The formula of the relationship between lateral area and the length of a side of the base and slant height in a square pyramid is 2sh.
The lateral area of a square pyramid is defined as the area covered by its slant of lateral faces. One side of each of these triangles coincides with one side of the base polygon.
The lateral area is the area of the faces of the pyramid without the base.
Each face is a triangle with base "s" and a height the same as the slant height - let's consider it as "h."
The area of each face is =0.5sh.
For the four faces the lateral area is 4*0.5sh=2sh.
To know more about the lateral area:
https://brainly.com/question/1601740
#SPJ4
Find a function rule for the line that passes through the origin (0,0) and the point (-6,-18).
The function of the line passing through the points (0,0) and (-6,-18) is y = 3x.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Points are (0,0) and (-6,-18)
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
m = -18/-6
m = 3
The equation of the line is given as
y - y₁ = 3 (x - x₁)
y + 0 = 3(x - 0)
y = 3x
Thus, the function of the line passing through the points (0,0) and (-6,-18) is y = 3x.
Learn more about slopes here:
https://brainly.com/question/3605446
#SPJ1
Let A = {1, 3, 5}. Then the number of equivalence relations in A containing (1, 3) is
If A = {1, 3, 5} then it must contain 9 equivalence relations.
What is an equivalence relation?A relation that is reflexive, symmetric, and transitive is called an equivalence relation.
A = {1, 2, 3}
For equivalence relation containing (1, 3)
For symmetric, it must consist (1, 3) and (3, 1).
For transitivity, it must consist (1, 3) and (3, 2) and (1, 2),(2, 1),(2, 3),(3, 1)
For reflexivity, it must consist (1, 1) and (2, 2),(3, 3)
⇒ R = {(1, 1),(2, 2),(2, 3),(3, 3),(1, 2)(1, 3),(2, 1),(3, 1),(3, 1)}.
learn more about equivalence relations here :
https://brainly.com/question/14307463
#SPJ1
HELPPPPPPP PLEASEEEEEEEEEEEEE
Applying the exterior angles theorem, the measure of angle JKL is: 22°.
What is the Exterior Angles Theorem?Exterior Angle Theorem states: "The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it."
Applying the exterior angles theorem, we would create the following equation:
m<JKL = m<KIJ + m<IJK
Substitute:
5x - 3 = 2x + 8 + x - 1
Solve for x
5x - 3 = 3x + 7
5x - 3x = 3 + 7
2x = 10
x = 5
m<JKL = 5x - 3 = 5(5) - 3
m<JKL = 22°
Learn more about the exterior angles theorem on:
https://brainly.com/question/11356657
#SPJ1
help asappppppppppop
Step-by-step explanation:
oh, come on. this can be easily answered by all the formulas and information from the other question.
again the area of a circle is
pi×r²
so, for the given area of 9pi this means the radius is
r = sqrt(9) = 3 cm
the slant height is 4 times the radius
L = 3×4 = 12 cm
the total surface area of a cone is again
pi×r(r + L) = pi×r² + pi×r×L
the lateral area alone (without the base area) is then
pi×r² + pi×r×L - pi×r² = pi×r×L
in our case
3.14×3×12 = 113.04 ≈ 113 cm²
The chart shows the number of rabbits a farmer observed on his farm over a period of nine weeks.
Find the third quartile of the data set.
The third quartile of the data set is 20, and option C is correct.
What are datasets?A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it. Data can be arranged for our study in the form of graphs, charts, or tables.
Given a chart for the number of rabbits, a farmer observed on his farm over a period of nine weeks.
week 1 2 3 4 5 6 7 8 9
rabbits 2 3 5 7 11 15 18 22 27
the formula of quartiles is
Lower Quartile (Q1) = (N+1) * 1 / 4
Middle Quartile (Q2) = (N+1) * 2 / 4
Upper Quartile (Q3 )= (N+1) * 3 / 4
here N = 9
third quartile(Q3) = (N+1) * 3 / 4
third quartile(Q3) = (9 + 1)3/4
third quartile(Q3) = 7.5 term
third quartile(Q3) is the term between 7th and 8th week
third quartile(Q3) = (7th term + 8th term)/2
7th term = 18
8th term = 22
third quartile(Q3) = (18 + 22)/2
third quartile(Q3) = 20
Hence option C is correct.
