A cylindrical tank has a diameter of 30m and height 20m.
a) Find its volume in m³, correct to two decimal places.
b) What is the capacity of the tank in litres?
Step-by-step explanation:
d = 30m, so r = 15m
h = 20m
We know,
V = πr^2h= (22×15×15×20)/7 [Taking π = 22/7]
= 14142.86m^3
= 14142875.14 litres
What is the slope of the line that passes through the points (-4, -6) and (1, -6)? Write your answer in simplest form
The slope of the line that passes through the points (-4, -6) and (1, -6) is zero and hence the line is parallel to the x-axis.
What is slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is its graph or rate of change is large.
We know slope(m) = (y₂ - y₁)/(x₂ - x₁).
Therefore, The slope of the line that passes through the points (-4, -6) and (1, -6) is,
m = (- 6 + 6)/(- 4 - 1).
m = - 0/5.
m = 0.
As the slope is equal to zero the line is parallel to the x-axis.
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PLEASE HELP I WILL GIVE BRIANLI EST
The number of students at the open house is B. 468.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We know if a and b are two quantities in a total quantity (ax + bx) the amount of a single quantity can be obtained by [a/(a+b)]× (ax + bx).
Given, The ratio of students to adults at the open house is 9 : 7 and the total number of students and adults at that place is 832.
Therefore,
The number of students is,
= (9/9+7)×832.
= (9/16)×832.
= 9×52.
= 468.
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if a Relation is a Function
in the
1) ((−1, 8), (0, 15), (1, –4), (2, 0)) 2) {(-5, 2), (5, 2), (0, -3), (3,-8)) 3) ((-2, 7), (6, 2), (−2, −3), (0, 9))
is a function
because there is not any
Points which have the
X-Coordinate and differen
y-Coordinates.
4) {(7,2), (4,-6), (2,-2). (4,-9)} 5) {(2, 3), (2, 4), (2, 5), (2,6)}
6) {(1,4), (2,4), (3, 4), (4-4)}
1). The relation given; { (−1, 8), (0, 15), (1, –4), (2, 0) } as given is a function.
2). The relation given; { (-5, 2), (5, 2), (0, -3), (3,-8) } as given is a function.
3). The relation given; { (-2, 7), (6, 2), (−2, −3), (0, 9) } as given is not a function.
4). The relation given; { (7,2), (4,-6), (2,-2). (4,-9) } as given is not a function.
5). The relation given; { (2, 3), (2, 4), (2, 5), (2,6) } as given is not a function.
6). The relation given; { (1,4), (2, 4), (3, 4), (4, -4) } as given is a function.
What is a function?It is important to know that a function is a special kind of relation in which case no one input value, x is assigned more than one output value.
On this note, when a relation is such that one of its input values is assigned two or more output values; such relation is not a function.
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shia has 6 new boxes of crayons . each box has 8 crayons he also has 7 crayons from an old box how many crayons does he have
The answer is: 55 crayons.
Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!
HELP ME PLEASE RIGHT NOW ASAP
The representation of the set builder notations are:
{y | 22.3 < y ≤ 77.5}: Set of values above 22.3 that do not exceed 77.5{w | w ∈ Z}: Set of all integers{x | x > -1}: Set of values greater than -2{t | t ∈ Q}: Set of all rational numbersHow to determine what the set builder notations representFrom the question, we have the following parameters that can be used in our computation:
The set builder notations
Solving: set builder notation 1
This is given as
{y | 22.3 < y ≤ 77.5}
The less than (<) operator means that the smallest value of y is greater than 22.3 and the operator ≤ means that the highest is 77.5
Solving: set builder notation 2
This is given as
{w | w ∈ Z}
The notation Z means integers
This means that the set w is the set of all integers
Solving: set builder notation 3
This is given as
{x | x > -1}
The greater than (>) operator means that the smallest value of y is greater than -1
Solving: set builder notation 4
This is given as
{t | t ∈ Q}
The notation Q means rational numbers
This means that the set t is the set of all rational numbers
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
it's none of the above its 27.5
The value of z varies inversely with the value of w. The constant of variation is 2. Which are possible values for z
3
and w? Check all that apply.
Oz=.
z = 1+₁ w = 2/1/201
O z = 2, w = 3
O z=
z = -1/₁w=2
O z
4,
= 1/5, w = 2/1/201
z = 1/2/3₁, w = 2/1/201
Answer:A,C,D
As a result of the inverse relationship between z and w, their product is constant.
