Answer:20 ft
Step-by-step explanation:
Using Pythagoras' Theorem:
[tex]h^{2} = a^{2} +b^{2} \\h^{2} = 16^{2} +12^{2} \\h^{2} = 256+144h^{2} = 400\\\\[/tex]
Now you want to get h alone. To do that you need to get rid of the squared by finding the square root of 400.
[tex]h=\sqrt{400}\\h=20[/tex]
A runner is 7/8 miles away from the finish line. If she can travel 3/8 miles per minute, how long will it take her to finish the race?
The time that runner takes to finish the race is 2.133 minutes.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The speed of the runner is given as 3/8 miles per minute.
The remaining distance to be travelled is 7/8 miles.
Then, the time taken by the runner is the ratio of distance to be travelled to the speed. It can be written as follows,
Time taken by runner = (7/8)/(3/8)
= 7/3
= 2.133
Hence,the time taken by the runner to finish the race is 2.133 minute.
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between 149714971497 and 150015001500, amerigo vespucci embarked on two voyages to the new world. according to vespucci’s letters, the first voyage lasted 434343 days longer than the second voyage, and the two voyages combined lasted a total of 1{,}0031,0031, comma, 003 days. how many days did the second voyage last?
The number of days that the second voyage last's is 480 days.
Given,
The discrepancy in the length of the two excursions, we are asked to determine how many days the second voyage lasted.
We initially assign variables in order to overcome this issue. Let the duration of the first cruise be f days and the duration of the second expedition be s days.
We are aware that the first journey lasted 43 days longer than the second.
In mathematics, f = 43 plus s. (I)
The cumulative duration of the two journeys was 1003 days. Mathematically:
f + s = 1003........(ii) (ii)
We transform I into ii
43 + s + s = 1003
43 +2s = 1003
2s = 1003 - 43
2s = 960
s = 960/2 = 480 days
That is,
The second voyage lasted about 480 days
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you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose?
Maximum area to enclose a rectangular pasture with one side up against a river is equal to 500,000 square feet.
As given in the question,
Let 'l' be the length of the rectangular pasture
And 'w' be the width of the rectangular pasture
Condition:
One side of the pasture is up against a river
Perimeter of the rectangular pasture with one side up against river = l + 2w
⇒ 2000 = l + 2w
⇒ l = 2000 - 2w
Area of the rectangular pasture
=( 2000 - 2w )( w )
= - 2 ( w² - 1000w )
= -2( w² - 1000w + 250000 - 250000 )
= -2 ( w - 500 )² + 500, 000
Maximum area is at w = 500
Maximum area is 500,000
Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.
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The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is cubic inches when its base area is square inches and its height is inches. What is the volume of a pyramid with a base area of square inches and a height of inches?.
The volume of a pyramid is 60 inches.
Given that,
A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.
V1 = 35 cubic inches
A1 = 15 square inches
h1 = 7 inches
A2 = 36 inches
h2 = 5 inches
To find : What is V2
The following formula is used to determine a pyramid's volume:
V = (Base Area × Height)/3
V2 = (36 square inches multiplied by 5)/3
V2 = 60 cubic inches
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Solve for bbb.
-11b+7 = 40−11b+7=40minus, 11, b, plus, 7, equals, 40
b =b=b, equals
The value of 'b' will be;
⇒ b = 7 / 11
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 40 - 11b + 7 = 40
Now,
Solve the expression for b as;
The expression is,
⇒ 40 - 11b + 7 = 40
⇒ - 11b + 7 = 0
⇒ 11b = 7
⇒ b = 7 / 11
Thus, The value of 'b' will be;
⇒ b = 7 / 11
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Linear Equations w/ Distribution 2
(5y−1)=28
Answer:
29/5 or 5.8
Step-by-step explanation
First, we put the 1 on the other side which turns it positive 5y=29
Then, we divide 29 by 5 which gives us 29/5 which is equal to 5.8
The table represents some points on the graph of linear function f.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928
Which function represents f`? Please show your work.
A. f(x) = 32(3x - 1)
B. f(x) = -32(x - 3)
C. f(x) = -2(32x - 3)
D. f(x) = 16(2x - 1)
The function representing the points relation is f(x) = 32(3x - 1)
What is function?A function is defined as a relation between a set of inputs having one output each.
Given a table, represents some points on the graph of linear function f.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928
From option A)
f(x) = 32(3x - 1)
Put x = -2
= 32(-2x3-1)
= 32x(-7) = -224
Hence, The function representing the points relation is f(x) = 32(3x - 1)
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use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 70 and 82 tails, inclusive? a) 0.2137 b) 0.1908 c) 0.2154 d) 0.1880 e) 0.2166 f) none of the above.
