The length of string will be used to hang each pennant is 3.9 meters.
The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.
Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.
And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.
the length of the string needed for 5 pennants is calculated as,
=> 0.65 x (5 + 1)
=> 3.9 meter.
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On the number line, a slow bug S and a fast bug F are moving in the positive direction from the point 0. The speeds of both bugs are constant. Both leave 0 at the same time, and four seconds later F has reached 12 and S has reached 8. If x is the point reached by F after t seconds, and y is the point reached by S after t seconds, express x and y in terms of t PLEASE HELP I NEEd help
If x is the point reached by F after t seconds, and y is the point reached by S after t seconds, then x = 3t, y = 2t. 30 seconds after leaving point 0, 30 units far apart are F and S. At 100 seconds, F and S will be 100 units apart.
The speed of F reached 12 units in 4 seconds or 3 units per second.
x = 3t
The speed of S reached 8 units in 4 seconds or 2 units per second.
y = 2t
x - y = 3t -2t = t
After 30 seconds, the bugs will be apart by (x -y) = 30 units
x - y = 100 = t
After 100 seconds, The bugs will be 100 units apart.
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Jenny went for a drive in her new car. She drove for miles at a speed of miles per hour. For how many hours did she drive?
Answer: t = d/s
Step-by-step explanation:
Time = Distance/Speed
Substitute values in
E.g.
Jenny went for a drive in her new car. She drove for 8 miles at a speed of 4 miles per hour. For how many hours did she drive?
8/4 = 2 hours
independent random samples are selected from two populations. the summary statistics are given below. assume unequal variances for the following questions. test if the mean of the first population is larger than that of the second population. what is the p-value (round off to second decimal place)?
The mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.
Population 1: N = 35,X = 5.3, S = 2.8
Population 2: N = 21, X = 4.9, S = 3.2
We can use the t-test to test if the mean of the first population is larger than that of the second population. The formula for this is:
t = (x1 - x2) / (S√((1/N1) + (1/N2)))
Where x1 is the mean of population 1, x2 is the mean of population 2, S is the pooled standard deviation, and N1 and N2 are the sample sizes of the two populations.
Plugging in our values, we get:
t = (5.3 - 4.9) / (3.2√((1/35) + (1/21))) = 1.68
Using an online calculator, we find that the corresponding p-value is 0.093. Therefore, we fail to reject the null hypothesis that the two populations have the same mean and conclude that the mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.
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at a bicycle manufacturer, it costs $72 to make the first bicycle, $83 to make the second, and $77 to make the third. what is the average cost per bicycle? give your answer to two decimals.
At the bicycle manufacturer, the average cost per bicycle is $77.
To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.
The total cost is of the bicycles is given by -
$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232
Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.
Hence, $232 ÷ 3 = $77
Therefore, the average cost per bicycle is $77.
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Ski lift cables are strung to the top of a 1200 foot mountain. The angle of elevation of the cables is 30 degrees. How long are the cables?
The cable is 805.4 ft long.
Draw a triangle to represent the situation.
Label the sides of the triangle.
Let x = length of cable
Let 1200 = height of mountain
Let 30 = angle of elevation
Use the Law of Cosines to solve for x.
x² = (1200)² + (1200)² - (2)(1200)(1200)cos(30)
x² = 288000 + 288000 - 1,728,000cos(30)
x² = 576000 - 1,728,000cos(30)
x = √576000 - 1,728,000cos(30)
x = √576000 - 1728000(0.866)
x = √576000 - 1511360
x = √646340
x = 805.4 ft
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L
The value, V, of a computer can be modeled by the function V(t) = 1, 300(. 61), where t is the number of years since the computer was purchased.
Which function best represents the value of the computer in months?
The function that best represents the value of the computer in months is V(t) = 1,300(.61^(t/12)).Where t is the number of months since the computer was purchased
The given function V(t) = 1,300(.61), models the value of a computer in terms of the number of years since it was purchased. The value of the computer is represented by the function V(t) which is directly proportional to (0.61) raised to the power of t. Divide the t by 12, because there are 12 months in a year, to get the value in months.
As a consequence, the calculation V(t) = 1,300(.61(t/12)) displays the computer's value in terms of months from purchase. It demonstrates the decline in the value of the computer over time.
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The fraction 5/5 is proper
A. True
B. False, this is an improper fraction. Its value is ____.
a car is traveling at a constant speed of 65 miles per hour. how many feet does it travel in 5 seconds?
Answer: 476.7 feet
Step-by-step explanation:
65 miles = 343200 feet
1 hour = 3600 seconds
(343200/3600) = 476.7 feet in 5 seconds
Which equation is set up correctly using the Pythagorean Theorem for the triangle below?
The equation that is set up correctly using the Pythagorean Theorem for the triangle below is 9^2 + x^2 = 15^2.
