Look at the expression and fill in the correct number in each blank.
The given expression has
term(s) with
1,500(1+1)*
factors.

Answer:

x=8 is true for the this condition

Step-by-step explanation:

4x<34

if x=8

4*8<34

32<34

which is true

if x=10

40 is not greater than 34, so it not satisfied the condition

A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high, the work done in pulling the rope to the top of the building is 1785 ft-lb.

To calculate the work done in pulling the rope to the top of the building, we need to use the formula:

W = F x d

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

In this problem, we can calculate the force required to pull the rope as the product of its weight per unit length (0.7 lb/ft) and the length of the rope (30 ft). Thus, the force required is:

F = 0.7 lb/ft x 30 ft = 21 lb

To calculate the distance over which the force is applied, we need to calculate the total length of the rope that needs to be lifted. This can be found using the Pythagorean theorem, as follows:

l = √(30^2 + 80^2) = 85 ft

So the distance over which the force is applied is 85 ft.

Now we can substitute the values for F and d into the formula for work to get:

W = F x d = 21 lb x 85 ft = 1785 ft-lb

This calculation shows how the formula for work can be used to calculate the energy required to lift an object against gravity over a given distance.

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Answer:

69 meters

Step-by-step explanation:

Answer:

1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:

r = 12 / 2 = 6 inches

The area of the pizza is then:

A = πr^2 = π * 6^2 = 36π square inches

2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:

increase = 6 * 0.25 = 1.5 inches

The new radius will then be:

new_r = 6 + 1.5 = 7.5 inches.

Step-by-step explanation:

Answer:

113.1, 8

The equation to find the area of a circle is:

Now we can input 12 into the equation:

To find the radius of a pizza that is %25 larger, we can use this equation:

Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.

Fitting the radius into the equation:

Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.

Answer:

Step-by-step explanation:

Advantages of Fifth Generatin of Computer:These computers are much faster than other generation computers. Development of true artificial intelligence.

Development of Natural language processing.

Advancement in Parallel Processing. Advancement in Superconductor technology. More user-friendly interfaces with multimedia features. Availability of very powerful and compact computers at cheaper rates.

Disadvantages of Fifth Generatin of Computer: They tend to be sophisticated and complex tools. ...

Example of Third Generation of Computer: Desktop.

The transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

The given functions are f(x)=x³ and g(x)= -(x-4)³+1.

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: Right 4 Units

Vertical Shift: Up 1 Units

Reflection about the x-axis: None

Reflection about the y-axis: Reflected

Vertical Compression or Stretch: None

Therefore, the transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.

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The dimensions will be as follows;

width is 5cm while the length is 20cm.

Let width = w

Let length = 4w (according to question)

Perimeter = 50cm

Perimeter formula for a rectangle = 2 (l +w)

Substituting in the variables (width and length)

2(w + 4w) = 50

2(5w) = 50

10w = 50

w = 5

Remember that length = 4w

length = 4w

length = 4(5)

length = 20cm

Therefore, the dimensions of the rectangle are 5cm by 20 cm.

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Answer:

Step-by-step explanation:

The required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.here,Let the cost of gas per gallon be x,Now according to the question,Cost of 8.4 gallons of fuel = 8.4xfrom the question,8.4x = 23.94Thus, the required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.

If the sales tax rate is 6% and if Sally buy rowboat priced at $842, the amount of tax she will pay,  $50.52

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To calculate the sales tax on the purchase of a sailboat priced at $842 with a sales tax rate of 6%, you can follow these steps:

1. Convert the sales tax rate from a percentage to a decimal by dividing by:

= 100: 6% ÷ 100

= 0.06.

2. Multiply the price of the sailboat by the sales tax rate to find the amount of tax:

= $842 × 0.06

= $50.52.

Therefore, Sally will pay $50.52 in sales tax for the purchase of the sailboat.

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Answer:

Step-by-step explanation:

is this in deltamath or bigideas? lol

(31.19-1.67)/24=x

"/" means divide.

Answer:

x=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

The addition of two numbers is 410+210 is 620.

From the given numbers,

First number is 410

Second number is 210.

One of the arithmetic operations is addition. The total of the numbers is provided. In other words, addition refers to the operation of adding the numbers together. "+" is the symbol used to denote addition. The outcome of the adding procedure is referred to as the sum. Addends are the numbers that are added together.

The following are the rules of addition operation:

Now,

⇒410+210=620

Therefore, the value is 620.

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The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.

Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.

Diameter (D)=10.

So the radius will be D/2.

Radius (R)=10/2=5.

The pie's circumference is given by:

C=2πR

C=2π*5

C= 10π (in)

Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,

Length of Arc (L)= 10π/6

L = 5π/3

L= 5(3.14)/3

L=5.234=5.24

Therefore the approximate arc length of one slice of pie is 5.24 inches.

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The measure of the other angle of the parallelogram is 22 degrees.

Opposite angles of a parallelogram are equal (or congruent).

Let the missing angle be represented by x.

Since the opposite angles of a parallelogram are equal (or congruent).

x = 2x - 22

Solve for x

2x - 22 = x

2x = 22 + x

2x - x = 22

x = 22°

Therefore, 22 degrees is the measure of the other angle.

Option C) 22° is the correct answer.

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Answer:

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Step-by-step explanation:

A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),

From the above data we can get,

k(x) = (x - 1)(x - 3)(x - 2i)

After expanding the equation ,

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Answer: 0.95m or 3/π

Step-by-step explanation:

Volume of cylinder = 2π[tex]r^{2}[/tex]*h

54 = 2π*9*h

divide 2π*9 on both sides

54/2π*9 = h

54/18π = h

3/π = h

h = 0.95 m

Answer:

Let's assume that the cost of each box of cookies is "x" dollars.

