The apothem and the lateral surface area are 5/2√3 and 210 square units while the surface areas are 210 + 75√3 square units and 339.90 square units
Calculating the apothem and the lateralGiven that
Side length, s = 5
The apothem is calculated as
a = 1/2√3 * s
Where
Side length, s = 5
So, we have
a = 1/2√3 * 5
Evaluate
a = 5/2√3
The lateral area of the prism is calculated as
LA = 6sh
So, we have
LA = 6 * 5 * 7
LA = 210
Calculating the surface areasThis is calculated as
SA = LA + 3√3 s²
So, we have
SA = 210 + 3√3 * 5²
Evaluate
SA = 210 + 75√3
In decimal form, we have
SA = 339.90
Hence, the decimal form of the surface area is 339.90 square units
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Write an equation for a line containing the points (-3,7) and (9,-1)
Answer:
y = (-2/3)x + 5
Step-by-step explanation:
To write the equation of a line, we need to find its slope and y-intercept using the given points.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:slope = (y2 - y1) / (x2 - x1)
Using the points (-3,7) and (9,-1), we can find the slope as:slope = (-1 - 7) / (9 - (-3))
= -8 / 12
= -2/3
Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept. The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1)
Using the point (-3,7) and the slope we just found (-2/3), we get:y - 7 = (-2/3)(x - (-3))
Simplifying this equation, we get:y - 7 = (-2/3)x - 2
y = (-2/3)x + 5
please help me out!! and number the answers with the number of the question please.
Answer:
Question 5 : 10% decay
Question 6 : Amar is right
Step-by-step explanation:
Josh does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 10 hours. He spends at most 8
hours doing cardiovascular work. He spends at most 6 hours on weight training. Let x denote the time (in hours) that Josh spends doing cardiovascular work.
Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
11
12-
IN
10
S
Continue
12 13
X
Save For Later
©2023
The figure of the shaded region is shown in graph.
Now, Based on the given information, we can create the following system of inequalities to represent Josh's weekly exercise program:
for he exercises for at least 10 hours;
⇒ x + y ≥ 10
And, When he spends at most 8 hours doing cardiovascular work is,
x ≤ 8
When, he spends at most 6 hours on weight training,
y ≤ 6
Hence, To graph these inequalities, we can start by graphing the three lines that represent each of the above equations.
The first inequality, x + y ≥ 10, represents a line with a y-intercept of 10 and a slope of -1.
The second inequality, x ≤ 8, represents a vertical line at x = 8.
The third inequality, y ≤ 6, represents a horizontal line at y = 6.
Thus, The figure of the shaded region is shown in graph.
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If a line has a slope of 3 and contains the point (-1, 4), what is its equation in point-slope form?
A. y+1=3(x-4)
B. y-1=3(x-4)
C. y-4=3(x-1)
D. y-4=3(x+1)
If a line has a slope of 3 and contains the point (-1, 4), its equation in point-slope form include the following: C. y - 4 = 3(x - 1).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (1, 4) and a slope of 3, a linear equation for this line can be calculated or determined by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = 3(x - 1)
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im just gonna give a image of the questions i give up on typing
Answer:
The answer is 43°
Step-by-step explanation:
137+137+x+43=360°
x+317=360
x=360-317
x=43°
An employee's monthly productivity M, in number of units produced, is found to be a function of the number t of years of service. For a certain product, a productivity function is shown below. Find the maximum productivity and the year in which it is achieved.
M(t)=-3t²+126t+150, 0≤t≤40
The maximum productivity is 2646 units per month and it occurs at 21 years of service.
To find the maximum productivity and the year in which it is achieved, we need to find the vertex of the parabolic function represented by the productivity function.
The vertex of a parabola in the form y = a[tex]x^{2}[/tex] + bx + c is located at the point (-b/2a, c - [tex]b^{2}[/tex]/4a).
In this case, we have:
M(t) = -3[tex]t^{2}[/tex] + 126t + 150
So, a = -3, b = 126, and c = 150.
The year of service, t, is restricted to the interval 0 ≤ t ≤ 40, which means that the maximum productivity will occur at either t = 0 or t = 40, or at the vertex of the parabola.
