Calculate s24 for the arithmetic sequence in which a13=1.9 and the common difference is d=3.7.

Answer:

see below

Step-by-step explanation:

Swap y and x, then solve for y.

Original:

... y = f(x) = x² -1

Swap y and x:

... x = y² -1

Add 1:

... x + 1 = y²

Take the square root:

... ±√(x+1) = y . . . . . matches the 3rd selection

Rewrite as the inverse relation: (not a function)

... f^-1(x) = ±√(x+1)

_____

Comment on the graph

The attached graph shows the function f(x) in red, and the inverse relation g(x) in blue. You will note that g(x) is double-valued for most values of x, so is not a function. The function and its inverse relation are mirror images of each other in the line y=x. (That is, swapping y and x changes the function to its inverse, and vice versa.)

The inverse function of f(x)=x^2-1, denoted as f^-1(x), is calculated as f^-1(x) = sqrt(x+1), if x>=0 and f^-1(x) = - sqrt(x+1), if x<0.

To find the inverse of the function f(x)=x^2-1, denoted as f^-1(x), first replace f(x) with y, so the equation becomes y = x^2 - 1. The next step is to swap x and y, giving you x = y^2 - 1. Now, you should solve this new equation for y, resulting in y = sqrt(x+1). However, considering the domain, we have to separate into positive and negative square roots. Therefore, the complete inverse function is f^-1(x) = sqrt(x+1), if x>=0 and f^-1(x) = - sqrt(x+1), if x<0.

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Answer:

The correct option is 1.

Step-by-step explanation:

Statement 1: AB is parallel to DC and AD is parallel to BC.

Reason: Definition of parallelogram

Statement 2:  ∠1 = ∠2, ∠3 = ∠ 4.

Reason: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Statement 3: BD = BD.

Reason: Reflexive Property.

Statement 4: ΔADB≅ΔCBD.

Reason: If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.

Statement 5: AB = DC, AD = BC.

Reason: Corresponding parts of congruent triangles are congruent.

The missing information for reason 2 in the chart is alternate interior angles .

Therefore the correct option is 1.

Answer:

[tex]\frac{\frac{51}{8}} {\frac{3}{8}}[/tex]

17 bags.

Step-by-step explanation:

We are asked to find the number of bags with weight 3/8 pound can be made from [tex]6\frac{3}{8}[/tex].

To find the number of

[tex]\text{Number of bags that can be made from available mix trail}=6\frac{3}{8}\div \frac{3}{8}[/tex]  

Convert mixed fraction into improper fraction.

[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\div \frac{3}{8}[/tex]  

Since we know that dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of 2nd fraction.

[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\times \frac{8}{3}[/tex]  

After cancelling out 8 from numerator and denominator we will get,

[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{3}[/tex]  

[tex]\text{Number of bags that can be made from available mix trail}=17[/tex]  

Therefore, 17 bags each of weight 3/8 pounds can be made from [tex]6\frac{3}{8}[/tex] pounds of mix trail.

Answer:

She spend 7.33 on each lunch.

Step-by-step explanation:

We have been given that Mrs. Johnson spend $611 buying for 78 students

If each lunch cots the same we have to find how much did she spend on each lunch:

We can calculate the price of each lunch  by dividing the total cost she spend upon the lunch she bought.

let the cost of each lunch be x

Hence, [tex]x=\frac{611}{78}=7.33[/tex]

Answer:

The correct option is 3. Capacity of smallest tank is 15-gallons.

Step-by-step explanation:

The graph shows the relationship between capacity of tank and combined length of fish it can hold.

The line passing through (0,1) and (1,2).

Slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{1-0}=1[/tex]

Slope intercept form of a line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

The slope of the line is 1 and the y-intercept is 1, therefore the equation of line is

[tex]y=x+1[/tex]                          ..... (1)

If we want four 2-inch platys, three 1-inch guppies and a 3-inch loach, then the combined length of fish is

[tex]4\times 2+3\times 1+1\times 3=8+3+3=14[/tex]

Therefore the combined length of fish is 14.

Put x=14 in equation 1.

[tex]y=14+1=15[/tex]

Therefore, the capacity of smallest tank is 15-gallons and option 3 is correct.

Answer: got answer from someone, 12 and 14 were wrong.

Step-by-step explanation:

connexus unit 8 lesson 1 PRACTICE!