Learn more about datasets;
https://brainly.com/question/24058780
#SPJ1
3. The mean hourly pay rate for financial managers in the Europe is $32.62, and the standard deviation is $2.32. Assume that pay rates are normally distributed. A. What is the probability a financial manager earns between $30 and $35 per hour? B. How high must the hourly rate be to put a financial manager in the top 10% with respect to pay? C. For a randomly selected financial manager, what is the probability the manager earned less than $28 per hour?
given that 1 euro = £0.75
what is the £ to euro exchange rate ?
£1 =
Answer:
[tex]\frac{4}{3}[/tex] or 1.333333333 euro
Step-by-step explanation:
Answer:
1 euro = £0.75
£1= 4/3 or 1.33333 repeating
Hope this helped!
Step-by-step explanation:
COMPARING FUNCTIONS A cross section of a birdbath can be modeled by y=(x-18)² – 4, where x
and y are measured in inches. The graph shows the cross section of another birdbath.
N
y=
75
To compare the two birdbaths, we can compare the equations for their respective cross sections.
What is cross sections?Cross sections are a two-dimensional representation of a three-dimensional shape or object. Cross sections can be used to help visualize the internal and external structure of an object, such as a building, machine, or living organism. They are also used to understand the physics and math of a certain area, such as the flow of air or the interactions of particles.
To compare the two birdbaths, we can compare the equations for their respective cross sections. The equation for the first birdbath is y=(x-18)² – 4, while the equation for the second birdbath is y=75. We can compare the two equations by looking at how the x-values affect the y-values. In the first equation, as x increases, y increases. In the second equation, y remains constant. This indicates that the second birdbath is a shallower bowl than the first birdbath.
To learn more about cross sections visit:
brainly.com/question/28257972
#SPJ1
A sand volleyball court has a perimeter of 50 meters. Its area is 136 square meters. What are the dimensions of the volleyball court?
Answer:
The dimensions of the sand volleyball court are 17 meters by 8 meters.
The following expression is equal to q". What is the value of n?
We can see here that the value of n = 16.
What is an expression?An expression in mathematics is a combination of numbers, variables, and mathematical operations that represent a mathematical value or concept. It can be a single term, such as "5x", or a combination of terms, such as "5x + 2". Expressions are used to describe mathematical relationships and equations, and they can be simplified, evaluated, and solved to determine a numerical value.
Below is how we got n.
We can see that having: [tex]\frac{(q^{4} )^{-3} }{q^{-15} }[/tex]
[tex]\frac{(q^{4} )^{-3} }{q^{-15} } = q^{n}[/tex]
Thus, [tex]\frac{(q^{4} )^{-3} }{q^{-15} } = \frac{q^{4-3} }{q^{-15} }[/tex]
∴ [tex]\frac{q^{4-3} }{q^{-15} } = q^{1-(-15)} = q^{1+15} = q^{16}[/tex]
Therefore, [tex]q^{n} = q^{16}[/tex]
Thus, n = 16.
Learn more about an expression on https://brainly.com/question/1859113
#SPJ1
Identify the 3 digit number of the millions period in 114,475,802.
PLS HELP ME ASAP ILL GIVE BRAINIEST:)
Which equation can be used to find the area of the of the parallelogram?
Responses
A A = 10(5 + 7)
B A = (7)(5)
C A = (15)(7)
D A = (15)(5)
Answer:The answer is D (15)(5)
Step-by-step explanation:
To find the area of a parallelogram the formula it b×h. Base and height and the base is 15cm and the height is 5cm so the answer is d because 7 isn't the base or height it is a slant.
Answer: C
Area = Base x Height (15)(5)
In a wind tunnel experiment, the force on a projectile due to the air resistance
was measured at different velocities:
Velocity (100 ft=sec) 0 2 4 6 8 10
Force (100 lb) 0 2.90 14.8 39.6 74.3 119
Find an interpolating polynomial p(t) = a0 + a1t + a2t^2 + a3t^3 + a4t^4 + a5t^5 for these data.
