Answers
Related Questions
'If vector a =k times vector b, what is the angle between a and b where k is a scalar quantity?,
Answers
Angle between vector a and vector b is 0 degrees or 180 degrees.
What is vector?
A vector is a quantity that not only indicates magnitude but also indicates how an object is moving or where it is in relation to another point or item. Euclidean vector, geometric vector, and spatial vector are other names for it.
In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.
What is scalar quantity?
Physical quantities with merely magnitude and no direction are referred to as scalar quantities. These physical quantities can be explained just by their numerical value without any further guidance. These physical values can be added according to the basic algebraic rules, and in this case, only their magnitudes are added.
GIVEN:
If vector a is equal to k (scalar quantity)times vector b.
then vector a and vector b are parallel to each other.
The angle between two parallel vectors is 0 degrees or 180 degrees.
So, the angle between vector a and vector b is
0 degrees or 180 degrees.
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fsUse the conversion 8 km/h = 5 mph to convert 32 m/s into mph. If your answer is a decimal, give it to 1 d.p.
Answers
Answer:
72mph
Step-by-step explanation:
To convert km/hr into m/s, simply multiply the speed value by 5/18
To convert 8Km/hr to m/s, multiply 8 by 5/18 or divide by 3.6
8 x 5/18 = 2.22m/s
You can say that 2.22m/s = 5mph since 8km/hr = 5mph
If 2.2m/s =5mph, 1m/s = 5mph/ 2.2 (Divide both sides by 2.2)
Then 32m/s = 5mph/2.2 x 32
2.25 x 32 = 72 mph
Using the conversion, 32 m/s is equivalent to 72 mph.
We have,
To convert 32 m/s to mph using the conversion factor 8 km/h = 5 mph,
We can follow these steps:
- Convert 32 m/s to km/h by multiplying by the conversion factor:
32 m/s x (3.6 km/h / 1 m/s) = 115.2 km/h
- Convert 115.2 km/h to mph using the conversion factor 8 km/h = 5 mph:
115.2 km/h x (5 mph / 8 km/h) = 72 mph
Therefore,
Using the conversion, 32 m/s is equivalent to 72 mph.
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Challenge A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 30% discount. Otherwise, you get a 25% discount. The table shows the results of 200 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? explain
Answers
Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.
Discount Number of customers Relative Frequency
10% 70 0.35
25% 99 0.495
30% 31 0.155
To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).
Relative frequency for 25% discount = 99/200 = 0.495
Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.
Step-by-step explanation:
I need to know the answer asap
Answers
256 is the lateral surface area.
What's the lateral surface area?
Side indicates the side of commodity. thus, lateral surface area is set up by chancing the face area of the sides of the object.
This is done by chancing the border of the base and multiplying it by the height of any three- dimensional figure.
For the given situation,
The sides of the triangle are 5 cm, 6 cm, 5 cm.
The length of the prism = 16 cm
The formula for lateral surface area of triangular prism is
LSA = (perimeter)(length)
On substituting the above values,
LSA = (5 + 6 + 5)(16)
= (16)(16)
= 256
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At the shelter 0.6 of the animals are dogs, If there are 260 totally animals how many are not dogs?
Answers
Answer: 104
Step-by-step explanation:
If .6 or 60% of the animals in the shelter are dogs, then we can multiply .6 by 260 to get how many are dogs.
.6 times 260 is 156.
260-156=104.
A = 1/2bh or A = bh/2
Area: 256.5 cm2
base: 27cm
What is the height?
Answers
Step by step
We know
Formula for area is A=1/2bh
Area is 256.5
b is 27
Plug these into your formula for Area and solve
256.5 = 1/2 (27) h
256.5 = 13.5 h
Divide both sides by 13.5 to solve for h
256.5/13.5 = 13.5/13.5 h
19 = h
Your height is 19cm
Question two, please help
2/10
Answers
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function f(x)equalsnegative 3. 439 x Superscript 4 Baseline plus 35. 952 x cubed minus 99. 139 x squared plus 41. 541 x plus 178. 192 where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 1999
Answers
The number of bald eagles in the state in the winter of 1999 is 273.909, where The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function.
by the given information the equation is
[tex]f(x) = -3.439(x)^4 + 35.952(x)^3 - 99.139(x)^2 + 41.541(x) + 178.192[/tex]
where x = number of years since 1996
The given quartic function must be changed to x = 3 in order to determine the number of bald eagles in the state during the winter of 1999:
[tex]f(3) = -3.439(3)^4 + 35.952(3)^3 - 99.139(3)^2 + 41.541(3) + 178.192[/tex]
When we condense this expression, we get:
f(3) = -3.439(81) + 35.952(27) - 99.139(9) + 41.541(3) + 178.192
f(3) = -1107.759 + 970.104 - 892.251 + 124.623 + 178.192
f(3) = 273.909
Hence, in the winter of 1999, there were roughly 273.909 bald eagles in the state.
