Answers
The required Length of the DC is 30.47 Units.
What is right angled triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
According to question:We have;
In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.
Then, In ΔABD
Sin∅ = BD/20
Sin(54°) = BD/20
BD = 0.809(20)
BD = 16.18
in ΔBDC
tan(28°) = BD/DC
DC = BD/tan(28°)
DC = 16.18/0.531
DC = 30.47 Units.
Thus, required Length of the DC is 30.47 Units.
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Related Questions
Are the ratios 4:6 and 2:3 equivalent? Yes or No
Answers
Answer:
Step-by-step explanation:
Yes, the ratios 4:6 and 2:3 are equivalent.
To see why, we can compare the proportions of the two ratios by dividing each term by the smaller term in each ratio.
In the ratio 4:6, if we divide both terms by 4, we get:
4/4 : 6/4 = 1 : 3/2
In the ratio 2:3, if we divide both terms by 2, we get:
2/2 : 3/2 = 1 : 3/2
Since both ratios reduce to the same proportion of 1 : 3/2, we can conclude that the ratios 4:6 and 2:3 are equivalent.
Ratios are mathematical expressions that compare two or more quantities. When two ratios are equivalent, it means that they represent the same proportion, even if the numbers in the ratios are different.
To compare the ratios 4:6 and 2:3, we divided each term in each ratio by the smallest term. This is because dividing each term by the same number will keep the proportion of the ratio the same.
For example, in the ratio 4:6, dividing both terms by 4 gave us the proportion of 1 : 3/2, which is the same as the proportion of 2:3 when divided by 2. This means that, even though the numbers in the two ratios are different, they represent the same proportion, and therefore the ratios are equivalent.
It's important to note that when comparing ratios, it's best to reduce the ratios to their simplest form so that the proportions are more easily compared.
T (ABCD) = (A'B'C'D'). If A is (6, −8), A' is (−2, 4), and B is (4, −6), what are the coordinates of B'?
A. (−4, −12)
B. (−8, −4)
C. (−4, 6)
D. (−2, −12)
Answers
Option C : (-4, 6) are the coordinates of B'.
What are meant by coordinates?
Coordinates are two integers (Cartesian coordinates) or often a letter and a number that identify a particular place on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: the horizontal x-axis and the vertical y-axis (vertical).
Given T(ABCD) = (A'B'C'D') and A = (6, -8) , A' = (-2, 4)
If B = (4, -6) then let B' = (x, y)
now, x - 4 = -2 - 6
x = 4 - 2 - 6 = -4
and y - (-6) = 4 - (-8)
y + 6 = 4 + 8
y = 6
Therefore, B' = (-4, 6)
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∠X = 89°, ∠Y = 90°, ∠Z = ?
Answers
∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°
→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°
→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°
angle Y and W are supplementary angles
so
→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°
angle X and Z are supplementary angles
so
→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
Therefore, the answer is
∠Z=40°
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To encourage bulk buying, a company reduces the list price of $4,000 per unit by
three cents times the number of units bought. Write a function statement for the
company's revenue (R) from a particular distributor that buys x units.
R(x) =
Answers
The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.
What is revenue?
Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.
The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:
R(x) = (4000 - 0.03x) * x
Where
4000 is the original list price per unit 0.03 is the discount per unit per unit purchased x is the number of units purchasedThe expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.
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a. A and D
b. B, C, and E
c. A,B,C,D, and E
d. A,D, and E
Answers
Answer:
b. B, C, and E
Step-by-step explanation:
The lateral surface area is the sum of the areas of all the faces except for the base.
The home range, in hectares, of a carnivorous mammal weighing w grams can be approximated by H(w)= 0.11w^1.36
Answers
When hired at a new job selling jewelry, you are given two pay options:
Option A: Base salary of $17,000 a year, with a commission of 8% of your sales
Option B: Base salary of $24,000 a year, with a commission of 4% of your sales
In order for option A to produce a larger income, you would need sell at least $
of jewelry each year.
