the first term of a geometric sequence is 400 and the common ratio is 0.5. what is the 5th term of the sequence.

Answers

Answer 1

Answer:

25

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence:

[tex]a_n=ar^{n-1}[/tex]

where:

a = first termr = common ratio[tex]a_n[/tex] = nth term

Given values:

a = 400r = 0.5n = 5

Substitute the given values into the formula and solve:

[tex]\implies a_5=400(0.5)^{5-1}[/tex]

[tex]\implies a_5=400(0.5)^{4}[/tex]

[tex]\implies a_5=400(0.0625)[/tex]

[tex]\implies a_5=25[/tex]

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Related Questions

Please help with this geometry question!

Answers

Answer:

second option

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Correct choice is 2

Since the two triangles ABE and ADE are congruent, their corresponding sides and angles are equal.

After observing all the options, we can conclude that :

Only angle AED and angle AEB are angles of given triangles and are actually equal.

[tex] \qquad \large \sf {Conclusion} : [/tex]

Option 2 is correct

3. Complete the table (showing work) and draw a graph of the logarithmic function f(x) = log 1/5 x

Answers

Answer:

Step-by-step explanation:

Three times a certain number decreased by 5 is equal to 31.

Answers

3x-5 = 31
hope this helps!

In a football tournament, each team played exactly 19 games. Teams get three points for everyone and one point for every time. At the end of the tournament, team Olympus got a total of 28 points. How many could team Olympus have tied?

Answers

We can actually deduce here that when the tournament ended, team Olympus have tied for 13, 10, 7, 4, 1 times.

What is inequality?

In Mathematics, inequality is used to express or show quantities that are less than, greater than, greater than or equal to,  less than or equal to.

The following can be seen in inequality expressions:

≤≥ ><≠

Looking at the question, we can see that each team plays exactly 19 games.

Every win (w) = 3

Every tie (t)= 1

Every loose = 0

But Olympus got a total of 28 points

Thus: 3w + t = 28 ---------(1)

Note that each team plays  19 games

Thus, T + W  ≤  19 --------------(2)

and T , W ≥ 0

Looking at equation (1) and (2)

=> 2W  ≥  9

=> W ≥ 4.5  

( match can be won in integers only )

=> W  ≥  5  

W - 5, 6, 7, 8, 9    

T - 13, 10, 7, 4, 1  

Loose - 1, 3, 5, 7, 9

Thus, team Olympus have tied for 13, 10, 7, 4, 1 times.

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If the r-value, or correlation coefficient, of a data set is 0.854, what is the
coefficient of determination to three decimal places?
A. 0.829
• B. 0.754
• C. 0.729
D. 0.854

Answers

Answer with explanation:
Coefficient of determination(r²), is defined as, how well the data values are associated with each other when Regression line is drawn. In regression analysis, the coefficient of determination measures , how well the regression predictions approximate the real data points, means it measures the closeness between two variables.The Value of r², lies between 0 to 1. If value of r²=1, it shows ,regression line that is data values are Perfectly associated with each other.
If ,r²=0, it means there is no variation between two variables.There is 0% variation between two variables.
→Coefficient of Variation=[Correlation coefficient]²
=r²
=(0.854)²
=0.854 × 0.854
=0.729316
=0.730(Approx)

Which of the graphs below shows the solution set of -7 < x <0

Answers

Answer:

none

Step-by-step explanation:

A. -7 <= x < 0

B. x <= -7 or x > 0

C. -7 < x <= 0

D. x < -7 or x >= 0

To create a graph to represent -7 < x < 0, draw empty circles at -7 and 0, then connect the two with a line.

Complete the table of inputs and outputs for the function.
f(x) = -5(x + 7)
X
-9
01
0
f(x)
0
-60

Answers

Answer:

10, -7, -35, 5

Step-by-step explanation:

f(9) = -5(-9 + 7) = 10

0 = -5(x + 7)

0 = x + 7

x = -7

f(0) = -5(0 + 7) = -35

-60 = -5(x + 7)

12 = x + 7

x = 5

if the diameter of a circular pond is x meter what is the measure of its circumference​

Answers

πx

Step-by-step explanation:

well pi is defined as the ratio of a circle's circumference to its diameter so just πx

BRIANLY FOR THE BEST EXPLANATION AND ANSWER!
Question: A circle has an area of 16mm². Find it's circumference.

Answers

Answer:

C ≈ 14.18

Step-by-step explanation:

Question Given:

A circle has an area of 16mm². Find it's circumference.

