Answer:
The balance after 37 years is $3869.99
Step-by-step explanation:
Given:
Principal (P) = $2,520Rate of Interest (R) = 1.16%Time (t) = 37 yearsCompounds Interest Monthly (n) = 12The Amount (A),
A = P (1 + [tex]\frac{R}{100n}[/tex][tex])^{nt}[/tex] if compound n times per year
Amount (A) at 37 years,
A = ($2,520) (1 + [tex]\frac{1.16}{100(12)}[/tex][tex])^{12 x 37}[/tex]
A = ($2,520) (1 + [tex]\frac{1.16}{1,200}[/tex][tex])^{444}[/tex]
A = ($2,520) (1.00096667 [tex])^{444}[/tex]
A = ($2,520) (1.5357)
A = $3869.9944
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College students (ages 18-26) tend to make decisions which are
tentative (more short-range) and support a desire for autonomy.
a result of a greater sense of commitment and stability.
more permanent choices.
College students (ages 18-26) tend to make decisions that are tentative (more short-range) and support a desire for autonomy. This depicts more permanent choices.
How to illustrate the information?
It should be noted that values are a compass that helps us make decisions and choices.
Choices characterize the stage of life we are in. For example 18-26 ages tend to make tentative choices, later 27-31 ages tend to make permanent choices, and ages 32-42 people make stable choices.
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PLEASE HELP!!
Write Y=x^2+4x+3 in standard form
Answer:
already in standard form
Step-by-step explanation:
the equation of a quadratic in standard form is
y = ax² + bx + c ( a ≠ 0 )
y = x² + 4x + 3 ← is in standard form
with a = 1 , b = 4 , c = 3
2. (06.03)
What is the solution to the following system of equations? (2 points)
y = -x2 – 5x − 4
y = -x² + 9x - 18
O (-1,-10)
O (1,-10)
O (-1,10)
(1.10)
Answer: (1, -10)
Step-by-step explanation:
Since both of the equations are set equal to y, we can conclude that:
[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]
If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]
Thus, the solution is (1, -10)
What do large differences of the mean of each group indicate
The Actual Question:
What do large differences of the means of each group indicate? Select the correct answer.
A. The large differences do not indicate any Significant meaning in the given context.
B. The peppers with different weights aren't properly distributed between the two groups.
C. There is not enough information to analyze the differences.
D. The peppers with different weights are properly distributed between the two groups
Answer:
B. The peppers with different weights aren't properly distributed between the two groups.
What is a mean?
A quantity having a value intermediate between the values of other quantities; an average, especially the arithmetic mean.
The considerable discrepancies in the means of each group imply that: B. the peppers with varying weights are not adequately divided across the two groups.
So in the given situation above in the question, it can be concluded that large differences of the means from each group indicates that the peppers that are not properly distributed between the 2 different groups have different weights.
Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
Answer:
[tex](x,y) = (5,-6)[/tex]
Step-by-step explanation:
[tex]\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\[/tex]
[tex]~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)[/tex]
[tex]\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\[/tex]
[tex]\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5[/tex]
[tex]y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6[/tex]
[tex]\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)[/tex]
The depth of a certain part of the Earth's seabed is 36,024 feet. How deep is it in (a) fathoms? (b) leagues (marine)?
The depth of the sea bed is 5104 fathom and 1.986 league
What is a Seabed ?The bottom of an ocean , the ocean floor is called Seabed .
It is given that
The depth of a certain part of the Earth's seabed is 36,024 feet
The depth in fathom is given by = depth in feet / 6
The depth in fathom is = 36024 / 6
= 5104 fathom
1 league = 6046.1 * 3 feet = 18138.1 feet
The depth in League (marine) = Depth in feet / 18138.1
The depth in League (marine) = 36024/18138.1
= 1.986 league
Therefore the depth of the sea bed is 5104 fathom and 1.986 league.
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What is the quotient of -27.375 divided by 7.5
A)–3.65
B)–0.365
C)0.365
D)3.65
Answer: A. -3.65
Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.
[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]
Knowing this, we can input it into the calculator and find the answer's sign.
[tex]-27.375/7.5=-3.65[/tex]
Therefore, the answer is A. -3.65.
