The angle of elevation from Jazmin to the top of the tree is 14°.
We are given that;
Top of tree= 24ft
String= 100ft
Now,
We can use any trigonometric ratio that involves opposite and hypotenuse sides, such as sine or cosine. Let’s use sine for this example.
sin θ = opposite / hypotenuse
sin θ = 24 / 100
sin θ = 0.24
θ = sin^-1 (0.24)
θ = 13.9° (rounded to the nearest degree)
Therefore, by the angle the answer will be 14°.
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Willow owns 225 books. Of them, 5/9 are
mysteries. How many of Willow's books
are mysteries?
A) 225
B) > 225
C) < 225
D) 0
(Side note:)please provide explanation
The quantity of Willow's books that are mysteries would be = 125 books.
How to calculate the quantity of his books that are mysteries?To calculate the quantity of books that are mysteries the following is carried out.
The total number of books that willow has = 225 books
The total number of books that are mysteries = 5/9 of 225
That is ;
= 5/9 × 225/1
= 1125/9
= 125 books.
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Jake measured a hotel and made a scale drawing. The scale of the drawing was 8 inches : 7 feet. If the actual length of a room in the hotel is 21 feet, how long is the room in the drawing?
Jake measured a hotel and made a scale drawing, the length of the room in the drawing is 24 inches.
If the scale of the drawing is 8 inches : 7 feet, this means that for every 8 inches in the drawing, there are 7 feet in real life.
To find out length of the room is in the drawing, we need to set up a proportion:
8 inches / 7 feet = x inches / 21 feet
where x is the length of the room in the drawing.
We can cross-multiply and solve for x:
8 inches × 21 feet = 7 feet × x inches
168 inches = 7 feet × x inches
Dividing both sides by 7, we get:
24 inches = x
Therefore, the length of the room in the drawing is 24 inches.
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Select the statement that shows equivalent measurements.
14 grams = 0.14 decagrams
14 grams = 1.4 decigrams
14 grams = 140 centigrams
14 grams = 14,000 milligrams
Answer:
14 grams = 14,000 milligrams
Step-by-step explanation:
since multiply the grams by 1000 will convert it to milligrams
Please answer this question as quick as possible I’ll give brainliest if it’s correct, thank you
Answer:
(a) 3581 N
(b) 6.1 kJ
(c) 4.5 kJ
(d) 74.6%
Step-by-step explanation:
(a) To lift the piano straight up, we need to counteract the force of gravity acting on it. The force required can be calculated using the formula F = mg, where F is the force, m is the mass of the piano, and g is the acceleration due to gravity. So, F = (230 kg) x (9.81 m/s^2) = 3581 N.
(b) The work done in lifting the piano is given by the formula W = Fd, where W is the work done, F is the force required to lift the piano, and d is the height to which the piano is lifted. So, W = (3581 N) x (1.7 m) = 6.1 kJ.
(c) Using a ramp reduces the force required to lift the piano. The force required can be calculated using the formula F = mg sinθ, where θ is the angle of inclination of the ramp. We are given that the force required is 300 N and the length of the ramp is 15 m. So, sinθ = F/mg = 300/(230 x 9.81) = 0.1416. Therefore, θ = sin^-1(0.1416) = 8.13 degrees. The work done using the ramp can be calculated using the formula W = Fd, where d is the height to which the piano is lifted. Using trigonometry, we can find that the height to which the piano is lifted is 1.53 m. So, W = (300 N) x (15 m) x sin 8.13 degrees = 4.5 kJ.
(d) The efficiency of the ramp is the ratio of the work output to the work input, expressed as a percentage. The work output is the same as the work done using the ramp, which is 4.5 kJ. The work input is the same as the work done when lifting the piano straight up, which is 6.1 kJ. So, the efficiency of the ramp is (4.5/6.1) x 100% = 74.6%.
using the gcf, what is the factored form of 75
Answer:
The prime factorization of 75 is:
75 = 3 * 5^2
The greatest common factor (GCF) of the number 75 is 1, since 1 is the highest factor that can be shared by all the prime factors of 75.
