Thus, the solution set for the cost of each notebook that can be bought by George is: (0 ≤ x ≤ 6).
Explain about the one variable linear equation:A linear equation is a one-variable equation of the a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.
Given that:
Total amount George has = $36.Number of books = 4Left amount = $12Let the cost of each notebook 'x'.So, the linear equation follows
Amount for 4 notebooks + Left amount = total amount
4*x + 12 ≤ 36
4x ≤ 36 - 12
4x ≤ 24
x ≤ 24/4
x ≤ 6
So, (0 ≤ x ≤ 6)
Thus, the solution set for the cost of each notebook that can be bought by George is: (0 ≤ x ≤ 6).
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What is the quotient of 100 ÷ 7.50
Answer:
13.3333333333 or 13.3
Step-by-step explanation:
yeah :3
Part A: Is it possible to make a triangle that is both equilateral triangle and a right triangle? Explain
Part B: Is it possible to draw a triangle with side lengths of 15, 15 and 20? Explain.
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
In 1949, Jackie Robinson hit .342 for the Brooklyn Dodgers; in 1973, Rod Carew hit .350 for the Minnesota Twins. In the 1970s the mean batting average was
.261 and the standard deviation was .0317. Determine which
batting average was more impressive.
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.
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Express 1:0.2:0.75 in their simple form
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
(A) 0
(B) 1
2
(D) 3
Si un garçon peut courir une distance de 10 mètres pendant qu'une voiture en parcourt
0, combien de mètres le garçon pourra-t-il courir pendant que la voiture parcourt 66 mètres?
(A) 12
(B) 90
(C) 22
(D) 25
10 x = 30
Une équipe d'ouvriers fabriquaient 1,000 uniformes par semaine. La production ayar
té augmentée de 20%, chaque ouvrier se vit obligé de confectionner 50 uniformes de plus
Combien y avait-il d'ouvriers dans cette équipe?
(A) 4
(B) 15
(C) 20
110
(D) 24
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.
C(t)=18(0.91)t
The initial temperature of the soda is 18 degrees Celsius.
Its temperature after 20 minutes is 2.73 degrees Celsius.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.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.
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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?
Which statement concerning the equation x² - 1 = x is true?
1. Its discriminant is 0, so it has no solution.
2. Its discriminant is 5, so it has two real solutions.
3. Its discriminant is 0, so it has one real solution.
4. Its discriminant is -3, so it has two complex solutions.
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.
WILL GIVE BRAINLIEST!!! NEED ASAP IM GETTING TIMED!!!!
Roger can finish his math homework in 6 hours. Trish can finish the same homework in 5 hours. What part of the homework will Roger and Trish finish if they work together for 1 hours?
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.
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whats the probility that she selects a non-mathamatical major, given that she choosees randomly from only sophmores From mrs. Burke's math class
The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.
What is the probability?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%.
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Question Completion:Mrs. Burke's Mathematics Class
Academic Year Mathematics Majors Non-Mathematics Majors
Freshmen 19 18
Sophomores 16 17
Juniors 11 15
Seniors 12 13
Use the estimated angle to find the distance of the life-raft from the lighthouse.
The correct angle of elevation for the lighthouse's top is roughly 1.91°.
How to find the distance of the lift-raft from the lighthouse?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°.
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The complete question in the form of the image below:
Answer questions 3 – 5 about the circle.
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.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 169 cm and a standard deviation of 2.2 cm. For shipment, 10 steel rods are bundled together.
Answer the following rounding to three decimals where appropriate.
Find the probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm.
P(M > 168.58) = ???
The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486
How to calculate the probabilityFirst, 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.
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Describe the following function
The transformation in the function y = -1/3f(x + 4) - 5 is described below
Describing the transformation in the functionFrom 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
Horizontal shift to the left by 4 unitsVertical stretch by a factor of 1/3Reflection across the x-axisLastly, vertical shift down by 5 unitsRead more about transformation at
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The acts in a talent competition consist of 10 instrumentalists, 12 singers, and 8 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first?
Answer:
P=4/15
Step-by-step explanation:
P(dancer first) = 8/30=4/15
7 A right rectangular prism is sliced by a plane perpendicular to its bases. A right cylinder is sliced the same way. Which statement about the plane sections that result is correct?
A Both plane sections have two pairs of parallel sides.
B The plane section of the prism has only straight sides, but the plane section of the cylinder does not.
C The plane section of the prism has four right angles, but the plane section of the cylinder does not.
D Both plane sections are the same shape as the bases of the three-dimensional figures from which they resulted.
100 POINTS!!!
Question:
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
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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
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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle.
questions 1)
m
question 2)
m
question 3)
m
The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.
Option D is correct.
How to solveif 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.
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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°
What is the area of one of the bases,b, of the prism b=_in2
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
The formula for the volume of a prism is V = area of base x height. What is the volume and surface area of each of these prisms? Show your thinking
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
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Anna wants to borrow $15,000 to buy a used sail boat. After looking at her financial situation, she realizes that she can only afford monthly payments of $300. The bank is offering financing at 6.1%. For how long will Anna need to finance the boat to stay within her monthly payment?
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
The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?
The graph of the function g(x) has an equation of g(x) = 6√(x - 3)
Identifying the graph of the function g(x)?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)
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a rectangle has a length of 5.25cm and area of 44.625cm2. what does the length of the rectangle have to be?
Answer:5.25cm
Step-by-step explanation:
1)look back at your question
2)look after the 6th word
solve for x in the following diagram
The measure of the side length x is 15.04.
What is the measure of the side length x?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.
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Directions - Answer the questions based on the following scenario and graph.
Jim and Cassie are both saving money each week in order to buy an awesome Bulls snapback hat (and leave the price stickers on it, of course). The hat costs $27.
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.
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The question is incomplete. The complete question will be -
Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2
PLease help
Jack measured 40 meters in his back yard. How many centimeters are equivalent to 40 meters? A 4,000 cm B 400 cm 4 cm D 0.4 cm
Therefore, 4,000 centimeters are equivalent to 40 meters. Hence, the answer is A) 4,000 cm.
What is equation?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
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Given the following similar triangles, what is the area of triangle B?
A 1
B 1.8
C 3.2
D 5
The calculated area of the triangle B is 1.8 square units
What is the area of triangle BFrom 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
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the perimeter of a triangle is 53 inches. the length of the one side is 15 inches the other two sides are congruent find the lengths
The area of a rectangular shaped rug is 81 square feet. If the rug is 9 ft long, what is ire perimeter?
The perimeter of the rug is 36ft
What is perimeter?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
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Which equation can be used to solve for x
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.
Daily runThe 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).
Weekly totalIn 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:
7(x +3.5x) = 56