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Spencer is researching the cost to rent office space in the Brookton Office Center. Office space is rented based on
the square footage of an office's floor area. A linear relationship exists between the square footage of the floor and
the yearly cost to rent that square footage, as shown in the table below.
Brookton Office Center
Yearly Rental Costs
Square
Footage
500
600
800
1,200
Yearly
Rental
Cost
$9,250
$11,100
$14,800
$22,200
Spencer budgeted $20,720 for his yearly office rental cost. The office space can be customized to the size needed.
What is the maximum amount of square footage he can rent in the Brookton Office Center?
Answers
Answer:
Step-by-step explanation:
Two storage sheds are to have the same area. One is square and one is regtangular. The rectangular she is 4 meters wide and 16 meters long
Answers
As per the given question, the length of the square shed is 8 meters.
Length of the sheet = 4m
Width of the sheet = 16m
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Since a rectangle's opposite sides are both equal and parallel, a parallelogram is another name for this geometric shape.
Using the formula for the area of the rectangle -
Area = Length x Width
Now,
Let the length of the square shed be x, therefore -
x² = 4(16) = 64
x = √64
= 8
Complete Question:
Two storage sheds are to have the same area. One is square and one is rectangular. The rectangular she is 4 meters wide and 16 meters long. What is the length of the square shed?
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What is the remainder when \( f(x)=-6 x^{23}+x^{11}-x^{6}+2 x \) is divided by \( x+1 \) ? The remainder is
Answers
The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.
Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).
Here is the given polynomial,
()=−6^23+^11−^6+2
We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).
(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6
Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:
()=(−)()+()
where q(x) is the quotient of the division.
So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:
The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.
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Find the arc length of the partial circle
Answers
Answer: 3π
Step-by-step explanation:
360 - 90 = 270°
Perimeter of full circle = πd = 4π
Arc length = [tex]\frac{270}{360}[/tex] × 4π = 3π
Find the values of the variables and the measures of the indicated angles.
Answers
Answer:
115°
Step-by-step explanation:
You want the measure of angle S opposite angle (4x+5)° in an inscribed quadrilateral in which the other two angles are (5x-2)° and (7x+2)°.
Inscribed quadrilateralThe measure of an inscribed angle is half the measure of the arc it intercepts.
Two opposite angles in an inscribed quadrilateral intercept arcs that total the full circle. Since the sum of double those angles is 360°, the sum of opposite angles of an inscribed quadrilateral is 180°—they are supplementary.
We can use this to find the value of x:
(5x -2)° +(7x +2)° = 180°
12x = 180 . . . . . . simplify
x = 15 . . . . . . . divide by 12
Now, the angle opposite S can be found to be ...
(4x +5)° = (4·15 +5)° = 65°
Angle S is the supplement of this:
S = 180° -65°
S = 115°
The mean of 50 observations was 250. Later it was found that the number 152 was wrongly copied as 102 for the computation of mean. Find the correct mean.
Answers
Answer:
[tex](250*50-102)+152[\tex]
The correct mean of the 50 observations is 249.96.
To find the correct mean, we need to adjust the value that was wrongly copied. The difference between 152 and 102 is 50, so the corrected total of the 50 observations would be:
Corrected total = (original total - 102) + 152
= [tex](250*50-102)+152[/tex]
= [tex]12498[/tex]
Therefore, the correct mean of the 50 observations is:
Correct mean = Corrected total / Number of observations
= [tex]12498 / 50[/tex]
= 249.96
Hence, the correct mean of the 50 observations is 249.96.
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it is known that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75 % of the colege students will take more than how many minutes when trying to find a parking spot in the library parking lot? O A. 32 minutes B. 42 minutes C. 28 minutes O D. 3.4 minutes
Answers
75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.
