The diagram shows a solid prism of length 15 cm. The cross section of the prism is the trapezium ABCD. Angle DAB = angle CDA = 90°. AB = 9 cm, DC = 6 cm and AD = 4 cm. Calculate the total surface area of the prism.​

The automobile is currently worth Rs 52,488. four years ago, it was worth 80,000.

Present Value A = Rs. 52,488

Depreciation rate r = 10 % per annum

Time t = 4 years

Let initial value be P

We know the formula, A =[tex]$\mathrm{P}\left(1-\frac{\mathrm{r}}{100}\right)^t$[/tex]

We obtain by substituting the supplied values.

52,488 =[tex]$\mathrm{P}\left[1-\frac{10}{100}\right]^4 \\[/tex]

52,488 = [tex]$\mathrm{P}(0.9)^4 \\[/tex]

[tex]$\mathrm{P}=\frac{52488}{0.6561} \\[/tex]

P = 80,000

The complete question is:

The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was

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Answer:

x > -9.5

Step-by-step explanation:

2x - 6 > -25

2x > -19

x > -19/2

x > -9.5

Answer:

y = 3x - 1

Step-by-step explanation:

In order to write this equation in slope intercept form, we first need to find the slope. I will take two points (2,5) and (1,2). We can find the slope either by counting the slope with [tex]\frac{rise}{run}[/tex] or we can calculate it using the formula [tex]\frac{y2-y1}{x2-x1}[/tex]

For the sake of simplicity, we will count it using [tex]\frac{rise}{run}[/tex]. Counting the slope between the two points, we get [tex]\frac{3}{1}[/tex] which simplifies to 3.

The y intercept crosses between the point (0, -1), so our y intercept is -1.

Thus, our equation of the line will be [tex]y=3x-1[/tex]

The required in the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y, which represents the amount of money in the savings account after x weeks.

The value of y depends on the value of x, so y is dependent on x. However, the value of x does not depend on the value of y, so x is independent.

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Answer:

hey! you can use it!!

Step-by-step explanation:

thanks

The converted value of 100 percent to a decimal is equal to 1 which is denoted by 1.00.

Converting 100 percent to decimal is divide 100 by 100 we get

1 percent is ( 1 / 100 )decimal

Substitute the required value of 100 percent we get,

⇒ 100 percent = ( 100 / 100 ) decimals

⇒ 100 percent = ( 1.00 ) decimals

Therefore, the conversion of 100 percent to decimal is given by 1.00 .

The above question is incomplete , the complete question is:

How to convert 100 percent as a decimal ?

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The rate of $18 an hour will be approximately  $157248  for a year .

In order to find how much $18 an hour is in a year,

We need to know how many hours are present in a year.

The number of weeks in 1 year is = 52 weeks ;

and 1 week consists of 168 hours , as 1 week has 7 days and 1 day has 24 hours .

So , 1 year (52 weeks) is = 52 × 168 = 8736 hours .

We get that 1 year consists of 8736 hours ,

Now , multiplying the number of hours by $18 ,

We get ,

⇒ 8736 × 18 = $157248 .

Therefore , $18 an hour will be $157248 for a year .

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Answer:

DB = approximately 16

Step-by-step explanation:

DEC is a right triangle => DC=10. Because all four sides are equal in a rhombus, then AD=AB=10. Then, because angle BAD is 53*2=106 degrees, we can use cosines. DB=sqrt(10^2+10^2-2*10*10cos(106deg))=15.9727102009.

The variable x has no true value in the similar shapes

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

The figure

Using the figure, we have the following ratio

3x : 4x - 1 = 4x - 1 : x² - x - 2

Factorize

3x : 4x - 1 = 4x - 1 : x² + x - 2x - 2

So, we have

3x : 4x - 1 = 4x - 1 : x(x + 1) - 2(x + 1)

This gives

3x : 4x - 1 = 4x - 1 : (x - 2)(x + 1)

Express as fraction

3x/(4x - 1) = (4x - 1)/(x - 2)(x + 1)

So, we have

3x(x - 2)(x + 1) = (4x - 1)(4x - 1)

Using a graphing tool, we have

x = undefined

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Taking choices that benefit the world on a microeconomic or macroecomomic level.

