Multiplying Polynomials Investigation:Arnold has a 6ftx6ft piece of cardboard to make a open box by cutting equal size squares from each corner,folding up the resulting flaps,and taping at the corners.Your task is to label dimensions on a sketch with the same size variable cut from each corner.

- How does each variable expression relate to length,width,and height of the box when folded?

-Based upon the variables you used,write a product for the volume?

-expand the product to write a volume function?

- what domain makes sense for the volume?

guess and check values to find the size cut that produces a maximum volume

*lgth ( )width ( ) hght ( ) volume ( )

you have to have 5 guesses

Answer:

Option A. 3.5x + 15 ≥ 55

Step-by-step explanation:

Points Rosh received for becoming a member = 15

Points Rosh received for visiting the moving theater = 3.5

Total points needed for a free movie ticket = 55

For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:

3.5x + 15 ≥ 55

So, option A gives the correct answer

Answer:

option. A

Step-by-step explanation:

I had the exacgt same question

Answer:

16.51

Step-by-step explanation:

In a parallelogram, the opposite angles are always equal in measure. So two of the angles in the parallelogram measure 39 degrees each.

The sum of angles of the parallelogram must be 360 degrees. Let the other two angles be x degree each. We can set up the following equation for the angles:

39 + 39 + x + x = 360

78 + 2x = 360

2x = 282

x = 141

This means, the other two angles measure 141 degree each. The shorter diagonal will be opposite to the shorter angle.

Hence, the diagonal opposite to the angle 39 degree will be the shorter one. A diagonal divides the parallelogram in two triangles. So we will have two sides and an included angle and we have to find the third side of the triangle which can be found using the law of cosines. Let the third side be c as shown in image below, using the law of cosines, we can write:

[tex]c^{2} = a^{2}+ b^{2} -2ab cos(\gamma)\\\\c^{2}=18^{2}+26^{2}-2(18)(26)cos(39)\\\\ c^{2}=272.59\\\\ c=16.51[/tex]

Thus the shorter diagonal will be 16.51 feet in measure.

To find the shorter diagonal of a parallelogram with given side lengths and angle, use the formula √(a^2 + b^2 - 2abcosθ).

To find the shorter diagonal of a parallelogram, we need to use the formula:

Shorter diagonal = √(a^2 + b^2 - 2abcosθ)

Where a and b are the sides of the parallelogram and θ is the angle between them.

Using the given information, we have a = 18 ft, b = 26 ft, and θ = 39°.

Substituting these values into the formula, we get:

Shorter diagonal = √(18^2 + 26^2 - 2(18)(26)cos(39°))

Calculating this expression gives us:

Shorter diagonal ≈ 9.15 ft

you got everything right

Answer:

option 2

2x²- x - 1

Step-by-step explanation:

We are given points: (-1,2), (0,-1) and (2,5)

Substitute each point one by one in the quadratic equation to check if the quadratic equation contains all points mention.

2) f(x) = 2x²- x - 1

   Point(-1,2)

   f(-1) = 2(-1)² -(-1) -1

   2 = 2 + 1 - 1

   2 = 2

  Point(0,-1)

   f(0) = 2(0)² -(0) -1

   -1 = 0 - 0 -1

   -1 = -1

  Point(2,5)

  f(2) = 2(2)² -(2) -1

  5 = 8 - 2 -1

  5 = 6 - 1

  5 = 5    

Answer:

1.    2x(-3x - 1)

-6x^2 - 2x

2.   -x(4 + 2x)

-4x - 2x^2

3.   -5x(-2x + 4)

10x^2 - 20x

4.   x(-2x - 2) + 3(-4x - 6x)

-2x^2 - 2x - 12x - 18x

-2x^2 - 32x

5.   2xy(-3x - 5y) + 4y(-2xy - 4x)

-6x^2y - 10xy^2 -8xy^2 - 16yx

-6x^2y -18xy^2 - 16yx

You just distribute (multiply) what's outside the parentheses with everything inside the parentheses.  Then, combine like terms.

Answer:

1.    2x(-3x - 1)

-6x^2 - 2x

2.   -x(4 + 2x)

-4x - 2x^2

3.   -5x(-2x + 4)

10x^2 - 20x

4.   x(-2x - 2) + 3(-4x - 6x)

-2x^2 - 2x - 12x - 18x

-2x^2 - 32x

5.   2xy(-3x - 5y) + 4y(-2xy - 4x)

-6x^2y - 10xy^2 -8xy^2 - 16yx

-6x^2y -18xy^2 - 16yx

Answer: 2.5 or 2 1/2

Step-by-step explanation:

You can convert the mixed fractions to decimal numbers:

- Divide the numerator by the denominator of the fraction.

