(2)

a) Solve 15n > 12n + 18

+

o

b) n is an integer and -2
Write down the possible values of n,

from smallest to largest.

All values must be separated by commas. Eg

(3)
. 5 =

Total marks: 5

If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.

If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.

The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.

Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.

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Here we have to compare a standard deviation of test statistic with the expected standard deviation of the population. So a chi square test is used. The chi square value got after the calculations is 31.348.

It is a hypothesis testing method. Significance level is 0.05.

The equation for chi square is

   Χ² = (n-1)s²/ σ₀²

        Lets look into what each term  means

       n is the sample size which is 40

        s² is the sample variance = 2.6²

       σ² is the population variance =2.9²

X² = (40-1)×2.6²/ 2.9²

    = 39× 6.76/ 8.41

    = 31.3483947681

    = 31.348

So the X² value is 31.348

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Answer:

y = 1/80

Step-by-step explanation:

[tex] \sf\frac {5}{8y} + 7 = \frac{3}{4y}- 3[/tex]

Substract 7 from both sides

[tex] \sf\frac {5}{8y} + 7 - 7 = \frac{3}{4y}- 3 - 7[/tex]

Calculate

[tex] \sf\frac {5}{8y} = \frac{3}{4y}-10[/tex]

Substract 3/4y from both sides

[tex] \sf\frac {5}{8y} - \frac{3}{4y} = \frac{3}{4y} - \frac{3}{4y} -10[/tex]

Calculate

[tex] \sf\frac {5}{8y} -\frac{3}{4y}= -10[/tex]

L.C.M = 32y²

[tex] \sf \frac{−4y}{ {32y}^{2} } = -10[/tex]

-4y/32y² Divide further

[tex] \sf \frac{ - 4}{ 32y } = -10[/tex]

Divide further

[tex] \sf \frac{ - 1}{ 8y } = -10[/tex]

Cross - multiply

[tex] \sf \: 8y \times - 10 = - 1[/tex]

Multiply

[tex] \sf \: - 80y = - 1[/tex]

Divide both sides by -80y

[tex] \sf \: \frac{ - 80y}{ - 80} = - \frac{ - 1}{ - 80} [/tex]

Calculate

[tex] \sf \: y = \frac{1}{80} [/tex]

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Emmanuel weighs 150 pounds. about 2 hours will it take him to metabolize one standard drink

Every hour, the body processes one normal drink. If you have 5 standard drinks, your body will take 5 hours to absorb the alcohol.

In general, the liver can digest one ounce of liquor (or one standard drink) in one hour. If you consume more than this amount of alcohol, your system will get saturated, and the excess alcohol will accumulate in your blood and physiological tissues until it can be metabolized.

It takes your liver around an hour to break down the amount of alcohol in a standard alcoholic drink (one beer, one glass of wine, or one shot).

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The problem is given as follows:
Prove: ΔLUZ ≅ ΔIDA

The triangles above can be said to be congruent because:

[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)

[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides)

[tex]\overline{UZ}[/tex] ≅ [tex]\overline{AD}[/tex] (Corresponding sides)

It is also given that:

m ∠ ULZ ≅ m ∠ ADI

since

[tex]\overline{ZL}[/tex] ≅ [tex]\overline{AI}[/tex] (Corresponding sides)

[tex]\overline{LU}[/tex]≅ [tex]\overline{DI}[/tex] (Corresponding sides) and

m ∠ ULZ ≅ m ∠ ADI ;

We can thus conclude that the ΔLUZ  ≅ ΔIDA

When two triangles are congruent, one can be moved (through one or more stiff movements) to coincide with the other. All congruent sides and angles will be found.

