Find the surface area of the box shown..

The area of the triangle GBC for the given condition of midpoint with a given area of ΔGMN = 6 equals 24.

In triangle ABC,

M is the midpoint of AB , N is the midpoint of AC

⇒ MN is parallel to BC

G is the intersection of BN and CM.

⇒ G is the centroid.

Centroid divides the line segment BN  and CM in the ratio

BG : GN = 2 : 1

CG : GM = 2 : 1

In ΔGMN and ΔGBC ,

MN || BC , BN and CM are transversal.

∠NMG ≅∠BCG  ( alternate angles)

∠MNG ≅ ∠CBG  ( alternate angles)

∠MGN ≅∠BGC ( vertically opposite angles )

By AA corollary,

ΔGMN is similar to ΔGBC

BG : GN = CG : GM

Area of triangle GMN = 6

Area of ΔGBC  / Area of ΔGMN = Square of the sides

⇒ Area of ΔGBC / 6 = ( 2 / 1 )²

⇒ Area of ΔGBC = 4 ( 6)

⇒ Area of ΔGBC = 24

Therefore, the area of the triangle GBC is equal to 24.

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Null hypothesis [tex]H_0[/tex] : p = 0.5 and alternative hypothesis [tex]H_1: $p \neq 0.5$[/tex]

The standardized statistic from the data is 3.1623

The observed standardized statistic is 3.1623

Based on the standardized statistic, we conclude that there is enough evidence to suggest that these monkeys can interpret human gestures better than random chance.

As per the given data: a choice between two boxes, 30 out of 40 monkeys approached the box that the human had gestured toward, and 10 approached the other box.

Here, p =  proportion of rhesus monkeys who tan interpret human gestures better.

a) Null hypothesis [tex]H_0[/tex] : p = 0.5

Alternative hypothesis [tex]H_1: $p \neq 0.5$[/tex]

b) Given, [tex]$\hat{p}=\frac{x}{n}=\frac{30}{40}=0.75, p_0=0.5$[/tex]

Standardized test statistic,

[tex]$Z=\frac{\hat{p}-p_0}{\frac{p_0\left(1-p_0\right)}{n}} \stackrel{H_0}{\sim} N(0,1)$[/tex]

Therefore the standardized statistic from the data = 3.1623

c) Assuming [tex]$H_0$[/tex] is true, the value of the observed standardized statistic is 3.1623 standard deviations above the mean(=0).

d) Now, p-value [tex]$=2 \times \min [p(z > 3.1623), p(z \leq 3.1623)]$[/tex]

= 0.00157

Since p-value <0.05, we reject [tex]$H_0$[/tex].

We conclude that there is enough evidence to suggest that these monkeys can interpret human gestures better than random chance.

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The value of the z-score corresponding to each position in the distribution is given by = { -2 , -1 , 0 , 1 , 2 }

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the z-scores corresponding to each position in the distribution be z

Now , the equation will be

The mean of the data μ = 50

The standard deviation of the data σ = 10

The value of x for the letters A, B, C, and D is given by { 30 , 50 , 60 , 70 }

Substituting the values in the equation , we get

The Z-score is calculated using the formula:

z = (x - μ)/σ

For letter A ,

z = ( 30 - 50 ) / 10

On simplifying the equation , we get

z = -20/10

z = -2

And , for letter B ,

z = ( 50 - 50 ) / 10

z = 0/10

z = 0

For letter C ,

z = ( 60 - 50 ) / 10

z = 10/10

z = 1

For letter D ,

z = ( 70 - 50 ) / 10

z = 20/10

z = 2

Now , the k-scores of the letters E , F , G and H is calculated by

The mean of the letters = 100

The standard deviation of the letters = 20

So , the k-scores of the letters are = { 60 , 80 , 100 , 140 }

Now , the mean of the data is given by = ( 60 + 80 + 100 + 120 + 140 ) / 5

So , the mean is μ = 500/5 = 100

Hence , the z-scores of the letters are solved

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The probability that at least one of them has been vaccinated is 0.9259.

