Jason has bought a new pool and has already measured some of the sides. Using the figure below and your knowledge of quadrilaterals, solve for x and y.

Answer:

1/2y > 22

Step-by-step explanation:

I think that's what you were asking, but I'm not sure

So the is more than tells you that you're going to use the greater than sign. and 1/2 of y is 1/2y because of means mulitiplication

hope this helps:)

Answer:

1/2y > 22  

Step-by-step explanation:

Write an equation for the number y:

1/2 of y is more than 22

1/2 * y is more than 22 ('of' equals multiply)

1/2y = more than 22 ('is' equals a equal sign)

1/2y > 22 ('more' is greater than and not greater than and equal since it doesn't state anything that it could acctually be equal to)  

1/2y > 22  

(You can solve for y if you need to find the value of the number)                      

Step-by-step explanation:

There are 2 questions in one.

1)

Roberta is 20 years older than Julian. In 4 years, Roberta's age will be twice Julian's age:

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

2)

Roberta is twice as old as David. In 10 years, Roberta will be 8 less than three times David's present age:

Correct choice is A

Answer:

Step-by-step explanation:

Use the mean and the standard deviation obtained from the last discussion and test the claim that the mean age of all books in the library is greater than 2005.

This is the last discussion:

The science portion of my library has roughly 400 books.

They are arranged, on shelves, in order of their Library of Congress

code and, within equal codes, by alphabetical order of author.

Sections Q and QA have a total of 108 books.

The bulk of the library was established in the early 1990s.

I used a deck of cards, removing the jokers and face cards, keeping

only aces (1) and "non-paints" (2 to 10). Starting from the start of

the first shelf, I would turn a card (revealing its number N) and I

would go to the Nth book. This uses ordinal numbers (1 would means the

"first" book, not a gap of 1).

The cards were shuffled sufficiently to assume that the cards have a

random order.

I sampled only the LC subsections Q and QA (therefore, not a true

sample of the entire library, as this classification is not purely

random).

Thus, I picked 21 books (the expected number being 108/5.5 = 19.6 --> 20 books)

The sampled dates of publication were (presented as an ordered set):

1967, 1968, 1969, 1975, 1979, 1983, 1984,

1984, 1985, 1989, 1990, 1990, 1991, 1991,

1991, 1991, 1992, 1992, 1992, 1997, 1999

The median date is 1990

The mean date is 1985.67

Variance = 84.93 ( Sum of (date-mean)^2 )

SQRT of variance = 9.2 (sample standard deviation)

The "sigma-one" confidence interval (containing 68% of the books), if

the sample were NOT skewed, and if the distribution were "normal"

would contain dates from "mean - 9.2" to "mean + 9.2"

Sigma-2 (95%) would have mean - 2(9.2) to mean + 2(9.2)

Sigma-3(99.7%) from "1985.67 - 3(9.2)" to "1985.67 + 3(9.2)"

1958.07 to 2012.6

There, you see one reason why the distribution is skewed (it is

possible to have books older than 1958, but it is impossible to have

book newer than 2012), but it still represents a usable model for the

library. If it applies to the entire library of 400 books, you would

expect one book (0.3% of 400) to fall outside the 3-sigma interval.

Answer: \(b=\sqrt{45}\) or b=6.71 in.

Step-by-step explanation:

Use Pythagorean Theorem

\(a^2+b^2=c^2\)

In this case, a=2in and c=7in, and we're solving for b.

\((2)^2+b^2= (7)^2\\4+b^2= 49\\b^2=45\\b=\sqrt{45}\)

Therefore, b=6.71 in.

The exam scores , that will lead to the better grade is

(a) the score of "X=40" in exam with μ = 50 , σ = 20 ;

(b) the score of "X=51" in exam with μ = 45 , σ = 2 ;

(c) Both the score will lead to better grades .

Part(a) : In order to find which score leads to better grade, we calculate the z-scores for both scores and compare :

The score of X = 74 on the first exam is :

⇒ z = (74 - 82)/8 = -1  ;

The score of X = 40 on the second exam is :

⇒ z = (40 - 50)/20 = -0.5  .

The z-score of -0.5 is > -1,

So , the score of X = 40 on the second exam lead to better grade because the score of 40 is closer to mean of second exam (50) and has a smaller deviation from mean (20) than score of 74 on first exam .

Part(b) :

The score of X = 51 on the first exam is :

⇒ z = (51 - 45)/2 = 3  ;

The score of X = 90 on the second exam is :

⇒ z = (90 - 70) / 20 = 1  .

The z-score of 3 is > 1 ,

So , the score of X = 51 on the first exam should lead to the better grade.

