Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists [tex]$$23.6 cm^3[/tex]
How to estimate the volume of metal in the hex nut?Diameter of the cylinder be d = 1.6 cm
Apothem of the hexagon be a = 2 cm
Thickness of the steel hex nut be t = 2 cm
Volume of the prism be [tex]V_p[/tex]
Volume of the cylinder be [tex]V_c[/tex]
Volume of metal in the hex nut,
[tex]$$V = V_p - V_c[/tex]
To estimate the volume of a prism,
[tex]$$V_p = A_b h[/tex]
Ab = n L a / 2
Number of the sides, n = 6
The side of the hexagon be L
Height of the prism, h = t = 2 cm
Central angle in the hexagon, A = 360°/n
A = 360°/6 = 60°
[tex]$tan (\frac{A}{2} )=(\frac{L/2}{a})[/tex]
simplifying the value of L, we get
[tex]$tan (\frac{60}{2} )=(\frac{L/2}{2})[/tex]
[tex]$tan 30}=(\frac{L/2}{2})[/tex]
[tex]$tan (\frac{\sqrt{3}}{3} )=(\frac{L/2}{2})[/tex]
Solving for L/2:
[tex]$\frac{2 \sqrt{3}}{3} =\frac{L}{2}[/tex]
Solving the value of L, we get
[tex]$2\frac{2 \sqrt{3}}{3} =L[/tex]
[tex]$\frac{4 \sqrt{3}}{3} =L[/tex]
[tex]$L=4 \sqrt{3}/3 cm[/tex]
Ab = n L a / 2
Substitute the values in the above equation, we get
[tex]$A_b=\frac{6 (4 \sqrt{3}/3)(2)}{2}[/tex]
[tex]$$A_b=24 \sqrt{3}/3 $$cm^2[/tex]
[tex]$A_b=8 \sqrt{3} cm^2[/tex]
[tex]V_p = A_b h[/tex]
substitute the values in the above equation, we get
[tex]$V_p=(8 \sqrt{3})(2)[/tex]
[tex]$V_p=16 \sqrt{3} cm^3[/tex]
[tex]$$V_p=16 (1.732) cm^3[/tex]
[tex]$$V_p=27.712 cm^3[/tex]
To estimate the volume of cylinder,
[tex]$V_c[/tex] = (π[tex]d^2[/tex]/4) h
Here, π = 3.14 and d = 1.6 cm
Height of the cylinder, h = t = 2 cm
substitute the values in the above equation, we get
[tex]$V_c=[3.14 (1.6) / 4] (2)[/tex]
[tex]$V_c=[3.14 (2.56) / 4] (2)[/tex]
[tex]$V_c=(2.0096) (2)[/tex]
[tex]$$V_c=4.019 cm^3[/tex]
Substitute the values in the equation, we get
[tex]$$V=V_p-V_c[/tex]
[tex]$$V=27.712 - 4.019[/tex]
[tex]$$V=23.693 cm^3[/tex]
[tex]$$V=23.6 cm^3[/tex]
Therefore, the volume of metal in the hex nut, to the nearest tenth exists [tex]$$23.6 cm^3[/tex].
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Which table represents a function?
Answer:
choice d
Step-by-step explanation:
I hand this question
The fact family model represents the relationship between the numbers 8, 7, and 15.
A triangle. 15 is in the top corner. 8 is in the bottom left corner. 7 is in the bottom right corner.
How do the numbers compare?
15 is 7 more than 8.
15 is 8 less than 7.
7 is 15 less than 8.
7 is 8 more than 15.
The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The fact family (number family) is a group of equations that derive from a set of numbers.
Fact Family Triangle are used for Addition, Subtraction, Multiplication and Division
The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.
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3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____. 78 6 -6
The supplied lines' point of intersection has the x coordinate is 6.
What is coordinate geometry?A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
The x coordinate of the location where the ensuing lines intersect must be chosen.
3x + 5y = 78 ...........................(1)
2x - y = 0 ...............................(2)
The given system of equations must be solved in order to determine the x coordinate of the site of intersection.
Equation (ii) provides us with
2x = y
y = 2x ........................(3)
Equation I yields the result when the value of y from equation (iii) is substituted.