Therefore, the factored form of 75 using the GCF is:
75 = 1 * 3 * 5^2
PLEASE MARK BRAILYEST! :D
Find the area I will give brainliest
The area of the triangle is 22 miles square
Finding the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
Where we have
Base = 11 miles
Height = 4 miles
using the above as a guide, we have the following:
Area = 1/2 * Base * Heigt
substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 11 * 4
Evaluate
Area = 22 miles square
hence, the area is 22 miles square
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In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Paul has scored 82 , 88 , and 87 on the first three. What range of scores on the fourth test will give Paul a C for the semester (an average between 70 and 79 , inclusive)? Assume that all test scores have a non-negative value.
Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).
The sum of the scores on the first three, hundred point tests
= 82 + 88 + 87 = 257.
The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.
The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.
Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.
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A homeowner installed and kitchen cabinets and countertops for $4,500.00. He paid 15% down and financed the balance with 24-month fixed installment loan with an APR of 7.0%. Determine the total final charge and monthly payment for the loan.
Answer:
4,500.00 rupees
Step-by-step explanation:
The simple interest charged on a 2-month loan of $22,000 is $521. Find the simple interest rate. (Round your answer to one decimal place.)
A _____________ shape is one that does not have an identifiable name. While still flat, 2-D enclosed areas, these shapes are more "freeform" and might resemble things that we see in nature.
Question 5 options:
Geometric
Organic
Symmetrical
Asymmetrical
A Organic shape is one that does not have an identifiable name. While still flat, 2-D enclosed areas, these shapes are more "freeform" and might resemble things that we see in nature.
What is Organic shape?Geometric shapes are well-defined, regular shapes described by mathematical formulas, including circles, squares, triangles, and rectangles. Symmetrical shapes exhibit mirror-like symmetry, like butterflies or snowflakes.
Organic shapes appear in natural objects like leaves or rocks; they are flowing and curvilinear in form, with varying size, proportions, and contours. Organic shapes are free from strict rules and symmetry, often used in art.
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In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase. Suppose that it takes you one hour to stroll at a constant speed up one spiral of this staircase, which has a radius of 28 feet and a height of 60 feet and makes 6 revolutions.
a)Assuming the spiral staircase is centered about the z-axis, find a vector parametric equation for the helical path you take from the point (28,0,0) to the point (28,0,60) that makes 6 revolutions during the time interval 0≤t≤1.
b)How far did you walk?
a) The vector parametric equation for the helical path is r(t) = <28cos(12πt), 28sin(12πt), 5t*12>, where t is the parameter and 0 ≤ t ≤ 1.
b) You walked a total distance of 840π feet.
a) To find the vector parametric equation for the helical path, we first note that the spiral staircase makes 6 complete revolutions as we climb from the bottom to the top. This means that as we climb 60 feet, we will make 6 full revolutions around the z-axis. Since the radius of the spiral is 28 feet, we can use the equation for a helix to describe our path.
r(t) = <28cos(θ), 28sin(θ), ht>
where θ is the angle of rotation around the z-axis and h is the height we have climbed. We know that we make 6 full revolutions, or 12π radians, as we climb from the bottom to the top, so we can substitute θ = 12πt. We also know that we climb 60 feet in one hour, so our height function is h(t) = 5t*12.
Thus, our vector parametric equation for the helical path is r(t) = <28cos(12πt), 28sin(12πt), 5t*12>, where t is the parameter and 0 ≤ t ≤ 1.
b) To find the distance we walked, we need to integrate the magnitude of the velocity vector over the interval [0,1].
The velocity vector is the derivative of the position vector:
v(t) = < -336πsin(12πt), 336πcos(12πt), 60>
The magnitude of the velocity vector is:
|v(t)| = sqrt((-336πsin(12πt))^2 + (336πcos(12πt))^2 + 60^2) = 336π
Thus, the distance we walked is:
distance = ∫|v(t)|dt from 0 to 1 = ∫336π dt from 0 to 1 = 336π(1-0) = 336π
Therefore, we walked a total distance of 840π feet.