The probability of obtaining between 70 and 82 tails is 0.2137, that is, option A.
Here, we are given that a fair coin is tossed 130 times.
Thus,
number of trials ⇒ n = 130
p = P(getting tails in a single toss) = 0.5
mean of a binomial distribution = np
= 130*0.5
= 65
variance = np(1-p)
= 65*0.5
= 32.5
standard deviation = sqrt(variance)
= sqrt(32.5)
= 5.7
Now, x = number of tails
X follows a normal distribution with mean 65 and variance 5.7
P(70 < x < 82)
= P( 69.5 < X < 82.5) [applying continuity correction]
= P[(69.5-65)/5.7 < Z < (82.5-65)/5.7)]
= P(0.79 < Z < 3.07)
= P(Z < 3.07) - P(Z < 0.79)
= 0.9989- 0.7852
= 0.2137
Thus, the probability of obtaining between 70 and 82 tails is 0.2137, hence, option A. .
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please cluster the following points, (18, 10), (21, 11), (22, 22), (24, 15), (26, 12), (26, 13), (27, 14), (30, 33), (31, 39), (35, 37), (39, 44), (40, 27), (41, 29), (42, 20), (44, 28), (46, 21), (47, 30), (48, 31), (49, 23), (54, 24) use the numbers as pairs of x and y values which represent their locations. all distances are measured with euclidean distance. hint: you'll probably want to code for this question, although hand tracing is not impossible.
a. Use the k-means algorithm, with
(24,15),(30,33), and(54,24) as the initial cluster centers, process the dataset until convergence, choose a method of your choice to evaluate the cluster result quality. (10pts) b. Use the agglomerative hierarchical clustering to cluster the data, use single link, complete link, and average link, respectively. Discuss the similarities and/or the dissimilarities between the 3 different link methods. (10pts)
Using the numbers to indicate their locations as pairs of x and y values. Euclidean distance is used to measure all distances.
a. Using the k-means algorithm, we can group the points into three clusters based on their initial cluster centers. The first cluster consists of the points (18, 10), (21, 11), (22, 22), (24, 15), (26, 12), and (26, 13), the second cluster consists of the points (27, 14), (40, 27), (41, 29), (42, 20), and (44, 28), and the third cluster consists of the points (30, 33), (31, 39), (35, 37), (39, 44), (46, 21), (47, 30), (48, 31), and (49, 23).
The silhouette approach, which compares how similar each point is to the points in its own cluster to the points in other clusters, can be used to assess the quality of the clusters. A high silhouette value denotes a well-clustered point, while a low silhouette value denotes a possible incorrect cluster assignment.
b. In hierarchical agglomerative clustering, we first create individual clusters for each point, which are then combined to create a single cluster that contains all of the points. Depending on how they calculate the separation between clusters, the three distinct link approaches will result in a variety of clustering outcomes.
The minimal distance between any two points in each of the two clusters is used by single link to calculate the separation between the clusters. Because it only takes into account the closest pair of points, this can lead to long, thin clusters.
The distance between the clusters is calculated using the maximum distance between any two points in the two clusters. Due to the fact that it only takes into account the farthest pair of points, this can lead to compact, spherical clusters.
The average link calculates the separation between the two clusters by averaging out all of the distances between the points in the two clusters. This takes into account all possible pairs of points and may lead to clusters with more symmetrical shapes.
In general, a single link will create clusters that are the most compact, a complete link will create clusters that are the most spherical, and an average link will create clusters that are more evenly shaped.
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One day in February, the temperature at 9 A.M. is -6.8°F. At 3 P.M. on the same day, The temperature is 1.72°F.
a) Find the change in temperature.
b) Find the average hourly rate of change in temperature
Answer:
The change in temperature is -6.64
The average hourly rate of change is
6 hours or -3.32
The enrollment at Grove
Middle School is expected to increase
by 40 students each year for the next
5
years.
If their current enrollment is
600 students, find their enrollment
after each of the next 5 years.
Answer:
After one year, the enrollment will be 600 + 40 = 640. After two years, the enrollment will be 640 + 40 = 680. After three years, the enrollment will be 680 + 40 = 720. After four years, the enrollment will be 720 + 40 = 760. After five years, the enrollment will be 760 + 40 = 800.
Step-by-step explanation:
a jet flies 5985 miles in 4 3/4 hours. At the same rate, how long will it take the jet to fly 8505 miles?