The x-coordinate of the vertex is given by -b/2a, which in this case is:
t = -b/2a = -126/(2(-3)) = 21
So, the maximum productivity occurs at t = 21 years of service.
To find the maximum productivity, we substitute t = 21 into the productivity function:
M(21) = -3[tex](21)^{2}[/tex] + 126(21) + 150 = 2646
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6
Select the correct answer.
What is the domain of y = cos(z)?
O A. [0, 00)
OB.
2T
O C. (-00,00)
O D. [-1, 1]
Reset
Next
2. A sphere has a great circle with a circumference of 10 pie meters. Find the radius. If the sphere is
cut in half, find the surface area of the closed hemisphere and its volume. Give exact answers in
terms of pie
The surface area of the two hemispheres combined is 100π square meters, and the volume of the two hemispheres combined is (500/3)π cubic meters.
The circumference of a great circle on a sphere is given by the formula C = 2πr, where r is the radius of the sphere.
In this case, we are given that the circumference of the great circle is 10π meters, so we can set up an equation:
10π = 2πr
Dividing both sides by 2π, we get:
r = 5
So the radius of the sphere is 5 meters.
When the sphere is cut in half, we get two equal hemispheres. The surface area of a closed hemisphere is given by the formula A = 2πr^2, where r is the radius of the hemisphere.
Since we are dealing with a radius of 5 meters, the surface area of one hemisphere is:
A = 2π(5^2) = 50π
Therefore, the surface area of the two hemispheres combined is:
2A = 2(50π) = 100π
The volume of a closed hemisphere is given by the formula V = (2/3)πr^3. Again, since we are dealing with a radius of 5 meters, the volume of one hemisphere is:
V = (2/3)π(5^3) = (2/3)π125 = (250/3)π
Therefore, the volume of the two hemispheres combined is:
2V = 2(250/3)π = (500/3)π
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3/8=4/7x what is x please help me omg
The value of the variable x = 21/32
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.
These expressions are also made up of certain arithmetic or mathematical operations.
These operations includes;
SubtractionDivisionAdditionMultiplicationBracketParenthesesFrom the information given, we have that;
3/8=4/7x
cross multiply the values, we have;
7x(3) = 8(4)
multiply the values and expand the brackets, we get the values;
21x = 32
Divide both sides by the coefficient of the variable x, we get;
x = 32/21
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If D = 2w? - w - 7 and C = 3w - 6, find an expression that equals D + 3C in
standard form.
The expression is equivalent to 10w - 25 = 0
How to determine the expressionIt is important to note that algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.
These expressions are also made up of arithmetic operations. These operations are;
BracketParenthesesSubtractionMultiplicationAdditionFrom the information given, we have that;
D = 2w - w - 7
C = 3w - 6
To determine the value of the expression D + 3C
substitute the expression
2w - w - 7 + 3(3w -6)
expand the bracket
2w - w - 7 + 9w - 18
collect the like terms and add
10w - 25 = 0
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What is the exact value of the angle that makes each equation true?
Enter your answers in the boxes.
] = √²
tan º = √³
1 = √3
COS
sin
The trigonometric value relations are solved and
a) cos 45° = √2/2
b) tan 30° = √3/3
c) sin 60° = √3/2
Given data ,
Let the trigonometric relations be represented as A
Now , the value of A is
a)
cos x = √2/2
On simplifying , we get
cos x = 1/√2
Taking inverse on both sides , we get
x = cos⁻¹ ( 1/√2 )
x = 45°
b)
tan x = √3/3
On simplifying , we get
tan x = 1/√3
Taking inverse on both sides , we get
x = tan⁻¹ ( 1/√3 )
x = 30°
c)
sin x = √3/2
Taking inverse , we get
x = 60°
Hence , the trigonometric relations are solved
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F
46°
6.8 yd
E
DE
D
please help and show work
Answer:
A
Step-by-step explanation:
0.15 × 12 = 1.8
ps : i'm not sure if it's true or not, but i think this is the answer. i'm sorry if i get you wrong
A drama department is building the set for an upcoming play. They want to build a tree line from the corner of the castle to the back corner of the stage. The dimensions of the stage and castle are shown. What is the length of the tree line, t, to the nearest foot? Show your work.