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Xzavier stops by Sweet Treats after school to get a birthday surprise for his mom. He has $11. The table shows the prices of his mom's favorite treats.
Sweet Treats
Candy Price per Pound
Chocolate-covered Cashews $13.88
Chocolate-Peanut Butter Cups $11.46
Chocolate-Caramel Bites $9.62
Gourmet Gummy Bears $8.24
After looking at the prices, Xzavier decides to get two different one-half pound bags of candy for his mom. Do not consider tax. If Xzavier spends the greatest amount possible for two different one-half pound bags of candy, which two candies did he buy?
A. chocolate-covered cashews and chocolate-caramel bites
B. chocolate-peanut butter cups and chocolate-caramel bites
C. gourmet gummy bears and chocolate-caramel bites
D. chocolate-peanut butter cups and gourmet gummy bears
Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.
How will Xzavier decide which two candids he buy?Xzavier should choose the two candies with the highest price per pound to maximize his spending.
The prices per pound are as follows:
$13.88 for chocolate-covered cashews
$11.46 for chocolate-covered peanut butter cups
$9.62 for Chocolate-Caramel Bites
$8.24 for Gourmet Gummy Bears
Chocolate-covered Cashews and Chocolate-Peanut Butter Cups are the two chocolates with the highest per-pound pricing.
As a result, Xzavier purchased a half-pound of Chocolate-covered Cashews and a half-pound of Chocolate-Peanut Butter Cups.
Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.
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What is the narrowest definition of the number -2
Step-by-step explanation:
The narrowest definition of the number -2 is that it is an integer that is less than zero and has an absolute value of 2. In other words, it is the additive inverse of the number 2, and can be written as "-2 = -1 * 2".
(2a^2)^3 fill in the blank
You have to apply the outside exponent to each piece inside the parentheses.
[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]
You have to apply the outside exponent to each piece inside the parentheses.
[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]
the odds in favor of an event are give compute the probability of the event enter the probability as a fraction 4 to 9
The probability of the event is 4/13 when the odds in favor of the event are 4 to 9.
When the odds in favor of an event are given as a ratio of "a to b", the probability of the event can be calculated as:
Probability of the event = a / (a + b)
In this case, the odds in favor of the event are 4 to 9.
Therefore, we have:
a = 4 (the number of favorable outcomes)
b = 9 (the number of unfavorable outcomes)
Substituting these values into the formula, we get:
Probability of the event = 4 / (4 + 9)
Probability of the event = 4 / 13
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Sasha has $850 into two accounts. Sasha will deposit $450 at 6% simple. She will deposit the rest at 2% compounded annually. Sasha will not make any withdrawals. How much more money will be in her account at 6% simple than at 2% compounded annually after 2 years.
Sasha will deposit $450 at 6% simple interest. The formula for calculating the balance of an account with simple interest is given by A = P(1 + rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), and t is the time in years.
In this case, the initial principal balance P is $450, the annual interest rate r is 6% or 0.06 as a decimal, and the time t is 2 years. Plugging these values into the formula gives us:
A = 450(1 + 0.06 * 2)
Evaluating this expression gives us a final amount of approximately $477 in the account after two years.
Sasha will deposit the rest of her money ($850 - $450 = $400) at 2% compounded annually. The formula for calculating the balance of an account with annual compounding is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per unit time (per year in this case), and t is the time in years.
In this case, the initial principal balance P is $400, the annual interest rate r is 2% or 0.02 as a decimal, n is 1 since it’s compounded annually, and the time t is 2 years. Plugging these values into the formula gives us:
A = 400(1 + 0.02/1)^(1 * 2)
Evaluating this expression gives us a final amount of approximately $416.16 in the account after two years.
Therefore, there will be approximately $60.84 more money in Sasha’s account at 6% simple interest than at 2% compounded annually after two years.
Please help me solve questions 10, 11, & 12!
Answer:
Pretty sure it’s A, D, A
Step-by-step explanation:
Knowledge Check 01
The allowance method of accounting for bad debts has the following advantages over the direct write-off method including: (You may
select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and
double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be
automatically graded as incorrect.)
