The surface areas of the regular solids are;
1. a. 150 ft²
b. 216 ft²
c. 894 mm²
2. a. 118 square units
b. 892 in²
3. a. 576·π square units
b. 1024·π square units
c. 100·π square units
4. a. 216·π square units
b. 48·π square units
c. 48·π square units
5. To complete the task, two circles of 1 ft radius should be cut from the carpet, followed by cutting a rectangular shape of width 4 ft and length of 2·π ft
What is the surface area of a solid?The surface area of a solid is the sum of the areas that form a boundary around the outer part of the solid.
1 The surface area of a cube is A = 6·s²
a. When s = 5, A = 6 × 5² = 150
The surface area of a square of side length s = f ft = 150 ft²b. When s = 6 ft, A = 6 × 6² = 216
The surface area of a square of side length, s = 6 ft = 216 ft²c. When s = 12 mm, A = 6 × 12² = 864
The surface area when the side length of the square is 12 mm is 894 mm²2. The surface area of a rectangular prism is; S.A. = 2·l·w + 2·h·w + 2·l·h
a. l = 2, w = 5, h = 7
Surface area = 2 × (2 × 5 + 5 × 7 + 2 × 7) = 118
The surface area = 118 square unitsb. l = 16 in, w = 11 in, h = 10 in
The surface area = 2 × (16 × 11 + 16 × 10 + 10 × 11) = 892
The surface area of the rectangular prism is 892 in²3. The surface area of a sphere, A = 4·π·r²
a. The radius of the sphere, r = 12
A = 4 × π × 12² = 576·π
The surface area of the square, A = 576·πb. r = 16, therefore;
A = 4 × π × 16² = 1024·π
The surface area when the radius is 16 units is 1024·π square unitsc. When the diameter, d = 10, we get;
A = 4·π·r² = 4·π·(d/2)² = 4·π·d²/4
A = 4·π·d²/4 = π·d²
Therefore; the surface area, A = π × (10 units)² = 100·π square unitsThe surface area of a sphere of diameter, d = 10 units is 100·π square units4. The surface area of a cylinder, A = 2·π·r·h + 2·π·r²
a. r = 6, h = 12, therefore;
A = 2×π×6×12 + 2×π×6² = 216·π
The surface area of the cylinder = 216·π square unitsb. r = 2, h = 10, therefore;
A = 2×π×2×10 + 2×π×2² = 48·π
The surface area of the cylinder = 48·π square unitsc. r = 3, h = 5, therefore;
A = 2×π×3×5 + 2×π×3² = 48·π
The surface area of the cylinder = 48·π square units5. The diameter of the cylinder = 1 ft
Height of the cylinder = 4 ft
The area for the carpet to cover the each of the top and bottom = π×1² ft² = π ft²
The area to cover the curved surface = 2 × π × r × h
Therefore, area of the curved surface = 2 × π × 1 × 4 = 8·π
Area of the curved surface = 8·π ft²
Two circular shapes of radius 1 ft should be cut, followed by a rectangle of side length, 4 ft, and width 8·π/4 ft = 2·π ft
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let r be the region bounded by the parabola y=x2 and the line y=4. (a) what is the volume of the solid generated when r is rotated about the line y=4 ?
The volume of the solid generated when r is rotated about the line y=4 is 512/15π
In math the term called volume in math is defined as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we know that let r be the region bounded by the parabola y=x² and the line y=4.
Then the volume of the solid generated when r is rotated about the line y=4 is calculated by using the formula,
=> V = π ∫ᵇₐ [(h - f(x))]² dx
Here we have to apply the values on it, then we get,
=> V = π ∫₋₂² [(4 - x²)]² dx
By Using symmetry this can be written as,
=> V = 2π ∫₋₂² [16 - 8x² + x⁴] dx
When Solving the integral, then we get,
=> V = 2π (16x - 8/3x³ + 1/5x⁵)²₀
Here by Applying the fundamental theorem of calculus, then we get,
=> V = 2π (16(2) - 8/3(2)³ + 1/5(2)⁵) - 2π (16(0) - 8/3(0)³ + 1/5(0)⁵)
When we simplify this then we get
=> V = 512/15 π
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Graph the inequality.
