the

1 can be added in is because the total cost includes the price of the item, not just the sales tax on it.

The central angle created by an arc length of 6.9813 in a circle with a radius of 4 is approximately 100 degrees when rounded to the nearest whole number.

The student is asking about the relationship between the arc length of a circle, the radius of the circle, and the central angle created by this arc. To find the central angle from the arc length and the radius, we use the formula:

arc length (As) = radius (r) x central angle (θ)

Here, we're given the arc length as 6.9813 and the radius as 4. Since the central angle is usually given in radians, we first perform the calculation in radians and then convert it to degrees if necessary.

The central angle in radians is:

θ (in radians) = arc length / radius

θ = 6.9813 / 4 ≈ 1.7453 radians

To convert radians to degrees, we multiply by,

(180/π).

Thus,

θ (in degrees) ≈ 1.7453 x (180/π) ≈ 100 degrees

And when rounded to the nearest whole number:

θ ≈ 100 degrees

So, the central angle created by the arc is approximately 100 degrees.

Answer:

B

Step-by-step explanation:

When you dilate a shape you change the size, changing the composition of isometries.

Option B is not a composition of isometries.

The composition of isometries refers to combining multiple isometries (transformations that preserve distance) to create a new transformation. To determine which of the options is not a composition of isometries, we need to verify if each option preserves distance. If any option does not preserve distance, it is not a composition of isometries. Let's analyze each option:

A. Reflection over x=2 then rotation 90 degrees clockwise about the origin: Both reflection and rotation are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin: Dilation, when the scale factor is not 1, does not preserve distance. Therefore, this option is not a composition of isometries.

C. Translation (x,y)-> (x-2, y+1) then reflection over the y-axis: Both translation and reflection are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

D. Reflection over the x-axis then reflection over the y-axis: Both reflections are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

In summary, option B is the only one that is not a composition of isometries.

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Answer:

The annual interest rate was 4.5% in Angela's college fund.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment when Angela was 10= US$ 5,000

Duration of the investment = 8 years

Balance of the account when Angela turned 18 = US$ 6,800

2. Let's find the annual interest rate of this investment after 8 years or 20 quarters, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment when Angela turned 10 = US$ 5,000

FV = Balance of the account when Angela turned 18 = US$ 6,800

number of periods (n) = 8

Replacing with the real values, we have:

6,800 = 5,000 * (1 + r) ⁸

6,800/5,000 = (1 + r) ⁸ (Dividing by 5,000 at both sides)

34/25 = 1⁸ + r⁸

34/25 - 1 = r⁸ (1⁸ = 1)

34/25 - 25/25 =r⁸ (1 = 25/25)

9/25 =  r⁸

0.36 = r⁸ (9/25 = 0.36)

⁸√0.36 = ⁸√r⁸

0.045 = r

r = 4.5%

The annual interest rate was 4.5% in Angela's college fund.

Answer:

The answer is 4.5

Step-by-step explanation:.

To determine the interest rate, substitute the numbers for the values in the I equals Prt formula. I equals one thousand eight hundred, P equals five thousand and t equals eight because the money was in the bank for eight years.

Multiply five thousand by eight.

Divide both sides by forty thousand and evaluate.

Finally, convert the decimal zero point zero four five to four point five percent.

Answer:

D) (x^-3*y^-12)/(x^15*y^-15)

Step-by-step explanation:

If you simplify that further, then you'll get x^(-18)*y^3.

Answer:

x is more than or equal to 35

Answer:

1. The car is slowing down at a rate of 2.5mph/s

2. The greatest acceleration is 10 mph/s.

3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.

Step-by-step explanation:

1. The deceleration of the car is from 16 seconds to 24 seconds is the slope [tex]m[/tex] of the graph from 16 to 24:

[tex]m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s[/tex]

the negative sign indicates that it is deceleration.

2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.

From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope [tex]m[/tex]:

[tex]m= \dfrac{45-5}{28-24}= 10mph/s[/tex]

3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.

The speed of the automobile in that interval, as we see from the graph, is 25 mph.

Answer:

-3 is the other solution.

Step-by-step explanation:

As, [tex]\frac{-4}{5}[/tex] is One of the solutions of the equations , So, it should satisfy the equation.

Putting [tex]\frac{-4}{5}[/tex]  in equation 5[tex]x^{2}[/tex] + bx + 12 = 0 ,

We get,

               5×[tex]\frac{-4}{5}[/tex]×[tex]\frac{-4}{5}[/tex]   +    b×[tex]\frac{-4}{5}[/tex]   +  12 = 0.

 5×[tex]\frac{16}{25}[/tex]  +  [tex]\frac{-4b}{5}[/tex]   +  12 = 0.

 After solving ,    16 - 4b  + 60  = 0.

                             4b = 76

                                b = 19.

So, the equation is  5[tex]x^{2}[/tex]  +  19x  + 12 = 0.