Formula:

C = 2√πA

Solve:

C = 2√πA

C = 2√(3.14 × 16)

C = 2√50.24

C = 14.1760361173

C ≈ 14.18

Hence, Circumference is approximately 14.18.

~Kavinsky

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Area of Circle :

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} [/tex]

Now, it's given that area of circle is : 16 mm²

Let's calculate Radius ~

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} = 16[/tex]

[tex] \qquad \sf  \dashrightarrow \: {r}^{2} = \cfrac{16}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = \sqrt{ \cfrac{16}{ \pi} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = { \cfrac{4}{ \sqrt{ \pi} } }[/tex]

Now,

[tex]\qquad \sf  \dashrightarrow \: circumference = 2\pi r[/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 2 \pi \cfrac{4}{ \sqrt{ \pi} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 8 \sqrt{ \pi} [/tex]

[ for approximate value take pi = 3.14 ]

[tex]\qquad \sf  \dashrightarrow \: c = 8 \sqrt{3.14} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c \approx 8 \times 1.77[/tex]

[tex]\qquad \sf  \dashrightarrow \: c \approx 14.18 \: \: mm[/tex]

Between which two integers is the value of √11?
9 and 10
5 and 6
7 and 8
O3 and 4
1 and 2

Answers

The square root of 9 is 3
The square root of 11 is ?
The square root of 16 is 4

Between 3 and 4

Find the value of x

Answers

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

x = 12°

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2x + 6 + 5x + 90 = 180[/tex]

[ by linear pair ]

[tex]\qquad❖ \: \sf \:7x + 6 = 180 - 90[/tex]

[tex]\qquad❖ \: \sf \:7x + 6 = 90[/tex]

[tex]\qquad❖ \: \sf \:7x = 90 - 6[/tex]

[tex]\qquad❖ \: \sf \:7x = 84[/tex]

[tex]\qquad❖ \: \sf \:x = 84 \div 7[/tex]

[tex]\qquad❖ \: \sf \:x = 12[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x = 12 \degree[/tex]

Find the surface area of the composite figure 4 cm 13 cm 3 cm 4 cm 12 cm SA = [?] cm² 5 cm 3 cm.

Answers

area of rectangle ( bottom)
12x4=48

side of rectangle ( 2 of them)
4x3x2=24

length of rectangle (2 of them)
12x3x2=72

area of triangle facing us ( 2 of them)
1/2x5x12x2= 60

top part of triangle
13x4= 52

back part of triangle :
4x5=20

total = add them all together
= 276

Simplify Negative 3 over 2 divided by 9 over 6. −4 −1 4 1

Answers

Answer:

Step-by-step explanation: -3/2 divided by 9/6

= -3/2 multiply (to divide fractions we multiply by their recipical) 6/9
Then, simplify
= -3/3 = 1
Answer: -1

Hope this helps lol

The simplified result is -1. The correct option is b.

Given that:

Expression, -3/2 ÷ 9/6

To solve the given expression, follow as:

Rewrite the division as multiplication by the reciprocal of the second fraction.

-3/2 ÷ 9/6 = -3/2 × (6/9)

Now, simplify the fractions:

-3/2 × (6/9) = -3/2 × (2/3)

-3/2 × (6/9) = - (3 × 2)/(2 × 3)

-3/2 × (6/9) = -6/6

Finally, the simplified expression is -6/6. However, further simplify it by dividing the numerator and denominator by their greatest common divisor, which is 6:

-6/6 = -1

So, the simplified result is -1. The correct option is b.

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Complete question:

Simplify Negative 3 over 2 divided by 9 over 6.

a. −4

b. −1

c. 4

d. 1

Will mark brainliest

Answers

The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.

Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.

So we have

[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]

The entire graph of the function g is shown in the figure below.
Write the domain and range of g using interval notation.

Answers

The domain of the function is [-4, 4) and the range of the function is [-5, 2)

How to determine the domain and the range of the function?

The domain

As a general rule, it should be noted that the domain of a function is the set of input values or independent values the function can take.

This means that the domain is the set of x values

From the graph, we have the following intervals on the x-axis

x = -4 (closed circle)

x =4 (open circle)

This means that the domain of the function is [-4, 4)

The range

As a general rule, it should be noted that the range of a function is the set of output values or dependent values the function can produce.

