find the number of terms in an AP given that it's first and last terms are a & 37a respectively and it's common difference is 4a​

Answer:

The triangle will triple in size.

Answer:

1/4

Step-by-step explanation:

Skateboards  : wheels

12                    :     48

Divide each part by 12

12/12              :    48/12

1                       :4

[tex]\huge\mathbb{\fcolorbox{red}{lavenderblush}{✰Answer}}[/tex]

There are Twelve skateboards have 48 wheels.,

we need to find the ratio of skateboards to wheels, in simplest form;

Hence,

Ratio of skateboard to wheel

Step-by-step explanation:

Given: [∀x(L(x) → A(x))] →

[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for

arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof

technique.

Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

We need to show that the above expression is unsatisfiable (False).

¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))

∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))

E.I with respect to x,

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))

E.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b

U.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Since P ∧ Q is P, drop L(a) from the above expression.

(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Apply distribution

(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))

Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to

(L(b) ∧ H(a, b) ∧ ¬A(b))

U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace

¬A(b) in the above expression with ¬L(b). Thus, we get,

(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.

This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows

from the premise.

15

Answer:

The interval that represents the middle 68% of her commute times is between 33.5 and 42.5 minutes.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 38 minutes, standard deviation of 4.5 minutes.

Determine the interval that represents the middle 68% of her commute times.

Within 1 standard deviation of the mean. So

38 - 4.5 = 33.5 minutes

38 + 4.5 = 42.5 minutes.

The interval that represents the middle 68% of her commute times is between 33.5 and 42.5 minutes.

9514 1404 393

Answer:

  7.056 × 10^31

Step-by-step explanation:

The applicable rule of exponents is ...

  (10^a)(10^b) = 10^(a+b)

__

  [tex](1.2\times10^{19})\times(5.88\times10^{12})=(1.2\cdot5.88)\times10^{19+12}\\\\=\boxed{7.056\times10^{31}}[/tex]

As you know, the commutative and associative properties of multiplication let you rearrange the order of the product to any convenient form. Here it is convenient to group the mantissas together and the powers of 10 together.

__

Additional comments

This is a product your scientific or graphing calculator can produce for you. Likely it will display the result in scientific notation because it won't have enough display digits to show you the product any other way. For smaller numbers, you can set the display mode to give you scientific notation.

If you choose to use a spreadsheet to perform this calculation, the numbers would be entered as 1.2e19 and 5.88e12. The result will be something like 7.056e31. You may have to format the display to show 3 decimal places.

The top part is the areas of the rooms in feet. You need to find the inches instead. Multiply them by 12.

20 x 12

20 x 12= 240

12 x 12=144

So the first one will be:

240 x 144

Second:

96 x 96

Third:

96 x 114

Fourth:

240 x 196

Fifth:

240 x 240

Sixth:

120 x 240

Hi there!  

»»————-　★　————-««

I believe your answer is:  

There is no solution to the equation.  

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\-3(4x-6)=7-12x\\-------------\\\rightarrow -12x+18 = 7 - 12x\\\\\rightarrow -12x + 18 - 18 = 7 - 18 -12x\\\\\rightarrow -12x=-12x-11\\\\\rightarrow-12x+12x = -12x+12x - 11\\\\\rightarrow 0 = -11\\\\\boxed{\text{This is a \underline{contradiction}. There is no solution.}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

after 10 months

Step-by-step explanation:

Let x be the number of months and y be the amount they still owe.

Sin Ian borrows $1000 from his parents, then the y-intercept b= 1000 since he owes $1000 when x = 0. He pays them back $60 each month The slope is then m = -60 . Substituting in b = 1000 and m = -60 into the slope-intercept form of a line then gives y= mx + b=-60x +1000.

Sin Ken borrows $600 from his parents, then the y-intercept b = 600 since he owes $600 When x= 0. He pays them back $20 per month so the amount he owes decreases $20 each month. The slope is then m = -20 . Substituting in

b= 600 and m = -20 into the slope-intercept form then gives y = mx +b = -20x + 600.

They will owe the same amount when they have the same y-coordinate. Therefore -60x+ 1000= y= -20x+600. Solve this equation for x:

-60x+ 1000 = -20x+ 600

1000 = 40x+ 600

400 = 40x

10=x

They will then owe the same amount after 10 months.