What is experimental probability?Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such tests are unpredictable. The chance of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times.
Given that, mean of 3.5 minutes and a standard deviation of 1 minute.
Now, for 75% we have:
P(X > x) = 0.75
The z-score is given by:
0.75 = (X - μ) / σ
Substituting the formula we have:
0.75 = (X - 3.5) / 1
0.75 = X - 3.5
X = 0.75 + 3.5 = 4.25.
Hence, 75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.
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MULTIVARIATE STATISTICS
(a) What are the two ways in which the exploratory factor
analysis (EFA) can be useful?
(b) Differentiate between principal component method
and factor analysis
Answers
(a) The exploratory factor analysis (EFA) can be useful in two ways: Dimensional Reduction: The dimensionality of a set of data can be reduced by exploratory factor analysis. Rather than dealing with several variables, it identifies the basic factors that describe the data set. This can be achieved by extracting factor information that shows the covariance structure of the variables that underlie the observations. Investigation of latent variables: Exploratory factor analysis can be used to determine whether an underlying dimension, such as depression or anxiety, underlies a collection of observable variables, such as feelings of depression, nervousness, or irritability. Latent variables are those that cannot be observed directly. (b) Factor analysis and principal component analysis are two techniques for data reduction that are frequently confused. The principal component analysis, on the other hand, is a technique that creates uncorrelated variables to replace the original variables. It can be viewed as a special case of factor analysis in which all of the extracted factors are used. It includes the raw data's total variance, which is defined by a few components. Principal component analysis is a method of data reduction that extracts uncorrelated factors from the original variables. The correlation structure of the original variables is utilized in factor analysis to define the underlying factors.
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In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was 300 grams
and mass was decreasing by 6% per day. Determine the mass of the radioactive
sample at the beginning of the 16th day of the experiment. Round to the nearest tenth
(if necessary).
Answers
Answer:
To solve this problem, we can use the formula for exponential decay:
m = m0(1 - r)^t
where:
m0 = initial mass (300 grams)
r = decay rate (6% per day, or 0.06)
t = time in days
We want to find the mass at the beginning of the 16th day, so t = 15:
m = 300(1 - 0.06)^15
m ≈ 107.4
Therefore, the mass of the radioactive sample at the beginning of the 16th day of the experiment is approximately 107.4 grams.
Urgent help is needed
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The volume of the hemisphere with diameter 9 is approximately 76.0435 cubic units.
What is hemisphere ?
A hemisphere is a three-dimensional geometric shape that consists of half of a sphere. It is formed by slicing a sphere into two equal parts along a plane that passes through its center. The term "hemisphere" comes from the Greek words "hemi," meaning half, and "sphaira," meaning sphere.
A hemisphere has a curved surface that is a portion of a sphere's surface, as well as a flat circular base that is formed by the plane of the cut. The diameter of the base is equal to the diameter of the original sphere, and the radius is half of the diameter.
To find the volume of the hemisphere, we first need to know its formula. A hemisphere is half of a sphere, so its volume is half of the volume of a sphere with the same radius.
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume and r is the radius.
Since the hemisphere has diameter 9, its radius is half of the diameter, which is:
r = 9/2 = 4.5
Substituting the value of r in the formula for the volume of a sphere, we get:
V = (4/3)π(4.5)³
V = (4/3)π(91.125)
V = 152.087
Since the hemisphere is half of a sphere with radius 4.5, its volume is half of the volume of that sphere, which is:
V_hemisphere = (1/2)V_sphere
V_hemisphere = (1/2)(4/3)π(4.5)³
V_hemisphere = 76.0435
Therefore, the volume of the hemisphere with diameter 9 is approximately 76.0435 cubic units.
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Hello!
Please help me for this geometry problem
I appreciate it!
Answers
Answer:
x = 48
Step-by-step explanation:
given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally, that is
[tex]\frac{x}{18}[/tex] = [tex]\frac{56}{21}[/tex] ( cross- multiply )
21x = 18 × 56 = 1008 ( divide both sides by 21 )
x = 48
find arc length of the partial circle
Answers
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (8)}{180}\implies s=4\pi[/tex]
There are 2 boys and 2 girls working on an art project. They are sharing 10 ounces of paint equally. How much paint should each child get? show work
Answers
Answer:
2.5 oz each
Step-by-step explanation:
2 boys and 2 girls
10 divided by 2 is 5, 5 is not an even number.
there would be 2 left after our calculation.
meaning that 2 in half's (hence .5) is 4 so each child would get 2.5 oz of paint.