Taking choices that benefit the environment, whether on an individual, national or international level.

Striving towards establishing inclusive and resilient forums that are broad-minded.

Establishing close connections with other nations to benefit global communities and address major societal issues like gender discrimination and marginalisation.

The key feature that is NOT present in the function h(x) is "The x-intercept of h(x) is (5, 0)".

To find the x-intercept of a function, we need to set the y-value to 0 and solve for x. In the case of h(x), we have two different equations for different ranges of x:

h(x) = (x - 5)² when 0 ≤ x ≤ 4

h(x) = -log₄(x + 6) when x > 4

Setting the first equation to 0 and solving for x, we get:

0 = (x - 5)²

0 = x - 5

x = 5

However, this value of x does not fall within the range of 0 ≤ x ≤ 4, so it is not a valid x-intercept for this equation.

Setting the second equation to 0 and solving for x, we get:

0 = -log₄(x + 6)

log₄(x + 6) = 0

4⁰ = x + 6

1 = x + 6

x = -5

This value of x also does not fall within the range of x > 4, so it is not a valid x-intercept for this equation either.

Therefore, the function h(x) does not have an x-intercept of (5, 0), and this is the key feature that is NOT present in the function.

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2) The probability that in a cricket match, a batswoman did not hit a boundary, when she hits it 6 times out of 30 balls played, is 80%.

3) The probability of a family having:

i) 2 girls = 31.67%

ii) 1 girl = 54.27%

iii) No girl = 14.06%

iv) The sum of the probabilities = 1 or 100%

The probability refers to the likelihood that an expected event or outcome occurs when there are many possible outcomes.

We compute probability as the quotient of the the expected success and the total number of successes.

Probability lies between zero and one and is usually expressed as a decimal, fraction, or percentage.

The number of boundary hits = 6

The total number of balls the batswoman played = 30

The probability that the batswoman did not hit a boundary = 1 - 6/30

= 0.8 or 80%.

The chance that the batswoman hit a boundary = 6/30 = 0.2 or 20%.

The total number of families with 2 children = 1,500

The number of families with 2 girls = 475

The number of families with 1 girl = 814

The number of families with 0 girl = 211

The probability of a family having:

i) 2 girls = 475/1,500 = 0.3167 or 31.67%

ii) 1 girl = 814/1,500 = 0.5427 or 54.27%

iii) No girl = 211/1,500 = 0.1406 = 14.06%

iv) The sum of the probabilities = 1 or 100%

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If the  fruit seller threw some rotten apples away and the ratio of apples to oranges became 1 : 4. The fruit seller threw away 630 rotten apples.

To find the number of rotten apples that the fruit seller threw away, we will need to use the given information and set up equations to solve for the unknown variable.

Let's start by using the given information that there were 2/3 as many apples as oranges. We can set up an equation to represent this relationship:

2/3 O = A

Where O is the number of oranges and A is the number of apples.

We are also given that the fruit seller had 2520 apples and oranges in total. We can set up another equation to represent this relationship:

O + A = 2520

Now, we can use the first equation to solve for one of the variables in terms of the other. Let's solve for A in terms of O:

A = (2/3)O

Now we can substitute this expression for A into the second equation:

O + (2/3)O = 2520

Simplifying this equation gives us:

(5/3)O = 2520

Now we can solve for O:

O = (3/5)(2520) = 1512

Now that we know the number of oranges, we can use the first equation to solve for the number of apples:

A = (2/3)(1512) = 1008

So the fruit seller originally had 1008 apples and 1512 oranges.

We are also given that after throwing away some rotten apples, the ratio of apples to oranges became 1:4. We can set up an equation to represent this relationship:

(A - X)/O = 1/4

Where X is the number of rotten apples that were thrown away.

Substituting the values we found for A and O into this equation gives us:

(1008 - X)/1512 = 1/4

Cross-multiplying and simplifying gives us:

4(1008 - X) = 1512

4032 - 4X = 1512

4X = 2520

X = 630


Therefore, the answer to the question is 630.

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Answer:

y= 400(0.77)^x

Step-by-step explanation:

The value decreases by 23% from,400 to 308 in 1 year. so if this continues then the equation would be y=400(0.77)^x.