3x + 5(2x) = 78
3x + 10x = 78
13x = 78
x = 78/13
x = 6.
As a result, the supplied lines' point of intersection has the x coordinate 6.
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I understand that the question you are looking is :
3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____.
A. 7
B.8
C. 6
D. -6
a man divides ₹90,000 among wife son and daughter in the ratio 1/3:1/4:1/6 . find amount received them
The mean salary at a local industrial plant is $29,300 with a standard deviation of $5400. The median salary is $24,500 and the 63rd percentile is $29,600.
Step 1 of 5: Based on the given information, determine if the following statement is true or false.
Approximately 63% of the salaries are less than or equal to $29,600
Step 2 of 5: Based on the given information, determine if the following statement is true or false.
Joe's salary of $39,320 is 1.80 standard deviations above the mean.
Step 3 of 5: Based on the given information, determine if the following statement is true or false.
The percentile rank of $25,000 is 50.
Step 4 of 5: Based on the given information, determine if the following statement is true or false.
Approximately 13% of the salaries are between $29,300 and $29,600.
Step 5 of 5: If Tom's salary has a z-score of 0.5, how much does he earn (in dollars)?
The true and false statement about the mean salary is illustrated below.
How to illustrate the information?The true false statement about the mean salary include:
Approximately 63% of the salaries are less than or equal to $29,600Joe's salary of $39,320 is 1.80 standard deviations above the mean.The percentile rank of $25,000 is 50.Approximately 13% of the salaries are between $29,300 and $29,600.When Tom's salary has a z-score of 0.5, the amount that he earns will be:
0.5 = (x - 29300)/5400
0.5 × 5400 = x - 29300
2700 = x - 29300
x = 29300 + 2700.
x = 32000
The amount he earns is 32000.
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A researcher reports that her obtained chi square of -17.56 is significant because it exceeds the critical chi square of -3.841 for an alpha of .05 with 2 degrees of freedom. What mistake has been made
The mistake that the researcher made is that; neither critical nor obtained Chi squares can have negative values
How to check the chi - square statistic?
A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables.
The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.
Now, Chi square (χ²) is the sum of a set of squared values, and as such it can never be negative. The minimum chi - squared value would be obtained if each Z = 0 so that χ² would also be 0. There is no upper limit to the χ² value. Similarly, the critical chi square cannot also be negative.
Thus, we can conclude that the mistake that the researcher made is that neither critical nor obtained Chi squares can have negative values
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Assume that adults have iq scores that are normally distributed with a mean of μ=100 and a standard deviation σ=15. find the probability that a randomly selected adult has an iq less than 130
The probability that a randomly selected adult has an IQ less than 130 is 0.9332
For given question,
We have been given adults IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15.
We need to find the probability that a randomly selected adult has an IQ less than 130
Sketch the curve.
The probability that X < 130 is equal to the area under the curve which is less than X = 130
Since μ = 100 and σ = 15 we have:
⇒ P ( X < 130 ) = P ( X- μ < 130 - 100 )
⇒ P ( X < 130 ) = P((X− μ)/ σ < 130 - 100/20 )
Since (X-μ)/σ = Z and (130 - 100)/20 = 1.5 we have:
P (X < 130) = P (Z < 1.5)
Now, we use the standard normal table to conclude that:
P (Z < 1.5) = 0.9332
Therefore, the probability that a randomly selected adult has an IQ less than 130 is 0.9332
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An athlete trains for 80 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 400min.
80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.
Find the required equation for the given question:Here in the question it is given that,
Athlete trains for 80 min each day,that is each day the athlete spends 80 min.
We have to assume the variable d the number of days the athlete spends training.Finally we have to find an equation that relates the number of days d that the athlete spends training when the athlete trains for 400 min.So we can write that,
400 min is the time spent by the athlete
400 min = number of days × time spent by the athlete in one day
400 min = d × 80
⇒ 80d = 400
Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.
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What can you say about the characteristics of a linear funct i on that has a slope of 0? write a careful explanation of your answer. you may provide a mathematical example if you wish to help you illustrate your points, but you must also use sentenc es as a part of a written description.
