When X = 5, Y is approximately equal to 27.34.
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
We are given that "Y varies directly as the cube of X", which can be written as:
Y = kX³
where k is a constant of proportionality. We need to find the value of k to solve for Y when X = 5.
Using the values given in the problem, we can write:
7 = k(4³)
Simplifying this equation, we get:
7 = 64k
Dividing both sides by 64, we get:
k = 7/64
Now that we know the value of k, we can solve for Y when X = 5:
Y = (7/64)(5³) = 27.34 (rounded to two decimal places)
Therefore, when X = 5, Y is approximately equal to 27.34.
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Let u = 4i-j, v = 5i + j. and w=i+6j.
Find the specified scalar
U*V+U*W
To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:
U·V + U·W
where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.
The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:
a · b = a1b1 + a2b2
Using this formula, we can find the dot product of U and V:
U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j
Next, we can find the dot product of U and W:
U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j
Now we can substitute these values into the original expression:
U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j
Therefore, the specified scalar is 17 + 23i·j.
On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
The correct answer is: A. Y intercept will be less and X will be less.
What is slope?A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:
slope equals (y2 - y1)/. (x2 - x1)
where any two points on the line (x1, y1) and (x2, y2) are.
The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.
Hence, A. Y intercept will be less and X will be less is correct.
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Spring Basketball Tournament Expenses and Income Guidelines:
1. A permit for the event is required and costs $75.60. It takes 8 hours to run a tournament for 8 teams.
2. Each player will be charged a $32 entry fee.
3. There will be exactly 8 players on each team.
4. The rent for a gym in a high school is $62.50 an hour.
5. A caretaker must be present for a Saturday permit and earns $56 an hour.
Will your Spring Basketball Tournament fundraiser make money? What adjustments might you make to this tournament to ensure that it is more profitable? Show your work and explain your thinking below.
If <2 is equivalent to (2x-8)• what is the value of c?
A 62•
B 35•
C 28•
D 18•
Reason:
[tex]\angle 1 = 62^{\circ}[/tex] because of the vertical angles theorem.
Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).
[tex]\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\[/tex]
Verify that segments with lengths of 21 inches, 72 inches, and 75 inches form a triangle. If so, determine whether they form a right triangle.
A. triangle, right triangle
B. triangle, isosceles triangle
C. triangle, obtuse triangle
D. triangle, acute triangle
Answer:
it would be C
Step-by-step explanation:
[tex]What is the logarithmic form of the exponential equation 4^{3} =(5x+4)[/tex]
The logarithmic form of the given exponential equation in the question, 4³ = (5x + 4) is Log₄ (5x + 4) = 3.
How to convert exponential equation to logarithmic form.The exponential-to-logarithmic format is useful because it makes it easy to compute large numeric expressions. Expressions involving exponential multiplication and division can be converted to addition and subtraction by applying logarithms. Logarithmic exponential form is a common means of converting mathematical expressions in one form to another form.
The exponential form aˣ = N is transformed and written logarithmically as LogₐN = x.
The exponential form of a for the exponent of x equal to N is converted to the logarithm of the number N in base a, equal to x.
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20. The volume of a large crate is 84 yd³. It is 23 yd wide and 4 yd high. What is the length of the crate?
Christine is reviewing her credit scores form the three major credit bureaus. Her experian score is 765 her equifax score is 748, and her transunion score is 758 what is Christine’s median credit score? (Round to the nearest whole point if applicable)
Answer: To find the median credit score, we need to arrange the three scores in order from lowest to highest:
748, 758, 765
The median is the middle value in this ordered list. Since there are three scores, the median is the second score, which is 758.
Therefore, Christine's median credit score is 758.
Step-by-step explanation:
4. This number line
number of minutes Diane read
week for 3 weeks.
0
200
100
300
How many minutes did she read after
the first week?
minutes
After the second week?
After the third week?
minutes
minutes
How many minutes did she read each
week? Explain how you know.
5. Diane reads the same number of minutes
each week. How many minutes does
she read after 4 weeks? After 5 weeks?
Skip count on the number line above to
find the answers.
After 4 weeks:
After 5 weeks:
minutes
minutes
4) Dane read an average of 400 minutes per week. 5) Diane will have read 2000 minutes after 5 weeks.
How to determine how many minutes did she read each week4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.
To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.
To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.
To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.
5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.
Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.
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FIND THR CIRCUMFERENCE OF A CD THAT HAS A RADIUS OF 6 CENTIMETERS
___cm
Answer:
Hm
Step-by-step explanation:
The formula to find the circumference of a circle is:
Circumference = 2πr
Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of radius, we get:
Circumference = 2 x π x 6
Circumference = 12π
Circumference ≈ 37.7 cm (rounded to one decimal place)
Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.
