What is 3/10 of 1/2 metre and why?

Answer:

z = -4 1/2

Step-by-step explanation:

1. First change the mixed fractions to improper fractions so it's easier

\(\frac{16}{5\\}/(z-\frac{1}{2}) = \frac{8}{3}/(z+\frac{1}{3})\)

2. Simplify

\(\frac{32}{5(2z-1)} = \frac{8}{3z+1}\)

3. Cross multiply

\(32(3z+1) = 5(2z-1) * 8\)

4. Simplify again (distributive property)

\(32(3z+1) = 40(2z-1)\)

5. Distributive property

\(32(3z+1) -> 96z+32\)  

\(40(2z-1) -> 80z-40\)

\(96z+32=80z-40\)

6. Subtract 32 from both sides

\(96z+32-32 = 80z-40-32\)

7. Simplify

\(96z = 80z-72\)

8. Subtract 80 from both sides

\(96z-80z=80z-72-80z\)

9. Simplify

\(16z=-72\)

10. Divide both sides by 16

\(\frac{16z}{16}=\frac{-72}{16}\)

11. Simplify

\(z=-\frac{9}{2} -> also = -4\frac{1}{2}\)

Sorry if it was too long but hope this helps! :)

And also try using symbolab cuz it gives step by step explanations it's really good!

The value of the equation f ( x ) is

f ( x ) = x³ + x² - 8x - 12

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( x + 2 )²( x -3 )   be equation (1)

Now , on simplifying the equation , we get

f ( x ) = ( x + 2 )²( x -3 )

f ( x ) = ( x² + 4x + 4 ) ( x - 3 )

Now , multiplying each term with ( x - 3 ) , we get

f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4

f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12

On simplifying the equation ,we get

f ( x ) = x³ + x² - 8x - 12

Now , the value of the equation f ( x ) = x³ + x² - 8x - 12

On graphing the equation , we get

The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below

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Answer:

Letter:C

Step-by-step explanation:

#CARRY ON LEARNING

Answer:

the ratio of the workers is 3:2

Answer: 45 degrees

Step-by-step explanation:

We know that :

\(\bigstar \ \ \boxed{\sf{sin\theta = \dfrac{Opposite \ Side}{Hypotenuse}}}\)

From the figure, We can notice that the side which is opposite to θ is 15 units

⇒   Opposite side = 15

We need to find the Length of Hypotenuse using Pythagorean theorem which is :

⊕   (Hypotenuse)² = (1st Leg)² + (2nd Leg)²

⇒   (Hypotenuse)² = (8)² + (15)²

⇒   (Hypotenuse)² = 64 + 225

⇒   (Hypotenuse)² = 289

⇒   Hypotenuse = Square root of 289

⇒   Hypotenuse = 17

\(\sf{\implies sin\theta = \dfrac{15}{17}}\)

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The value οf P(x > 104) is 0.1587 οr apprοximately 15.87%.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο find the prοbability οf P(x > 104) fοr a nοrmal distributiοn with mean οf 98 and standard deviatiοn οf 6, we need tο standardize the value οf 104 using the fοrmula:

z = (x - μ) / σ

where z is the standard scοre, x is the value we want tο find the prοbability fοr, μ is the mean οf the distributiοn and σ is the standard deviatiοn.

Plugging in the values, we get:

z = (104 - 98) / 6 = 1

Nοw we need tο find the area tο the right οf this value οn the standard nοrmal distributiοn table οr calculatοr.

Using a standard nοrmal distributiοn table οr calculatοr, we find that the area tο the right οf z = 1 is 0.1587.

