A warehouse worker uses a forklift to move boxes that weigh either 45 pounds or 70 pounds each. Let x be the number of 45-pound boxes and y be the number of 70-pound boxes. The forklift can carry up to either 60 boxes or a weight of 3000 pounds.

The total number of boxes that a forklift can carry is???


The total weight that the forklift can carry is ______ 3000 pounds.
Greater than, Less than, or Equal to

Write an inequality that models the number of boxes the forklift can carry. The inequality should contain x, y, and an inequality sign.


Write an inequality that models the amount of weight the forklift can carry. The inequality should contain x, y, and an inequality sign.

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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Answer:

B

Step-by-step explanation:

This is correct because it is the only one in proper set notation.

Hope it helps!

Answer:

2880 cubic meters.

Step-by-step explanation:

To find the area of a rectangular prism, multiply the length width and height.
20*12*12=144*20=2880

The volume of the Rectangular Prism is 2880 cubic meters.

Rectangular prism can be defined as a" 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid".

According to the question,

Length of the rectangular prism = 20 meters

Height of the rectangular prism = 12 meters

Width of the rectangular prism = 12 meters

Formula for Rectangular Prism = length × breadth × height

= 20 × 12 × 12

= 2880 cubic meters.

Hence, the volume of the Rectangular Prism is 2880 cubic meters.

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)

To evaluate the limit of the function as x approaches 0, where f(x) = sin(x)/x, we can use L'Hôpital's rule.

According to L'Hôpital's rule, if we have an indeterminate form of the type 0/0 or ∞/∞, we can take the derivative of the numerator and denominator until we reach a determinate form.

Let's differentiate the numerator and denominator:

\(\begin{align}f(x) &= \frac{\sin(x)}{x} \\f'(x)&=\frac{d}{dx}(\sin(x)) \\ &= \cos(x)\end{align}\)

\(\begin{align}f(x) &= \frac{\sin(x)}{x} \\f'(x)&=\frac{d}{dx}(x) \\ &= 1\end{align}\)

Now we can evaluate the limit as x approaches 0 using the derivatives:

\(\begin{align}\lim_{x \to 0} f(x) &= \lim_{x \to 0} \frac{\sin(x)}{x} \\ &= \lim_{x \to 0} \frac{\cos(x)}{1} \quad \text{(using L'Hôpital's rule)} \\ &= \cos(0) \\ &= 1 \end{align}\)

Therefore, the limit of f(x) as x approaches 0 is 1.

Answer:

x= -3/2, 1/2

Step-by-step explanation:

actor out the common term 2x+3.

(2x+3)(2x+3-4)=0

2 Solve for x

x= -3/2, 1/2

​  

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

Answer:

The answer is most likely -1 31/33

I have a hard time with fractions so I usually just go into my calculator and change it to a decimal. For example with -5 1/3 I would insert 1/3 into my calculator to change it to a decimal and then simply tack on the -5 to it. So in decimal form 1/3 is 0.333... so with the -5 added on its -5.333... Do the same for the other number and then divide. You will get -1.9393... all you have to do is go into your calculator and try out 11/12 or 31/33 to see which equals 0.9393... because those are the only options with a -1. In this case 31/33 equals 0.9393 s -1 31/33 is the answer

The solution of the system of equation are;

⇒ x = - 2

⇒ y = 0

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ 5x - 4y = - 10

⇒ - 4x + 5y = 8

Now,

Find the solution as;

The system of equation are,

⇒ 5x - 4y = - 10  ..(i)

⇒ - 4x + 5y = 8   ..(ii)

Multiply by 4 in equation (i) + Multiply by 5 in equation (ii);

⇒ 20x - 16y + (- 20x + 25y) = - 40 + 40

⇒ 9y = 0

⇒ y = 0

And,  - 4x + 5y = 8

⇒ - 4x + 0 = 8

⇒ x = - 2

Thus, The solution of the system of equation are;

⇒ x = - 2

⇒ y = 0

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Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

The supportive statement regarding the trapezoid based on the information is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

The non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The missing statement to support all other statements would be that m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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Answer:

\(P(\bar X>3.4) = 0.385\)

Step-by-step explanation:

Relevant Data provided according to the question is as follows

\(\mu\) = 3.2

\(\sigma\) = 0.8

n = 4

According to the given scenario the calculation of probability that the sample means will be more than 3.4 pounds is shown below:-

\(z = \frac{\bar X - \mu}{\frac{a}{\sqrt{n} } }\)

\(P(\bar X>3.4) = 1 - P(\bar X\leq 3.4)\)