What does "inverse connection" actually mean?There is an inverse relationship between two parameters when they are connected, where the value of one parameter tends to decrease as the value of the other parameter increases. It's often described as a "bad friendship" in conversation.
According to the information:z * W is equal to 1.
The statement indicates that the constant's value is 2/3, so:
z * w = 2/3
The result of solving for any of the variables is:
either w = (2/3) / z or z = (2/3) / w
The following values fit that relation:
z w = (2/3) / z
-8/9 (2/3) / (-8/9)
= - (2/3) * (9/8) = -3/4
- 4/9 (2/3) / (-4/9)
= - (2/3) * (9/4) = - 3/2
- 2/9 (2/3) / (-2/9)
= - (2/3) * (9/2) = - 3
2/9 (2/3) / ( 2/9)
= (2/3) * (9/2) = 3
4/9 (2/3) / (4/9)
= (2/3) * (9/4) = 3/2
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The diagonals of a quadrilateral ABCD intersects each other at the point O such that AO/BO=CO/DO.Prove that ABCD is a trapezium.
Answer:
Step-by-step explanation:
To prove that a quadrilateral ABCD is a trapezium when the diagonals intersect at a point O such that AO/BO=CO/DO, we can use the fact that opposite sides of a trapezium are parallel.
First, let's draw a diagram to represent the given information:
[asy]
pair A, B, C, D, O;
A = (0,0);
B = (2,0);
C = (3,2);
D = (1,2);
O = intersection point(A-C, B--D);
draw(A--B--C--D--cycle);
draw(A-C);
draw(B--D);
label("A", A, W);
label("B", B, E);
label("C", C, E);
label("D", D, W);
label("O", O, N);
label("$\theta_1$", (B+O)/2, NE);
label("$\theta_2$", (O+D)/2, NE);
label("$\theta_3$", (O+C)/2, NW);
label("$\theta_4$", (A+O)/2, NW);
[/asy]
Since the diagonals intersect at point O, the angles formed by the diagonals at O are supplementary (that is, they add up to 180 degrees). In other words, we have:
θ1 + θ2 = 180 degrees
θ3 + θ4 = 180 degrees
Since AO/BO=CO/DO, the triangles AOB and COD are similar. This means that the ratios of their sides are equal. We can write this as:
AO/BO = CO/DO
We can also write this as:
AO/DO = CO/BO
Then, since the angles formed by the diagonals at O are supplementary, we have:
θ1 + θ2 = 180 degrees
θ1 + θ4 = 180 degrees
Subtracting these two equations gives us:
θ2 - θ4 = 0
Since the angles are equal, they are also opposite angles of the quadrilateral ABCD. Therefore, the opposite sides of AB and CD are parallel, which means that ABCD is a trapezium.
YZ ≅ VW, WX ≅ UV, and XY ≅ UZ. Complete the proof that △UVZ ≅ △XWY.
Use the drawing tools to form the correct answer on the graph.
Plot function g on the graph.
On solving the provided question, we cans ay that - in given inequality equation to -7 < x < -2; -2 < x < 3
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
-7 < x < -2
-2 < x < 3
and 3 > x > 8
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Round 0.21545977 to the nearest hundredth
Answer:
0.22
Step-by-step explanation:
Since 5 rounds up, it would be 0.22
Answer:
0.22 Is the answer.
I wish you luck on your assignments.
I’ve been stuck on this for about a week, I know it might seem easy but I’m very bad at fractions and my teacher won’t help me
On solving the provided question we can say that - the increased value in fraction will be [tex]3\frac{1}{4}[/tex]
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
we have,
initial = [tex]4\frac{5}{6}[/tex]
increased by = [tex]4\frac{1}{4}[/tex]
son difference is = [tex]3\frac{1}{4}[/tex]
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When fitting a pipe into an existing fitting it allows a diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005" what's the maximum allowable pipe diameter? a. 0.496, b. 0.501, c. 0.499, d. 0.541
Considering that the diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005". the maximum allowable pipe diameter is 0.501''
How to find the maximum allowable pipe thicknessThe maximum allowable pipe diameter is calculated by
finding the total thickness of pipe
= interior diameter + 2 * pipe thickness
= 0.49 + 2 * 0.005
= 0.49 + 0.01
= 0.50
The diameter variance gives the range of the allowable diameter to ± 0.001 for maximum allowable pipe diameter we use + 0.001
hence
= 0.50 + 0.001
= 0.501
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In a village, the cases of a particular infectious
disease have been exponentially decreasing at
a rate of 95% per year since the people started
receiving the vaccine. If there were 200 cases
in the village to start with, predict the number
of cases after 2 years.
