1. Fill in the blanks:
a) 1 lakh = _______ ten thousand.
b) 1 million = _______ hundred thousand.
c) 1 crore = _______ ten lakh.
d) 1 crore = _______ million.
e) 1 million = _______ lakh.

You have to evaluate the functions for different inputs.

2. g(4)

The function g(x) is defined as follows

This means that the function g(x) has two parts.

• When the value of x is less than five, g(x)=-|1/2x-4|-1

• When the value of x is greater than or equal to 5, g(x)=x²-5

For g(4) you have to use the equation for the first part of the function since x=4 is less than 5

3. f(-7/2)

The function f(x) is defined as:

• When x is less than or equal to -3, f(x)=-5

• When x is greater than -3 and less than 4, f(x)= 1/3x-1

• When x is greater than or equal to 4, f(x)=|x-5|-2

For f(-7/2) you have to determine to which interval of the function does x=-7/2 belongs. If you express the fraction as a decimal value you get that it is -3.5.

This value is less than -3 so we have to use the first part of the function:

The function is constant (horizontal line) at f(x)=-5 until it reaches x=-3

4. h(-1/2)

The function h(x) is defined as follows:

This function has three parts:

• When x is less than or equal to -1, h(x)=x²-1

• When x is greater than -1 or less than or equal to 4, h(x)=4 →for this interval of definition, the function is constant

• When x is greater than 4, h(x)=-4x+1

To determine the value of h(-1/2) you have to determine to which segment it belongs.

x=-1/2 is grater than -1, so the value of h(-1/2) corresponds to the second part of the function:

5. h(6)

You have to determine the value of h(x) when x=6, as mentioned above (item 4.) This function has three parts:

• When x is less than or equal to -1, h(x)=x²-1

• When x is greater than -1 or less than or equal to 4, h(x)=4

• When x is greater than 4, h(x)=-4x+1

x=6 corresponds to the third part of the function, then h(x)=-4x+1

Replace the expression with x=6 and calculate

6. g(6)

You have to determine the value of g(x) when x=6.

This function is defined for two intervals:

• When the value of x is less than five, g(x)=-|1/2x-4|-1

• When the value of x is greater than or equal to 5, g(x)=x²-5

x=6 is greater than 5 so for this value the corresponding definition of the function is g(x)=x²-5

Replace the value of x in the expression and calculate:

7.f(-3/2)

You have to calculate the value of f(x) when x=-3/2, the function f(x) is defined for three intervals:

• When x is less than or equal to -3, f(x)=-5

• When x is greater than -3 and less than 4, f(x)= 1/3x-1

• When x is greater than or equal to 4, f(x)=|x-5|-2

x=-3/2 is greater than -3 but less than 4, so this value of x corresponds to the second interval of the function. For this interval f(x)=1/3x-1

Using proportions, it is found that her new balance after she makes one new transaction for $351 is of $3,861.

A proportion is a fraction of a total amount.

Rae's unpaid credit card balance was $3,744, then considering the APR of 12.5%, when she makes the payment it will be 112.5% of that, that is:

B = 1.125 x 3744 = $4,212.

Considering the payment of $351:

4212 - 351 = $3,861.

Her new balance after she makes one new transaction for $351 is of $3,861.

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Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

\(-3y=-4x+5\) and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

\(y=\frac{4}{3}x-\frac{5}{3}\) So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

\(y-5=-\frac{3}{4}(x-3)\)* and

\(y-5=-\frac{3}{4}x+\frac{9}{4}\) and

\(y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}\) so

\(y=-\frac{3}{4}x+\frac{29}{4}\)** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form

C. The depth of the dish is 96 inches.

The symmetry of the parabola indicates that  when the depth is 6 inches, that the edge is 48 inches (half of 96) to the right and left of the axis of symmetry.

This implies that this parabola passes through (48, 6).

To determine how high the focus is above the vertex. The conic form of a parabola with its vertex at the origin is given as;

y = (1/4c)x²

where;

From the equation above, we can substitute the value of our coordinates and solve for c.

6 = (1/4c)(48²)

24c = 2304

c = 2304/24

c = 96 inches

Thus, the depth of the dish is 96 inches.

