A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 80 pounds. The truck is transporting 60 large boxes and 65 small boxes. If the truck is carrying a total of 4975 pounds in boxes, how much does each type of box weigh? X Large box: pounds Small box: ( pounds 5 ?

The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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He borrowed $24,000.

Answer:

\(\sqrt{231}\) cm

Step-by-step explanation:

The Pythagorean theorem is a mathematical principle that relates to the three sides of a right triangle. The formula for this is:

\(a^2 + b^2 = c^2\)

In this case, the hypotenuse (c) is 16 cm, and one of the legs (a) is 5 cm. We can plug in the values and solve for the missing value.

\(5^2+b^2=16^2\)

\(25+b^2=256\)

\(b^2=256-25\)

\(b^2=231\)

\(b = \sqrt{231}\) cm

Answer:

x = a(y+17)^2 + 2 where a < 0

Step-by-step explanation:

Since the parabola is horizontal, the formula of the parabola is x = a(y-h)^2 + k where (h,k) is the vertex.

Since it opens to the left, a must be negative. The vertex is (-17, 2), so h = -17 and k = 2.

Substituting these in, we find that the equation is

x = a(y+17)^2 + 2 where a is a real number that is less than 0 (i.e. negative)

I hope this helps! :)

Matrix-vector multiplication is a linear operation because it satisfies the properties of scalar multiplication and vector addition, which are a(u+v) = au + av and a(cu) = cau, where a is a scalar and u and v are vectors.

Matrix-vector multiplication is a fundamental operation in linear algebra, where a matrix is multiplied by a vector to produce another vector. This operation is considered linear because it adheres to certain properties.

The first property is scalar multiplication, which states that multiplying a vector u by a scalar a and adding it to another vector v (a(u+v)) is equivalent to multiplying u by a (au) and v by a (av) separately and then adding the results (au + av). In other words, the operation distributes over vector addition.

The second property is the distributive property of scalar multiplication, which states that multiplying a vector u by a scalar c and then multiplying the resulting vector (cu) by another scalar a is equivalent to multiplying u by the product of the two scalars (cau). This property allows the scalar multiplication to be distributed over scalar multiplication.

These properties ensure that matrix-vector multiplication preserves the linearity of the underlying vector space. They enable the manipulation and analysis of systems of linear equations, transformations, and other mathematical operations involving matrices and vectors.

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Answer:

let p = cost of 1 plain wrapping paper

let h = cost of 1 shiny rolls wrapping paper

Write an equation for each statement,

" Eugene sold 3 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $168 "

3p + 11h = $168

Jill sold 10 rolls of plain wrapping paper and 11 rolls of shiny wrapping paper for a total of $252."

10p + 11h = $252

Use elimination here,

10p + 11h = $252

3p + 11h = $168

subtraction eliminates h, find p

7p = $84

p = 84/7

p = $12 for wrap of plain paper

Find h using the 1st original equation

3(12) + 11h = 168

36+ 11h = 168

11h = 168 - 36

11h = 132

h = 132/11

h = $12 for shiny wrapping paper

Therefore each plain wrapping paper costs $12 and each shiny wrapping paper costs same $12 !

Answer:

x = 51°

Step-by-step explanation:

The sum of all angles in a triangle is 180°.  (Angle Sum Property)

We already know 2 angles, the right angle and the 39°.

(x + 90 + 39)° = 180°

(x + 129)° = 180°

x = (180 - 129)°

x = 51°

Answer:

X=  70.5

Step-by-step explanation:

The area of a triangle is 180

180 - 39 = 141

141/2 = 70.5

70.5 + 70.5 + 39 = 180

Step-by-step explanation:

Start at the orgin.

The y intercept in the equation is -1 so I would shift 1 unit down to the orgin at (0,-1)

Then at the point, since the slope is -4. I would go down -4 units then go over 1 unit to the right.. So the next point would be (1,-5) then so on and so on.

You can check if your graph is correct by writing out specific points on the linear equation and making sure there slope is equal to -4.

a. The probability that facility B receives twice (or more) orders than facility A in T days is given by P(X ≥ 2λAT), where X follows a Poisson distribution with mean λBT. b. The probability that facility C receives twice (or more) returned products of A compared to B in T days is given by P(Y ≥ 2λAraT).

a) The probability that facility B receives twice (or more) orders than facility A in a fixed amount of time (T days) can be calculated using the Poisson distribution and the concept of order arrival rates.

The probability that facility B receives twice (or more) orders than facility A in T days is given by P(X ≥ 2λAT), where X follows a Poisson distribution with mean λBT.

To calculate this probability, we first need to determine the mean number of orders received by facility A in T days, which is λAT. Then, using the Poisson distribution, we can calculate the probability that facility B receives two or more orders in T days, considering its mean arrival rate λBT. By subtracting this probability from 1, we obtain the final result.

b) To calculate the probability that facility C receives twice (or more) returned products of A compared to B in T days, we need to consider the probability of product A and B being returned (ra and rb, respectively), and the concept of Poisson distribution for order processing.