Based on the given information, Gail sold a total of 3 + 4 + 1 = 8 boxes of cookies this week, and Mr. Millbrook gave a $7 donation. Therefore, the total amount of money collected this week is:

8x + 7

Since we know that Gail sold 10 boxes of cookies last week and collected the same amount of money, we can set up an equation:

10x = 8x + 7

Solving for x, we get:

2x = 7

x = 3.50

Therefore, each box of Girl Scout cookies costs $3.50.

Step-by-step explanation:

To prove that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, we will use mathematical induction.

Base case: For k = 1, removing the root of a 1st order binomial tree results in zero smaller binomial trees, which is true.

Inductive hypothesis: Assume that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, for some positive integer k.

Inductive step: We want to prove that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders.

By definition, a (k+1)-th order binomial tree, denoted by B(k+1), is formed by joining two k-th order binomial trees, denoted by Bk, with one of them as the leftmost child of the root of the other. Let us remove the root of B(k+1) to obtain a new binomial tree, denoted by B'.

Since B(k+1) is formed by joining two k-th order binomial trees, we can apply the inductive hypothesis to each of them to obtain that removing their roots results in k smaller binomial trees each. Let these smaller binomial trees be denoted by B1, B2, ..., Bk and C1, C2, ..., Ck,

respectively.

Now, consider B' and observe that it is a k-th order binomial tree, since it has k children, each of which is a smaller binomial tree. Moreover, B' is obtained from B(k+1) by removing the root, which is the parent of the two k-th order binomial trees Bk and Ck. Thus, we have decomposed B' into k smaller binomial trees, namely B1, B2, ..., Bk and C1, C2, ..., Ck.

Therefore, we have shown that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders, which completes the induction.

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Answer:

1.25 laps per minute

Step-by-step explanation:

5 laps in 4 minutes so distance over time is equal to rate so

5/4=1.25

The required weight of a hippo in pounds is given as 3,000 pounds.

What is a unit of measurement?

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,
One ton is equal to 2,000 pounds, so a hippo that weighs 1.5 tons would weigh,

1.5 tons × 2,000 pounds/ton = 3,000 pounds

Therefore, the hippo at the zoo weighs 3,000 pounds.

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The length of B'C' after the translation of the original object is; B'C' = 3 units

Translation in transformation is simply defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

Now, from the attached image, we see that;

AB = 7 units

BC = 3 units

CD = 4 units

DA = 5 units

Now, by virtue of the definition of translation, it means that the translated object will retain the same dimensions. Thus;

B'C' = 3 units

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Answer:

1) 16pi square cm

2) 112pi cubed cm

3) 351.68 cubed cm

Step-by-step explanation:

Question 1: The base of a cylinder is a circle. To find the area of a circle, we can use the formula A = pi(r^2). the radius is 4 centimeters. 4^2 = 16.

The answer to the question is 16pi square cm

Question 2: This question is asking for the volume of the cylinder. To find the volume of the cylinder, we must multiply the area of the base by its height. we know the area of the base is 16pi. 16pi x 7(the height) = 112 pi.

The answer to the question is 112 pi cubed cm

Question 3: If pi were to be 3.14, we just need to substitute pi in the equation for question two with 3.14:

16(3.14) x 7 = 351.68

The answer is 351.68 cubed cm

Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.

Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.

One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.

The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.

Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.

In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.

Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.

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The cost of each order of french Fries is $1.75.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Wendell purchased a hot dog and 3 orders of French fries for $6.00.

If the hot dog cost $2.25.

Then the cost of Hot dog

= 6 - 2.25

= 3.75

and, the cost of each order of French Fries

= 3.75 / 3

= $1.25

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The required probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The total number of ways to choose any 2 students from a group of 12 is given by the combination formula:

C(12,2) = 12! / (2! * 10!) = 66

This means there are 66 total ways for Mr. Mackinson to choose any 2 students from the class.

To calculate the probability of choosing 2 girls, we need to count the number of ways to choose 2 girls from the group of 6 girls. We can use the combination formula again:

C(6,2) = 6! / (2! * 4!) = 15

This means there are 15 ways for Mr. Mackinson to choose any 2 girls from the class.

So the probability of Mr. Mackinson choosing 2 girls is:

P(2 girls) = number of ways to choose 2 girls / total number of ways to choose 2 students

= C(6,2) / C(12,2)

= 15 / 66

= 0.2273

Therefore, the probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

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Answer: 825 workers altogether

Step-by-step explanation:

well, if the ratio is 4.5 men to every woman, we just have to multiply 150 by 4.5, which means there will be 675 male workers and 150 female workers.

The function g(x) can be written as -

g(x) = f(x - 1)

Graph translation is a process of moving the graph over the dimensional plane either vertically, horizontally or both.

A translation can take place either horizontally or vertically as -

Given are the graphs of exponential functions f(x) and g(x).

We can write the exponential function g(x) as -

g(x) = f(x - 1)

Therefore, the exponential function g(x) can be written as -

g(x) = f(x - 1).

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Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.

In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.

Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:

x + y = 120

The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:

4.17(120) = 501.6

We can also find the cost of the high-quality and cheaper beans in terms of x and y:

5.25x is the cost of the high-quality beans

2.00y is the cost of the cheaper beans

The total cost of the two types of beans is the sum of their individual costs:

5.25x + 2.00y

Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:

5.25x + 2.00y = 501.6

Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:

x = 120 - y (from the first equation)

5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)

Simplifying and solving for y, we get:

630 - 5.25y + 2.00y = 501.6

3.25y = 128.4

y ≈ 39.5

Now we can use this value of y to find x:

x = 120 - y

x = 120 - 39.5

x ≈ 80.5

Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.

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