The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b
How to determine the characteristics of a linear function that has a slope of 0?A linear equation is given as:
y = mx + b
Where m represents the slope of the linear equation.
When the value of is 0
i.e. m = 0, the equation becomes
y = 0 *x + b
Evaluate
y= b
The above equation is a horizontal line that passes through the y-axis at y= b
Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b
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A certain disease has an incidence rate of 0.1%. If the false negative rate is 4% and the false positive rate is
2%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
Answer:
probability of the personal information on the direction of the personal information to my house
Please help
Thank you!
The given transformation is a reflection across the y-axis that changes the coordinates EFGH into E'F'G'H' as follows:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
What is the transformation rule for reflection?The transformation rules for reflection are:
Reflection at y-axis: y = f(-x);
Reflection at x-axis: y = -f(x);
Calculation:The given polygon has four vertices EFGH.
Their coordinates are:
E(-4, -1), F(-2, -1), G(-1, -2), and H(-1, -4)
When the transformation rule: reflection across the y-axis is applied, the coordinates become:
y = f(-x); rule
For E(-4, -1), x-coordinate is -4. So, -(-4) = 4
⇒ E'(4, -1)
For F(-2, -1), x-coordinate is -2. So, -(-2) = 2
⇒ F'(2, -1)
For G(-1, -2), x-coordinate is -1. So, -(-1) = 1
⇒ G'(1, -2)
For H(-1, -4), x-coordinate is -1. So, -(-1) = 1
⇒ H'(1, -4)
Thus, the transformed coordinates are:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
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If two angles are right angles, then they are adjacent.
True
False
Answer:
False
Step-by-step explanation:
If two angles are right angles, then they are congruent.
Very much appreciated skin!!!
Answer:
6
Step-by-step explanation:
Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.
[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]
The length of AC is simply x, therefore 6
Malik randomly picked two numbers from 1 to 9 (including 1 and 9). the same number could be picked more than once. the first of the two numbers he picks is odd and less than 5. what is the probability that the sum of the two numbers malik picks is less than 5, given that the first number is odd and less than 5?
The probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5 is 0.0494.
What is a probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.
Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Probability of an event P(E) = Number of favourable outcomes/Total number of outcomes.
Calculation for the given condition;
Either 1 or 3 must be present if a given integer is odd and smaller than 5.
The likelihood that it was picked from a set of nine numbers is (2/9).
The probability that the first integer is 1 is 50/50.
If it is and their combined number is less to 5, the second number will either be 1, 2, or 3.
The likelihood that it was picked out of the nine numbers is (3/9).
Additionally, there is a 50/50 probability that the first digit will be 3.
A second number is 1 if it is and the sum would be less than 5.
It was selected with a 1 in 9 chance of being one of the other 8 numbers.
The total probability is;
= (2/9) times [ (0.5 x 3/9) + (0.5 x 1/9) ]
= (2/9) times [ (1.5/9) + (0.5/9) ]
= (2/9) times [ 2/9 ] = 4/81
= 0.0494
Therefore, the probability that the sum of the two numbers malik picks is less than 5 is 0.0494.
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Answer:
See image
Step-by-step explanation:
Plato
is the identity for addition for rational number a) 1 b) 0 c) -1 d) 1/2
The identity for addition for rational numbers is zero which is the option b.
Given addition of rational numbers.
We are required to find the identity for the addition of rational numbers.
Rational numbers are those numbers which can be written in the form of p/q and q cannot be equal to zero because if q is equal to zero the whole fraction will become infinity. The numbers whih cannot be written as p/q are known as irrational numbers.
From the all option zero is the identity for addition for rational numbers. This means if a is a rational number. Then a+0=0+a=a.
Hence the identity for addition for rational numbers is zero which is the option b.
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(08.05 MC)The following box plot shows the number of books sold each day at a bookstore for 40 days. How many days did the bookstore sell 2 to 12 books?
A box plot is drawn with end points at 0 and 16. The box extends from 2 to 12 and a vertical line is drawn inside the box at 7
2
4
10
20
Considering the given box-and-whisker plot, it is found that the bookstore sold between 2 to 12 books in 20 days.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.From the plot given in this problem, the have that:
The 25th percentile is of 2.The median is of 7.The 75th percentile is of 12.This means that the percentage of days in which between 2 to 12 books were sold is:
P = 75 - 25 = 50%.