      After factorizing , 5[tex]x^{2}[/tex]  + 15x + 4x + 12 = 0.

                                    5x(x+3) + 4(x+3) = 0

                                     (5x+4)(x+3) = 0

Clearly the roots of the equation are  -3 and [tex]\frac{-4}{5}[/tex] .

So, the other solution is -3.

Answer:

The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]

Step-by-step explanation:

Given as :

The net force = F Newton

The mass of the object = m kg

The acceleration = a  m/s²

Now, As The force is define as the product of mass and velocity

So, F = m × a

Now, Again , if the acceleration = 8 a

and The force decrease to [tex]\frac{F}{2}[/tex] = 0.5 F

So, Let The mass = M

∵ F = m × a

∴ mass = [tex]\frac{\textrm Force}{\textrm acceleration}[/tex]

Or. M = [tex]\frac{\textrm 0.5 F}{\textrm 8 a}[/tex]

or, M =0.0625 × [tex]\frac{F}{a}[/tex]

∴ M = 0.0625 × m = [tex]\frac{m}{16}[/tex]

so, The mass =  [tex]\frac{m}{16}[/tex]

Hence The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]  Answer

Final answer:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). If the force is decreased to F/2, the mass that would accelerate at a rate 8a can be found by rearranging the equation and solving for mass.

Explanation:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), expressed as F = ma.

If the force is decreased to F/2, the new force is now (F/2). To find the mass (m) that would accelerate at a rate 8a, we need to rearrange the equation as follows:

(F/2) = m * (8a)

To solve for the mass (m), we divide both sides of the equation by (8a), which gives us:

m = (F/2)/(8a)

Therefore, the mass that would accelerate at a rate 8a when the force is decreased to F/2 is (F/2)/(8a).

Answer:

Yeah I'm here harmony plz tell

Step-by-step explanation:

Answer:

It can be solve this in two ways,

1) as if the h(x) = 5x and 2) as if h(x) = 5 + x

1) If h(x) = 5x and k(x) = 1/x

Then (k o h) (x) = k ( h(x) ) = k(5x) = 1/(5x)

2) If h(x) = 5 + x and k (x) = 1/x

Then (k x h)(x) =k ( h(x) ) = k (5+x) =  1 / [5 + x]

1/(5+x) is the correct answer

Step-by-step explanation:

Final answer:

Set-builder notation is a method to define intervals through a property shared by all members. The notation for the given intervals includes conditions that represent the endpoints or infinity, expressing the range of the variable in each set.

Explanation:

Writing intervals in set-builder notation involves describing a set through a property that its members share. Here is the set-builder notation for each interval provided:

To express these sets, we use 'x' as our variable and conditions such as x < 6 that define the range of values 'x' can take. The 'U' symbol represents the union of two sets, indicating that the set includes all elements from both intervals.

Answer:

The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  

Step-by-step explanation:

Given as :

The total money earn by Katelynn in tow weeks = $ 1240

The money earn by Katelynn in first week = $ 480

Let The money earn by Katelynn in second week = $x

Now,

From equation

The total money earn by Katelynn in tow weeks = The money earn by Katelynn in first week  + The money earn by Katelynn in second week

Or,  $ 1240 =  $ 480 + $ x

Or, $ x =  $ 1240 - $ 480

So, x = $ 760

So, The money earn in second week is $ 760

∴ The algebraic equation to model the situation is $ x = $ 1240 - $ 480

Hence ,  The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  Answer

Answer:

7.92 Feet

Step-by-step explanation:

Since area is Length × Height in comparison to perimeter being Length + Length + Height + Height, the equation is simply:

3 × 2.64 = 7.92 Feet

Final answer:

The area of Richard's painting is calculated by multiplying the length of 3 feet by the width of 2.64 feet, which equals 7.92 square feet.

Explanation:

To calculate the area of Richard's rectangular painting, we use the formula for the area of a rectangle, which is the product of its length and width. In this case, the length of the canvas is 3 feet and the width is 2.64 feet. So, the calculation to find the area will be as follows:

Area = Length × Width

Area = 3 feet × 2.64 feet

Area = 7.92 square feet

Therefore, the area of Richard's painting is 7.92 square feet.

Answer:

34, 35, 36

Step-by-step explanation:

34 + 35 + 36 = 105

Answer:

34

35

36

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 105.

We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 105. Therefore, you can write the equation as follows:

X + X + 1 + X + 2 = 105

To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 105

3X + 3 = 105

3X + 3 - 3 = 105 - 3

3X = 102

3X/3 = 102/3

X = 34

Which means that the first number is 34, the second number is 34+1 and third number is 34+2. Therefore, three consecutive integers that add up to 105 are:

34

35

36

Answer:

Step-by-step explanation:

100%-54%=46%

46%*25.6m=11,776,000

25,600,000+11,776,000=

37,376,000 Answer

Svetlana can allow her hair to grow for 10 months.

