Find measure a and b

The terms of an arithmetic sequence are generated by adding a fixed term [tex]r[/tex] every time.

So, we start with [tex]a_1=15[/tex], and we continue with [tex]a_2=15+r[/tex], [tex]a_3=15+2r[/tex] and so on.

As you can see, the general rule is [tex]a_n = 15+(n-1)r[/tex]

With this information, we can derive [tex]r[/tex], knowing that

[tex]a_{100} = 307 = 15+99r \iff 99r = 292 \iff r = \dfrac{292}{99}[/tex]

So, the sum of the first 100 terms is

[tex][tex]\displaystyle \sum_{i=0}^{99} 15+i\dfrac{292}{99} = \displaystyle \sum_{i=0}^{99} 15 + \displaystyle \dfrac{292}{99}\sum_{i=0}^{99} i = (15\cdot 99) + \dfrac{292}{99}\dfrac{99\cdot 100}{2} = 1485 + \dfrac{490342}{99}[/tex]

Answer:

 1           1

------ + -------    

r^7      s^12

Step-by-step explanation:

r^(-7) + s^(-12) can be re-written as

 1           1

------ + -------    by putting to use the rule:

r^7      s^12

                1

x^(-a) = ----------

              x^a

For this case, we must simplify the following expression:

[tex]r ^ {- 7} + s ^ {- 12}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, rewriting the expression we have:

[tex]\frac {1} {r ^ 7} + \frac {1} {s ^ {12}}[/tex]

Answer:

[tex]\frac {1} {r ^ 7} + \frac {1} {s ^ {12}}[/tex]

Option D

Answer:

6 Slices Of Cheese Remaining

Step-by-step explanation:

50% of the cheese is 16 slices, so add on 50% + 25% and you get 24 slices...

if you do 32-24 you have 8 slices remaining and if you eat 25% of the 8 slices you have 6 slices left.

Final answer:

The property illustrated in the equation is the Commutative Property of Addition. It states that the order in which numbers are added does not affect the sum.

Explanation:

The equation showcases the Commutative Property of Addition. This property asserts that altering the order of addends doesn't impact the sum. Specifically, the given equation, 6 + 4 + 3, demonstrates this property as it equals 6 + 3 + 4. In essence, rearranging the sequence of addends doesn't alter the total, underscoring the flexibility of addition. This fundamental property simplifies mathematical operations, allowing for easier manipulation and calculation of sums, regardless of the order in which numbers are combined.

The Commutative Property of Addition plays a pivotal role in arithmetic, streamlining calculations and enhancing mathematical efficiency.

Answer:

The average speed of the car is [tex]s = 24\ mph[/tex]

Step-by-step explanation:

The average speed is defined as

[tex]s = \frac{d_1}{t}[/tex]

Where

s is the speed

d is the displacement made

t is the time it took to perform the displacement d.

On the first trip the speed was 20 mph and the displacement was 60 miles. Then we find the time [tex]t_1[/tex]

[tex]s = \frac{d}{t}[/tex]

[tex]t_1 = \frac{d_1}{s}\\\\t_1 = \frac{60}{20}\\\\t_1 = 3\ h[/tex]

On the second trip the speed was 30 mph and the distance traveled was the same: 60mph

We calculate [tex]t_2[/tex].

[tex]t_2 = \frac{60}{30}\\\\t_2 = 2\ h[/tex].

Now we can calculate the average speed for the entire route

[tex]s = \frac{d_1 + d_2}{t_1 + t_2}\\\\s = 60 +\frac{60}{3} +2\\\\s = \frac{120}{4}\\\\s = 24\ mph[/tex]

Answer:

Speed =  24 mph

Step-by-step explanation:

Distance traveled in the two way trip

2*(60 miles) = 120 miles

Time it took to arrive to the destination (first travel, 60 miles, 20mph)

Speed = distance/ time

t = distance/ speed = (60 miles) / (20 mph) = 3 hours

Time it took to come back (return travel, 60 miles, 30 mph)

t = (60 miles) / (30 mph) = 2 hours

Total time = (3 +2)  hours = 5 hours

So the average speed is

Speed = (120 miles) / (5 hours)  = 24 mph

Answer:

$78.00

Step-by-step explanation:

First, you would have to figure out how many tiles she would need. 3 inches is  equal to 6 feet according to the scale part, and then it would be 12 tiles because it is half a foot for the tiles. Then 3 1/2 would be 7 feet, and then 14 tiles. 12 plus 14 equals 26, and 26 times $3.00 is $78.00

Amy will pay $3.00 for the tiles for her bathroom floor.

A fraction represents a part of a whole.

The scale is 1/2 inch = 1 foot.