The 0.77 comes from decaying 23%, meaning 1-0.23 = 0.77

this is just a quick addition to the good reply above by "varnanaik"

so she bought it for 400 bucks, but hell a year later went down to 308?  Let's find the rate of depreciation

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 308\\ P=\textit{initial amount}\dotfill &\$400\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases}[/tex]

[tex]308 = 400(1 - \frac{r}{100})^{1} \implies \cfrac{308}{400}=1-\cfrac{r}{100}\implies \cfrac{77}{100}=\cfrac{100-r}{100} \\\\\\ 77=100-r\implies r+77=100\implies r=\stackrel{ \% }{23} \\\\[-0.35em] ~\dotfill\\\\ A=400(1-\frac{23}{100})^x\implies A=400(1-0.23)^x\implies {\Large \begin{array}{llll} A=400(0.77)^x \end{array}}[/tex]

The economic life cycle analysis does not take into account factors such as technological advancements or changes in regulatory requirements, which can affect the optimal replacement interval.

Yet, it is important to review and update the analysis periodically to ensure that the replacement interval remains optimal.

There are the normal steps for calculating the optimum replacement interval using the economic life cycle analysis:

1. Estimate the annual maintenance and repair costs for the item, based on historical data or industry standards.

2. Estimate the annual operating costs for the item, such as energy or fuel costs.

3. Compare the total cost of ownership for the item over its expected useful life to the cost of replacing the item with a newer or more efficient model.

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Using the percentage formula it is obtained that there are 40 number of pages in the book.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

Let's use "x" to represent the total number of pages in the book.

According to the problem, Daniel has read 80 percentage of the book, which means he has read -

8/100 = 0.8x pages

He still has 8 pages left to finish, so we can set up an equation -

0.8x + 8 = x

Solving for x, we can subtract 0.8x from both sides -

0.8x + 8 - 0.8x = x - 0.8x

8 = 0.2x

Then, we can divide both sides by 0.2 to get -

x = 40

Therefore, there are 40 pages in the book.

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the volume of the sugar cone is closest to 14.14 cubic inches.

How to determine?

The volume of a cone can be calculated using the formula V = (1/3)πr²2h, where r is the radius of the base, h is the height of the cone, and π is approximately 3.14.

In this case, the diameter of the cone is 3 inches, which means the radius, r, is half of that or 1.5 inches. The height of the cone is given as 6 inches.

Plugging these values into the formula, we get:

V = (1/3)π(1.5²2)(6)

V ≈ 14.14 cubic inches

Therefore, the volume of the sugar cone is closest to 14.14 cubic inches.

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Answer:

Below

Step-by-step explanation:

Similar triangles due to A - A - A

Set up ratios

QR is to RS   as  QP is to TS

(x+2) / (2x-5) = 3/5       Cross multiply to get

5x+10 = 6x-15               subtract 5x from both sides of the equation

10 = x - 15                     add 15 to both sides

25 = x

Answer:

15

Step-by-step explanation:

q/4=60
Just divide 60 by 4. :)

Answer:

Peyton = 45.69 seconds to run the race

Step-by-step explanation:

Karen = 43.52 seconds

Peyton = k + 2.17

Peyton = 43.52 + 2.17

Peyton = 45.69 seconds

Answer:

45.69

Step-by-step explanation:

If Peyton's time running the race was 2.17 seconds more than Karen's time, then we can calculate Peyton's time by adding 2.17 seconds to Karen's time.

Karen's time: 43.52 seconds

Peyton's time: 43.52 + 2.17 = 45.69 seconds

Therefore, Peyton's time running the race was 45.69 seconds...

Answer:

Earned Income

Step-by-step explanation:

I get this money from chores I do around the house and my side job of selling sandwiches to my classmates (this is just an example you can personalize it)

Answer:

hypotenuse squared

Step-by-step explanation:

for example

if we have a triangle with sides 6,8, and 10

then

36+64=100

the complete equation is

[tex]\sqrt{a^{2} +b^2[/tex]=c

The conversion of the weight 68 kg from Kilogram to lbs will be equal to 149.914 lbs.

The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.

One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.

One pound is equal to 0.45359237 kilograms.