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The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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Answer:

x = -8, x =0  and x =6

Step-by-step explanation:

f(x) = 0 means when it crosses the x axis or when y = 0

There are 3 places when it crosses the x axis

x = -8, x =0  and x =6

Answer:

a. 539.54

b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. 540

d. 25.54%

Step-by-step explanation:

Given that:

A polling company reported that 53​% of 1018 surveyed adults said that secondhand smoke is "very harmful."

Complete parts​ (a) through​ (d) below.

a. What is the exact value that is 53​% of 1018​?

The 53% of 1018 is :

=\(\dfrac{53}{100} \times 1018\)

= 0.53 × 1018

= 539.54

b. Could the result from part​ (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why​ not?

No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?

Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 \(\approx\) 540.

d. Among the 1018 ​respondents, 260 said that secondhand smoke is  is "not at all harmful.''  What percentage of respondents said that secondhand smoke is  "not at all harmful"?

Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :

= \(\dfrac{260}{1018} \times 100 \%\)

= 25.54%

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

The utilization of two or more additional numbers that compares is known as the ratio.

The ratio of red to blue in purple 1 and purple 2 will be 1:2 and 1:3, respectively. The table is given below.

Purple #1              Purple #2

Red: Blue             Red: Blue

  1      2                    1      3

 2      4                   2      6

 3      6                   3      9

For the same quantity of blue, the two highlighted rows demonstrate this. Purple 1 then utilizes more red than Purple 2.

Purple 1 is thus a redder hue of purple than Purple 2.

Purple 2 is a more blue-based purple than Purple 1.

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Answer:

the rotated point B is then at (3, -7)

Step-by-step explanation:

the specification says a rotation of -90 degrees (counter clockwise) around the point (0, 0).

a turn by 90 degrees in any direction brings it always into the next quadrant, because every quadrant represents 90 degrees.

the rotated point will have the same distance from the center, of course. and the angle of the connection line center to B to the negative x-axis will be then the same as the angle of the connection line to the rotated point to the negative y-axis.

just think about rotating the original graph by -90 degrees. point B stays on the grid were it is and moves with the grid, and we just flip the coordinate axis.

so, it will be (3, -7).

Z (-7,-1)

When you rotate about the origin, the x and y just become negative :)

The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}. Thus, the correct option is D.

Given that:

A coin is tossed.

A spinner has 3 equal sections: Red, White, and Blue.

The samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The total number of samples is calculated as,

Total samples = 2 x 3

Total samples = 6

The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}.

Thus, the correct option is D.

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Answer:

4

Step-by-step explanation:

2+2 is 4

The equivalent formula that does not involve integrals is A(x) = 2x - 2x^2 + 4x - 4.

The First Fundamental Theorem of Calculus states that if f(x) is a continuous function on the interval [a, b], then the function F(x) = integral^x_a f(t) dt is an antiderivative of f(x), meaning that its derivative is equal to f(x). Therefore, if we have the antiderivative of a function, we can use the derivative to find an equivalent formula without an integral.

In this case, the derivative of the antiderivative of f(t) = 4 - 2t is f(t) = 4 - 2t, which is the original function. So, the equivalent formula for A(x) is A(x) = 2x - 2x^2 + 4x - 4, which does not involve integrals.

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the answer is 10

because

Answer:

The answer is -3/7.

Hope this answer helps.

The solution of the expression will be;

⇒ x = - 3/7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 3.1 = - 3.5x - 4.6

Now,

Solve the equation as;

The expression is,

⇒  - 3.1 = - 3.5x - 4.6

⇒ 3.5x = 3.1 - 4.6

⇒ 3.5x = - 1.5

⇒ x = - 1.5 / 3.5

⇒ x = - 15/35

⇒ x = - 3/7

Thus, The solution of the expression will be;

⇒ x = - 3/7

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Answer:

see explanation

Step-by-step explanation:

Given the translation rule

(x, y ) → (x - 4, y + 2 )

This means subtract 4 from the original x- coordinate and add 2 to the original y- coordinate, that is

a point (4 , - 4 ) → (4 - 4, - 4 + 2 ) → (0, - 2 )

The resulting graph would result in moving input x by --4  horizontally and Output y by +2 vertically.