Length of bathroom = 3 inches × (1 foot / 24 inches)

= 1/8 feet

Width of bathroom = [tex]3\frac{1}{2}[/tex] inches(1 foot / 24 inches)

= 7/24 feet

We need to calculate the total area of the bathroom floor in square feet:

Area of bathroom floor = (length) x (width)

= (1/8 feet) x (7/24 feet)

= 7/192 square feet

Since each tile measures 1/2 foot on each side, the area of each tile is:

Area of one tile = (1/2 feet) x (1/2 feet) = 1/4 square feet

Total area of tiles needed = (area of bathroom floor) / (area of one tile)

= (7/192 square feet) / (1/4 square feet)

= 7/48 tiles

Amy will need to purchase 1 tile at a cost of $3.00 per tile, so the total cost of the tiles for her bathroom floor will be:

Total cost = (number of tiles) x (cost per tile)

= 1 tile x $3.00/tile = $3.00

Hence, Amy will pay $3.00 for the tiles for her bathroom floor.

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Answer:

c=3

Step-by-step explanation:

c^3 =27

Take the cube root of each side

(c^3) ^ 1/3 = 27 ^ 1/3

c = 3

We know that 3*3*3 = 27

Answer:

1.7

Step-by-step explanation:

Of means multiply and is means equals

W = 5% *34

Change to decimal form

W = .05 *34

W =1.7

Move all terms not containing  x  to the right side of the inequality.

Answer: x > 5

Answer:

Length (cm)      Width (cm)

       6                      18

       8                      24

       10                     30

       12                     36            

Step-by-step explanation:

Length (cm)           Width (cm)

       6           (x3)          18

       8           (x3)          24

       10         (x3)          30

       12         (x3)          36            

Answer:

9.4 inches

Step-by-step explanation:

The distance between the opposite corners is the diagonal.

We can find this using the Pythagorean theorem.  The diagonal is the hypotenuse.

a^2 +b^2 = c^2

8^2 +5*2 = c^2

64+25 = c^2

89=c^2

Take the square root of each side

sqrt(89) = sqrt(c^2)

sqrt(89) = c

9.433981132=c

Rounding to the nearest tenth

9.4 inches = c

I can’t read the small sticky notes take a closer picture

Answer:

Melissa will be able to hold 8 1/4 containers of rice.  

Step-by-step explanation:

1 pound= 16 oz

132/16= 8.25

Answer:

Step-by-step explanation:

Let's work in pounds everywhere.  Convert 132 oz of rice into lb:

132 oz          1 lb

----------  ·  ------------  =  8.25 lb

     1            16 oz

Melissa will be able to fill 8 1-lb containers with rice, but will have 0.25 lb left over.

If she wants 10 lb of rice and is curious regarding how many oz that would be, take this 10 lb and multiply it by the conversion factor shown above:

10 lb        16 oz

--------  ·  ---------  =  160 oz

   1           1 lb

Answer:

0.18

Step-by-step explanation:

This is a very simple problem that can be solved with a simple formula.

When there are two independent events A and B, the formula is:

P(A and B) = P(A) * P(B)

So we just need to multiply P(A) and P(B) to get P(A and B).

Thus,

P(A and B) = P(A) * P(B) = 0.60 * 0.30 = 0.18

Answer:

P (A and B) = 0.18

Step-by-step explanation:

We are given that A and B are independent events which means that occurrence of one event does not have any impact on the other event.

Given that P(A)=0.60 and P(B)=0.30, we are to find the probability P(A and B).

To find this, we just simply need to multiply the probabilities of the two events.

P (A and B) = 0.60 × 0.30 = 0.18

I think the possible distance between them is 153 feet because 128 feet is the smallest so it would be the bottom, 143 feet and 153 feet would be the sides because they are the closest in size.

Answer:

The possible distance between them is 153 feet because 128 feet is the smallest so it would be the bottom, 143 feet and 153 feet would be the sides because they are the closest in size.

Step-by-step explanation:

The person who answered this is correct, also, please mark me brainliest, i took the test and got 100% hope this helps:)

Answer:

22 sqft.

Step-by-step explanation:

Calculate the area of the car: (15*6)=90

Subtract the area of the car from the area of the driveway to find the area leftover: 112-90=22 sq ft not covered.

Answer:

= 1/36

Step-by-step explanation:

The probability of roiling a 5 is 1/6, while,

that of rolling a 3 is 1/6

Therefore;

The probability of having a 5 the first time and a 3 the second time will be the product of the probability of having a 5 and the probability of having a 3.

= 1/6 × 1/6

= 1/36

Answer:

The correct answer is 1/36

Step-by-step explanation:

It is given that, single die is rolled twice

The sample space consists of,

(1, 1), (1, 2) ....... (1, 6)

.

.

(6, 1) ............. (6, 2)

Total = 36

To find probability

The possible outcome is (5, 2)

The probability of rolling a 5 the first time and a 2 the second time = 1/36

the correct answer is 1/36

Answer:

30

Step-by-step explanation:

1/2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

1/3 3 6 9 12 15 18 21 24 27 30

1/5 5 10 15 20 25 30

The answer is 143312

Answer:

it is  143312                                    

Answer:

b

8+3^2=17 ..

Answer:

B

Step-by-step explanation:

Please, please try to understand the concept before turning to here.