Step-by-step explanation:

Current length of hair = 3cm

Growth per month = 1.5cm

Let, m be the number of months.

As she wants her hair no longer than 18cm, therefore, according to given statement;

1.5m + current length of her hair ≤ 18

[tex]1.5m+3\leq 18\\1.5m\leq 18-3\\1.5m\leq 15[/tex]

Dividing both sides by 1.5

[tex]\frac{1.5m}{1.5}\leq \frac{15}{1.5}\\m\leq 10[/tex]

Svetlana can allow her hair to grow for 10 months.

Keywords: linear inequality, division

Learn more about linear inequalities at:

#LearnwithBrainly

Answer: 4) 7c ^2d - 7c + 4d - 10

Explanation:

First write equastion as seen:

5c^2d - 4c + 3d - 3 + 2c^d - 3c+ d - 7

Next add the c^2d’s together:

7c^2d - 4c + 3d - 3 + 3c + d - 7

Add the c’s together:

7c^2d - 7c + 3d - 3 + d - 7

Add the d’s:

7c^2d - 7c + 4d - 3 - 7

Lastly add the normal numbers:

7c^2d - 7c + 4d - 10

Thus, that is your answer!

Hope this helps! :)

Answer:

Initial value for Mrs. White is $600 more than Mrs. Brown.

The rate of change is same for both.

Step-by-step explanation:

Cost of car purchased by Mrs. White = $3,000

Rate at which she pays for the car = $300 per month

Cost of car purchased by Mrs. Brown = $2,400

Rate at which she pays for the car = $300 per month

So,

Initial value for Mrs. White was =$3,000

Initial values for Mrs. Brown was =$2,400

difference in initial values  [tex]=3000-2400[/tex]  =$600

∴ Initial value for Mrs. White is $600 more than Mrs. Brown.

Rate of change of payment due for  Mrs. White = $300 per month

Rate of change for payment due for Mrs. Brown = $300 per month

∴ The rate of change is same for both.

Since Mrs White had a higher initial value than Mrs Brown and both having same rates of change, therefore Mrs. White will take a longer time to pay the due.

Answer:

TRUE.

a = -3 is a Solution to the equation 4a + 3 = -9  

Step-by-step explanation:

Given:

a = -3

4a + 3 = -9

Proof for Solution:

Let there be two part of the equation, left-hand side and right hand side.

If a  = -3 is a solution ,

left-hand side = right hand side

left-hand side = 4a +3

                       = 4×-3 + 3...............{ For a = -3}

                       = -12 + 3

                       = -9

                       = right hand side

∴ left-hand side = right hand side

∴ a = -3 is a Solution to the equation 4a + 3 = -9  

Answer:

The volume of sphere is 500 in³

Step-by-step explanation:

Given:

Diameter of sphere is 10 in.

Now, to find the volume we need radius.

Radius(r) = half of the diameter

[tex]r=\frac{10}{2}[/tex]

[tex]r=5[/tex]

And, now putting the formula to get the volume of sphere:

[tex]volume(v)=\frac{4}{3}\pi r^{3}[/tex]

Putting the value of π = 3.

[tex]v=\frac{4}{3} \times 3.14\times 5^{3}[/tex]

[tex]v=1.33\times 3.14\times 125[/tex]

[tex]v=522.025[/tex]

So, the volume is 522.025 in³.

By estimating the value the volume is 500 in³.

Therefore, the volume of sphere is 500 in³.

Answer:

B

Step-by-step explanation:

for those that didnt understand like me

Answer:

Face, beacuse it's pointing at the flat surface

Note that this is the equation of a line, since you can rewrite it as

[tex]3x-4y=6 \iff 4y=3x-6 \iff y=\dfrac{3}{4}x-\dfrac{3}{2}[/tex]

Now just choose two values for x and compute the correspondent y values:

[tex]x=0 \implies y=-\dfrac{3}{2}[/tex]

So, the line passes through the point (0, -3/2).

[tex]x=2 \implies y=\dfrac{3}{2}-\dfrac{3}{2}=0[/tex]

So, the line passes through the point (2, 0)

Now, draw on a coordinate plane the two points and connect them, and you'll have the line.

Answer:

1st and 2nd graph are decreasing functions

Step-by-step explanation:

Increasing function means, as we go from left to right, the function goes "ABOVE" and thus, increases.

Decreasing function means, as we go from left to right, the function goes "DOWN" and thus, decreases.

We will look at all the 4 graphs given. We look from "LEFT-TO-RIGHT".

The first one goes "DOWN", so its decreasing.

The second one also goes "DOWN, so this is decreasing as well.

The third one goes "UP", so it is increasing.

The fourth function stays the same, so it is neither increasing nor decreasing. It is constant.

Thus,

1st and 2nd graph are decreasing functions, only