Write a cosine function that has an amplitude of 4, a midline of 2 and a period of1

Answer:

1) (Un) is a geometric sequence.

2) Un+1 - Un ≤ 0.

3) (Un) is decreasing.

4) (Un) is convergent.

5) sum = 155

Step-by-step explanation:

Un+1 = 0.5Un

U₀ = 80

1) U is a geometric sequence (reason : Un+1 = 0.5Un).

2) Un+1 - Un = 0.5Un - Un = Un×(0.5 - 1) = -0.5Un ≤ 0 (because Un ≥ 0).

Remark: use Mathematical induction to prove that Un ≥ 0

3) Un+1 - Un  ≤ 0

then

Un+1 ≤ Un  

then

the sequence U is decreasing.

4) U is decreasing and Un ≥ 0

Then U is convergent.

5)  Since U is geometric sequence with first term U0 = 80 and common ratio = 0.5 .

Important: review the sum of consecutive terms of a geometric sequence.

Then

[tex]U_0+ U_1+ U_2+ U_3+ U_4=U_{0}\times \frac{1-\left( 0.5\right)^{5} }{1-0.5}=160\times(1-\left( 0.5\right)^{5} )=155[/tex]

Answer:

(2, 0) and (-7, 0)

N

C.

b.

(2, 0) and (-2, 0)

There are no x-intercepts

d.

(9, 0) and (-2, 0)

Please select the best answer from the choices provided

O A

B

C

Step-by-step explanation:

Answer:

a) Time spent, x (minute): 50 < x ≤ 60

b) Time spent, x (minute): 20 < x ≤ 30

Step-by-step explanation:

a) The modal class is the class interval with the highest frequency in a frequency table which is 21 (right column)

b) Find the total amount of Frequency:

12 + 18 + 11 + 9 + 8 + 21 = 79

to find mid number through the data set divided by 2:

79 / 2 = 39.5

so add up the frequency till you reach 39.5 (max)

12 + 18 = 30

30 + 11 = 41   this passes through 39.5 so the median is in the 3rd row

Answer:

  5.83 miles

Step-by-step explanation:

Bill's net distance west of his starting point is -4+7 = 3 miles. His net distance north of his starting point is 5 miles. The straight-line distance will be the hypotenuse of a right triangle with legs 3 miles and 5 miles. That distance is given by the Pythagorean theorem:

  d² = (3 mi)² +(5 mi)² = 34 mi²

  d = √34 mi ≈ 5.83 mi

Bill is 5.83 miles on a direct line from his starting point.

_____

The attached calculator screenshot shows the sum of the travel distances. The angles are bearings measured clockwise from north. The angle of the sum indicates Bill is about 31° west of north relative to his starting point.

    [tex]\large\boxed{\sf inverse \ variation}[/tex]

           [tex]\sf \large\boxed{\sf xy = 12}[/tex]

The coordinates are given in the table. Plot the points and draw a smooth curve on the graph. Identify the type of curve it forms.

After identification, it looks like a inverse graph.

Constant variable:

Inverse variation: xy = a   [a is constant]

Equation: xy = 12 or y = 12/x

Answers:

This is an Inverse variation

The equation is y = 12/x which is the same as saying xy = 12

======================================================

Explanation:  

Notice that for each column, the x & y values multiply to 12.

This tells us that x*y = 12 which rearranges to y = 12/x

All inverse variation equations are of the form y = k/x which is equivalent to xy = k.

As x increases, y decreases, and vice versa.

Answer:

3

Step-by-step explanation:

a²+6.1²=6.8²

a²+37.21=46.24

-37.21 -37.21

a² = 9.03

a = √9.03

a = 3

Answer: 29

Step-by-step explanation:

all triangles equal to 180

180-97-54=29

Answer:

see explanation

Step-by-step explanation:

(a)

the volume (V) of the cylinder is calculated as

V = πr²h ( r is the radius and h the height ) , then

V = π × a² × 2a = 2a³π

(b)

the volume of the prism is calculated as

V = Ah ( A is the cross- sectional area and h the height ) , then

a²b = 2a³π ( divide both sides by a² )

b = 2πa

Check the picture below.