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

The proportion of people vaccinated is 58%.

Three people are selected at random, that is, n=3

p=0.58,

the probability mass function,

[tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

[tex]p(X=0)= ^{3}C_{x}0.58^{0}(0.42)^{3-0 } = 0.07408[/tex]

p( X≥1)= 1 - p(X=0)

          = 1 - 0.07408

          = 0.9259

The probability that at least one of them has been vaccinated is 0.9259.

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To determine the times at which v(t) has a local minimum and maximum, we need to find the critical points of the function. A critical point is a value of t for which either the first derivative, v'(t), or the second derivative, v''(t), is equal to zero or does not exist.

The first derivative of v(t) is given by:

v'(t) = a + 2bt + y

Setting v'(t) equal to zero and solving for t, we get:

0 = a + 2bt + y

t = -a / 2b = -(3 m/s^4) / (2(-24 m/s^2)) = 3/48 s

The second derivative of v(t) is given by:

v''(t) = 2b

Since b is negative, v''(t) is negative, so v(t) has a local maximum at t = 3/48 s.

Similarly, since the second derivative is constant and negative, the function v(t) has a local minimum.

Therefore, the times at which v(t) has a local minimum and maximum are 3/48 s and 3/48 s, respectively, expressed as two numbers separated by a comma: 3/48 s, 3/48 s.

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Answer:

n=212.9

Step-by-step explanation:

= 4068 + 55n/60 + n = 64.1

= 4068 + 55n = 64.1 ( 60 + n )

= 4068 + 55n = 3846 + 64.1n

= 55n - 64.1 = 3846 - 4068

= - 9.1n = 222

= -9.1n/-9.1 = 222/-9.1

n = 212.9.

Answer:

E. Accommodation sales were € 120 000 per month

Step-by-step explanation:

[tex]1 + \frac{2}{3} = \frac{5}{3} [/tex]

[tex]restaurant \: sales \: = \frac{200 \: 000}{5} \times 2 = 80 \: 000[/tex]

[tex]accommondation \: sales = \frac{200 \: 000}{5} \times 3 = 120 \: 000[/tex]

To have a balanced budget, you must B. have your gross pay equal your spending and savings.

A balanced budget is a financial plan in which expenses are equal to or less than the amount of revenue generated. This means that the government or organization is not spending more money than it takes in and is not running a deficit. The result is a balanced financial position, where there is no debt and assets are equal to liabilities.

This indicates that there is no shortfall and that the person is spending just what they get as their gross income.

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Answer: Iced tea, Water, and Soda, or 12/16

Step-by-step explanation: 3/4 of 16/16 is 12/16, and 7/16+3/16+2/16=12/16

14 litres of an 80% acid solution, Let the amount of water needed to create a solution with 60% water be x litres.

Distilled water or pure water are not mixtures. When there are simply water molecules present, there are no additional pollutants or components in the water, making it pure.

A pure material or compound made of oxygen and hydrogen is called water. A mixture would be water that has other substances physically dissolved in it.

20% * 14=0.2*14=2.8 L of water is what you have now

(2.8+x)/(14+x)=60% (amount of water/total amount of solution must equal 60%)

(2.8+x)/(14+x)=60/100

Simplify the fraction 60/100 to 3/5

(2.8+x)/(14+x)=3/5

Cross multiply

5(2.8+x)=3(14+x)

14+5x=42+3x

5x-3x=42-14

2x=28

X=28/2

X=14 L of pure water must be added

Check:

14+2.8=16.8 and 14+14=28

16.8/28=168/280=42/70=6/10=60/100=60%

Therefore, 60%  litres of pure water should be mixed with a 5 litre solution of 80% acid to produce a mixture that is 70% water

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The rate at which the number of wolves in the forest is changing at t = 7 weeks is 20.932 wolves per week.

