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1/2 is the factor which converts right angled triangles ΔRPQ to ΔVAQ

Triangle: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane

Both the triangles are right angled triangles at ΔVAQ and ΔRPQ

side AV=3 units and AQ=4 units

side RP=6 units and PQ=8 units

AV is half of RP and AQ is half of PQ

AV=1/2(RP) and AQ=1/2(PQ)

1/2 factor converts ΔRPQ to ΔVAQ

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Answer:

Dennis needs to sell 54 more

Step-by-step explanation:

Answer:

Perimeter

P = 24.2

Step-by-step explanation:

Perimeter

P = 9 + √(6^2 + 6^2) + √(3^2 + 6^2) = 24.2

We are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

Given that, n=550 (Sample size, Number of trials), p=0.6 (Sample proportion) and 1−α=0.9 (Confidence level).

The confidence interval is one of the most used for estimating population parameters in statistics. It is common to perform an interval with a known confidence level to find a range of values that show us information about the population.

Using the standard error of the sample proportions [tex]ME=z_{\alpha /2}.\sqrt{\frac{p(1-p)}{n} }[/tex]

[tex]=z_{0.9/2}.\sqrt{\frac{0.6(1-0.6)}{550} }[/tex]

[tex]=z_{0.45}.\sqrt{\frac{0.6(0.4)}{550} }[/tex]

= 0.1736 × √(0.24/550)

= 0.1736 × 0.0208

= 0.00361

Confidence interval = 0.6±0.00361

= (0.6+0.00361, 0.6-0.00361)

= (0.6036, 0.5963)

Therefore, we are 90%sure that the interval (0.6036, 0.5963) contains the true population proportion.

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The total mass of sugar used is 1.7 kg.

The mass of sugar he has left is 0.3 kg.

In mathematics, a fraction is a numerical value that represents a portion of a whole. The entire can be any number, a specific value, or an item. Fractions are written as p/q.

Given:

Total mass of sugar Mr tan has = 2 kg

Fraction of sugar used to make dessert = 1/4 kg

Fraction of sugar used to bake some cakes = 3/5 kg

The total mass of sugar used is calculated as,

= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes

Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg

Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg

Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg

Mass of sugar left =  Total mass of sugar - Total mass of sugar used

                             = 2 kg - 1.7 kg  = 0.3 kg

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The approximate height of the door is 84in

A rectangle is a polygon with 4 sides and 4 right angles.

It has 2 lines of symmetry and one of that lines is called a diagonal.

Rectangles are cut into two to form right angled triangles.

The rectangle is divided into two right angled triangles

with a diagonal of 94 inches, base = 42 inches.

The height of the rectangle, the base and the diagonal form a right angled triangle.

By Pythagoras,

[tex](94)^{2}[/tex] = [tex](42)^{2}[/tex] + [tex](height)^{2}[/tex]

8836 = 1764 + [tex](height)^{2}[/tex]

[tex](height)^{2}[/tex] = 8836 - 1764 = 7072

height = [tex]\sqrt{7072}[/tex] = 84 inches

In conclusion, the height of the rectangular door is 84 inches approximately.

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Answer: B is the answer to the question

Step-by-step explanation:

[tex]5 \div 6 \times 2100 = 1750[/tex]

when the minute hand rotated through 1260° time will became 5:30 PM

Complete angle:-

                             A complete angle is a type of angle that measures 360°.A complete angle deals with one full rotation measuring 360°.

      In an hour or in 60 minute, minute hand covers a 360° angle.

   According to question,

                              initially it is 2:00PM,that is minute hand at 12 and hour hand at 2

       it is given that minute hand has rotated through 1260°

                        1260° = 3 x 360° + 180°

                                                             which means minute hand will have three complete rotation and one half rotation.

            when minute hand rotated through 360° angle then hour hand will move from 2 to 3.

              And again in second rotation, when minute hand rotated through 360° angle then hour hand will move from 3 to 4.

             Again in third rotation, when minute hand rotated through 360° angle then hour hand will move from 4 to 5.

           As of now, minute hand have taken three complete rotation and so hour hand reached at 5

                 Now, when minute hand rotated through 180° (one half rotation),minute hand will reach at 6 from 12.

           So, right now the position of hour hand is between 5 and 6 and the position of minute hand at 6.

            hence,  time will be 5:30 PM

                            Option A is correct

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By using distributive property, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

In order to quickly solve equations, a number is distributed across the integers in the brackets. When using the distributive property of multiplication, for instance, to resolve the expression 4(2 + 4), we would do so as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24.