Answers
Answer:
$175,000
Step-by-step explanation:
We can use a system of inequalities to solve this problem
Let X be the sales of jewelry in $
Option A
Base salary = $17,000
Commission: 8% of sales
Commission at 8% =8% x $X = 8/100 x $X = $0.08X
Total remuneration = 17,000 + 0.08X
Option B
Base salary = $24,000
Sales = X$
Commission = 4% of $X = 4/100 x $X = $0.04X
Total remuneration = 24,000 + 0.04X
For Option A to be a better deal(higher income)
Total remuneration on Option A > Total remuneration on Option B
17,000 + 0.08X ≥ 24,000 + 0.04X
(we are using ≥ symbol though the question does state larger income, later on it states at least how many $ worth of sales)
Subtract 0.04X from both sides:
17,000 + 0.08X - 0.04X >= 24,000 + 0.04X -0.04X
17,000 + 0.04X >= 24,000
Subtract 17,000 both sides:
17,000 - 17,000 + 0.04X ≥ 24,000 - 17,000
0.04X ≥ 7,000
X ≥7000/0.04
X ≥ $175,000
So under Option A, you would need to sell at least $175,000 worth of jewelry to make a larger income.
Actually at $175,000 the income from both options are equal
Hana Coffee Company roasts and packs coffee beans. The process begins by placing coffee beans into the Roasting Department. From the Roasting Department, coffee beans are then transferred to the Packing Department. The following is a partial work in process account of the Roasting Department at July 31: ACCOUNT Work in Process—Roasting Department ACCOUNT NO. Date Item Debit Credit Balance Debit Credit July 1 Bal., 6,300 units, 2/5 completed 14,112 31 Direct materials, 283,500 units 595,350 609,462 31 Direct labor 113,500 722,962 31 Factory overhead 28,400 751,362 31 Goods transferred, 284,000 units ? 31 Bal., ? units, 2/5 completed ? Required: Question Content Area 1. Prepare a cost of production report, and identify the missing amounts for Work in Process—Roasting Department. If an amount is zero, enter "0". When computing cost per equivalent units, round to two decimal places.
Answers
Based on the information provided, we can prepare a cost of production report for the Roasting Department as follows: (see attached images)
What is a Cost of Production Report?A Cost of Production Report is a document that summarizes the total costs incurred by a company to manufacture a product or provide service during a specific period of time.
The report provides information on the direct materials, direct labor, and factory overhead costs that were involved in producing the item, as well as any other costs associated with the production process.
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Find the common difference of the arithmetic sequence -1,7,15,…
Answers
The common difference of the given arithmetic sequence is 8.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given arithmetic sequence is -1, 7, 15,....
Common difference = Second term - First term
= 7-(-1)
= 7+1=8
Common difference = Third term - Second term
= 15-7
= 8
Therefore, the common difference is 8.
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The solution is, the common differences are -3, -20, -10, -2, 5.
What is common difference?In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.
here, we have,
So we just need to take different pairs of consecutive terms and see if their difference is always the same:
1) The differences are:
32 - 35 = -3
29 - 32 = -3
26 - 29 = -3
So yes, this is an arithmetic sequence and the common difference is -3
2) The differences are:
-23 - (-3) = -20
-43 - (-23) = -20
-63 - (-43) = -20
This is an arithmetic sequence, and the common difference is -20
3) The differences are:
-64 -(-34) = -30
-94 -(-64) = -30
-124 -(-94) = -30
This is an arithmetic sequence and the common difference is -30
4) The differences are:
-40 -(-30) = -10
-50 - (-40) = -10
-60 - (-50) = -10
This is an arithmetic sequence and the common difference is -10
5) The differences are:
-9 - (-7) = -2
-11 - (-9) = -2
-13 - (-11) = -2
This is an arithmetic sequence, and the common difference is -2
6) The differences are:
14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
This is an arithmetic sequence, and the common difference is 5.