To find the rate at which the number of wolves in the forest is changing at t = 7 weeks, we can evaluate the function E(t) at t = 7:

E(7) = 31 cos(0.11 * 7^2) = 31 cos(4.97)

Using a calculator, we can find that cos(4.97) = 0.672. So,

E(7) = 31 X 0.672 = 20.932

This means that the rate at which the number of wolves in the forest is changing at t = 7 weeks is 20.932 wolves per week.

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510,000,000 million km²

Let us represent the total surface area of the earth as = x

We are told in the question that:

Water covers 70.8%, or about 3.61 × 10⁸ km², of the Earth's surface.

70.8% = 0.708

Hence,

0.708 × x = 3.61 × 10⁸

x = 3.61 × 10⁸/0.708

x = 361000000/0.708

x = 509,887,005.65km²

Therefore, the total surface are the earth approximately to the nearest million = 510,000,000 million km²

This is the number "510 million"

=======================================================

Work Shown:

The times 10⁸ means "times 100 million"

3.61 x 10⁸ = 3.61 * 100 million = 361 million

S = surface area of the earth

70.8% of S = water coverage area

70.8% of S = 361 million square km

0.708S = 361 million square km

S = (361/0.708) million square km

S = 509.887 million square km

S = 510 million square km

S = 510,000,000 square km

Answer:

what can i do please send me a question?

The third option from the top is correct

Answer:

4/7

Step-by-step explanation:

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Step-by-step explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

Answer:

correct

Step-by-step explanation:

y=x²

if you calculate the square of x, they all equal to Y

Answer:

Susie is correct

Step-by-step explanation:

The relationship between this function is that each x-value is being multiplied by a square of 2 to get the y-value.

-4²= 16

-2²=4

0²=0

2²=4

4²=16

6²=36

I hope this helps!

The formula of the relationship between lateral area and the length of a side of the base and slant height in a square pyramid is 2sh.

The lateral area of a square pyramid is defined as the area covered by its slant of lateral faces. One side of each of these triangles coincides with one side of the base polygon.

The lateral area is the area of the faces of the pyramid without the base.

Each face is a triangle with base "s" and a height the same as the slant height - let's consider it as  "h."

The area of each face is =0.5sh.

For the four faces the lateral area is 4*0.5sh=2sh.

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Answer:

-------------------------------

The perimeter of given semicircle is the sum of the diameter and half of the circumference:

The volume of the triangular prism is 2,160 ft³.

The volume of a triangular prism can be calculated using the formula V = BH, where B is the area of the base of the triangle and H is the height of the prism.

In this case, the base of the triangle is 1 / 2 bh = 1 / 2 (18 x 12) = 108 square ft. The height of the prism is 20 ft. Therefore, the volume of the triangular prism is V = Bh = ((108 sq ft) (20 ft)) cubic ft = 2,160 ft³.

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The perimeter of triangle QRS is 36 cm.

In the given triangle QRS,

SQ + RS + RQ = Perimeter of triangle QRS

Locate SQ:

10 cm = SN = SM (tangents drawn from an external point)

2 cm = QL + QN (tangents drawn from an external point)

SN + NQ = SQ

SQ = 10 + 2 = 12 cm

Locate RS:

RM + MS = RS

8 - 2 = 6 cm RM = RL

MS = 10 cm (given)

Therefore,

RS = 6 + 10 = 16 cm

RQ = 8 cm (given) (given)

Thus:

SQ + RS + RQ = Perimeter

Circumference = 12 + 16 + 8 = 36 cm

The complete question:

"Find the perimeter of triangle QRS

Figure is attached below."

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Thus, 25 newspapers are required to make the most profit.

Profit is the amount of money you have after covering business expenses.

Gross, operational, and net profits are the three basic categories of profit.

