What is the sum of arithmetic series 19+25+31+37+… Where n=9 ?

For any isosceles right triangle (aka 45-45-90 triangle), the hypotenuse is always equal to sqrt(2) times the leg. If x is the leg and y is the hypotenuse, then

[tex]y = x*\sqrt{2}[/tex]

which solves to

[tex]x = \frac{y}{\sqrt{2}}[/tex]

from here we plug in the given hypotenuse y = 10 to get the final answer. Optionally we could rationalize the denominator, but your teacher has chosen not to.

Answer:b

On edge

Step-by-step explanation:

Answer:

(a) 25 degrees

(b) -11 degrees

(c) 38 degrees

Step-by-step explanation:

The temperature function is:

[tex]T(t) = -t^2+4t+34[/tex]

(a) The average value for a temperature is:

[tex]M=\frac{1}{b-a}* \int\limits^b_a {f(x)} \, dx[/tex]

In this particular case, the average temperature is:

[tex]M=\frac{1}{9-0}* \int\limits^9_0 {T(t)} \, dt \\M=\frac{1}{9}* \int\limits^9_0 {(-t^2+4t+34)} \, dt \\M=\frac{1}{9}* {(-\frac{t^3}{3}+2t^2+34t)}|_0^9\\M=\frac{1}{9}*( {(-\frac{9^3}{3}+2*(9^2)+34*9)-0)[/tex]

[tex]M=25[/tex]

The average temperature is 25 degrees.

(b) The expression is a parabola that is concave down, therefore there are no local minimums, which means that the minimum temperature will be at one of the extremities of the interval:

[tex]T(0) = -0^2+4*0+34=34\\T(9) = -9^2+9*4+34=-11[/tex]

The minimum temperature is -11 degrees.

(c) The maximum temperature will occur at the point for which the derivate of the temperature function is zero:

[tex]T(t) = -t^2+4t+34\\T'(t)=-2t+4=0\\2t=4\\t=2[/tex]

At t = 2, the temperature is:

[tex]T(2) = -2^2+4*2+34=38[/tex]

The maximum temperature is 38 degrees.

Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

Answer:  12 Tbsp

Step-by-step explanation:

Note: 1 Tbsp = 3 tsp

2 tsp x 21 = 42 tsp

42 tsp ÷ 3 = 12 Tbsp

Answer:

they represent the same line

Step-by-step explanation:

i went to desmos graphing calculator and put x+3y=5 in the first spot then i put 4x+12y=20 below that and it showed me what the lines looked like

Both the equation represent the same line

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

x + 3y = 5

4x + 12y = 20

Now , the equation 4x + 12y = 20 can be simplified as

4x + 12y = 20

Divide by 4 on both sides ,

x + 3y = 5

Therefore , x + 3y = 5 is the same equation

Hence , both the equation represent the same line

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Answer:

x = - 3h

Step-by-step explanation:

Given

[tex]\frac{x}{h}[/tex] + 1 = - 2 ( subtract 1 from both sides )

[tex]\frac{x}{h}[/tex] = - 3 ( multiply both sides by h )

x = - 3h

Step-by-step explanation:

[tex] \frac{x}{h + 1} = - 2[/tex]

Cross multiply

We have

-2(h + 1) = x

Expand the terms in the bracket

We have the final answer as

x = -2h - 2

Hope this helps you

Answer:

Step-by-step explanation:

29 is 6 more than K

Let's create an equation

[tex]29 = 6 + k[/tex]

Move variable to L.H.S and change its sign

Similarly, move constant to R.H.S and change its sign

[tex] - k = 6 - 29[/tex]

Calculate

[tex] - k = - 23[/tex]

Change the sign on both sides of the equation

[tex]k = 23[/tex]

Hope this helps..

Best regards!!

The equation for the statement 29 is 6 more than K is solved and K = 23

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists  mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by the statement below

29 is 6 more than K

On simplifying , we get

29 = 6 + K

Subtracting 6 on both sides , we get

K = 29 - 6

K = 23

Therefore , the value of K is 23

Hence , the equation is K = 23

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Answer:

21 feet 4 inches

Step-by-step explanation:

Ellie bought two planks of wood that were each 4ft 3in long

Total length of these two planks = 4ft 3in + 4ft 3in = 8 feet 6 inches

she also bought  two planks of wood that were each 6 ft 5in long

Total length of these two  6 ft 5in planks =  6 ft 5in +  6 ft 5in = 12 feet10 inches

Thus, total length of all the woods purchased = Total length of 4ft 3in two planks  + Total length of the two  6 ft 5in planks

= 8 feet 6 inches + 12 feet 10 inches

adding feet with feet and inches with inches term

= 20 feet 16 inches

we know that 12 inches is equal to 1 feet

thus, 16 inches can be written as 1 feet 4 inches

thus,

20 feet 16 inches will be same as 21 feet 4 inches

The total length of the wood Ellie purchased is 21 feet 4 inches.

Answer:

156.75 tons

Step-by-step explanation:

627/4 = 156.75

Answer:

156(3/4)

Step-by-step explanation:

with this your divide.