First, complete the equation:
Remaining Amount = 200(1-0.95)²
The number remaining in the village is 30.
How many people remain?We have to note that the case in which the population of the community is being reduced because of the fact that the community is being ravaged by disease is a case of a decrease in the population and is a problem of exponential decrease.
Then we would have that;
N =Noe^-rt
N = Number at time t
No = Initial number
r = spread rate
t = time taken
Then;
N = 200e^-0.95 * 2
N = 30
Thus, they would have only 30 people left.
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Mississipi has the lowest income at 40.6 thousand dollars.Mississippi also has about 207 bacherlors degree per 1000 people what does the linear model estimate for that number of bachelors degrees per 1000 per person for Mississippi based on the median income? How good is this estimate?
Answer: A linear model is a type of mathematical equation that describes the relationship between two variables, such as median income and the number of bachelor's degrees per 1000 people. In order to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income, you would need a linear equation that describes that relationship.
Without that equation, it's not possible to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income.
Additionally, without more information about the data that the model was trained on, the correlation between median income and the number of bachelor's degrees per 1000 people and how accurate and reliable the model is, it's difficult to determine the goodness of this estimate. However, in general, a linear model may provide only a rough estimate, especially if the relationship between the variables is complex or non-linear.
Step-by-step explanation:
Will mark brainliest!!
Consider the circumscribed angle. Determine the value of x.
1)
x = 12
2)
x = 29
3)
x = 4.75
4)
x = 17
Answer:
x = 12
Step-by-step explanation:
i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]
ii. 29 - 5 = 2x
iii. 24 = 2x
iv. x = 24/2
v. x = 12
help yall please!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Well it would be funchen because as you see it just makes sence
Answer:
not a function
Step-by-step explanation:
In a function, an input gives only one output. As you can see from the graph, the input which is 4 produces 3 different outputs which are 2, 3 and 4, thus it cannot be a function.
Question 5 of 10
Mackenzie took out a payday loan for $1100 that charged a $95 fee. If the
loan matures in 2 weeks, what is the approximate effective interest rate of the
loan?
OA. 862%
OB. 86%
OC. 76%
OD. 762%
What constant term should be used to complete the square?
x2.5x+_ _ _ =7
4/25
49/25
-49/25
25/4
The constant term that should be used to complete the square? x2 - 5x + _____ = 7 is 25/4
What is quadratic equation ?
A quadratic equation in the variable x is of the form. ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. • Roots of a quadratic equation : A real number α is said to be a root of the. quadratic equation ax2 + bx + c = 0, if aα2 + bα + c = 0.
Given:
x^2-5x+c=7, the constant term c will be obtained using the formula:
c=(-b/2a)²
The quadratic equation in its generic form is:
ax^2 + bx + c
To complete squares we must add the following term:
(b / 2) ^ 2
The equation is:
ax^ 2 - 5x + k = 7
By completing squares we have:
x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2
Rewriting:
x ^ 2 - 5x + 6.25 = 7 + 6.25
Hence, A constant term should be used to complete the square is 25/4 or 6.25.
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5x35 65x76 what the the total
The solution to the above math arithmetic is 5115.
Addition and subtraction are what?Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.
What exactly is an algebraic question?This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.
For instance, 5 + 6 = 11 and 11 - 6 = 5.
5x35 + 65x76=5115
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Write an expression to represent: 2 times the difference of x and 3
Answer:
2(x-3)
Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.
Which equation is part of the same fact family as 5 x 4 =20?
You are a researcher studying the health habits of people living in a large rural area. In particular, you are interested in the amount of weight gained early in life.
You want to estimate the population mean of all weight gains for the area's baby girls in their first year. To estimate the population mean of all such weight
gains, you select a random sample of 15 baby girls from this area and you record the weight (in kg) each gained in their first year. Assume the population is
approximately normally distributed.
Based on your sample, follow the steps below to construct a 90% confidence interval of the weight gains in the first year for all the area's baby girls. (If
necessary, consult a list of formulas.)
