In terms of paying less in interest, which is more economical for a $150,000 mortgage: a 30-year fixed-rate at 8% or a 20-year fixed-rate at 7.5%? How much is saved in interest?

The question is solved by carefully analyzing the given figures and working step by step to avoid double counting of items. Adding numbers to find total whales and then subtracting or combining them as required gives the specific group numbers.

This question requires calculations around the given number of whales and their specific dislikes. Let's address each part of the question step by step:

A. To find out the total number of whales surveyed, we add all the mentioned whales together, including those with no dislikes.
B. To find out the number of whales disliking at least one thing, we subtract the whales with no dislikes from the total number of whales.
C. To find out the number of whales that dislike Captain Ahab but not giant squids, we need to remove the whales that dislike both these things.
D. To determine the number of whales that dislike either giant squids or pollution, we need to avoid counting the whales that dislike both twice.

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Answer:

A number

Step-by-step explanation:

the sum of four and two of a number = equals ten

The created word problem involves Sam and his apples. Here, the variable 'x' represents the number of apples Sam's friend has. By solving the equation, we deduce that Sam's friend has 3 apples, so Sam originally had 10 apples.

Let's create a word problem for the equation 2x + 4 = 10:

Sam has twice as many apples as his friend. If Sam gives 4 apples to his friend, he will only have 10 apples left. How many apples did Sam have originally?

In this problem, the variable 'x' represents the number of apples Sam's friend has. Therefore, to solve the problem, you would subtract 4 from both sides of the equation to get 2x = 10 - 4. Simplifying gives you 2x = 6. Finally, dividing both sides of the equation by 2 gives you x = 3. So, Sam's friend has 3 apples, meaning Sam originally had 2 * 3 + 4 = 10 apples.

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We find that the telephone pole is 1.8 meters tall.

To figure out the height of the telephone pole, we can use similar triangles. Picture a right triangle formed by the telephone pole, the ground, and the wire, and another smaller triangle formed by Leah standing 2.5 meters from the pole, reaching the point where her head touches the wire 1.5 meters above the ground. Because these two triangles are similar, we can set up a proportion.

The large triangle's height is the height of the pole (H), and its base is 3 meters. The smaller triangle's height is Leah's height (1.5 meters), and its base is 2.5 meters. Using the similar triangles:

H (height of the pole) / 3 meters (distance from pole to cable ground attachment) = 1.5 meters (Leah's height) / 2.5 meters (Leah's distance from the pole)

H / 3 = 1.5 / 2.5

H = (1.5 / 2.5) * 3

H = 1.8 meters

Therefore, the telephone pole is 1.8 meters tall.

Answer:

The answer to your question is: the first option is correct

Step-by-step explanation:

We know that X - A = B  , then   X = A + B

           A      2        -7               B     -9       5

                    6         1                        1       -1      

X will be the sum of the two matrix given

X    =                A        +         B                  =    

                      2 - 9             -7 + 5                       -7         -2

                      6 +1               1 - 1                           7          0

                                                                    The first option is correct

Answer:

The first option

Step-by-step explanation:

Answer:

x = 20

y = 110

Step-by-step explanation:

5x + 45 + 3x - 25 = 180

those angles are supplementary (they make a straight angle in segment CD)

Solving that you get:

8x + 20 = 180

8x = 160

x = 20

Evaluating:

5(20) + 45 = 145

3(20) - 25 = 35

2(20) - 5 = 35

Now in segment AB:

y + (2x - 5) + (3x - 25) also sum 180, because they form a straight angle

y + 35 + 35 = 180

y = 110

Answer: Our required equation describes the relationship between cost and number of flowers purchased is [tex]2X+3Y=40[/tex]

Step-by-step explanation:

Since we have given that

Total amount he spent on flowers = $40

Let the number of small flowers be 'X'.

Let the number of large flowers be 'Y'.

cost of small flowers = $2

cost of large flowers = $3

According to question, it becomes,

[tex]2X+3Y=40[/tex]

Hence, our required equation describes the relationship between cost and number of flowers purchased is [tex]2X+3Y=40[/tex]

The equation that describes this situation is.