र
y ≥ x-5
Answer:
Step-by-step explanation:
Using the graph attached, find all the point(s) such that the sum of their coordinates is equal to 7.
Answer: B, C, A.
Step-by-step explanation: positive, not negative
If the equation has one solution,
what number CAN'T the value of
h be?
h(- 2x + 5) = 4x + 5
Answer:
-2.5
Step-by-step explanation:
We can start by isolating h on one side of the equation:
4x + 5 = h(-2x + 5)
Divide both sides by -2x + 5:
(4x + 5) / (-2x + 5) = h
Now, since the equation has only one solution, the value of h must be well-defined for all values of x except those that would make the denominator equal to zero. This happens when -2x + 5 = 0, or when x = (5 - 5) / (-2) = -2.5.
So, the value of h cannot be determined when x = -2.5. This means that the value of h cannot be equal to -2.5.
unit 4 homework 6 congruent triangles proofs
#4 and 6
1) The proof that ΔFEH ≅ΔFGH is given as follows:
ΔFH bisects ∠EFG (Given)
∠FEH ≅ ∠ FGH.
FH = HF (Given)
∠EFH ≅ ∠FHG (Angle Bisector Theorem)
Thus, ΔFEH ≅ΔFGH (Angle - Side - Angle Theorem)
2) The proof that ΔPQR ≅ ΔTSR is:
∠RPQ ≅ ∠RTS - Given
R is the midpoint of QS - Given the Definition of Midpoint
QR ≅ RS - Definition of Midpoint
∠PRQ ≅ ∠SRT Vertical Angles
Thus: ΔPQR ≅ ΔTSR - Angle - Angle - Side Theorem.
3) the proof that ΔABC ≅ Δ DCB is given as follows:
ΔABC and ΔDCB are Right Angled Triangles
AB ≅ DC - Given
BC ≅CB - Reflective Properties; thus
ΔABC ≅ ΔDCB - Hypothenus Leg Theorem.
What is the Hypotenuse Leg Theorem?
According to the hypotenuse-leg (HL) theorem, if the hypotenuse and a leg of a right triangle are both congruent with the corresponding hypotenuse and leg of another right triangle, the triangles are congruent. According to the HL theorem, these triangles are congruent.
There is one exception to this rule: when the angles are straight angles. Using words: The triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle.
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Scott fixed two vases if flowers for Lana. Vase J contained 14 carnations and half a dozen of roses. Vase K contained 15 carnations and a dozen daises. Which statement is true?
A.The probability of randomly selecting a carnation from Vase J is greater than the probability of randomly selecting a carnation from Vase K.
B. The probability of randomly selecting a carnation from Vase K is less than 50%.
C. The probability of randomly selecting a carnation from Vase J is 1/14
D. The probability of randomly selecting a carnation from vase K is greater than the probability of randomly selecting a carnation from vase J.
The answer to option D) is yes. The likelihood of choosing a carnation at random from vase K is higher than the likelihood of choosing one at random from vase J.
What are examples and probability?The possibility is determined on the range of potential outcomes. the estimated number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping the coin and receiving heads is 1 in 2. (a head or tail). We write P(heads) = 12 here.
What in mathematics is probability?Roughly simply, probability is the chance that everything will exist. When we wouldn't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes.
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Ben helped his dad make soup. Their recipe made 15 cups. If they eat 2 cups, will their leftovers fit in a 64-ounce container.
Answer:
No, it would not fit because one cup is 8 ounces and if you times 8 and 13 it 104 so it would not fit they would need another container.
Step-by-step explanation:
hope it helps
a rectangle has a length of 4 meters and a width of 150 centimeters what is the perimeter of the rectangle in meters
The perimeter of the rectangle with a length of 4 meters and a width of 150 centimeters is 11 meters.
What is the perimeter of the rectangle?A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The perimeter of a rectangle is expressed as;
Perimeter = 2( length + width )
Given the data in the question;
Length of rectangle = 4 metersWidth of rectangle = 150 cm = ( 150/100 )m = 1.5 metersPerimeter = ?Plug the values into the above equation.
Perimeter = 2( length + width )
Perimeter = 2( 4 meters + 1.5 meters )
Perimeter = 2( 5.5 meters )
Perimeter = 11 meters
Therefore, the perimeter is 11 meters.