1) B

2) C

3) A

4) C

5) B

6) A

7) D

8) A

9) D

10) A

11) A

12) not C

13) D

14) not C

15) B

Answer:

The correct option is a. The length of MN is 25.

Step-by-step explanation:

Given information: MQ = 10 in, NP = 3 in and QP=24 in.

If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is

[tex]l=\sqrt{d^2-(r_1-r_2)^2}[/tex]

[tex]24=\sqrt{d^2-(10-3)^2}[/tex]

Square both sides.

[tex]576=d^2-49[/tex]

[tex]625=d^2[/tex]

Take square root both sides.

[tex]25=d[/tex]

Therefore  length of MN is 25 and option a is correct.

To find MN in the given pulley system, we can use the concept of similar triangles.

In the pulley system shown in the figure, we can use the concept of similar triangles to find MN. The triangle MQP is similar to the triangle MNP. This means that the ratios of their corresponding sides are equal.

So we have:

MQ/MP = NP/MN

Substituting the given values:

10/24 = 3/MN

Cross multiplying:

10 * MN = 24 * 3

MN = (24 * 3) / 10

MN = 72/10

MN = 7.2 inches

Therefore, the length MN is approximately 7.2 inches.

Answer:

C = 45.8 or C = 117.69

Step-by-step explanation:

Remark

Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.

Given

AB = 15

<A = 35

point C opposite line AB such that CB = 12 These givens give a unique answer.

Solution

Sin(35) / 12 = Sin(C) / 15                     Multiply both sides by 15

15*Sin(35) / 12 = Sin(C)                       Find 15/12

1.25*sin(35) = Sin(C)                           Write Sin(35)

1.25*0.5736 = Sin(C)                          Multiply the left

0.71697 = Sin(C)                                 Take the inverse Sin

C = 45.805 degrees                          This is the angle opposite AB

Angle B = 180 - 35 - 45.805 = 99.2

Ambiguous Case                    

If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.

I will set up the Sin law for you, and let you solve it

Sin(B) / 12 = Sin(35)/15

When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees

C = 180 - 35 - 27.31 = 117.69

So that's two values that C could have. I think that's all given these conditions.

Two Cases or None

<A = 35 degrees

AC = 15

CB = 12

This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.

Answer:

729

Step-by-step explanation:

[(-1)^3]^2 /[(-3)^-3]^2

= 1 * [(-3)^3]^2

= 1 * 729

= 729

Answer:

729

To solve this, we need to start on the inside and work out; solving one part at a time.

[{(-1)^3 / (-3)^-3}]^2

1. (-1)^3 = -1

2. (-3)^-3 = - 1/27

3. (-1) / (- 1/27) = 27

4. 27^2 = 729

Answer:  1773.6 yards   5320.8 feet  64324.8 inches

Step-by-step explanation:  

1 mile in yards = 1760                                                                                         40.8 feet in yards = 13.6      1760 + 13.6 = 1773.6 yards

1 mile in feet = 5280 + 40.8 = 5320.8 feet

1 mile in inches  = 63360

40.8 feet in inches = 964.8

63360 + 964.8 = 64324.8 inches

hope this helps :)

To find the angle of elevation between the ground and the ladder, we can use the tangent function and the given measurements. The angle is approximately 39.8 degrees.

To find the angle of elevation between the ground and the ladder, we can use trigonometry. Since the top of the ladder is 20 feet above the ground and the ladder is 25 feet long, we can use the opposite and adjacent sides of a right triangle. The trigonometric function that relates these sides is the tangent function:

tan(angle) = opposite/adjacent

Plugging in the known values, we get: tan(angle) = 20/25

Using a calculator to find the inverse tangent (arctan) of both sides, we get the angle to be approximately 39.8 degrees to the nearest degree.

Answer:

11 minutes

Step-by-step explanation:

Do 16 mins. 30 secs. divided by 1.5, since that is what you divide the miles by to get the base amount. The answer is 11 minutes.

Answer:

–24 + −8 × 324

Step-by-step explanation:

Well, if you go through the answer choices, there is only one that gives you the correct answer.  The product is -2672, and the only answer choice that this satisfies is the second one.