- Add the result to the whole number.

Thenyou have:

Barbara's time: [tex]3\ 3/10=3+0.3=3.3[/tex]

Donna's time: [tex]2\ 4/5=2+0.8=2.8[/tex]

Cindy's time: [tex]4\ 3/5=4+0.6=4.6[/tex]

Nicole's time: [tex]2\ 1/10=2+0.1=2.1[/tex]

As you can see, the fastest girl is Cindy and the slowest girl is Nicole.

Then, you must make the following subtraction to calculate the difference:

[tex]4.6-2.1=2.5[/tex] or 2 1/2

Answer:

Cindy's correct time is 3 2/5 (for the portfolio assignment that this question goes with).

Step-by-step explanation:

Answer:

the answer is 119g

Step-by-step explanation:

x-120/4.3=-0.25

x-120=-1075

x=118.925=119g

Approximately 40% of the tomatoes weigh less than 119 g.

The correct answer is option D.

A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.

It measures the unusual or extreme a particular data point is compared to the rest of the distribution

We have,

To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.

The CDF gives the probability that a random variable is less than or equal to a given value.

Given that the mean of tomato weight is 120 grams and the standard deviation is 4.3 grams,

We can use this information to find the probability that a randomly selected tomato weighs less than a certain amount.

Let's calculate the z-score for each option:

A. 111 g:

z-score = (111 - 120) / 4.3 ≈ -2.093

B. 114 g:

z-score = (114 - 120) / 4.3 ≈ -1.395

C. 117 g:

z-score = (117 - 120) / 4.3 ≈ -0.698

D. 119 g:

z-score = (119 - 120) / 4.3 ≈ -0.233

Now, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) of the standard normal distribution to find the probability corresponding to each z-score.

The option with the highest probability, or approximately 40%, is the correct answer.

Based on the calculations, it appears that option D. 119 g has the highest probability of approximately 40% for a tomato weighing less than that amount.

Thus,

Approximately 40% of the tomatoes weigh less than 119 g.

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Answer:

4(9x-4)

Step-by-step explanation:

➷ Find the greatest common factor between the two values:

In this case, it is 4

This value will go outside the parenthesis

Divide each of the values by 4:

36x/4 = 9x

-16/4 = -4

The final answer is 4(9x - 4)

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➷ The perimeter is the sum of all the lengths

206 - (59 + 94) = 53

It is 53 inches.

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Answer:

53 inches.

Step-by-step explanation:

Perimeter =  sum of the 3 sides so the third side

= 206 - 94 - 59 = 53.

Answer:The answer is x=12

Step-by-step explanation: 2*6=12 and 12/6=2

Answer:

x = 12

Step-by-step explanation:

12/6 = 2

[tex]\bf \begin{array}{ccll} problems&minutes\\ \cline{1-2} 12&45\\ 20&x \end{array}\implies \cfrac{12}{20}=\cfrac{45}{x}\implies \cfrac{3}{5}=\cfrac{45}{x}\implies 3x=225 \\\\\\ x=\cfrac{225}{3}\implies x=75[/tex]

It takes 75 minutes to solve 20 math problems.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here it takes 45 minutes to solve 12 math problems thus to solve 1 math problem it will take t= 45/12

                                            =3.75 minutes

Thus to solve 20 math problems it will take t₂₀=3.75×20

                                                                            =75 minutes

Hence, It takes 75 minutes to solve 20 math problems.

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Diagonal = SQRT(8^2 + 12^2 + 30^2)

Diagonal = SQRT(64 + 144 + 900)

Diagonal = SQRT(1108)

Diagonal = 33.3 feet

Answer:

See below

Step-by-step explanation:

What the significance level tells us is that, in this case, there is only a 5% chance that the change in results from the sample happened by random chance.  So that means that most likely the change in results did not happen by random change, and something happen between the times the samples were taken.  In this case, the experiment.

P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05.

P = 0.05 does not represent the probability that the null hypothesis is true or false, nor does it signify that the outcome is 5% higher in one group compared to the other. Instead, P = 0.05 is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as the one observed. In simpler terms, it indicates the likelihood of obtaining the observed results, or results more extreme, under the assumption that there is no true effect or difference between the groups.