627/4=156.75

as a mixed numer it would 156(3/4). It is 3/4 because the number ends in .75

Answer: 14 cans

Step-by-step explanation:

Given, Total area to paint = 400 square meters

approximately 3.28 feet in a meter.

So, 400 square meters = 400 x (3.28)² square feet

i.e. Total area to paint  = 4303.36 square feet

One gallon of paint requires for every 300 square feet.

One liter contains approximately 0.264 gallons

Then, One gallon = [tex]\dfrac{1}{0.264}\approx3.78\text{ liters}[/tex]

So, 3.78 liters paint requires for every 300 square feet.

Paint requires for each square feet = (3.78)÷(300) liters

Total paint required  = (Total area to paint ) x (Paint requires for each square feet)

= (4303.36)x (3.78)÷(300)

≈54.22 liters

Each can contains 4 liters of paint.

Smallest number of cans required = (Total paint required )÷ 4

=(54.22 ) ÷ 4

= 13.55≈ 14

Hence, 14 cans are required .

Answer:

12 / 253

Step-by-step explanation:

There are a total of 4 + 4 + 9 + 6 = 23 cookies in the bag, therefore, there are 23 * 22 = 506 ways to pick one cookie, eat it, and then pick another cookie. There are 6 ways to choose the first cookie (because there are 6 oatmeal cookies) and 4 ways to choose the second cookie (because there are 4 chocolate chip cookies) so there are 6 * 4 = 24 successful ways. The probability is thus 24 / 506 = 12 / 253.

Step-by-step explanation:

Q8.  

Step 1.

35.4 - 31 = 4.4

Step 2.

4.4 ÷ 31 = 0.1419....

Step 3.

0.1419.... x 100 = 14.19...

Step 4.

To one decimal place = 14.2% increase

Q9.

Step 1.

£10 ÷ 40 articles = £0.25 = 25p (this is the answer to part a)

Step 2.

32p x 40 articles = £0.32 x 40 articles = £12.80 (this is the answer to part b)

Step 3.

£12.80 - £10 = £2.80 (this is the answer to part c)

Step 4.

£2.80 ÷ £10 = 0.28

Step 5.

0.28 x 100 = 28% (this is the answer to part d)

Hope this was what you were looking for :)

(Also, hi to a fellow Brit - there aren't that many of us around here)

Bluey :)

Answer:

1

Step-by-step explanation:

We can find the slope using

m= ( y2-y1)/(x2-x1)

   = ( -8 - -4)/( 4 - 8)

   =  ( -8 +4)/( 4 - 8)

   = -4 / -4

   = 1

Answer:

slope equals 1

Step-by-step explanation:

To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1

Answer:

Step-by-step explanation:

The standard equation of an ellipse centered at the point (h,k) is

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1[/tex]

where a is the distance from the center to one of the vertex. We have the relation [tex]c= \sqrt[]{a^2-b^2}[/tex] where c is the distance from one of the focus to the center.

The distance between one vertex and the center is 5. So a=5. The distance from one focue to the center is 3. Then c =3. So we have that [tex]b^2 = a^2-c^2 = 16[/tex]

so the equation is

[tex]\frac{(x-2)^2}{25}+\frac{(y-2)^2}{16} = 1[/tex]

Answer:

y = 60 *x

Step-by-step explanation:

The rate is 180 miles / 3 hours = 60 miles per hour

Check by dividing 300 miles / 5 hours = 60 miles per hour

y = 60 *x  where y is miles and x = time

Answer:

Step-by-step explanation:

Answer:  1) [tex]\pm \sqrt{x+4}[/tex]

               2) see graph

               3) Choose one color from the graph

               4) D: x ≥ -4

                   R: y ≥ 0 for [tex]\sqrt{x+4}[/tex]     or      y ≤ 0   for [tex]-\sqrt{x+4}[/tex]

Step-by-step explanation:

1) To find the inverse, swap the x's and y's and solve for y:

Given: y = x² - 4

Swap: x = y² - 4

    x + 4 = y²

  [tex]\pm \sqrt{x+4}=y[/tex]

2) see attachment. Red and Blue combined creates the graph of the inverse.

3) Choose either the positive (red graph) or the negative (blue graph).

red graph: [tex]y= \sqrt{x+4}[/tex]

blue graph: [tex]y= -\sqrt{x+4}[/tex]

4) Domain reflects the x-values of the function.  The x-values for the red graph is the same as the blue graph so the answer will be the same regardless of which equation you choose.

Domain: x ≥ 0

Range reflects the y-values of the function.  The y-values differ between the positive and negative inverse functions. Positive is above the x-axis. Negative is below the x-axis.

Range (red graph): y ≥ 0 for  [tex]y= \sqrt{x+4}[/tex]

Range (blue graph):  y ≤ 0 for [tex]y= -\sqrt{x+4}[/tex]

Answer: 32

Step-by-step explanation:

Answer: 3 hours

Step-by-step explanation:

Here is the correct question:

Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?

Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.

Karen can also paint 1/x in 1 hour

Both of them will paint the house in 3/2 hours.