2X + 3Y = 40

Let's define:

X = number of small flowers

Y = number of large flowers.

We know that Jane spent $40 on the flowers, and each small flower costs $2 and each large flower costs $3, then the total cost of the X and Y flowers is:

2*X + 3*Y

And that must be equal to 40, which is the amount she spent.

2X + 3Y = 40

That is the equation.

learn more about equations at:

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Answer: 17.5cm

Steps: 70m = 700cm

40cm = 40cm

700cm/40cm

=17.5cm

vous êtes les bienvenus, baisers cher!

Answer:

40 cm

Step-by-step explanation:

She has one ribbon of 40 cm and another ribbon of 70 m

First, we have to change 70 m to cm, to do this we know that 1m = 100 cm

so we multiply 70*100 = 7,000 cm.

Now we have to find the longest length she can cut the ribbons in centimeters.

To do this we have to find the Greatest Common Factor of 40 and 7000 to know what is the longest length she can cut the ribbons.

To find the Greatest Common Factor we have to find the factors for each number:

Factors of 40:

1, 2, 4, 8, 10, 20, 40

Factors of 7000

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40

The Greatest Common Factor is 40, so she can have pieces of 40 cm long.

Answer:

The answer to your question is: AC = 20

Step-by-step explanation:

Data

   AB = 2x - 4

   BC = 4x

   AC = 2x + 12

   AC = ?

            AB + BC = AC

        2x - 4 + 4x = 2x + 12

       6x - 4 = 2x + 12

       6x - 2x = 12 + 4

       4x = 16

       x = 16/4

       x = 4

AB = 2(4) - 4 = 8 - 4 = 4

BC = 4(4) = 16

AC = 2(4) + 12 = 8 + 12 = 20

         4 + 16 = 20

         20 = 20

Answer:

[tex]8.53\°[/tex]

Step-by-step explanation:

we know that

The grade of a road can be thought of as rise/run, and you usually see it as a percentage.

So, a 15% grade is the same as a grade of 15/100; for every 15 units the road goes up vertically, it goes 100 units horizontally

see the attached figure to better understand the problem

Let

[tex]\theta[/tex] -----> angle does the road come up from the ground

The tangent of angle theta is equal to the ratio of the opposite side by the adjacent side

[tex]tan(\theta)=\frac{15}{100}[/tex]

[tex]\theta=tan^{-1}(\frac{15}{100})=8.53\°[/tex]

Answer: 1

Step-by-step explanation:

Ok so 2/2=1

So 1^-4 is

(-1)(-1)(-1)(-1)=1

Answer:

  x^3 +x +2 +3/(x -1)

Step-by-step explanation:

Synthetic division can be done using a divisor with a power of the variable other than one, but the most straightforward application of it uses a binomial divisor with a variable coefficient of 1. Fortunately the divisor in this problem is the difference of squares, so can be factored into two divisors. We can make use of synthetic division to divide by one of them, then we can use it again with the other divisor.

  = ((x^5 +2x^2 +2x +1)/(x +1)) / (x -1)

  = (x^4 -x^3 +x^2 +x +1)/(x -1)

  = x^3 +x +2 + 3/(x -1)

The remainder from the second division is simplified by the fact that there is no remainder from the first division. If desired, the final remainder can be expressed over the original divisor as (3x +3)/(x^2 -1) by multiplying numerator and denominator by the first divisor, (x+1).

_____

The synthetic division tableaux are attached. First, we divide by (x+1), then that result is divided by (x-1).

We assume you've been shown how this works. If not, there are numerous web sites and videos that can explain better than is possible in this space.

Answer: 2.4

Step-by-step explanation:

5 /12-long division think bus stop method

5 goes into 12 twice with 2 remaining

2.