Part(c) :

The score of X = 62 on the first exam is :

⇒ z = (62 - 50) / 8 = 1.5  ;

The score of X = 23 on the second exam is :

⇒ z = (23 - 20) / 2 = 1.5  .

Both scores have the same z-score of 1.5, they should lead to the same grade.

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Answer:

perfect square / rational

4

Step-by-step explanation:

Answer:

root of 16. or 4

Step-by-step explanation:

Answer:

\(u=16.0024213\)

Step-by-step explanation:

\(-4.13(u-19)=12.38\\-(4.13u-4.13*19)=12.38\\-(4.13u-78.47)=12.38\\(-4.13u+78.47)+(-78.47)=12.38+(-78.47)\\-4.13u+78.47-78.47=12.38-78.47\\-4.13u=-66.09\\\frac{4.13u}{4.13} =\frac{66.09}{4.13} \\u=\frac{66.09}{4.13} \\u=16.0024213\)

Answer:

0.

Step-by-step explanation:

I am assuming you want to evaluate

(sin10+cos10)²(1-sin20)-cos²20

That evaluates to 0.

Answer:     \(a_{1}\) = 3 ;  \(a_{k}\) = \(a_{k - 1}\) + 2.5, where k ≥ 2

Step-by-step explanation:

To define a sequence recursively, we must state the first term and then state a rule for how each successive term can be described from the one before it. For instance, suppose I had the sequence 5, 8, 11, 14, ...

The first term would be \(a_{1}\) = 5

Each successive term where subscript k = 2 for the second term, 3 for the third, and so on, would be  \(a_{k}\) = \(a_{k - 1}\) + 3

So, for my example, the recursive definition for that sequence would be

       \(a_{1}\) = 5 ;  \(a_{k}\) = \(a_{k - 1}\) + 3, where k ≥ 2

In the exercise you have, we go up 2 terms from the first to the third and the value goes up 5 units. We go up 4 terms from the third term to the 7th, we go up 10 units. Apparently, we go up 2.5 units in value as we go from one term to the very next one.

So ...

        \(a_{1}\) = 3 ;  \(a_{k}\) = \(a_{k - 1}\) + 2.5, where k ≥ 2

This happens to be an arithmetic sequence, because we go up the same amount from one term to the next, but please do not assume that is  required for creating a recursive definition. It is not.

I hope this helps.

The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)

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Answer:

\(\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)\)

Step-by-step explanation:

Given dimensions:

Given value of π :

To find:

Solution:

Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.

\( \pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}\)

where,

Plug/substitute them onto the formulae,then simplify it using PEMDAS.

\( \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3\)

\( \rm \: Volume_{(Cylinder)} = \pi(49)(3)\)

\( \rm \: Volume_{(Cylinder)} = 147\pi \: \)

\( \rm \: Volume_{(Cylinder)} = 147 \times 3.14\)

\( \rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3} \)

\( \boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \: \)

Hence, we can conclude that:

The volume of the cylinder is approximately

461.6 m³.

\( \rule{225pt}{2pt}\)

Answer:

1) 2(x+1)(x+5)

2) (x-10)(x-4)

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Substitute the values in the expression, we have:

\(\displaystyle{|-1-3|+4}\)

Evaluate:

\(\displaystyle{|-4|+4}\)

Any real numbers in the absolute sign will always be evaluated as positive values. Thus:

\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)

Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.

\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_a(2)=f\hspace{5em} \log_a(3)=g\hspace{5em}\log_a(5)=h \\\\\\ 2^f=a\hspace{8em}3^g=a\hspace{7em}5^h=a\)

Lacey's new balance in the account is -$3.85.

What is account balance?

Lacey’s bank account balance = –$45.10

she deposits  = $65.00

Debit card for a purchase = $23.75

Updated balance = –$45.10+$65.00-$23.75= -$3.85

Lacey's new balance in the account is -$3.85.

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Answer: 44

Step-by-step explanation:

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

\(x=-3+2cos\theta,\:y=5+2sin\theta\\\\x+3=2cos\theta,\: y-5=2sin\theta\\\\(x+3)^2=4cos^2\theta,\: (y-5)^2=4sin^2\theta\\\\(x+3)^2+(y-5)^2=4cos^2\theta+4sin^2\theta\\\\(x+3)^2+(y-5)^2=4(cos^2\theta+sin^2\theta)\\\\(x+3)^2+(y-5)^2=4(1)\\\\(x+3)^2+(y-5)^2=4\)

Thus, the first option is correct. Trying all the other options will not get you the desired rectangular equation.

