The valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.
Let's solve each inequality step by step:
1. Two less than a number (x) is no more than 5:
The inequality is given as x - 2 ≤ 5. Adding 2 to both sides, we get x ≤ 7. This means that any number less than or equal to 7 satisfies the inequality.
2. Seven subtracted from 4 times a number (x) is more than 13:
The inequality is given as 4x - 7 > 13. Adding 7 to both sides, we get 4x > 20. Dividing both sides by 4, we obtain x > 5. So any number greater than 5 satisfies the inequality.
3. The sum of two times a number (x) and -2 is at least 8:
The inequality is given as 2x - 2 ≥ 8. Adding 2 to both sides, we get 2x ≥ 10. Dividing both sides by 2, we have x ≥ 5. So any number greater than or equal to 5 satisfies the inequality.
4. Four added to 3 times a number (x) is less than 19:
The inequality is given as 3x + 4 < 19. Subtracting 4 from both sides, we get 3x < 15. Dividing both sides by 3, we obtain x < 5. So any number less than 5 satisfies the inequality.
Based on the above solutions, the valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. These numbers can be represented on a number line graph by marking the appropriate points and shading the corresponding regions.
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proportional relationships 7th grade
Answer/ Step-by-step explanation:
---
Proportional relationships are relationships between two variables where their ratios are equivalent.
---
Lets take a look at example one attached image:
The constant of proportionality is the value of y when x = 1 in a proportional relationship.
On which line does y = 1/2 when x = 1?
Only line C has a y- value less than 1 when x = 1, but how can we be sure that the constant of proportionality is exactly 1/2?
If the constant of proportionality of a proportional relationship is 1/2 then:
y = 1/2x (like rise over run (slope), rise up 1 unit, and run right 2 units)
We can try the point (2, 1), and plug in the values into the equation, where x = 2, y = 1.
(1) = 1/2(2)
1 = 1
Line C has a constant proportionality of 1/2 between x and y.
--------
Example 2, 3, and 4 is a worked out example on khan academy (attached images)
Consider the chart of LCD Television sets and population below. Round your ratio as a decimal to 6 places. Round the Owners per 100 to one decimal.
City
Number of Owners
Total Population
Ratio as decimal
Owners per 100
Indianapolis
6,245
0.90 million
New York
911,216
18.6 million
Cairo
10,598
19.1 million
Beijing
959,611
21.2 million
Tokyo
1,700,510
26.5 million
Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7
New York: Ratio as decimal: 0.049018, Owners per 100: 4.9
Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1
Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5
Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4
To calculate the ratio as a decimal and the owners per 100 for each city, we need to divide the number of owners by the total population and perform some additional calculations.
Let's calculate the ratio as a decimal for each city:
For Indianapolis:
Number of Owners: 6,245
Total Population: 0.90 million
Ratio as decimal: 6,245 / 0.90 million
= 6,245 / 900,000
= 0.006939
For New York:
Number of Owners: 911,216
Total Population: 18.6 million
Ratio as decimal: 911,216 / 18.6 million
= 911,216 / 18,600,000
= 0.049018
For Cairo:
Number of Owners: 10,598
Total Population: 19.1 million
Ratio as decimal: 10,598 / 19.1 million
= 10,598 / 19,100,000
= 0.000554
For Beijing:
Number of Owners: 959,611
Total Population: 21.2 million
Ratio as decimal: 959,611 / 21.2 million
= 959,611 / 21,200,000
= 0.045336
For Tokyo:
Number of Owners: 1,700,510
Total Population: 26.5 million
Ratio as decimal: 1,700,510 / 26.5 million
= 1,700,510 / 26,500,000
= 0.064198
Now, let's calculate the owners per 100 for each city by multiplying the ratio as a decimal by 100:
Owners per 100 for Indianapolis: 0.006939 * 100 = 0.6939
Owners per 100 for New York: 0.049018 * 100 = 4.9018
Owners per 100 for Cairo: 0.000554 * 100 = 0.0554
Owners per 100 for Beijing: 0.045336 * 100 = 4.5336
Owners per 100 for Tokyo: 0.064198 * 100 = 6.4198
Therefore, rounding the ratio as a decimal to 6 places, and the owners per 100 to one decimal, we have:
Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7
New York: Ratio as decimal: 0.049018, Owners per 100: 4.9
Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1
Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5
Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4
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what is an example of "⊂-maximal element"?