5 / 12.^2000

5 does go into 20 4 times

So you end up with

2. 4

5/12.0

Hope this helps

Answer:

Answer:

12/5=2.4

Showing the work

We know that

12/5

is the same as

12÷5

Then using

Long Division for 12 divided by 5

and rounding to a Max of 3 Decimal Places gives us

=2.4

Good day

Answer:

2/3 of the track

Step-by-step explanation:

5/7 • 4/5 is 2/3 so Sarah ran 2/3 around the track.

Answer:

  6

Step-by-step explanation:

The largest factor that is common to all these numbers is 6. That is the number of pencil boxes Lana can fill.

  18 = 6×3

  24 = 6×4

  36 = 6×6

___

Each of her six (6) pencil boxes will have 3 pencils, 4 erasers, and 6 crayons.

Answer:

  see below

Step-by-step explanation:

If (x+5) is a factor of p(x), then the value x=-5 will make that factor be zero. The product p(x) of which it is a part will also be zero, so p(-5) = 0.

Since p(-5) = 0 at x=-5, there will be an x-intercept at x=-5.

Dividing something by a factor of that thing will always give a remainder of zero. So, p(x)/(x+5) has a remainder of 0.

Answer:

Memory Locations assigned

a) 58 b) 60 c) 52 d) 3  

Step-by-step explanation:

We are given that:

h(k) = k mod 101

To find the memory location, we need to evaluate the modulus value abbreviated as mod, k modulo n, which returns the value of remainder when k is divided by 101.

a) 104578690

104578690 mod 101 = 58

b) 432222187

432222187 mod 101 = 60

c) 372201919

372201919 mod 101 = 52

d) 501338753

501338753 mod 101 = 3

The memory locations assigned by the hashing function h(k) = k mod 101 to the Social Security numbers are: a) 81, b) 14, c) 15, and d) 38.

The hashing function h(k) = k mod 101 assigns memory locations to records based on the modulus operation. To find the memory locations assigned to the Social Security numbers given, we need to calculate the result of k mod 101 for each number.

Therefore, the memory locations assigned to the records are:

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Answer:

B. Changes in the fair value of the investors ownership shares of the investee

Step-by-step explanation:

The fair value option is defined as the alternative for any business that helps them to record its financial instruments at their fair values.

The answer is : Changes in the fair-value of the investor's ownership in shares of the investee.

Multiply the time per day by the number of days per week.

6/8 x 6 = (6 x 6)/8 = 36/8 = 4 1/2 hours a week.

Hey!

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

Answer:

[tex]\large\boxed{Natalie~reads~4~\frac{1}{2}~hours~a~week! }[/tex]

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

Solution:

~Turn six into improper fraction

6 = 6/1

~Multiply

6/8 * 6/1 = 38/8

~Simplify

38/8 = 4 1/2

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

Hope This Helped! Good Luck!

Answer:

10 in each with 5 left over

Step-by-step explanation:

Final answer:

You need to pull out 6 socks to guarantee a pair of one color, 11 socks to guarantee two pairs, and 7 socks to be certain you have a pair of black socks.

Explanation:

To guarantee that you have a pair of one color when selecting from a mix of 10 pairs of socks (5 black and 5 blue), you must consider the worst-case scenario. This occurs when you alternatively pick one of each color. Therefore, after picking 5 black and 4 blue socks, the next sock you pick will guarantee a pair. So, you need to pull out 6 socks to ensure a pair of one color (5 of one color and 1 of the other).

To have two good pairs, you would continue this pattern. After the first pair is secured with 6 pulls, you would possibly pick the alternating color for the next 4 pulls, and then any subsequent sock would complete a second pair of one color. In total, this would require pulling out 11 socks to ensure two pairs.

To be certain you have a pair of black socks, prepare for the possibility of pulling out all 5 blue socks first. After these 5, the next 2 socks you pull out will be black, giving you at least one pair of black socks. Therefore, you would need to pull out 7 socks to be certain.