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Find the lower quartile for the data. {63, 74, 63, 76. 73, 70, 74, 69, 69, 65, 70, 70, 72, 70, 65}
A. 65
B. 68
C. 66
D. 67
Answers
Answer:
65
Step-by-step explanation:
The lower quartile for the given data is 65. To calculate this, we first need to sort the data in ascending order: {63, 63, 65, 65, 69, 70, 70, 70, 70, 72, 73, 74, 74, 76}. The lower quartile is then calculated as the median of the lower half of the data, which is 65.
Factor out the greatest common factor from the expressions below to find an equivalent ex
pression. (Hint First combine the like terms and them find the GCF and factor the expression
4 16p+5+9p+25
Answers
The solution is, the Factor out the greatest common factor from the expression is 5(5p+6).
What is GCF?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.
here, we have,
given expression is,
16p+5+9p+25
=25p+30
=5(5p+6)
Hence, The solution is, the Factor out the greatest common factor from the expression is 5(5p+6).
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Solve for x with the given measures
Answers
x = -64
y = -63
z = -57
Step by step
the sum of the interior angles of a parallelogram is 360 degrees. The opposite interior angles are equal.
60 = -y -3
Add 3 to both sides
60 + 3 = -y -3 +3
Simplify
63 = -y or
y = -63
We know the sum of both angles = 60 + 60 = 120
360 - 120 = 240
So the sum of the other two angles = 240
Since the opposite interior angles are equal they will each equal half, or = 120.
-2z + 6 = 120
Subtract 6 from both sides
-2z +6 -6 = 120 -6
Simplify
-2z = 114
Divide
-z = 57
z = -57
Check your work
-2z + 6 = 120
-2(-57) +6 = 120
114 + 6 = 120
120 = 120 ✅
-2x -8 = 120
Add 8 to both sides
-2x -8 +8 = 120 +8
Simplify
-2x = 128
Divide
-x = 64
x = -64
Check your work
-2x -8 = 120
-2(-64) - 8 = 120
128 -8 = 120
120 = 120 ✅
Margaux pays $19 for postage. What is the mass of her parcel?
Answers
To find the mass of her parcel, you must solve the equation for the input when the output is of 19.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
For this problem, we have that the numeric value is of $19, hence the equation must be solved for the input variable to find the mass of the parcel.
Missing Information
The problem is incomplete, hence the general procedure to solve it was presented.
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You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes.
Answers
The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.
a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.
From the problem statement, we know that:
2x + y = 10 (jog around the block twice and the park once in 10 minutes)
2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)
These are the two linear equations that represent the given situation.
b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.
We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:
(2x + 3y) - (2x + y) = 22 - 10
2y = 12
y = 6
So, it takes 6 minutes to jog around the park.
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Complete question:
You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.
a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:
b. how long does it take you to jog around the park? it takes you minutes to jog around the park.
This right circular cylinder has a radius of 8 in. And a height of 15 in. What is its volume, v?.
Answers
The volume of the cylinder is approximately 9,558.4 cubic inches.
The volume V of a right circular cylinder is given by the formula:
V = πr^2h
where r is the radius of the circular base and h is the height of the cylinder.
In this case, the radius is 8 inches and the height is 15 inches. Substituting these values into the formula, we get:
V = π(8^2)(15)
= π(64)(15)
= 3,040π cubic inches
Therefore, the volume of the cylinder is 3,040π cubic inches. If you want an approximate value, you can use the approximation π ≈ 3.14 and calculate:
V ≈ 3,040(3.14)
≈ 9,558.4 cubic inches
So, the volume of the cylinder is approximately 9,558.4 cubic inches.
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please help me. i don't know how to do this.
Answers
- 54 is the value of x in the linear equation .