*Records estimated bad debts expense in the pertod when the related sales are recorded.
Records estimated bad debts expense when the account receivable is determined to be uncollectible.
*Reports accounts receivable on the balance sheet at the estimated amount of cash to be collected
• Reports sales on the income statement at the estimated amount of cash to be collected.
The correct options are - A. In the period in which the corresponding sales are recorded, records the expected bad debt expenditure. and C. Reports accounts receivable at the estimated amount of cash to also be collected on the balance sheet.
Explain the benefits of allowance method:The measure that the company uses to set aside money for its bad debts or uncollectible accounts is known as the allowance method of accounting. This accounting technique reflects the accrual basis.
The key benefit of applying the allowance technique in business is that it enables the company to give interested parties accurate financial reporting. By the allowance approach, the precise account receivable with in balance sheet can be estimated. Also, the management will be able to make decisions about their creditors plus bad debt collection with the use of these trustworthy disclosures. The business can determine the precise number of account heads there in statement of business by conducting a proper examination of its holdings and receivables.Know more about the allowance method
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Correct question:
The allowance method of accounting for bad debts has the following advantages over the direct write-off method including: (You may select more than one answer. ):
A. Records estimated bad debts expense in the period when the related sales are recorded.
B. Records estimated bad debts expense when the account receivable is determined to be uncollectible.
C. Reports accounts receivable on the balance sheet at the estimated amount of cash to be collected
D. Reports sales on the income statement at the estimated amount of cash to be collected
QUICKLY HELP ME! Trigonometry
The value of tan (2∅) in the right triangle is - 960 / 644.
How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
15² + 8² = 17²
Let's find ∅ using trigonometric ratios,
tan ∅ = opposite / adjacent
tan ∅ = 15 / 8
Therefore,
tan 2∅ = 2 tan ∅ / 1 - tan² ∅
tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²
tan 2∅ = 30 / 8 ÷ 1 - 225 / 64
tan 2∅ = 15 / 4 ÷ 64 - 225/ 64
tan 2∅ = 15 / 4 ÷ -161 / 64
tan 2∅ = 15 / 4 × 64 / -161
tan 2∅ = - 960 / 644
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The value of tan (2∅) in the right triangle is - 960 / 644.
How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
15² + 8² = 17²
Let's find ∅ using trigonometric ratios,
tan ∅ = opposite / adjacent
tan ∅ = 15 / 8
Therefore,
tan 2∅ = 2 tan ∅ / 1 - tan² ∅
tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²
tan 2∅ = 30 / 8 ÷ 1 - 225 / 64
tan 2∅ = 15 / 4 ÷ 64 - 225/ 64
tan 2∅ = 15 / 4 ÷ -161 / 64
tan 2∅ = 15 / 4 × 64 / -161
tan 2∅ = - 960 / 644
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Find the partial fraction decomposition of 15/(x-7)(x+3)
Answer:
[tex]\frac{15}{(x-7)*(x+3)} = \frac{3/2}{x-7} + \frac{-3/2}{x+3}[/tex]
Step-by-step explanation:
Set up the partial fraction decomp:
[tex]\frac{15}{(x-7)*(x+3)} = \frac{A}{x-7} + \frac{B}{x+3}\\[/tex]
Multiply across:
[tex]15 = (\frac{A}{x-7} + \frac{B}{x+3})*(x+3)*(x-7)\\15 = A(x+3) + B(x-7)\\[/tex]
You can do this two ways from this point, you can plug in values for x to solve for A and B individually or set up a system of equations to find A and B
[tex]15 = Ax + 3A + Bx -7B\\Ax + Bx = 0\\3A - 7B = 15\\[/tex]
From the first equation we can see that A = -B, plugging into the second equation we get that
-10B = 15, so therefore B = -3/2 and because of the first equation A = 3/2 giving us our answer
6 Harpreet wants to put tiles on the ceiling of a room.
He has this sketch of the ceiling.
11 m
5.5 m
Harpreet knows one pack of ceiling tiles
covers an area of 3.24 m²
costs £34.95
4m
9m
Ceiling tiles can be cut and joined.