What happens if you try to use a polynomial of degree less than 5?
To find an interpolating polynomial, we need to fit a polynomial to the given data points. The simplest way to do this is by using the Lagrange Interpolating Polynomial formula:
p(t) = ∑ (y_i * l_i(t))
where y_i = the y-value of the data point
l_i(t) = Lagrange basis polynomial for data point i, defined as:
l_i(t) = (∏ (t-t_j)) / (t_i-t_j) for all j ≠ i
Using this formula, we can find the interpolating polynomial for the given data points:
p(t) = 0.0006t^5 - 0.0222t^4 + 0.2436t^3 - 1.0528t^2 + 2.2080t + 2.0400
So the interpolating polynomial for this data is a 5th degree polynomial, which means that it is necessary to use a polynomial of at least degree 5 in order to accurately fit the data.
If we try to use a polynomial of degree less than 5, the polynomial will not fit the data points accurately, and the difference between the polynomial and the actual data points will be significant. This means that the results of the wind tunnel experiment would be inaccurate if we use a polynomial of lower degree.
To learn more about interpolating polynomial:
https://brainly.com/question/13424852
#SPJ4
Find the slope of each line.
Answer:
m = 1/4
Step-by-step explanation:
Slope is defined as
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
There are two solid points
(4,0) (-4,-2)
So using that equation
=(-2-0)/(-4-4)
=(-2)/(-8)
=1/4
Slope is 1/4
at which point or points (marked a-e) is the object moving the slowest without being at rest? explain your reasoning.
In the given position-versus-time graph, the object moving the slowest without being at rest is at point B.
A position-versus-time graph illustrates how far an object has travelled from its starting position at any given time since it started moving. The vertical axis describes the position of the object, and the horizontal axis describes the time.
The slope of the graph indicates the speed of the moving object. Hence, the value of the slope at a particular time indicates the speed of the object at that instant. Hence, the steeper the line is, the greater the slope of the line and the faster the object's motion is changing.
In the given graph, at points A, C and E, the slope is zero; the object is not moving, hence at rest. At the point, D slope is steeper as compared to the slope at point B. Hence, the object is moving slower at point B as compared to point D.
To know more about Position-versus-time graph, here
brainly.com/question/24852543
#SPJ4
--The given question is incomplete; the complete question is
"The figure shows the position-versus-time graph for a moving object. At which point or points is the object moving the slowest without being at rest?"--
The point b divides the ac in the ratio 2:3
Work out the vector OC in terms of an and b. SImplify your answer
Answer:
Where is your question
Step-by-step explanation:
I need it to solve the problem
In one class, homework is worth 55% of the final grade, each of 3 projects is worth 10%, and a final exam is worth 15%. (a) If a student has an 82 homework average and a 96 on the first project, what is the student's grade at this point? (b) If the same student from part (a) gets a 74 on the second project and a 71 on the third project, what is the lowest grade the student can get on the final exam to overall in the course? (a) The grade at this point is (Simplify your answer. Round to the nearest tenth as needed.)
The worth of the homework is 55% and worth of final exam is 15%. The worth of each three projects is 10%
a) Finding the student's grade, If a student has an 82 homework average and a 96 on the first project.
Students grade = 82(55%) + 96(15%)
= 45.1 + 14.4
Students grade= 59.5
(b) Finding the lowest grade the student If a student gets a 78 on the second project and a 76 on the third project.
Let G be the lowest grade in the final exam.
It was stated that the lowest grade the student can get on the final exam to get an 80 overall in the course:
82(55%) + (96 +74 + 71)(25%) +G (15%)= 82
45.1 +60.25 + G0.15 = 82
Making G the subject of the relation we have
G0.15 = 82 -105.35
G0.15 = --23.35
G= 155-100
Therefore the lowest grade is 55
Learn more about students projects on https://brainly.com/question/29987934
#SPJ1
PLEASE HELP........URGENT
Answer:
1. 184-x
2. 90
3. y=4x/3-23/3
Step-by-step explanation:
1. 180-(x-4)=184-x (supplementary angles)
2. 180/2=90 (supplementary angles)
3. y=-3x/4+2
y+5=(4/3)(x-2)
y=4x/3-23/3
determine the number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n.
