A trapezium of area 140cm square has parallel sides 10cm apart and one of these 16m long. Find the length of the other parallel side​

The first term of the geometric progression will be 128.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

Given that the common ratio of the geometric series is ( 1 / 4 ) and the sum of the first four terms is 170.

The first term of the geometric series will be calculated as:-

[tex]S_n = a_1\dfrac{(r^n-1)}{r-1}[/tex]

[tex]170 = a_1\dfrac{(\dfrac{1}{4}^4-1)}{\dfrac{1}{4}-1}[/tex]

a₁ = ( 170 x 64 ) / 85

a₁ = 2 x 64

a₁ = 128

Therefore, the first term of the geometric progression will be 128.

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The amount of flour that Rosemary needs for the increased recipe of cookie is 138 2/3 batches.

The quantity of flour and sugar needed for a batch of cookie recipe are written as mixed numbers. A mixed number is a non-integer that consists of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is smaller than the denominator.

In order to determine the quantity of flour that would be needed for 3 1/4 batches, multiply the amount of flour needed for one batch of cookie by the number of batches to be made.

Multiplication is the process that is used to determine the product of two or more numbers. The sign that represents multiplication is x.

Amount of flour needed for 3 1/4 batches = flour needed for one batch x number of batches

42 2/3 x 3 1/4

128 / 3 x 13/4 = 416 / 3  = 138 2/3 batches

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An inequality to determine the rate of temperature decrease in degrees Celsius per day d, from Monday to Thursday is 30°c - 3d [tex]\leq[/tex] 20°c

Let's assume the constant rate of decreasing the temperature be d degree Celsius.

So, the total decrease in temperature in three days is 3d degree Celsius.

Given,

The temperature on Monday is 30° c

Then,

The temperature on Thursday (which is 3 days later) will be 30°c - 3d

Since the pool opens when the temperature is higher than 20°c,

The equation to determine the rate of temperature decrease in degrees Celsius per day will be 30°c - 3d [tex]\leq[/tex] 20°c

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The vertex of the equation is (1, -1).

The equation of a parabola in vertex form is,

y = a(x-h)² + k

The coordinates of the vertex are (h,k) respectively and a is a constant.

Given:

y =  x² - 2x

Rearrange the given equation in the form of the equation of the parabola in vertex form using the method of completing the square.

y = (x² - 2x + 1) - 1

y = (x - 1)² - 1

Therefore, the vertex of the equation is (1, -1).

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The answers to all the subparts are given below:

So, (A) Chebyshev's theorem is used:

So,

Therefore, the minimum proportion of commuters who are within two standard deviations of the mean is:

(B) Minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the​ mean:

Here, k = 1.5

Consequently, the shortest commute within two standard deviations of the mean is:

Within 1.5 standard deviations, commute times:

(C) Minimum percentage of commuters who have commute times between 6 minutes and 48.6 ​minutes:

So,

Therefore, the answer to all the subparts are given below:

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The correct question is given below:
The mean commute time to work for a resident of a certain city is 27.3 minutes. Assume that the standard deviation of the commute time is 7.1 minutes to complete parts​ (a) through​ (c).

​(a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the​ mean?

nothing​% ​(Type an integer or a​ decimal.)

​(b) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the​ mean? What are the commute times within 1.5 standard deviations of the​ mean?

The minimum percentage of commuters in the city that has a commute time within 1.5 standard deviations of the mean is nothing​%. ​(Round to one decimal place as​ needed.)

The commute times within 1.5 standard deviations of the mean are between nothing and nothing.

​(Type an integer or a decimal. Use ascending​ order.)

​(c) What is the minimum percentage of commuters who have commute times between 6 minutes and 48.6 ​minutes?

nothing​% ​(Round to one decimal place as​ needed.)

Answer:

it’s B

Step-by-step explanation:

just took the test

Answer:

D.105

Step-by-step explanation:

sum of measures of the three angles equal 180

therefore measure of angle B equal 180-(52+23)=105 degree

The number of weeks that they will they have same number of baseball cards is 5 weeks.

