Choose the correct description of the graph of the compound inequality 3x + 1 > 10 and 4x 20.
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
B. A number line with an open circle on 3, shading to the left and a closed circle on 5, shading to the right
C. A number line with an closed circle on 3, shading to the left, and a open circle on 5, and shading to the right
D. A number line with a closed circle on 3, an open circle on 5, with shading in between.
we have in this problem
[tex] 3x+1 > 10 [/tex] ------> inequality [tex] 1 [/tex]
[tex] 4x \leq 20 [/tex] ------> inequality [tex] 2 [/tex]
Solve the inequality [tex] 1 [/tex]
[tex] 3x+1 > 10\\ 3x > 10-1\\ 3x > 9\\ x > 3 [/tex]
the solution is the interval------> (3,∞)
Solve the inequality [tex] 2 [/tex]
[tex] 4x \leq 20\\\\ x \leq \frac{20}{4} \\\\ x \leq 5 [/tex]
the solution is the interval------> (-∞,5]
Find the solution for the system
(3,∞) ∩ (-∞,5]--------> (3,5]
therefore
the answer is the option
A. A number line with an open circle on 3, a closed circle on 5, and shading in between.
Write two equivalent fractions for each. 1/2 and 4/5
A cylindrical rain barrel has a radius of 2 feet and holds a total of 30 cubic feet of water. How tall is the rain barrel? Use 3.14 for pi. Round your answer to the nearest hundredth.
Instructions:Select the correct answer from each drop-down menu.
Angle θ lies in the second quadrant, and sin θ = 35.
cos θ = -4/5 -3/5 3/5 4/5
tan θ = -4/3 -3/4 3/4 4/3
Use complete sentences to describe how a postulate becomes a theorem.
A postulate becomes a theorem through logical deduction and proof, starting with the postulates and leading to an indisputably true conclusion. Each step in a proof must follow logically from the ones before it, and the end result is a statement that holds true without premises, recognized universally in mathematics.
A postulate becomes a theorem through a process of logical deduction and proof. In mathematics, a postulate is an assumed statement used as a starting point for further reasoning and arguments. When we begin with our starting definitions and postulates, we can logically deduce new conclusions or theorems. If we can provide a proof of a statement A and show that it is definitely true based on the postulates and previously established theorems, then A becomes a theorem. Each line in a proof must follow from the rules cited, which are based on earlier lines of the proof or established logic. Once we derive the final conclusion, if every line of the proof is legitimate, then the whole proof is legitimate, and the sentence can be considered a theorem.
Moreover, a theorem is a statement that is true without any premises, meaning it derives from logical deductions of the initial assumptions. A theorem is proven via indisputable, step-by-step logical deductions. To illustrate, if an experiment or an established fact contradicts existing theories, it may lead to the development of a new theorem, as was the case with the postulates of Special Relativity. Ultimately, something is recognized as a theorem if it is a tautology—true in all possible models—thus making it a universally accepted truth in mathematics.
James is participating in a 5-mile walk to raise money for a charity. he has received $200 in fixed pledges and raises $20 extra for every mile he walks. use a point-slope equation to find the amount he will raise ifhe completes the walk.
Answer:
The amount James will collect if he completes the walk is $ 300
Step-by-step explanation:
The line can be understood as an infinite set of points aligned in a single direction. A line can be expressed by an equation that follows the model y = m * x + b, where "x" e "y" are the variables in a plane. In this expression m is called the slope of the line and is related to the inclination of the line, and b is the independent term and is the value of the point at which the line cuts to the vertical axis (y axis) in the plane.
In general, the slope represents the variation of y with respect to the variation of x. That is, if the value of "x" varies, the value of "y" will also vary. On the other hand, the value of "b", being the interserction with the y-axis, means that the value of "x" must be zero. Then it represents the initial condition of the problem. Then, in this case, James has initially received $ 200 in fixed commitments, 200 being the value of "b". James raises an additional $ 20 for every mile he walks, so the value of the "m" slope is 20 and "x" represents every mile James walks.