The number of vectors (x1, x2 . . ., xn) such that each xi is either 0 or 1 and n where k is a non-negative integer less than or equal to n is 2^n.
Each xi in the vector (x1, x2, ..., xn) can be either 0 or 1. Therefore, there are 2 possibilities for each xi. The number of vectors that can be formed by combining these values is equal to the number of combinations of 2 possibilities, taken n times.
This is equivalent to 2^n. For example, if n = 2, then there are 2 possibilities for x1 (either 0 or 1) and 2 possibilities for x2 (either 0 or 1). The total number of vectors that can be formed is 2 * 2 = 2^2 = 4. In general, the number of vectors that can be formed is equal to 2^n.
Learn more on vectors :
https://brainly.com/question/25705666
#SPJ4
I need a little help...
In case of the following perpendicular triangles-
Part 1) x=8
Part II mRSU=133°
mUST=47° (Part 3).
mWSV=43° (Part 4).
5th Part mVSU=137°
Explanation in detail:
To better understand the issue, please examine the accompanying figure.
Part 1) Determine the value of x.
We are aware that
mRSU and mUST are auxiliary angles (by linear pair)
so m∠RSU+m∠UST=180°
We now have
m∠RSU=(17x-3)°
m∠UST=(6x-1)°
Substitute the provided values for x and solve
Part 2) Determine the value of mRSU.
We now have
m∠RSU=(17x-3)°
replace the value of x
m∠RSU=17(8)-3=133°
Part 3) Determine the value of mUST.
We now have
m∠UST=(6x-1)°
replace the value of x
m∠UST=6(8)-1=47°
Part 4) Determine the value of mWSV.
We are aware that
mRSW=mUST ——-> by means of vertical angles
so
m∠RSW=47°
mRSW+mWSV=90° ----> issue presented (SV perpendicular RT)
Substitute mRSW for the value of mWSV and solve for mWSV.
47°+m∠WSV=90°
m∠WSV=90°-47°=43°
Part Part 5) Determine the value of mVSU.
We are aware that
m∠VSU=m∠VST+m∠UST
We now have
mVST=90° ----> provided issue (SV perpendicular RT)
m∠UST=47°
substitute
m∠VSU=90°+47°=137°
Learn more about perpendicular from here;
https://brainly.com/question/1202004
#SPJ1
What is the answer for
( f - g )(6)=
Answer: 6f-6g
Step-by-step explanation:
Into how many parts should you divide 30?
It depends on the purpose of dividing 30. There is no specific answer for dividing 30 into a certain number of parts. It can be divided into any number of parts, as long as it is a whole number.
Answer:
it depends upon ur requirement that hw many parts is needed by u
Step-by-step explanation:
like if u need 2 parts it can happen by having 15 on one side and 15 on the other similarly it,s the way to divide it to many parts required by u
Frankie wants to use her 8.39 m long ladder
against a wall, as shown below.
The instructions state that the angle between
her ladder and the ground should be in the
range 74° to 77°.
Calculate the maximum distance that the
base of her ladder should be placed from the
wall.
Give your answer in metres to 2 d.p.
Answer:
2.31m
Step-by-step explanation:
Trigonometry:
cosθ = adjacent/hypotenuse
cos(74) = adjacent/(8.39)
adjacent = 8.39 × cos(74)
adjacent = 2.3125974152
2.31 (to 2 d.p.)
I don't understand this, USE YOUR SKILLS AND HELP MEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
$102
Step-by-step explanation:
It cost $25.50 per inch. They want to buy 4 inches.
Inch 1 Inch 2 Inch 3 Inch 4
v v v v
25.50 + 25.50 + 25.50 + 25.50 is the same as 25.50 · 4 which equals 102
a test has 20 questions and is worth 100 points. the test consists of x true/false questions worth 4 points and y multiple choice questions worth 8 points each. How many of each type of question are on the test?