Answer:

It's C

Step-by-step explanation:

Answer:

The midpoint is (3,-1)

Step-by-step explanation:

The midpoint of a segment is found by adding the ends together and dividing by 2

midpoint = (x1+x2)/2 , (y1+y2)/2

                =(9+-3)/2 , (-9+7)/2

                = 6/2, -2/2

                =3,-1

Answer:

A

Step-by-step explanation:

We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.

Triangle - 0.5 *b*h

Rectangle - b*h

Triangles

There are two triangles on either side. The height is 1.5. The base is 1.8.

0.5(1.5)(1.8)=1.35 meters squared

Since there are two, we will add 1.35+1.35 in our final calculation.

Rectangles

We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).

4(2.5)=10

Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.

Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.

Top - 3(2.5)=7.5

Bottom-3(2.5+1.8)=12.9

Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.

Back - 4(3)=12

Front- 3(2.5)=7.5

Slant - 3(2.3)=6.9

We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.

Answer:

2/3 of 450 is 300 :)

Answer:

[tex]-7<x\leq 9[/tex]

Step-by-step explanation:

The domain is the set of all x-values. We can find the domain by finding the left boundary of the graph (the furthest left x-value) and then the right boundary (the furthest right x value).

The furthest left x-value is -7. Notice it has a large open circle here that is not filled in. This means the function does not include -7 but includes numbers very close to it like-6.999999..... We sue use an inequality sign without an equal to to write -7. x >-7.

The furthest right x value is 9. It has a closed circle or "filled in" circle so we write with an equal to sign. [tex]x\leq 9[/tex].

We combine the two into [tex]-7<x\leq 9[/tex].

Answer:

D. $2.81

Step-by-step explanation:

The statement says that the price of a cantaloupe goes up 4 cents each month and that the cost of the cantaloupe was $1.25 on the first month. Tto determine the cost in the 40th month, you have to multiply 4 cents for 39 months as the price for the first month was given and then you have to add this with the price for the first month:

0,04*39= 1.56

1.56+1.25= $2.81

The price in the 40th month is $2.81.

Answer:

Shiloh initially invested $125, which grows annually at a rate of 2.5%.

Step-by-step explanation:

The balance in the account is given by the following exponential expression,

[tex]125(1.025)^t[/tex]

Exponential growth formula is

[tex]A= P(1+r)^t[/tex]

Where P is the initial amount invested

r is the rate of interest

When we compare the formula with given expression , we can see that we have 125 in the place of P

So initial amount invested is $125

Now we find out 'r'

1+ r = 1.025

Subtract 1 on both sides

r= 0.025

To get percentage we multiply by 100

0.025 * 100 = 2.5%

Shiloh initially invested $125, which grows annually at a rate of 2.5%.

Answer:

Step-by-step explanation:

corresponding angles are congruent to eachother  for example 1&3, 5&7, 2&4, 8&6

Answer:

Option B, C, D are the correct options

Step-by-step explanation:

When two parallel lines are intersected by a transverse then two angle which are relatively at the the same position are called as corresponding angles.

As given in the picture attached, ∠1 and ∠2 are corresponding angles.

Similarly, ∠3 and ∠4 re corresponding angles.

Now we come to our question. In this question corresponding angles are

1) 2 and 4

2) 6 and 8

3) 1 and 3

4) 5 and 7

Therefore, Options. B, C and D are the correct options.

Answer: 25000

Step-by-step explanation:

.1=10%

So, 2500/.1=25000

25000*.1=2500

Answer:

Width of rectangular storage room= 5 feet.

Step-by-step explanation:

Let x be the width of storage room.

We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.

We are also given that the area of the room is 40 square feet.

Since the area of a rectangle is length times width.

[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]

Let us substitute our given values in area formula.

[tex]40=x*(x+3)[/tex]

Upon distributing x we will get,

[tex]40=x^2+3x[/tex]

[tex]x^2+3x-40=0[/tex]

Now let us factor out our quadratic equation using splitting the middle term.

[tex]x^2+8x-5x-40=0[/tex]

[tex]x(x+8)-5(x+8)=0[/tex]

[tex](x+8)(x-5)=0[/tex]

[tex]x+8=0[/tex] or [tex]x-5=0[/tex]

[tex]x=-8[/tex] or [tex]x=5[/tex]

Since width can not be negative, therefore, the width of rectangle will be 5 feet.

Let us verify our answer.

Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.

Given: Area=40 square feet.

