a clay model of a new car is 7 in. long if the car is 21 ft long how could you find the scale used to make the model
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The unit rate per batch of cookies is 2.75 as Lennon uses 5 1/2 cups of flour for every 2 batches of cookies she bakes.

To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.

When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.

Based on the given conditions, formulate:

(5 1/2)/2

We have to find the common denominator and write the numerators above the common denominator.

(((5×2)/2)+(1/2))/2

Now, we have to calculate the product or quotient:

((10/2)+(1/2))/2

Now, write the numerators over common  denominator,

((10+1)/2)/2

Then, calculate the sum or difference:

(11/2)/2

=11/4

=2.75 (or) 2 3/4

Therefore, the unit rate per batch of cookies is 2.75.

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The expression for the height of the tree after t years will be

H = 2.6t + 6.7.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Height(H) of a tree that begins at 6.7 feet and increases by 2.6 feet per year.

Let t represent the number of years.

∴ H = 2.6t + 6.7 is the expression that represents the height of the tree after t years.

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The general solution of the given differential equation is

cos(x) y = [y ln|sec(x) + tan(x)| - C] x.

Therefore, we do not have any transient terms in the general solution

cos(x) dy dx (sin(x))y = 1.

Note: A transient solution is a solution of a differential equation that goes to zero as time goes to infinity.

The given differential equation is

cos(x) dy dx (sin(x))y = 1.

Here, the independent variable is x, and the dependent variable is y.To determine whether there are any transient terms in the general solution

cos(x) dy dx (sin(x))y = 1,

we need to find its general solution as follows:Integrating the given differential equation, we have:

∫(sin(x))y dy = ∫sec(x) dx

On integrating the above expression, we get:

(cos(x)/y) + C = ln|sec(x) + tan(x)|

Here, C is the constant of integration.

Now, we can express the general solution of the given differential equation as follows:

cos(x) y = [y ln|sec(x) + tan(x)| - C] x  

(multiplying both sides by x)

Therefore, the general solution of the given differential equation is

cos(x) y = [y ln|sec(x) + tan(x)| - C] x.

Therefore, we do not have any transient terms in the general solution

cos(x) dy dx (sin(x))y = 1.

Note: A transient solution is a solution of a differential equation that goes to zero as time goes to infinity.

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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Answer:

the daylilies cost: $5

The roses cost:$3

The tulips cost:$1

Step-by-step explanation:

Answer:

6 7/8 pints

Step-by-step explanation:

The amount of water in a barrel decreases 9 5/8 pints in 7 weeks. The water decreases the same amount each week. What is the change in the amount of water in pints in the barrel in 12 weeks?

From the question, we know that:

7 weeks = 9 5/8 pints

12 weeks = x

Cross Multiply

7x = 12 × 9 5/8

x = 12 × 9 5/8/7

x =( 12 × 77/8 ) ÷ 7

x = 12 × 77/8 × 1/7

x = 12 × 11/8

x = 16 1/2 pints

The change in the amount of water in pints in the barrel in 12 weeks is calculated as:

16 1/2 pints - 9 5/8 pints

Lowest common denominator = 8

7 + (4 - 5/8)

7 + (-1/8)

= 6 7/8 pints

Answer:

x+y=-1

2x+2y=8

the correct answer is B

Answer:

AC = 32.0274615...

Step-by-step explanation:

First, you have to find ∠C which is simply 180 - 75 - 44. (Since there are 180° in a triangle) That would result in 61°. Then you have to set up the law of sines which is:

sin(∠C)/AB = sin(∠B)/AC

Since we are finding AC, we have to isolate it on one side of the equation:

AC = [sin(∠B) * AB]/sin(∠C)

Then, let's substitute the values for ∠B, ∠C, and AB to get:

AC = [sin(75°) * 29]/sin(61°)

After using a calculator"

AC = 32.0274615...

Hope this helps :)

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

Step-by-step explanation:

y=3x^2+12x = 3x (x+4)

zeroes: x={0, -4}

y = x^2+20x+100 = (x+10)^2

zeroes: x = -10 (twice)  

or x={-10, -10}

Answer:

S

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

115.395 min

Step-by-step explanation:

First we find the volume of 6 cm of water. We use the formula:

\(\pi *radius^2 *height\)

\(\pi *35^2*6 = 23,079 cm^3\)

1 L/min = 1000 cm^3 / min

0.2 L/min = 200 cm^3 /min

\(\frac{23,079}{200} = 115.395 min\)

10 minutes ago — 9. The painter bought 8 cans of paint for $12.99 each. How much did he spend on paint?​ · 9. 25 students each paid $6.50 to go to the museum ...