Translate the word problem into a system of equations, with x representing true/false questions and y representing multiple choice questions:
(1) [tex]x+y=20[/tex] <-- a test has 20 total questions
(2) [tex]4x+8y=100[/tex] <-- the test is worth 100 total points
Now we have a system of two equations with two unknowns, which we can solve with the elimination method.
Let's multiply equation (1) by -4 so that we can eliminate x from the system:
[tex]-4x-4y=-80[/tex]
Now, add this new equation to equation (2) to eliminate x so that we only have one variable left:
[tex]4y=20[/tex]
Solve for y:
[tex]y=5[/tex]
Now, substitute this value for y into either the original equation (1) or (2). I will do equation 1 for simplicity:
[tex]x+5=20[/tex]
Solve for x:
[tex]x=15\\[/tex]
Notice that we now have values for both x and y, so we are done. We now know that there are 15 true/false questions and 5 multiple choice questions on the test!
A regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles. It has a lateral surface area of 57 square centimeters. What is the surface area of the regular triangular pyramid?
The surface area of the regular triangular pyramid is 76 square centimeters.
What is a regular triangular pyramid?A three-dimensional object with a triangle base and three triangular faces is known as a regular triangular pyramid.
Given:
A regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles.
It has a lateral surface area of 57 square centimeters.
The area of a 3-dimensional object's sides, excluding its base and top, is referred to as its lateral surface area.
A total of four face areas make up the surface area of a triangular pyramid.
The area of one face = lateral surface area / 3
57 / 3 = 19
The surface area = 19 x 4 = 76
Therefore, the surface area is 76 square centimeters.
To learn more about the pyramid;
https://brainly.com/question/17615619
#SPJ1
fill in the blanks in the above anova table.at 95% confidence, test to determine whether or not the means of the 3 populations are equal. the denominator degrees of freedom is
In this case, the denominator degrees of freedom is 18 - 3 = 15.
The denominator degrees of freedom for this ANOVA test is the total number of observations in the sample minus the number of groups, or n-k.
The denominator degrees of freedom are the total number of observations in the sample minus the number of groups being compared. This value is used in statistical tests such as ANOVA to determine the probability of obtaining a given value of the test statistic, and it is also used in calculating the standard error of the mean. In ANOVA, the denominator degrees of freedom is equal to the total sample size minus the number of groups.
Learn more about confidence level:
https://brainly.com/question/17212516
#SPJ4
Patrick wants to buy some songs and videos from an online media
store.
Songs (s) cost $1 each.
Videos (v) cost $2.50 each.
Patrick wants to spend at least $25 at the store.
Which inequality represents the number of songs and videos Patrick
could buy if he wants to spend at least $25 at the store?
.
.
.
A. s+2.5v≥25
B. s+2.5v ≤25
C. 2.5s+v≤25
D. 2.5s+v≥25
Answer:
s + 2.5v ≥ 25
Step-by-step explanation:
Framing inequalities:Cost of 1 song = $1
Cost of 's' songs = s * 1 = s
Cost of 1 video = $2.50
Cost of 'v' videos = 2.50 * v = 2.5v
As he wants to spend at least $ 25, he wants to buy for an amount equal to $ 25 or more than $ 25.
Total amount to spend ≥ $ 25
s + 2.5v ≥ 25
Please help me with this question.
For given trigonometric function csc^2x(1-cos^2x)=1 to established option D is a key step.
What are trigonometric functions?
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions.
Now,
given function is csc^2x(1-cos^2x)=1
=csc^2x(sin^2x)
=1/sin^2x*sin^2x
=1
Hence,
For given trigonometric function csc^2x(1-cos^2x)=1 to established option D is a key step.
To know more about Trigonometric functions visit the link
https://brainly.com/question/9880303?referrer=searchResults
#SPJ1
I have to go to the park and park in the park
On solving the provided question we can say that by unitary method 1/4 tickets sold were bought by teachers , so teachers bought = 20/4 = 5, so students cost was = 15*8 = $120
What is unitary method?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
by unitary method
1/4 tickets sold were bought by teachers ,
so teachers bought = 20/4 = 5
so students cost was = 15*8 = $120
To know more about unitary method visit:
brainly.com/question/28276953
#SPJ1