Problem 2

\(x=3-6cos\theta,\: y=-2+3sin\theta\\\\x-3=-6cos\theta,\: y+2=3sin\theta\\\\\frac{x-3}{-6}=cos\theta,\: \frac{y+2}{3}=sin\theta\\ \\ \frac{(x-3)^2}{36}=cos^2\theta,\: \frac{(y+2)^2}{9}=sin^2\theta\\ \\ \frac{(x-3)^2}{36}+\frac{(y+2)^2}{9}=cos^2\theta+sin^2\theta\\\\ \frac{(x-3)^2}{36}+\frac{(y+2)^2}{9}=1\)

Therefore, the first option is correct. This equation is in the form of an ellipse with a horizontal major axis length of 12 (half is 6) and a vertical minor axis length of 6 (half is 3), with its center at (3,-2).

Problem 3

Not sure which equation needs to be used for this problem

Problem 4

\(x=-7cos\theta ,\:y=5sin\theta\\\\-\frac{x}{7}=cos\theta,\: \frac{y}{5}=sin\theta\\ \\ \frac{x^2}{49}=cos^2\theta,\: \frac{y^2}{25}=sin^2\theta\\ \\\frac{x^2}{49}+\frac{y^2}{25}=cos^2\theta+sin^2\theta\\ \\ \frac{x^2}{49}+\frac{y^2}{25}=1\)

This equation is in the form of an ellipse with a horizontal major axis length of 14 (half is 7) and a vertical minor axis length of 10 (half is 5). See attached graph.

Problem 5

Eliminate the parameter:

\(x=-t^2-2,\:y=-t^3+4t\\\\x+2=-t^2\\\\-x-2=t^2\\\\\pm\sqrt{-x-2}=t\\\\y=-t^3+4t\\\\y=-(\pm\sqrt{-x-2})^3+4(\pm\sqrt{-x-2})\)

Attached below is the graph of the curve, which corresponds with the first option.

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

nice!

Step-by-step explanation:

Answer:

Mrs. Appleton will give 4 cookies to each of her children. and 4 will be left over.

Step-by-step explanation:

24÷5 = 4

The cookies each child gets = 4.

The cookies were leftover = 4

In order to convert an improper fraction to a mixed number, we must divide the numerator by the denominator. After the division, the mixed number exists constructed in such a manner that the quotient that exists acquired becomes the whole number, the remainder evolves into the new numerator and the denominator stays exact.

Convert improper fractions to mixed numbers

Convert to mixed number = Quotient(Remainder/ divisor)

\($\frac{24}{5} = 4 \frac{4}{5}\)

Therefore, Quotient = 4

Remainder = 4

divisor = 5

Therefore, cookies were leftover = 4

cookies each child gets = 4.

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Answer:

\(slop = \frac{y2 - y1}{x2 - x1} \\ considertwo \: points \: \: 5 \: 17and \: 6 \: 18 \\ y - y1 = \frac{y2 - y1}{x2 - x1} (x - x1) \\ y - 17 = \frac{18 - 17}{6 - 5} (x - 5) \\ y - 17 = x - 5 \\ y = x - 5 + 17 = x + 12 \\ good \: luck\)

Answer:

f(x)=x+12

Step-by-step explanation:

To check if it is right:

plug in the numbers to the equation

f(x)=5+12=17

f(x)=6+12=18

Answer:

It will take 7.5 gardeners to plant 45 trees in 45 minutes

Step-by-step explanation:

It takes 3 gardeners 30 minutes to plant 18 trees.

Let's determine the rate of this 3 gardeners

Rate= 18 trees/30 minutes

Rate= 2/5 trees per minute

So 3 gardeners= 2/5 trees per minute

But then one Gardner= 2/(3*5) trees per minute

One Gardner=2/15 trees per minute

Let's determine the number of gardeners it will take to plant 45 trees in 45 minutes

One Gardner=2/15 trees per minute

X(22 /3)= 2/15*(22.5/3)

It will take 7.5 gardeners to plant 45 trees in 45 minutes

Answer:

g(x) is obtained by shift the function f(x) down 7 units by subtracting 7 units from f(x).

Step-by-step explanation:

We are given that

\(g(x)=f(x)-7\)

We have to identify  the transformation that occurs to create the graph of g(x).

To identify  the transformation that occurs to create the graph of g(x)

We will subtract the 7 from f(x).

Let f(x) be any function

\(g(x)=f(x)-k\)

It means g(x) obtained by  shift the function f(x) down  k units by subtracting k units from f(x).

Therefore, g(x) is obtained by shift the function f(x) down 7 units by subtracting 7 units from f(x).

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Answer:

51.6

Step-by-step explanation:

Add them together and divide by 4

Answer: it would be D. 53.6

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