What is Pythagorean theorem?The concept that will be used here is Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides:
According to theorem, the (adjacent)^2 + (opposite)^2 = (hypothenus)^2.
a^2+b^2=c^2
The 9^2 + x^2 = 15^2
Therefore, option C is correct.
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help please 4.2 + 2.5a = 9.2
Answer: a = 2
Step-by-step explanation: 2.5 x 2 = 5 5 + 4.2 = 9.2
[tex]4.2+2.5a=9.2[/tex]
Rearrange:
[tex]2.5a+4.2=9.2[/tex]
Subtract 4.2 from both sides:
[tex]2.5a+4.2-4.2=9.2-4.2[/tex]
[tex]2.5a=5[/tex]
Divide both sides by 2.5:
[tex]\dfrac{2.5a}{2.5} =\dfrac{5}{2.5}[/tex]
[tex]\fbox{a = 2}[/tex]
help !
the third term of an arithmetic sequence is -2 and the 8th term is -32. write a function to describe this sequence
Answer:
Step-by-step explanation:
The answer would look like (30n-44)/7
1. An architect is drafting plans for a new supermarket. There will be a space 144 inches
long for rows of nested shopping carts. The first cart is 34 inches long and each nested
cart adds another 10 inches. The architect want to know how many shopping carts will
fit in each row.
We see the same three numbers in situations 10,34 and 144.
In the first situation, there is one shopping cart with a length of 34 and then an unknown number of carts with a length of 10. Similarly, an architect has 34 dollars saved and will save 10 each week for an unknown number of weeks. Both situations have one part of 34 and then equal parts of size 10 that add together to 144. The equation is: 34 + 10x = 144.
Since it takes 11 groups of 10 to get from 34 to 144, the value of x in these two equations is ( 144 -34) ÷ 10 = 11.
There will be 11 shopping carts in each row and it will take 11 weeks to raise the money.
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Substitute these values for B-A; A=7, B=2
Answer:
-5
Step-by-step explanation:
Our given equation is B-A, and we know that B = 2 and A = 7. Through what we know, we can plug in the variables' values and solve:
2 - 7 (from B-A)
= -5
Answer:
value for b-a is -5
if subsituition is only done b-a = 2-7
Step-by-step explanation:
if b=2
a=7,
b-a= 2-7
=-5
Trapezoid ABCD, median EF
DC=2x-1, AB=5x+1, EF=3x+2 x=
The value of EF , DC , AB are 40,14, 37 respectively.
What is trapezoid ?
Trapezoid can be defined as the 4-sided shape in which it has one of sides parallel to it .
ABCD is trapezoid with median EF
so,
DC+AB = 2EF
(2x+10) + (3x+20) = 2 * 4x
5x + 30 = 8x
8x-5x = 30
3x = 30
x = 30/3
x = 10
EF = 4x = 4*10 = 10
3x+10(x-2) = 2 (4x+10)
3x+10x-20 = 8x+20
5x = 40
x = 8
DC = 3x = 32
7(x-2) + (4x-6) = 2*3x
7x-14+4x-6 = 6x
5x = 20
x = 4
DC = (7*(4-2) ) = 14
(2x+3) + (8x+5) = 2*6x
8 = 2x
x = 4
AB = 8*4+5 = 37
Therefore, The value of EF , DC , AB are 40,14, 37 respectively.
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Write an expression that is equivalent to
5(3r-8). State the property that justifies
your answer.
Answer:
15r-40
Step-by-step explanation:
By the Distributive Property, [tex]5(3r-8)=5(3r)+5(-8)=15r-40[/tex]
Parking lots A and B each charge a set fee for parking plus an hourly rate.
Hours Parked48Lot A Cost ($)19. 00/33. 00
Lot B Cost ($)20. 00/32. 00
How many more dollars does it cost per hour to park in Lot A than in Lot B? Give the answer as a decimal showing dollars and cents
It costs $0.208 more per hour to park in Lot A than in Lot B.
We know that the total parking hours = 48
Also, the cost of parking for Lot A= ($)19. 00/33. 00 and for Lot B = ($)20. 00/32. 00
To find out how many more dollars it costs per hour to park in Lot A than in Lot B, we will subtract the hourly rate of Lot B from the hourly rate of Lot A.
The hourly rate of Lot A is (33.00 - 19.00) / 48 = $0.541 (dollars and cents)
Similarly, the hourly rate of Lot B is (32.00 - 20.00) / 48 = $0.333 (dollars and cents)
So the difference in cost per hour is $0.541 - $0.333 = $0.208 (dollars and cents)
Therefore, it costs $0.208 more per hour to park in Lot A than in Lot B.
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Fill in the table using this function rule:
Y=-5x+3
X Y
-1 ?