The length of the tree line, t, to the nearest foot, is 20 ft.
We have,
From the figure,
t can be considered as the hypotenuse.
And,
The other two sides are::
15 - (7 + 5) = 15 - 12 = 3
30 - 10 = 20
Now,
Applying the Pythagorean theorem,
t² = 3² + 20²
t² = 9 + 400
t² = 409
t = 20
Thus,
The length of the tree line, t, to the nearest foot, is 20 ft.
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Find an equation of the line containing the given points. Use function notation to write the equation. ( 2/7,3/7) and (-1/7,11/14).
F(x)=
Answer: F(x) = (-5/6) x + 13/42
Step-by-step explanation: The provided points are (x1, y1) = (2/7, 3/7) and (x2, y2) = (-1/7, 11/14) respectively.
The following formula can be used to determine the slope of the line connecting the two points:
m = (y2 - y1)/(x2 - x1)
m = (11/14 - 3/7)/(-1/7 - 2/7)
m = (5/14)/(-3/7)
m = -5/6
In order to construct the equation of the line, we can now utilize the point-slope form:
y - y1 = m(x - x1)
The result of substituting the values of m, x1, and y1 is:
y - 3/7 = (-5/6)(x - 2/7).
A food critic collected data on the lengths of time customers waited for their food
1/2, 1/4, 3/4, 1/2,1/4, 1/2, 1
What is the difference between the longest time and the shortest time that customers waited?
Answer:
Hi
You can identify which is the shortest and longest by converting the fractions to decimal or by finding the L.C.M
The longest time is 1
and the shortest is 1/4
The difference would be 1-1/4= 3/4
Se compra un lote de CD´s de tres marcas diferentes: 500 CD´s de la marca A, 400 de la marca B y 100 de la marca C. Se sabe que el porcentaje de CD´s defectuosos para cada una de las marcas es del 1% para A, el 1.5% para B y el 2% para la marca C. Si se toma un CD al azar del lote: a) Calcular la probabilidad de que el CD elegido sea defectuoso
Entonces, la probabilidad de que el CD elegido al azar sea defectuoso es del 1.3%.
Para calcular la probabilidad de que el CD elegido al azar sea defectuoso, debemos considerar la proporcion de CD's defectuosos para cada marca y su cantidad en el lote total.
En primer lugar, podemos calcular el número total de CD's en el lote:
500 (marca A) + 400 (marca B) + 100 (marca C) = 1000 CD's
Luego, podemos calcular el número de CD's defectuosos para cada marca:
Marca A: 1% de 500 CD's = 5 CD's defectuosos
Marca B: 1.5% de 400 CD's = 6 CD's defectuosos
Marca C: 2% de 100 CD's = 2 CD's defectuosos
Por lo tanto, el numero total de CD's defectuosos en el lote es:
5 (marca A) + 6 (marca B) + 2 (marca C) = 13 CD's defectuosos
Finalmente, la probabilidad de que el CD elegido al azar sea defectuoso es simplemente la proporción de CD's defectuosos en el lote total:
P(CD defectuoso) = 13/1000 = 0.013 o 1.3%
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a rock is thrown into a still pond and causes a circular ripple. if the radius of the ripple is increasing at a rate of 4 feet per second, how fast is the circumference changing when the radius is 19 feet
The rate of change of the circumference is 8π feet per second
Given data ,
The circumference of a circle is given by C = 2πr, where r is the radius. We need to find how fast the circumference is changing when the radius is 19 feet and the rate of increase of the radius is 4 feet per second.
We can start by taking the derivative of both sides of the equation C = 2πr with respect to time t:
dC/dt = 2π(dr/dt)
Here, dC/dt represents the rate of change of the circumference with respect to time, and dr/dt represents the rate of change of the radius with respect to time.
We are given that dr/dt = 4 feet per second, so we can substitute this value into the equation above:
dC/dt = 2π(4) = 8π
So when the radius is 19 feet, the circumference is C = 2π(19) = 38π feet. At this point, the rate of change of the circumference is dC/dt = 8π feet per second.
