You invest $5000 into an account earning 4% interest compounded quarterly. Write an
equation to represent the amount of money you will have in your account after 8 years?

Answer:

Well the following inequality [tex]x<-3[/tex] as a graph is in the image below.

Answer:

C. 32,768

Step-by-step explanation:

Step 1

Convert the number of hours to minutes

2.5 hours to minutes = 2 hrs 30 minutes to minutes is calculated as

1 hour = 60 minutes

2 hours 30 minutes =

Cross multiply

(60 minutes × 2 hours) + 30 minutes = 150 minutes.

Step 2

We are told in the question that the bacteria population doubles every 10 minute interval

Find the number of intervals in 150 minutes

= 150 minutes / 10 minutes interval

= 15 intervals

Step 3

The number of bacteria present after 2.5 hours is calculated using the formula of

= Amount of bacterium × 2ⁿ

Where n = number of intervals = 15

Amount of bacterium = single bacterium = 1

Number of bacteria = 1 × 2¹⁵

= 32,768

Therefore, when you start with a single bacterium in a petri dish, the number of bacteria that will there be in 2.5 hours is 32,768

Answer:

A ≈ 254.5 in²

Option C

Step-by-step explanation:

Area of a Circle Formula: A = πr²

d = 2r

Since we are given diameter d, we simply divide by 2 to get radius r:

r = 18/2 = 9

Then we simply plug it into the formula:

A = π(9)²

A = 81π

A = 254.469

A circle with a radius of 9 inches has an area of 254.3 square inches. The of aarea  circle is calculated using the formula πr², where π is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.

Hence, the correct option is C.

The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius of the circle. In this case, the radius is 9 inches, so the area is given by:

In this case, the radius is 9 inches, so the area of circle is given by,

Area = pi × [tex]9^{2}[/tex]

Area = 3.14 × 81

Area= 254.3

The value of pi is approximately 3.14, so the area of the circle is approximately 254.3. However, the question asks for the area rounded to the nearest tenth, so the answer is 254.3.

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9514 1404 393

Answer:

  Cone Z, cylinder Y

Step-by-step explanation:

Pointy objects such as pyramids and cones have 1/3 the volume of a prism (or cylinder) with the same base area. So, for a cone and cylinder of the same base area to have the same volume, the cone must be 3 times as high.

The figures described as having that relationship are ...

  cone Z, cylinder Y

_____

Additional comment

The perimeter of a prism is not sufficient to define its base area, unless the shape of the base is well-enough defined. However, the perimeter of the base is useful for determining the lateral surface area. Unfortunately, that is not of any interest in this problem.

Answer:

x = 31.64

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 36 = 23/x

x tan 36  =23

x = 23/tan 36

x=31.63686382

Rounding to 2 decimal places

x = 31.64

Answer:

D. 31.64

Step-by-step explanation:

Answer:

No it doesn't have the same surfaces

The cuboid A and B have different surface areas.

The surface area of a three-dimensional object is the total area of all its faces.

SA=2lw + 2lh + 2hw

Where,

SA is the surface area of a cuboid

l is the length of the cuboid

h is the height of the cuboid

w is the width of the cuboid

Let the area of each cube is one unit.

So, for the cuboid A

Length = 3 unit

Width = 2 unit

Height = 3 unit

Therefore, the surface area of cuboid A = ( 3 × 2 + 3 × 2 + 2 × 2 ) 2

⇒ Surface area of cuboid A = 32 square unit

For cuboid B

Length = 4 unit

Width = 1 unit

Height =  3 unit

Therefore,

The surface area of cuboid B = (4 × 1 + 4 × 3 + 3 × 1)2

⇒ Surface area of cuboid B = 38 square unit

Hence, the cuboid A and B have different surface areas.

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Answer:

√2x+8=x-8

2x+8=x^2-16x+64

-x^2+18x-56=0

x^2-18x+56=0

x(x-4)-14(x-4)=0

(X-4)(x-14)=0

x=4(extraneous) ,x=14

—> x=14

Step-by-step explanation:

Answer: (14,6)

Step-by-step explanation:

Right on edg 2022.