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Answer: B 11/15

Step-by-step explanation: 11/15 = 22/30> 20/30

but 11/15 = 110 /150 < 120/150 = 30/50

Answer:

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Step-by-step explanation:

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Answer:

Cosine theta equals x, sine theta equals y and tangent theta equals y over x,

Step-by-step explanation:

Cos0=sin (90 degrees -0)

Sin0= cos ( 90 degrees -0)

Answer:

sin θ = Perpendicular / Hypotenuse

Step-by-step explanation:

The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse. sin(θ + 2nπ) = sin θ for every θ

Answer:

66.67% probability that all selected components function properly

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the components are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

Desired outcomes:

2 components which function properly, from a set of 5. So

\(D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10\)

Total outcomes:

2 components, from a set of 6. So

\(T = C_{6,2} = \frac{6!}{2!(6-2)!} = 15\)

Probability:

\(p = \frac{D}{T} = \frac{10}{15} = 0.6667\)

66.67% probability that all selected components function properly

In this problem, we have that

The value is a statistic because it is a numerical measurement describing some characteristic of a sample.

The answer is option B

The two column table method to prove \(\overline{BC}\) ║ \(\overline{AD}\), (\(\overline{BC}\) is parallel to \(\overline{AD}\)) can be presented as follows;

Step         Statement                     Reasons

1   \({}\)             \(\overline{AB}\) ≅ \(\overline{CD}\)                      Given

\({}\)                \(\overline{BC}\) ≅ \(\overline{AD}\)

2                \(\overline{AC}\) ≅ \(\overline{AC}\)                     Reflexive property

3.  \({}\)          ΔABC ≅ ΔCDA               SSS congruency property

4. \({}\)           ∠BCA ≅ ∠DAC               CPCTC

5.            \(\overline{BC}\) ║ \(\overline{AD}\)                        Converse of Alt. Interior ∠s theorem

Parallel segments or lines are lines that maintain a specified distance between them through their length, and therefore, they do not meet.

The details of the reasons used in the two column method are as follows;

Reflexive property of congruency

The reflexive property of congruency states that each geometric shape or figure is congruent to itself.

SSS congruency rule

The SSS (acronym for Side-Side-Side) congruency rule states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent

Converse of Alt. Int. ∠s theorem

The converse of the alternate interior angles theorem states that if the alternate interior angles formed between two segments are congruent, then the two segments are parallel.

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9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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The missing values are:

angle DGE = 45 degrees

angle EDG = 85 degrees

FD = 10

GD = 10√2

EG = (20 + 13√3) / 2

The missing sides in the figure is solved as follows

angle DGE = angle BAG = 45 degrees (alternate angles are equal)

angle EDG = angle ADC (vertical angles are equal)

angle ADC + 45 + 50 = 180 (sum of angles in a triangle)

angle ADC = 180 - 50 - 45

angle ADC = 85 degrees

Since DGE = 45 degrees and FG = 10

tan 45 = FD / FG

tan 45 = FD / 10

FD = 10

solving for GD

GD² = FD² + FG² = 10² + 10² = 200

GD = 10√2

solving for EG

EG = EF + FG

cos 50 = EF / 13

EF = 13 cos 50 = 13√3 / 2

EG = EF + FG = 13√3 / 2  + 10 = (20 + 13√3) / 2

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Answer:

A is answer

Step-by-step explanation:

please follow me

Answer:

B and C

Step-by-step explanation:

Since m and n are parallel, we can call the two lines extending from the point B transversals.

\(m\angle{1} = 60^\circ\) because they are vertical angles

\(m\angle{2} = 20^\circ\) from the corresponding angles theorem.

\(m\angle{4} = 60^\circ\) from the corresponding angles theorem.

\(m\angle{3} = 100^\circ\) because angle 2 and 4 sum to 80, and \(m\angle{2} + m\angle{3} + m\angle{4} = 180^\circ\) because it is a straight angle.

From this, we can see which ones are true.

A is false because angle 2 is 20 degrees.

B is true because angle 3 is 100 degrees.

C is true because angle 2 + angle 4 = 20 + 60 = 80 degrees.

D is false because angle 2 + angle 3 = 20 + 100 = 120 degrees.

Therefore, only B and C are true.