The correct answer is a set S is T-finite if every nonempty subset X of the power set P(S) has a maximal element u, meaning there is no other element v in X such that u is a subset of v.
On the other hand, if a set S does not satisfy the condition of being T-finite, it is referred to as T-infinite.The notation "T" in this context represents Tarski, referring to the mathematician Alfred Tarski, who contributed to the study of set theory and lattice theory.In set theory, Tarski introduced the concept of T-finiteness to define a notion of finiteness for sets based on their subsets. A set S is considered T-finite if every nonempty subset X of the power set P(S) (the set of all subsets of S) has a maximal element u. This means that for any subset X, there exists an element u in X such that there is no other element v in X that properly contains u.
For example, consider the set S = {1, 2, 3}. The power set P(S) includes subsets such as {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. According to Tarski's T-finiteness, for any nonempty subset X from P(S), there should exist a maximal element. In this case, each nonempty subset has a maximal element because every subset has a largest element that cannot be properly contained within any other subset.
On the other hand, if a set S does not satisfy the condition of T-finiteness, it is considered T-infinite. This means that there exists a nonempty subset X of P(S) for which there is no maximal element. In other words, there are subsets within the power set that do not have a largest element.
Tarski's T-finiteness provides an alternative way to define finiteness based on the behavior of subsets within a set. It is a concept used in the study of set theory and has connections to other areas of mathematics, such as lattice theory.
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A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table.
Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.
Answer:
Gender and passing the test appear to be ________, as the probability of each event occurring does not depend on the other. Both males and females pass or fail the test with similar likelihoods. To confirm this independence, you could perform a chi-square goodness-of-fit test comparing observed frequencies to expected frequencies under the null hypothesis of independence between gender and test outcome. If the calculated p-value from the test exceeds your chosen significance level, you can conclude that there is sufficient evidence to reject the null hypothesis, indicating that gender and passing the test are dependent.
Need Help Asap
70s = b
How many wing beats in one minute (60 seconds)?
Answer:
4,200
Step-by-step explanation:
70s = b
70(60) = b
4200 = b
Helping in the name of Jesus.
Example 2: Use the Venn diagram to determine each set and the number of elements in each set.
helpppp
Using the Venn diagram, each set and the number of elements in each set are:
a. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}
b. A = {1, 3, 4, 5, 6, 8}
c. B = {4, 5, 6, 7, 9, 11}
d. C = {6, 8, 9, 12}
e. A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}
f. A ∩ B = {4, 5, 6}
How to Use the Venn diagram to determine each set and the number of elements in each set?A Venn diagram is a pictorial representation used to visualize the relationships between different sets of objects or concepts.
a.) U is the universal set. This implies it contains all the elements in the set. Thus:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}
b.) A is all element (number) is set A (circle A). Thus:
A = {1, 3, 4, 5, 6, 8}
c.) B is all element is set B (circle B). Thus:
B = {4, 5, 6, 7, 9, 11}
d.) C is all element is set C (circle C). Thus:
C = {6, 8, 9, 12}
e.) A ∪ B is all element is sets A and B (circles A and B). Thus:
A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}
f.) A ∩ B is all element is sets A and B (circles A and B) have in common. Thus:
A ∩ B = {4, 5, 6}
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What is 98 in exponential form
We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.
To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.
Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:
We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.
To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.
98 ÷ 10 = 9.8
Since 9.8 is still greater than 1, we need to continue dividing by 10.
9.8 ÷ 10 = 0.98
Now, we have reached a value less than 1, so we stop dividing.