In hypothesis testing, researchers start with a null hypothesis (H0) that states there is no effect or difference between the groups being compared. The alternative hypothesis (Ha), on the other hand, posits that there is a significant effect or difference. The p-value quantifies the strength of evidence against the null hypothesis. A low p-value (such as P = 0.05) suggests that the observed results are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.

When a study reports a statistically significant improvement in Verbal GRE performance with P = 0.05, it means that the probability of obtaining the observed improvement (or a more significant one) under the assumption of no actual effect is 5% or less. Therefore, there is strong evidence to suggest that the technique used in the experiment does indeed have a positive impact on students' Verbal GRE scores.

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1 cup = 8 ounces

so you'll have 5 ounces in each cup

5/8+5/8+5/8=15/8 (roughly 15 ounces or just under 2 cups of water)

Answer:

A - 8

Step-by-step explanation:

(21-5)/2

16/2 = 8

Answer: Jack is 8 years old (option A)

Step-by-step explanation:

Hi, to answer this question we have to write an equation using the information given:

Twice : Means that the age of jack (j) is multiplied by 2 (2j),  

Plus 5: we have to add 5 (2j+5).  

Is 21: all is equal to 21.

Mathematically speaking:

2j +5 =21

Solving:

2j =21-5

2j =16

j= 16/2

j=8

Option A). 8

Feel free to ask for more if needed or if you did not understand something.

Answer:

Angle of 1 part: 40°

Angle of 2 parts: 80°

Step-by-step explanation:

Angles in a circle / Equal parts of a circles = Angle of 1 part

360/9 = 40°

40 x 2 = 80

Answer:

The answer is ; m∠BEH = 55°

Step-by-step explanation:

Answer:

The original selling price was [tex]\$75[/tex]

Step-by-step explanation:

Let

x-----> the original selling price

we know that

[tex]100\%-20\%=80\%=80/100=0.80[/tex]

so

[tex]0.80(x)=60[/tex] -----> equation that represent the situation

solve for x

Divide by 0.80 both sides

[tex]x=60/0.80=\$75[/tex]

ANSWER:

HOPE IT HELPED YOU ☺

Answer:

Yes - he is correct

Step-by-step explanation:

If she has 75 pennies, she would have 15 rows with 5 pennies in each row with a 3:5 ratio for the rectangle.

Lata's father is correct.

Rectangle is a type of quadrilateral having two opposite sides that are equal in measurement.All the angles of Rectangle are of 90°.

Area of rectangle = Length * Width

Perimeter of rectangle =2(length + width)

Given,

Total number of pennies Lata have  = 75

If she arranges the pennies in 15 rows with 5 pennies in each row.

i.e; 15 * 5 = 75

Then she will get Rectangle of side of length 15 and width 5

So, her father is correct.

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Answer:

5/7 or 71%

Step-by-step explanation:

4/7 (blue) + 1/7 (belt) = 5/7

Answer: Probability of event A = 0.57

Probability of event B = 0.14

Step-by-step explanation:

The data is:

2 blue shirts

1 red shirt

1 blue jacket

1 red belt

1 blue pair of pants

1 red pair of pants

the total number of garments is: 2 + 1 + 1 + 1 + 1 + 1 = 7

the number of blue ones is: 2 + 1 + 1 = 4

the number of belts is: 1

then, the probability of selecting at random one blue garment is equal to the number of blue ones divided the total number:

Pa = 4/7 =0.57

the probability of selecting the belt is equal to the number of belts divided the total number of garments, this is:

Pb = 1/7 = 0.14

Answer: [tex]149^{\circ}[/tex]

Step-by-step explanation:

From the given figure, the measure of central angle FDG is given by :-

[tex]\angle{EDG}=\angle{EDF}+\angle{FDG}\\\\=83^{\circ}+66^{\circ}\\\\=149^{\circ}[/tex]

We know that the measure of arc in degrees is equals the measure of the central angle that intercepts the arc.

Now,the measure of arc EFG is given by :-

[tex]Arc\ \text{EFG}=\text{Central angle EDG}=149^{\circ}[/tex]

Answer:

36

Step-by-step explanation:

1. 48 divided by 3= 12

2. 12 x 3= 36

Answer: Third option.

Step-by-step explanation:

Calculate the area of the gate (including the glass panel) which has the shape of a trapezoid.