Hope this helps, thanks :)
Answer: 2 1/2
Step-by-step explanation:
The graph plots four equations, A, B, C, and D:
Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7.
Which pair of equations has (4, 8) as its solution?
Equation A and Equation C
Equation B and Equation C
Equation C and Equation D
Equation B and Equation D
(It is not option D or A)
Answers
Answer: To find the equation that passes through (4, 8), we need to check which equation contains that point.
Line A has an equation of y = (2/5)x + (194/5). Plugging in x = 4, we get y = (2/5)(4) + (194/5) = 198/5, which is not equal to 8.
Line B has an equation of y = (-5/5)x + 30. Plugging in x = 4, we get y = (-5/5)(4) + 30 = 26, which is not equal to 8.
Line C has an equation of y = (13/13)x - 7. Plugging in x = 4, we get y = (13/13)(4) - 7 = -3, which is not equal to 8.
Line D has an equation of y = (-27/7)x + (491/7). Plugging in x = 4, we get y = (-27/7)(4) + (491/7) = 377/7, which is not equal to 8.
Therefore, none of the given equations has (4, 8) as its solution.
Step-by-step explanation:
One pump can fill a swimming pool in 4 hours. A second pump can fill the pool in 6 hours. If the pool starts empty, what part of the pool will be filled in each situation? The first pump works for 2 hours and the second pump works for 3 hours.
Answers
Answer:
1/2 of the pool is filled, and in the second situation, the entire pool is filled.
Step-by-step explanation:
Let's start by finding the hourly filling rate of each pump. The first pump can fill the pool in 4 hours, so its hourly rate is 1/4 of the pool. The second pump can fill the pool in 6 hours, so its hourly rate is 1/6 of the pool.
For the first situation, the first pump works for 2 hours, so it fills 2/4 or 1/2 of the pool. The second pump does not work in this situation, so it fills 0 of the pool. Therefore, the total amount of the pool filled is 1/2.
For the second situation, the first pump works for 2 hours and fills 1/2 of the pool. The second pump works for 3 hours and fills 3/6 or 1/2 of the pool. Therefore, the total amount of the pool filled is 1/2 + 1/2 = 1.
So, in the first situation, 1/2 of the pool is filled, and in the second situation, the entire pool is filled.
Mike's Bakery recently spent a total of $392 on new equipment, and their average hourly operating costs are $9. Their average hourly receipts are $10. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?
Answers
For Mike's Bakery the total expenses will be $3528 and the total receipts will be $3920 and it will take 392 hours.
Let number of hours the bakery needs to operate in order to make back the amount it invested in equipment be = "h".
To find "h", we need to find the profit per hour,
The profit per hour is = difference between hourly receipts and hourly operating costs;
Profit per hour = Hourly receipts - Hourly operating costs
Profit per hour = $10 - $9
Profit per hour = $1
The total profit required to make back the $392 investment is = $392,
We know that,
⇒ Total profit = (Profit per hour) × (Number of hours)
⇒ $392 = $1 × h
⇒ h = $392/$1
⇒ h = 392
So, bakery needs to operate for 392 hours to make back the amount it invested in equipment.
To calculate the total expenses and receipts, we can use the following formulas:
⇒ Total expenses = (Operating costs) × (Number of hours)
⇒ Total expenses = $9 × 392
⇒ Total expenses = $3528
⇒ Total receipts = (Hourly receipts) × (Number of hours)
⇒ Total receipts = $10 × 392
⇒ Total receipts = $3920
Therefore, the total expenses is $3528 and total receipts is $3920.
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Find the sum or type
"impossible"
[3 -8] +[4 -5 -6]
Answers
These matrices have various dimensions, making it difficult to determine their total. Because of this, the sum of these matrices is either undefinable or unattainable.
Due to their various dimensions, it is difficult to find the sum of these matrices.
One row and three columns make up the second matrix, whereas two rows and one column make up the first matrix. Two matrices can only be added if they share the same dimensions. To be more precise, two matrices can only be added if they have the same number of rows and columns.
The matrices [3 -8] and [4 -5 -6] cannot be added together since they have different numbers of rows and columns. Because of this, the sum of these matrices is either undefinable or unattainable.