Hence, out of 40 days, the amount of days is:
0.5 x 40 = 20 days.
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A parabola opens up and passes through (-4, 2) and (6, -3). How do you know that (-4, 2) is not the vertex
Answer:
Step-by-step explanation:
The minimum is at the vertex of this parabola because it opens up.
Now if (-4, 2) is the minimum then all the y values on the parabola must be > 2,
But we are given that y = -3 is on the graph ( the point (6,-3) - that is y < 2 here,
Therefore (-4, 2) cannot be the vertex .
Find the mean 35 40 12 16 25 10
Answer: Mean = 23
Step-by-step explanation:
Given information:
35, 40, 12, 16, 25, 10
Given formula:
[tex]Mean~=~\frac{Sum~of~terms}{Number~of~terms}[/tex]
Substitute values into the formula
[tex]Mean~=~\frac{35~+~40~+~12~+~16~+~25~+~10}{6}[/tex]
Combine like terms
[tex]Mean~=~\frac{75~+~28~+~35}{6}[/tex]
[tex]Mean~=~\frac{103~+~35}{6}[/tex]
[tex]Mean~=~\frac{138}{6}[/tex]
Simplify the fraction
[tex]\Large\boxed{Mean=23}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
I don't understand the question
Answer: 7 pigeons sitting on the branches, 5 pigeons under the tree
=12 in total
Step-by-step explanation:
Upper branch has x pigeons, lower has y.
Top branch said: "If one of you flies up to us our number will be double yours":
Well, if one of the bottom branch flies up, the top branch will have x+1 birds and the bottom will have (y−1). The top will have double the bottom, so:
x+1=2(y−1)
Top branch said: "If one of us flies down to you, our numbers will be equal":
Now, the top branch will have x−1 and the bottom y+1. The numbers should be equal:
x−1=y+1
Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.
x2 = 4y
x2 = –6y
y2 = x
y2 = 10x
y2 = –3x
y2 = 5x
Parabolas could Lauren be describing are:
c) y2 = x
d) y2 = 10x
F) y2 = 5x
What exactly is a parabolic curve?The intersection of a cone with a plane that is parallel to the side of the cone results in the formation of a parabola, which is a symmetrical open plane curve. Under the influence of gravity, the route taken by a projectile takes the form of a curve similar to this one.
In the question that is presented to her, Lauren gives an example of a parabola that has a positive non-zero coordinate value on focus
Generally, the equation for focus is mathematically given as
y=a(x-h)^2+k
In conclusion
c) y2 = xd) y2 = 10xF) y2 = 5xRead more about Parabola
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In what percentage of such groups (of 400) would 150 or fewer improve? round your answer to one decimal place
The percentage of such groups (of 400) would 150 or fewer improve is 16.60.
The percentage is a relative value indicating the hundredth component of any quantity. One percent (symbolized 1%) is the 100th element; as a result, 100 percent represents the entirety and 2 hundred percent specifies twice the given amount. percentage.
As finding 10% of a variety of means to divide through 10, it is not unusual to assume that to locate 20% of a variety you must divide through 20 and so on. Take into account, to discover 10% of the number of manner dividing through 10 because 10 is going into one hundred ten times. consequently, to discover 20% of various, divide via five due to the fact 20 is going into 100 five times.
In arithmetic, a percentage is a number or ratio expressed as a fraction of one hundred. it's far frequently denoted by the usage of the percentage signal, "%", although the abbreviations "pct.", "pct" and on occasion "computer" also are used. A percent is a dimensionless wide variety; it has no unit of size.
In what percentage of such groups (of 400) would
150
fewer improve?
i. e. PC X ≤ 150)
By using
-continuity correction we have to find.
PCX 150.5)= P "X-M1.6.150.5-160°
9.8
= p[ 2 < -0.97
By using the standard Normal table we get,
0.1660
P(X ≤150)
= 0. 1660 = 16.60 (
16.60 percent of such groups (of 400) would 150
fever improve.
