George went to the store to buy notebooks.

- He had $36 to spend.

- He purchased 4 notebooks.

- After buying the notebooks, George had less than $12 left.

-What is the solution set for x, the cost of each notebook?

The measure of the side length x is 15.04.

The figure in the image is a right triangle.

Angle θ = 43 degrees

Adjacent to angle θ = 11

Hypotenuse = x

To determine the measure of the side length x, we use the trigonometric ratio.

Note that: cosine = adjacent / hypotenuse

Plug in the values:

cos( 43° ) = 11 / x

Solve for x

x = 11 / cos( 43° )

x = 15.04

Therefore, the value of x is 15.04 units.

Learn more about trigonometric ratio here: brainly.com/question/28016662

#SPJ1

Answer:

The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -1, and c = -1. So:

x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)

x = (1 ± sqrt(5)) / 2

Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.

Answer: 6

Step-by-step explanation:

Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².

Answer:

Step-by-step explanation:

B= area of the triangle 1+area of triangle 2

(1/2*3*1)+(1/2*2*1)

=1.5+1

=2.5

Roger and Trish can complete 11/30 of the math homework in 1 hour if they work together.

What is an expression?

An expression is a sentence that has at least two numbers/variables and at least one math operation.

According to the given information:

Let the total amount of work in the math homework is 1.

In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work.

If they work together for 1 hour, then the total amount of homework they can finish is the sum of the parts each of them can finish in one hour:

1/6 + 1/5 = 5/30 + 6/30 = 11/30

So together they can finish 11/30 of the homework in one hour.

To know more about expressions visit: https://brainly.com/question/13947055

#SPJ1

The volume of the prism is V = 4000 cm³

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the prism be h = 10 cm

Let the width of the prism be w = 20 cm

Let the length of the prism be l = 20 cm

So , the base area of prism = l x w

Base area = 400 cm²

Now , the volume of the prism is V = 400 x 10

V = 4000 cm³

Hence , the volume of prism is V = 4000 cm³

To learn more about volume of prism click :

https://brainly.com/question/11336446

#SPJ1

The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

Learn more about probability on

https://brainly.com/question/24756209

#SPJ1

Answer:

47 months

Step-by-step explanation:

find 6.1% of 15k then divide that by 300

6.1% = 915

15,000 - 915 = 14085

14085 divided by 300 is 46.95 then rounded is 47

for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

To know more about equation , visit:

https://brainly.com/question/29657983

#SPJ1

for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

To know more about equation , visit:

brainly.com/question/29657983

#SPJ1

In 1973, the batting average of .350 of Rod Carew is more impressive as it has a higher z-score of 2.81

To establish which batting average was more spectacular, we must compare it to the mean and standard deviation of 1970s hitting averages. The case of Jackie Robinson,

z = (x - μ) / σ

z = (.342 - .261) / .0317

z = 2.56

For Rod Carew,

z = (x - μ) / σ

z = (.350 - .261) / .0317

z = 2.81

A higher z-score indicates a more impressive performance relative to the mean. As a result, Rod Carew's .350 batting average was more spectacular, as it had a higher z-score of 2.81 than Jackie Robinson's z-score of 2.56.

To know more about standard deviation, visit,

https://brainly.com/question/475676

#SPJ1

The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.

Option D is correct.

if angle A is obtuse and if a > b then the triangle has one solution

We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.

Finding remaining sides c and ∠B and ∠C

Using the Law of sines to find ∠B

a/sin A = b/sin B

7/sin 119° = 4/sin B

7 * sin B = 4 * sin 119

7*sin B = 4(0.874)

sin B = 3.496/7

B = sin^-1(0.4994)

B = 29.96 = 30°

We know that sum of angles of triangle = 180°

So, 180° = 119° + 30° +∠C

180° = 149° + ∠C

=> ∠C = 180° - 149°

∠C = 31°

Now finding c

b/sin B = c /sin C

4/Sin 30 = c/sin 31

4* sin 31 = c*sin 30

4*0.515 = c* 0.5

=> c =  4*0.515/0.5

c = 4.12 ≈ 4

So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.

Read more about triangles here:

https://brainly.com/question/17335144

#SPJ1

Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree

A = 119°, a=7, b=4

Question 7 options:

one solution; c ≈ 7; B = 30°; C = 119°

no solution

one solution; c ≈ 4; B = 31°; C = 30°

one solution; c ≈ 4; B = 30°; C = 31°

The correct angle of elevation for the lighthouse's top is roughly 1.91°.