Answer:

B 30% you can divide 160 the total by 10then multiply and you can check B and C

Answer:

Step-by-step explanation:

Concepts used :

sum of angles at a point on straight line is 180

if a transversal intersects two parallel lines then alternate angles are equal.

____________________________________________

∠∠∠∠∠

m∠1 + m∠2 + m∠3 = 180   ____________(A)

reason :sum of angles at a point on straight line is 180

these angles lie on LAM at point A

m∠1  = m∠5

Reason: alternate angles  y ∥ x and AC is transversal

m∠3  = m∠6

Reason: alternate angles  y ∥ x and AB is transversal

Substituting m∠1  with  m∠5 and m∠3  with m∠6

in equation A---m∠1 + m∠2 + m∠3 = 180

m∠5 + m∠2 + m∠6 = 180

Hence proved.

Answer:

The answers are below. Hope this helped. I sacrificed my answers ˙-˙ :)

Step-by-step explanation:

<1 congruent to <5                Given

<3 congruent to <6               Alternate Interior Angles theorem

m<1 = m<5                             Alternate Interior Angles theorem

m<3 = m<6                            Definition of congruent angles

m<1+m<2+m<3=m< LAM      Definition of congruent angles

m<1+m<2+m<3=180             Angle additon postulate

m<5+m<2+m<6=180            Definition of straight angle

Answer:

Step-by-step explanation:

Write and solve an equation of ratios:

 9        4

----- =  -----

 x         10

Then 4x = 90, and x = 22.5

It will take exactly 22.5 cans of paint to cover 10 rooms.  The painter must buy 23 cans.

Answer:

y = -x + 7

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]

Step 1: Find slope

m = (6 - 3)/(1 - 4)

m = -1

Step 2: Find b

y = -x + b

6 = -1 + b

b = 7

Step 3: Rewrite linear equation

y = -x + 7

Answer:

y = -x + 7

Step-by-step explanation:

(x1, y1) = (4 , 3)

(x2, y2) = (1 , 6)

[tex]slope=\frac{y_{2}-y{1}}{x_{2}-x_{1}}\\\\=\frac{6-3}{1-4}\\\\=\frac{3}{-3}\\\\=-1\\\\y-y_{1}=m(x-x_{1})\\\\[/tex]

m = - 1;  (4,3)

y - 3 = (-1)(x -4)

y - 3 = -x + 4

y = -x + 4 + 3

y = -x + 7

Answer:

A square

Step-by-step explanation:

Since the base is a square, any plane of the pyramid parallel to the base is shaped like a square (except the very top one which is a point).

Square shape will you get if you take a cross section of a square pyramid parallel to its base

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

'A square pyramid is a  three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.'

According to the given problem,

If a square pyramid is cut along the plane, then the cross-section of the solid is square. Because it is a square pyramid.

Hence, we concluded that square could be formed by slicing the square pyramid by a plane.

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Answer:

The quotient is 10x + 16

The remainder is 28x² + 10x + 22

Step-by-step explanation:

x³ - 3x² + x - 2) 10x⁴ - 14x³ - 10x² + 6x - 10 (10x + 16

                       10x⁴ - 30x³+ 10x² - 20x

                                16x³ - 20x² + 26x - 10

                                16x³ - 48x² + 16x - 32

                                          28x² + 10x + 22

Therefore, the quotient is 10x + 16

The remainder is 28x² + 10x + 22

Answer:  see below

Step-by-step explanation:

Given ax² + bx + c = 0

If a > 0 (positive), then parabola opens UP

If a < 0 (negative), then parabola opens (DOWN)

Axis of Symmetry: [tex]x=\dfrac{-b}{2a}[/tex]

Max/Min: Plug axis of symmetry into the given equation and solve for y.

1) y = x² + 11x + 24

      a=1   b=11

a> 0 so parabola opens UP

[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(11)}{2(1)}=\dfrac{-11}{2}=-3.5\\\\\\\text{Minimum:}\quad y=(-3.5)^2+11(-3.5)+24 = -6.25[/tex]

2) y = -x² - 6x - 8

      a=-1   b=-6

a< 0 so parabola opens DOWN

[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-6)}{2(-1)}=\dfrac{6}{-2}=-3\\\\\\\text{Maximum:}\quad y=(-3)^2-6(-3)-8 = 1[/tex]

3) y = x² - 2x + 3

      a=1   b=-2

a> 0 so parabola opens UP

[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-2)}{2(1)}=\dfrac{2}{2}=1\\\\\\\text{Minimum:}\quad y=(1)^2-2(1)+3 = 2[/tex]

4) y = x² + 4x + 4

      a=1   b=4

a> 0 so parabola opens UP

[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(4)}{2(1)}=\dfrac{-4}{2}=-2\\\\\\\text{Minimum:}\quad y=(-2)^2+4(-2)+4 = 0[/tex]

5) y = 3x² + 21x + 30

      a=3   b=21

a> 0 so parabola opens UP

[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(21)}{2(3)}=\dfrac{-21}{6}=-3.5\\\\\\\text{Minimum:}\quad y=3(-3.5)^2+21(-3.5)+30 = -6.75[/tex]

Answer:

Rolling a 4 on the first try has a probability of (1/6). Meaning, it is one event out of the six possible events of the die. Rolling a 4 a second time also has a probability of (1/6), because nothing has changed on the die.

Answer:

Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5

Step-by-step explanation:

The answer above is correct.

Answer:

(-2 ; -5)

Step-by-step explanation:

7*x - 2*y = -4

(7/2)*x - (2/2)*y = -4/2

(7/2)*x - y = -2

(7/2)*x + 2 = y

3*x - 5*y = 21 - 2

3*x - 5*y = 19

3*x - 5*[(7/2)*x + 2] = 19

3*x - 35/2*x - 10 = 19

- 29/2*x = 29

- 1/2*x = 1

x = -2

⇒ y = -5

Answer : (-2 ; -5)

Answer:

Let the fourth angle be x

Angles in a quadrilateral add up to 360°

To find the fourth angle add all the known angles and subtract them from 360°

That's

x + 120+37+48=360

x + 205 = 360

x = 360-205

x = 155°

Therefore the fourth angle is 155°

Hope this helps

Answer:

They are equivalent.

Step-by-step explanation:

You can tell because 4:1 can go into 12:3.

If you multiply 4 by 3 you will get 12.

If you multiply 1 by 3 you would get 3.

12:3=4:1

Hope this helps!

Step-by-step explanation: Two ratios are equal if the fractions that represent the are equal.

So we first write the ratios 4 : 1 and 12 : 3 as the fractions 4/1 and 12/3.

Now, to determine whether the two fractions are equal,

we write each fraction in lowest terms.

Notice that 4/1 or 4 is already in lowest terms.

So let's move on.

12/3 can be simplified to 4.

So we have 4 = 4 which is true.

So that's how we know the ratios 4 : 1 and 12 : 3 are equal.

Answer: 5 hours and 15 mins

Step-by-step explanation: 45 mins x 7 = 5 hours and 15 mins. I checked so it should be correct. [tex]45x2= 1[/tex]hour and 30 mins.So I multiplied 1 hr 30 x 3 which gave me 4 hr 30 then added 45 mins, then I got 5 hr 15 min.

So in conclusion the answer is 5 hours and 15 mins.

                                                                                                 Thank You                                                                      

Answer:

zero or undefined

Answer:

it's d zero.

Step-by-step explanation:

just took the test

Answer:

It's asking you to write the function in a factored form  for example g(x) or f(x) that's why its asking for you to use the x as the variable.

Step-by-step explanation:

Answer:

C = (2,2)

Step-by-step explanation:

B = (10 ; 2)

M = (6 ; 2)

C = (x ; y )

|___________|___________|

B (10;2)            M (6;2)             C ( x; y)

So:

dBM = dMC

√[(2-2)^2 + (6-10)^2] = √[(y-2)^2 + (x - 6)^2]

(2-2)^2 - (6-10)^2 = (y-2)^2 + (x - 6)^2

0 + (-4)^2 = (y-2)^2 + (x - 6)^2

16 = (y-2)^2 + (x - 6)^2

16 - (x - 6)^2 = (y-2)^2

Also:

2*dBM = dBC

2*√[(2-2)^2 + (6-10)^2] = √[(y-2)^2 + (x - 10)^2]