The perimeter of the given triangle is 3x² + 2 units
and its two sides are given in the figure. Find its
third side.
Step-by-step explanation:
Perimeter is the total of all three sides added together:
2x^2 + x + 3x^2 -3 + ? = 3x^2 + 2 Simplify a bit on the L
5x^2 + x -3 + ? = 3x^2 + 2 subtract 5x^2 from both sides
x-3 + ? = - 2x^2 + 2 subtract x from both sides
-3 + ? = - 2x^2 - x + 2 finally, add 3 to both sides
? = - 2x^2 -x + 5
It costs $350 to spend 4 nights at the Econo Motel. It costs $475 to spend 6 nights at the Bluebird Inn. Which of these statements is true?
Answer: A
Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.
Find the probability for each problem. Then, drag the problem to the correct column.
1.) The probability of rolling two even numbers would be = 1/4
2.) The probability of rolling one even and one odd number = 1/2
3.) The probability of flipping tails on a coin and by rolling a factor of 6 on a six sided die would be = 1/3
How to calculate the probability of the various given events?To calculate the probability the formula that should be used is given as follows;
probability = possible outcome/sample space
For question 1.):
Sample space when two dice are thrown = 36
possible outcome = (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)= 9
Probability = 9/36 = 1/4
For question 2.)
Sample space when two dice are thrown = 36
possible outcome = 18
probability = 18/36 = 1/2
for question 3.)
Sample space when two dice are thrown = 12
possible outcome = 4
probability = 4/12 = 1/3
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PLEASE HELP ON QUESTION!!!
A rectangular field has a perimeter of 150cm
Field is 15 m longer than it is wide . The width of field is a meters.
A) write down equation for this information.
If answers correct I'll rate 5 stars , a thanks and maybe brainliest.
Tina pet sits to earn extra money. She charges a flat service fee of $20, plus $15 per day. If one of her customers spent less than $125, which of the following inequalities could be used to solve for x, the number of days the customer paid for pet sitting?
Therefore, **x < 7** is the inequality that may be utilized to find x
What is inequality?A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).
For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".
Let x represent how many days the client paid for pet sitting.
$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.
We are aware that the customer's purchase was under $125. Consequently, we can write:
20 + 15x < 125
Putting this disparity simply:
15x < 105
x < 7
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A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot? Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot is 4.9 pounds.
What is the fractional idea?Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.
A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.
Total shipment = 7/10 pound
number of equal lots = 7
then, 7 x weight = 7/10
weight = 4.9
Therefore, the weight of each lot is 4.9 pounds.
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This pattern follows the rule add 2. What is another feature of this pattern? (4 points) An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots. a The terms appear even, odd, even, odd. b All the terms are even. c Two terms are even, then two terms are odd. d All the terms are odd.
The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.
Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.
This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.
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A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
Select all equations that have n = 6 as a solution. 2 + n = 6 n + 6 = 12 4 • n = 24 n • 3 = 2
The only equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.
How do equations work?An equation is a collection of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division that are balanced by the equal sign. The equation's right-hand side (RHS) is on the right, and its left-hand side (LHS) is on the left.
To check if a given equation has n = 6 as a solution, we simply substitute n = 6 into the equation and see if it is true.
2 + n = 6 : 2 + 6 = 8, not true for n = 6.
n + 6 = 12 : 6 + 6 = 12, true for n = 6.
4 • n = 24 : 4 • 6 = 24, true for n = 6.
n • 3 = 2 : 6 • 3 = 18, not true for n = 6.
Therefore, only the equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.
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What’s the length of side AB?
tan = 1/√3= perpendicular/ base
1/√3 = AB / AC
AB / 6 = 1/√3
AB = 6/√3
Marcus buys a car for $45,000. If he finances it for 5
years at an annual interest rate of 8.5%, what will his
monthly payment be?
Answer:
M ≈ $933.24
Step-by-step explanation:
To calculate Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5%, we can use the formula for the monthly payment on a loan:
M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)
where:
M is the monthly payment
P is the principal (in this case, $45,000)
r is the annual interest rate (in this case, 8.5%)
n is the number of monthly payments (in this case, 5 years * 12 months/year = 60 monthly payments)
Substituting the given values, we get:
M = $45,000 * (0.085/12) * (1 + 0.085/12)^60 / ((1 + 0.085/12)^60 - 1)
Using a calculator, we get:
M ≈ $933.24
Therefore, Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5% is approximately $933.24.
1. If it takes you 2¹/2 hours to assemble one unit, how many units will you complete in 15 hours?
(Note: Change 2¹/2 to an improper fraction before calculating.)
Answer:
Step-by-step explanation:
Make a chart.
units hours
2 5
4 10
6 15
what is one of the zeros of the function shown in this graph?