This means that the range is the set of y values

From the graph, we have the following intervals on the y-axis

y = -5 (closed circle)

y = 2 (open circle)

This means that the range of the function is [-5, 2)

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The Bourassas decide to sell a home for $440,000. They are charged a real estate commission of 8% of the selling price, title insurance that is 1.4% of the selling price, and an escrow fee of $775.
(a)
What amount (in dollars) do the Bourassas receive after fees?
$
(b)
What percentage of the selling price was fees? Round to the nearest tenth of a percent.
%

Answers

The amount received net of expenses is $397865 and the percentage of the sale price was 10%.

Given that Bourassas decides to sell a house for $ 440,000. You will be charged a real estate fee of 8% of the sale price, property insurance of 1.4% of the sale price, and an escrow fee of $ 775.

The declared retail price is $ 440,000.

Real estate commission = 8% of the sale price

Real Estate Fee = (8/100) × 440000

Real Estate Fee = 8 × 4400

Real Estate Fee = $ 35,200

Security insurance costs of the title = 1.4% of the sale price

Cost of title insurance = (1.4 / 100) × 440 000

Cost of title insurance = 1.4 × 4400

Title Insurance Cost = $ 6160

The escrow fee assigned is $ 775.

(a) In determining the amount received after deducting the sale price of the property commission, title insurance and escrow fees, we receive

Amount received after fees = sale price - real estate commission - title insurance - escrow fees

Amount received after fees = 440000-35200-6160-775

The amount received after fees = $397865

(b) To find the percentage of sale price, add together all the terms real estate commission, title insurance and escrow fees and divide by the sale price we get

Percentage of selling price=((35200+6160+775)/440000)×100

Percentage of sale price = (42135/440000) × 100

Percentage of sale price = 9.57

Percentage of sale price = 10% (rounded down)

Hence Bourassas decides to sell a house for $440,000, then the amount Bourassas will receive after expenses is $397,865 and the percentage of the sale price of expenses is 10%.

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A man can take a same time to row 13km downstream and 7km upstream.His speed in still water is 5km/hr.The speed of stream is

Answers

Answer:

0.6 km/hr

Step-by-step explanation:

Speed downstream: 13/5= 2.6 km/hr

Speed upstream: 7/5= 1.4 km/hr

Therefore, Velocity of current is: 1/2 (2.6-1.4) km/hr = 1/2(1.2) km/hr

PLS HELP ME ASAP I NEED THE ANSWER NOW BEFORE 5 mins PLS Help ME I WILL MARK BRAINLIST IF YOUR ANSWER IS CORRECT AND WAS ANSWERED 4 MIN AGO HELP ME PLSSS

The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 42 hours.

1 day
24 hours
12 hours 12 hours


1 and 1 over 4. days (wrong)

1 and 1 over 2. days

1 and 3 over 4. days

2 days

Answers

Answer:

42 - 24 = 18

18/24 = 3/4

the answer would be 1 and 3/4 days

Answer:

1 and 3 over 4 days

Step-by-step explanation:

Since 24 hours is 1 day  all we have to do is divide 42 into 24 and see what the resulting fraction is

42/24 = 7/4  (reducing to lowest fraction)

7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)

Answer:
1 and 3 over 4 days

please help, I have been on this question for a while. Lotta yummy PTS

Answers

Answer:

[tex]y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3[/tex]

Step-by-step explanation:

Given equation:

[tex]y=\left|\dfrac{1}{2}x-2\right|+3[/tex]                            

Translation

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

When translating a graph to the right, subtract the number of units from the x variable.

Translating the given graph one unit to the right:

[tex]f(x-1) \implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3[/tex]

Simplifying:

[tex]\implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3[/tex]

[tex]\implies y=\left|\dfrac{1}{2}x-\dfrac{1}{2}-2\right|+3[/tex]

[tex]\implies y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3[/tex]

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6/(v+4) + 2/(v-6)
What is the answer?

Answers

Answer:

8v-28/v^2-2v-24

Step-by-step explanation:

1. Find common denominator

2. Combine fractions with common denominator

3. Re-order terms so constants are on the left

In how many possible ways can this be accomplished if there are 25 members on the board of directors

Answers

Answer:  13800

Explanation:

There are 25 choices for president. Then we have 25-1 = 24 choices for the secretary, and 24-1 = 23 choices for treasurer. This countdown (25,24,23) is because any given person cannot serve in more than one position.

Multiply out those values: 25*24*23 = 13800

Side note: you could use the nPr permutation formula as an alternative path. Plug in n = 25 and r = 3.