The probability that facility C receives twice (or more) returned products of A compared to B in T days is given by P(Y ≥ 2λAraT), where Y follows a Poisson distribution with mean λBrbT.

First, we determine the mean number of returned products of A in T days, which is λAraT. Then, using the Poisson distribution with mean λBrbT, we can calculate the probability that facility C receives two or more returned products of A in T days. Subtracting this probability from 1 gives us the desired result.

By following these calculations, we can determine the probabilities related to the order reception and return processes in the given facilities.

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Answer:

  x° = arcsin(15.5/26.9×sin(73°))

Step-by-step explanation:

The law of sines tells you the sine of an angle is proportional to the length of the opposite side:

  sin(x°)/15.5 = sin(73°)/26.9

  sin(x°) = (15.5/26.9)sin(73°) . . . . . multiply by 15.5

Using the inverse function, we can find x.

  x° = arcsin((15.5/26.9)sin(73°))

The number of combinations is calculated using the formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players and k is the number of players to be selected for the lineup. In this case, n = 15 and k = 9. By substituting these values into the formula, there are 5005 ways to select 9 players for the starting lineup from a roster of 15 players.



Using the formula for combinations, C(n, k) = n! / (k!(n-k)!), we substitute n = 15 and k = 9 into the formula:

C(15, 9) = 15! / (9!(15-9)!) = 15! / (9!6!).

Here, the exclamation mark represents the factorial operation, which means multiplying a number by all positive integers less than itself. For example, 9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1.

Calculating the factorials and simplifying the expression, we have:

15! / (9!6!) = (15 * 14 * 13 * 12 * 11 * 10 * 9!) / (9! * 6!) = 15 * 14 * 13 * 12 * 11 * 10 / (6 * 5 * 4 * 3 * 2 * 1) = 5005.

Therefore, there are 5005 ways to select 9 players for the starting lineup from a roster of 15 players.

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The program calculates the percentage of doubles and displays the result in the Serial Monitor when power is applied to the Arduino.

To write a script that runs through a loop 10,000 times to estimate the probability of rolling doubles with two dice using Arduino, one can follow the below steps:

Define variables and initialize the random seed.

The variables required are `dice1`, `dice2`, `count`, `total`, and `percentage`.The `randomSeed()` function is used to initialize the random number generator.

In the `setup()` function, the function `Serial.begin()` is used to initiate the Serial Monitor with a baud rate of 9600.```
int dice1, dice2, count = 0, total = 0;
float percentage = 0.0;
void setup() {
 Serial.begin(9600);
 randomSeed(analogRead(0));
}

The `for` loop runs for 10,000 times and generates random numbers between 1 and 6, representing each dice.```
for (int i = 1; i <= 10000; i++) {
 dice1 = random(1, 7);
 dice2 = random(1, 7);

If both dice have the same number, increment the count by 1.```
 if (dice1 == dice2) {
   count++;

Add 1 to the total irrespective of whether it's a double or not.```total++;
}

After the loop, calculate the percentage of doubles and print the result to the Serial Monitor.

percentage = (count / float(total)) * 100;
Serial.print("Percentage of doubles: ");
Serial.print(percentage);
Serial.println("%");

The final program would look like this:```int dice1, dice2, count = 0, total = 0;
float percentage = 0.0;
void setup() {
 Serial.begin(9600);
 randomSeed(analogRead(0));
}
void loop() {
 for (int i = 1; i <= 10000; i++) {
   dice1 = random(1, 7);
   dice2 = random(1, 7);
   if (dice1 == dice2) {
     count++;
   }
   total++;
 }
 percentage = (count / float(total)) * 100;
 Serial.print("Percentage of doubles: ");
 Serial.print(percentage);
 Serial.println("%");
 while (true) {}
}

The `while (true)` loop at the end is used to keep the program running and displaying the result in the Serial Monitor.

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Answer:

y = 3x + 4

Step-by-step explanation:

Remember, you find slope values by finding two points on lines within the slope.

Slope= y2-y1/ x2-x1.

(x,y)

I found (0,4), 1, and (2,2), 2.

The answer is -8/2, simplified, -4/1.

Hope this helped.

By using unitary method, it can be calculated that Height of the tree is 30 feet

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

A shadow of 4.5 feet long is casted  by my friend 5 feet tall

A shadow of 1 feet is casted by an object of height \(\frac{5}{4.5} \ feet\)

A shadow of 27 feet is casted by a tree of height \(\frac{5}{4.5}\times 27 \ feet\)

A shadow of 27 feet is casted by a tree of height 30 feet

Height of the tree is 30 feet

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The output when three workers are hired is 5 units..

To find the output when three workers are hired, we need to first determine the total cost and then use the marginal cost to calculate the output.

Find the total cost when three workers are hired.
Average total cost (ATC) = Total cost (TC) / Output (Q)
$50 = TC / Q
Since fixed cost (FC) is $130 and the marginal cost (MC) is $40 per worker, the total cost can be found by adding the fixed cost and the cost of the three workers.
TC = FC + 3(MC)
TC = $130 + 3($40)

Calculate the total cost.
TC = $130 + $120
TC = $250

Use the total cost and average total cost to find the output.
$50 = $250 / Q
Q = $250 / $50
Q = 5

Therefore, the output when three workers are hired is 5 units.