Answer:

a) ∀x ∃f F(x, f)

b) ∃e ∀y F(e, y)

c) ∀x ∃y F(x, y)

d) ¬∃x ∀y F(x, y) ≡ ∃x ∀y ¬F(x, y)

e) ∃x ∃y F(x, y)

f) ¬∃x ∃f ∃j [F(x, f) ∧ F(x, j)] ≡ ∃x ∃f ∃j ¬[F(x, f) ∧ F(x, j)]

g) ∃n ∃a ∃b [F(n, a) ∧ F(n, b)]

Step-by-step explanation: F (x, y) "x can fool y,"

domain consists of all people in the world

a) Everybody can fool Fred.

Let's say Fred = f ∈ y

∀x ∃f F(x, f)

b) Evelyn can fool everybody.

Let's say Evelyn = e ∈ x

∃e ∀y F(e, y)

c) Everybody can fool somebody.

∀x ∃y F(x, y)

d) There is no one who can fool everybody.

¬∃x ∀y F(x, y) ≡ ∃x ∀y ¬F(x, y)

e) Everyone can be fooled by somebody.

∃x ∃y F(x, y)

f) No one can fool both Fred and Jerry.

Let's say Fred = f ∈ y

Let's say Jerry = j ∈ y

¬∃x ∃f ∃j [F(x, f) ∧ F(x, j)] ≡ ∃x ∃f ∃j ¬[F(x, f) ∧ F(x, j)]

g) Nancy can fool exactly two people.

Let's say Nancy = n ∈ x

Let's say person 1 = a ∈ y

Let's say person 2 = b ∈ y

∃n ∃a ∃b [F(n, a) ∧ F(n, b)]

The statements are expressed using quantifiers as shown above. The symbols ∀, ∃, ¬, ∧, and → represent "for all," "there exists," "not," "and," and "implies," respectively.

Step 1: Define the domain and predicate.

Domain: All people in the world.

Predicate: F(x, y) means "x can fool y"

Step 2: Express each statement using quantifiers.

a) Everybody can fool Fred: ∀x F(x, Fred)

b) Evelyn can fool everybody: ∀y F(Evelyn, y)

c) Everybody can fool somebody: ∀x ∃y F(x, y)

d) There is no one who can fool everybody: ¬∃x ∀y F(x, y) or ∀x ∃y ¬F(x, y)

e) Everyone can be fooled by somebody: ∀y ∃x F(x, y)

f) No one can fool both Fred and Jerry: ∀x ¬(F(x, Fred) ∧ F(x, Jerry))

g) Nancy can fool exactly two people: ∃y₁ ∃y₂ (y₁ ≠ y₂) (F(Nancy, y₁) ∧ F(Nancy, y₂) ∧ ∀y ((y ≠ y₁ ∧ y ≠ y₂) → ¬F(Nancy, y)))

Complete question:

Let F (x, y) be the statement "x can fool y," where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) Everybody can fool Fred.

b) Evelyn can fool everybody.

c) Everybody can fool somebody.

d) There is no one who can fool everybody.

e) Everyone can be fooled by somebody.

f) No one can fool both Fred and Jerry.

g) Nancy can fool exactly two people.

Answer:

Just find the distance of the vertices of the quadrilateral ( such as : AB, BC, CD DA )by using distance formula...

Then if opposite sides of quadrilateral is equal then it is rectangle .....

hope you understand...

Answer:

The number of adults tickets sold was 894 and the number of children tickets sold was 335

Step-by-step explanation:

Let

x ----> the number of adults tickets sold

y ----> the number of children tickets sold

we know that

x+y=1,229 -----> equation A

35x+27y=40,335 ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (894,335)

see the attached figure

therefore

The number of adults tickets sold was 894 and the number of children tickets sold was 335

To solve for the number of adult and child Broadway show tickets sold, we set up and solve a system of equations. After calculation, we find that 894 adult tickets and 335 child tickets were sold.

The question asks to determine the number of adult and child tickets sold when tickets to a Broadway show cost $35 for adults and $27 for children, with a total of 1229 tickets sold for a total amount of $40335. This is a typical example of a system of equations problem.

