Dots sells T-shirts ($2) and shorts ($3). In April, total sales were $576. People bought 3 times as many T-shirts as shorts.

How many T-shirts and shorts did Dots sell?

Final answer:

To find the dimensions and volume of a square-based box with the greatest volume under the given conditions, we need to maximize the volume. The dimensions of the box should be 54 inches by 54 inches by 54 inches, and the volume is 157,464 cubic inches.

Explanation:

The airline policy states that the sum of the length, width, and height of the baggage must not exceed 162 inches. To find the dimensions and volume of a square-based box with the greatest volume under these conditions, we need to maximize the volume of the box.

Let's assume the length, width, and height of the box are all equal to a. Therefore, the sum of the three dimensions is 3a.

According to the policy, 3a must not exceed 162 inches, so we have:

3a ≤ 162

a ≤ 54

Since the length, width, and height of a square-based box are all equal, a is the side length of the square base. Therefore, the dimensions of the box should be 54 inches by 54 inches by 54 inches, and the volume can be calculated as:

Volume = a³ = 54³ = 157,464 cubic inches.

the answer is log3x=2!

hope this helps :D. just took a test online and this was one of the questions. got it right btw.

Kaia will pay a $1,500 deductible and the remaining 20% not covered by insurance after the deductible, totaling to $1,680 for her braces.

To calculate how much Kaia will need to pay for her braces, we need to take into account her insurance deductible and the percentage her insurance will cover after that deductible is paid. Kaia's braces cost $2,400, so let's break it down step-by-step:

Kaia pays her insurance deductible, which is $1,500. So, $2,400 - $1,500 = $900 remains.

Her insurance then covers 80% of the remaining $900. To calculate this, we use 80% of $900: ($900 x 0.80) = $720.

Since the insurance pays $720 of the remaining cost, Kaia is left with 20% of $900 to pay out of her pocket. To calculate this, we take 20% of $900: ($900 x 0.20) = $180.

Therefore, Kaia will need to pay $1,500 (deductible) plus $180, for a total of $1,680.

The amount of Honey produced by 1000 hives is the multiplication of 1000 to 85 thus 85000 pounds will be produced.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

As per the given question,

Larson's Honey Farm usually produces 85 pounds of honey per year.

If one family is producing 85 pounds of honey per year then,

1000 hives will produce ⇒ 85 × 1000 = 85000 pounds.

Hence "The amount of Honey produced by 1000 hives is the multiplication of 1000 to 85 thus 85000 pounds will be produced".

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The expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i) which correct option(B).

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, b are real numbers and i is an imaginary number.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

(B) (9 + 4i) + (–1 – 7i)

⇒ (9 + 4i) + (–1 – 7i)

⇒ 9 + 4i –1 – 7i

Rearrange the terms like wise and apply arithmetic operations

⇒ 9 - 1 + 4i - 7i

⇒ 8 – 3i

Hence, the expression of (9 + 4i) + (–1 – 7i) has the sum (8 – 3i).

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Answer: the first part is option B

the second part is option C

Step-by-step explanation:

The solution of given system of equations is [tex]\boxed{(10,-1)}[/tex].

Further explanation

The system of equations is given  as follows:

[tex]\begin{aligned}x+3y&=7\\2x-4y&=24\end{aligned}[/tex]

The equations are the form of linear equation in two variables.

The general form of linear equation in two variables is [tex]ax+by+c=0[/tex] where [tex]a,b,c[/tex]are real numbers.

Here, the system of equations is as follows:

[tex]x+3y=7[/tex]      .....(1)

[tex]2x-4y=24[/tex]  ......(2)

Now, we can rewrite the equation (1) as follows:

[tex]x=7-3y[/tex]  

Substitute the value of [tex]x=7-3y[/tex] in equation (2) as follows:

[tex]2(7-3y)-4y=24[/tex]  

Solve the above expression to find the value of [tex]y[/tex].