Hence , when the radius is 19 feet, the circumference is increasing at a rate of 8π feet per second
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StartFraction n Over 32 EndFraction = StartFraction 1 Over 16 EndFraction a. n = one-half c. n = 2 b. n = 4 d. n = 512
The solution of the fraction is n = 2 (option c).
Now, let's consider the equation n/32 = 1/16, where n is a variable that we want to solve for. This equation tells us that the ratio of n to 32 is equal to the ratio of 1 to 16. In other words, if we divide n by 32, we get the same result as if we divide 1 by 16.
To solve for n, we can use algebraic techniques to isolate the variable on one side of the equation. One way to do this is to multiply both sides of the equation by 32, which gives us:
n = (1/16) * 32
We can simplify the right-hand side of this expression by multiplying 1/16 by 32, which gives us:
n = 2
Therefore, the answer to this problem is n = 2. (option c).
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Complete Question:
n/32 = 1/16. Fine the value of n.
a. n = one-half
b. n = 4
c. n = 2
d. n = 512
hi would like some help asap
Answer:
B. quadratic
Step-by-step explanation:
You want to know the kind of function that would best fit the points shown on the graph.
SlopeThe points on the graph demonstrate a slope that starts out positive and decreases through 0 to a slope with a negative value.
A linear function has a constant slope.
An exponential function has a continuously increasing or continuously decreasing slope.
A quadratic function has a slope that changes sign, matching the slope of the curve joining the given points.
The equation that best fits the given data will be quadratic.
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araceli renta un local rectangular de 4.2 metros de frente y 7.3 metros de largo para su panaderia, ¿cuantos metros cuadrados tiene el local que rento?
The number of square meters that the space that Araceli rents is, is 30. 66 square meters.
How to find the area ?The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.
The given width is 4. 2 meters and the length is 7. 3 meters.
The area of the space in square meters is therefore :
Area = Length × Width
Area = 7. 3 meters × 4. 2 meters
Area = 30. 66 square meters
In conclusion, the space that Araceli rents has an area of 30. 66 square meters.
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Find TU and the area of △UVW.
The value of TU is 31.7 cm and the area of the triangle is 69.08 cm².
Give is triangle UVW, we need to find the value of TU and the area of the triangle UVW,
So, using the trigonometric ratios,
Sin 49° = TU/WU
TU = Sin 49° × WU
TU = Sin 49° × 42
TU = 31.7 cm
So, TU is the height of the triangle UVW, we know that the area of a triangle = 1/2 × height × base
= 1/2 × 31.7 × 44
= 31.7 × 22
= 69.08 cm²
Hence the value of TU is 31.7 cm and the area of the triangle is 69.08 cm².
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The radius of a cylindrical construction pipe is 1.5ft. If the pipe is 16ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
If the radius of a cylindrical construction pipe is 1.5ft, the volume of the construction pipe is approximately 452 cubic feet.
To find the volume of a cylinder, we use the formula V = πr²h, where r is the radius of the base, h is the height, and π is a constant approximately equal to 3.14.
In this problem, the radius is given as 1.5ft and the height is given as 16ft. Therefore, we can plug in these values to get:
V = π(1.5ft)²(16ft)
Simplifying this expression, we get:
V = 9π(16ft)
Using the value 3.14 for π, we can approximate the volume as:
V ≈ 9(3.14)(16ft) ≈ 452ft³
It's important to include the correct unit in the answer, which in this case is cubic feet.
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Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find C'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
a
{vanilla, strawberries, sprinkles}
b
{chocolate, hot fudge, peanuts, whipped cream}
c
{vanilla, hot fudge, sprinkles, whipped cream}
d
{chocolate, strawberries, sprinkles}
The complement of a set C, denoted by C', contains all the elements of the universal set that are not in C. In this case, the universal set is A, which contains all the flavors and toppings available.