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if we throw uniformly at random a point on segment [0,1], then its expected position is 1/2. what are the expected positions of two random points on segment [0,1]?
If we throw uniformly at random a point on segment [0,1], then its expected position is 1/2. the expected positions 1/3 and 2/3 of two random points on segment [0,1] are [0,1/3],[1/3,2/3]and[2/3,1]
In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen. Given the interval is [0,1]
Then it's expected position is 1/2
So [0,1/2] and[1/2,1]
Now we get the two expected positions
I. E three intervals
So (1-0)/3
=1/3
So 1/3 and 2/3 are expected positions
They are [0,1/3],[1/3,2/3]and[2/3,1]
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The cost of 78 apples is £27.30. (a) Find the approximate (b) Find the approximate cost of 49 apples. cost of 698 apples.
Salut/Hello!
Answer: a) £244 ; b) £17
Step-by-step explanation:
First we need to know the cost of one apple.
27.30 : 78 = £0.35
a) [I'm going to assume you meant 698 apples here]
£0.35 x 698 = £244.3 with the approximate of £244
b) £0.35 x 49 = £17.15 with the approximate of £17
I hope it was helpful! :]
for a 13-person team, on average, how many overtime hours will each person need to work?
Based on the numerical data, we can estimate that 26 more labor hours will be necessary to satisfy the labor hours required without overtime.
What is Overtime?The Fair Labor Standards Act, enacted by the federal government, places a cap on the number of hours per week (40 hours) that businesses may demand their employees to perform in exchange for regular pay. Employers were now required to give employees who put in more than 40 hours of work additional compensation in the form of overtime pay.
Hence,
Overtime pay is usually 1.5 times the employee's regular hourly wage.
So, if an employee is paid $15 per hour, their overtime rate is $22.50 per hour ($15 multiplied by 1.5).
If another employee is paid $25 per hour, overtime is $37.50 per hour ($25 x 1.5).
It would require 26 more labor hours will be necessary to satisfy the labor hours required without overtime.
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Write a system of linear equations for the graph below.
Y=
Y=
The system of linear equations for the given graph is: y = 1/2x + 6; y = -3x - 1
The graph of a linear equation.The graph of a linear equation follows a slope-intercept form y= mx + b, where m is the slope and b is the y-intercept. We can determine the graph of a linear equation by merely looking at the graph and finding two points on the graph from which the slope of the graph can be determined the represent it as a linear equation.
The linear equation can now be converted to a standard form to determine the system of the linear equation.
From the graph.
The first upper graph to the right shows the point (-2, 5) and (0,6)
The second graph to the left shows the point (-2, 5) and (0,-1)
The slope of the first graph = (6 - 5 )/(0--2) = 1/2; The y-intercept = 6
In slope-intercept form, we have:
y = 1/2x + 6 ----- (1)
The slope of the second graph = (-1 - 5)/(0--2) = -6/2 = -3
The y-intercept = -1
In slope-intercept form: y = -3x - 1 ------- (2)
y = 1/2x + 6
y = -3x - 1
Therefore, we can conclude that the system of linear equations for the given graph is: y = 1/2x + 6; y = -3x - 1
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Find the perimeter of the composite figure below. (semicircle). Round to the nearest tenth. Use π = 3.14
take upper base = 12
take upper base = 12right side= 20
take upper base = 12right side= 20apply pythagorus
take upper base = 12right side= 20apply pythagorus .
take upper base = 12right side= 20apply pythagorus .= 13
now semi circle= 2 pi r/2 = pi × (11/2)
add all
12 +20+13× 5.5pi
Answer:
64.27cm
Step-by-step explanation:
Total perimeter =
semicircle + Length of rectangle + Breadth of rectangle and triangle +
hypotenuse of Triangle
semicircle = pi x r (r = radius)
= 3.14 x 11/2
= 17.27 cm -----------------(1)
Length of rectangle = 12cm (Given) ----------------------(2)
Base (rectangle and triangle) = 20cm (Given) --------------------(3)
Hypotenuse = Root of (20-11)^2 + 12^2
= Root of 9^2 + 12^2
= Root of 81 + 144
= Root of 225
= 15cm ---------------------------(4)
By adding (1), (2), (3) and (4) we get
= 17.27 + 12 + 20 + 15
= 64.27cm
what is the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended waranty
The probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty = 0.493
Here, 21% of customers purchase extended warranty.