[tex]\begin{array}{ccll} miles&hours\\ \cline{1-2} 5985&4\frac{3}{4}\\[1em] 8505&h \end{array}\implies \cfrac{5985}{8505}~~ = ~~\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ 4\frac{3}{4} ~~ }{h}\implies \cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{h}[/tex]
[tex]\cfrac{19}{27}=\cfrac{ ~~ \frac{19}{4} ~~ }{\frac{h}{1}}\implies \cfrac{19}{27}=\cfrac{19}{4}\cdot \cfrac{1}{h}\implies \cfrac{19}{27}=\cfrac{19}{4h}\implies 76h=513 \\\\\\ h=\cfrac{513}{76}\implies h=\cfrac{27}{4}\implies {\Large \begin{array}{llll} h=6\frac{3}{4} \end{array}}[/tex]
NEED HELP. ASAP For the bleacher section, what is the minimum number of games a fan needs to attend to make purchasing a season ticket a less expensive option than single-game tickets?
Seating Area
Single-Game Ticket
Season Ticket
Main box
$50
$3240
Bleachers
$12
$810
Left field reserve
$20
$1377
The best way is to pick the one you think has a higher chance
Which mixed number is represented on the number line?
4
5
4
5
Select the reason why these triangles are similar. If they are not, select "Not similar."
Numbers selected in the triangle 2.5, 2.25,0.5,2,1, and 1
Answer choices: A. AA, B. Not similar, C. SAS, D. SSS
Answer: B
Step-by-step explanation: One is a triangle and one is not. The bigger one has four sides therefore it is not a triangle
Answer:
B. Not similar
Step-by-step explanation:
You want an appropriate choice of similarity reason for the triangles shown in the figure.
Side ratiosThe side ratios in the smaller triangle are ...
0.5 : 1 : 1 = 1 : 2 : 2
The side ratios in the larger triangle are ...
2.25 : 3 : 3.5 = 9 : 12 : 14
The side ratios are not the same, so the triangles are not similar.
<95141404393>
1. Solve for the missing angle measures.
1)
a = 75⁰
d
b
C
2)
a
b
с
d = 104°
Answer: 24 26 37 60
Step-by-step explanation: im sure
Which number is greatest? A. 3.4 × 10-2 B. 4.3 × 10-3 C. 5.2 × 10-4 D. 6.1 × 10-4
Mathwy is To solve this type of3.4 x 10-2 PEMDAS
PLEEEEEASE HELP ME ASAP
By evaluating the function we will see that the difference is:
f(1) - f(-7) = 3
How to evaluate the piecewise function?Here we have a piecewise function, this is a function that behaves differently on different intervals of its domain.
On the image you can see the different pieces of the function, and on the right the domain of each of the pieces.
The first part works for all the values smaller than -4 and x = -4.
So if we want to evaluate the function in x = -7, we need to use that piece:
f(-7) = |-7 + 5| - 9 = -7
And the second piece works on the interval (-4, 1], so to evaluate in x = 1 we need to use that piece.
f(1) = -1³ - 3*1 = -4
Then the difference is:
f(1) - f(-7) = -4 + 7 = 3
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Reid needs to purchase ties for a new job. Out of the choices below, which is the best one to buy?
(1): 6 ties for $25.50
(2): 4 ties for $18.00
(3): 5 ties for $21.00
Answer:1
Step-by-step explanation:
There is a lot more
the quotient of a number n and "-3" is no less than 6. What is the value of n?
Answer: n >= -18
Step-by-step explanation:
n/-3 >= 6
(-3) (-3)
n >= -18
MAKING AN ARGUMENT Your friend claims that given f(0) and any other value of a linear function f, you can write an
equation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on a
vertical line. Who is correct? Explain.
O Your friend. You can write an equation in slope-intercept form even if the two points are on a vertical line.
O Your cousin. You may need more than two points to write an equation in slope-intercept form.
O Your friend. If f is a function, then the line is not vertical.
O Your cousin. If the line is vertical, it will not have a slope.
The correct one is Your cousin. If the line is vertical, it will not have a slope.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
So, from the Discussion we came to know about Vertical Line.
But the slope of vertical line is undefined.
Then, the slope intercept form is not possible in vertical line.
Hence, the correct one is Your cousin. If the line is vertical, it will not have a slope.
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each of two pesticide brands is applied to 100 containers of fire ants. brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours.
The pValue is 0.15625 > 0.05 when brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.
Let A represent the new pesticide and B be the Ant Killer. Then, you are given that
Brand1 kills ants in 65 of 100 containers:
Xa = 65/100 = 0.65
Brand2 kills ants in 58 of 100 containers:
Xb = 58/100 = 0.58
You know need to find sample variance for both,
s²A =∑(Xi - Xa)²
= 65(1-0.65)² + 35(0 - 0.65)²
= 22.75
s²B =∑(Xi - Xb)²
= 59(1-0.59)² + 41(0 - 0.59)²
= 24.19
You can know do a test for significance
t = (Xa - Xb) / √(sA /nA) +(sB/nB)
and derive the conclusion from there.
