To be able to buy a new computer, Lisa decides to save for 5 years. She opens a savings account with $600. The account pays simple interest at an annual rate of 4%. She doesn't make any more deposits. Answer the following questions. If necessary, refer to the list of financial formulas. (a) How much total interest will Lisa earn? ${ (b) What will the total amount in the account be (including interest)? $ X​

First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.

Since the maximum height h is equal to 225 ft which is close to 300 ft we can conclude that Marc hit the ball near the top of the tower.

The concept used in this problem is the quadratic function and finding the maximum or minimum value of a quadratic function.

The x-coordinate of the vertex, which is the highest or lowest point on the graph, can be found using the formula:

=> x = -b / 2a

Here we have

The formula for the shot is h(x) = -16xsquared + 120x,

Where h is the height of the ball and x is the number of seconds the ball is in the air.

To mathematically prove that Marc hit the ball near the top of the tower, find the maximum height reached by the ball and compare it with the height of the tower.

To find the maximum height reached by the ball, find the vertex of the parabolic function h(x).

As we know

The x-coordinate of the vertex is given by:

x = -b / (2a)

Where a and b are the coefficients a and b

In this case, a = -16 and b = 120, so we have:

x = -120 / (2(-16)) = 3.75 seconds

The maximum height reached by the ball is given by:

h(3.75) = -16(3.75)² + 120(3.75) = 225 feet

To prove that Marc hit the ball near the top of the tower, we need to compare the maximum height reached by the ball (225 feet) with the height of the tower (300 feet).

Since the ball hit near the top of the tower, we can assume that it was close to the highest point of the tower when it was hit.

Therefore,

Since the maximum height h is equal to 225 ft which is close to 300 ft we can conclude that Marc hit the ball near the top of the tower.

Learn more about Quadratic functions at

https://brainly.com/question/12120831

#SPJ1

The type of the relation are

A linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.

In the given expressions:

Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".

Read more about linear relations at

https://brainly.com/question/30318449

#SPJ1

Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.

What is frequency?

Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).

The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.

The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.

The experimental and theoretical probabilities do not match exactly. For example, the experimental  of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.

The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.

Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).

To know more about frequency visit:

https://brainly.com/question/254161

#SPJ1

Commplete Question:

A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:

Field Trip Number of times selected

A                8

B                16

C               9

D                12

E                5

Apply math models to analyze the data and answer the following questions:

What is the experimental probability of selecting each field trip?

What is the theoretical probability of selecting each field trip?

Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?

What is the relative frequency of selecting each field trip?

Based on the data, which field trip appears to be the most popular?

The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

To know more about angles of arc visit:

https://brainly.com/question/29886231

#SPJ1

There are 78 grams of cashews in the trail mix.

What is weight?

Weight is the measure of the gravitational force exerted on an object due to its mass. It is commonly measured in units of mass, such as kilograms or pounds. Weight can vary depending on the gravitational pull of the planet or other celestial body on which the object is located. For example, an object that weighs 100 kilograms on Earth would weigh less on the Moon due to the Moon's lower gravitational force. It is important to distinguish between weight and mass, as they are not the same thing. Mass is a measure of the amount of matter in an object, whereas weight is a measure of the force exerted on an object by gravity.

If 65% of the total weight is made up of nuts, then the weight of nuts in the trail mix is 0.65 × 200g = 130g

Out of the 130g of nuts, 3/5 are cashews. So the weight of cashews in the trail mix is (3/5) × 130g = 78g

Therefore, there are 78 grams of cashews in the trail mix.

Learn more about weight here,

https://brainly.com/question/28218480

#SPJ1

The equation of the line is: y = 0.5x + 4 and the inequality is H > 74.25

To find the equation of a line that passes through two points, we need to use the slope-intercept form of a linear equation:

y = mx + b

The slope is calculated as

m = (y2 - y1) / (x2 - x1)

m = (11 - 4) / (14 - 0)

m = 7/14

m = 1/2

m = 0.5

Next, we have

y = mx + b

4 = 0.5(0) + b

b = 4

So the equation of the line is: y = 0.5x + 4

Part A: The equation that could be used to find the value of s is:

12s + 5.04 = 15.48

To find the value of s, we need to isolate the variable on one side of the equation.

We can do this by subtracting 5.04 from both sides and then dividing both sides by 12:

12s + 5.04 - 5.04 = 15.48 - 5.04

12s = 10.44

s = 10.44/12

s = 0.87

Therefore, Jacy paid $0.87 to download each song.

To represent the number of hours, h, that Tara plans to work this month as an inequality, we can use the fact that she plans to work more hours than last month.

