Madge has cut out two triangular shapes from a block of wood, as shown below. Are the two shapes similar? Show your calculations.

Answer:

3:1

Step-by-step explanation:

90:30 simplified is 3:1

Неоднородное ДУ второго порядка. Детали в аттаче.

To express the phrase "Three times a number, decreased by five" as an algebraic expression, we can use the variable x to represent the unknown number: 3x - 5

Now, let's simplify this expression: Given that the unknown number is represented by x, we can substitute it into the expression above. Substituting x into the expression, we have: [tex]3(x) - 5 3x - 5[/tex] Therefore, the algebraic expression representing "Three times a number, decreased by five" is [tex]3x - 5.[/tex] At this point, there is no further simplification possible since the expression is already in its simplest form.

For example, let's assume the unknown number x is 7. We can plug in this value to evaluate the expression: [tex]3(7) - 5 = 21 - 5 = 16[/tex] Similarly, if x is -2, the calculation would be: [tex]3(-2) - 5 = -6 - 5 = -11[/tex] In conclusion, the algebraic expression 3x - 5 represents the phrase "Three times a number, decreased by five."

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Answer:

40

Step-by-step explanation:

As the lawn size increases by 4 the weight increases by 8

Step-by-step explanation:

Is it helpful ?

plz let me know

Answer:

The Probability would be 2.78%

Step-by-step explanation: Hope this helps :)

Answer:

True.

Step-by-step explana

-4/5 + 4/5 is 0

Answer:

Alanna is 32 years old

Step-by-step explanation:

Hi there!

We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.

Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x

Alix is 10 years older than Tamia, so Alix must be x+10 years old

Alanna is twice as old as Tamia, so she must be 2x years old

We're also given that Alix+Alanna+Tamia=74

When we substitute it with the expressions we have, it becomes:

x+x+10+2x=74

now combine like terms

4x+10=74

subtract 10 from both sides

4x=64

divide both sides by 4

x=16

We found the value of x (Tamia's age)

However, the problem asks for Alanna's age, which we have set as 2x

So Alanna is 2*16, or 32 years old

Hope this helps! :)

Answer:

32 years

Step-by-step explanation:

that is the procedure above

Answer:

Interest Earned ₹ 1,800

Principal Amount ₹ 10,000

Total Value ₹ 11,800

The cost of the loan for Mandy will be $11800 and the total interest for 3 years will be $1800.

Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

In another word, if the principle amount is the same in each time period then the interest will also same for every time period.

Given that

Principle amount = $ 10000

Time period = 3 years

Rate of interest = 6%

Rate of interest at the end of 1st year

10000 × 6/100 ⇒ $600

Since in simple interest rate of interest remain same so

Rate of interest for 3 years

3 × 600 = $ 1800 hence rate of interest will be $1800.

Cost of the loan = principle amount + total interest

Cost of the loan = 10000 + 1800 ⇒ $11800 will be the cost of the loan.

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Answer:

a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.

b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.

c) Expected number of acceptable specimens among the ten is 7.938.

d) Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

Step-by-step explanation:

a )

[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]

b )

[tex]c = 1.96 * 3 = 5.88[/tex]                    { Since Z = 1.96 for 95% CI refer table.}

c )

Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]

d )

Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

Answer:

The Third one

Step-by-step explanation:

Your Welcome :)

Graph of the function is attached below.

Correct option is D.

As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:

Definition of exponential function

In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant  called the base of the function, which must be greater than 0.

Given, exponential function

f(x) = (1/4)4ˣ

exponential function is defined for x∈R

Putting x = 0

f(0) = (1/4)4⁰

f(0) = 1/4

Point on curve is (0,1/4)

Putting x = 1

f(1) = (1/4)4¹

f(1) = (1/4)4

f(1) = 1

Point on curve is (1,1)

Putting x = 2

f(2) = (1/4)4²

f(2) = (1/4)16

f(2) = 4

Point on curve is (2,4)

Putting x = 3

f(3) = (1/4)4³

f(3) = (1/4)64

f(3) = 16

Point on curve is (3,16)

Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.

Hence, graph of the function is drawn as follows.

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Answer:

The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is​. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation  the equation of the straight line will be.

Step-by-step explanation:

Answer:

The appropriate answer is "$12".