The formula for calculate the area of a trapezoid is:

[tex]A=\frac{h}{2}(B+b)[/tex]

Where h is the height, B is the larger base and b is the smaller base.

In this case:

[tex]B=10ft\\b=7ft\\h=5ft[/tex]

Substituting, you get:

[tex]A_{gate}=\frac{5ft}{2}(10ft+7ft)=42.5ft^2[/tex]

Calculate the area of the rectangular glass panel, with the formula:

[tex]A_{panel}=l*w[/tex]

Where the lenght is [tex]l=1.43ft[/tex] and the width is [tex]w=0.71ft[/tex]

Then:

[tex]A_{panel}=(1.43ft)(0.71ft)=1.01ft^2[/tex]

The area he needs to paint is:

[tex]A=A_{gate}-A_{panel}\\A=42.5ft^2-1.01ft^2\\A=41.49ft^2[/tex]

If painting the gate costs $2.50 per ft², for 41.49 ft² he will have to spend:

[tex]=(41.49)(\$2.50)\\=\$103.725[/tex]

Therefore the answer is the third option.

To calculate the cost of painting the gate, find the area of the glass panel by multiplying its length and width. Multiply the area by the cost per square foot to find the total cost.

To calculate the cost of painting the gate, we need to find the area of the glass panel first. Let's say the length of the panel is 'l' feet and the width is 'w' feet. The area of a rectangle is given by the formula A = l × w. Once we have the area, we can multiply it by the cost per square foot ($2.50) to find the total cost. So the formula to calculate the cost of painting the gate is: Cost = Area × Cost per square foot. Substitute the values you know into the formula and solve for the cost.

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ANSWER

The height of the square pyramid is 4.8m

EXPLANATION

The volume of a square pyramid is calculated using the formula:

[tex]Volume = \frac{1}{3}(base \: area) \times height[/tex]

It was given that;

The volume of the square pyramid is

[tex]25 \frac{3}{5} {m}^{3} [/tex]

The side length of the square base is

[tex]4m[/tex]

We substitute the given values and then solve for the height.

[tex]25 \frac{3}{5} = \frac{1}{3}( {4}^{2} ) \times height[/tex]

We solve for the height to obtain;

[tex]height = \frac{25 \frac{3}{5} }{ \frac{16}{3} } [/tex]

We simplify to get;

[tex]height = 4.8m[/tex]

Hence, the height of the square pyramid is 4.8 meters.

Answer:

The height of the square pyramid is 4.8 meters.

Step-by-step explanation:

I just know

Answer: option a.

Step-by-step explanation:

To solve the given exercise nad write the expression as a single logarithm, you must keep on mind the following properties:

[tex]ln(a)+ln(b)=ln(ab)\\m*ln(a)=ln(a)^m[/tex]

Therefore, by applying the properties shown above, you can rewrite the expression given, as following:

[tex]lnx^{2}+3lny=lnx^2+lny^3=ln(x^2y^3)[/tex]

Then, the answer is the option a.

Answer:

4.02

Step-by-step explanation:

4+0.02=4.02

The number represented by the expanded form (4 × 1) + (2 × 0.01) can be presented in other forms such as decimal form (4.02), fraction form (402/100), percentage form (402%), or scientific notation (4.02 x 100).

The expanded form of a number is a way of breaking down the number into its parts. In this specific question, the expanded form of the number given is (4 × 1) + (2 × 0.01). This form shows the number 4.02 in a decomposed format. To write the number 4.02 in another format, we can use the decimal form, fraction form, percentage form, or even scientific notation.

For instance:

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Answer:

B

Step-by-step explanation:

We can use the logarithm property shown below to evaluate this:

[tex]Log(x*y*z)=logx+logy+logz[/tex]

Now we can write Log 12 as Log (2*2*3).

Using the rule, we can write:

Log (2*2*3) = Log 2 + Log 2 + Log 3

We are given values of Log 2 and Log 3, plugging these we get:

Log (2*2*3) = Log 2 + Log 2 + Log 3

Log (2*2*3) = 0.3010 + 0.3010 + 0.4771 = 1.0791

Answer choice B is right.

We can factor out 12 using 2 and 3.

log(12) = log(2^2 * 3)

Rewrite it using the product rule [ log(xy) = log(x) + log(y) ]

log(2^2 * 3) = 2 log(2) + log(3)

Simplify using the given values.

2(0.3010) + 0.4771

0.602 + 0.4771

1.0791

Therefore, the answer is b. ≈ 1.0791

Best of Luck!