So, the probability p = 0.21
It takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty is nothing but none of the first three buy.
This means, we find probability P(X = 0) when n = 3.
Using Binomial distribution formula for probability,
P(X = 0) = ³C₀ (0.21)⁰ (1 - 0.21)⁽³ ⁻ ⁰⁾
P(X = 0) = ³C₀ (0.21)⁰ (0.79)⁽³ ⁻ ⁰⁾
P(X = 0) = 0.493
Therefore, the required probability is 0.493
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The complete question is:
The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible
items are chosen at random one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who
purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independentWhich of the following is closest to the probability that X > 3;
that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?
PLEASE HELP RIGHT AWAY When angle A + angle B = 90 deg what relationship formed by tan angle A and tan angle B? Select all that apply.
The relationship between tan A and tan B is: tan A * tan B = 1
How to determine the relationshipFrom the question, we have the following parameters that can be used in our computation:
angle A + angle B = 90 deg
When angle A + angle B = 90 degrees,
The two angles are complementary, meaning they add up to 90 degrees.
In this case, the relationship between tan A and tan B is:
tan A * tan B = 1
This is known as the tangent addition formula.
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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $1400 and her stock in Company B was worth $7100. The stock in Company A has decreased 5% since last year and the stock in Company B has decreased 9%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Answer:
Total decrease as a percentage 12.4%
Step-by-step explanation:
Please find the attachment for detail
Which equation is an equation of a circle with a radius of 3 and its center is at (5, -2)?
Responses
(x - 5)² + (y + 2)² = 9
(x + 5)² + (y - 2)² = 9
(x - 5)² + (y + 2)² = 3
(x + 5)² + (y – 2)² = 3
The correct equation of the circle is the first option which is
(x - 5)² + (y + 2)² = 9
What is a circle?
A circle is a collection of all points in a plane that is uniformly distanced from a fixed point. The fixed point is referred to as the circle's centre. The radius of a circle is the separation between the centre and any point along its circumference.
The general equation of the circle is
(x-h)² + (y-k)² = r²
where r = radius of the circle
(h,k) = centre of the circle
Given,
radius r = 3
centre = (h,k) = (5,-2)
According to the above equation,
(x-5)² + (y-(-2))² = 3²
(x-5)² + (y+2)² = 9
Therefore the correct equation of the circle is the first option.
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The 4th term of a geometric sequence is -25 and the 9th term is 25/32. find the 15th term
The 15th term of the geometric progression is a₁₅ = 25/2048
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the 15th term of the geometric progression be a₁₅
Now , the 4th term of the GP is a₄ = -25
The 9th term of the GP is a₉ = 25/32
Now , nth term of a GP is aₙ = arⁿ⁻¹
Substituting the values in the equation , we get
a₄ = ar³ = -25 be equation (1)
a₉ = ar⁸ = 25/32 be equation (2)
Divide equation (2) by equation (1) , we get
r⁵ = -( 1/32 )
r⁵ = - ( 1/2 )⁵
So , the common ratio r = -1/2
Now , the first term of the GP a is calculated by
ar³ = -25
when r = -1/2
a ( -1/2 )³ = -25
a/8 = 25
a = 200
Now , the 15th term of the geometric progression a₁₅ = ar¹⁴
Substituting the values in the equation , we get
a₁₅ = 200 ( -1/2 )¹⁴
a₁₅ = 200/16,384
a₁₅ = 25/2048
Hence , the 15th term of the GP is 25/2048
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Rearange the equation to make b the subject. a = 1/4 b.
The value of the equation a = (1/4)×b in terms of a is b = 4a.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression a = (1/4)×b.
Now, Making 'b' the subject is the same as solving for 'b'.
We know when a term is multiplied by another term moving it to the other side we have to take its reciprocal.
Therefore, a = (1/4)×b.
b = a×(4/1).
b = 4a.
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The price of a jumper is increased by 17% and is now $319.31.
Find the original price of the jumper.
Answer in $
In linear equation, $54.3 is the original price of the jumper.
Which equation is linear equation ?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
17% of 319.41
17/100 * 319.41
= 54.2997
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what are the critical values for the decision rule when the level of significance is 0.10? round your answer to two decimal places.