From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:
98 =[tex]10^1[/tex] + 2
Therefore, we can write 98 in exponential form as:
98 = [tex]10^3[/tex]
In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.
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Name: Salem A
Score:
Unit # 12 - Lesson #4 Exit Ticket: The spinner shown below has
three sections. If the pointer is spun one time, which number is it
most likely to land on? Explain your choice.
3
1
2
The number the spinner is most likely to land on is 2
Which number is it most likely to land on?From the question, we have the following parameters that can be used in our computation:
The spinner
From the spinner, we have the number that covers the largest area to be 2
i.e.
Largest area = 2
This means that the number it is most likely to land on is 2 and it has the highest probability
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What is the meaning of "[tex] \varphi (x,y)[/tex] be [tex] y\wedge \phi (x)[/tex] "?
The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.
The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.
The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.
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Enter the number that belongs in the green box
The angle measure that belongs in the green box is given as follows:
70.67º.
What is the law of sines?We consider a triangle with side lengths and angles related as follows, as is the case for this problem:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
The relation for this problem is given as follows:
sin(x)/12 = sin(76º)/12.34
Applying cross multiplication, the missing angle measure is given as follows:
sin(x) = 12 x sine of 76 degrees/12.34
sin(x) = 0.9436.
x = arcsin(0.9436)
x = 70.67º.
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Si un hombre camina en promedio a una velocidad de 4 2/5 km por hora, ¿qué tan lejos puede llegar en 2 2/3 de hora?
Escribe el resultado en fracción.
Si un hombre camina a una velocidad promedio de 4 2/5 km por hora, podemos calcular la distancia que puede recorrer en 2 2/3 horas.
Primero, convertimos la velocidad promedio a una fracción impropia. 4 2/5 se puede expresar como 22/5. Por lo tanto, la velocidad es de 22/5 km por hora.
Luego, multiplicamos la velocidad por el tiempo para obtener la distancia. En este caso, la multiplicación sería (22/5) * (8/3) = 176/15 km.
Entoncs, el hombre puede llegar a una distancia de 176/15 km en 2 2/3 horas.
En resumen, el resultado es 176/15 km.
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An employee at a company is paid based on years of experience and years of education. Write the equation for their salary.
Salary, S, is 35,000 plus the product of 2,000 and years of experience, X, plus the product of 3,000 and years of education, D.
S=35,000x+2,000D
S=2,000x+3,000D
S=35,000+2,000x+3,000D
S+35,000=2,000x+3,000D
The compensation equation for the employee may be stated as follows:
[tex]\text{S}=35000+2000\text{x}+3000\text{D}[/tex]What is a equation?A equation is a mathematical statement that claims the equivalence of two expressions. Equations are used in mathematics, science, engineering, and many other professions to express connections between variables and to solve problems.
If s denotes income, x denotes years of experience, and d denotes years of education.
The employee's remuneration is computed as the basic wage of $35,000 + $2,000 for each year of experience plus $3,000 for each year of study. In deciding an employee's wage, this equation considers both their experience and education.
Therefore, [tex]\text{S}=35000+2000\text{x}+3000\text{D}[/tex] is the compensation equation for the employee.
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this distance between two floors is 9'0 1/2". if 14 raisers are to be used in a set of stairs, what is the height of each raiser?
If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.
To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.
First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:
9 feet = 9 * 12 = 108 inches
0 1/2 inch = 0.5 inch
Total height = 108 + 0.5 = 108.5 inches
Next, we divide the total height by the number of risers (14) to find the height of each riser:
Height of each riser = Total height / Number of risers
Height of each riser = 108.5 inches / 14
Using a calculator, we can compute:
Height of each riser ≈ 7.75 inches
Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.
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The Fahrenheit temperature readings on 66 Spring mornings in New York City are
summarized in the table below. Construct and label a frequency histogram of the data
with an appropriate scale.
Temp (°F) Number of Days.
30-39
2
40-49
26
50-59
28
60-69
8
70-79
2
Graph answer Click and drag to make a rectangle. Click a rectangle to delete it.