TO REITERATE YET AGAIN, use the Pythagorean Theorem.

a^2+b^2=c^2.

If this equation checks out, it is a right triangle.

Answer:

Acute

Step-by-step explanation:

All the angles are less than 90 degrees

Adjaadjacent angles are angles that are the vertex but vertical angles are lines that cross each other.

Answer: Second option.

Step-by-step explanation:

As you can see in the graph attached, the lenght of the side AB is 2 units.

The formula for calculate the area of  rectangle is:

[tex]A=l*w[/tex]

Where l is the length and w is the width.

Therefore, if the area of the rectangle to be drawn is 10 square units and you know AB=2 units and CD  lies vertically below BA , then you can solve for the length:

[tex](10units^2)=(2units)l\\l=5units[/tex]

Therefore C and D are located at:

[tex]C=B(-1, 3-5)=> C(-1,-2)[/tex]

[tex]D=A(1, 3-5)=> D(1,-2)[/tex]

Answer:

The correct answer is,

Option 2).  C(-1, -2), D(1,-2)

Step-by-step explanation:

It is given that,If the area of the rectangle to be drawn is 10 square units

To find the length of rectangle

From the figure we get length of AB = 2 units

Therefore Area = length * breadth = 10

Therefore length = 10/2 = 5 units

To find the points of C and D

we have B(-1, 3)

The point C is 5 units below the point B

Therefore C(-1, 3-5) = C(-1,-2)

we have A(1, 3)

The point D is 5 units below the point B

Therefore D(1, 3-5) = A(1,-2)

Therefore the correct answer is option 2

Answer:

A (3,-2)

Step-by-step explanation:

x = t-1

y = -sqrt(t)

Let t= 4

x = 4-1 = 3

t = -sqrt(4) = -2

The (x,y) coordinate is (3,-2)

Answer:

1890 yd³

Step-by-step explanation:

V = ½Ah

= ½ × 210 × 27

= 1890 yd³

The  volume of the pyramid is 1890 yd³.

Answer:

Option A

A B C D

Step-by-step explanation:

Line of symmetry means that line which cut anything into two two halves.

It could horizontal, vertical and diagonal.

A - vertical line of symmetry

B - horizontal line of symmetry

C - horizontal line of symmetry

D - horizontal line of symmetry

And it is an example of Spherical symmetry:

If the organism is cut through its centre, the resulting parts look the same.

The correct option is a.

The list given entirely contain letters with line symmetry. Line symmetry means that one half of an image or shape exactly matches the other half.

The question asks about line symmetry in letters. Line symmetry, also known as reflection symmetry or mirror symmetry, means that one half of an image or shape exactly matches the other half along a line of symmetry.

Looking at the options given:

a. A, B, C, D—B, C and D have horizontal line of symmetry; A has vertical line of symmetry.

b. W, X, Y, Z—X, W and Y have line symmetry, but Z do not.

c. L, M, N, O—M and O have line symmetry, but L and N do not.

d. S, T, U, V—T, U and V have line symmetry, but S do not.

Therefore, only option a is correct. Since, the list given entirely contain letters with line symmetry.

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Answer:

776.46 m

Step-by-step explanation:

According to the scenario it is a question of right angle triangle

To find the height of the plane above the ground we will use trigonometry identity.

here Ф = 15°

        opposite = height

        hypotenuse = 3000m

Plug values in the formula above

height = sin(15)(3000)

           = 776 .46 m

(make sure your calculator is in degree mode)

Answer:

776.46 m

Step-by-step explanation:

The angle of elevation is 15 degrees which is measured from the horizontal.

The height above the ground is the opposite side of the triangle, the hypotenuse is the 3000 m and the angle of elevation is 15 degrees.

The sine ratio is the one one that ties the relationship;

Therefore;

sin 15 = x/3000

x = sin 15 × 3000

   = 776.46 m

I believe it is because it would be he most simplistic answer to be honest because for example 10,8 it is the same as 5,4 so u would put 5,4 because it is simplified so put (2.1,0) as your answer

The ordered pair that is a solution to the equation represented by the graph is (-2.5, 3).

Here's my reasoning:

- The graph intersects the x-axis at (2.1, 0): This means that any point on the x-axis, including (2.1, 0), has a y-value of 0. However, this doesn't guarantee that (2.1, 0) is a solution to the equation itself.

- The graph passes through the point (-2.5, 3): This means that the equation of the graph must yield a y-value of 3 when x = -2.5. Therefore, (-2.5, 3) is a solution to the equation.

The other points are not on the graph itself:

- (0, 0.6) is above the x-axis but not on the graph's line.

- (-1, 1.8) is also above the x-axis but not on the graph's line.

Therefore, the only ordered pair that is a solution to the equation represented by the graph is (-2.5, 3).

Answer:

2/3 or 0.6667

Step-by-step explanation:

L (length) = A/W (area/width)

L = 1/3 / 1/2

1/3 * 2/1 = 2/3