Let H be the total number of hours that Tara works this month.

Then we can write:

H > 16.5 + 19 + 23 + 15.75

Simplifying the right-hand side, we get:

H > 74.25

Therefore, the inequality that represents the number of hours, h, Tara plans to work this month is: H > 74.25

Read more about linear relation and inequality at

https://brainly.com/question/30318449

https://brainly.com/question/30390162

#SPJ1

Therefore , the solution of the given problem of percentage comes out to be D) 28% is the right response.

The shorthand "a%" is used in statistics to represent a number or metric that may be expressed as a percentage of 100. Additionally strange spelling include "pct," "pct," as "pc." The approach that is most frequently employed for this is the percentage symbol ("%"). Any hints or set proportions of any part for the total are also unknown. Since numbers commonly add up to 100, they are effectively integers.

Here,

According to the facts provided, 30% of the male population and 60% of the people in Math Town are male.

This suggests that between 30% and 60% of people have brown eyes.

Let's figure out what proportion of the entire population is equal to 30% of 60%:

=> 30% of 60% = (30/100) * (60/100)

=>  0.3 * 0.6

=>  0.18 or 18%

Therefore, brown eyes are present in Math Town's overall population of 18%.

Since the only other gender listed is females and we are aware that 18% of the population as a whole has brown eyes, we can infer that 18% of women also have brown eyes.

Therefore, D) 28% is the right response.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Verify the identity for sin 4x+ sin 12x / cos 4x + cos 12x -= tan (8x) will give a value of sin (8x) / cos (8x)

Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It has a wide range of applications in various fields, including engineering, physics, navigation, and astronomy.

There are six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are defined based on the ratios of the sides of a right triangle.

Learn more about trigonometry on;

https://brainly.com/question/24349828

#SPJ1

The capacitor voltage is 7.95 V and the inductor current is 0.015 A or 15 mA.

To calculate the capacitor voltage and inductor current in the given circuit, we first need to calculate the total resistance and the total reactance.

Total resistance:

Rt = R1 + R2 + R3 + R4 + R5

Rt = 270 + 122 + 15 + 470 + 100

Rt = 977 Ω

Total reactance:

Xt = XL - XC

XL = ωL = 2πfL = 2 × π × 60 Hz × 800 µH = 301.59 Ω (inductive reactance)

XC = 1 / (2πfC) = 1 / (2 × π × 60 Hz × 500 × 10^-6 F) = 530.3 Ω (capacitive reactance)

Xt = 301.59 - 530.3

Xt = -228.71 Ω

The negative value of reactance indicates that the circuit is capacitive.

Total impedance:

Zt = √(Rt² + Xt²) = √(977² + (-228.71)²) = 1000 Ω

Now we can calculate the current through the circuit using Ohm's law:

I = V / Zt = 15 V / 1000 Ω = 0.015 A

The voltage drop across the resistor R2 is:

VR2 = IR2 = 0.015 A × 122 Ω = 1.83 V

The voltage drop across the capacitor is:

VC = IXC = 0.015 A × 530.3 Ω = 7.95 V

The voltage drop across the inductor is:

VL = IXL = 0.015 A × 301.59 Ω = 4.52 V

Therefore, the capacitor voltage is 7.95 V and the inductor current is 0.015 A or 15 mA.

learn more about capacitor voltage: https://brainly.com/question/14883923

#SPJ1

Answer:

x equals 8 due to 8^2 being 8x8=64

Step-by-step explanation:

Liam needs 0.25 yards of wire for the top of each sculpture.

Let's assume that Liam needs x yards of wire for the top of each sculpture.

Since Liam is making 8 sculptures, he will need 8x yards of wire in total for the tops of all the sculptures.

We also know that Liam needs one yard of wire for the base of each sculpture.

So he will need 8 yards of wire in total for the bases of all the sculptures.

Therefore, the total amount of wire Liam needs is:

8x yards for the tops + 8 yards for the bases = 10 yards in total

Simplifying this equation, we get:

8x + 8 = 10

Subtracting 8 from both sides, we get:

8x = 2

Dividing both sides by 8, we get:

x = 0.25

Therefore, Liam needs 0.25 yards of wire for the top of each sculpture.

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

(a) The total surface area of the triangular prism is 560 in².

(b) The surface area of the cuboid is 944 ft².

(c) The surface area of the cylinder is  678.58 in².

Cuboid;

The surface area of the cuboid is calculated as;

S.A = 2(12 x 16  +  12 x 10  + 16 x 10)

S.A = 944 ft²

Cylinder:

The surface area of the cylinder is calculated as follows;

S.A = 2π x 6 (6 + 12)

S.A = 678.58 in²

The surface area of a triangular prism can be calculated by summing the areas of its individual faces.