To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.
The temperature ranges and their corresponding frequencies are as follows:
30-39: 2 days
40-49: 26 days
50-59: 28 days
60-69: 8 days
70-79: 2 days
To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.
Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.
Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.
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The length of a rectangular banner is 5 feet longer than its width. If the area is 66
square feet, find the dimensions.
Answer:
The length should be 11 feet and the width should be 6 feet. 11 feet is 5 feet more than 6 feet. 11 feet times 6 feet is 66 square feet.
Step-by-step explanation:
Un cultivo de 32 200 bacterias aumenta un 25% cada 20 minutos. ¿Cuál será la población de bacterias al transcurrir 4 horas?
Para calcular la población de bacterias al cabo de 4 horas, primero necesitamos determinar cuántos intervalos de 20 minutos hay en 4 horas.
4 horas son equivalentes a 240 minutos. Dividiendo 240 minutos entre 20 minutos por intervalo, obtenemos 12 intervalos.
Dado que la población de bacterias aumenta un 25% cada 20 minutos, podemos aplicar este crecimiento a cada intervalo de 20 minutos.
Para cada intervalo de 20 minutos, la población de bacterias aumentará en un 25%.
Por lo tanto, podemos calcular la población de bacterias al final de los 12 intervalos de la siguiente manera:
Población final = Población inicial * (1 + tasa de crecimiento)^número de intervalos
Población inicial = 32,200 bacterias
Tasa de crecimiento = 25% = 0.25
Número de intervalos = 12
Población final = 32,200 * (1 + 0.25)^12
Realizando los cálculos, obtenemos la población final de bacterias al cabo de 4 horas.
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What is Navems manufacturing cycle efficiency (MCE) for its elevators
The manufacturing cycle efficiency (MCE) of Navems for its elevators is 38.6%
The correct answer choice is option A.
What is Navems manufacturing cycle efficiency (MCE) for its elevators?Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time.
Value-added production time;
Inspection time = 12 days
Process time = 5 days
Total = 17 days
Total cycle time:
Wait time = 12 days
Inspection time = 12 days
Process time = 5 days
Move time = 6 days
Queue time = 9 days
= 44 days
Hence,
Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time × 100
= 17 days / 44 days × 100
= 38.63636363636363
Approximately,
38.6%
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Determine the equation of the circle graphed below
Answer:
(x-2)^2 + (y+3)^2 = 5.1^2
Step-by-step explanation:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where h and k are the x and y values of the center of the circle respectively and r stands for the radius.
The center is given to us, at (2, -3) so we can plug that in:
(x-(2))^2 + (y- (-3))^2 = r^2
Simplify:
(x-2)^2 + (y+3)^2 = r^2
We can also solve for the radius by getting another point given to us: (3,2).
Using the pythagorean theorem, we can find how far the two points are away from each other:
a^2 + b^2 = c^2
1^2 + 5^2 = c^2
1 + 25 = c^2
26 = c^2
c ~ 5.1
Plug the radius we solved for in for r:
(x-2)^2 + (y+3)^2 = 5.1^2
the perimeter of a semicircle protractor is 14.8cm,find it's radius
The radius of the semicircle protractor is approximately 4.693 cm.
Given,Perimeter of a semicircle protractor = 14.8 cm.
To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.
Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =[tex](1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693[/tex] cm.
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100 Points! Geometry question. Find x and y. Please show as much work as possible. Photo attached. Thank you!
Answer: x=2, y=4
Step-by-step explanation:
Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.
Thus: x=2, and y=4
Answer:
x = 2
y = 4
Step-by-step explanation:
If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.
As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.
Therefore, the two expressions with the x-variable are equal.
Similarly, the two expressions with the y-variable are equal.