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The 90% confidence interval for the proportion of young adults who think the U.S. is ready for a woman president is (55.5%, 64.5%).

Given that 60% of the 258 young adults said the U.S. is ready for a woman president.

we have p = 0.60.

Since we want a 90% confidence interval, the z-score is 1.645 (corresponding to a 90% confidence level).

CI = 0.60 ± 1.645 × √(0.60 (1 - 0.60)) / 258)

Calculating the expression inside the square root:

√(0.60(1 - 0.60)) / 258) ≈ 0.025

Now, substituting the values:

CI = 0.60 ± 1.645× 0.025

Calculating the values inside the interval:

CI = (0.60 - 1.645 × 0.025, 0.60 + 1.645× 0.025)

= (0.555, 0.645)

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Answer:

19 cups of water.

Step-by-step explanation:

1:2 ratio

1=9.5

2=9.5*2= 19

Answer:

19 cups of water.

Answer:

c=5

Step-by-step explanation:

4c-12=8

4c=20

c=5

Answer:

10

Step-by-step explanation:

Answer:  The length of one side is 9m.

Step-by-step explanation:

If area is 81 square meters, that means A = 81 m^2.

Since A = s^2, we can substitute s^2 for A.  Then

(s^2) = 81 m^2

Take the square root of both sides to solve for s:

(s^2)^(1/2) = (81 m^2)^(1/2)

s = 9 m

The given sequence alternates between the number 2 and a series of odd numbers, increasing by 4 each time. The task is to calculate the sum of the first 100 terms of this sequence.

To find the sum of the first 100 terms of the sequence, we can observe that the sequence consists of two different types of numbers: the number 2 and a series of odd numbers. The odd numbers in the sequence can be expressed as a pattern: starting from 5, each subsequent odd number is obtained by adding 4 to the previous odd number. To calculate the sum of the first 100 terms, we can divide the terms into two groups: the terms with the number 2 and the terms with odd numbers. The terms with the number 2 occur every other term, so there will be 50 terms with the number 2. The terms with odd numbers follow the pattern of increasing by 4, starting from 5. We can use the arithmetic series formula to find the sum of these terms.

The sum of an arithmetic series can be calculated using the formula: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term. In this case, n = 50 (since there are 50 odd numbers), a = 5 (the first odd number), and l = 5 + 4(n - 1) (the last odd number). Plugging these values into the formula, we can find the sum of the terms with the odd numbers. Finally, we can calculate the sum of the first 100 terms by adding the sum of the terms with the number 2 (which is 2 multiplied by the number of terms, 50) to the sum of the terms with the odd numbers. This will give us the desired result.

In conclusion, the sum of the first 100 terms of the given sequence can be obtained by finding the sum of the terms with the number 2 (50 × 2) and the sum of the terms with the odd numbers (using the arithmetic series formula). This approach allows us to calculate the sum accurately by considering the alternating nature of the sequence and utilizing the concept of arithmetic series.

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Answer:

175

Step-by-step explanation:

use the calculator

Answer:

3/4 or 3 quarters or 3 4ths

Can I get brainliest?

~Hope this helps!! Stay safe!~

Answer: I got 3/4? I hope it's correct T v T

Step-by-step explanation:

Let's factorise it :

\(\: {\qquad \dashrightarrow \sf ( {x}^{3} - 5)(x + 3) }\)

\(\: {\qquad \dashrightarrow \sf {x}^{3} (x + 3) + [-5(x + 3)] }\)

Using Distributive property we get :

\(\: {\qquad \dashrightarrow \sf {x}^{3} + {3x}^{3} + ( - 5x - 15) }\)

\(\: {\qquad \dashrightarrow \sf {x}^{3} + {3x}^{3} - 5x - 15 }\)

\(\: {\qquad \dashrightarrow \sf 4{x}^{3} - 5x - 15 }\)

⠀

Therefore,

\(\: {\qquad \dashrightarrow \sf ( {x}^{3} - 5)(x + 3) =4{x}^{3} - 5x - 15}\)

Answer:

I think that Nick is correct because you are going to have to make your answer positive and when you do the two fractions -4/9 + -6/9 are going to be   6/9 + 4/9 and there is already a addition sign in the last problem we are just going to keep it there. And when we add we get 10/9 or 1 1/9

If i get it wrong please don't hate im just in 7 grade ok :(

Answer:

Solution given:

Gobriella is correct.

Nick change - to + in second line.

Answer:

100cm^2

Step-by-step explanation:

5×2=10 which is one side

base×height=area

10×10=100

Answer:

its losing 60 gallons an hour

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation

the two interior angles add up to the exterior.

Answer:

10 is the hypotenuse

Step-by-step explanation:

a² + b² = c²

Given:

a = 8

b = 6

Work:

a² + b² = c²

8² + 6² = c²

64 + 36 = c²

100 = c²

\(\sqrt{c^2} =\sqrt{100}\)

c = 10

Step-by-step explanation:

hope it is helpful to you