We have,

[tex]-3\left(7x^{2}+3x\right)[/tex]

Using Distributive Property, A(B+C) = AB+AC

[tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

Hence, [tex]-3\left(7x^{2}+3x\right) = -21x^{2} -9x[/tex]

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The probability that x is less than or equal to 38 is 0.9861.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 38

μ = mean = 5

σ = standard deviation = 15

z-score = (38 - 5) / 15

z-score = 33 / 15

z-score = 2.2

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score =  2.2

probability = 0.9861

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The Point-slop form for X is X = 5Y+15, and the Point-slop form for Y is [tex]\frac{X-5}{5}[/tex],  for the line with a slope 1/5 and passing through the point ​(-4​, -5​).

Finding the slop form using the formula  [tex]m=\frac{Y_{1} - Y_{2} }{X_{1} -x_{2} }[/tex]

The equation for x.

Here m=1/5.

∴  [tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]

[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4)

[tex]\frac{1}{5}[/tex] × X+5 = Y+4

X+5= 5Y+2O

X=5Y+20-5

X=5Y+15

∴Point-slop for X is X=5Y+15.

Solving for Y.

[tex]\frac{1}{5}=\frac{Y-(-4)}{X-(-5)}[/tex]

Simplifying and Solving.

[tex]\frac{1}{5}[/tex] × X-(-5) = Y-(-4), Taken  0n  X-(-5) the right side.

       [tex]\frac{1}{5}[/tex] × X+5 = Y+4

X+5= 5Y+2O

X+5-20=5Y

X-15=5Y

Taking 5 0n the right side.

[tex]\frac{X-15}{5}[/tex] = Y

∴ Point-slop form for Y is [tex]\frac{X-5}{5}[/tex]

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The number of times the value 1.5 exceeds the value 0.15 is 10, which is obtained by dividing both values.

We divide a by b to find how many times greater a number is than b; thus, to calculate how many times greater a number is, we use a division operation.

To determine how many times greater a number is than b, we compare them, i.e. divide them.

As an example:

50/10 = 5, indicating that 50 is five times greater than ten.

We must determine how many times the value 1.5 is greater than the value 0.15.

For this , let us divide 1.5 by 0.15

Number of times the value is greater = 1.5/0/15

                                                              = 10

Therefore, the number of times the value 1.5 is greater than the value 0.15 is 10.

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Answer:

(-3,6)----> (0,5)

(9,-8)----> (6,-9)

Step-by-step explanation:

The translation T(3,-1) shows that we need to add three units to the x-coordinates and -1 unit to the y-coordinates, as follows in the answer above.

Answer: 7.3 < 12

Step-by-step explanation:

The value of the given monomial, -8[tex]m^{4}n^{4}[/tex], when m = 0.5 and n = 2 is -8.

According to the question,

We have the following monomial:

-8[tex]m^{4} n^{4}[/tex]

We have m = 0.5 and n = 2.

Now, putting these values of m and n in the monomial:

-8 [tex](0.5)^{4} (2)^{4}[/tex]

(Please note that when a power is there on a number then it means that to solve the expression we have to multiply the base as many times as the given power. For example, in this case, we will multiply 2 four times and the result will be 16. This concept is applicable to every expression we are solving whether the base is in decimal or in fraction or a integer.)

-8*0.0625*16

-128*0.0625

-8

Hence, the value of the given monomial is -8.

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The correct option is A, the system of inequalities is:

On the graph, we can see two lines.

One is a dashed line (so we need to use the symbols > or < ) and it is horizontal, such that the line is:

y = -3

And the shaded region is above that line, so the inequality is:

y > -3.

The other inequality is below a line y = -x, and we can see that the line is solid (so we use the symbols ≤ or ≥).

Then here the inequality is.

y ≤ -x

Then the system of inequalities is:

y > -3.

y ≤ -x

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Answer:

-5 1/3

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

A negative times a negative is a positive. So your answer will be positive.

When multiplying a whole number times a fraction, you multiply the whole (big) number times the top number (numerator) and just keep the bottom number (denominator) the same.

5 × 1/3

Is 5×1 on TOP and just keep the 3 on the bottom.

(5×1)/3

5/3

5/3 is the best answer, but if you are being asked for a "mixed number" then 5/3 is the same as 1 2/3.

Answer:

0

Step-by-step explanation:

use a calculator =)

or

[tex]\sqrt[3]{125} = 5\\\sqrt{25} = 5\\ so , 5 - 5 = 0[/tex]

Answer:

hello!