Find the value of z.
answer choices
A. 40
B. 56
C. 62
D. 80

Answers

Answer:

40°

Step-by-step explanation:

Using external angle intercepted arcs calculation:

    50° = 1/2 (210-x)    shows x = 110°

then z = 360 - 210 -110 = 40°

can I return notebooks to target?

Answers

Answer: yes, as long as you haven't used them. :)

Step-by-step explanation:

If AC is a diameter and Arc AD = 90. Find ∠DAC. Round your answer to the nearest tenth.

Answers

Answer:

45°

Step-by-step explanation:

it is an inverted angle within a circle

Answer:  45 degrees

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

Explanation:

Minor arc AD is the shortest path from A to D along the circle's edge. This is 90 degrees. Minor arc AD combines with DC  to get arc ADC

Arc ADC is a semicircle because of the diameter AC. Any semicircle has a measure of 180 degrees.

So,

(minor arc AD) + (minor arc DC) = arc ADC

(minor arc AD) + (minor arc DC) = 180

(90) + (minor arc DC) = 180

minor arc DC = 180 - 90

minor arc DC = 90

AD and DC are 90 degrees each.

Then notice that inscribed angle DAC subtends minor arc DC. Use the inscribed angle theorem to determine angle DAC is 90/2 = 45 degrees

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the equation of the circle whose center and radius are given.

center ( 5, 6), radius = 3

Answers

The  equation of the circle whose center and radius are given as center ( 5, 6), radius = 3 is; x² + y² - 10x - 12y + 52 = 0

How to find the equation of a circle?

We know that the general form of equation of a circle whose center is (h, k) and radius is r is expressed as;

(x - h)² + (y - k)² = r²     --- (1)

We are given;

Center coordinate; (h, k) = (5, 6)

radius; r = 3

Plug in the values of h = 5 , k = 6 and r = 3 into the equation to get;

(x - 5)² + (y - 6)² = 3²

Expanding the equation gives;

x² - 10x + 25 + y² - 12y + 36 = 9

x² + y2 - 10x - 12y + 52 = 0

Thus the  equation of the circle whose center and radius are given as center ( 5, 6), radius = 3 is; x² + y² - 10x - 12y + 52 = 0

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Two triangles are similar. The sides of the first triangle are 4,5,and 6. The largest side of the second triangle is 24. Find the perimeter of the second triangle.

Answers

Answer:

The perimeter of the second triangle is 60 units.

Step-by-step explanation:

If two triangles are similar, their corresponding sides will be k times greater or smaller, where k is the scale factor.

We have two corresponding sides given, 6 and 24 or 6k. Using this info, find the value of k:

k = 24/6 = 4

The other sides of the larger triangle are:

4k = 4*4 = 165k = 5*4 = 20

The perimeter is the sum of sides:

P = 16 + 20 + 24 = 60

5
1
The measure of Z1 =
O 55
O62.5
110
5

Answers

Answer: 55

Step-by-step explanation:

Congruent angles intercept congruent chords, so since the circumference of a circle is 360 degrees, the arc angle 1 is inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

What are congruent angles?

Congruent angles exist as two or more angles that exist identical to each other. Therefore, the measure of these angles exists equivalent to each other. The kind of angles does not create any distinction in the congruence of angles, which implies they can be acute, obtuse, exterior, or interior angles.

The Inscribed Angle Theorem states that the measure of an inscribed angle exists half the measure of its intercepted arc. Inscribed angles that intercept the exact arc exist congruent. This exists named the Congruent Inscribed Angles Theorem and exists shown below.

∠ A D B and ∠ A C B intercept, so m ∠ A D B = m ∠ A C B.

Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

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Identify the slope and y-intercept of the line y = ×/2 -7​

Answers

Answer:

Slope: [tex]-\frac{1}{5}[/tex]   Y-intercept: (0,0)

Step-by-step explanation:

By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].

solve this equations 3x+4x-8=6(x-3)+x

Answers

Answer:

no solutions

Step-by-step explanation:

Mira buys a gold ring for ₹ $8740$ inclusive of $15\%$ tax. The ring was sold at a discount of $5\%$ .
What is the marked price of the ring? ₹

Answers

The marked price of the ring given the cost as 8740 inclusive of 15% tax and discount of 5% is $7,283.3.

Marked price

Cost of the gold ring = $8740Tax = 15%Discount = 5%Marked price = x

8740 = x + (15% of x) + (5% of x)

8740 = x + (0.15x) + (0.05x)

8740 = x + 0.15x + 0.05x

8740 = 1.20x

x = 8740 / 1.20

x = 7283.33333333333

Approximately,

x = $7,283.3

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