PLEASE HELP ME WITH THESE 2 QUESTIONS

The perimeter of the equilateral triangle is 48 cm

equilateral triangle

An equilateral triangle is a type of triangle in which all three sides are equal in length and all three angles are also equal, measuring 60 degrees each.

Given that: the area of an equilateral triangle is 64√3 cm²

The formula for the area of an equilateral triangle is given by:

A = (√3)/4  ×  a²

Where a is the length of the side

64√3 = (√3)/4  ×  a²

4 × 64√3 = (√3) ×  a²

4 × 64 = a²

a² = 4 × 64

a² = 256

a = √256

a = 16 cm

Perimeter of the equilateral triangle = a + a + a = 3a

Perimeter of the equilateral triangle = 3 × 16 = 48 cm

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The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.

As given in the question,

Number of six sided dice to be rolled = 4

Number of outcomes on one dice = 6

Total number of outcomes of 4 dice = 6⁴

                                                            = 1296

Conditions for the product of the numbers of top faces all four dice is prime:

Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),

( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)

Total number of favourable outcomes = 12

Required Probability = 12 / 1296

                                  = 1 / 108

Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.

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The surface area of the box as a function of x will be f(x) = x² + 20000/x² where x is the length of the square base's edge.

Here it is given that the box has a square base.

This implies that length = breadth

Now, the volume of a box = lbh = 5000 cu in

where l is the length of the box. b is the breadth of the box, and h is the height of the box.

or, x²h = 5000

or, h = 5000/x²

Let the surface area function be f(x) where x is the length of the edge of the square base.

Since the box is open, the surface area will be

lb + 2bh + 2lh

= x² + 10000/x² + 10000/x

= x² + 20000/x²

Hence the surface area as a function of x will be

f(x) = x² + 20000/x²

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Answer:

11.857

Hope this helps!

Answer: p≈11.86

Step-by-step explanation:

[tex]p=\sqrt{5.2^3} \\\\p=\sqrt{5.2^2(5.2)} \\\\p=5.2\sqrt{5.2}\\\\p\approx5.2(2.28)\\\\p\approx11.86[/tex]

In the figure of triangles given figure C is not similar

Not similar

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

In figure  C no information is given about the angles hence they are not similar.

Figure B is similar by Side - Side - Side (SSS) and shows a proportion of 2

Figure D is similar by Side - Angle - Side (SAS), the include angle here are equal by vertical angle theorem

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Answer: M=1

Step-by-step explanation:

hope this help!

The common ratios of the sequence are 4 and 1/4

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

Sequence 1

1, 2, 4, 8, 16,...

The common ratio is the quotient of a term and the previous term

Using the first term and the second term, we have

Common ratio = Second term/First term

Substitute the known values in the above equation, so, we have the following representation

Common ratio = 2/1

Evaluate

Common ratio = 2

Sequence 2

Here, we have

48, 12, 4, 2,...

The common ratio is the quotient of a term and the previous term

Using the first term and the second term, we have

Common ratio = Second term/First term

Substitute the known values in the above equation, so, we have the following representation

Common ratio = 12/48

Evaluate

Common ratio = 1/4

Hence, the common ratio is 1/4

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Answer:

8%

Step-by-step explanation:

1. Subtract the larger number from the smaller:

  3780 - 3500 = 280

2. Divide the result from step 1 by the FIRST salary amount:

   280 ÷ 3500 = 0.08  NOTE: Order Matters!!!

3. Change the decimal to a percent

When a=4, b=1, and c=3, the value of the given expression, which is |a-b|²-c, is 28.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Here,

|a-b|²=(4-(-1))²

=25

25-(-3)

=28

The value of given expression that is |a-b|²-c is 28 when a=4, b=−1, and c=−3.

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Answer:

Response bias would be something where answers would be skewed one way or another because of the way you asked. So maybe ask something embarrassing for someone to admit, like asking random students if they pick their nose. Some people will answer truthfully as no, and the people who do will likely also say no because they do not want to tell you that.

The probability of odds as a decimal rounded to the nearest hundredth is 0.398.

The probability of odds is given by the formula -

Probability of odds = probability odds ÷ probability (1 + odds)

Probability odds = 0.66

Probability (1 + odds) = 1 + 0.66

Performing addition on Right Hand Side of the equation

Probability (1 + odds) = 1.66

Keep the values in formula to find the probability of odds

Probability of odds = 0.66/1.66

Performing division on Right Hand Side of the equation

Probability of odds = 0.398

Hence, the probability of odds is 0.398.

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The probability that the next person will purchase exactly one costume is 67%.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

53 visitors purchased no costume.

151 visitors purchased exactly one costume.

22 visitors purchased more than one costume.

Total visitor = 53 + 151 + 22

= 226

Probability that the next person will purchase exactly one costume will be:

= Those with one custome / Total visitors × 100

= 151 / 226 × 100

= 67%

The probability is 67%.