Answer:

  (d)  944 mm³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the distance between bases.

__

Here, the base of the prism is a rectangle with a semicircle on top. The circle has a diameter of 9 mm, so a radius of 4.5 mm. The area of the semicircle is ...

  A = 1/2πr² = 1/2π(4.5 mm)² ≈ 31.809 mm²

The area of the rectangle is the product of its length and width.

  A = LW = (9 mm)(6 mm) = 54 mm²

So, the total base area is ...

  31.809 mm² +54 mm² = 85.809 mm²

The prism volume is this area multiplied by the length of the figure:

  V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³

The volume of the figure is about 944 mm³.

Answer:

Option C: 9³

Step-by-step explanation:

9 * 9 = 81

( 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 +9 )

81 * 9 = 729

( 81 + 81 + 81 + 81 + 81 + 81 + 81 + 81 + 81)

Answer:

Find the interest. Formula interest = PRT Principal x rate x time

910.00 x 1.75% x 1 =

910.00 x 0.0175 x 1 =

15.93 is the interest.

Step-by-step explanation:

Answer:

x = -24

Please mark brainliest :)

Answer

-24

Step-by-step explanation:

Answer:

3 hours

Step-by-step explanation:

$190 - $55 = $135 that the plumber charged for labor

$135/$45 = 3 hours that the plumber spent fixing the sink

Answer:

8km 323m

Step-by-step explanation:

The total distance given by summing up all the distances traveled using different means.

Distance by bus = 5km 28m

Distance by car = 2 km 265 m

Distance on foot = 1 km 30 m

(1km + 2 km + 5km) + (30m + 265m +28m) = 8km + 323m

Step-by-step explanation :

Here we have been given with the distance travelled by Abhishek through bus , car and foot. We're asked to calculate the total distance travelled by him.

But we will first convert the distance which is in kilometres into metres in order to do that. And after that we will add them all.

• Distance travelled by bus :

> Bus = 5km 28m

> Bus = 5 × 1000 + 28

> Bus = 5000 + 28

> Bus = 5028 m

• Distance travelled by car :

> Car = 2km 265m

> Car = 2 × 1000 + 265

> Car = 2000 + 265

> Car = 2265m

• Distance travelled by foot :

> Foot = 1km 30m

> Foot = 1 × 1000 + 30

> Foot = 1000 + 30

> Foot = 1030m

★ Now, total distance would be calculated as follows :

>> Total distance = (5028 + 2265 + 1030) m

>> Total distance = (7293 + 1030) m

>> Total distance = 8323 m

Therefore,

Answer:

$0.01

Step-by-step explanation:

Convert gallons to ounces:

0.03125 Gallons of milk per serving

0.03125/2.48=0.0126008

Simplify:

0.01.

One portion costs 1 cent.

The area of the training field is 5606.48 m².

Area can be defined as the region bounded by a plane shape.

To calculate the area of the training field, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the training field is 5606.48 m².

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Answer:

b

Step-by-step explanation:

7w^2-18w/w^2-5w+6

The simplest form of the expression is 7w/w^2+6, the correct option is A.

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that;

4w/w-2 + 3w/w-3

Now,

we can multiply the numerator and denominator by the missing factor. For example

w−24w​=(w−2)(w−3)4w(w−3)​

w−33w​=(w−2)(w−3)3w(w−2)​

Add the fractions with the LCD as the common denominator. To do this, we can add the numerators and keep the denominator. For example:

w−24w​+w−33w​=(w−2)(w−3)4w(w−3)+3w(w−2)​

Simplify the numerator by distributing and combining like terms. For example:

(w−2)(w−3)4w(w−3)+3w(w−2)​=(w−2)(w−3)4w2−12w+3w2−6w​

(w−2)(w−3)4w2−12w+3w2−6w​=(w−2)(w−3)7w2−18w​

=7w/w^2+6

Therefore, by the given expression the answer will be 7w/w^2+6.