A triangular prism has three rectangular faces and two triangular faces.

The formula for the surface area of a triangular prism is:

Surface Area = Area of triangular faces + Area of rectangular faces

To calculate the area of a triangular face, we can use the formula for the area of a triangle:

Area of a triangle = (base × height) / 2

Given that S₁ = 8 in, S₂ = 12 in, S₃ = 8 in, and the length between the two triangular faces is 18 in, we can proceed with the calculations.

The area of the triangular face with dimensions S₁ = 8 in and S₂ = 12 in is:

Area of triangular face 1 = (8 in × 12 in) / 2 = 48 in²

The area of the triangular face with dimensions S₂ = 12 in and S₃ = 8 in is:

Area of triangular face 2 = (12 in × 8 in) / 2 = 48 in²

The area of the triangular face with dimensions S₃ = 8 in and S₁ = 8 in is:

Area of triangular face 3 = (8 in × 8 in) / 2 = 32 in²

Now, let's calculate the area of the rectangular faces.

Area of rectangular face 1 = 18 in × 12 in = 216 in²

Area of rectangular face 2 = 18 in × 12 in = 216 in²

Finally, we can sum up all the areas to get the total surface area of the triangular prism:

Surface Area = Area of triangular faces + Area of rectangular faces

Surface Area = 48 in² + 48 in² + 32 in² + 216 in² + 216 in² = 560 in²

Learn more about surface area here: https://brainly.com/question/76387

#SPJ1

Answer:

D. b=1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.

The area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...

  A = LW

  750 = y(y -5)

This equation can be rearranged into several different forms:

  y² -5y = 750 . . . . . . . multiply it out

  750 -y(y -5) = 0 . . . . . subtract the right side expression

  (y +25)(y -30) = 0 . . . . factor it

to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer

Answer: 76 pages

Step-by-step explanation:

700 photo spaces = 100%

-The total

168 photo spaces = 24%

-The number of empty spaces in the album.

- Find 24% of 700:

70(10%) x 2 = 140

7(1%) x 4 = 28

140 + 28 = 168

532 photo spaces = 76%

- The number of photos in the album

700 - 168 = 532

Finding the number of pages.

-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.

532 ÷ 7 = 76.

The probability that a person has the virus given that they have tested positive is 3.24%.

The probability that a person does not have the virus given that they test negative is 99.93%.

Here we have following probabilties:

P(A)=1/300, P(A')=1-(1/300)=299/300

P(B|A)=0.80, P(B|A')= 0.08

From the law of total probability is

P(B)=P(B|A)P(A)+P(B|A')P(A')

[tex]=0.80\cdot \frac{1}{300}+0.08\cdot \frac{299}{300}\\\\=0.0824[/tex]

By the Baye's theorem we have

P(A|B) = [tex]\frac{P(B|A)P(A)}{P(B)}\\\\=\frac{0.80\cdot \frac{1}{300}}{0.0824}\\\\=0.0324[/tex]

So the probability that a person has the virus given that they have tested positive is 3.24%.

(b)

From the law of total probability is

P(B')=P(B'|A)P(A)+P(B'|A')P(A')

[tex]=0.20\cdot \frac{1}{300}+0.92\cdot \frac{299}{300}\\\\=0.9176[/tex]

By the Baye's theorem we have

P(A'|B')=[tex]\frac{P(B'|A')P(A')}{P(B')}\\\\=\frac{0.92\cdot \frac{299}{300}}{0.9176}\\\\=0.9993[/tex]

So the probability that a person does not have the virus given that they test negative is 99.93%.

To know more about probability, visit:

https://brainly.com/question/24756209

#SPJ1

Step-by-step explanation:

6^2 / 6^1   x    6^12 / 6^8   =

6^(2-1)      x    6^(12-8)   =

6^1          x    6^4   =

6^(1+4)  =   6^5     or  = 7776

Answer:

[tex]25.5h = 153[/tex]

[tex]h = 6[/tex]

The height is 6 feet, so A is correct.

Answer:

90 cubic feet

Step-by-step explanation:

3 feet × 5 feet × 6 feet = 90 cubic feet

Answer:

100

Step-by-step explanation:

12x + 2y ← substitute x = 7 and y = 8 into the expression

= 12(7) + 2(8)

= 84 + 16

= 100

Answer:

3125

32

Step-by-step explanation:

[tex]formula = a {r}^{n - 1?} [/tex]

r=5

2

a=1

n=6

1×5 (6-1)

2

5 (5)

2

=3125

32

Since the discriminant is negative, the equation has two complex conjugate roots is -19.