Answer:
x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.
What is the degree of -4x to the power of 3 + 6x to the power of 4 -1
A company is criticized because only 13 of 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it’s not surprising given that only 40% of all their employees are women. What do you think? Test an appropriate hypothesis and state your conclusion.
To test whether the proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole, we can perform a hypothesis test.
Null Hypothesis: The proportion of women in executive-level positions is equal to or greater than the proportion of women in the company as a whole.
Alternative Hypothesis: The proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole.
Using a significance level of 0.05, we can perform a one-tailed z-test for the difference in proportions.
Assuming a total sample size of 43 executives and a proportion of women in the company as a whole of 0.4, we find that the expected number of women in executive-level positions would be 43*0.4 = 17.2.
Using a z-test, we find that the test statistic is z = (13-17.2)/sqrt(0.4*0.6/43) = -1.89.
Using a z-table, we find that the p-value for z = -1.89 is approximately 0.029.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole. The company's explanation is not sufficient to account for the observed discrepancy.
~~~Harsha~~~
A certain college had 3,000 students enrolled in
2015. The college predicts that after 2015, the
number of students enrolled each year will be 2%
less than the number of students enrolled the year
before. Which of the following functions models the
relationship between the number of students
enrolled, f (x), and the number of years after 2015,
x?
A. f(x) = 0.02x(3000)*
B. f(x) = 0.98x(3000)*
C. f(x) = 3000(0.02)*
D. f(x) = 3000(0.98)*
The function that models the relationship between the number of students enrolled, f(x) and the number of years after 2015, x, is D. f(x) = 3000(0.98)*.
What is a function?Mathematically, a function defines a mathematical relationship or an algebraic expression involving one variable (the independent variable) and another variable (the dependent variable).
There are four main types of mathematical functions, including:
Constant Function, example, the polynomial function of degree zero.Linear Function, for example, the polynomial function of degree one.Quadratic Function, for example, the polynomial function of degree two.Cubic Function, the polynomial function of degree three.The number of students enrolled in 2015 = 3,000
The annual decrease in students enrollment = 2%
Let f(x) the model modeling the relationship between the number of students enrolled and the number of years after 2015.
Let the number of years after 2015 = x.
Thus, the correction function is D. f(x) = 3000(0.98)*.
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Question 1 of 10 What is the area, measured in square centimeters, of the green shape pictured below? Do not include units in your answer. Icm 1cm Answer here
21 is the area, measured in square centimeters, of the green shape pictured below.
What is square?
Square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).
the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.
The rectangle:
The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared
two right triangles:
The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9
Next, we add the two areas together: 12+9 = 21
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A rectangular flower bed measures 10m by 6m. It has a path 2m
wide around it. Find the area of the path
The area of the path is 80 square meters.
Given: A rectangular flower bed measures 10m by 6m. It has a path 2m wide around it.
To Find: The area of the path.
Solution: We need to subtract the area of the inner rectangle from the area of the outer rectangle.
So,
The outer rectangle has dimensions 14m by 10m (adding 2m to each side of the flower bed), so its area is:
A outer = 14m x 10m = 140 m²
Now,
The inner rectangle has dimensions 10m by 6m (the original dimensions of the flower bed), so its area is.
A inner = 10m x 6m = 60 m²
Now,
The area of the path.
A path = A outer - A inner
= 140 m² - 60 m²
= 80 m²
Thus, The area of the path is 80 square meters.
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In which
situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
What is expression?Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.
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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?
Use the given frequency distribution to find the
(a) class width.
(b) class midpoints of the first class.
(c) class boundaries of the first class.
1) Weight (in pounds)
Class Frequency, f
135 - 139 6
140 - 144 4
145 - 149 11
150 - 154 15
155 - 159 8
For the given frequency table, (a) 5 (b) 137 (c) lower class boundary is 132.5, and the upper class boundary is 141.5.
What is a frequency table ?
A frequency table is a tabular summary of data showing the frequency (i.e., the number of occurrences) of each category or value in a data set. It usually consists of two columns: one listing the categories or values and the other listing the corresponding frequencies. Frequency tables are commonly used to summarize categorical data, but they can also be used to summarize numerical data by grouping it into intervals or classes.
Now,
(a) The class width is the difference between the upper class limit and the lower class limit. For this frequency distribution, we can see that the class width is the same for each class and is equal to 5.
(b) The class midpoints are found by taking the average of the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. So, the class midpoint is (135 + 139) / 2 = 137.
(c) The class boundaries are found by adding and subtracting half of the class width to the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. The class width is 5, so half of the class width is 2.5. The lower class boundary is 135 - 2.5 = 132.5, and the upper class boundary is 139 + 2.5 = 141.5.
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