Finally, the equation of the line represented is:
y=20*x+200
One type of linear equation is the point-slope form, which provides the slope of a line and the coordinates of a point on it. The point-slope form of a linear equation is written as
y-y1 = m (x-x1)
where m is the slope and (x1, y1) are the coordinates of the point.
In this particular case, it was mentioned that the value of the slope is 20. The values of (x1, y1) must be known. In this case, James initially received $ 200 in fixed commitments, meaning that the value of x1 = 0 and the value of y1 = 200. Replacing these values in the desired equation you get:
y-200=20*(x-0)
y-200=20*x
To find the amount that will be collected if you complete the walk, you must replace the value of x (which represents each mile walked) by 5, the distance to travel on the walk:
y-200=20*5
y-200=100
y=100+200
y=300
The amount James will collect if he completes the walk is $ 300
Elements are _____.
a chemical substance composed of atoms of two or more different types of atoms
substances that are made up of only one type of atom
subatomic particles with a positive charge
only found on earth
Answer: substances that are made up of only one type of atom
Step-by-step explanation:
Element is a pure substance which is composed of atoms of similar elements. Example: Carbon (C)
Compound is a pure substance which is made from atoms of different elements combined together in a fixed ratio by mass. Example: water [tex]H_2O[/tex]
The subatomic particles with a positive charge are called as protons and are located in the nucleus of the atom.
Thus elements are substances that are made up of only one type of atom.
Write 3.71 as a percentage.
Use the given endpoint R and midpoint M of line RS to find the coordinates of the other endpoins.
R(6,0), M(0,2) ...?
20+ POINTS!!!!
Which transformations are isometries? Select all that apply.
A. Reflection
B. Translation
C. Dilation
D. Rotation
Isometries are transformations that preserve lengths and angles. Reflection, Translation, and Rotation are isometries, while Dilation is not because it changes the size of the figure.
Explanation:The student's question asks to identify which transformations are isometries. An isometry is a transformation in geometry that preserves lengths and angles, meaning that the figure's shape and size remain unchanged. The four options given are Reflection, Translation, Dilation, and Rotation.
A. Reflection is an isometry because it produces a mirror image of the original figure, preserving distances and angles.B. Translation is an isometry, as it slides a figure to a new location without altering its shape or size.C. Dilation is not an isometry because, while angles remain unchanged, it alters the size of the figure by scaling it up or down.D. Rotation is an isometry because it turns a figure around a point, keeping its shape and size.Therefore, the transformations that are isometries are Reflection, Translation, and Rotation.
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Divide. Express your answer in lowest terms. You MUST show your work to receive credit for this problem.
-15/16 divided by (-3/4)
Why is it a good idea to check to see if your answer is reasonable?
Sometimes we can miss steps or incorrectly do a step. When we solve the equation we might think we have the right answer. If you double check your answer and input your answer into the equation, you can see if it is truly correct. Doing this makes sure that you won't get the question wrong
what is the circumference of a child's swimming pool that has a radius of 3 feet
The circumference of a child's swimming pool with a radius of 3 feet is approximately 18.84 feet. We derive this using the formula for the circumference of a circle, namely C = 2πr.
Explanation:In the realm of Mathematics, the circumference of a circle can be calculated using the formula C = 2πr, where C represents the circumference, π is a constant approximately equal to 3.14, and r is the radius of the circle. In the case of a child's swimming pool with a radius of 3 feet, we substitute the radius (r) into the formula to get: C = 2*3.14*3= 18.84 feet. Therefore, the circumference of the child's swimming pool is approximately 18.84 feet.
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Henry is playing with a standard deck of cards what is the probability that the next card he flips over is a jack or red?
Choose the relationship symbol that makes the statement true.