\(= 1 - P \frac{\bar X - \sigma}{\frac{a}{\sqrt{n} } } \leq \frac{3.4 - \sigma}{\frac{a}\sqrt{n} }\)

Now, we will solve the formula to reach the probability that is

\(= 1 - P \frac{\bar X - 3.2}{\frac{0.8}{\sqrt{4} } } \leq \frac{3.4 - 3.2}{\frac{0.8}\sqrt{4} }\)

\(= 1 - P (Z \leq \frac{0.2}{0.4})\)

\(= 1 - P (Z \leq 0.5})\)

\(= 1 - \phi (0.5)\)

= 1 - 0.6915

= 0.385

Therefore the correct answer is

\(P(\bar X>3.4) = 0.385\)

So, for computing the probability we simply applied the above formula.

Answer:

its  21

Step-by-step explanation:

its not 21 i really dont know

Answer:

158 cm²

Step-by-step explanation:

Surface Area

Answer:

158 cm²

Step-by-step explanation:

Given dimensions of the right rectangular prism:

Surface area = 2(wl + hl + hw)

                      = 2(3 × 8 + 5 × 8 + 5 × 3)

                      = 2(24 + 40 + 15)

                      = 2(79)

                      = 158 cm²

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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Slope of y = -⅓x + 3 is -⅓ (on comparing with m of y = mx + c)

As the required line is perpendicular to this, slope of the required line = - 1 / (-⅓) = 3

Equation:

=> y - y1 = m(x - x1)

=> y - 0 = (3)(x - (-2))

=> y = 3(x + 2)

=> 3x - y + 6 = 0

1. The rule states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord (i.e., (a1 x a2) = (b1 x b2), where a1 and a2 are segments of chord A, and b1 and b2 are segments of chord B).

2. The rule states that the product of the length of the external segment of one secant and the length of the entire secant equals the product of the length of the external segment of the other secant and the length of the entire secant (i.e., (e1 (e1 + i1)) = (e2 (e2 + i2)), where e1 and e2 are the external segments and i1 and i2 are the internal segments).

3.  The rule states that the square of the length of the tangent segment equals the product of the length of the external segment of the secant and the length of the entire secant (i.e., t^2 = e * (e + i), where t is the length of the tangent segment, e is the external segment, and i is the internal segment).

The three rules of segments are:

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The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

680

Step-by-step explanation:

Answer:

680

Step-by-step explanation:

10 to the  2nd power is 10 times 10 which is 100.

Now, 6.8 times 100 is 680.

Hope this helps you!!

The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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Answer: 4000

Step-by-step explanation:

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:

y = -9x + 4

The equation for slope is y=mx + b

The correct answer is The mean price is 50.

The median price is 41.111.

The modal price is 52.857.

The standard deviation price is 22.271.

The data table represents the prices (in R) of 50 items purchased by a shopper is,

Price                       Frequency

0<20                            6

20<40                          0

40<60                          18

60<80                          13

80<100                         4

Explanation:

The mean of the data is the average of the given values.

The mean of the data is calculated as,

Price                   frequency (f)     Mid point (xi)                 f.xi

0-20                          6                         10                            60

20-40                        9                         30                           270

40-60                        18                        50                           900

60-80                        13                        70                           910

80-100                       4                         90                           360

Total                          50                       250                        2500

Mean = ∑fx1/N

Mean = 2500/50

Mean = 50

Price                   frequency (f)     cf

0-20                          6                  6      

20-40                        9                 15    

40-60                        18                33  

60-80                        13                46      

80-100                       4                 50  

Total                          50               150

The median class is 40 -60 as cf ≥ N/2

which is 33 ≥ 25

medain = 40 + |25-15|/18 ×20

medain = 40 + 200/18

median = 41.111

Mode = lower limit + f1-f0/2f1-f0-f2 × height

Here, f1 is the frequency of the modal class = 18.

f0 is the frequency of the preceding modal class = 9.

f2 is t/he frequency of the succeeding modal class = 13.

Mode = 40+ 18-9/2(18)-9-13

Mode = 52.857

Hence, the modal price is 52.857.

Price                   frequency (f)     Mid point (xi)                 f.(xi)^2

0-20                          6                         10                            600

20-40                        9                         30                           8100

40-60                        18                        50                           45000

60-80                        13                        70                           63700

80-100                       4                         90                           32400

Total                          50                                                       149800

The standard deviation of the data is calculated as,

SD = √(∑f(x1)^2)/N - (mean)^2

SD = √149800/50- (50)^2

SD = 22.271

Hence, the standard deviation of the data is 22.271.

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