To find complex conjugate roots of a polynomial, you can follow these steps:

Identify the complex roots of the polynomial: Use the quadratic formula or any other method to find the roots of the polynomial. If the roots are complex, they will be of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Check for conjugate pairs: If a complex root is of the form a + bi, then its complex conjugate will be a - bi. Check if the polynomial has any other root of the form a - bi. If so, then the two roots are complex conjugates.

For example, suppose you have a polynomial with the equation:

[tex]x^3 - 4x^2 + 7x - 10 = 0[/tex]

Using a calculator or other methods, you can find that one of the roots of this polynomial is approximately 1.72 + 0.98i. To check if this is part of a complex conjugate pair, you can check if the polynomial has another root of the form a - bi.

One way to do this is to use polynomial long division to divide the original polynomial by the quadratic factor (x - (1.72 + 0.98i)) (x - (1.72 - 0.98i)).

To determine the number and type of roots of the equation x^2 - 3x + 7 = 0, we need to use the discriminant, which is given by the formula b^2 - 4ac.

In this case, a = 1, b = -3, and c = 7. Substituting these values into the formula, we get:

[tex]b^2 - 4ac = (-3)^2 - 4(1)(7) = 9 - 28 = -19[/tex]

Since the discriminant is negative, the equation has two complex conjugate roots.

To know more about quadratic visit:

https://brainly.com/question/22364785

#SPJ1

Answer:

1 b

2.c

ythis the best choice

The circumference and the areas and the volumes are calculated below

For a cylinder with a radius of 10 and a height of 2:

For a cylinder with a radius of 2 and a height of 10:

Read more about circumference at

https://brainly.com/question/12823137

#SPJ1

The measure of the longer diagonal is approximately 26.01 units, rounded to two decimal places.

A parallelogram is a four-sided flat geometric shape, with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other, and the opposite angles are equal in measure. A parallelogram can also be thought of as a slanted rectangle, where the sides are not perpendicular to each other.

Let's denote the longer diagonal of the parallelogram as "d". We know that the diagonals of a parallelogram bisect each other, so the shorter diagonal, which is 12 units, divides the parallelogram into two congruent triangles. Let's use the Pythagorean theorem to find the height of one of these triangles:

a² + b² = c²

where a = half of the shorter diagonal = 12/2 = 6 units, b = height of the triangle, and c = half of the longer diagonal.

Substituting the given values, we have:

6² + b² = c²

36 + b² = c²

b² = c² - 36

Now, let's use the fact that the sides of a parallelogram are parallel and opposite in direction to write another equation:

c² = (19 + 10)²

c² = 729

Substituting this value into the previous equation, we have:

b² = 729 - 36

b² = 693

Taking the square root of both sides, we get:

b ≈ 26.33

Since the height of the parallelogram is perpendicular to the longer diagonal, we can see that the longer diagonal is the hypotenuse of a right triangle with legs of 10/2 = 5 units and 26.33 units. Using the Pythagorean theorem again, we can solve for the longer diagonal:

a² + b² = c²

where a = 5, b = 26.33, and c = the longer diagonal.

Substituting the given values, we have:

5² + 26.33² = c²

676.56 = c²

c ≈ 26.01

Therefore, the measure of the longer diagonal is approximately 26.01 units, rounded to two decimal places.

To know more about parallelogram visit:

https://brainly.com/question/970600

#SPJ1

Answer: f'(x) = 10

Step-by-step explanation: To find f'(x), we need to take the derivative of g(x) with respect to x.

The derivative of 3x is 3, and the derivative of 7x is 7. Since the derivative of a constant is 0, the derivative of -1 is 0. Therefore, we can simplify g(x) to:

g(x) = 3x + 7x - 1 = 10x - 1

The derivative of 10x is 10, and the derivative of a constant is 0. Therefore, f'(x) = 10.

A timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

What is the unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement that is equivalent in value. The need for unit conversion arises because different units are used to measure the same physical quantity in different countries or regions, or in different fields of study.

Making a model of the geologic time scale with a scale of 1 centimeter equals 1 million years means that each centimeter on the timeline represents 1 million years of geologic time.

To create the model, we can start by determining the total length of the timeline we want to create.

Let's say we want to include the entire Phanerozoic Eon, which spans approximately 541 million years.
To represent this on our timeline, we would need a total length of 541 centimeters.

However, we need to keep in mind that 100 cm is equal to 1 meter, which is a little longer than 3 feet.

Therefore, a timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

To  learn more about the unit conversion visit:

https://brainly.com/question/13016491

#SPJ1