Profit potential, p = S p C + C b

S p = Selling price

C = Unit cost of purchase

C b Goodwill lost per unit due to backorders or shortages

p ′ = 12 − 8 + 1.5

=  ₹ 5.5

l = C - C b + C h, where C is the loss per unit.

A = Scrap value/unit

holding cost/unit = C

l = 8 − 2 + 0

l =  ₹ 6

p ( S − 1 ) ≤ p /p + l ≤ p ( s )

At this point, p / p + l = 5.5 / 5.5 + 6 = 0.4783 = 47.83 %

Thus, 25 newspapers are required to make the most profit.

The Complete Question.

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Answer: 3 1/3

2/3 x 5 = 10/3 = 3 1/3

2 x 5/3 = 10/3 = 3 1/3

Answer:

[tex]= \dfrac{10}{3}[/tex]

Step-by-step explanation:

We can rewrite any whole number as itself over 1.

For example, [tex]5 = \dfrac{5}{1}[/tex].

We can use this tactic to rewrite one of the given (equivalent) expressions. I'll use the one on the left side of the equation.

[tex]\dfrac{2}{3} \times 5 = \dfrac{2}{3} \times \dfrac{5}{1}[/tex]

Then, we can simplify the multiplication of fractions by multiplying out the both the numerators and denominators.

[tex]= \dfrac{2}{3} \times \dfrac{5}{1}[/tex]

[tex]= \dfrac{2\times 5}{3 \times 1}[/tex]

[tex]= \dfrac{10}{3}[/tex]

The domain and the range of the functions are:

Function 1

Given that

f(x) = 5x - 2, x < 1

         x - 7, x ≥ 1

The functions in the piecewise function are linear functions

Because there are no hole in the domain value, this means that the range and the domain are the set of real numbers

Function 2

Given that

g(x) = -x , x < -5

         3, x > -5

The functions in the piecewise function are also linear functions

However, there is a hole in the domain value at x = -5

This means that the domain incudes all real values except -5

While the range is 3 and values greater than 5

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The domain and range of the two piecewise functions are:

Please refer to the attached graphs below for each piecewise function's graph.

f(x) = {5x-2, if x < 1}

        {x - 7, if x ≥ 1}

From the given function, we can make the first graph. We know that the domain for each function individually are:

f(x) = 5x - 2, if x < 1

dom f(x) = (-∞,1)

Range = (-∞, 3)

f(x) = x - 7, if x ≥ 1

dom f(x) = (1, ∞)

Range = (-6, ∞)

By combining both function's domains and range, we can find the piecewise function domain and range are:

D =  (-∞,∞) --> include 1

R =  (-∞,∞)

g(x) = {-x, if x < -5}

         {3, if x > -5}

From the given function, we know each domain and range are:

g(x) = -x, if x < -5

dom g(x) = (-∞, -5)

Range = (5, ∞)

g(x) = 3, if x > -5

dom g(x) =  (-5, ∞)

Range = 3

By combining both functions' domain and range, we got:

dom =  (-∞, -5) ∪  (-5,∞) --> not including 5

Range =  (3, ∞)

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the option b is equal to the rational expression when x≠-6?

Answer:

[tex]\dashrightarrow \: \frac{ {x}^{2} - 36}{x + 6} \\ \\ \dashrightarrow \: \frac{( \cancel{x + 6})(x - 6)}{\cancel{x + 6}} \\ \\ \dashrightarrow\boxed{ \: x - 6 \: }[/tex]

therefore , option ( B ) is correct.

• Step 2 was done by keeping in mind the algebraic identity "a² - b² = ( a + b )( a - b)"

hope helpful! :)

Answer:

(-2 - 4) / (-4 - 4) = -2 / 0 = -2

Step-by-step explanation:

The slope of the line passing through the points (-4 [1] [2], 4) and (-4, -2) is -2. This can be calculated using the formula m = (y2 - y1) / (x2 - x1), which in this case would be (-2 - 4) / (-4 - 4) = -2 / 0 = -2.