0 ?
1 ?
2 ?
Answer:
X Y
-1 8
0 3
1 -2
2 -7
Step-by-step explanation:
Using the x values of the table, simply plug in those x values, replacing the x in the equation. For example:
y = -5x + 3
y = -5 * 2 + 3
y = -10 + 3
y = -7
(2x-5y)+(6y+5x²)=15y
Answer:
5x² + 2x = 14y
Step-by-step explanation:
2x - 5y + 6y + 5x² = 15y
the only terms we can combine are 5y and 6y; the others are not 'like'
2x + y + 5x² = 15y
5x² + 2x = 14y
Oscar feels that in order to get a decent amount of honey there should be at least 15000 bees in the colony estimate how many months it will take oscar until he has 15000 bees
a. The function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]
b. To graph the function, f(x), you can use a graphing calculator or software such as Excel or a Python library like Matplotlib.
c. It will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.
The problem states that Oscar wants to own a bee colony and extract honey from the hive. He starts with a colony of 5,000 bees and the number of bees grows exponentially with a growth factor of 12% each month. To solve this problem, we can use the exponential growth formula to determine the number of bees in the colony based on the month.
The exponential growth formula is [tex]P(t) = P_0 * (1 + r)^t[/tex] where
P(t) is the population at time t[tex]P_0[/tex] is the initial populationr is the growth ratet is the number of time periods.In this case, [tex]P_0[/tex] = 5000, r = 0.12, and t = x (the number of months). So, the function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]
In order to get a decent amount of honey, Oscar feels that there should be at least 15,000 bees in the colony. To estimate how many months it will take Oscar until he has 15,000 bees, we can set f(x) = 15,000 and solve for x.
By doing this, we get x = log(15000/5000) / log(1.12) ≈ 7.9 months. This means it will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.
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The complete question is:
Oscar wants to own a bee colony so that he can extract honey from the hive. He starts a colony with 5,000 bees. The number of bees grows exponentially with a growth factor of 12% each month.
a. Write a function, f(x), for the bee population that can be used to determine the number of bees in the colony, based on the month, x.
b. Use technology to graph the function, f(x).
c. Oscar feels that in order to get a decent amount of honey, there should be at least 15,000 bees in the colony. Estimate how many months it will take Oscar until he has 15,000 bees.
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can someone help this thank you
Answer: slope = [tex]\frac{1}{4} x[/tex]
point on the line= (0,-4.25)
Step-by-step explanation:
[tex]y+3\\[/tex] = [tex]\frac{1}{4} (x-5)[/tex]
[tex]y=\frac{1}{4} x-\frac{5}{4} -3\\\\y= \frac{1}{4}x -3\frac{5}{4} \\\\y=\frac{1}{4}x -\frac{17}{4}[/tex]
therefore the value with the x is the gradient so the gradient (slope) is [tex]\frac{1}{4} x[/tex]
since the y-intercept is [tex]-\frac{17}{4}\\[/tex] get the simplified version in decimals which is -4.25... so the point will be (0,-4.25)
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Nyoko wrote these two questions.
Equation 1: 6x-5+2x = 4(2x-1) - 1
Equation 2: 3x +7 = bx+7
Part A
Nyoko says that Equation 1 has one solution. Do you agree with her? Explain your reasonings.
Part B
Can Nyoko find a value for b in Equation 2 so that the equation has no solutions? Explain Your REASONING!
a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.
b) Nyoko cannot find a value of b so that the equation has no solutions.
How to solve the equations?The equation 1 is given as follows:
6x - 5 + 2x = 4(2x - 1) - 1.
Combining the like terms and applying the distributive property, the simplified equations are given as follows:
8x - 5 = 8x - 4 - 1
8x - 5 = 8x - 5.
As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.
The equation 2 is given as follows:
3x + 7 = bx + 7.
A system of linear equations will have zero solutions when:
The equations have the same slope.The equations have different intercepts.As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.
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South the inequality. The temperature of the freezer is never greater than -2°C. Yesterday the temperature was -10°C but it increased at a steady rate of 1. 5°C per hour. How long in hours and minutes did the temperature increase inside the freezer?
It took approximately 5.3 hours for the temperature inside the freezer to increase from -10°C to -2°C.
If the temperature inside the freezer increased by 1.5°C per hour, and it started at -10°C, then to reach -2°C the temperature inside the freezer would have had to increase by 8°C.
To find out how long it took for this to happen, we can use the formula:
Temperature increase/rate of increase = time
8°C / 1.5°C per hour = 5.3 hours (approx).
The temperature was exactly -10°C at the start and exactly -2°C at the end. It means that the temperature increased by 1.5°C per hour on average.
