Find the 51th term of the arithmetic sequence 25, 12 and -1

The distance between X(-9,2) and Y(5,-4) is 15.23 units.

The distance formula states that if there are 2 points A(x1, y1) and B(x2, y2), then the distance between the two points is given by the formula-

[tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]

Here, we are given that there are 2 points- X(-9, 2) and Y(5, -4)

So here we can say that,

x1 = -9, y1 = 2

and x2 = 5, y2 = -4

Now, plugging in the values given above in the distance formula we will find XY as follows-

XY = [tex]\sqrt{(-9-5)^{2} + (5+4)^{2} }[/tex]

XY = [tex]\sqrt{(-14)^{2} + (9)^{2} }[/tex]

XY = [tex]\sqrt{196+ 81 }[/tex]

XY = [tex]\sqrt{277 }[/tex]

The square root of 277 is approximately 15.23.

Thus, XY = 15.23

Therefore the value of XY to the nearest hundredth is 15.23 units.

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Answer:

4 1/2  and 7 1/4

Step-by-step explanation:

y=1/2x-3

The graph shows that the line moves up 1 and right 2, up 1 and right 3, etc., and that b is the y intercept. It denotes a positive 1/2 slope.

The y intercept is -3 because the line crosses the y axis at -3. The shaded region has to be below the line. Our response is the second graph in the first row.

so

y= 1/2x -3

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Answer:

See below

Step-by-step explanation:

Refer to the attachment.

Given:

(A ∧∼B) ∨ (A ∧ ∼C)

Solving steps:

≡A∧(∼B∨∼C). . . . . Distributive Law

≡A∧∼(B∧C). . . . . . De Morgan's Law

≡∼(∼A)∧∼(B∧C). . . . . . Double Negation Law

Hence,

(A ∧∼B) ∨ (A ∧ ∼C)≡∼(∼A)∧∼(B∧C) [Proven]

Answer:

A variable is a quantity that may change within the context of a mathematical problem or experiment.

The answer is K^2 = 711.6Y on solving the given equation.

Given that, 1 = 711.6Y/K^2 and we have to solve it for the value of K^2. For this we simply have to solve the given equation steps wise. So, let's proceed to solve the equation.

1 = 711.6Y/K^2

Now, multiply K^2 with 1, we get

K^2 = 711.6Y

So, the value of k^2 will be equal to Y times 711.6 and further we can solve it for the various value of Y.

Let us suppose, we have to solve the above equation for the specific value of Y.

So, put Y = 1

On solving, we get

K^2 = 711.6x1

K^2 = 711.6

K = (711.6)^(1/2)

K = 26.67

∴ K^2 = 711.6Y is the equation we will get on solving the equation given to us in the question.

Hence, K^2 = 711.6Y is the required answer.

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Answer:

12

Half of 24 is 12

I hope this helps C:

Answer:

23.5

Step-by-step explanation:

i hope this is helpful :)

Answer:

[tex]Cupcakes = 7[/tex]

Step-by-step explanation:

Given

[tex]Total\ Sprinkles = 134[/tex]

[tex]Sprinkle\ per\ cupcake = 18[/tex]

Required

Determine the number of cupcakes

To do this, we simply divide the total cups of sprinkle by the sprinkles per cupcake

[tex]Cupcakes = \frac{Total\ Sprinkles}{Sprinkle\ Per\ Cupcake}[/tex]

This gives:

[tex]Cupcakes = \frac{134}{18}[/tex]

[tex]Cupcakes = 7.44[/tex]

[tex]Cupcakes = 7[/tex] approximated

Hence, 7 cupcakes are needed

Answer:

it is an integer.

Step-by-step explanation:

Answer:

Interger because it's a whole number and whole numbers are intergers.  Hope this helps pls give brainliest

Step-by-step explanation:

the answer its 120 hope helps you

Answer:

Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]

Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]

Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]

Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]

Step-by-step explanation:

We are given [tex]f(x)=2x-6[/tex]

We need to match the transformations.

1) shifts f(x) 4 units down.

When function f(x) shifts k units down the new function becomes f(x)-k

In our case

[tex]g(x)=2x-6-4\\g(x)=2x-10[/tex]

So, Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]

2) Stretches f(x) by a factor of 4 away from x-axis

When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)

[tex]g(x)=2(4x)-6\\g(x)=8x-6[/tex]

So, Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]

3) Shifts f(x) 4 units right

When function f(x) shifts h units right the new function becomes f(x-h)

[tex]g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14[/tex]

So,  Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]

4) Compress f(x) by a factor of 1/4 toward the y-axis

When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)

[tex]g(x)=1/4(2x-6)\\g(x)=1/2x-3/2[/tex]

Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]

(Option Not given)

(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)

Answer:

o dont know

Step-by-step explanation:

Answer:

2x^2 - 6x

Step-by-step explanation:

2x(x-3)

= 2x^2 - 6x

Answer:

I believe the answer is a imaginary number... I only know the fist one I'm sorry..