From the information given, Ty and Elijah each decide to collect baseball cards. It should take about Ty has 37 cards and Elijah has 42 cards to begin with. Ty decides to buy 4 more cards each week and Elijah decides to buy 3.

Therefore, the expression for Ty will be:

= 37 + 4x

The expression for Elijah will be:

= 42 + 3x

where x = number of cards

Therefore, this will be:

37 + 4x = 42 + 3x

4x - 3x = 42 - 37.

x = 5

The number of weeks is 5.

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Ty and Elijah each decide to collect baseball cards. Ty has 37 cards and Elijah has 42 cards to begin with. Ty decides to buy 4 more cards each week and Elijah decides to buy 3. In how many weeks will they have same number of baseball cards?

This can be re-inserted into our vertex equation to obtain. y=2(x−2)2+3.

In "standard form," if your instructor desires it, we can expand the right side to get:

Write a quadratic function with a vertex of (2, "-3)" to show results

Find write a quadratic function with vertex of instead (2, -3)

Answer 1

A quadratic's common vertex form is. y=m(x−a)2+b.

In light of the vertex, this becomes (2,3).

So, we do. 11=m(4−2)2+3. f(x) = a(x - h)2 + k, where a, h, and k are constants, is the vertex form of a quadratic function (h, k). If the vertex form of the quadratic parent function f(x) = x2 is used, then y = a(x - h)2 + k, where a = 1, h = 0, and k = 0.

Putting it simply: 8=m(2)2. 8=4m. m=2.

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Answer:5.44

Step-by-step explanation:

3.2x1.7

Using proportional relationships, we have that:

a) They are defined as follows:

b) The relation is Out of State Team = 1/5 x Residents.

A graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

Voice instructor notices that only one out of every ten of her students can sing soprano, hence the constant is:

k = 1/10 = 0.1.

Then the relationship is:

Soprano = 0.1 x Students.

Two out of every six vehicles are trucks, hence the constant is:

k = 2/6 = 1/3.

Hence the relationship is:

Trucks = 1/3 x Vehicles.

Then, in item b, we want to write a relation that has a constant between those represented on the previous relations, that is, between 1/10 and 1/3.

One possible constant is of 1/5. Supposing that one out of five New York City residents root for out of state NFL teams, the relation is:

Out of State Team = 1/5 x Residents.

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The Last box-and-whisker plot represents the data 6, 7, 9, 9, 20, 22, 26, 28, 29, 30.

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solution

To factorize the Trinomial, we seek two numbers such that the product is -14 and the addition is 5

We have

Pair Product sum

(-2, 7) -14 5

Hence we have

Hence the correct option is C

Answer:

Step-by-step explanation:

Find the Inverse y=2x. y=2x y = 2 x. Step 1. Interchange the variables. x=2y x = 2 y. Step 2. Solve for y y

Answer: The inverse of the function y = 2x2 + 2 is f-1(x) = √(x - 2) / √2.

Answer:

See picture

Step-by-step explanation:

The parameters are ΔUVW with side UW extended to X then m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)° then the value of x = 9°.

The given parameters exist;

ΔUVW with side UW extended to X

m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)°

We have that m ∠UVW + m ∠WUV + m ∠VWU = 180° (Sum of the interior angles of a triangle theorem)

Therefore, m ∠VWU = 180° - (m ∠UVW + m ∠WUV)

Also, we have that m ∠VWX and m ∠VWU exist supplementary angles, (The sum of angles on a straight line)

∴ m ∠VWX + m ∠VWU = 180° (Definition of supplementary angles)

m ∠VWU = 180° - m ∠VWX

∴ m ∠VWX = (m ∠UVW + m ∠WUV)

Substituting the values in the above equation, we get;

(8x -12)° = (3x + 4)° + (x + 20)°

simplifying the above equation, we get

8x - 3x - x = 4 + 20 + 12

4x = 36

x = 36/4 = 9

Therefore, the value of x = 9°.