Calculate the total cost of the packs of ceiling tiles Harpreet has to buy.
(6)
w transaction list
ournal entry worksheet
<
1
2
3
Transactions
Note: Enter debits before credits.
4
Record the entry to receive October's rental bill of $1,200; set it aside.
Pont Even
5
6
General Journal
Debit
C
The journal entry for the given information is below:
How to solveJournal entries:
S.no. Accounts title andd explanations Debit $ Credit $
a. Accounts receivable 2500
Service revennue 2500
b. Cash account 2000
Service revenue 2000
c. Cash account 500
Unearned service revenue 500
d. Accounts receivabale 1500
Cash account 1500
e. Rent Payable 500
Cash account 500
f. Rent expenses 750
Rent payable 750
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The following loan is discounted. Find (a) the discour P = $1510.00, r=42%, t = 4 years Part: 0 / 3 Part 1 of 3
The triangular front has a base of how many feet and a height of how many feet? The length of the tent is __ft?
The Dimensions of the tent are: Base of triangular face (b): 4.46 ft, Height of triangular face (0.5b): 2.23 ft, Length of tent (b + 1): 5.46 ft.
What is a triangular prism?With two triangular bases and three rectangular sides, a triangular prism is a three-dimensional geometric form. The rectangular faces link the matching edges of the bases, which are connected by the parallel triangular bases. This produces a form with a triangular cross-section along the prism's length. The distance between the vertices of the triangle bases is referred to as the length, whereas the height of the prism is the perpendicular distance between the bases.
Given:
Volume of tent = [tex]63 ft^3[/tex]
Let's assume the base of the triangular face of the tent is "b" feet. The height of the triangular face is half of the base, so it would be "0.5b" feet.
The length of the tent is given to be 1 foot more than the base, so the length would be "b + 1" feet.
Mathematically, the volume of a triangular prism can be given by:
[tex]Volume = (1/2) * base * height * length[/tex]
Substituting the given values and rearranging the formula to solve for "b":
[tex]63 = (1/2) * b * (0.5b) * (b + 1)\\126 = b^2 * (0.5b) * (b + 1)\\0.5b^3 + 0.5b^2 - 126 = 0[/tex]
Solving this cubic equation, we get "b ≈ 4.46" (rounded to two decimal places).
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Gina Wilson unit 9 Transitions I need help on the back page
Part a: translation: (x,y) ---> (x + 1, y - 8); D'(3, -1), E'(8, -2), F'(4, -8), G'(-1, -7).
Part b: reflection : in the x axis :D'(2,-7), E'(7,-6), F'(3,0) and G'(-2,-1).
Explain the term "translation":In geometry, a translation is a transfer that occurs either laterally to the left or right as well as vertically up or down.
It may also consist of a mix of the two. Instead, you should evaluate the coordinates of the important locations in the first and second figures if you need must describe a translation. The number of units that have been moved horizontally, vertically, and in which directions are noted verbally.
Given that:
Parallelogram DEFG withvertices D(2,7), E(7,6), F(3,0) and G(-2,1).Part a: translation: (x,y) ---> (x + 1, y - 8)
D(2,7) -> D'(2 + 1, 7 - 8) = D'(3, -1)
E(7,6) -> E'(7+ 1,6- 8) = E'(8, -2)
F(3,0) -> F'(3+ 1,0- 8) = F'(4, -8)
G(-2,1) -> G'(-2+ 1,1- 8) = G'(-1, -7)
Thus, the coordinates of D'E'F'G' - D'(3, -1), E'(8, -2), F'(4, -8), G'(-1, -7).
Part b: reflection : in the x axis
vertices D(2,7), E(7,6), F(3,0) and G(-2,1).
value of x will remain same, but y get negative.
(x,y) -- (x, -y)
D'(2,-7), E'(7,-6), F'(3,0) and G'(-2,-1).