<
=
>
The cable supporting a ski lift rises 2 feet for each 5 feet of horizontal length. The top of the cable is fastened 1320 feet above the cable’s lowest point. Find the lengths b and c, and find the measure of the angle theta.
To find the lengths b and c of the cable supporting the ski lift, use the Pythagorean theorem. To find the measure of angle theta, use the tangent function.
Explanation:To find the lengths b and c, we can use the Pythagorean theorem. Since the vertical rise of the cable is 2 feet for every 5 feet of horizontal length, we can create a right triangle where the vertical leg is 2x and the horizontal leg is 5x. The hypotenuse of this triangle, which represents the length of the cable, is 1320 feet. Using the Pythagorean theorem, we can solve for the value of x and then find the lengths b and c.
b = 5x = 5 * (1320 / √(25 + 4))
c = 2x = 2 * (1320 / √(25 + 4))
Next, to find the measure of angle theta, we can use the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side (2x) to the length of the adjacent side (5x). Therefore, tan(theta) = 2x / 5x = 2x / (5 * (1320 / √(25 + 4))). Taking the arctangent of both sides of the equation will give us the measure of theta.
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The lengths b and c are 3300 feet and 1320 feet respectively, and the angle theta is approximately 21.8°.
To solve this problem, let's denote:
- b is horizontal length from the lowest point to where the cable is fastened.
- c is vertical rise from the lowest point to where the cable is fastened.
- theta is angle that the cable makes with the horizontal.
From the problem statement:
- The cable rises 2 feet for each 5 feet of horizontal length. This gives us the slope of the cable:
[tex]\[ \frac{c}{b} = \frac{2}{5} \][/tex]
- The cable is fastened 1320 feet above the lowest point, which means:
[tex]\[ c = 1320 \text{ feet} \][/tex]
Now, solve for b:
[tex]\[ \frac{c}{b} = \frac{2}{5} \][/tex]
[tex]\[ \frac{1320}{b} = \frac{2}{5} \][/tex]
Cross-multiplying to solve for b:
[tex]\[ 1320 \times 5 = 2 \times b \][/tex]
[tex]\[ 6600 = 2b \][/tex]
[tex]\[ b = \frac{6600}{2} = 3300 \text{ feet} \][/tex]
Now, we have:
[tex]\[ b = 3300 \text{ feet} \][/tex]
[tex]\[ c = 1320 \text{ feet} \][/tex]
To find [tex]\( \theta \)[/tex], use the tangent function:
[tex]\[ \tan(\theta) = \frac{c}{b} = \frac{1320}{3300} = \frac{2}{5} \][/tex]
Therefore, the measure of angle [tex]\( \theta \)[/tex] is:
[tex]\[ \theta = \tan^{-1}\left(\frac{2}{5}\right) \][/tex]
Using a calculator to find [tex]\( \theta \):[/tex]
[tex]\[ \theta \approx \tan^{-1}(0.4) \][/tex]
[tex]\[ \theta \approx 21.8^\circ \][/tex]
The complete question is
The cable supporting a ski lift rises 2 feet for each 5 feet of horizontal length. The top of the cable is fastened 1320 feet above the cable’s lowest point. Find the lengths b and c, and find the measure of the angle theta.
Find sin (45+theta) - cos(45-theta) ...?
In many cases, ________ integration is more profitable than ________ integration.
Final answer:
Vertical integration may be more profitable by allowing firms to control more of the supply chain, reducing costs, and improving efficiency. It can help protect against competitive threats such as adverse selection and free riders. However, the decision depends on context, including budgetary constraints and the need to protect proprietary information.
Explanation:
In many cases, vertical integration is more profitable than horizontal integration. Vertical integration occurs when a company expands its operations into an earlier or later stage in the value chain. This approach can be advantageous because it allows a firm to control more aspects of its supply chain, which can reduce costs and improve efficiency. For example, upstream integration happens when a business expands into an earlier stage, such as a car manufacturer beginning to produce its own steel. Conversely, downstream integration occurs when the expansion is to a later stage, like a manufacturer opening retail outlets.