We then add them together which gives:

1/6 + 1/x = 3/2x

The lowest common multiple is 6x

1x/6x + 6/6x = 9/6x

We then leave out the denominators

1x + 6 = 9

x = 9 - 6

x = 3

Karen working alone will paint a house in 3 hours.

Answer:

theater

pls mark me as BRAINLIEST

Answer:

[tex]\boxed{x = 15}[/tex]

Step-by-step explanation:

Let the number be x

Condition:

[tex]2x - \frac{2}{3} x = 20[/tex]

Multiplying 3 to both sides

=> 3(2x) - 2x = 3(20)

=> 6x - 2x = 60

=> 4x = 60

Dividing both sides by 4

=> x = 15

Answer:

15

Step-by-step explanation:

Let x be that number.

2/3 of x subtracted from twice of x is 20.

2x - 2/3x = 20

Solve for x.

Combine like terms.

4/3x = 20

Multiply both sides by 3/4

x = 60/4

x = 15

The number is 15.

Answer:

5sqrt(2)

Step-by-step explanation:

you can split 50 into sqrt(25×2)

and the sqrt(25) is 5, so than your left with just the 2 in the sqrt.

Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

Answer:

Cosx is the answer.

Step-by-step explanation:

We have to simplify the trigonometric fraction given in this question.

[tex]\frac{\text{Cotx}}{\text{Cscx}}[/tex]

Further we can rewrite this ratio in the simplified form.

Since, Cot x = [tex]\frac{\text{Cosx}}{\text{Sinx}}[/tex] and Cosec(x) = [tex]\frac{1}{\text{Sinx}}[/tex]

Now substitute these simplified forms of Cotx and Cscx in the given fraction.

[tex]\frac{\text{Cotx}}{\text{Cscx}}[/tex] = [tex]\frac{\frac{\text{Cosx}}{\text{Sinx}}}{\frac{1}{\text{Sinx}}}[/tex]

      = [tex]\frac{\text{Cosx}}{\text{Sinx}}\times \text{Sinx}[/tex]

      = Cosx

Therefore, Cosx will be the answer.

Answer:

3.924×10∧-9

Step-by-step explanation:

Royal flush contains five cards and it's probability is 0.3924%≈0.003924

Straight contain five cards and it's probability is 0.0001%≈0.000001

The probability including straight and royal flushes will be 0.003924×0.000001≈3.924×10∧-9

Answer:

This is skewed torwards the right. Or in other words positively skewed distribution.

Step-by-step explanation:

All of the values are fairly close together torwards the lower range. While 50.20 is more of an outlier, so this graph would gradualy skew to the right.

Answer:

P(9) = 1/9

Step-by-step explanation:

From the contingency table, we see that 9 appears 4 times out of the 36 possible outcomes, therefore the probability of having a sum of 9 is

P(9) = 4/36 = 1/9

The probability that the sum is 9 is 1/18.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The sample space of rolling two dice has 36 possible outcomes.  

Remember that the sample space is a set that contains all possible outcomes.  

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Let E = the event of getting a sum of that number is 9

favorable outcomes = (5,4) (4,5)

So, n(E) = 2

Sample space n(S) = 36

p(E) = n(E)/n(S)

p(E) = 2/36

p(E) = 1/18

Hence, the probability that the sum is 9 is 1/18.

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Answer:

b = 4/3

Step-by-step explanation:

In an exponential equation:

f(x) = a (b)ˣ

Evaluated at x+1:

f(x+1) = a (b)ˣ⁺¹

The ratio between them is:

f(x+1) / f(x)

= (a (b)ˣ⁺¹) / (a (b)ˣ)

= b

So the decay factor b can be found by dividing the consecutive y values.

b = 16 / 12

b = 4/3

Answer:

C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Step-by-step explanation:

A confidence interval let us make an inference about a population parameter from a sample statistic. In this case, a sample proportion let us infere aout the population proportion with a certain degree of confidence.

With this confidence interval, we are 99% confident that the polpulation proportion falls within this interval. This means that there is 99% chances of having the population proportion within this interval.

To estimate the population proportion of adults who do not believe in UFO's we should have to construct another confidence interval with the proportion (1-p), but this parameter can not be estimated from the confidence interval for p.

Answer:

y={-5,-4,-5/2,-13/3}

Step-by-step explanation:

a.f(-2)=y=1/2(x)-4

substitute -2for x

y=1/2(-2)-4

y=-1-4

y=-5

b.f(0)

y=1/2(0)-4

y=0-4

y=-4

c.f(3/2)

y=1/2(3/2)-4

3/2-4

find the L.C.M=2

3/2-4/1

3-8/2

-5/2

d.f(-2/3)

y=1/2(-2/3)-4

-2/6-4

2 into itself 1 ,2 into 6 ,3

-1/3-4

find the least common multiple equal to 3

-1/3-4/1

-1-12/3

y=-13/3

Answer:

16

Step-by-step explanation:

(-8)^4/3

-(8^1/3)⁴

-(∛8)⁴

-(2)⁴

-2⁴

= 16

Answer: the ^^^^ right I check it

Step-by-step explanation: