INVESTING Maria invests $1000 in a savings account that pays 4% interest compounded annually. The value of the account A at the end of five years can be determined from the equation log10 A = log10[1000(1 + 0.04)5]. Write this equation in exponential form

Answer:

  4.73%

Step-by-step explanation:

  y = 3×2^(t/15) = 3×(2^(1/15))^t = 3×1.0472941^t

In this form, ...

  1 +r = 1.0472941

  r = .0472941 ≈ 4.73%

The daily increase is about 4.73%.

Answer:

4 days

Step-by-step explanation:

She recorded date for 16 days, and 1/4 of the days were clear blue skies.

One way to find this is to multiply 16 and 1/4

16*1/4=4

Another way is to first convert 1/4 to a decimal

1/4=0.25

Then multiply 16 and 0.25

16*0.25 =4

So, 4 out of 16 days had clear blue skies

Answer:

Please read the answer below

Step-by-step explanation:

The general form of a sinusoidal function is given by:

[tex]f(x)=Asin(\omega x)[/tex]   (1)

where A is the amplitude, and the period is given by:

[tex]T=\frac{2\pi}{\omega}[/tex]

The image of a function is the available values of the function f(x) in the domain of f(x). For sinusoidal function the image of f(x) is determined with the aid of the amplitude.  For example, in the case of (1), f(x) varies from -A to A.

Due to the information given above you have (the plots are attached below):

a)

[tex]f(x)=3sin(x)\\\\T=\frac{2\pi}{1}=2\pi\\\\Im\ f(x)=[-3,3][/tex]

b)

[tex]f(x)=1-sin(3x)\\\\T=\frac{2\pi}{3}\\\\Im\ f(x)=[0 \ ,2][/tex]

in the last case the first term of f(x) modifies the image of f(x) because the sinusoidal function is displaced to y=1.

c)

[tex]f(x)=-1+2sin(0.5x)\\\\T=\frac{2\pi}{0.5}=4\pi\\\\Im\ f(x)=[-3,1][/tex]

Answer:

X=10.8 and X=1.1

Step-by-step explanation:

Δ= b^2-4ac

= (-6)^2-4(1)(3)

=24

X1=

[tex] \frac{6 + \sqrt{24} }{ {1}^{2} } [/tex]

=10.8

X2=

[tex] \frac{6 - \sqrt{4} }{ {1}^{2} } [/tex]

=1.1

Answer:

The average total cost per hour of training is $70.5

Step-by-step explanation:

The form of the linear function is f(x) = m x + b, where

∵ The gym charges a $615 yearly fee for membership plus

   $50 for each hour of personal training

- That means the initial amount is 615 and the average rate is 50

∴ m = 50 dollars per hour

∴ b = 615 ⇒ fixed fee

- Substitute m and b in the form of the linear function

∴ c(x) = 50 x + 615, where c(x) is the cost per year for x

   training hours

∵ A member works with a personal trainer for 30 hours in a year

- That means x = 30

∴ x = 30

- Find the total cost of this year by substituting x by 30

∴ c(30) = 50(30) + 615

∴ c(30) = 1500 + 615

∴ c(30) = 2115

∴ The total cost of this year is $2115

To find the average cost per hour divide the total cost by the number of the training hours

∵ Average cost per hour = 2115 ÷ 30

∴ The average cost per hour = 70.5 dollars

∴ The average total cost per hour of training is $70.5

Based on the number of hours and the cost per hour of using the trainer, the average cost per hour is $70.50 per hour.

First find the total cost of using a trainer for 30 hours.

= Fixed membership cost + (Cost per hour x Number of hours)

= 615 + (50 x 30)

= $2,115

The total cost for the year is $2,115.

The average cost per hour will be:

= Total cost / Number of hours

= 2,115 / 30

= $70.50

In conclusion, the total average cost per hour is $70.50.

Find out more at https://brainly.com/question/24157928.

Answer:

25 & 2

Step-by-step explanation:

The minimum unit cost to manufacture a car for the given quadratic cost function C(x) = 0.5x^2 - 130x + 17,555 is found by using the vertex formula. The x-coordinate of the vertex is -(-130)/(2*0.5) = 130, which yields the minimum unit cost of $9,105 when substituted back into the function.

To find the minimum unit cost for manufacturing cars in the given scenario, we need to analyze the cost function C(x) = 0.5x2 - 130x + 17,555. This is a quadratic function, which is parabolic in shape, generally either opening upwards or downwards. In this case, we have a positive coefficient for the x2 term, which means the parabola opens upwards and the vertex of this parabola will give us the minimum point or the minimum cost for producing cars.

The vertex of a quadratic function expressed in the form ax2 + bx + c can be found using the formula -b/(2a) for the x-coordinate of the vertex. In this case, a = 0.5, b = -130, so the x-coordinate of the vertex is -(-130)/(2*0.5) = 130. Plugging this value into the original function will give us the minimum unit cost C(130).

The calculation is as follows:

C(130) = 0.5 * (130)2 - 130 * (130) + 17,555

C(130) = 0.5 * 16,900 - 16,900 + 17,555

C(130) = 8,450 - 16,900 + 17,555

C(130) = 9,105

Therefore, the minimum unit cost to manufacture a car in this scenario is $9,105.

Answer:

1.8

Step-by-step explanation:

9/10 times 2 equals 1.8

/Answer:

The answer would be 18/10.

Step-by-step explanation:

This is because when you add fractions with common denominators, like 9/10+9/10, you don't add the denominators. But if you multiply 9/10*2 it would be like 9/10*2/1 which would equal 18/10 still.

Answer:

-1.13 m/s

Step-by-step explanation:

Parameters given:

Mass of first footballer, M = 92 kg

Initial velocity of first footballer, U = 6.5 m/s (taking North to be the +ve y axis)

Mass of second footballer, m = 85 kg

Initial velocity of second footballer, u = -6.0 m/s (taking South to be the -ve y axis)

Final velocity of first footballer, V = 2.0 m/s

We need to find the final velocity of the second football (v)

Applying the principle of conservation of momentum, we have that, in a system:

Total Initial Momentum = Total Final Momentum

(M * U) + (m * u) = (M * V) + (m * v)

(92 * 6.5) + (85 * -6) = (92 * 2) + (85 * v)

598 - 510 = 184 + 85v

88 = 184 + 85v

88 - 184 = 85v

-96 = 85v

=> v = -96 / 85

v = -1.13 m/s

The final velocity of the 85 kg player is -1.13 m/s i.e 1.13 m/s South

Final answer:

To find the unknown velocity of the 85.0 kg football player after the collision, we use the conservation of momentum, setting up an equation based on the initial and final momenta of both players and solving for the unknown velocity.

Explanation:

The question concerns the topic of conservation of momentum during a collision between two football players, which falls under the category of Physics. To solve for the velocity of the 85.0 kg football player after the collision, we can use the principle that the total momentum before the collision is equal to the total momentum after the collision in an isolated system.

The total momentum before the collision can be calculated as follows:

Momentum of the 92.0 kg player = mass × velocity = 92.0 kg × 6.50 m/s (North).

Momentum of the 85.0 kg player = mass × velocity = 85.0 kg × 6.00 m/s (South).

Since they are moving in opposite directions, we assign a positive direction (e.g., north) as positive momentum and the opposite direction (south) as negative momentum.

The total momentum after the collision consists of:

Momentum of the 92.0 kg player = 92.0 kg × 2.00 m/s (North).

Momentum of the 85.0 kg player = 85.0 kg × v (where v is the unknown velocity).

By applying the conservation of momentum, we can write the equation:

(92.0 kg × 6.50 m/s) + (85.0 kg × -6.00 m/s) = (92.0 kg × 2.00 m/s) + (85.0 kg × v).

Solving for v gives:

v = [(92.0 kg × 6.50 m/s) - (92.0 kg × 2.00 m/s) - (85.0 kg × -6.00 m/s)] / 85.0 kg.

Calculate the value to find the final velocity of the 85.0 kg player.

v = 10.87 m/s

Answer:

8 were absent

Step-by-step explanation:

20% of 40 is 8

Answer:

32 students were present

Step-by-step explanation:

total students =40

absent percent=20%

present percent= 100-20

=80%

total present student =80%of 40=32

Answer:

THE ANSWER IS 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

3, 3, 4, 4, 5, 9

The median is 4

Answer:

47/62

Step-by-step explanation:

62 total games won 47 therefore 47/62

Final answer:

The fractional part of the games won by Betsy's softball team is 47/62, representing the number of games won out of the total games played.

Explanation:

To calculate the fractional part of the games won by Betsy's softball team, you need to divide the number of games won by the total number of games played. The team won 47 games and lost 15 games, giving a total of 47 + 15 = 62 games played.

The fraction representing the part of the games won is therefore 47/62. When simplified, this fraction may be reduced to a simpler form by finding the greatest common divisor and dividing both the numerator and the denominator by it. However, as 47 is a prime number and does not divide evenly into 62, the fraction can't be simplified further. Therefore, the fractional part of the games won by the team is 47/62.

Answer:

Option C)

[tex]-7<-2[/tex]

Step-by-step explanation:

We are given the following in the question:

"-7 and a number 5 units to the right of -7"

The nubmer 5 units to the right of -7 will be:

[tex]=-7 + 5\\=-2[/tex]

The number line shows the two marked points.

As observed from the number line, we can write the inequality:

[tex]-7<-2[/tex]

Thus, the correct option is

Option C)

[tex]-7<-2[/tex]

Answer:

its d not c  so -7<-2 is the awnser

Answer:

Out of 240,000 feet² of the field 62,800 feet² was being watered.

Step-by-step explanation:

We have a figure with 32 circles and diameter of each circle is 50 feet. We have to find how much area is being watered. Assuming that each circle represents the Area of the field which is being watered.

We can find the area of one circle and multiply that by 32 to find the area of all 32 circles. This will give us the area of the field that is being watered.

Since, radius is half of the diameter, the radius of each circle will be r = 25 feet.

Area of a circle is calculated as:

Area = πr²

Substituting the value of r = 25 and π = 3.14, we get:

Area of one circle = 3.14 x (25)² = 1962.5 feet²

Since area of 1 circle is 1962.5 feet² , area of 32 circles will be = 32 x 1962.5 = 62,800 feet²

The field is rectangular in shape with length = 600 feet and width = 400 feet.

Area of a rectangle is the product of its length and width. So area of the entire field will be:

Area of field = 600 x 400 = 240,000 feet²

This means, out of 240,000 feet² of the field 62,800 feet² was being watered.

Answer:

Step-by-step explanation:

1.65

Answer:

1.65

Step-by-step explanation:

choose  $16.50 / 10 pounds =   $1.65

The question is asking for the sum of 50 and 21. This is a mathematical operation known as addition. Following the steps of addition, the sum of 50 and 21 equals 71.

The question is essentially asking for the sum of 50 and 21. In Mathematics, when we talk about 'equal to', we are referring to the result of an equation or mathematical operation.

So, to find out what is equal to 50 + 21, you simply add these two numbers together. The process is as follows:

After following these steps, you will find that 50 + 21 equals 71.

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Answer:

when x is 2. f(2)=3(2)+1. f(2)=6+1. f(2)=7.

Step-by-step explanation:

Answer:

The line that is congruent to angle 4 is angle 1

hope this helped :)

Angle 4 is congruent to Angle 2 because they are alternate interior angles formed by the transversal intersecting two parallel lines.

Congruence of Angles

Angle 4 ≈ Angle 2 (alternate interior angles)

Answer:

5 km/h

Step-by-step explanation:

In this problem, Lashonda swam 4 km against the current. So the distance covered in this case is

[tex]d_1=4 km[/tex]

Calling [tex]v[/tex] the velocity of Lahonda without the current, and [tex]c[/tex] the velocity of the current, in this situation Lahonda's velocity is

[tex]v-c[/tex]

So we can write:

[tex]t_1=\frac{d_1}{v-c}[/tex]

where [tex]t_1[/tex] is the time taken to cover the distance.

When Lashonda swims with the current, her velocity is

[tex]v+c[/tex]

So we can write

[tex]t_2=\frac{d_2}{v+c}[/tex]

where

[tex]d_2=16 km[/tex] is the distance covered in this case, and [tex]t_2[/tex] the time taken.

The velocity of the current is

[tex]c=3 km/h[/tex]

Since Lashonad takes the same time to cover the two distances,

[tex]t_1=t_2[/tex]

So we can write

[tex]\frac{d_1}{v-c}=\frac{d_2}{v+c}[/tex]

And solving for v, we find Lashonda's velocity without the current:

[tex]d_1(v+c)=d_2(v-c)\\d_1 v+d_1c = d_2v-d_2c\\v(d_2-d_1)=c(d_1+d_2)\\v=\frac{d_2+d_2}{d_2-d_1}c=\frac{16+4}{16-4}(3)=5 km/h[/tex]

Final answer:

To find Lashonda's swimming speed without the current given the rate of the current and the distances swam with and against it.

Explanation:

The rate of the current is 3 kilometers per hour. To find the speed of Lashonda without the current, we can set up equations using the formula: speed = distance/time.

Let's denote Lashonda's speed in still water as x kilometers per hour. When swimming against the current, her effective speed is x - 3 km/h, and when swimming with the current, her effective speed is x + 3 km/h.

By setting up and solving the equations, we find Lashonda's speed without the current is 9 kilometers per hour.

Answer:

The distance from the feet to the wall is 9 ft

Step-by-step explanation:

Using trig,

We must use cosine to find the missing side.

The equation is cos 60 = [tex]\frac{adjacent}{18}[/tex]

The cosine of 60 is 1/2

So, we multiply 1/2 by 18

to get 9

Hope this helps!

Branliest would really be nice!

Answer:

190.8 square inches

Step-by-step explanation:

The area of one of its triangular sides is given by A = bh/2 were b = base = 9 inches and h = perpendicular height = 6.1 inches.

A = bh/2. Since we have 4 triangular sides, the total area of its sides  A₁ = 4A = 4bh/2 = 2bh = 2 × 9 × 6.1 = 109.8 square inches.

The area of is base is the area of a square = 9² = 81 square inches.

So te total surface area is 109.8 square inches + 81 square inches = 190.8 square inches

Answer:

190.8

Step-by-step explanation:

Answer: the answer is x-h and y-K

Step-by-step explanation:

This represents the side lengths of the right triangle that is formed

For this case we have that by definition, the area of a rectangle is given by:

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

Where:

w: Is the width of the rectangle

l: is the length of the rectangle

According to the data of the statement we have:

[tex]A = 81-x ^ 2\\w = 9-x[/tex]

So, the length is given by:

[tex]l = \frac {A} {w}\\l = \frac {81-x ^ 2} {9-x}[/tex]

We factor the numerator:

[tex]l = \frac {(9 + x) (9-x)} {9-x}[/tex]

We simplify:

[tex]l = 9 + x[/tex]

So, the length is [tex]9 + x[/tex]

Answer:

[tex]9 + x[/tex]

Answer:

c. 96

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

There are 4 different flower boxes with different-size bases that can hold exactly 16 cubic feet of soil when using whole-number dimensions. These consist of dimension combinations of 1x1x16, 1x2x8, 1x4x4, and 2x2x4 feet.

Mrs. Wilton is planning a rectangular flower box that should have a volume of 16 cubic feet. To find how many flower boxes with different-size bases can hold exactly 16 cubic feet of soil, we need to find all the possible combinations of whole-number dimensions (length, width, and height) that when multiplied together equal 16 cubic feet. We must remember that volume is calculated as Length x Width x Height. Since 16 is the volume in cubic feet, we look for whole-number factors of 16.

Here are the possible whole-number dimension sets (in feet) for a volume of 16 cubic feet:

1 x 1 x 16 (Height can be 1, 16, or any factor of 16)

1 x 2 x 8 (Height can be 2, 8, or any factor of 16)

1 x 4 x 4 (Height can be 4 or any factor of 16)

2 x 2 x 4 (These dimensions are interchangeable)

Each of these dimensions gives a different base size for the flower box, and all ensure the volume is 16 cubic feet. Thus, there are 4 different flower boxes with different-size bases that will hold exactly 16 cubic feet of soil.

Answer:

q/9

Step-by-step explanation:

The quotient is an number or variable that is the product of division. My answer may be reversed or wrong, but it should be close to the correct one.

Answer:

The answer to your question is the letter C.

Step-by-step explanation:

Data

sin Ф = 1/5

cos Ф = ?

To solve this problem use trigonometric functions.

1.- The first condition is that the angle must be in the first quadrangle

(0° < Ф < 90°).

2.- Write the trigonometric function sine.

           sin Ф = Opposite side / hypotenuse   and sin Ф = 1/5

then, Opposite side = 1     hypotenuse = 5

3.- Use the Pythagorean theorem to find the adjacent side.

           Hypotenuse² = Opposite side² + Adjacent side²

-Solve for Adjacent side

            Adjacent side² = Hypotenuse² - Opposite sie²

-Substitution

            Adjacent side² = 5² - 1²

-Simplification

            Adjacent side² = 25 - 1

            Adjacent side ² = 24

            Adjacent side = √24

4.- Find the cosФ

             cos Ф = Adjacent side/hypotenuse

-Substitution

             cosФ = √24 / 5

Answer:

b = 34m

Step-by-step explanation:

Answer:

Depends on which base you mean, the longer base would be b=41.67

The shorter base would be a=39.67

Hope this helps :)

Answer:

D

Step-by-step explanation:

one way to determine whether or not something is a function is to use the vertical line test

You can draw vertical lines all along the figure and if the same vertical line touches 2 parts of the graph we know this is not a function due to there being 2 outputs for the same x value

d is a vertical line and therefore will not pass this test