Given:

The expression is:

[tex]25-10\div 2+3[/tex]

To find:

Part A: The expression using parentheses so that the expression equals 23.

Part B: The expression using parentheses so that the expression equals 3.

Solution:

Part A:

In option A,

[tex](25-10)\div 2+3=15\div 2+3[/tex]

[tex](25-10)\div 2+3=7.5+3[/tex]                       [Using BODMAS]

[tex](25-10)\div 2+3=10.5[/tex]

In option B,

[tex]25-10\div (2+3)=25-10\div 5[/tex]

[tex]25-10\div (2+3)=25-2[/tex]                      [Using BODMAS]

[tex]25-10\div (2+3)=23[/tex]

In option C,

[tex](25-10)\div (2+3)=15\div 5[/tex]

[tex](25-10)\div (2+3)=3[/tex]

In option D,

[tex]25-(10\div 2)+3=25-5+3[/tex]

[tex]25-(10\div 2)+3=28-5[/tex]                     [Using BODMAS]

[tex]25-(10\div 2)+3=23[/tex]

After the calculation, we have [tex]25-10\div (2+3)=23[/tex] and [tex]25-(10\div 2)+3=23[/tex].

Therefore, the correct options are B and D.

Part B: From part A, it is clear that

[tex](25-10)\div (2+3)=3[/tex]

Therefore, the correct option is C.

Answer:

7x - 8

Step-by-step explanation:

Hope this helps!

Answer:

question please so I can help you

Answer:

y - 2 = 1/3(x - 3)

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Plug in the slope:

y - y1 = m(x - x1)

y - y1 = 1/3(x - x1)

Plug in the given point:

y - y1 = 1/3(x - x1)

y - 2 = 1/3(x - 3)

So, the correct answer is y - 2 = 1/3(x - 3)

Answer:

27.3

Step-by-step explanation:

27.3

Answer:

Plays a musical instrument

Top left

Plays a sport: 0.46

Plays a musical instrument

Top right

Does not Play a sport: 0.54

Does not play a musical instrument

Bottom Left

Plays a sport: 0.73

Does not play a musical instrument

Bottom right

Does not Play a sport: 0.27

Step-by-step explanation:

I hope this helps you! :D

Answer:

572.6

Step-by-step explanation:

400 = 220 [tex]x^{5}[/tex]

ln(400/220) = 5 ln(x)

ln(x) = .1195

x = [tex]e^{.1195}[/tex]

x = 1.127

Y = 220[tex](1.127)^{8}[/tex]

Y= 572.6

Step-by-step explanation:

14 For which equation is the solution set {-5,2}?. 15 Which equation has the same solutions as. 2x. 2 + x - 3 = 0.

Answer:

Point estimate of the corresponding population mean = $8,213

Step-by-step explanation:

Given:

Average cost of a wedding reception (x) = $8,213

Total number of sample (n) = 450

Standard deviation = $2185

Find:

Point estimate of the corresponding population mean

Computation:

Average cost of a wedding reception (x) = Point estimate of the corresponding population mean

Point estimate of the corresponding population mean = $8,213

Answer:

11 2/3%

Step-by-step explanation:

Change in Amount  =335,000 – 300,000

Percent Increase

Original Amount

300,000

35,000

2

=0.11666=11.666%=11-%

300,000

3

(https://imgur.com/a/U6c1pes) - For more clear explanation.

Given:

The stem and leaf plot of a data set is given.

Legend:1|0 represents 10.

To find:

The original data set for the given stem and leaf plot.

Solution:

It is given that 1|0 represents 10 in the given stem and leaf plot. Using this, the original data set from the given stem and leaf plot is:

10, 11, 14, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 38, 40, 41.

These values are in ascending order.

Therefore, the original set of data is 10, 11, 14, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 38, 40, 41.

Answer:

yes that are similar

Step-by-step explanation:

because the angles are both 50 degrees

similarity statement:

triangle DEF= triangle JEH

hope that helps bby<3

Answer: B

Step-by-step explanation:

Answer:

-5ºC < 5ºC is an inequality that compares temperatures.

B is the correct answer for the multiple choice question.

9514 1404 393

Answer:

  38

Step-by-step explanation:

The product of the given numbers is 38.4888. Rounding this to two significant digits gets you 38.