The Perimeter of equilateral triangle with side length 6 mi is given by 18 meter.

Given the equation is, P = 3s

where P is the perimeter of equilateral triangle with side length of s.

Now given that the side length of triangle is 6 mi.

So, s = 6 mi

Thus, the perimeter of such triangle is, P = 3*6 = 18 mi.

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a. Standard deviation = 71.66 ; b.  SE =  13.08 ; c. CI = (503.08, 556.59) ; d. CI (503.08, 556.59) matches the result from part (c). e. The true mean number of walks per team in a season is between 503.08 and 556.59.

a. Number of teams included in the dataset = 30

Mean number of walks = 529.83

Standard deviation = 71.66

b. The standard error for the mean is given by SE = s/√n

Where s is the standard deviation and n is the sample size. SE = 71.66/√30SE = 13.08

This is the same value given under "SE Mean" in the computer output.

c. To compute a 95% confidence interval for the mean number of walks per team in a season, we use the formula:

CI = x ± tα/2 (s/√n)

where x is the sample mean, s is the standard deviation, n is the sample size, tα/2 is the t-value for the desired confidence level and degrees of freedom (df = n - 1).

For a 95% confidence interval, α = 0.05/2 = 0.025 and df = 29.t

0.025,29 = 2.045 (using a t-table)

CI = 529.83 ± 2.045 (71.66/√30)

CI = (503.08, 556.59)

d. The confidence interval given in the computer output is: 95% CI (503.08, 556.59)

This matches the result from part (c).

e. The 95% confidence interval tells us that we are 95% confident that the true mean number of walks per team in a season is between 503.08 and 556.59.

In other words, if we were to repeat the sampling process many times, 95% of the confidence intervals we obtain would contain the true population mean.

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The expression "3' - '2' + 'm' / 'n'" is invalid because it combines character literals and arithmetic operations. The expression "3' - '2' + 'm' / 'n'" is not valid in most programming languages.

It attempts to mix character literals ('3', '2', 'm', 'n') with arithmetic operations (-, +, /), which is not meaningful. In programming languages, characters are typically represented using character literals enclosed in single quotes.

While arithmetic operations are performed on numerical values. The expression should be revised to ensure that the operations are performed on numerical values rather than character literals.

For example, if 'n' and 'm' represent numerical values, the expression could be written as "3 - 2 + m / n" to perform arithmetic operations correctly.

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the answer is: 1,2,3

the inequality represents less than, meaning the value of z is less than 4

which leaves us with 3 numbers, 1, 2 and 3

Answer:

less

Step-by-step explanation:

We assume price of a shirt is $100.

Initially price is increased by 10%: 100+10=110

Then it is reduced by 10%: 110-11=99

Now price of a shirt is $99.

Answer is price of a shirt is less than it was at the start.

The exact value of tan 120° is -√3. This means that at the angle of 120 degrees, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle is equal to the negative square root of 3.

To find the exact value of tan 120° using a double-angle identity, we can utilize the tangent double-angle identity, which states:

tan(2θ) = (2tanθ) / (1 - tan^2θ)

In this case, we want to find the value of tan 120°, so we can rewrite it as tan(2 * 60°), since 2θ is equal to 2 * 60°.

Let's substitute θ = 60° into the double-angle identity:

tan(2 * 60°) = (2 * tan 60°) / (1 - tan^2 60°)

We know that the tangent of 60° is equal to the square root of 3 (√3). Therefore, we can substitute tan 60° with √3:

tan(2 * 60°) = (2 * √3) / (1 - (√3)^2)

Now, we simplify the expression further:

tan(2 * 60°) = (2√3) / (1 - 3)

                  = (2√3) / (-2)

                  = -√3

Therefore, the exact value of tan 120° is -√3.

In summary, using the tangent double-angle identity, we found that the exact value of tan 120° is -√3. This means that at the angle of 120 degrees, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle is equal to the negative square root of 3.

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the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h

Let's define the variables:

B = speed of the boat in still water.

S = speed of the stream.

When the boat travels downstream, the total speed of the boat will be equal to the sum of the speed of the stream and the speed of the boat in still water:

speed = B + S

When the boat goes downstream, the speed will be:

speed = B - S

Now, also remember the relation:

speed*time = distance.