Step-by-Step Solution:

Let x be the number of adult tickets sold and y be the number of child tickets sold.

We have two equations:

To solve the system, multiply the first equation by -27 to eliminate y:

Add this result to the second equation:

Divide by 8 to find x:

Substitute x = 894 into the first equation to find y:

Therefore, 894 adult tickets and 335 child tickets were sold.

Answer:

y=-x-4

Step-by-step explanation:

first-divide the 3 over to the side x is on

then subtract the y over to the other side. THEN MOVE THE X BACK THE THE SIDE WITH 4. tHEN DIVIDE -X BY -1 TO GET RID OF THE NEGATIVE AFTERYOU SHOULD PUT THE NEGATIVE SIGN TO THE X.

Answer:

See the picture please

Step-by-step explanation:

Answer:

M = 16

H = 25

F = 50

Step-by-step explanation:

Let's use for abbreviation M for Martina's messages, H for Hong's messages and F for Felipe's messages.

Now we need to write the given information as equations.

Martina, Hong, and Felipe sent a total of 91 text messages

(1) M + H + F = 91

Hong sent 9 more messages than Martina.

(2) H = M + 9

Felipe sent 2 times as many messages as Hong

(3) F = 2 * H

Now with this system, we need to replace the letters to leave only M in the first equation.

(4) M + (M + 9) + (2*(M + 9)  = 91

(5) 4*M + 27 = 91

(6) M = (91-27) / 4

Then we find the answer:

M = 16

H = 25

F = 50

The number of text messages sent by Martina, Hong, and Felipe, you solve the equation m + (m + 9) + 2(m + 9) = 91, which results in Martina sending 16 messages, Hong sending 25, and Felipe sending 50.

The problem involves solving a system of equations to find out how many text messages Martina, Hong, and Felipe each sent. Let's define Martina's number of messages as m.

Then Hong's number would be m + 9, and Felipe sent 2(m + 9) because he sent twice as many as Hong.

The total number of messages sent by all three is given as 91. This gives us the equation: m + (m + 9) + 2(m + 9) = 91. Simplifying, we get:
m + m + 9 + 2m + 18 = 91
4m + 27 = 91
4m = 64
m = 16.

Now that we've found Martina's number, we can calculate the others:
Hong: 16 + 9 = 25
Felipe: 2 * 25 = 50. So, Martina sent 16 messages, Hong sent 25, and Felipe sent 50.

Answer:

  10^-5 or 1/100,000

Step-by-step explanation:

That probability of 5 events in a row is the 5th power of the probability of one of them, assuming they are independent.

  0.1^5 = (10^-1)^5 = 10^-5

The probability of a hurricane hitting five years in a row, given an annual probability of 0.10, is calculated by raising 0.10 to the power of 5. The result is 0.00001, or 0.001%.

The probability of a hurricane hitting during any one year in the designated area is 0.10, making it a fairly rare event. The student wants to know what the probability is that this will occur five years in a row. In probability theory, we calculate the likelihood of independent events happening consecutively by multiplying their individual probabilities together.

In this example, each year is an independent event, meaning one year's hurricane occurrence does not impact the likelihood of a hurricane in the subsequent year. Given that the annual probability of a hurricane is 0.10, if we want to find the probability of a hurricane hitting for five consecutive years, we simply raise this probability to the power of 5.

So, the probability of Victor experiencing a hurricane five years in a row is 0.10 to the power of 5, equivalently written as (0.10)^5.

This equals 0.00001 (or 0.001% if written as a percentage). This demonstrates that the likelihood of experiencing a hurricane five years in a row given an annual probability of 0.10 is quite miniscule.

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Answer:

Step-by-step explanation:

The converse of a conditional swaps the "if" and "then" clauses. Here, that makes the converse read ...

  If an angle is acute, then it is 60 degrees.

Since an acute angle may have any non-negative measure less than 90°, it is not true that its measure is necessarily 60°.