[tex]\begin{aligned}14-6y-4y&=24\\14-10y&=24\\-10y&=24-14\\-10y&=10\\y&=-1\end{aligned}[/tex]  

Therefore, the value of [tex]y[/tex] is [tex]-1[/tex].

Now, Substitute the value of [tex]y=-1[/tex] in equation (1) to get the value of [tex]x[/tex].

[tex]\begin{aligned}x+(3\times(-1))&=7\\x-3&=7\\x&=7+3\\x&=10\end{aligned}[/tex]  

Therefore, the value of [tex]x[/tex] is [tex]10[/tex].

The solution of given system of equations is [tex](10,-1)[/tex].

Option (a)

In option (a) it is given that the solution is [tex](2,-6)[/tex].

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (a) is incorrect.

Option (b)

In option (b) it is given that the solution is [tex](10,-1)[/tex].

As per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (b) is correct.

Option (c)

In option (c) it is given that the solution is [tex](-2,8)[/tex].

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (c) is incorrect.

Option (d)

In option (d) it is given that there are infinte solution.

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex] which is a unique solution.

Therefore, option (d) is incorrect.

Learn more

1. Problem on the equation of the circle https://brainly.com/question/1952668

2. Problem on the center and radius of an equation https://brainly.com/question/9510228

3. Problem on the general form of the equation of the circle https://brainly.com/question/1506955

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations in two variables

Keywords: Linear equations in one variable, linear equations in two variables, function, sets, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open interval.

Answer:

The construction depicts the inscribing of a hexagon in a circle.

Step-by-step explanation:

These are the following steps to inscribe a hexagon in a circle.

1. We mark a point anywhere on the circle. This mark is the first vertex of the hexagon.

2. Now we will set the compass on this vertex and set the width to the center of the circle. This is the radius of the circle.

3. Now we will make an arc across the circle which is the next vertex of the hexagon.

4. Now moving the compass on to the next vertex and drawing another arc, which becomes the third vertex of the hexagon.

5. Repeat step 4 until all vertices are marked.

6. Lastly, we will draw a line between each successive pairs of vertices, for a total of six lines.

Now we can see a hexagon inscribed in a circle.

Answer:

Option C

output=0.5(input)+1.5

Step-by-step explanation:

Let

y------> the output

x------> the input

we have

[tex]A(-1,1), B(5,4)[/tex]

Find the slope

The formula to calculate the slope between two points is equal to

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

substitute the values

[tex]m=\frac{4-1}{5+1}[/tex]

[tex]m=\frac{3}{6}=0.5[/tex]

Find the equation of the line

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=0.5[/tex]

[tex]A(-1,1)[/tex]

substitute

[tex]y-1=0.5(x+1)[/tex]

[tex]y=0.5x+0.5+1[/tex]

[tex]y=0.5x+1.5[/tex]

remember that

y=output

x=input

substitute

output=0.5(imput)+1.5

Final answer:

To find the height of the Statue of Liberty, we set up an equation considering the total height of the pedestal and the height difference between the statue and the pedestal. Solving the system of linear equations, we determine that the height of the Statue of Liberty itself is 46.05 meters.

Explanation:

To find how tall the Statue of Liberty is, excluding its pedestal, we can set up an equation based on the information given. Let's denote the height of the Statue of Liberty as S, and the height of the pedestal as P.

We know that the total height of the Statue of Liberty and its pedestal is 92.99 meters, and we can express that as:

S + P = 92.99

Additionally, it is given that the pedestal is 0.89 meters taller than the Statue of Liberty, so we have:

P = S + 0.89

Using substitution, we can replace P in the first equation with S + 0.89:

S + (S + 0.89) = 92.99

This simplifies to:

2S + 0.89 = 92.99

To find the height of the Statue of Liberty (S), we subtract 0.89 from both sides of the equation:

2S = 92.99 - 0.89

2S = 92.10

And then we divide both sides by 2 to solve for S:

S = ​92.10 / 2

S = 46.05

So, the height of the Statue of Liberty itself is 46.05 meters.

The ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \), where \( r_A \) and \( r_B \)[/tex] are the radii of disks A and B, respectively.

Linear acceleration ( a ) of a point on the rim of a rotating disk is given by [tex]\( a = r \alpha \)[/tex], where ( r ) is the radius of the disk and [tex]\( \alpha \)[/tex] is the angular acceleration.

Since both disks are rotating with constant angular acceleration, the linear acceleration of a point on the rim of each disk is directly proportional to the radius of the disk.

Therefore, to find the ratio of the linear accelerations, we only need to compare the radii of the two disks.

Let [tex]\( r_A \) and \( r_B \)[/tex] be the radii of disks A and B, respectively.

The ratio of linear accelerations is given by [tex]\( \frac{a_A}{a_B} = \frac{r_A \alpha}{r_B \alpha} \)[/tex].

Notice that the angular accelerations cancel out since both disks have the same angular acceleration.

Thus, the ratio simplifies to [tex]\( \frac{r_A}{r_B} \)[/tex].

This ratio represents how many times larger the radius of disk A is compared to the radius of disk B.

For example, if [tex]\( r_A = 2r_B \)[/tex], then the linear acceleration of a point on the rim of disk A is twice that of disk B.

Therefore, the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \)[/tex].

Complete Question:

For the two disks in problem 3, what is the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B? Please show detailed calculation.

Answer:

23.06

Step-by-step explanation:

The 95% confidence interval for the mean number of hours Americans spend relaxing or engaging in enjoyable activities post-work is between 1.38 and 1.92 hours per day, which signifies the statistical range where the true mean likely falls. This statistic is crucial for understanding leisure's role in health and well-being.

The 95% confidence interval given in the General Social Survey of (1.38, 1.92) hours for the mean number of hours spent relaxing or pursuing activities after an average workday suggests that we can be 95% confident that the actual mean number of hours all Americans have for such activities falls within this range. This is an important statistic considering that leisure and recovery are essential for well-being, mental health, and stress prevention, as pointed out by researchers like Sonnentag & Zijlstra and Juliet Schor. Juliet Schor also highlighted that Americans have significantly declined in leisure time. The comparison of leisure time across different countries, such as Americans working more hours compared to Europeans, adds context to the importance of this interval in reflecting Americans' potential lack of leisure that could impact health.

The calculated coordinates of the point P is P (-3/2, -3/2)

From the question, we have the following parameters that can be used in our computation:

A = (1, 6)

Also, we have

B = (-2, -3)

And we have the partition to be

m : n = 5 : 1

The coordinate of the partition is calculated as

P = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

P = 1/(5 + 1) * (5 * -2 + 1 * 1, 5 * -3 + 1 * 6)

This gives

P = 1/6 * (-9, -9)

So, we have

P = (-3/2, -3/2)

Hence, the coordinate is P = (-3/2, -3/2)

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To find the coordinates of point P along the directed line segment AB, we can use the concept of section formula and plug in the given values to find the coordinates (-3/2, -3/2).

To find the coordinates of point P along the directed line segment AB, we can use the concept of section formula. The section formula states that if a point P divides a line segment AB in the ratio m:n, then the coordinates of P can be found using the formula:

P(x,y) = [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)]

Using this formula, we can plug in the values: m=5, n=1, x1=1, y1=6, x2=-2, y2=-3 to find the coordinates of point P.

P(x,y) = [(5*(-2) + 1*1)/(5+1), (5*(-3) + 1*6)/(5+1)] = [(-10+1)/6, (-15+6)/6] = [-9/6, -9/6] = (-3/2, -3/2)

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Answer:

7%(plzzzz brainlist thiss!!!)

Step-by-step explanation:

x = amount at 15%

90-x = amount of 55%

0.15x + 0.55(90-x) = 0.47(90)

0.15x +49.5 - 0.55x = 42.3

49.5 - 0.40x = 42.3

-0.40x = -7.2

x = -7.2 / -0.4 = 18 kg of 15% copper

90-18 = 72 kg of 55% copper