The triangles are congruent if two sides and the included angle of one triangle are congruent to the corresponding sections of another triangle. [Side - Angle - Side]

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The length of the north side of the house is 2x^2 + 9x - 32

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

The figure

On the figure, we have

North side = 5x - 4 + x^2 - 23 + x^2 + 4x - 5

Evaluate

North side = 2x^2 + 9x - 32

Here, we have

Length = 2x + 1

Width =  x^2 + 4x - 5

So, we have

Area = (2x + 1) * (x^2 + 4x - 5)

Area = 2x^3 + 8x^2  -10x + x^2 + 4x - 5

Area = 2x^3 + 9x^2 - 6x - 5

Here, we have

Length = 5x - 4

Width =  5x + 4

So, we have

Area = (5x - 4) * (5x + 4)

Area = 25x^2 - 16

From the figure, we have

Dimensjon = 5x - 4 by (2x + 1 + x + 6 - 5x - 4)

Dimensjon = 5x - 4 by - 2x + 3

Hence, the dimension of the bathroom is 5x - 4 by - 2x + 3

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With a sales tax rate of 7.8%, the tax amount is $11.72.

A sales tax rate is the percentage of the sale price of a good or service that is added on as a tax. It is usually applied to the final purchase price of a product or service and is paid by the consumer at the time of purchase.

Since the sales tax rate is 7.8% and Kiara buys a box of dirt priced at $150.24. Thus, the tax amount can be determined as follows:

Tax amount  = 7.8/100 × $150.24

Tax amount  = $11.72

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Answer: 13/20

Step-by-step explanation: First to find the first part, we need to find a common denominator. So we must ask ourselves, which number is a multiple that both 5 and 4 have in common? The answer then would be 20. So, it would look like this:

[tex]\frac{1}{4} = \frac{?}{20}[/tex]

[tex]\frac{2}{5} = \frac{?}{20}[/tex]

So to find what "?" equals for both fractions, we must use this formula:

Amount =  Right denominator / Left denominator (1st part)

So, now we do 20 / 5 and 20 / 4

20 / 5 = 4

20 / 4 = 5

So, the 2nd part is taking the quotient from that and multiplying it by the left numerators. This would look like this:

5 * 1 = 5

4 * 2 = 8

So your "?" should look like this:

[tex]\frac{1}{4} = \frac{5}{20}[/tex]

[tex]\frac{2}{5} = \frac{8}{20}[/tex]

Then, you'd just add! So, 8 + 5 = 13 and 20 + 20 would stay that same ; 20. So your result is [tex]\frac{13}{20}[/tex]

I hope this helped!

Answer:

x = 15

Step-by-step explanation:

Because the first part is division.... x/5, you'd want to multiply by that same number to get X alone. So you'd multiply by 5

Because of that

x = (3)(5)

x = 15

[tex]\dfrac{x}{5} =3[/tex]

Multiply both sides by 5:

[tex](\dfrac{x}{5} )\times5=(3)\times5[/tex]

[tex]\fbox{x = 15}[/tex]

For Figure 2, Triangles are congruent by SSS (side side side).

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now ,

As in given figure for triangles

2 sides of both are parallel and one is common for both

Hence,

           These are congruent by SSS theorem.

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Answer:

4x(7x5) = 4x(35)

To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 7x5 = 35. Then we can multiply 4 with that result, which gives us 4x35 = 140. So the final value of the expression is 140.

Answer: 140

Step-by-step explanation:

4 x (7 x 5)

7 x 5 = 35

4 x 35

= 140

Answer:

B

Step-by-step explanation:

tangent formula is the line facing the angle divided by the shorter one. so 1/root3

Answer:

Option B.

[tex]tan(30)=\frac{1}{\sqrt{3} }[/tex]

Step-by-step explanation:

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse.

TOA is for tangent.

So we can say the tangent of angle x is the opposite side divided by the adjacent side.

[tex]tan(x)=\frac{O}{A}[/tex]

In this triangle we are given

[tex]O=1\\A=\sqrt{3} \\H=2[/tex]

Therefore

[tex]tan(30)=\frac{1}{\sqrt{3} }[/tex]

The height of the trapezoid with an area of 24cm² and base lengths of 9 cm and 7 cm is 3cm.

A trapezoid is simply a quadrilateral with at least one pair of parallel sides.

The area of a trapezoid is expressed as;

A = 1/2(a+b)h

Given that;

Plug in the values into the above formula and solve for h.