Step-by-step explanation:

I think this because a rational number is a number that is real. A Whole number is one without decimals. A natural number is something that is also real. I really hope this is helpful.

It should be noted that rounding off 0.586 to the nearest hundredth will be 0.59.

It should be noted that rounding to the nearest hundredth simply means the rounding of any decimal number to its nearest hundredth value.

Fyr example, it should be noted that in the decimal, hundredth means 1/100 or 0.01. For example, the rounding of 3.267 to its nearest hundredth is 3.23.

It should be noted that in this case, it should be noted that rounding off 0.586 to the nearest hundredth will be 0.59.

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The best first step in solving m–2(m–4)≤3m for m will be A. Distribute -2 through the parentheses.

It should be noted that an inequality simply means a relation between the expressions that are unequal.

It should be noted that the best first step in solving m–2(m–4)≤3m for m will be to distribute -2 through the parentheses.

This is important in order to have variables of m and then solve accordingly.

In conclusion, the best option is A.

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Answer:

B. 5 and 1/4 percent

Step-by-step explanation:

Step one:

given

principal= $2460

time= 3 and 1/2 years= 3.5 years

SI= $452

Required

The rate

Step two:

we know that

SI= PRT/100

substituting our data we have

452= 2460*R*3.5/100

452=8610R/100

cross multiply

452*100= 8610R

divide both sides by 8610

45200/8610= R

R= 5.25%

R= 5 and 1/4 percent

Answer:

They are now dead

Step-by-step explanation:

Jake Paul

Answer: 24

I am bad at explaining so i wouldn't help there

Answer:

24

Step-by-step explanation:

75% is also 3/4. 3/4 out of 32 can be 3 x 32/4 which is 3 x 8, or 24.

Answer:

A. 3(2x - 12) = 2(3 + 2x - 12)

B. Length = 6, width = 3

Step-by-step explanation:

l = 2x - 12

w = 3

Area = 3(2x - 12)

Perimeter = 2(3 + 2x - 12)

if A = P

3(2x - 12) = 2(3 + 2x - 12)

6x - 36 = 6 + 4x - 24

6x - 4x = 6 - 24 + 36

2x = 18

x = 9

Length = 2x - 12 = 2(9) - 12 = 18 - 12 = 6

Answer: 7 8 9 7 6 12 2 0

Step-by-step explanation:

Answer:

1) -8m +4+p

2) 10-3t

3)im not sure for the rest

Step-by-step explanation:

Answer:

Step-by-step explanation:

so the equation will be: y = 5 + 3.50x. y is the total cost, and x is the number of hours. To solve for 6 hours, just plug 6 into the equation so: y = 5 + 3.50(6) = 26. So the answer is: it costs $26.00 to rent a drill for 6 hours.

A (i think)

Step-by-step explanation:

Answer:

The answer is "[tex]8\pi[/tex]"

Step-by-step explanation:

[tex]\to r(v,u) =(4 \cos v, 4 \sin v,u) \\\\0\leq v \leq 2\pi, \ \ 4\leq u\leq 5\\\\\to r_v= (-4 \sin v, 4 \cos v, 0)\\\\\to r_u=(0,0,1)[/tex]

[tex]\to r_v\times r_u = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4 \sin v& 4 \cos v& 0\\0&0&1\end{array}\right| \\\\[/tex]

                [tex]= (4 \cos v, -4 \sin v, 0)[/tex]

[tex]|r_v \times r_u| = \sqrt{16 \cos^2 v +16 \sin^2 v}\\\\[/tex]

             [tex]= \sqrt{16( \cos^2 v + \sin^2 v)}\\\\= \sqrt{16(1)}\\\\= \sqrt{4^2}\\\\=4[/tex]

Calculating the surface area:

[tex]=\int^{2\pi}_{0} \int^{5}_{4} 4 \ du \ dv \\\\=\int^{2\pi}_{0} 4[4]^{5}_{4} \ dv \\\\=\int^{2\pi}_{0} 4[5-4] \ dv \\\\=\int^{2\pi}_{0} 4 \ dv \\\\=4 [v]^{2\pi}_{0}\\\\= 4 \times 2\pi\\\\= 8\pi[/tex]

This question is based on the parametrization. Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.

Given:

The portion of the cylinder [tex]x^{2} +y^{2} = 16[/tex] between the planes z=4 and z=5.

Let u=z and v=θ and use cylindrical coordinates to parameterize the surface.

We need to express the area of the surface as a double integral.by using parametrization.