I hope this helps! Pls mark brainliest!! :)
1 If the population of a town increases by 280 people per year, then the growth is LINEAR (or constant). If the population in 2022 is 120,500, then what will the population be in 2023?
The population in the year 2023 is 120,780.
The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.
So, according to the question statement, we have that
y=280x+b where x is the number of years past and y is the population in the xth year.
According to the given problem population in 2022 will be 120,500.
Suppose that the initial population is taken at 2000.
Hence, 120,500=280×(2022-2000)+b
⇒b=120,500-280×22
⇒b=120,500-6,160
=114,340
So, the Linear equation becomes
y=280x+114,340
⇒y=280×(2023-2000)+114,340
⇒y=120,780
Hence, the population in the year 2023 is 120,780.
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6ac+bd-3bc-2ad help
Answer:
(2a-b)(3c-d)
Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.
The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]
Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.
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suppose the theoretical probability of winning a prize in the carnival game 0.18 based on this probability how many more customers would u have expected to win a prize
The number of customers I would have expected to win the prize is 6.
How many more customers would I have expected to win the prize?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Based on the probability, the number of customers I would have expected to win: 0.18 x 300 = 36
How many more people I would have expected to win : 36 - 30 = 6
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Please answer all three of the questions <3
Answer:
1) D because the answer to 8.42*10^3=8420
and 8420 lies between 8400 and 8500
2) C because when you take the absolute value of -2.3 and -3.2, they become positive numbers => 2.3 < 3.2
3)D because 6 < 6.3 < 6.6
Hope it helps!
Consider the proof.
Given: In △ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A)
Triangle A B C is shown. A perpendicular bisector is drawn from point B to point D on side A C. The length of B C is a, the length of D C is b minus x, the length of A D is x, the length of A B is c, and the length of B D is h.
Statement
Reason
1. In △ABC, BD ⊥ AC 1. given
2. In △ADB, c2 = x2 + h2 2. Pythagorean thm.
3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm.
4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication
5. a2 = b2 – 2bx + c2 5. substitution
6. In △ADB, cos(A) = StartFraction x Over c EndFraction 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a2 = b2 – 2bccos(A) + c2 8. ?
9. a2 = b2 + c2 – 2bccos(A) 9. commutative property
What is the missing reason in Step 8?
Pythagorean theorem
definition of cosine
substitution
properties of multiplication
The missing reason in Step 8 is substitution
When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.
According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa
The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.
Option C, from the list of alternatives, is the one that best explains statement 8.
Hence missing reason in Step 8 is substitution
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Answer: OPTION C
Step-by-step explanation:
EDGE22
I don’t understand this question can someone please help
Answer:
the second option listed
(A = 53 degrees)
(a = 13.3)
(c = 16.6)
Step-by-step explanation:
SOH CAH TOA
(sin = opposite / hypotenuse)
(cos = adjacent / hypotenuse)
(tan = opposite / adjacent)
For this question, you are provided an angle (37), and its opposite (10)
so, we can solve for either sin or tan first.
tan = opposite / adjacent
tan 37 = 0.7535540501
0.7535540501 = 10/a [multiply by a]
0.7535540501a = 10 [divide by [0.7535540501]
a = 13.2704482163
rounded to the nearest tenth, a = 13.3
we know that the three angles shown here must add up to 180
so,
90 + 37 + A = 180
127 + A = 180
- 127 - 127
A = 53
--this is enough information to answer, but I will also solve side c to prove my answer
c = hypotenuse
a²+ b²=c²
[13.3]² + [10]² = c²
176.89 + 100 = c²
276.89 = c²
√276.89 = √c²
16.6400120192 = c
c = 16.6 (rounded to the nearest tenth)
**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer
Acontinous random variable X has a pdf given by p(x) = (5x4 0≤x≤1 0, otherwise) Let Y=X3. Find the probability distribution function
I'll use the method of transformations.
If [tex]f_X(x)[/tex] denotes the PDF of [tex]X[/tex], and [tex]y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}[/tex], we have
[tex]f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|[/tex]
[tex]\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}[/tex]
[tex]\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}[/tex]
True or False? A corollary is a statement that can be easily proved by using theorem.