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A number m is multiplied by 4/7 is greater than 12/5 write this sentence as an inequality
Answer: m * 4/7 > 12/5
Find the area of a circle with diameter, d = 5.8m. Give your answer rounded to 1 DP.
The area of the circle is 26.4 square meters
How to determine the area of the circleFrom the question, we have the following parameters that can be used in our computation:
Diameter, d = 5.8 meters
Start by calculating the radius of the circle
r = 5.8/2
Evaluate
r = 2.9
The area of the circle is then calculated as
A = πr²
Where
r = radius
substitute the known values in the above equation, so, we have the following representation
A = 3.14 * 2.9²
Evaluate
A = 26.4
Hence, the area is 26.4 square meters
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I need to find the area. SOMEONE PLS HELP ME
Answer: 31
Step-by-step explanation:
Let's find the trapezoid area first:
(8-2 + 4) 3 / 2
= 10*3/2
= 15
And then the rectangle:
2 * 8
= 16
add the two areas together
15+16 = 31
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PLEASE HELP
sketch the graphs of the linear inequality. :)
The graph of the linear inequality is shown below.
What is linear inequality?
A linear inequality is one that, if the equals relation were employed in place of the inequality, would result in a linear equation. The direction of the inequality is reversed when both sides are multiplied or divided by a negative integer to solve it. The solution set refers to all possible answers to an inequality.
We are given y < -x-4
In order to sketch the graph of the inequality, we need to have two points.
So, first let's put x = 0
So, we get y = -4
Now, let's put y = 0
So, we get x = -4
Thus, we get the points as (0,-4) and (-4,0)
From the points, the graph is sketched which is shown below.
Hence, the graph of the linear inequality is obtained.
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Since, there are multiple questions, so the question answered above is attached below
Help on #12 please
The diagonals of rhombus PQRS intersect at T
The missing measures by using the rhombus LMNO graphic is, 90° is the measure of LPM,the PMN measurement is 102°, LN is 10 units in length.
Rhombus definition?A rhombus is a unique type of quadrilateral with four sides that is similar to a parallelogram. In a rhombus, the opposing sides are parallel and the opposing angles are equal.
LMNO LON = 102° NP = 5 units for a rhombus.
According to the rhombic characteristics, all of the sides are congruent (equal), hence LM = MN = NO = OL and the opposite angles are also equal, and the opposite sides are parallel.
Therefore, LON = 102° = LMN.
Since adjacent angles add up to 180 degrees.
L + M thus equals 180 degrees.
∠M + ∠N = 180°
∠N + ∠O = 180°
∠O + ∠L = 180°
So, ∠N = 180° - ∠O = 180° - 102° =78°
∠L = 180° - ∠O = 180° - 102° =78°
∠M = 180° - ∠L = 180° - 78° =102°
Alternatively, we can say that each of the two diagonals in a rhombus is the perpendicular bisector of the other. Diagonals bisect each other at an angle of 90°.
Thus, LPM = NP0 = MPN = LPO = 90 degrees.
So, 90° is the measure of LPM.
The PMN measurement is 102°.
LN is 10 units in length.
The completre question is,
Rhombus LMNO has mLON = 102° and NP = 5 units.
The Rhombus L M N O is depicted. Drawn as parallel lines, they connect at point P and extend from point L to point N and from point M to point O, respectively. Congruence exists on every side.
You may locate the missing measures by using the rhombus LMNO graphic.
° is how much LPM is measured.
° is used to measure PMN.
Units are the length of LN
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I am stuck on this homework question can anyone help ?
Answer:
10 cases
Step-by-step explanation:
We are given the equation: y = -0.25x + 85, where y is the # of cases, and x is the # of students who received the vaccine.
The question asks for the # of cases if 300 students received the vaccine. Since we know that 300 students received the vaccine, we can plug that in for x in the equation above, since x is that unit:
y = -0.25(300) + 85
Now, we can solve:
y = 10
Therefore, there will be 10 cases if 300 students received the vaccine.
Will the following side lengths form a right triangle?
12 ft, 16 ft, 20 ft
Answer:
The three side lengths given, 12 ft, 16 ft, and 20 ft can form a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 20^2 = 12^2 + 16^2, so the sides 12 ft, 16 ft and 20 ft can form a right triangle.
Select the correct answer from each drop-down menu. Consider the absolute value function f(x) = -|x + 2| + 2. The vertex of the function is a at .
The vertex of the function is at - 2
Hown to find the vertexThe vertex of the function is at the point (a, 2), where the value of x, denoted as 'a', is the x-coordinate of the vertex.
To find the value of 'a', we can use the formula for the x-coordinate of the vertex, which is -b/2a, where b and a are the coefficients of the x-squared and x terms, respectively, in the standard form of the equation (y = ax^2 + bx + c).
Since the function is already in vertex form, we can directly read the value of 'a' from the equation which is -2.
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