Step-by-step explanation:

As per the question,

Price per ticket,

= [tex]4+k[/tex]

Number of people,

= [tex]1800-90k[/tex]

Now,

The revenue (R) will be:

= [tex]Price \ per \ ticket\times Number \ of \ people[/tex]

By putting the values, we get

= [tex](4+k) (1800-9k)[/tex]

= [tex]-90k^2+1440k+7200[/tex]

or,

⇒ [tex]R'=1440-180k=0[/tex]

⇒                     [tex]180k=1440[/tex]

⇒                          [tex]k=\frac{1440}{180}[/tex]

                               [tex]=8[/tex]

hence,

The ticket price will be:

= [tex]4+k[/tex]

= [tex]4+8[/tex]

= [tex]12[/tex] ($)

Answer:

0.21

Step-by-step explanation:

There's 21 kids with a cell phone and no tablet

so 21/100 = 0.21

Answer:

Answer: 3) R(n) = 1200(1.002)n - 100n

Step-by-step explanation:

After n months, which function represents Chet’s net worth, R(n)?

(1) R(n) = 1200(1.002)n + 100n

(2) R(n) = 1200(1.002)12n + 100n

(3) R(n) = 1200(1.002)n - 100n

(4) R(n) = 1200(1.002)12n - 100n

Answer: 3) R(n) = 1200(1.002)n - 100n

Net worth is the amount of his savings minus his debt,

Everything in the problem is in terms of months, so there is no need to multiply the exponent by 12, which would convert n years into months.

Answer: The coefficient before x^4 is 60

Step-by-step explanation:

Hey! So I am not an expert at this, but you have to use the binomial theorem

I have attached of the Pascals Triangle (one shows the row numbering as well)

Basically in a pascal triangle, you add the two numbers above it to get the next number below

As you can see, the rows start from 0 instead of 1

The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms

NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)

Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)

It would be 15 × 2^4 × (1/2)^2 = 60

The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power

Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)

Answer:

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

There are 750 identical plastic chips numbered 1 through 750 in a box

This means that [tex]a = 1, b = 750[/tex]

What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?

[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Answer:

se supone que debes usar el SINE RATIO ya que se trata del lado opuesto y la hipotenusa.

Answer:

Step-by-step explanation:

A + B = 750

A = 1.5 B

~~~~~~~~~~~~~~

750-B = 1.5 B

750 = 1.5 B + B

750 = B(1.5 +1)

750 = B (2.5)

B = 300

A = 450

9514 1404 393

Answer:

  B.  relative maximum of 8.25 at x=2.5

Step-by-step explanation:

A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...

  x = -5/(2(-1)) = 5/2

The value of the extreme is ...

  f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25

The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.

The function has a relative maximum of 8.25 at x = 2.5.

__

A graphing calculator can show this easily.

9514 1404 393

Answer:

  it depends on the accuracy and resolution required of the answer

Step-by-step explanation:

The shaded portion appears to be about half the length of the unshaded portion, suggesting the shaded amount is 1/3.

__

Using a pair of dividers, one could determine the number of times the shaded portion fits into the whole bar. Depending on how much is left over, the process could repeat to determine the approximate size of the remaining fraction relative to the bar or to the shaded portion. (Alternatively, one could replicate the length of the bar to see what integer number of shaded lengths fit into what integer number of whole lengths.)

One could measure the shaded part and the whole bar with a ruler, then determine the relative size of the shaded part by dividing the first measurement by the second. The finer the divisions on the ruler, the better the approximation will be.

Answer:25

Step-by-step explanation:

Answer:

— Ang salitang entrepreneur ay hango sa salitang French na entrepende na nangangahulugang?

first and last one i think

What you know about rollin' down in the deep?

When your brain goes numb, you can call that mental freeze

When these people talk too much, put that sh*t in slow motion, yeah

I feel like an astronaut in the ocean, ayy

What you know about rollin' down in the deep?

When your brain goes numb, you can call that mental freeze

When these people talk too much, put that sh*t in slow motion, yeah

I feel like an astronaut in the ocean

Step-by-step explanation:

x⁴(4x+1)

4x⁵+x⁴

degree is 5

Answer:

I would say 100 since 256.78 is closer to 100 then 1000 or 10

Step-by-step explanation:

Answer:

105 in³

Step-by-step explanation:

Volume of triangular prism = base area * height

here

base area =  (10*7)/2 = 35

height = 3

Volume = 35* 3 = 105