What in mathematics is a 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.
f(X) = x² + 7x - 4
A) f(-2) + f(4) = - 14 + 40 = 26
B) f(-2) - f(4) = - 14 - 40 = -54
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Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. x −4 −3 −2 P(X=x) 0.55 0.39 0.06 Answer Keyboard Shortcuts First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision. Decide Reason
Answers
Answer:
x −4 −3 −2
P(X=x) 0.55 0.39 0.06
Step-by-step explanation:
How many cans of a nutritional supplement as a patient in just over seven days if each can contains 12 Ozzie in the mountain just per day is 1080 milliliters is vegan
Answers
Answer:
Second Option : 21
Step-by-step explanation:
At 1080 ml per day for 7 days, the patient would have to ingest 1080 x 7 = 7,560 ml
Since the can capacity is given in oz we have to convert both values to the same units
1 ml = 0.033814 fl oz
Therefore 7,560 ml ≡ 7,560 ml x 0.033814 fl oz
= 255.634 oz
Since each can holds 12 oz, the number of cans = 255.634/12
= 21.3
From the answer choices, the closest to this value is Second Option : 21 cans
A collection of nickels, dimes, and quarters consist of
11
coins with a total of
$1.70
. If the number of dimes is equal to the number of nickels, find the number of each type of coins.
Answers
The number of each type of coins are 3 nickle, 3 dime and 5 quarters.
What are coins?A usually flat piece of metal issued by governmental authority as money.
Given that, a collection of nickels, dimes, and quarters consist of 11 coins with a total of $1.70
We know that, the values are:
quarters (q) = 25 cent, nickles (n) = 10 cent, dime (d) = 5 cent:
q + n + d = 11 coins…(x)
25q + 10n + 5d = 170 cents
Since, d = n
Therefore,
q + 2n = 11
25q + 15n = 170
q + 2n = 11...(i)
5q + 3n = 34...(ii)
Put q = 11-2n, in eq(ii)
Therefore,
5(11-2n)+3n = 34
55-10n+3n = 34
7n = 21
n = 3
Put n = 3 in eq (i)
q = 11-6
q = 5
Put the values of n and q in eq (x)
3+5+d = 11
d = 3
Hence, the number of each type of coins are 3 nickle, 3 dime and 5 quarters.
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Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros.
Answers
Negative: 1
Answer:
(a) Possible number(s) of positive real zeros: 3
(b) Possible number(s) of negative real zeros: 1
Step-by-step explanation:
Descartes' Rule of Signs tells us the maximum number of positive and negative roots.
Positive root case
[tex]f(x)=-3x^4+2x^3-x^2+9x+7[/tex]
As there are 3 sign changes, the maximum possible number of positive roots is 3.
Negative root case
[tex]\begin{aligned}f(x)&=-3(-x)^4+2(-x)^3-(-x)^2+9(-x)+7\\&=-3x^4-2x^3-x^2-9x+7 \end{aligned}[/tex]
As there is one sign change, the maximum possible number of negative roots is 1.
The ratio of the length to width of a rectangle is 3 to 2. If the length of the rectangle is 1 3/4 feet, what is the area of the rectangle in square inches?
Answers
Answer:
If the ratio of the length to width of the rectangle is 3 to 2, we can write the length and width as:
length = 3x and width = 2x
where x is a common factor that can be determined once we know one of the dimensions.
Since the length of the rectangle is given as 1 3/4 feet, we can set x = 1 3/4:
length = 3x = 3 * 1 3/4 = 5 1/4 feet
width = 2x = 2 * 1 3/4 = 3 1/2 feet
Now that we know the length and width of the rectangle, we can calculate its area in square inches:
area = length * width = 5 1/4 * 3 1/2 = 18 3/8 square feet
To convert from square feet to square inches, we multiply by 12^2 = 144:
area = 18 3/8 * 144 = 2664 square inches
So the area of the rectangle is 2664 square inches.
1 1/2 + 3 2/3 + 2/3 equals what?
Answers
Answer: 35/6 or 5 and 5/6
Step-by-step explanation:
Answer:
35/6
Step-by-step explanation:
Mary can jog twice as fast as she can walk. She was able to jog the first 13.5 miles to
her grandmother's house, but then she tired and walked the remaining 1.5 miles. If the
total trip took 1.5 hours, then what was her average jogging speed?
Answers
Answer: Let's call Mary's walking speed "w". Then, her jogging speed is 2w.
The total distance of the trip was 13.5 + 1.5 = 15 miles.