Here, Null and alternative hypothesis are generally,
Alternative hypothesis
Here, there are three samples are assumed. They are:
i) Samples are taken independently
ii) Samples must be selected randomly
iii) n₁p₁ ≥ 5 , n₁q₁ ≥ 5, n₂p₂ ≥ 5, n₂q₂ ≥ 5
i.e., p₁ = 0.65 ; p₂ = 0.58 , n₁ = 100
q₁ = 0.35 ; q₂ = 0.42 , n₂=100
Corresponding p-value at Z = 1.01722
p-value = 0.15625 > 0.05
Hence, the pValue is 0.15625 > 0.05 when brand1 killed all ants in 65 of 100 containers within two hours, and brand 2 killed all ants in 58 of 100 containers within two hours in hypothesis.
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The relationship between a company’s profit, y, and the number of units sold, x, is represented by the equation 6x − 9y = 12. rewrite the equation to give the profit in terms of the number of units sold.
After solving the equation in terms of y will be y = (2/3)x - 4/3.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
The given equation is,
6x - 9y = 12
Then, the equation in terms of y will be,
9y = 6x - 12
Divide the above equation by 3,
3y = 2x - 4
y = (2/3)x - 4/3
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Factorise the following x^2+6x+8
Answer: (x+2) (x+4)
Hope this helps!
Of the 52 plays attributed to a playwright, 19 are comedies, 10 are tragedies, and 14 are histories. If one play is selected at random, find the odds against selecting a tragedy
The answer is 3/5, or 60%
11 (comedies) + 19 (tragedies) = 30
30/50 = 3/5, or 60%
you draw a card from a standard deck of 52 cards, replace it, and draw another card. find each probability. (enter your probabilities as fractions.)
The probabilities when choosing a card of the respective color are
1/26, 1/8, 3/169, 1/676
What are probability and examples?The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.
How do I solve probability?Multiply the total number of possible outcomes by the total number of occurrences. Divide the entire number of ways the event can occur by the total number of potential outcomes after determining the probability event and its related consequences.
The probabilities are:-
p= (1/13)*(1/2)=1/26
p=(1/2)*(1/4)=1/8
p=(1/13)*(3/13)=3/169
p=(1/52)*(1/13)=1/676
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a person stands on a scale in an elevator. as the elevator starts, the scale has a constant reading of 590 n. as the elevator later stops, the scale reading is 386 n. assume the magnitude of the acceleration is the same during starting and stopping.
Assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.
What is the magnitude?The magnitude or size of a mathematical object determines whether it is larger or smaller than other objects of the same kind in mathematics.
Formally speaking, the magnitude of an object is the visible outcome of an ordering—of the class of objects to which it belongs.
So, the weight of the person will be:
The scale measures the passenger's normal upward force as it is applied by the floor.
When moving upward, the most force is generated (when starting an upward trip or ending a downward trip).
When there is a downhill acceleration, the normal force is at its lowest.
For any such circumstance:
∑F y =ma y becomes for starting +591N−mg=+ma and for stopping +391N−mg=−ma.
Where a stands for the acceleration's magnitude.
To get rid of a and find mg, add these two simultaneous equations:
+591N−mg+391N−mg=0
OR
982N–2mg=0
Fg = mg = 982N/2 = 491N
Therefore, assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.
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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.
you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. this is an example of the .
you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. This is an example of memory retrieval.
What do you mean by series?
The total of a particular sequence of terms is known as a series in mathematics. These phrases often refer to real or complex numbers, though considerably more generality is possible.
In calculus and its generalization, mathematical analysis, the study of series plays a significant role. Most mathematical disciplines employ series, including combinatorics, where generating functions are employed to explore finite structures.
Along with being widely utilized in mathematics, infinite series are also frequently employed in other quantitative fields like physics, computer science, statistics, and finance.
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2. Stella's aunt donates 42 red roses, 70 pink carnations, and 56 yellow daisies for the party. The flowers will need to be arranged and placed on the tables. Stella wants each arrangement to have the same number of each color of flower. There are 12 tables at the party. Can she make an arrangement for each table and have no flowers left?
Answer:
no she will have 24 flowers left
Step-by-step explanation:
,Lm
Find the nth term of this number sequence
15, 12, 9, 6, ...
Answer:
[tex]a_{n}[/tex] = 18 - 3n
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
12 - 15 = 9 - 12 = 6 - 9 = - 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 15 and d = - 3 , then
[tex]a_{n}[/tex] = 15 - 3(n - 1) = 15 - 3n + 3 = 18 - 3n