Consider the diagram drawn below, P is the position of the person in the lift-raft, B is the base of the lighthouse and the T is top of the lighthouse.

The diagram shows that the angle produced between the person in the life raft's line of sight to the top of the lighthouse and the horizontal is equal to the angle formed by the top of the lighthouse's height. Call this angle "[tex]\alpha[/tex]".

a) The distance "d" between the life raft and the lighthouse can be calculated using trigonometry.

[tex]tan\alpha = \frac{opposite}{adjacent} \\tan\alpha = \frac{20}{d}[/tex]

putting the value of [tex]\alpha[/tex] = 3 degrees put into the above equation.

[tex]tan3 = \frac{20}{d}[/tex]

[tex]d = \frac{20}{tan3}[/tex]

d = 354.14 (rounded to 2 decimal points

The life raft is therefore roughly 354.14 meters away from the lighthouse.

b)

Let's now calculate the proper angle of elevation for the situation when the life raft is 600 meters from the lighthouse.

[tex]tan\alpha = \frac{opposite}{adjacent}\\ tan\alpha = \frac{20}{600}[/tex]

solving for [tex]\alpha[/tex] we get,

[tex]\alpha = tan^{-1} (\frac{20}{100})\\\alpha = 1.91 degree\\[/tex]

Since the life raft is 600 meters from the lighthouse, the correct angle of elevation for the lighthouse's top is roughly 1.91°.

Learn more about the angle of elevation here:

https://brainly.com/question/16716174

#SPJ1

The complete question in the form of the image below:

The transformation in the function y = -1/3f(x + 4) - 5 is described below

From the question, we have the following parameters that can be used in our computation:

y = f(x)

The transformed function g(x) is given as

y = -1/3f(x + 4) - 5

The sequence of transformation on the transformed function is as follows

Read more about transformation at

https://brainly.com/question/4289712

#SPJ1

Answer:

P=4/15

Step-by-step explanation:

P(dancer first) = 8/30=4/15

The graph of the function g(x) has an equation of g(x) = 6√(x - 3)

From the question, we have the following parameters that can be used in our computation:

f(x) = 3√x

The transformed function g(x) is given as

g(x) = 2f (x − 3)

In f(x) = 3√x , we have

f(x - 3) = 3√(x - 3)

Multiply both sides by 2

So, we have

2f(x - 3) = 2 * 3√(x - 3)

Evaluate the products

2f(x - 3) = 6√(x - 3)

Recall that

g(x) = 2f (x − 3)

So, we have

g(x) = 6√(x - 3)

This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)

Read more about transformation at

https://brainly.com/question/4289712

#SPJ1

Answer:

20 : 4 : 15

Step-by-step explanation:

1 : 0.2 : 0.75

1 : 2/10 : 75/100

1 : 20/100 : 75/100

(×100)

100 : 20 : 75

(÷5)

20 : 4 : 15

The calculated area of the triangle B is 1.8 square units

From the question, we have the following parameters that can be used in our computation:

Triangle A and B

Where

Area of A = 1/2 base * height

Sp, we have

Area of A = 1/2 * 2 * 5

Next, we have

Area of B = Area of A * Scale factor^2

Using the above as a guide, we have the following:

Area of B = 1/2 * 2 * 5 * (3/5)^2

Evaluate

Area of B = 1.8

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Therefore, 4,000 centimeters are equivalent to 40 meters. Hence, the answer is A) 4,000 cm.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

Since there are 100 centimeters in one meter, we can convert meters to centimeters by multiplying the length in meters by 100.

So, to convert 40 meters to centimeters, we can multiply 40 by 100:

40 meters = 40 x 100

= 4,000 centimeters

To know more about equation,

https://brainly.com/question/9312365

#SPJ1

Answer:

A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.

B. Yes, it is possible. By the Triangle Inequality Theorem:

15 + 15 > 20, and 20 + 15 > 15

Jim's rate of savings (slope): 3

Cassie's rate of savings (slope): 3

Jim's y intercept: 3

Cassie's y intercept: 12

Jim's Savings Equation: y = 3x + 3

Cassie's Savings Equation: y = 3x + 12

Number of weeks it will take to Cassie to save $27: 5

Number of weeks it will take to Jim to save $27: 8

Yes, Jim and Cassie's rates parallel.