The total time she spent jogging was 1.5 hours, so the time she spent walking was 1.5 - 1.5 = 0 hours.
Her average speed for the whole trip was 15 miles / 1.5 hours = 10 miles per hour.
So, we can set up the equation:
(13.5 miles / 2w) + (1.5 miles / w) = 1.5 hours
We can substitute 2w for jogging speed and w for walking speed, and simplify:
(13.5 miles / 2w) + (1.5 miles / w) = 1.5 hours
13.5 / 2w + 1.5 / w = 1.5
27 / 2w = 1.5
2w = 27 / 1.5
2w = 18
Finally, we can find Mary's jogging speed by dividing the expression for 2w by 2:
w = 18 / 2
w = 9
So, Mary's jogging speed was 9 miles per hour.
Step-by-step explanation:
Which of the following equations represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3?
(y + 10)2 = 12(x – 4)
(y – 10)2 = –12(x + 4)
(x + 10)2 = 12(y – 4)
(x – 10)2 = –12(y + 4)
Answers
(x - 10)² = -12 (y + 4) represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3 .
What's a vertical parabola?
A vertical parabola has its axis of symmetry at x = h, and the vertex is (h, v). With this information, you can find the focus and directrix. The focus is the distance from the vertex to the focus is 1/(4a), where a can be found in the equation of the parabola (it is the scalar in front of the parentheses).
we know that
If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola
The equation of a vertical parabola is equal to
4p(y - k) = (x - h)²
where
(h,k) is the vertex
In this problem we have
(h,k) = (10, –4)
p= -3
substitute
4*(-3)(y - (-4)) = (x - 10)²
-12 (y + 4) = (x - 10)²
or
(x - 10)² = -12 (y + 4)
Hence , option D is correct.
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Please help I have no clue on what to do I will give you guys multiple points if you are able to help.
Answers
Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.
How to graph this information?First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:
The average body temperature is 98.6 F (37 C). But normal body temperature can range between 97 F (36.1 C) and 99 F (37.2 C) or more.According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.
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Find the equation of the line L
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-3}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +1}{-3 +1} \implies \cfrac{ 2 }{ -2 } \implies - 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies y +1 = - 1 ( x +1) \\\\\\ y+1=-x-1\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}[/tex]
Find the Value of X
A. 4
B. 8
C. 22
D. 14
Answers
Answer:B
Step-by-step explanation:
5x+15=55
5x=40
x=8
The period of a function represents _____.
the displacement of x at which the graph begins to repeat
the displacement of y at which the graph begins to repeat
the displacement of y from the central axis of the wave
the displacement of x from the central axis of the wave
Answers
Hakeem made 5% of his free throws over the season. If he shot 200 free throws, how many did he make?
Answers
Hakeem made 10 shots. The solution has been obtained by using proportions.
What is proportion?
Two numbers are compared. It is known as a proportion in mathematics. The law of proportion states that if two sets of given numbers rise or decrease in the same ratio, they are considered to be directly proportionate to one another.
We are given that Hakeem made 5% of his free throws over the season.
He shot 200 free throws and was able to make 5% from them.
So,
Number of throws he made = Number of free throws x Percentage made
Using this, we get
⇒Number of throws he made = 200 x 5%
⇒Number of throws he made = 10
Hence, Hakeem made 10 shots.
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D. Higher Order Thinking A sequence has both even and odd numbers. It follows a subtraction pattern. Can the pattern be subtract 4? Subtract 5? Explain.
Answers
Regarding the pattern, we have that:
The pattern cannot be subtract 4.The pattern can be subtract 5.How to identify the correct pattern?Regarding subtraction by even numbers, we have that:
When an even number subtracts an even number, the result is even.When an even number subtracts an odd number, the result is odd.Hence the pattern cannot be subtract 4, as the sequence would be composed either by all even numbers or all odd numbers.
Regarding subtraction by odd numbers, we have that:
When an odd number subtracts an even number, the result is odd.When an odd number subtracts an odd number, the result is even.We can see that the results alternate, hence the pattern can be subtract 5.
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