According to the question,

It is given that u=z and v=[tex]\theta[/tex],

Therefore, r(v,u) = (4 Cos v,4 Sin v, u)

Range of v : 0 [tex]\leq[/tex] v [tex]\leq[/tex] 2[tex]\pi[/tex]

Range of u : 4 [tex]\leq[/tex] u [tex]\leq[/tex] 5

[tex]\rightarrow r_v= (-4 \;sin\; v,4\;cos\; v,0)\\\rightarrow r_u=(0,0,1)[/tex]

[tex]\rightarrow r_u \times r_v =\begin{bmatrix} \hat{i}& \hat{j} & \hat{k}\\ -4\; sin\;v & 4\; cos\; v & 0 \\ 0 & 0 & 1\end{bmatrix}\\\\=(4 cos v,\;-4 sin v ,0)\\\\\left | r_v \times r_u \right | = \sqrt{16cos^{2}v+16sin^2v } \\\\= \sqrt{16(cos^{2}v+sin^2v) }\\\\=\sqrt{16}\\\\=4[/tex]

Now calculating the surface area,

[tex]=\int\limits^{2\pi}_0\int\limits^5_4 4 du\; dv\\\\=\int\limits^{2\pi}_0 4[u]^5_4 dv\\\\=\int\limits^{2\pi}_0 4[5-4] dv\\\\\\=\int\limits^{2\pi}_0 4dv\\\\\\=4[v]^{2\pi}_0 = 4(2\pi-0)= 8\pi[/tex]

Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.

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The statement 'The ratio 4/7 : 8/21 has a unit rate of 3/2.' is True.

In this question, we have been given a statement 'The ratio 4/7 : 8/21 has a unit rate of 3/2.'

We need to check whether the statement is True or False.

We have been given the ratio of two fractions.

4/7 : 8/21

We know that for any non zero real numbers a, b, c, d,

a/b : c/d = a/b × d/c

So, we can write given ratio as,

4/7 : 8/21

= 4/7 × 21/8

= 3/2

In the given statement, it is mentioned that, the ratio 4/7 : 8/21 has a unit rate of 3/2.

This means, the given statement is correct.

Therefore, the statement 'The ratio 4/7 : 8/21 has a unit rate of 3/2.' is True.

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probability of a randomly selected bag weighing between 15.6 ounces and 16.4 ounces is 0.68269.

probability of a randomly selected bag weighing between 15.2 ounces and 16.8 ounces is 0.9545.

probability of a randomly selected bag weighing less than 14.8 ounces is 0.0013499.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean serve as a unit of measurement for the Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given, Given that the weights of bags of potato chips are normally distributed with an average weight of 16 ounces and a standard deviation of 0.4 ounces. thus,

μ = 16

σ = 0.4

for randomly selected bags weighing between 15.6 ounces and 16.4 ounces

x₁ = 15.6

x₂ = 16.4

Z score = ( x - μ)/σ

z₁ = (15.6 - 16) / 0.4

z₁ = -1

z₂ = (16.4 - 16)/ 0.4

z₂ = 1

From the table of normal distribution (z²)

the probability of getting the value between -1 to 1 is = 0.68269

for randomly selected bags weighing between 15.2 ounces and 16.8 ounces

x₁ = 15.2

x₂ = 16.8

Z score = ( x - μ)/σ

z₁ = (15.2 - 16) / 0.4

z₁ = -2

z₂ = (16.8 - 16)/ 0.4

z₂ = 2

From the table of normal distribution (z²)

the probability of getting the value between -2 to 2 is = 0.9545

for randomly selected bags weighing less than 14.8 ounces.

x = 14.8

Z score = ( x - μ)/σ

z = (14.8 - 16) / 0.4

z = -3

From the table of normal distribution (z²)

the probability of getting a value less than 14.8 = 0.0013499

Therefore, The probability that a randomly chosen bag will weigh between 15.6 and 16.4 ounces is 0.68269. The probability that a randomly chosen bag will weigh between 15.2 and 16.8 ounces is 0.9545. The probability that a randomly chosen bag will weigh less than 14.8 ounces is 0.0013499.

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Answer:

[tex]1\ pound = \$ \frac{2}{3}[/tex]

6 pounds of kiwis cost $4

Step-by-step explanation:

Given

[tex]x = pound\ of\ kiwis[/tex]

[tex]y = price\ in\ dollars[/tex]

[tex](x,y) = (3,2)[/tex]

Solving (a): Price of 1 pound kiwi

The given parameters can be translated to be:

3 pounds costs $2

i.e.

[tex]3\ pounds = \$2[/tex]

To get the cost of 1 pound, we divide both sides by 3

[tex]\frac{3\ pounds}{3} = \frac{\$2}{3}[/tex]

[tex]1\ pound = \frac{\$2}{3}[/tex]

[tex]1\ pound = \$ \frac{2}{3}[/tex]

Solving (b): What does (6,4) represent

This can be rewritten as:

[tex](x,y) = (6,4)[/tex]

Recall that the representation is:

[tex]x = pound\ of\ kiwis[/tex]

[tex]y = price\ in\ dollars[/tex]

By comparison:

[tex]x = 6\\ y = 4\\[/tex]

So, the above can be translated to mean.

6 pounds of kiwis cost $4

Answer:

6 pounds of kiwis cost $4

Step-by-step explanation:

Answer:

2/3+1/5=10/15+3/15=13/15

Step-by-step explanation:

Hope this helps!