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Mrs. Bailey has equal numbers of nickels and quarters but the value of the quarters is $1.80 more than the value of the nickels. What is the total value of all coins together in dollars and cents
Total value of all coins together is $2.7
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
1 Nickel = $0.05 and 1 quarter = $0.25.
Let number of nickels and number of quarter be x.
According to the situation
x.(0.25) = $1.80 + x.($0.05)
x(0.25 - 0.05) = $1.80
x (0.2) = $1.80
x = $1.80/0.2
x = 9 coins
Therefore total value of the currency is 9(0.05 + $0.25) = 9 (0.3) = $2.7
Thus total value of all coins together is $2.7.
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please help 20 points!!!!!
hree students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. The samples are shown in the table. (a)Fill in the sample means in the table. Do not round your answers. Sample Backpack weight (in pounds) Sample mean 1 3, 7, 8, 3, 7, 9, 6, 8 2 8, 6, 4, 7, 9, 4, 6, 7 3 9, 4, 5, 8, 7, 5, 9, 6
(b)Use the table to calculate the range of the sample means. Rangeofsamplemeans:
(c)The students are going to use the sample means to estimate the mean backpack weight of their schoolmates. Select all the true statements below.
A single sample mean will tend to be a worse estimate than the mean of the sample means.
The mean of the sample means will tend to be a worse estimate than a single sample mean.
The closer the range of the sample means is to 0, the less confident they can be in their estimate.
The farther the range of the sample means is from 0, the less confident they can be in their estimate.
Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,
(a) The sample means of the backpacks are: 6.375,6.375,6.625
(b) Range of sample means: 0.25
(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.
For the first sample, mean= 6.375
For the second sample, mean= 6.375
For the third sample, mean= 6.625
Range of sample means=Maximum Mean- Minimum Mean
= 6.625 - 6.375
= 0.25
The students will estimate the average backpack weight of their classmates using sample means, the true statement is:
The closer the range of the sample means is to 0, the more confident they can be in their estimate.
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please help meeeeee please please please
Answer:
quadratic: -3x²linear: 0x or "none"constant: 1Step-by-step explanation:
This is a question about naming parts of a polynomial. The attached image has more on the subject.
DegreeThe word "degree" refers to the number of times a variable is a factor in a term. When there is only one variable, the degree of the term is the exponent of the variable. A missing exponent is understood to be 1. A missing variable is understood to have a degree of 0.
When there are two or more variables, the degree of the term is the sum of their exponents.
In some cases, we're only interested in the degree associated with a particular variable. For example, 7x²y³ is a 5th-degree term that is 2nd degree in x and 3rd degree in y.
Quadratic termA "quadratic" term is one that has degree 2, or one in which the variable of interest has degree 2.
In the given function definition, the term -3x² is the quadratic term.
Linear termA "linear" term is one that has degree 1.
In the given function definition, there is no linear term.
If you must identify one, it would be 0x, a degree-1 term with a coefficient of 0.
Constant termA "constant" term is one that has no variables, or no variables of interest. It has degree zero.
For example, in the expression x² +2ax +a², when we are concerned with the variable x, the a² term is called the "constant" term because it does not contain the variable x. The same expression could be considered as a quadratic in 'a', in which case the x² term would be the "constant term."
In the given function definition, the term 1 is the constant term.
The SkyWheel has 42 glass enclosed gondolas. What is the measure of each central angle between gondola cars, to the nearest hundredth degree? (just write the numerical answer, no units) (5 points)
Answer:
8.57.
Step-by-step explanation:
that would be 360/42
= 8.5714
how do i solve this by factors
f(x) = (x+6) (x+4)
Answer:
[tex]x^{2} +10x+24[/tex]
Step-by-step explanation:
Answer:
=(x+1)^2-25
Step-by-step explanation:
=x(x−4)+6(x−4)
=x^2−4x+6x−24
=x^2+2x−24
=x^2+2x+1−25
=(x+1)^2-25
Two LORAN radio stations A and B are 160 kilometers apart and send a simultaneous radio signal to a ship.
The signal from B arrives 0.0003 seconds before the signal from A. If the signal travels 300,000 kilometers per second, find the equation of the hyperbola on which the ship is positioned. Use a coordinate system where the origin is the midpoint between the stations, and the stations lie on the x-axis.