5*8=40.

Hence, width of rectangular storage room is 5 feet.

Answer:

$8

Step-by-step explanation:

A group of tourists spends $156 to rent snorkels and fins.

They rented 15 snorkels and 18 pairs of fins.

Renting a snorkel costs four times as much as renting a pair of fins.

Let us assume that the rental cost of a pair of fins is x, so the rental cost of snorkel will be 4x.

Then total cost of 15 snorkels and 18 pairs of fins will be,

[tex]=15(4x)+18x[/tex]

[tex]=60x+18x[/tex]

[tex]=78x[/tex]

But it is given as $156, so

[tex]\Rightarrow 78x=156[/tex]

[tex]\Rightarrow x=2[/tex]

Therefore, the rental cost of a pair of fins is $2 and cost of snorkel is [tex]2\times 4=\$8[/tex]

Answer:

A

Step-by-step explanation:

3/24=9/72        3*3=9    24*3=72      x=3

3/9=y/12         9/3=3        12/3=4      y=4

X=3 y=4

Answer:

her son is 20, Mrs. Johnson is 60

Step-by-step explanation:

if her son is x, Mrs. Johnson is 3x,

Ten years ago,

her son is x-10, Mrs. Johnson is 3x-10,

so:

3x-10=5(x-10)

x=20

Answer:

D. He can increase the number of trials.

Step-by-step explanation:

Jonas is conducting an experiment using a 10-sided die. So the theoretical probability of rolling a 3 in a single trial is, [tex]\dfrac{1}{10}[/tex]

So the theoretical expected outcome of 3 in 20 roll would be,

[tex]=\dfrac{1}{10}\times 20=2[/tex]

But when he rolled the die 20 times, where four of those rolls resulted 3.

Which is 2 times more than the theoretical expectation.

Increasing the number of trials from 20, the expected outcome will increase.

As the number of trials is multiplied with [tex]\dfrac{1}{10}[/tex], so bigger the number is from 20, bigger the value.

As we know,

[tex]E(x)=n\cdot P(x)[/tex]

If we want to increase the expected value, we have to increase the number of trials.

Answer with explanation:

Number of faces of this unique Die = 10

Theoretical  probability of rolling a 3 [tex]=\frac{1}{10}[/tex]

Now, the die is rolled 20, times.

Number of times, the rolls results in 3= 4

Probability of rolling '3' [tex]=\frac{4}{20}=\frac{1}{5}[/tex]

but, if you roll the die twenty times, Probability of rolling '3' should be [tex]=\frac{2}{20}=\frac{1}{10}[/tex]

When we want, theoretical probability and experimental probability,match each other, the number of trials should be large enough to get closer and better results.

The adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer:

D: He can increase the number of trials.

Answer:

In 2020 building price is $ 887761

Step-by-step explanation:

Time = 2020 - 2010 = 10 years

In 2011 building price = 375000 × [tex]\frac{9}{100}[/tex] + 375000 =$408750

In 2012 building price = 408750 × [tex]\frac{9}{100}[/tex] + 408750 =$445537.5

In 2013 building price = 445537.5 × [tex]\frac{9}{100}[/tex] + 445537.5 =$485635.88

In 2014 building price = 485635.88 × [tex]\frac{9}{100}[/tex] + 485635.88 = $529343.11

In 2015 building price = 529343.11 × [tex]\frac{9}{100}[/tex] + 529343.11 = $576983.99

In 2016 building price = 576983.99 × [tex]\frac{9}{100}[/tex] + 576983.99 =$628912.55

In 2017 building price = 628912.55 × [tex]\frac{9}{100}[/tex] + 628912.55 =$685514.68

In 2018 building price = 685514.68 × [tex]\frac{9}{100}[/tex] + 685514.68 = $747211

In 2019 building price = 747211 × [tex]\frac{9}{100}[/tex] + 747211 =$814459.99

in 2020 building price = 814459.99 × [tex]\frac{9}{100}[/tex] + 814459.99 =$887761.38 ≈ $887761

Second method

Total time(t) = 10 years

Rate(r) = 9%

Principal value = $375000

Now,

          selling price (in 2020) = principal value [tex](1+\frac{r}{100}) ^{t}[/tex]

            = 375000 [tex](1+\frac{9}{100} )^{10}[/tex]  = $887761.38    ≈$887761