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Step-by-step explanation:

In order to solve this equation, you will need to use the following steps:

First, simplify the left side of the equation by performing the operation of multiplying 0.5 and (2x-8) to get 0.5(2x-8)=x-4.

Then, subtract 3 from both sides of the equation to get x-4=3x+28.

Next, subtract 3x from both sides of the equation to get -3x+x-4=28.

Combine the like terms on the left side of the equation to get -2x-4=28.

Add 4 to both sides of the equation to get -2x=32.

Finally, divide both sides of the equation by -2 to get x=16.

Therefore, the value of x that makes the equation 3-0.5(2x-8)=(3x+28) true is 16.

The required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.

Given that,
John deposits $ 8,000 in a certificate of deposit that pays .8% interest, compounded semi-annually.

Investment is defined as when an individual is spend money on something that returns him or her higher money than the money they or invest.

Here,

Interest earned in the 6 months,
= 8000 [0.08/2]
= $320
Balance after a year,
Amount = principal [1 + rate/n]ⁿ
= 8000[1 + 0.08/2]²
= $8652.8

Thus, the required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.

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Answer:

D) AAA

Step-by-step explanation:

The simplified form of the given expression, (2c7)(9c), is 18c⁸

From the question, we are to simplify the given expression
The given expression is

(2c7)(9c)

First, we will write the expression properly

The given expression written properly is

(2c⁷)(9c)

Now, we will simplify the expression

Simplifying the expression

(2c⁷)(9c)

Multiply

2c⁷ × 9c

Collect like terms

2×9 × c⁷ × c

18 × c⁷⁺¹

18 × c⁸

18c⁸

Hence, the expression is 18c⁸

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After using the arithmetic: They sold 40 small bowl of ice cream and 23 large bowl of ice cream.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the standard operations on numbers—addition, subtraction, multiplication, division, operation, and extraction of roots.

Main body:

Cost of small bowl of ice cream = $2.25

Cost of large bowl of ice cream  = $3

Total number of bowls sold = 63

total value  = $159

let number of small bowls be x and  large bowl be y.

Hence ,

x +y = 63                       ---(1)

2.25 x +3 y = 159          ---(2)

from equation 1 substitute the value of x in equation 2 .

2.25 x + 3 (63- x) = 159

2.25 x + 189 - 3x = 159

taking like terms to one side ,

3x - 2.25x = 189-159

0.75x = 30

x = 40

so x = 40 then y = 23.

Hence they sold 40 small bowl of ice cream and 23 large bowl of ice cream.

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At the significance level, 0.01

p-Value=0.973 > 0.01 which implies fail to reject null hypothesis and no evidence to support the claim.

So, there is no reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes.

We have given that,

A study conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction.

x₁-bar = 8.8 micromoles

Standaard deviations, s₁= 1.2

x₂-bar = 7.5 ; s₂ = 1.5

n₁ = 12 ; n₂ = 15

significance level = 0.01

Consider the Null hypothesis and alternative hypothesis othesis

H₀ : μ = 0.5

Hₐ : μ > 0.5

Consider,

Pooled Standard Deviation = √(((n₁ - 1)s₁² + (n₂- 1)s₂²)/(n₁ + n₂-2))

plugging all known values

= sqrt(((12-1)(1.2²) + (15 -1)(1.5²))/(12+15-2))

Sp = 1.3761

Now , test statistic :

t =((x₁-bar - x₂-bar) - 0.5) / (Sp×√(1/n₁+ 1/n₂))

substitute all known values we get,

= ((8.8 - 7.5) - 0.5) / (1.3761× sqrt(1/12 + 1/15))

=> t = 1.5

Degree of freedom = n₁+ n₂ - 2

= 12 + 15 - 2

= 25

Now the p-value corresponding to t = 1.5 & df = 25 is 0.073

Here p-value > 0.01 (significance level) thus, we fail to reject null hypothesis.

So there is no enough evidence to support the claim.

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The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units

What is the distance between two points?

Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

The distance from A to B is the same as the distance from B to A

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane

Given data ,

Let the first point be A ( x₁ , y₁ )

The value of A ( x₁ , y₁ ) = A ( -2 , -5 )

Let the second point be B ( x₂ , y₂ )

The value of B ( x₂ , y₂ ) = B ( -7 , -7 )

Now , the distance between the two points is given by the formula

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

where D is the distance

Substituting the values in the equation , we get

Distance D = √ [ ( -7 - (-2) )² + ( ( -7 - (-5) )² ]

On simplifying the equation , we get

Distance D = √ (-7 + 2 )² + ( -7 + 5 )²

Distance D = √ ( -5 )² + ( -2 )²

So , the value of D is

Distance D = √ ( 25 + 4 )