To convert kilograms (kg) to pounds (lbs), you can use the following formula:

To convert kilograms to pounds, multiply your figure by 2.20462

To convert 68 kg to lbs, you can multiply 68 by 2.20462:

68 kg X 2.20462 lbs/kg

= 149.914 lbs

Therefore, 68 kg is equal to 149.914 lbs.

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The complete question may be:

What is 68 Kg weight in lbs?

The volume of this solid is 18 cubic units.

This solid is a triangular prism with a triangular base and a height of 9 units. To calculate the volume of the solid, we can use the formula V=Bh, where B is the area of the base and h is the height. The base of the prism is a right triangle with sides of length 9, 9, and 6. We can use the Pythagorean Theorem to calculate the length of the hypotenuse of the triangle, which is equal to 12. We can then use the formula for the area of a triangle, A=1/2bh, to calculate the area of the base, which is equal to 27. We can then multiply this by the height, 9, to get the volume of the solid, which is 18 cubic units.

This solid is a triangular prism with a triangular base and a height of 9 units. To calculate the volume of the solid, we can use the formula V=Bh, where B is the area of the base and h is the height. The base of the prism is a right triangle with sides of length 9, 9, and 6.

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The area in which tulips are planted is 4247.625 square meters.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

To calculate the area of the triangle described as;

= 1/2 x length of the base segment x height of the triangle.

Given:

All the grass patches have equal areas.

From the diagram;

the shape of patch 2 is rectangular.

And the dimensions of the rectangle are 120.5 meters by 70.5 meters.

Two triangles of equal areas are formed by the division of patch 2 diagonally.

The area in which tulips are planted is,

= 1/2 x base x height

= 1/2 x 120.5 x 70.5

= 8495.25/2

= 4247.625 square meters.

Therefore, the area is 4247.625 square meters.

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Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.

The component technique is a technique of troubles where you first calculate the worth of a single item, then multiply a certain value to get the answer. Simply defined, a single product value is extracted from either a specified multiple using the one method. For contrast, 40 pens will costs you 400 rs, or $1.01. The method used to execute this might be regulated. a solitary nation. anything seems to have a distinctive component.  (Classic Algebra, Quantitative Analysis, Math and science of Matrix or Operators).

given

1% of $500 = $5

Total Saving from $500 to $ 860

860 / 5 = 172

Now percentage of growth :-

172/500 *100

17200/500 = 34.4

Hence, the rate of change Sergio savings = 34.4%

Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.

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The y-intercept of a linear function is the point at which the graph of the function crosses the y-axis. This point is represented by the coordinate (0, b), where b is the y-intercept.

In the given graph, we can see that the graph of the linear function crosses the y-axis at the point (0, -5). Therefore, the y-intercept of the graph of this function is -5.

To summarize, the y-intercept of the graph of this function is -5.

Answer: -5

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The converted value of the 12inches to millimeters using scale factor is equal to ( 304.8 ) millimeters .

One inch is equal to 25.4 millimeters

Now multiply both the side of the expression by 12 we get,

⇒ ( 12 × 1 ) inches = ( 12 × 25.4 ) millimeters

⇒ 12 inches = ( 304.8 ) millimeters

Therefore, using the scale factor of inches to millimeter the required 12 inches is equal to 304.8 millimeters.

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a) matrix is 4 x5 , null space is 3 dimensional then rank = 2. b) A is 6x7 matrix :  the column vectors with leading 1's of the row vectors forms a basis for column space. Maximum possible dimension for Col(A) = 6.

A matrix's rank is defined as the largest number of its characteristic equation columns (or rows). A matrix's rank is limited to a handful of its rows and columns.

A square matrix has columns (rows) that are only linearly independent if the matrix is not unique. To put it another way, any nonsingular matrix of order m has rank m. The symbol for a matrix A's rank is (A).

A null matrix has 0 rank. No non-zero rows or columns exist in a null matrix. There are no distinct rows or columns as a result. Hence, a null matrix has a rank of 0.

a) matrix is 4 x5 , null space is 3 dimensional then rank = 2

b) A is 6x7 matrix :  the column vectors with leading 1's of the row vectors forms a basis for column space.

Maximum possible dimension for Col(A) = 6

c) If null space = {0,0,0,0,0}, then

The for Ax= B, column vector B is the solution for the system.

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