Answer:

Should be 3 units away from the picture

Step-by-step explanation:

I hope this helps! ;)

The coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

The image of EFG under the dilation with scale factor and center of dilation has to be drawn.

The coordinates or the triangle are E(-2,2), F(-2,-2) and G(2,-2). The new points after the dilation are,

\(E'(-2\times\dfrac{3}{2},2\times\dfrac{3}{2})=E'(-3,3)\\F'(-2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=F'(-3,-3)\\G'(2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=G'(3,-3)\)

The dilated image of triangle EFG is attached below.

Thus, the coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).

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Answer:

I think the answer is B Aponi uses 75 beads

Step-by-step explanation:

150/2 = 75

The statement "The whole number has one digit if and only if the whole number is less than 10" is true for converse statement. Then the correct option is C.

A inverse statement is one that is derived by opposing the supposition and result of a relative clause.

Let p: The whole number has one digit.

Let q: The whole number is less than 10.

The statement "The whole number has one digit if and only if the whole number is less than 10" is true for converse statement.

If p → q, then, q → p

Then the correct option is C.

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In a right triangle, given an angle, the ratio between the opposite side of this angle by the hypotenuse is equal to the sine of the angle. Using this relation in our triangle, we have

The linear function that represent this problem is 7y = 22x + 127, and the temperature at 11:15am is 53.19 degrees

a.

We can take two points from this to find the slope and y - intercept to determine the linear function.

A(6, 59)

B(13, 81)

The slope of a linear equation has a formula of ;

m = y₂ - y₁ / x₂ - x₁

m = 81 - 59 / 13 - 6

m = 22/7

Using the slope to find the y - intercept, we need just one point;

y = mx + c

59 = 22/7(13) + c

59 = 286/7 + c

c = 59 - 286/7

c = 127/7

The equation can be written as;

y = 22/7x + 127/7

rewriting this;

7y = 22x + 127

b. The temperature at 11.15am

Substituting this into the equation;

7y = 22(11.15) + 127

7y = 372.3

y = 53.19 degrees Fahrenheit

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Translation:

The room temperature at 6 am was 59 degrees Fahrenheit. It was increasing linearly until 1 pm when the thermometer marked 81 degrees. a) Write a linear equation that shows the temperature as a function of time in that interval. b) Calculate with this equation the temperature at 11:15 am. Round to the nearest tenth of a degree Fahrenheit if necessary.

The rate of change for the relationship, given the data is -2.25 gallon/min

Velocity is simply defined as the rate of change of displacement with time. Mathematically, it can be expressed as:

Velocity = displacement / time

With the above idea in mind, we can obtain the rate of change for the given relationship. This is illustrated below:

Rate = Change in gallon / change in time

Rate = (36.25 - 38.5) / (8 -7)

Rate = -2.25 / 1

Rate of change = -2.25 gallon/min

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The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

the first one (y=\(\frac{1}{3}\)x+3 and 3x-y=2)

Step-by-step explanation:

y=\(\frac{1}{3}\)x+3 is the red line, while 3x-y=2 is blue.

For red, the slope is 1/3 because the y value of the function only increases by one (between x values 0 and 3) while the x value increases by 3.  The y intercept is also 3.

Blue can also be rewritten as 3x-2=y.  From this, we can get a lot of information.  the y-intercept is 2, and the slope is 3.

Answer:

x=−17

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

1) 2 (5x+9) = 6x+26 --> 10x + 18 = 6x + 26

This is because you would multiply 2 by the numbers inside the parentheses.

2)  10x + 18 = 6x + 26  --> 4x +18 = 26

You would subtract the 6x from each side so it would cancel out the 6 on the right and you would get 4x on the left.

3) 4x +18 = 26 --> 4x = 8

Subtract 18 from both sides canceling out the 18 on the left and giving you 8 on the right.

4) 4x = 8 --> x = 2

Divide both sides by 4.

Answer:

could you repost the same question so i can understand it better ?

Step-by-step explanation:

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Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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