A = 1/2(a+b)h

A = 1/2(a+b)h

2A = (a+b)h

2A/(a+b) = h

h = 2A/(a+b)

h = ( 2 × 24cm² ) / ( 9cm + 7cm )

h = 48cm² / 16cm

h = 3cm

Therefore, the value of height h is 3cm.

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Line a which passes (1, 4) has a constant of proportionality of 4.

Line b runs through (5, 2), with a constant of proportionality of 2/5.

The constant of proportionality is often represented by the letter "k" and it is used in a mathematical relationship known as a proportionality relationship. The proportionality relationship can be written as y = kx, where y and x are the two variables and k is the constant of proportionality.

This means that the value of y is directly proportional to the value of x and is equal to k times the value of x. The value of k can be found by dividing the value of y by the value of x, when the two variables are in proportion.

Line a passes through the (1, 4), therefore:

constant of proportionality = y/x = 4/1 = 4.

Line b passes through the (5, 2), therefore:

constant of proportionality = y/x = 2/5.

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Answer:

-45

Step-by-step explanation:

f(x) = -2x² + 5

f(-5) = -2(-5)² + 5

= -2(25) + 5

= -2 × 25 + 5

= -50 + 5

= -45

Answer:

1.9

Step-by-step explanation:

11.1 /3 =3.7 for beads + pendants per necklace

pendant =3.7-1.8 =1.9

m is the angle formed by the two parallelogram sides that are next to each other. Because all angles in a parallelogram are equal, m is equal to all other angles in the parallelogram.

A parallelogram is a four-sided form having two parallel sides and four right angles on each side. Both sides are straight and opposite sides are equal in length. A parallelogram's opposing angles are also equal.

M is the angle subtended by the parallelogram JKLM. A parallelogram is a four-sided form with parallel and equal-length opposing sides. A parallelogram's angles are also equal in size. As a result, m is an angle of the parallelogram JKLM and is proportional to the other angles of the parallelogram JKLM.

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The predicted average rate of change of the company's sales turnover, in millions of dollars, over the interval [9, 11] is $92.08 per year.

To find the predicted average rate of change of the company's sales turnover over the interval [9, 11], we need to find the slope of the line that best fits the data points provided.

The slope of the line can be calculated using the formula:

(change in y) / (change in x) = (S(x2) - S(x1)) / (x2 - x1)

We can use any two of the provided data points to find the slope. Using the data points (9, $1,061.08) and (7, $876.92), we get:

(change in y) / (change in x) = ($1,061.08 - $876.92) / (9 - 7) = $184.15 / 2 = $92.08 per year

This is the average rate of change of the company's sales turnover over the interval [9, 11]. So the answer is C. $92.08 per year.

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Awnse choice cAnswer:

Step-by-step explanation:

Answer:

x = 140 degrees

Step-by-step explanation:

this polygon has 6 sides

to find the number of degrees of the six interior angles you can use this formula:

(n-2)*180 where 'n' equals the number of sides

(6-2)*180 = 4(180) = 720 degrees

starting with the 'x' angle and going clockwise, we have the following:

x + 90 + 104 + 123 + 155 + 108 = 720

x + 580 = 720

x = 720 - 580

x = 140

The cost of one steak burger is $4.5 and the cost of one order of fries is $2.25.

To find a cost using an equation, you need to first identify the variables involved in the equation.

Variables are values that can change, such as the price of an item or the quantity of an item. Next, you must determine the value of each variable.

Once you have all the values, plug them into the equation and solve for the cost. For example, if you have an equation where x is the cost, y is the quantity, and z is the price per item, you would plug in the values of y and z and solve for x.

The answer you get would be the cost of the item. Additionally, you can use the equation to find the cost of multiple items by changing the value of the variable y to represent the amount of items you need.

After plugging in the new values into the equation, you can solve for the cost of all the items.

Let x be the fries and y be the steak burgers.

From the following information, the equation are as follows:

2x + 3y = 18 ---------equation 1

3x + 2y = 15.75 -------equation 2

To find cost of one steak burger and cost of one order of fries,

Multiply by 3 in equation 1 and 2 in equation 2,

6x + 9y = 54 -------3

6x + 4y = 31.5 -----4

Subtracting the equation 3 and 4, we get

5y = 22.5

y = 22.5/5

y = 4.5

Substitute y=4.5 in eq 1,

2x + 3(4.5) = 18

2x = 4.5

x = 2.25

∴ The cost of one steak burger is $4.5

∴The cost of one order of fries is $2.25.