What is the slope of the following graph? (write your answer as a fraction unless divided by 1. Do not use spaces in your answer)
The slope of the graph is 4/5
How to determine the slopeUsing the formula
Slope = Δ y-axis / Δ x- axis
y2 = -4
y1 = 0
x2 = -5
x1 = 0
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Substitute the values into the formula
Slope = [tex]\frac{-4 - 0}{- 5 - 0}[/tex]
Slope = [tex]\frac{-4}{-5}[/tex]
Slope = [tex]\frac{4}{5}[/tex]
Therefore, the slope of the graph is 4/5
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5.2 Two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm. 5.2.1 Draw the sketch. (2) 5.2.2 Calculate AB (a chord to a smaller circle), correct to 2 decimal places. (6)
The length of the chord AB will be 6.08 cm
A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension. A chord is, more broadly speaking, a line segment connecting two points on any curve, such as an ellipse.
Given two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm
We have to find the length of chord AB drawn to smaller circle
Given:
PQ = 13 cm
R = 7 cm
r = 4 cm
The formula to find length of chord is as follow:
Length of chord = 2 x √(R²-d²)
Where,
R = radius of circle
D = Perpendicular distance from center of circle to chord
So,
PQ = 2 x √(R²-d²)
13 = 2 x √(7²-d²)
d = 2.59 cm
Now,
AB = 2 x √(r²-d²)
AB = 2 x √(4²-2.59²)
AB = 6.08 cm
Hence the length of chord AB will be 6.08 cm
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1
√
x
If
y
=
3
when
x
=
36
find,
y
when
x
=
9
Answer:
3y= 36×9x
3y=324x
y=324÷3
y=108 ans
6. What is the cube of 8?
A. 64
B. 2
C. 512
D. 24
Answer : C. 512
step-by-step explanation :
8 8(square) = 8² = 8 × 8= 64 8(cube) = 8³ = 8 × 8 × 8 = 64 × 8 512
[tex]\qquad\qquad\qquad\boxed{\bf\:\: \: (c) \: 512}[/tex]
[tex] \purple{\bold{\underline{\underline{ Cube \: of \: 8 \: is = 512:}}}}[/tex]
[tex]\red{\bold{\underline{\underline{so \: option \:( c ) \: is \: correct \: \: :}}}}[/tex]
[tex]\orange{\bold{\underline{\underline{ more \: additional \: information \: :}}}}[/tex]
if a number is multi by by itself 3 then the obtained number is called cube.the cube of a natural number is that given number raised to the power 3PROPERTIES -: cube of all even natural number is always even.cubes of all odd natural number are odd.the cube of natural number ending a zero has 3 on it.the cube of the natural number ending with one was one is it unit digitcube of negative number always negative.To find Cubes -:
direct methodalternate methodcolum methodTo find Cube Root -:
prime factorizationsuccessive subtraction method.estimation methodHow to translate a graph of y= absolute value of x to obtain the graph of y= absolute value of x-6
Answer: Translate the graph of y=|x| 6 units to the right.
2, 9, 11, 18, 20, 27,
the next 3 numbers.
Answer:
29, 36, 38
Step-by-step explanation:
The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.
The Wilson family had 5 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had
at least 3 girls?
at most 3 girls?
The expression represents the probability of getting exactly 3 heads is,
[tex]C(n,r)(0.5)^3(0.5)^6[/tex]
We have given
Aron flips a penny 9 times.
We have to determine
Which expression represents the probability of getting exactly 3 heads
What is binomial distribution?The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.
The binomial probability formula shown has variables that represent:
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).
r is the number we want to find (here, we want the probability of 3 heads, so r = 3).
p is the probability of success (here, success means getting heads.
So, in a coin flip the probability of heads is always 1/2, so p = 1/2).
Therefore, The expression represents the probability of getting exactly 3 heads is;
[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]
[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]
Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].
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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,
Probability (x≥3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰
= 0.5
Probability (x≤3)
= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵
= 0.8125
Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.
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Select the correct answer from each drop-down menu.
Need helpp
(1st image of dropdown menu is the drop down menu on top an the second image is the second dropdown menu beneath it)
Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.
Triangle ABC and triangle RQP are similar based on side-angle-side criterion.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.
Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.
Triangle ABC and triangle RQP are similar based on side-angle-side criterion.
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Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3?
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 1.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = negative 3 and it crosses the x-axis at x = negative 5.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 7.