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The inverse of the given function is f^-1(x)=  (x - 63) /14

A function's reverse function F is a function that reverses the action of f (sometimes known as the inverse of f). If the inverse of f exists, it is designated by f -1 and exists only if f is bijective. The graph of the inverse of a function shows the function and the inverse of the function, which are both plotted over the line y = x. This graph's line traverses the origin and has a slope value of 1.

The first step is to open the brackets

So now we get, f(x)= 14x - 63

Let f(x) be y so this  becomes y= 14x+ 63

Now interchange the variables and we will get

x= 14y+ 63

(x- 63)/14= y

Replace y by f^-1(x).

f^-1(x)= (x - 63) /14

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Answer: c x=3

Step-by-step explanation:

Simplify it you will get

2-x=x-4 then minus x and four so you will get

2x=6 divide

X=3

The digits at ones place are 8 and the hundredth place is 9.

The number which is left to the decimal is considered in one's places as proceeding with the numbers tens places and the hundredth place is obtained. Similarly on the right side moving towards the right gives tenth place and hundredth place.

18.09

(1) - It is in the Tens place

(8) - Ones place

(.) - Decimal point

(0) - Tenth place

(9) Hundredth place

Therefore, The digits at one place are 8 and the hundredth place is 9.

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Answer: v = 17°

Step-by-step explanation:

All triangles add up to 180°.

[tex]94+35+3v=180[/tex]

[tex]3v=51\\v=17[/tex]

Answer:

Step-by-step explanation:

v=51

The distances of the ships makes a right angled triangle. Ship A sails at 25 mph in direction QP, towards north. Ship B sails at 14 mph in direction QR, towards east.

Therefore, the distance between the two ships at 1 P.M. would be the distance between PR.

Applying Pythagoras Theorem,

[tex]P^{2} +B^{2} = H^{2}[/tex]

[tex](PQ)^{2} + (QR)^{2} = (PR)^{2} \\PR= \sqrt{(PQ)^{2} + (PR)^{2} } \\= \sqrt{(25)^{2} + (14)^{2} } \\= \sqrt{821} mph[/tex]

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The complete table will be;

In 2 years, The amount of salary = $35,200

In 5 years, The amount of salary = $31,200 + 5 x $4,000 =  $51,200

In 10 years, The amount of salary = $71,200

In x years, The amount of salary =  =  $31,200 + $4,000x

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A high school graduate can make $31,200 per year.

Any additional year of training or schooling can increase the salary by $4,000 per year.

Now, In one year, Salary = $31,200

So, In 2 years, The amount of salary = $31,200 + $4,000

                                                        = $35,200

In 5 years, The amount of salary = $31,200 + 5 x $4,000

                                                  = $31,200 + $20,000

                                                  = $51,200

In 10 years, The amount of salary = $31,200 + 10 x $4,000

                                                   = $31,200 + $40,000

                                                   = $71,200

In x years, The amount of salary = $31,200 + x × $4,000

                                                  = $31,200 + $4,000x

Thus, The complete table will be;

In 2 years, The amount of salary = $35,200

In 5 years, The amount of salary = $31,200 + 5 x $4,000 =  $51,200

In 10 years, The amount of salary = $71,200

In x years, The amount of salary =  =  $31,200 + $4,000x

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Using the given linear function, we have that:

a) The equation in standard form is: h - 3.34r - 81.2 = 0.

b) The intercepts are given as follows: h-intercept = 81.2, r-intercept = -24.31.

c) The predicted height is of 164.7 centimeters.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In standard format, the equation is given by:

y - mx - b = 0.

In which:

For this problem, the equation is:

h = 81.2 + 3.34r.

In standard format, the equation is:

h - 3.34r - 81.2 = 0.