The given information is:

In 8 hours the boat can:

go 12 km upstream and 40km downstream.

We now need to define another variable, T, as the time that the boat travels upstream.

Then we can write this as:

12km = (B - S)*T

If the boat travels T hours upstream, and travels for a total of 8 hours, then the amount of time that travels downstream is 8h - T, then we can write:

40km = (S + B)*(8h - T)

Similarly, when we have:

"it can go 16 km upstream and 32 km downstream in the same time."

we can define a new variable T', and write:

16km = (B - S)*T'

32km = (S + B)*(8h - T')

Then we have a system of 4 equations:

16km = (B - S)*T'

32km = (S + B)*(8h - T')

40km = (S + B)*(8h - T)

12km = (B - S)*T

And we need to solve this for S and B.

To do it, we need to isolate one of the variables in one of the equations.

Let's isolate T in the last equation:

T = 12km/(B - S)

now we can replace that in the third equation to get:

40km = (S + B)*(8h - 12km/(B - S))

So now we have 3 equations:

16km = (B - S)*T'

32km = (S + B)*(8h - T')

40km = (S + B)*(8h - 12km/(S - B))

Now we need to do the same thing, this time let's isolate T' in the first equation and replace it in the second one:

T' = 16km/(B - S)

Replacing it in the second equation we get:

32km = (S + B)*(8h - T')

32km = (S + B)*(8h - 16km/(B - S))

So now we have two equations:

40km = (S + B)*(8h - 12km/(B - S))

32km = (S + B)*(8h - 16km/(B - S))

Let's simplify these:

40km = 8h*(S + B) - 12km*(S + B)/(B - S)

32km = 8h*(S + B) - 16km*(S+ B)/(B - S)

Now we can multiply both equations by (B - S) to get:

40km*(S - B) = 8h*(S + B)*(B - S) - 12km*(S + B)

32km*(S - B) = 8h*(S + B)*(B - S) - 16km*(S+ B)

Let's keep simplifying this:

40km*(B - S) + 12km*(S + B) =  8h*(S + B)*(B - S)

32km*(B - S)  + 16km*(S+ B) = 8h*(S + B)*(B - S)

Now we get:

52km*B - 28km*S = 8h*(S^2 + B^2)

48km*B - 16km*S = 8h*(S^2 + B^2)

Notice that the right side of these equations is the same thing, then we can write:

52km*B - 28km*S = 48km*B - 16km*S

(52km - 48km)*B = (28km - 18km)*S

4km*B  =  10km*S

B = (10/4)*S

B = (5/2)*S

Now we can replace this in one of our two equations, let's use the first one:

48km*B - 16km*S = 8h*(S^2 + B^2)

48km*(5/2)*S - 16km*S = 8h*( S^2 + ( (5/2)*S)^2)

Now we can solve this for S

104km*S = 8h*( S^2 + 25/4*S^2)

104km*S = 8h*(29/4*S^2) = 48h*S^2

104km*S = 48h*S^2

dividing at both sides by S we get:

104km = 48h*S

104km/48h = S = 2.167 km/h

And using B = (5/2)*S

We can find the speed of the boat:

B = (5/2)*2.167 km/h = 5.418 km/h

Then:

the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h

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Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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Therefore , the solution of the given problem of surface area comes out to be  240 tiles will cover the floor.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

Let's first determine how many 6 inch squares are required to span the floor:

=> 80 square feet is the size of the floor (8 feet by 10 feet).

We require the following because each 6-inch square spans an area of => (1/2) ft x (1/2) ft = 1/4 square feet:

=>  80 square feet 1/4 square foot = 320 tiles in a row of 6 inch tiles.

Since a 12 inch square encompasses a space that is 1 foot by 1 foot, we require:

=>  80 square feet /  12 inch square tile,

which equals 80 tiles.

Using 12 inch squares rather than 6 inch squares allows us to save the following amount of tiles:

=> Number of 6 inch tiles - Number of 12 inch tiles = 320 - 80 = 240 tiles

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The absolute value is:

Work/explanation:

First, we will evaluate 2-7.

It evaluates to -5.

Now, let's find the absolute value of -5 by using these rules:

\(\sf{\mid a\mid=a}\)

\(\sf{\mid-a \mid=a}\)

Similarly, the absolute value of -5 is:

\(\sf{\mid-5\mid=5}\)