Solving for x:
[tex]\boxed{\begin{aligned}\dfrac{3}{2}x+2&=x+3\\\\\dfrac{3}{2}x+2-x&=x+3-x\\\\\dfrac{1}{2}x+2&=3\\\\\dfrac{1}{2}x+2-2&=3-2\\\\\dfrac{1}{2}x&=1\\\\2 \cdot \dfrac{1}{2}x&=2 \cdot 1\\\\x&=2\end{aligned}}[/tex]
Solving for y:
[tex]\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}[/tex]
$21,000 is deposited for 2 years in an account earning 4% interest. (Round your answers to two decimal places.)
(a) Calculate the interest earned if interest is compounded semiannually.
$
(b) Calculate the interest earned if interest is compounded quarterly.
$
(c) How much more interest is earned on the account when the interest is compounded quarterly?
$
To calculate the interest earned in each case, we can use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
where:
A is the final amount (including principal and interest)
P is the principal amount (initial deposit)
r is the interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Given:
P = $21,000
r = 4% = 0.04
(a) If interest is compounded semiannually, n = 2 (twice a year), and t = 2 years. Plugging these values into the formula, we get:
A = 21000(1 + 0.04/2)^(2*2) - 21000
Calculate A to find the final amount and subtract the principal to get the interest earned.
(b) If interest is compounded quarterly, n = 4 (four times a year), and t = 2 years. Plugging these values into the formula, we get:
A = 21000(1 + 0.04/4)^(4*2) - 21000
Calculate A to find the final amount and subtract the principal to get the interest earned.
(c) To find the difference in interest earned when compounded quarterly, subtract the interest earned in part (a) from the interest earned in part (b).
By calculating the interest earned and the difference in interest, we can determine the specific amounts.
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The set intersection X' ∩ Y' is expressed as; {e, 24}
How to find the intersection of the sets?We are given the sets as;
U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}
X = {a, b, c, 20, 21, 22}
Y = {b, d, f, 19, 21, 23}
Union of the sets A and B , denoted A ∪ B , is the defined as the set of all objects that are a member of A , or B , or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} . Intersection of the sets A and B , denoted A ∩ B , is the set of all objects that are members of both A and B
Thus:
X' ∩ Y' is as follows;
X' = {d, e, 19, 23, 24}
Y' = {a, c, e, 20, 22, 24}
X' ∩ Y' = {e, 24}
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The number of $10 tickets sold is 1210 tickets.
The number of $20 tickets sold is 1344 tickets.
The number of $30 tickets sold is 827 tickets.
How to determine the number of each type of tickets sold?In order to write a system of linear equations to describe this situation, we would assign variables to the number of each tickets sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of $10 tickets.Let the variable y represent the number of $20 tickets.Let the variable z represent the number of $20 tickets.Since the basketball team sold 3381 tickets overall, 134 more $20 tickets than $10 tickets and the total sales are $63,790, a system of three linear equations to model this situation is given by;
x + y + z = 3381
y - x = 134
10x + 20y + 30z = 63790 ⇒ x + 2y + 3z = 6379
Next, we would solve the system of three linear equations simultaneously as follows;
x + x + 134 + z = 3381
2x + 134 + z = 3381
z = 3247 - 2x
x + 2(x + 134) + 3(3247 - 2x) = 6379
x = 1210 tickets.
For the value of y, we have:
y = x + 134
y = 1210 + 134
y = 1344 tickets.
For the z-value, we have:
z = 3247 - 2x
z = 3247 - 2(1210)
z = 827 tickets.
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Complete Question:
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3381 tickets overall. It has sold 134 more $20 tickets than $10 tickets. The total sales are $63,790. How many tickets of each kind have been sold?
How many $10 tickets were sold?
How many $20 tickets were sold?
how many $30 tickets sold?
Julio tiene 12 años de edad y su padre tiene 42 años. ¿Cuántos años tendrá Julio cuando su padre tenga el doble de su edad?
Julio will be 30 years old when his father is twice his age.
To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.
Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.
For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.
Setting up an equation to solve for x:
x + 30 = 2x
Simplifying the equation, we subtract x from both sides:
30 = x
Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.
Therefore, Julio will be 30 years old when his father is twice his age.
Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?
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What is the amplitude?