Cassie will be able to buy the hat first.

We know that the slope intercept form of a straight line is,

y = mx + c, where m is the slope of the line and c is the y intercept.

For the straight line for Cassie:

The line passing through the points (0, 12) and (1, 15).

So the slope = (15 - 12)/(1 - 0) = 3

The y intercept is = 12.

Equation of the straight line is: y = 3x + 12 ....... (i), where y represents earning in dollars and x represents the time in weeks.

For the straight line for Jim:

The line passing through the points (0, 3) and (1, 6).

So the slope = (6 - 3)/(1 - 0) = 3

The y intercept is = 3

Equation of the straight line is: y = 3x + 3 .......... (ii), where y represents earning in dollars and x represents the time in weeks.

Since the slope of both are equal so the rates of both are parallel.

Substituting the value y = 27 in equation (i) and (ii) we get,

equation (i): 3x + 12 =27

3x = 27 - 12

3x = 15

x = 15/3

x = 5

So Cassie needs 5 weeks to save $27.

Equation (ii): 3x + 3 = 27

3x = 27 - 3

3x = 24

x = 24/3

x = 8

So Jim needs 8 weeks to save $27.

Hence Cassie will be able to buy the hat first.

To know more about straight line here

https://brainly.com/question/25969846

#SPJ1

The question is incomplete. The complete question will be -

Answer:

  (a)  7(x +3.5x) = 56

Step-by-step explanation:

You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.

The morning run is given as x.

The evening run is 3.5 times as long, so is 3.5x

The total mileage each day is (x +3.5x).

In 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:

  7(x +3.5x) = 56

Answer:5.25cm

Step-by-step explanation:

1)look back at your question

2)look after the 6th word

The initial temperature of the soda is 18 degrees Celsius.

Its temperature after 20 minutes is 2.73 degrees Celsius.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

When time, t = 0, the initial value can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]

C(0) = 18(1)

C(0) = 18 degrees Celsius.

When time, t = 0 = 20, the temperature can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]

C(20) = 2.73 degrees Celsius.

Read more on exponential equation here: brainly.com/question/28939171

#SPJ1

Complete Question:

A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.

[tex]C(t)=18(0.91)^{t}[/tex]

Find the initial temperature of the soda and its temperature after 20 minutes?

The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.

Probability refers to the chance or likelihood of an event occurring given many possible events that could have occurred.

Probability is expressed as a quotient of the expected event or success and the total possible events, outcomes, or successes.

The number of Sophomores in Mathematics Majors = 16

The number of Sophomores in Non-Mathematics Majors = 17

The total number of Sophomores in Mrs. Burke's Mathematics Class = 33

The probability of selecting a non-Mathematical major, given that Mrs. Burke chooses randomly from only Sophomores = 51.5% (17 ÷ 33 x 100)

Mrs. Burke's Mathematics Class

Academic Year   Mathematics Majors   Non-Mathematics Majors  Total

Freshmen                          19                             18                                 37

Sophomores                     16                             17                                 33

Juniors                               11                             15                                 26

Seniors                              12                             13                                25

Total                                 58                            63                                121

Thus, the likelihood of choosing a non-Mathematical major from the Sophomores is 51.5%.

Learn more about probabilities at https://brainly.com/question/13604758.

#SPJ1

Mrs. Burke's Mathematics Class

Academic Year   Mathematics Majors   Non-Mathematics Majors

Freshmen                          19                             18

Sophomores                     16                             17

Juniors                               11                             15

Seniors                              12                             13

Answer:

3. radius = 9.4

4. radius = 22.6

5. diameter = 13.3

Step-by-step explanation:

The diameter of a circle = 2 * radius

For problem 3 and 4,  you need to multiply the given radius by 2 to get the diameter.

For problem 5, you need to divide the diameter by 2 to get the radius.

The perimeter of the rug is 36ft

Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.

Perimeter of a rectangle is expressed as ;

P = 2(l+w)

The area of the rug is 81ft²

area = l× w

length = 9ft

width of the rug = 81/9 = 9ft

Therefore the perimeter of the rug will be

P = 2(l+w)

P= 2( 9+ 9)

P = 2 × 18

P = 36 ft

therefore the perimeter of the rectangular rug is 36ft

learn more about perimeter from

https://brainly.com/question/19819849

#SPJ1

Answer:

13.3333333333 or 13.3

Step-by-step explanation:

yeah :3