You Welcome! :)

The least squares approximating line y=zo + zix for each of the following sets of data points is (1, 1), (3, 2), (4, 3), (6, 4)

This line is determined by minimizing the distance between the data points and the line. The method of least squares is used in many areas, including regression analysis and trend analysis.

To find the least squares approximating line for a set of data points, you need to use the following formula:

=> y = b0 + b1x,

where b0 is the y-intercept and b1 is the slope of the line.

You can use this formula to find the values of b0 and b1 that minimize the difference between the data points and the line.

For example, let's take a look at the first set of data points (1, 1), (3, 2), (4, 3), (6, 4). To find the least squares approximating line, we need to calculate the values of b0 and b1.

This can be done by using a mathematical formula that involves finding the sum of the squares of the differences between the data points and the line.

Therefore, option (a) is correct.

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The amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage is $55,398.6

Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is often reported as an annual percentage rate, interest expense or revenue is sometimes expressed as a dollar figure (APR). The compensation a lender or financial organization receives for giving out money is called interest.

Given a family wants to purchase a house that cost $135,000,

down payment = $20,000

mortgage = $1,15,000

Case 1: For a 15-year mortgage their monthly payment would be 776.85

there will be 12 payments in a year

total amount to be paid in 15 years = 15*12*776.85

total amount to be paid in 15 years =  $1,38,033

Case 2: For a 30-year mortgage their monthly payment would be 537.31

total amount to be paid in 30 years = 30*12*537.31

total amount to be paid in 30 years = $1,93,431.6

the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage is

$1,38,033 - $1,93,431.6 = $55,398.6

Hence the amount they would save is $55,398.6.

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The correct question is,

determine the amount they would save on the cost of the house if they selected the 15 year mortgage rather than the 30 year mortgage.

The number of ways in which the runners can finish first, second and third as required from the task content is; 166,320 ways.

It follows from the task content that the number of ways in which runners can finish first, second and third is to be determined from a total of 56 runners.

On this note, this situation describes an arrangement and hence is best represented as a permutation as follows;

⁵⁶P₃

= 166,320.

Ultimately, the number of ways in which the runners can finish is; 166,320.

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The measure of angle x = 50° and y = 40°.

A angle is formed when two rays intersect. The point of intersection is called the vertex point .

Given is that in rectangle ABCD in which -

m ∠EAB = (4x+6)°  

m ∠DEC = (10−11y)°

m ∠EBC = 60°

We can write -

∠AEB = ∠DEC = (10 - 11y)°

Now, we know that the external angle is the sum of two interior opposite angles. So -

∠EBC = (4x + 6) + (10 - 11y)

4x - 11y + 16 = 60

4x - 11y = 54

and

(4x + 6) + (10 - 11y) + 30 = 180

4x - 11y = 144

Solving graphically, we get -

x = 50°

y = 40°

Therefore, the measure of angle x = 50° and y = 40°.

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The radius of the pencil is 3.32mm

The formula for determining the volume of a cylinder is expressed as;

V = πr²h

Given that the parameters are;

From the information given, we have that;

The volume of the cylinder = 110 π mm³

The height of the cylinder = 10mm

Now, substitute the values, we get

110π = πr² × 10

Multiply the values

110π = 10πr²

Divide both sides by the coefficient of r², we get;

r² = 110π/10

r² = 11

Find the square root of both sides

r = 3. 32mm

Hence, the value is 3.32mm

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Option A is the correct answer. The probability of the nearest hundredth of the pointer landing on a non-shaded area is 0.66.

An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle. It contains a total of 360° degrees all the way around the center.

To know the Probability of the non-shaded area first we have to add the shaded area.

The sum of the shaded angles 48°+45°+122°+52° =145°.

As we know that the total angle of a  circle=360°.

Now divide the sum of the shaded angles by the total angle of the circle.

i.e=145°/360°

non-shaded area=0.66

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