Decision-making in the context of integration strategies can be influenced by various factors. In situations where protecting against problems of adverse selection and free riders is difficult, vertical integration might be preferred. The concept of double marginalization, where a single vertically integrated firm can achieve higher profits than two separate firms operating at different stages of the value chain, is also a key consideration.
Nevertheless, the decision to integrate vertically or pursue other strategies depends on the specific context and the internal and external factors affecting the business. For instance, if a company holds certain production or planning secrets, vertical integration might help in safeguarding this proprietary information. Conversely, if budget constraints are a significant concern, a less costly option might be adopted even if it's not as effective as vertical integration.
Describe the key features of the parabola y2 = 8x.
Answer: The value of p is 2. The parabola opens to the right. The focus is at (2,0). The equation of the directrix is x=-2.
Step-by-step explanation:
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.19 percent a year and that the 1988 population was 6.9 million, write an expression for the population as a function of time in years. (Let t=0 in 1988.)
P=?
hint: logistic function
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.19 percent a year and that the 1988 population was 6.9 million, write an expression for the population as a function of time in years. (Let t=0 in 1988.)
P=?
Answer:
[tex]P(t) = 6900000 e^{0.0019t}[/tex]
Step-by-step explanation:
Equation for an exponential growth:
[tex]P(t) = P_{0} e^{kt}[/tex].............(1)
Where [tex]P_{0}[/tex] = The initial population of Switzerland at time t = 0
At t = 0 in 1988, the population was [tex]P_{0} = 6.9 million[/tex]
k = 0.19% = 0.19/100 = 0.0019
The population as a function of time becomes:
[tex]P(t) = 6900000 e^{0.0019t}[/tex]
Final answer:
The expression for Switzerland's population growing exponentially at a 0.19 percent yearly rate from a 1988 population of 6.9 million is calculated using the exponential growth formula, resulting in P = 6.9e^0.0019t.
Explanation:
Assuming that Switzerland's population is growing exponentially at a continuous rate of 0.19 percent a year and that the 1988 population was 6.9 million, the expression for the population as a function of time in years is derived using the equation for continuous exponential growth. Let t=0 in 1988, then the population at any year t can be given by the formula P = P0ert, where P0 is the initial population, r is the rate of growth, and e is the base of the natural logarithms. Here, P0 = 6.9 million and r = 0.0019 (since 0.19% is 0.19/100 = 0.0019). Therefore, the expression for the population as a function of time in years from 1988 is P = 6.9e0.0019t.
A driving license number has 6 digits (between 1 to 9). The first two digits are 12 in that order, that third digit third digit is bigger than 6, the fourth one can be equally divided divided by 3 and the fifth digit is 3 times bigger than sixth one. How many license numbers can be made using this arrangement?
27, 36, 72, 112 ...?
Simplify completely: 3x+18 / 18
1) x
2) 3x
3) x+6 / 6
4) x+18 / 6 ...?
Answer: 3.) x+6/6
Proof of validity is shown below.
Related Rates Problem: The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius. The volume of the rind is growing at the rate __?__ cubic centimeters per week at the end of the fifth week. Assume that the radius is initially zero. ...?
To find the rate at which the volume of the rind is growing, we calculate the volume of the entire watermelon and the volume of the watermelon not including the rind, at the end of the fifth week. Then, calculate the derivative of this volume difference with respect to time.
Explanation:The topic at hand is related rates in calculus, specifically applied to a growing spherical watermelon. The rate of growth of the radius is given as 2 centimeters per week. The thickness of the rind is always one-tenth the radius, but we're interested in the volume of the rind. We use the formula for the volume of a sphere: V = (4/3)πr³, where r is the radius.