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The distance travelled by Yusuf in 2 hours is 104 miles.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given that, Yusuf drove 156 miles in 3 hours.

We determine the speed of Yusuf.

Speed = Distance / time

Speed = 156 miles / 3 hours

Speed = 52 miles per hour

Now, the distance travelled in 2 hours will be;

Speed = Distance / time

Distance = Speed × time

Distance = 52 miles per hour × 2 hours

Distance = 104 miles.

Therefore, the distance covered is 104 miles.

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Answer:

(3x+4)+55°+85°=180°

(3x+4)+140°=180°

(3x+4)=180°-140°

(3x+4)=40°

3x+4=40

3x=40-4

3x=36

x=12

(3x+4)

(3×12)+4

=40°

Answer:

d

Step-by-step explanation:

The set up percent equation is:

4600 = m . 5000

The percent of books that are fiction will be:

m = 92%.

Now, According to the question:

A relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Number of books in the town's library = 5,000

Number of books that are fiction= 4,600

The set up percent equation is:

4600 = m . 5000

where, m is the books' fiction

The percent of books that are fiction will be:

m = 4600/5000 × 100

m = 92%.

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Answer: Your answer would be 2x ⋅ (2x) ⋅ 11

Step-by-step explanation: I hope this helps!

Answer: 16/24

Step-by-step explanation: You should convert 7/8 and 2/3 to get a common denominator, in this situation the common denominator is 24. You multiply 2/3 by 8 on both sides of the fraction and the same with 7/8 except with 3. When you convert it 7/8 becomes 21/24 which is the total amount of grapes she bought, the amount she used comes out to be 16/24.

1.21 Canadian dollars is equivalent to 1 US dollar

A monetary exchange rate, also known as a foreign exchange rate, is the rate at which one currency can be exchanged for another. Exchange rates are determined by the foreign exchange market and can fluctuate based on supply and demand.

Since an automobile in Toronto sells for 25,500 Canadian dollars and the same car sells in Detroit for 21,000 US dollars.

Thus, 25,500 Canadian dollars equivalent in US dollars will be:

25,500 Canadian dollar /21,000 US dollars  = 1.21

Thus, 1.21 Canadian dollar is equivalent to 1 US dollar dollars

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The percent error in this measurement would be 16%.

1. Calculate the difference between the measured speed and the actual speed: 5 mph - 4.2 mph = 0.8 mph

2. Calculate the percent error: (0.8 mph / 4.2 mph) x 100 = 19.05%

3. Round to the nearest whole number: 19.05% = 19%

The percent error in this measurement is 19%, which means that the measured speed was 19% higher than the actual speed.

This can be caused by a variety of factors, including the radar gun being set to an incorrect sensitivity, the speed of the ball being too high for the radar gun to accurately measure, or the radar gun not being able to accurately detect the speed of the ball due to environmental factors such as wind or lighting.

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If 40% of Belorussian territory is covered in forests , and the total area is 80153 mi² , then the percent that is not covered in forests is 60% and land area is  48,091.8mi²  .

the total land area of Belorussian territory is = 80153 mi²  ;

the percent of land area covered in forest is = 40% ;

So , the percent that is not covered in Forest is = 100 - 40 = 60% ;

and the land area not covered in forest is = 60% of 80153 ;

= 0.6 × 80153 ;

= 48,091.8 .

Therefore , the percentage that is NOT forests is 60% .

The given question is incomplete , the complete question is

Over 40% of Belorussian territory is covered in forests, this is why they have a green stripe on their flag is Belarus total area is 80153 mi² , What percentage is NOT forests ?

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7.67 times 10^-² in standard notation can be written as 0.0767.

To convert scientific notation to standard notation, you can simply move the decimal point to the left or right as many times as indicated by the exponent of the power of 10. In this case, the exponent is -2, so you move the decimal point 2 places to the left. The result is 0.0767.