Translations are defined by saying how much a point is moved to the left/right and up/down. Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically.

Given the point  (x - 4, y + 2), we can clearly observe that the graph would move vertically by +2 units while the input will be in the -ve x-axis direction from right to left and thus will move negatively by -4.

Hence, The resulting graph would result in moving input x by --4  horizontally and Output y by +2 vertically.

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ball starts at 26m

1st bounce = 13 m

2nd bounce = 6.5 m

3rd bounce = 3.25 m

4th bounce = 1.625 m

5th bounce = 0.8125 m

6th bounce = 0.40625 m

7th bounce = 0.203125 m

answer: 0.203125 meters

The equation of the perpendicular line is y = -1/3x

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

y = 3x + 2

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 3

This means that the slope is 2

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/3

The equation of the line is then calculated as

y = mx

Where

m = -1/3

So, we have

y = -1/3x

Hence, the line has an equation of y = -1/3x

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1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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Answer:

The ultimate answer according to the question is is 40 trees in one row.

Step-by-step explanation:

Let no. of trees in one row be X.

There are 42 rows,

or, 42X= 1596

or, X= 1596/42

So, X=38

Now, while rounding off to the nearest ten 38 goes to 40.

Answer:   y=1/8*x+2

Step-by-step explanation:

The equation of any tangent line is y=a*x+b  (1)

To the equation of the tangent line we have to find the coefficients a and b   and the to substitute them to equation (1).

As we know  a=y'(x0) ( where x0=16)

So y'(x)= (√ (x) )' = 1/(2*√x)

a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8

So lets substitute a in equation (1):

y=1/8 *x+b

Now we have to find b

We know that the point (16, 4) belongs to the tangent line.

That means

4=1/8*16+b => 4=2+b => b=2

SO the equation of the tangent line is y=1/8*x+2

Answer:

Step-by-step explanation:

Quarter implies 4. If there were 20 items, and you broke them into quarters, each quarter would have 5 items.

The Percent error of the measurement is -0.5%

What is Percent error ?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error. The precision of the computer device or a measurement error can lead to an approximation error.

The total distance Dani travelled = 1600

The total distance her GPS shows = 1592

Since,

Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100

The Actual number = 1600

The Estimated number = 1592

Percentage Error = ((1592 - 1600) / 1600) x 100

                              = (-8/1600) x100

                              = (-1 / 200) x 100

                              = (-1 / 2)

                              = (-0.5)%

Hence, The Percentage Error is -0.5%

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The perimeter of the smaller figure among the two figures with similarity ratio of 4:3 is 18cm.

A ratio is a number that allows one quantity to be expressed as a fraction of another quantity. Two numbers in a ratio can only be compared if they have the same units. Use ratios to compare two things.  

The similarity of two similar shapes is the ratio of each pair of corresponding sides. Simply put, when two figures are found to be similar, all pairs of corresponding sides have the same proportions. 

According to the information:

Perimeter of larger figure= 24cm

Let, perimeter of smaller figure be "x"

So,

4:3 = 24/x

4/3 = 24/x

⇒x = (24 x 3)/4

⇒x = 72/4

⇒x = 18

Thus the perimeter of smaller figure is 18cm.

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Answer:

18 meters = 1800 milimeters

Step-by-step explanation:

Hope this helps!      :3

plz mark as brainliest!

Answer:

Just search it up. The answer is 1800

Step-by-step explanation:

Type.

Or there's another way.... you multiply if you want to convert a unit that is greater to smaller, and you divide if you want to convert a smaller unit to a larger one.

For example hours to minutes:

You cross out the word that matches. Here it's hour.

3.15 hours X 60 min/1 hour=189 min

189min X 60 sec/1min=11340 sec

and if it's from smaller to greater you divide, get it?

Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

Answer:

\(f(x)\longrightarrow-\infty\), as \(x\longrightarrow+\infty\)

Step-by-step explanation:

We can see that the larger the input, the smaller the output