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Correct question:
Parallelogram DEFG with vertices D(2,7), E(7,6), F(3,0) and G(-2,1):
a: translation: (x,y) ---> (x + 1, y - 8)
b: reflection : in the x axis
I want to know what the scale factor is of this
Answer:
scale factor = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the side corresponding to WX is EH
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{EH}{WX}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
what's the area of a circle with a 74ft diameter use 3.14 for pie
Area of a circle is given by
[tex]\text{A} = \pi \times r^2[/tex]
We need to know the radius
[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]
[tex]\text{r} = \dfrac{\text{74}}{2}[/tex]
[tex]\text{r} = 37 \ \text{mm}[/tex]
The radius is 37 mm and pi = 3.14
[tex]\text{A} = 3.14 \times (37)^2[/tex]
[tex]\text{A} = \boxed{\bold{4298.66 \ \bold{mm}^2}}[/tex]
If the area of the map of the triangle is 2 square inches. and on the map itself the whole shaded region 1 inch =1/4 square inches; then what is the area of the shaded region in the picture
A.1/2 square inches
B.1/8 square inches
C.8 square inches
D. some other solution
The area of the shaded region on the actual triangle is: 2/16 = 1/8 inches²
So the answer is (B) 1/8 inches².
What is area?The size of a two-dimensional surface or region, such as a floor's surface, a painting's face, or the contours of a piece of land, is measured in terms of area.
It represents the amount of space that is enclosed or occupied by the surface or region under consideration and is typically measured in square units, such as square metres or square feet.
The area of the shaded region on the actual triangle is related to the area of the shaded region on the map by the square of the scale factor. In this case, the scale factor is 1 inch = 1/4 square inches, so the square of the scale factor is:
(1/4)² = 1/16
This means that the area of the shaded region on the actual triangle is 1/16th the area of the shaded region on the map.
The area of the shaded area on the map is 2 inches², matching the area of the triangle on the map, which is 2 inches²
Therefore, the shaded area on the actual triangle has the following area:
2/16 = 1/8 inches².
Therefore, the response is (B) 1/8 inches².
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Identify which of the following is a geometric sequence. A. 3, 12, 48, . . . B. 3, 1, , . . . C. 0, 1, 3, 9, . . . D. 3, 6, 12, 21, . . .
The geometric sequence in the list of options is A. 3, 12, 48, . . .
Identify the geometric sequence.A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number.
A. 3, 12, 48, . . . is a geometric sequence because each term is obtained by multiplying the previous term by 4.
B. 3, 1, . . . is not a geometric sequence because there is no fixed ratio between terms.
C. 0, 1, 3, 9, . . . is not a geometric sequence because the ratio between terms is not constant.
D. 3, 6, 12, 21, . . . is not a geometric sequence because the ratio between terms is not constant.
Therefore, the only geometric sequence is A. 3, 12, 48, . . .
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Answer:
3, 12, 48, . . .
Step-by-step explanation:
got it right
A group consists of six men and seven women. Three people are selected to attend a conference. a. In how many ways can three people be selected from this group of thirteen? b. In how many ways can three women be selected from the seven women? c. Find the probability that the selected group will consist of all women.
a)There are 286 ways to select any three people from the group of 13.
b)There are 35 ways to select three women from the group of seven women.
c) The probability that the selected group consists of all women is 0.122 or approximately 12.2%
What is probability?
Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage between 0% and 100%. It is used to quantify uncertainty and make predictions in various fields such as mathematics, statistics, physics, engineering, economics, and social sciences
a. The total number of ways to select three people from a group of 13 is given by the combination formula,
C(13, 3) = 13! / (3! × (13 - 3)!) = 286
Therefore, there are 286 ways to select any three people from the group of 13.
b. The number of ways to select three women from a group of seven women is given by the combination formula,
C(7, 3) = 7! / (3! × (7 - 3)!) = 35
Therefore, there are 35 ways to select three women from the group of seven women.
c. To find the probability that the selected group consists of all women, we need to find the number of ways to select three women from the group of seven women and divide it by the total number of ways to select three people from the group of 13:
P(all women) = C(7, 3) / C(13, 3) = 35 / 286 = 0.122
Therefore, the probability that the selected group consists of all women is 0.122 or approximately 12.2%.
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