Step-by-step explanation:

firstly lets convert the mixed fraction into a single fraction itself

thats 5/4

if each rope contributes to 5/4 meters then a rope with 8 pieces would be 5/4 x 8 which gives you the answer 10

Answer:

Step-by-step explanation:

The distance between two points is represented by the following equation;

Therefore, if the endpoints of WX are (-5,-1) and X(2,6):

[tex] = 9( - 6 + 8i) - 3i( - 6 + 8i) \\ = - 54 + 72i + 15i - 24 {i}^{2} \\ = - 54 + 87i - 24 {i}^{2} [/tex]

ATTACHED IS THE SOLUTION

Answer:

1. How much did the 2 lb of the first type of candy cost the owner?

2x

2. How much did the 3 lb of the second type of candy cost the owner?

3*1.5 = 4.5

3. How much did the two types of candy cost the store owner in total?

2x + 4.5

4. How much money will the store owner get if she sells all of the new mixture?

(2 + 3)*2.5 = 12.5

5. Write an equation to find the cost per pound of the first candy

2x + 4.5 = 12.5

6. Solve the equation to find the owners cost of the first candy per pound

2x + 4.5 = 12.5

2x = 8

x = 4

Answer:

28

Step-by-step explanation:

2 x 7 = 14

Number should be in between 26 and 31

So,

14 x 2 = 28

28 has one of its prime factors as 2 and 7.

Hence,

28 is the number which is in between 26 and 31 it has the prime factors of 2 and 7.

Answer:

Step-by-step explanation: Given prime factors: 2, 7

 By multiplying, 2 X 7= 14

 Given, number is between 26 and 31

       therefore, 14 X 2= 28 (since 2 is a prime factor)

        ans: 28

Answer:

x=8

larger angle=113

smaller angle=67

Step-by-step explanation:

8x+3=a(Vertically opposite angle)

a+14x+1=180°(Angles between parallel line)

8x+3+14x+1=180°

22x+4=180°

22x=176°

x=8

omg what is the......................

Answer:

10

Step-by-step explanation:

486-466 = 20

1/2 x 20 = 10

:]

Answer:

an expression that equals 10

Step-by-step explanation:

486 - 466 = 20

1/2 of 20 is 10

You don't list choices.

You need an expression that equals 10.

Answer:

x=1

Step-by-step explanation:

3x−1+2=4

Add −1 and 2 to get 1.

3x+1=4

Subtract 1 from both sides.

3x=4−1

Subtract 1 from 4 to get 3.

3x=3

Divide both sides by 3.

x=

3

3

​

Divide 3 by 3 to get 1.

x=1

The formula for calculating simple interest is expressed as

I = PRT

where

I represents the interest

P represents the principal or initial amount invested

R represents the interest rate

T represents the time in years

From the information given,

P = 11750

R = 7.5%

Recall, percentage is expressed in terms of 100. Thus,

R = 7.5/100 = 0.075

T = 3

By substituting these values into the formula,

I = 11750 x 0.075 x 3

I = 2643.75

Total interest = 2643.75 rupees

Total amount = principal + total interest

By substituting the values,

Total amount = 11750 + 2643.75

Total amount =

Answer: 11750 + 2643.75

Step-by-step explanation:

The formula for calculating simple interest is expressed as

I = PRT

where

I represents the interest

P represents the principal or initial amount invested

R represents the interest rate

T represents the time in years

From the information given,

P = 11750

R = 7.5%

Recall, percentage is expressed in terms of 100. Thus,

R = 7.5/100 = 0.075

T = 3

By substituting these values into the formula,

I = 11750 x 0.075 x 3

I = 2643.75

Total interest = 2643.75 rupees

Total amount = principal + total interest

By substituting the values,

Total amount = 11750 + 2643.75

The exponents' best option will be determined by

a + b's value is seven.

How often a number is multiplied by itself is indicated by the exponent.

For instance

In this case, 2 is multiplied by 4

Now in ( m times)

The base is designated as a, and the power is designated as m.

There are some indexing laws.

[tex]1)a^m \times a^n = a^{m+n}\\2)\frac{a^m}{a^n} = a^{m-n}\\3) (a^m)^n = a^{mn}\\4) (ab)^m = a^mb^m\\5) a^0 = 1\\6) a^{-m} = (\frac{1}{a})^m[/tex]

Here,

[tex](2^a)(2^b) = 128\\[/tex]

[tex]2^{a+b} =2^7[/tex] [According to laws of indices]

[tex]a + b = 7[/tex]

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Complete Question

If [tex](2^a)(2^b) = 128\\[/tex], then a  + b is equal to?