squares of side x are cut from each corner of an 8 inches x 5 inch in rectangle, so that its sides can be folded to make a box with no top. define a function in terms of x that can represent the area of the base of the box
​

Answer:

36yd²

Step-by-step explanation:

uhm, we're just gonna assume that the 6yd stands for one of the sides, so the formula for area of a square is:

side x side = area

plug:

6 x 6 = 36

so the area of the square is 36yd²

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

Step-by-step explanation:

ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle

Answer:

200 minutes

Step-by-step explanation:

24 / 3 = 8

25 * 8 = 200

200 minutes

The rate will be 8.33 minutes per picture. Then the number of minutes will be 200 minutes.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Clayton draws 3 pictures in 25 minutes. Then the rate is given as,

Rate = 25 / 3

Rate = 8.33 minutes per picture

He drew 24 pictures this week. Then the number of minutes is calculated as,

⇒ 24 x 8.33

⇒ 200 minutes

The rate will be 8.33 minutes per picture. Then the number of minutes will be 200 minutes.

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Function is increasing in the domain of interval (1, ∞).

A quadratic function is a mathematical function of the form:

f(x) = ax² + bx + c

where "a", "b", and "c" are constants, and "x" is the variable.

From the given table of ordered pairs, we can see that the function k is a continuous quadratic function that passes through the points (-1, 0), (0, 2), (2, 5), (3, 4), and (4, 5).

We can estimate the slope of the function between each pair of consecutive points in the table. For example, between (-1, 0) and (0, 2), the slope is positive, so the function is increasing in the interval (-1, 0). Between (0, 2) and (2, 5), the slope is also positive, so the function is increasing in the interval (0, 2). However, between (2, 5) and (3, 4), the slope is negative, so the function is decreasing in the interval (2, 3).

Finally, between (3, 4) and (4, 5), the slope is positive, so the function is increasing in the interval (3, 4). Therefore, the function k is increasing over the intervals (-1, 0) and (3, 4).

So, the correct answer is option A: (1, ∞).

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The total surface area of the triangular prism using the net is 96 square units

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

The net of a triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 2 * 3 * 7 + 6 * 7+ 2 * 1/2 * 2 * 6

Evaluate

Area = 96

Hence, the surface area is 96 square units

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Answer:

the answer of this question is given in above picture, look

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

Answer:

The constant rate of change is 3

Step-by-step explanation:

Given

x   y

2   6

4   12

6   18

8   24

Required

Determine the constant rate of change

Represent the constant rate of change with k.

k is calculated using:

\(k = \frac{y}{x}\)

When y = 24; x = 8

So, we have:

\(k = \frac{24}{8}\)

\(k = 3\)

\(\text{Area of rectangle} = \text{length} \times \text{width}\\\\~~~~~~~~~~~~~~~~~~~~~~~=4 ~\text{ft}~\times ~2 ~\text{ft}\\\\~~~~~~~~~~~~~~~~~~~~~~~=8~ \text{ft}^2\\\\~~~~~~~~~~~~~~~~~~~~~~~=1152~\text{in}^2\)

Answer:

13 and 389

Explanation:

Let the two positive integers be x and y

If a positive integer is 38 more than 27 times another, then;

x = 27y+ 38 ...1

If their product is 5057, then;

xy = 5057 .....2

Substitute equation 1 into 2

(27y + 38)y = 5057

Expand the bracket

27y^2 + 38y = 5057

27y^2 + 38y - 5057 = 0

Factorize

27y^2 -351y + 389y - 5057 = 0

27y(y-13) + 389(y-13) =0

(27y+389)(y−13) = 0

27y + 389 = 0 and y - 13 = 0

27y = -389 and y = 13

Since y is a positive integer, hence y = 13

Substiute y = 13 into equation 1;

x = 27y+ 38 ...1

x = 27(13)+ 38

x = 351 + 38

x= 389

Hencethe two positive integers are 13 and 389

Answer:

a)

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Step-by-step explanation:

a)

Given data population proportion 'p' = 19% =0.19

                                                          q  = 1-p = 1- 0.19 =0.81

Given  two people are randomly​ selected

 Given n = 2

Let 'X' be the random variable in binomial distribution

\(P(X=r) =n_{C_{r} } p^{r} q^{n-r}\)

The probability that both will be hopelessly romantic is

                   \(P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}\)

                     P(X = 2)   = 1 × 0.0361

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 1-P(x<1)

                            = 1 - ( p(x =0)

                            = \(1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}\)

                           = 1 - (0.81)²

                           = 1 -0.6561

                           = 0.3439

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

From the given figure, let's solve for the varibles s and y.

Angle 110 and (y - 28) form a linear pair.

Angles on a straight line are supplementart angles and supplementray angles sum uo to 180 degrees.

Thus, we have:

(y - 28) + 110 =180

y - 28 + 110 = 180

y + 82 = 180

Subtract 82 from both sides:

y + 82 - 82 = 180 - 82

y = 98°

To solve for x, apply the corresponding angles theorem.

Angle 110 degree and (5x + 15) are corresponding angles.

Corresponding angles are congruent.

Thus, we have:

5x + 15 = 110

Let's solve for x.

Subtract 15 from both sides:

5x + 15 - 15 = 110

5x = 110

The value of the fraction -6 3/5 -(-7 4/15) + 2 1/5 will be 2 13/15.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

The value of the fraction -6 3/5 -(-7 4/15) + 2 1/5 will be:

= -6 3/5 -(-7 4/15) + 2 1/5

= 7 4/15 + 2 1/5 - 6 4/5

= 7 4/15 + 2 3/15 - 6 9/15

= 9 7/15 - 6 9/15

= 2 13/15

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Answer:

24 times 9

Step-by-step explanation:

216 trees were planted

Answer:

-6.27

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Answer: 280

Step-by-step explanation:

40/100 x 200 = 80

80 + 200 = 280 the next day

or you can use the compound interest formula to work out for a specific amount of time

The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.

Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.

In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.

However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.

So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.

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The complete question is :

Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

Answer:

36

Step-by-step explanation:

It's the biggest number.

Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

2x-4

Step-by-step explanation:

5x-(4+3x)

5x-4-3x

5x-3x-4

2x-4

Answer:

5 units

Step-by-step explanation

Answer:

3

Step-by-step explanation:

I was too lazy to provide an explanation

The pair of equations that can be used to find x and y are:

x + y = 62

(1.02)x = 7

The form of the pair of equations would be:

hours worked last week + hours worked this week = total hours worked both weeks equation 1

(1 + percent increase/100) x hours worked last week = hours worked this week equation 2

x + y = 62 equation 1

(1 + 20/100) ×x = y

(1.02)x = 7 equation 2

The two equations can be solved using either of these three methods:

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Answer:7

Step-by-step explanation:

Answer:

X=10

Step-by-step explanation:

4.5x +55=100

Answer:

X=10

Step-by-step explanation:

4.5x +55=100

Answer:

-11

Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

f(3) means that you plug in 3 for x in the entire equation of f(x)

This means when f(x) = -3x - 2

f(3) = -(3)(3) - 2

= -9 -2

= -11