4*[(0)^2 + (-4)^2] = (y-2)^2 + (x - 10)^2

4*(16) = (y-2)^2 + (x - 10)^2

64 = (y-2)^2 + (x - 10)^2

64 = 16 - (x - 6)^2 + (x - 10)^2

48 = (x - 10)^2 - (x - 6)^2

48 = x^2 - 20*x + 100 - x^2 + 12*x - 36

48 = - 20*x + 100 + 12*x - 36

8*x = 16

x = 2

Thus:

16 - (x - 6)^2 = (y-2)^2

16 - (2 - 6)^2 = (y-2)^2

16 - (-4)^2 = (y-2)^2

16 - 16 = (y-2)^2

0 =  (y-2)^2

0 = y - 2

2 = y

⇒ C = (2,2)

Answer:

B, x≥2

Step-by-step explanation:

54 - 10x ≤ 20 + 7x - subtract 20

34 - 10x ≤ 7x - add 10x to 7x

34 ≤ 17x - divide 34 by 7

2 ≤ x - flip the equation - x ≥ 2

Hope this is helpful!

Answer:

Choice B

Step-by-step explanation:

TRUST ME. IF YOU WANT EXPLANATION:

54 - 10x < = 20 +  7x

54 - 20 < = 7x + 10x

34 < = 17x

34/17 < = x

2 < = x.....or x > = 2....its B trust me

Answer:

The answer is p/6-4/5.

hope it helps

Answer:

no

Step-by-step explanation:

Answer:

an = an-1 * (-5)

a1= 2

Step-by-step explanation:

The recursive formula is

an = an-1 * r

a1= initial term

where a1 is the initial term and r is the common ratio

a1 =2 or the starting term

r = second term / first term = -10/2 = -5

an = an-1 * (-5)

a1= 2

Answer:

The correct answer is D

Step-by-step explanation:

2 and -5

Answer:

*regular-sized hot dog contest has greater variability

*The difference in the medians of the two contests is approximately 2 times the interquartile range.

Step-by-step explanation:

Variability of the data from both contests can be compared using the range or interquartile range of each set of data from both contests.

The greater the value of the range or interquartile range, the greater the variability.

Range for regular-sized hot dog contest = 32 - 17 = 15

Range for Jumbo-sized hot dog contest = 22 - 8 = 14

Interquartile range for regular-sized hot dog contest = 27 - 22 = 5

Interquartile range for jumbo-sized hot dog contest = 16 - 11 = 5

Median for regular-sized hot dog contest = 23

Median for jumbo-sized hot dog contest = 14

The difference in the median of both contests = 23 - 14 = 9, which is approximately 2 times the interquartile range (5)

Thus, results for the regular-sized hot dog contest has greater variability, be side its range is 5, which is greater than that for jumbo-sized contest.

The difference in the medians of the two contests is approximately 2 times the interquartile range.

The interquartile range of both contests is 5. The median difference between both contests is 9, it is approximately 2 times 5. (i.e. 9/5 = 1.8 ≈ 2).

Answer:

15%

Step-by-step explanation:

25% fail math

60% of the 25% above fail science

thus,

[tex] \frac{25}{100} \times 60\%[/tex]

=15% of total student

Answer:

V( 3, -8 )

Step-by-step explanation:

Parable equation is of the form:

( x - h )² = 4p*(y - k)

In that expression, vertex has coordinates V ( h, k )

Then all we have to do is transform the given equation

y = x² - 6x + 1       or     x² - 6x  = y - 1          (1)

We can get a  perfect square trinomial in the first member of the equation according to:

x²  -  6x   =   ( x - 3 )²  - 9

(x - 3 )²   = x² - 6x  + 9

By substitution  en equation (1)

( x - 3 )² - 9 = y - 1

( x - 3 )² = y -1 + 9

( x - 3 )² = y + 8

( x - 3 )² = (y + 8 )

Then vertex coordinates are

V( 3 , -8)

Answer:

2^1

According to the product of powers with the same base, a^m * a^n = a^m+n.

Basically, when you're multiplying exponents with the same base, you can add the powers together to get the answer.

2^6 * 2^-5

The bases are the same, so we can apply this rule.

6 + -5 = 1

This gives you the answer of 2^1.