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Answer:

[tex]P(\text{Male}|\text{Divorced})\approx0.092[/tex]

Step-by-step explanation:

[tex]\displaystyle P(\text{Male}|\text{Divorced})=\frac{P(\text{Male and Divorced})}{P(\text{Male})}=\frac{\frac{9.6}{214.7}}{\frac{104.5}{214.7}}\approx0.092[/tex]

We can even break this down further by simply only looking at the total amount of males, and finding the proportion of males that are divorced, which is [tex]\frac{9.6}{104.5}\approx0.092[/tex], the same value.

Note that P(Male | Divorced) means the probability of choosing a male, given (|) that person is divorced.

Answer:

Here is the answer hope it helps:)

Answer:

10πcm

Step-by-step explanation:

radius of the circle= 5cm

circumference of a circle has the formular

= 2πr

= 2×π×5

then In terms of pi

= 10πcm

Answer:

E = energy (measured in joules)m = mass (measured in kilograms)c = the speed of light (186,300 miles per second, or 3 x 108 ms-1

Step-by-step explanation:

Answer:

Area = 28 cm^2

Step-by-step explanation:

Triangle Area = 1/2 * 5 * 4 = 10 cm^2

Big Rectangle = 4 * 3 = 12 cm^2

Small Rectangle = 4 * 1.5 = 6 cm^2

Total Area = 10 + 12 + 6 = 28 cm^2

Answer:

Step-by-step explanation:

Discussion

Area of the Triangle

3 4 5 is the first triangle most people encounter when they begin their study of the Pythagorean Theorem. You can show this to be true by trying it.

c = 5

b = 3

a = 4

c^2 = a^2 + b^2           Equation  Substitute values

c^2 = 3^2 + 4^2           Expand

c^2 = 9 + 16                 Combine

c^2 = 25                       Take the square root of both sides.

√c^2 = √25

c = 5                     Which is exactly what you are given.

A right triangle has the property of Area = 1/2 * a * b using the values given above.

Find the area of the triangle

Area = 1/2 a * b                          

Area = 1/2 3 * 4                                                    

Area =                                                               6

Find the area of the rectangle

L = 3 + 1.5 =4.5                        Just add the two parts of the vertical line together.

w = 8 - 4 = 4

Area of the rectangle = L * w   Substitute values

Area of the rectangle = 4.5 * 4

Area of the rectangle =                                18         Add

Total area                                                      24

Answer

24 cm^2

Answer:

136

Step-by-step explanation:

simple as you can remember, the area of a parallelgram has the exact formula as the rectangle,

lw = a.

This brings us to 8 × 17, which is 136.

5/9

you can use a common denominator of 36, and multiply the numerators of each fraction by whatever number the denominator had to be multiplied by to get to 36

14/36+15/36-9/36

then you add and subtract

20/36=

5/9

Answer:

Volume of cylinder = pi r^2 h

1225 pi = pi×r^2×25

r^2= 1225/25=49

so, r= 7 cm

Answer:

C

Step-by-step explanation:

Formula to get the area

A = r^2π

A = 16^2π

A= 804.24 cm^2

As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.

Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.

To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.

The area of a circle is given by the formula:

A = [tex]\pi r^2[/tex]

Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:

A = [tex]\pi 18^2[/tex]

A = 324π

So, the area of the whole circle is 324π square cm.

The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:

100° / 360° = 5/18

Therefore, the area of the shaded sector is:

A = (5/18) * 324π

A = 90π

Using 3.14 as an approximation for π, we get:

A ≈ 90 * 3.14

A ≈ 283

Thus, the approximate area of the shaded sector is 283 square cm, which is option D.

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