(a) Click on "Take Sample" to see the results for your random sample.
Take Sample
Sample size:
0
Point estimate:
0
Number of baby girls
4
Sample standard deviation:
0
15
Sample mean
Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your 90%
confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute".
Standard error:
5.538
Margin of error:
Sample standard
deviation
1.921
X
Confidence
level
S
Critical value
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
Define median.When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.
Here,
(48, 51, 65, 71, 61, 45, 48, 72, 74, 66, 43, 47, 70, 66, 45) sample data; sample mean, x = 58.133; sample size, n = 15; standard deviation, s = 11.6;
Standard deviation equals sd/√(n)
where, n = sample size and sd = standard deviation
Margin of error is equal to t alpha/2 and the standard error is (11.6/√( (15)) = 2.995. (standard error)
where ta/2 is the t-table level of significance, alpha is 0.05 from the standard normal table, the two-tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145, and the margin of error is 2.145 * 2.995, which equals 6.425. The confidence interval for this margin of error is [58.133 6.425] = [51.708, 64.558].
being that,
sample data: (48 , 51 , 65 , 71 , 61 , 45 , 48 , 72 , 74 , 66 , 43 , 47 , 70 , 66 , 45 )
sample mean, x =58.133
standard deviation, s =11.6
sample size, n =15
level of significance, alpha = 0.05
from standard normal table, two tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145
we use CI = x ± t a/2 * (sd/ √((n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 58.133 ± t a/2 ( 11.6/ sqrt ( 15) ]
= [ 58.133-(2.145 * 2.995) , 58.133+(2.145 * 2.995) ]
= [ 51.708 , 64.558 ]
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
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What is a quadratic function (f) whose zeros are -2 and -11
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have [tex]x1[/tex]=2 [tex]x2[/tex]=-11
then quadratic function will be
(x+2) (x+11)
[tex]x^2+2x+11x+22[/tex]
[tex]x^2+13x +22[/tex]
this is our required quadratic equation.
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Complete question is: Write a quadratic function f whose zeros are 2 and -13.
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have x¹ = 2 x² = -11
then quadratic function will be
(x+2) (x+11)
x² + 2x + 11x + 22
x² + 13x + 22
This is our required quadratic equation.
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The complete question is-
Write a quadratic function f whose zeros are 2 and -13.
-5 + -3 + 9= please help i'm stuck
Answer:
1
Step-by-step explanation:
Answer:
I believe it is 1
Step-by-step explanation:
multiply the sum by the difference of 19 and 57
Answer:2009#73
Step-by-step explanation:
3939+373
Ie,ek
Solve Using substitution 3x+5y=-28 Y=x+4
Answer:
(-6, -2) x=-6, y=-2
Step-by-step explanation:
3x + 5(x+4) = -28
3x + 5x+20=-28
8x+20=-28
8x=-48
x=-6
Y=-6+4
y=-2
To purchase 12,100 worth of machinery for her business, Latoya made a down payment of 1800 and took a business loan for the rest. After 3 years of paying monthly payments of 313.36, she finally paid off the loan.
A, what was the total amount latoya ended up paying for the machinery. (including down payment and monthly payments)
B. How much interest did latoya pay on the loan
The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96
The amount of interest that Latoya paid was $ 980.96
How to find the total amount paid ?The total amount paid by Latoya for the machinery can be found as :
= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )
= 1, 800 + ( 313. 36 x 12 x 3 )
= $ 13, 080 .96
The total interest paid on the loan was :
= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment
= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800
= $ 980.96
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i really need help with this, i dont get how to identify outliners and gaps stuff, please help?
On solving the provided question, we can say that - the plotting data will be done by 3 to 24 ; 6 to 61 ; 5 to 56; 1 to 15
what is plotting data?A graph that demonstrates the relationship between two or more variables is the most common way to depict a data set using a chart. Both hand-drawn and computer-drawn diagrams are acceptable. Start at the origin and move 2 units to the right before moving 3 units up to draw the coordinates for the point 2,3 on the coordinate plane. Make your points clear. As a result, the pink dot with the letter P on it denotes 2.3. A number line containing each value in your data collection should be first created before making a line chart. Then, on the number line, put an X (or dot) over each value of the data. Put an X over the number for each time a value appears in a record where it does.
so we have to plot data from the given data, we can do by
3 to 24 ; 6 to 61 ; 5 to 56; 1 to 15
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