The equation of the hyperbola on which the ship is positioned is x²/2025-y²/4375=1
Given that radio stations, A and B are 160 kilometers apart and the signal from B arrives 0.0003 seconds before the signal from A and the signal travels 300,000 kilometers per second.
The distance between radio station A and B are d=160 km.
The time is t=0.0003s.
The speed of the signal travel is v=300000 km/s.
Consider both radio stations A and B lie at foci on the x-axis.
The origin lies at the midpoint between the stations.
The distance of one of the stations from the origin is,
c=d/2
c=160km/2
c=80km
The centre of the hyperbola lies at (0,0), so both stations lie at coordinates points of (-80,0) and (80,0).
The expression for the difference in distance is,
I=vt
I=300000×0.0003
I=90km
The semi-major axis of the hyperbola is,
a=I/2
a=90km/2
a=45km
The expression for the semi-minor axis of the hyperbola is,
b²=c²-a²
b²=(80)²-(45)²
b²=6400-2025
b²=4375
The expression for the hyperbola on which the ship is positioned,
x²/a²-y²/b²=1
x²/(45)²-y²/4375=1
x²/2025-y²/4375=1
Hence, the equation of hyperbola on which the ship is positioned for radio stations, A and B are 160 kilometers apart and signal from B arrives 0.0003 seconds before the signal from A is x²/2025-y²/4375=1.
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A juggler is performing her act using several balls. she throws the balls up at an initial height of 4 feet, with a speed of 15 feet per second. this can be represented by the function h(t) = −16t2 15t 4. if the juggler doesn't catch one of the balls, about how long does it take the ball to hit the floor? 7.52 seconds 1.15 seconds 0.47 seconds 0.22 seconds
The ball will take 1.15 seconds to hit the floor.
It is given that,
A juggler is performing her act using several balls. The height as a function of time is given by :
[tex]h(t) =-16t^{2} + vt +s[/tex].............(1)
where,
v is the speed of the ball
s is initial height
t is time taken
Putting h(t) = 0 and solving equation (1)
[tex]-16t^{2} + vt +s = 0[/tex]
[tex]-16t^{2} + 15t +4 = 0[/tex]
On solving above equation using graphing calculator and solving for t we get, t = 1.154 second.
Hence, the correct option is (b) " 1.15 seconds ".
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Find the surface area of the figure.
8 in.
8 in.
12 in.
12 in.
8 in.
10 in.
SA = [? ]in.²
10 in. SA
Enter P
I
The surface area of the rectangular prism shown in the figure is 512 in²
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Surface area = 2(8 * 8) + 2(12 * 8) + 2(8 * 12) = 512 in²
The surface area of the rectangular prism shown in the figure is 512 in²
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(02.02)A shape is shown on the graph:
24
-5 -4 -3 -2 -1
2-
C
Á
B
A
0
0
-24
-3-
-4-
-5-
-6-
-8-
-2
Which of the following is a reflection of the shape?
Based on the shape shown on the graph, the reflection of the shape would be b) A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair 2, negative 2 and 4, negative 2, and 2, negative 6.
What shape is the reflection?The coordinate grid that the shape would be reflected across is the y axis to get a reflection in the negative side of the x axis.
The first reflection would be of the point that is (2,2). It would be reflected to become (-2, 2).
The second reflection would be of point (2, 6) which would then be reflected to become (-2, 6).
Finally the third point would be of point (4, 2) which would then become (-4, 2).
In conclusion, the reflection was across the y axis.
Options include:
a) A coordinate grid is shown from positive 8 to negative 8 on the axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair negative 2, 2 and negative 4, 2 and negative 4, 6.b) A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair 2, negative 2 and 4, negative 2, and 2, negative 6.c) A coordinate grid is shown from positive 8 to negative 8 on the axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair negative 2, 2 and negative 2, 4 and negative 6, 2.d) A coordinate grid is shown from positive 8 to negative 8 on the axis and from positive 8 to negative 8 on the y-axis. A triangle is shown on ordered pair 2, negative 2 and 2, negative 4 and 6, negative 2.Find out more on reflection at https://brainly.com/question/1908648
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