On a coordinate plane, a cubic function is shown. It has a point of inflection at x = 6 and it crosses the x-axis at x = 5.
The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.
The function we have is:
y = ∛(x - 5)
So cubic root is given
Here we notice that when x = 0, we have:
y = ∛-5, this is the y-intercept
And when x = 5 we have:
y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.
Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5
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Answer:A
Step-by-step explanation: Edge 2022
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.
Answer:
Formula of Trapezoid:
A = (a + b) × h / 2
The formula can be derived in different ways. for now, we have discussed two ways:
1. By using the formula of a triangle
2. By dividing into different sections
Step-by-step explanation:
1. By using the formula of a triangle
One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.
Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.
The image is attached below.
Connect vertices P and R with a diagonal.
Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).
Its area is
S1=[tex]\frac{1}{2} *PQ*RM[/tex]
Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).
Its area is
S2=[tex]\frac{1}{2} *SR*PN[/tex]
Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.
They both are equal to the altitude of the trapezoid h.
Therefore, we can represent areas of our two triangles as
S1=[tex]\frac{1}{2}*PQ*h[/tex]
S2=[tex]\frac{1}{2}*SR*h[/tex]
Adding them together, we get the area of the whole trapezoid:
S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]
which is usually represented in words as "half-sum of the bases times the altitude".
2. By dividing into different sections
Trapezoid PQRS is shown below, with PQ parallel to RS.
Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)
We are going to derive the area of a trapezoid by dividing it into different sections.
If we drop another line from Q, then we will have two altitudes namely PT and QU.
Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)
From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that
=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]
Simplifying, we have
=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]
Factoring we have,
=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]
But, [tex]a+ b_{1} + c[/tex] is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.
Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]
We have discussed two ways by which we can derive area of a trapezoid.
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Celia needs 75% of the marks in an exam to pass. She gets 4/5 of the marks. Does she pass the course? Show your working to justify your answer
Answer:
Yes, she passes with 80%
Step-by-step explanation:
4 divided by 5 = 0.8
0.8 multiplied by 100 = 80%
80% is greater than the required 75% needed to pass
Answer:
Yes
Step-by-step explanation:
First lets establish the key points
We know she needs 75% to pass and she gets 4/5 of the marks
Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8
.75 = 75%
.8 = 80%
80% > 75%
Meaning She PASSED!!!
4. You must make 3000 bags of product for a customer by 5 pm. You started work at 7 am today. By 9 am you have
made 500 bags. If you continue at this pace with no interruptions or machine issues, what percent (%) of 3000
will be complete by 11 am?
Answer:
33.33%
Step-by-step explanation:
from 7 to 9 it's 2 hours and you make 500
and 7 to 11 is 4 hours so you make 1000
then do 1000/3000 to find the percentage you have made
1000/3000 is 33.3333333333...% (the 3333.... never ends)
What’s a 106.7 gpa into weighted form like on the 4.0 scale??
A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
As 106.7 out of 100 gives 106.7% calculated below:
Percentage formula = (Obtained value/total value) x 100.......eq(1)
Putting values:
= (106.7/100) x 100
= 106.7%
Now finding 106.7% of 4:
Putting values in eq (1):
106.7% = (Obtained value/4) x 100
106.7/100= (Obtained value/4)
1.067= (Obtained value/4)
4 x 1.067 = Obtained value
4.268 = Obtained value
Then 106.7% of 4 will be equal to 1.067 x 4 = 4.268
A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.
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A dairy farmer wants to make 45% protein supplement and a standard 15% protein ration to make 1800 pounds of high grade 35% protein ration how many pounds of each should be used.
1200 pounds of protein supplement and 600 pounds of standard protein is used.
Let a be the protein supplement and b be the standard protein.
Given that protein supplement and standard protein make 1800 pounds of high grade protein.
i.e., a+b = 1800 ------- (1)
45% a + 15% b = 35% 1800
0.45a + 0.15b = 1800 (3.5)
By (1), a = 1800 - b
Substituting, we get
0.45 (1800-b) + 0.15b = 630
810 - 0.45 b + 0.15b = 630
- 0.3 b = - 180
b = -180/-0.3
b = 600
Substituting b = 600 in (1),
we get
a = 1200.
Hence, 1200 pounds of protein supplement and 600 pounds of standard protein is used.
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