Distance D = √29 units

So , the approximate value of distance D = 5.39 units

Therefore , the value of Distance D = 5.4 units

Hence ,

The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units

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Answer:

the rate of change is 3x(slope)

The mean age of the combined distribution of both men and women in the course is 20.47 years

What is average/mean ?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Mean age of men , M = 20.7 years

Mean age of Women , W = 20.2 years

Percentage of Men = 54%

Percentage of Women = 46%

Recall, :

Mean, μ = np

The mean age of men in the distribution = (20.7 × 54%) = 11.178 years

The mean age of women in the distribution = (20.2 × 46%) = 9.292 years

The mean age of the combined distribution is :

11.178 + 9.292 = 20.47 years

Therefore, the mean age of the combined distribution is 20.47 years

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The value of p is 18, it can be find out by using concepts of line and slope of a line.

What is the slope of a line?

Slope of line measures its steepness. Mathematically, its calculated as "rise over run".

Slope of a line : (y2 - y1)/(x2-x1)

In the given que,

given graph equation is of line ,

to find slope of graph : we need to differentiate the equation

[tex]\frac{d}{dx}[/tex](3y + 2x = 7) = 3[tex]\frac{dy}{dx}[/tex] + 2 = 0

So, [tex]\frac{dy}{dx}[/tex] = -2/3

We, if any line are perpendicular then

slope of one * slope of two = -1

So, slope of 1 = (-9-6)/(8-p)

                       = -15/(8-p)

     slope of 2 = -2/3

     Now product of both = -15/(8-p) * (-2/3 )

By simplifying all these equation,

we get p = 18.

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[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.

Multiply the integer by itself.

[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]

[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]

Simplify

[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]

[tex]=4+4i-1[/tex]

Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.

[tex]4+2i+21i+1(-1)[/tex]

Simplify and use the a+bi formula in standard form.

[tex]3+4i[/tex]

A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.

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Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}[/tex]

now, the y-intercept occurs when x = 0, recheck the picture below.

The differences in dependent measures between levels are the main effects

The differences in the dependent measure between the levels of one variable within one level of another variable are known as simple main effects. These effects can be tested statistically to determine if they are statistically significant, which would indicate that the difference between the levels of the first variable is meaningful within the context of the second variable.

One independent variable having a certain degree of another independent variable is the simple main effect of a factorial experiment. The levels of the other independent variable are averaged over the primary effect of one independent variable. Results for a straightforward main effect are examined as though every level of the other independent variables had its own experiment.

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Answer: C - I agree

D - Square root 50 lies between integers 7 and 8

E - Find the closest integer to 40

Step-by-step explanation: C - 7/9 will be 0.77777778 which you can simplify to 0.777

D - The square root of 50 is 7.07106781187 so it is between the integers 7 and

E - The square root of 40 is 6.32455532034 which so find the clossest integer to 40

Answer:

2.8

Step-by-step explanation:

Set aside the 2 for now.

Divide 4÷5=0.8  NOTE: Order Matters!!

Add: 2 + 0.8 = 2.8  (Just put the 2 to the Left of the decimal.)

Therefore the percentage of increase in yearly sales is 35% by last year.

Percentage refers to a number that is "out of one hundred." As with fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When utilizing percentages, the total is regarded as being composed of 100 equally sized components. In addition to the abbreviation "pct," which is used less frequently, the symbol "%" is used to denote percentages in numbers.

Here,

the company sold a total of 720,460 pictures  Last year.

This year, they sold 972,621 pictures

therefore first we have to find the difference between the last year and this year pictures sold

it comes out to be,

=>972,621-720,460=252,161

Therefore the increase in percentage this year=

=> 252,161/720460 * 100

=>0.35*100

=> 35%

Therefore the percentage of increase in yearly sales is 35% by last year.

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Therefore, the student would pay $2,994.20 more over the life of the loan than if they paid in cash.

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics. Some common examples include: Interest rates on loans and credit cards, Discounts on sale items in stores, Tax rates on income or purchases, Probability of events occurring, Performance metrics in sports and other competitions. Percentages can be converted to decimals or fractions for calculations, and vice versa.

Here,

If the student pays in full with cash, the total cost of the car is $10,000.

If the student chooses to finance the car, the monthly payment is $216.57 and the number of months is 60. The total amount paid over the life of the loan is:

Total paid = Monthly payment * Number of months

= $216.57 * 60

= $12,994.20

The amount paid over the life of the loan is the difference between the total paid and the initial cost of the car:

Amount paid over life of loan = Total paid - Initial cost

= $12,994.20 - $10,000

= $2,994.20

The correct answer is option O: $2,994.20.

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Answer:

(-1.732,0) and (1.732,0)

Step-by-step explanation:

Ignore f(x). The solutions are also called x-intercepts and zeros. So the solutions would be where the parabola crosses the x axis. In my answer ignore the 0 in the coordinates. Just put in the -1.732 and 1.732.