Answer:

63.44degrees

Step-by-step explanation:

Given that;

tan(A-45) = 1/3

A-45 = arctan(1/3)

A - 45 = 18.44

A = 18.44+45

A = 63.44degrees

Hence the value of A is 63.44degrees

Answer:

The smallest possible length is 0.83m

Step-by-step explanation:

Given

[tex]Volume = 565L[/tex]

Required

The smallest length of the tank

Since the tank is cubical, then the volume is:

[tex]Volume = Length^3[/tex]

This gives:

[tex]565L= Length^3[/tex]

Express as [tex]m^3[/tex]

[tex]\frac{565m^3}{1000} = Length^3[/tex]

[tex]0.565m^3 = Length^3[/tex]

Take cube roots of both sides

[tex]0.8267m = Length[/tex]

Rewrite as:

[tex]Length = 0.8267m[/tex]

Approximate

[tex]Length = 0.83m[/tex]

Step-by-step explanation:

de hecho, la respuesta está en la imagen de arriba

Answer:

Your answer would be B

Step-by-step explanation:

So right away you can get rid of a and d since they are positive numbers, there is no positive numbers in the graph were the line is.

So we know that the y-intercept is -2 (as you can see the line pass through (0,-2))

And we know the y intercept is -8 (since the line pass through (-8,0))

so you are left with b and c, c is incorrect because the -2 goes through the y-intercept not the x.

The right choice is b, it states that the x-intercept -8 pass through the line, the y-intercept is -2

Your welcome and hoped this helped!

Step-by-step explanation:

we can simplify the stuff inside the parentheses to

[tex] \frac{ {x}^{3} }{2y} [/tex]

now we need to multiply it with itself, giving us

[tex] \frac{ {x}^{6} }{4 {y}^{2} } [/tex]

so yeah, D is the correct answer

Answer:

F(-2)= g(-2)

Step-by-step explanation:

F(-2)= g(-2), both function have the same points of intersect.

Answer:

The base reduces at 3.75cm/min

Step-by-step explanation:

Given

Let

[tex]h \to altitude[/tex]

[tex]b \to base[/tex]

[tex]A \to Area[/tex]

So:

[tex]\frac{dh}{dt} = 1.5cm/min[/tex]

[tex]\frac{dA}{dt} = 1.5^2cm/min[/tex]

The area of a triangle is:

[tex]A = \frac{1}{2}bh[/tex]

Calculate b when [tex]A =88cm^2; h =8cm[/tex]

[tex]A = \frac{1}{2}bh[/tex]

[tex]88=\frac{1}{2} * b * 8[/tex]

[tex]88 =b * 4[/tex]

Solve for b

[tex]b = 88/4[/tex]

[tex]b = 22[/tex]

We have:

[tex]A = \frac{1}{2}bh[/tex]

Differentiate with respect to time

[tex]\frac{dA}{dt} =\frac{1}{2}(h\frac{db}{dt} + b\frac{dh}{dt})[/tex]

Substitute the following values in the above equation

[tex]\frac{dh}{dt} = 1.5cm/min[/tex]        [tex]\frac{dA}{dt} = 1.5^2cm/min[/tex]      [tex]b = 22[/tex]     [tex]h = 8[/tex]

[tex]1.5 = \frac{1}{2}(8 * \frac{db}{dt} + 22 * 1.5)[/tex]

Multiply both sides by 2

[tex]3 = 8 * \frac{db}{dt} + 22 * 1.5[/tex]

[tex]3 = 8 * \frac{db}{dt} + 33[/tex]

Collect like terms

[tex]8 * \frac{db}{dt} = 3 -33[/tex]

[tex]8 * \frac{db}{dt} = -30[/tex]

Divide both sides by 8

[tex]\frac{db}{dt} = -\frac{30}{8}[/tex]

[tex]\frac{db}{dt} = -3.75[/tex]

Answer:

3/14

Step-by-step explanation:

Probability = # of favorable outcomes / # of possible outcomes

Favorable outcomes = we want to find the probability of pulling a blue marble. There are 3 blue marbles so 3 is the number of favorable outcomes

Possible outcomes: to find the number of possible outcomes we simply find the total number of marbles

3 + 7 + 4 which equals 14

So possible outcomes = 14

We now plug in the values into the probability formula

The probability of pulling a blue marble is 3/14

Answer:

3/14

Step-by-step explanation:

you add the red marbles, blue marbles, and green marbles together, which equal 14. Out of the 14, there are only 3 blue marbles so it would be 3/14.