The critical values for a decision rule at a level of significance of 0.10 (i.e., a 10% significance level) depend on the type of hypothesis test you are conducting and the specific distribution you are using.
The decision criteria is based on certain test statistic results (for example, reject H0 if Z > 1.645). A given test's decision rule is determined by three factors: the research or alternative hypothesis, the test statistic, and the degree of significance.
A crucial value is the value of the test statistic that establishes the upper and lower boundaries of a confidence interval or the statistical significance threshold in a statistical test.
Critical values for a hypothesis test are determined by a test statistic that is particular to the type of test and the significance level, alpha, which specifies the test's sensitivity.
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What is the image of (-6,-5) after a reflection over the x-axis?
Answer:
6,5
Step-by-step explanation:
7. Fill in the blanks below to make each statement true.
a. Fewer than 15% of coins were
of the coins were quarters.
b. Exactly
c. Nickels, dimes, and quarters account for
of the total number of coins.
Fewer than 15% of coins were quarters. Exactly 80% of the coins were nickels, dimes, and quarters. Nickels, dimes, and quarters account for 95% of the total number of coins.
What is the quarters?Quarters are coins that are used in many countries as a form of currency. Quarters are generally made of metal and are round in shape. They are typically smaller than other coins, such as dimes and nickels, and have a value of 25 cents (or one-fourth of a dollar). Quarters are often used in everyday transactions, such as buying candy or a newspaper, or to pay for parking. In the United States, there are five different designs of quarters in circulation, each representing a different state or territory.
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The most popular size pizza at pizza parlor is a large with a 12-inch radius.What is the circumstance of the pizza?
Answer:
37.17
Step-by-step explanation:
I took the test
Answer: The circumference of the pizza is 37.7 inches.
Given data :
Diameter of the pizza = 12 inches
So,
Radius of the pizza = 12/2
= 6 inches
So,
Circumference of the pizza
= 2×π×radius
= 2×22/7×6
= 37.7 inches (answer)
Find the missing side of each triangle. Round to the nearest tenth if necessary.
I found the answer with the ruluer it's 11.3
In circle B with the measure of minor arc AC= 126°, find m/ADC.
Answer:
Step-by-step explanation:
=63
The measure of arc ADC in circle B with the measure of minor arc AC= 126° is 234°.
Given that the measure of minor arc AC = 126°, we can find the measure of arc ADC using the following formula:
m/ADC = 360° - m/AC
Plugging in the values, we get:
m/ADC = 360° - 126° = 234°
Therefore, the measure of arc ADC is 234°.
Here is the explanation:
A minor arc is an arc that is less than 180°.
The measure of a minor arc is equal to the measure of the central angle that intersects it.
The measure of a whole circle is 360°.
Therefore, the measure of arc ADC is equal to the difference between the measure of the whole circle and the measure of minor arc AC. This difference is 360° - 126° = 234°.
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the chi square value of a given dihybrid analysis is 0.47. if the degrees of freedom in the analysis were 3, would the null hypothesis be rejected?
If the chi square value of a dihybrid analysis is 0.47 , and degree of freedom in analysis were 3 , then the null hypothesis will not be rejected because 0.47 < 7.815 .
To determine whether to reject or accept the Null Hypothesis, a critical value of chi-square with a given level of significance is used.
If the calculated chi-square value is greater than the critical value, then the null hypothesis is rejected. and
If the calculated chi-square value is less than or equal to the critical value, then the null hypothesis is not rejected.
The critical value of chi-square for a level of significance and degrees of freedom can be found using a chi-square distribution table.
With a level of significance of 0.05 and 3 degrees of freedom, the critical value of chi-square is 7.815.
that means ⇒ 0.47 < 7.815, the null hypothesis would not be rejected at a level of significance of 0.05 .
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2000 a month for 15 months with 4% interest
Answer:
1200
Step-by-step explanation:
4% of 2000 is 80 then do 80*15 and you get 1200
Calculate the difference and enter it below.
--12-(-8)
Answer: -4
Step-by-step explanation:Since subtracting a negative number is the same as adding a positive number, -12 - (-8) can be rewritten as -12 +8. Counting 8 up from negative 12 leaves us with negative 4.
Can someone help me with this aleks