The calculated value of the amplitude of the function is 3
How to determine the amplitude of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 3sin[2(θ - 90)] + 2
A sinusoidal function is represented as
f(x) = Asin(B(x + C)) + D
Where
Amplitude = A
using the above as a guide, we have the following:
Amplitude = A = 3
Hence, the amplitude of the function is 3
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Question
What is the amplitude?
y = 3sin[2(θ - 90)] + 2
Which tables could be used to verify that the functions they represent are inverses of each other? Select two options.
2
-6-10-14
0
0
0
0
X
Y
X
y
-5 -3
4
0
X
y
-14-10-6
0
-4 -2 0 3
X
-5
y -14 -10 -6
X -14
y 4
-5
-4
0
-10
2
-3 0 3 9
0
4
-3
0
4
4
5
-6
4
0 -3 -5
0 2
4
6 10
Answer:
A, D
Step-by-step explanation:
You want to identify the tables that represent inverse functions.
Inverse functionFor every ordered pair (x, y) of a function, there is an ordered pair (y, x) of its inverse function.
ApplicationThe first table shown has an ordered pair (x, y) = (4, -14). That means its inverse function must have the ordered pair (-14, 4). The two tables with that characteristic are shown in the attachment.
<95141404393>
Instructions are as given:
Find the degree, the leading term, the leading coefficient, the constant term and the end behavior of the given polynomial.
p(t)=-t²(3 - 5t) (t²+ t + 4)
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The given polynomial is:
p(t) = -t²(3 - 5t)(t² + t + 4)
To find the degree of the polynomial, we need to determine the highest power of t in the expression. This is given by:
degree = 2 + 1 + 2 = 5
So the degree of the polynomial is 5.
The leading term of the polynomial is the term with the highest power of t. This is given by:
leading term = -t² * 5t² = -5t^4
So the leading term of the polynomial is -5t^4.
The leading coefficient of the polynomial is the coefficient of the leading term. This is given by:
leading coefficient = -5
So the leading coefficient of the polynomial is -5.
The constant term of the polynomial is the term that does not contain any powers of t. This is given by:
constant term = -t²(3)(4) = -12t²
So the constant term of the polynomial is -12t^2.
To find the end behavior of the polynomial, we need to determine what happens to the value of the polynomial as t approaches positive or negative infinity. Since the degree of the polynomial is odd, we know that the end behavior will be opposite for t approaching positive or negative infinity. We can use the leading term to determine the end behavior:
- as t approaches positive infinity, the leading term approaches negative infinity, so the end behavior is p(t) → -∞ as t → ∞
- as t approaches negative infinity, the leading term approaches positive infinity, so the end behavior is p(t) → ∞ as t → -∞
So the end behavior of the polynomial is:
- p(t) → -∞ as t → ∞
- p(t) → ∞ as t → -∞
help me please i would appreciate it so so much
The proportional sides/corresponding sides of the triangles are ST/XY = RT/YZ = SR/XZ.
The value of a and b are 5 and 20 respectively.
What is the corresponding sides of the two similar triangles?Corresponding sides refers to a pair of matching sides that are in the same spot in two different shapes.
ST/XY = RT/YZ = SR/XZ
ST/XY = 3/15
= 1/5
RT/YZ = 4 ÷ 1/5
= 4 × 5/1
YZ, b = 20
Hypotenuse² = opposite² + adjacent²
5² = 3² + 4²
25 = 9 + 16
25 = 25
Therefore,
SR = a = 5
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A grid shows the positions of a subway stop and your house. The subway stop is located at (4,
-2), and your house is located at (-9,-6). What is the distance, to the nearest unit, between
your house and the subway stop?
A. 6
B. 9
C. 14
D. 15
Please awnser asap I will brainlist
Answer:
A ∩ B = {7, 8}
Step-by-step explanation:
A = {1, 2, 5, 7, 8}
B = {6, 7, 8, 9}
A ∩ B = set of elements in both A and B
A ∩ B = {7, 8}