From the equation, the h-intercept is of 81.2. To find the r-intercept, we have to solve for r when h = 0, hence:

3.34r + 81.2 = 0.

3.34r = -81.2

r = -81.2/3.34

r = -24.31.

For item c, the radius is given by r = 25, hence the height will be given as follows:

h = 81.2 + 3.34(25) = 164.7.

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Answer:

x = 2√174, -2√174

x ≈ 26.38

Step-by-step explanation:

23² + x² = 35²

529 + x² = 1225

-529         -529

----------------------

x² = 696

√x² = √696

x = 2√174, -2√174

----------------------------------------------------------------------------------------------------------

b = √c² - a²

b = √35² - 23²

b ≈ 26.38

I hope this helps!

Isaac need to invest $ 36720.

Given,

Isaac is going to invest in an account paying an interest rate of 6.3% compounded monthly.

and,  the value of the account to reach $57,000 in 7 years.

To find the how much would Isaac need to invest.

Now, According to the question:
Let x be the invest in an account.

Based on the given conditions,

formulate:

x . [tex]([/tex]1 + 6.3%/ 12[tex])^7^.^1^2[/tex] = 57000

Solve the equation

x . (1 + 0.063/12[tex])^7^.^1^2[/tex] = 57000

Convert decimals to integers

x . (1 + 63/12000[tex])^7^.^1^2[/tex] = 57000

Reduce the fraction

x . (1 + 21/4000[tex])^7^.^1^2[/tex] = 57000

x . ([tex]\frac{4000+21}{4000})^8^4[/tex] = 57000

Calculate the sum or difference

x . (4021 / 4000[tex])^8^4[/tex] = 57000

x = [tex]\frac{57000}{(\frac{4021}{4000})^8^4 }[/tex]

Simplify using exponent rule with same exponent :

[tex](ab)^n = a^n . b^n[/tex]

x = [tex]\frac{57000 . 4000^8^4}{4021^8^4}[/tex]

Solve the above equation, we get

x = 36720

Hence, Isaac need to invest $ 36720

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The equations with parentheses added to make them true are;

Parentheses indicate that operations within it should be completed first before those that are outside the parentheses.

The given terms of the equations can be regrouped with parentheses to make the equations true as follows;

1. 4 × 3 + 7 - 6 × 1 + 4 = 20

The above equation gives;

3 + 7 - 6 = 4

Therefore;

4 × 3 + 7 - 6 × 1 + 4 = 4 × (3 + 7 - 6) × 1 + 4

4 × (3 + 7 - 6) × 1 + 4 = (4 × 4) × 1 + 4

(4 × 4) × 1 + 4 = 16 × 1 + 4 = 16 + 4 = 20

Which gives;

2. 60 - 18 ÷ 2 + 4 + 10 ÷ 2 = 12

60 - 18 = 42

2 + 4 = 6

The first four terms, therefore gives;

(60 - 18) ÷ (2 + 4) = 7

10÷2 = 5

Which gives;

60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2

(60 - 18) ÷ (2 + 4) + (10÷2) = 7 + 5 = 12

Which gives;

60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2 = 12

The expression is therefore;

3. 80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 44

80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - 36 ÷ (2 + 6 - 2) × (5 + 1)

(2 + 6 - 2) = 6, and (5 + 1) = 6

Therefore;

80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - ((36 ÷ 6) × 6)

80 - ((36 ÷ 6) × 6) = 80 - ((36 × 6) ÷ 6)

80 - ((36 × 6) ÷ 6) = 80 - (36 × 1) = 44

Therefore;

4. 3 × 5 + 4 - 2 × 2 + 6 - 4 = 15

3 × 5 + 4 - 2 × 2 + 6 - 4 = 3 × (5 + 4) - (2 × (2 + 6) - 4)

3 × (5 + 4) - (2 × (2 + 6) - 4) = 3 × 9 - (16 - 4)

3 × 9 - (16 - 4) = 27 - 12 = 15

Therefore;

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