The function that represents the number of likes each day is[tex]\(c(n) = 143(3)^{n-1}\)[/tex]. Therefore, the correct answer is option D.

The function [tex]\(c(n) = (3)n - 1\)[/tex] models the number of likes each day, where [tex]\(n\)[/tex] is the number of days since the video was posted.

On the first day, there were 143 likes.

To find the function that shows the number of likes each day, we need to substitute [tex]\(n = 1\)[/tex] into the given function and solve for the number of likes.

Substituting [tex]\(n = 1\) into \(c(n) = (3)n - 1\)[/tex], we get:

[tex]\[c(1) = (3)(1) - 1\][/tex]

[tex]\[c(1) = 3 - 1\][/tex]

[tex]\[c(1) = 2\][/tex]

So, on the first day[tex](\(n = 1\)),[/tex] there were 2 likes. Since the problem states that there were actually 143 likes on the first day, the correct function should take this into account. Therefore, the correct function is:

[tex]\[c(n) = 143(3)^{n - 1}\][/tex]

Thus, the correct option is:

[tex]D. \(143(3)^{n-1}\)[/tex]

The correct function modeling the number of likes each day with 143 initial likes and tripling daily is:  [tex]\[ c(n) = 143 \times 3^{n-1} \][/tex]

This aligns with the given exponential growth pattern.

To determine which function models the number of likes each day, let's consider the following:

- The initial number of likes is 143. This is the base case.

- The function is described as having 3 times more likes each day. This suggests an exponential growth pattern.

To derive the correct function, we need to incorporate this growth rate into the initial likes:

Given the base case (the first day) has 143 likes, and the number of likes triples each day, the correct function should start with the initial likes (143) and then account for the exponential increase by multiplying by the growth factor raised to the appropriate power.

This can be represented mathematically as:

[tex]\[ c(n) = 143 \times 3^{n-1}. \][/tex]

Let's break it down:

- Exponential Growth: Multiplying by 3 every day suggests exponential growth with a base of 3.

- Initial Value : The function starts with 143 likes.

- Days Since Posting : The exponent  n-1 accounts for the base case.

If  n = 1 , then [tex]\( 3^{n-1} = 3^{0} = 1,[/tex] which preserves the initial value of 143.

This leads us to option D , which correctly models the number of likes each day:

[tex]\[ c(n) = 143 \times 3^{n-1}.[/tex]  

Question :

Every day, there are 3 times more likes on an internet video of a cat which is modeled by the function c(n) = (3)n − 1, where n is the number of days since the video posted. On the first day, there were 143 likes. What is the function that shows the number of likes each day?

A. c(n) = (3)(143)^{n-1}

B. c(n) = 143^{n-1}

C. c(n) = (3)143 − n

D.143(3)^{n-1}

Answer:

9 cats were fed that evening.

Step-by-step explanation:

6 divided by 2/3 equals 9, so 9 cats were fed that evening.

Hope this helps! ☺

Answer:

There are 9 cats in total

Step-by-step explanation:

Let x be the no. of cats

Each cat received cup of food = [tex]\frac{2}{3}[/tex]

Caps received by x cats = [tex]\frac{2}{3}x[/tex]

We are given that 6 cups of cat food were shared

So, [tex]\frac{2}{3}x=6[/tex]

[tex]x=\frac{3}{2} \times 6 [/tex]

[tex]x=9 [/tex]

Hence there are 9 cats in total .

The correct answer is True, as z must be expressible as a linear combination of the linearly independent vectors x and y, putting z in the Span{x, y}.

If x and y are linearly independent, and if the set {x, y, z} is linearly dependent, then it must be the case that z can be expressed as a linear combination of x and y. This is because in a linearly dependent set, at least one of the vectors can be written as a combination of the others. Since x and y are linearly independent, they cannot be written in terms of each other, leaving z to be the vector that depends on x and y. Therefore, z is in the Span{x, y}. The correct answer to the question is True.