At the end of the fifth week, the radius is 2 cm/week x 5 weeks = 10 cm, therefore the outer radius of the watermelon is 10 cm and the inner radius is 9 cm (since the rind is one-tenth the radius). Therefore, the volume of the rind would be given by the volume of the watermelon minus the volume of the interior of the watermelon not including the rind. We can then calculate the derivative of the volume of the rind with respect to time to find the rate at which the volume is increasing at the end of the fifth week.
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The teachers at Albany Middle School want to determine which elective classes students would be interested in taking next year. They surveyed all students in art class. The results are shown is the table. Can teachers make a valid conclusion form the data? Why or why not?
When it comes to making a valid conclusion, D) No. Students currently taking an art class would be more likely to want to take another art class.
Why can the teachers not make a valid conclusion?
The sample in this case is limited to students who are already enrolled in the art class. Since the survey only includes students from the art class, it might not be representative of the entire student population at Albany Middle School.
Students who have chosen to enroll in the art class may have a specific interest or affinity for art, and their preferences may not be reflective of the broader student body.
If the goal is to determine elective preferences for the entire student population, it would be more appropriate to survey a random and diverse group of students rather than solely focusing on those already in the art class.
Options are:
A) Yes. Most students like to do art.
B) No. Students in middle school would probably like to take drama.
C) Yes. Students in an art class are a good group to get a sample of the general population.
D) No. Students currently taking an art class would be more likely to want to take another art class.
Fill in the blanks: When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the _____ of the radical, and the numerator becomes the _____ of the ______.
When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand.
What is a expression? What is a mathematical equation? What are exponents and radicals?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. An exponent is just a convenient way of writing repeated multiplications of the same number. Radicals involve the use of the radical sign. These are also called surds.We have to fill the given blanks as given in question.
The complete statement is -
When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand.
Therefore, the complete statement is -
When you rewrite an expression with a fractional exponent in radical form, the denominator becomes the index of the radical, and the numerator becomes the exponent of the radicand.
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Find the percent of tip:
Cost of meal $18.50, Tip $2.59
13%
14%
15%
16%
To find the percent of the tip on a meal, divide the tip by the total cost of the meal and multiply the result by 100. In this case, the tip is 14% of the cost of the meal.
Explanation:To find the percentage of the tip given on a meal, we use the formula for percent, which is part divided by whole multiplied by 100. In this case, the 'part' is the tip, which is $2.59, and the 'whole' is the cost of the meal, which is $18.50.
Step 1: Divide the tip by the cost of the meal, i.e., 2.59 / 18.50. This equals approximately 0.14.
Step 2: Multiply this result by 100 to convert it to a percentage. 0.14 * 100 equals 14.
So, the percentage of the tip given on the meal is 14%.
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Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1.25 per ride. Which function can be used to determine how much money he has left over after x rides?
A) f(x) = 1.25x + 64
B) f(x) = -16x + $80
C) f(x) = -1.25x + 64
D) f(x) = -1.25x - 64
Natasha has a gross income of $66,429. She can make adjustments of $14,490 for business losses, $3,584 for business expenses, and $4,813 for constitutions to her retirement plan. What's Natasha's adjusted gross income?
A. $109,971
B. $22,887
C. $72,522
D. $43.542
Answer: D. $43,542
Step-by-step explanation:
The adjusted gross income of any person is person's gross income minus the certain deductions.
Given : Natasha has a gross income of $66,429.
She can make adjustments of $14,490 for business losses, $3,584 for business expenses, and $4,813 for constitutions to her retirement plan.
Total deductions : [tex]\$14,490 +\$3,584 +\$4,813=\$22,887[/tex]
Now, Natasha's adjusted gross income will be :-
[tex]\text{Gross income - Total deductions}[/tex]
i.e. [tex]\$66,429-\$22,887=\$43,542[/tex]
Hence, Natasha's adjusted gross income = $43,542
factor:
4tan^2x-(4)/(cotx)+sinx(cscx) ...?
Travel time: 3.5 hours
Speed: 60 miles per hour
d = distance traveled
Which equation shows
the distance traveled?