Given data ,
a) {vanilla, strawberries, sprinkles}
This set contains vanilla, strawberries, and sprinkles but does not contain any elements from C. Therefore, C' = A - {vanilla, strawberries, sprinkles} = {chocolate, hot fudge, peanuts, whipped cream}.
b) {chocolate, hot fudge, peanuts, whipped cream}
This set contains all the elements of C but does not contain any elements from A that are not in C. Therefore, C' = A - C = {vanilla, strawberries, sprinkles}.
c) {vanilla, hot fudge, sprinkles, whipped cream}
This set contains hot fudge, sprinkles, and whipped cream but does not contain any elements from C. Therefore, C' = A - {hot fudge, sprinkles, whipped cream} = {vanilla, chocolate, strawberries, peanuts}.
d) {chocolate, strawberries, sprinkles}
This set contains strawberries and sprinkles but does not contain any elements from C. Therefore, C' = A - {strawberries, sprinkles} = {vanilla, chocolate, hot fudge, peanuts, whipped cream}.
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After running 5/6 of an hour konner is 1/3 of the way
The number of hours that Konner is left with till they can reach their destination is 1 ¹ / ₃ hours
How to find the number of hours ?We can start by using a proportion to set up an equation to solve for the time needed to arrive:
Distance traveled / total distance = time traveled / total time
Using a ratio, we infer that 5 / 6 of an hour is equivalent to 1 / 3 of the way.
This means that if there are 2 / 3 of the way left, the hours left till Konner reaches is:
= 5 / 6 x 2
= 10 / 6
= 5 / 3
= 1 ¹ / ₃ hours
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Question is:
How much longer till he arrives ?
10) Se invierten $8,000 a una tasa de interés compuesta continua del 4%, por lo que se puede usar la fórmula v(t)=8,000e.c para encontrar el valor de la inversión después de t años. ¿Después de cuántos 0.041 años se duplicará el valor de la inversión?
The number of years that it would take for the investment to double, given a continuous compounding rate, is 17. 33 years.
How to find the time to double ?The formula for continuous compound interest is given by:
[tex]A = Pe ^{rt}[/tex]
We are given $ 8, 000 and want to know how long it would take for this amount to double and become $ 16, 000.
The formula would be:
[tex]16,000 = 8, 000 e ^{0.04 t}2 = e ^{0.04t}[/tex]
ln ( 2 ) = 0 .04t
t = ln ( 2 ) / 0. 04
= 17. 33 years
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The population, P, of bacteria in a culture can be calculated at any time, t, using the equation P= a(2). In the equation, the initial number
of bacteria is a. The initial number of bacteria in two different cultures were 100 and 125.
How do the two populations compare over time?
The solution is, Option B.) one culture will have always 50 more bacteria than the other.
We have,
Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.
Given:
We have,
The population, P, of bacteria in a culture can be calculated at any time, t, using the equation P= a(2).
In the equation, the initial number of bacteria is a.
The initial number of bacteria in two different cultures were 100 and 125.
so, in one cultures population, P, of bacteria is = 100(2)
= 200
in the other cultures population, P, of bacteria is = 125(2)
= 250
so, we get,
the two populations compare over time = 250 - 200
= 50
Hence, The solution is, Option B.) one culture will have always 50 more bacteria than the other.
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Solve for x Round to the nearest tenth, if necessary.
Answer:
The answer is approximately 24
Step-by-step explanation:
tan0 =x/adj
tan15=x/90
x=90×tan15
x≈24
What is two thousand four hundred divided by fifty nine
Answer:40.6779661017
Step-by-step explanation:
please solve this ixl sucks
Filled box will be:
Box 1: Sum of angles on starlight line is 180°.
Box 2: m ∠LQR + m ∠MQR = 180°
Box 3: m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR
Box 4: m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR
Box 5: If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel.
From the given figure we have to prove that LM ∥ NP.
m ∠LQR + m ∠QRN = 180° [Given]
m ∠LQR + m ∠MQR = 180° [Sum of angles on starlight line is 180°]
m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR [Transitive property of Equality]
m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR [Subtraction property of Equality]
m ∠QRN = m ∠MQR [Definition of Congruence]
LM ∥ NP [If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel]
Hence it is proved that, LM ∥ NP.
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