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Trapezoids 1 and 2 are similar. The perimeter of Trapezoid 1 is 240 centimeters and the perimeter of Trapezoid 2 is 150 centimeters. What is the ratio x:y ?
Answers
The answer of the given question based on perimeter of trapezoid the ratio will be x:y is 8:5.
What is Trapezoid?A trapezoid is quadrilateral with at least one pair of the parallel sides. The parallel sides are called bases of trapezoid, and non-parallel sides are called legs.
Let's denote the lengths of the four sides of Trapezoid 1 as a, b, c, and d, and the lengths of the corresponding sides of Trapezoid 2 as m, n, p, and q, respectively. Then we have:
a + b + c + d = 240 (perimeter of Trapezoid 1)
m + n + p + q = 150 (perimeter of Trapezoid 2)
Since Trapezoid 1 and Trapezoid 2 are similar, we can write:
m = ax
n = bx
p = cy
q = dy
where x and y are the ratios of the longer and shorter bases of Trapezoid 1 to Trapezoid 2, respectively.
Substituting these expressions into the equations for the perimeters of the trapezoids, we get:
a(x+y) + b(x+y) + c(x+y) + d(x+y) = 240
(ax+bx+cy+dy) = 150
Simplifying these equations, we get:
(a+b+c+d)(x+y) = 240
(a+b+c+d)(x+y)(x/y) = 150
by Dividing second equation by first, we will get:
x/y = 240/150 = 8/5
Therefore, the ratio x:y is 8:5.
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What is the advantage
of a two-way relative frequency table for
showing relationships between sets of
paired data?
Answers
A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.
A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.
The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:
Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.
Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.
Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.
In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.
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The first equation in the system models the height, h, of a falling volleyball as a function of time, t. The second equation models the height, h, of the hands of a player jumping up to spike the ball as a function of time, t. Which statement describes the situation modeled by this system?
StartLayout Enlarged Left-Brace 1st Row h = 14 minus 16 t squared 2nd Row h = 7 + 24 t minus 16 t squared EndLayout
The volleyball is 7 feet above the ground at the instant the player begins her jump.
The volleyball is 14 feet above the ground at the instant the player begins her jump.
The volleyball is 16 feet above the ground at the instant the player begins her jump.
The volleyball is 24 feet above the ground at the instant the player begins her jump.
Answers
Answer:
The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.
B is correct.
Step-by-step explanation:
Here we have two situation of system of models.
[tex]\text{The height (h) of a falling volleyball as function of time (t):h}(t)=14-16t^2[/tex]
[tex]\text{The height (h) of the hands of a player as function of time (t):h}(t)=7-24t-16t^2[/tex]
We need to find the height of ball above the ground at the instant the player begins jump.
At t=0, player begins jump.
We put t=0 into [tex]h(t)=7+24t-16t^2[/tex]
Height of player hand at t=0 , h=7 feet.
Now we will set t=0 for first model.
[tex]h(0)=14-16\times0^2 \ = > 14[/tex]
Thus, The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.
B is correct.
Answer: B
Step-by-step explanation:
EDGE 2023
Find the height of a cone with a radius of 12 inches and a volume of 1,281.12 cubic inches.
Answers
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ V=1281.12 \end{cases} \implies 1281.12=\cfrac{\pi (12)^2 h}{3} \\\\\\ (3)(1281.12)=144\pi h\implies \cfrac{(3)(1281.12)}{144\pi }=h\implies 8.50\approx h[/tex]
Points C and D are plotted on a graph.
C has coordinates (1, -5) and D has coordinates (6, 4)
Calculate the length of the line segment CD.
Leave your answer to 2 decimal places.
Answers
Answer:
The length of line segment CD is 10.3 units (rounded to 2 decimal places).
Step-by-step explanation:
To find the length of line segment CD, we need to use the distance formula, which is:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Here, (x1, y1) = (1, -5) and (x2, y2) = (6, 4).
So, substituting these values in the distance formula, we get:
Distance = √[(6 - 1)^2 + (4 - (-5))^2]
= √[5^2 + 9^2]
= √(25 + 81)
= √106
≈ 10.3 (rounded to 2 decimal places)
Therefore, the length of line segment CD is 10.3 units (rounded to 2 decimal places).
Hope this helps!