If you have a grade of 54.96 and you take a summative test worth 80%, it would bring up your grade by the following calculation:
New grade = (54.96) + (80/100) * (100 - 54.96)
New grade = 54.96 + (0.8) * (45.04)
New grade = 54.96 + 36.032
New grade = 90.992
So, your new grade would be 90.992
It's worth noting that this calculation assumes that the summative test is worth 80% of your overall grade, and that your previous grade was 54.96 out of 100. If this isn't the case, the result will be different.
An equation for a tangent to the graph of y = arcsin(x/2) at the origin is: O y=2 O x=2y O y = 4x Ο πx = 2y
The equation for a tangent to the graph of y = arcsin(x/2) at the origin is y = x.
To find the equation for a tangent to a graph at a certain point, we need to find the slope of the tangent at that point. To do this, we can use the derivative of the function. In this case, the function is y = arcsin(x/2). Using the chain rule, we can find the derivative of this function:
y' = d/dx(arcsin(x/2))
= d/dx(sin^-1(x/2))
= 1/√(1 - (x/2)^2)
Now, to find the slope of the tangent at the origin (0,0), we can plug x = 0 into this derivative:
y'(0) = 1/√(1 - (0/2)^2) = 1
So the slope of the tangent at the origin is 1. To find the equation of the tangent, we can use the point-slope form of a line:
y - y1 = m(x - x1) where,
(x1, y1) is the point at which the tangent touches the graph (in this case, the origin) m is the slope of the tangent.Plugging in the values for the origin and the slope we found above:
y - 0 = 1(x - 0)
or, y = x
So the equation for the tangent is y = x. But the options are incorrect.
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Emily wants to plan a garden in her backyard Emily's mom says she can make a card and that has a width of 5/6 yard and a length of 1/4 yard what is the area of Emilys new garden?
Therefore , the solution of the given problem of surface area comes out to be 0.2083 yard square.
Exactly what is surface area?A surface is a measurement of how much overall space an object's surface takes up. Surface area of a three-dimensional shape is determined by the total area of its surroundings. Surface area is the term used to describe a triangular shape's entire surface area. The particular area of each face on a cube with six square faces can be added up to determine the cube's surface area. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice. A three-dimensional shape's surface area is calculated as the sum of all the space it occupies.
Here,
Given : width : 5/6 yard
and length = 1/4 yard
To find the area = length * width
=> area = 5/6 * 1/4
=> area = 5/24
=> 0.2083 yard square.
Therefore , the solution of the given problem of surface area comes out to be 0.2083 yard square.
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10. Which of the following must be true?
Note that in the above mathematical scenario involving two similar triangles, the option that MUST be correct is AC < FH (Option C) This solution is arrived at using the Open Mouth Theorem.
What does the Open Mouth Theorem state?The above-stated Theorem in Geometry asserts that if two sides of two triangles are congruent and the included angle differs, then the greater angle is opposite the longer side.
This theorem is known as the Open Mouth Theorem because it is based on the idea that the two sides of a triangle are "pivoted" at their common vertex.
Please keep in mind that this theorem only works if we know two pairs of sides are congruent like this.
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Question 4(Multiple Choice Worth 2 points)
(Slope LC)
What is the slope of the line that contains the points (2, -8) and (-4,4)?
2
1/2
-1/2
-2
Answer:
the slope is -2
Step-by-step explanation:
hope this helps!!
Willy and Billy each have a rock collection.
• The number of rocks in Willy’s collection can be represented by x.
• The number of rocks in Billy’s collection is 223 times the number in Willy’s collection.
• The total number of rocks in both collections is 110.
What is x, the number of rocks in Willy’s collection?
The number of rocks in Willy’s collection is 30
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split
In this case, the number of rocks in Willy’s collection can be represented by x and the number of rocks in Billy’s collection is 2 2/3 times the number in Willy’s collection.
The appropriate equation to illustrate this will be:
x + 2 2/3x = 110
3 2/3x = 110
x = 110 ÷ 11/3
x = 110 × 3/11
x = 30
There'll be 30 rocks
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What did you include in your answer? Check all that apply.
Parallel lines have the same slope.
Parallel lines have equal slopes.
Parallel lines have different y-intercepts.
Parallel lines have different x-intercepts.s.
The lines that are true in the following statements are, Parallel lines have the same slope. Parallel lines have equal slopes. Parallel lines have different y-intercepts. Parallel lines have different x-intercepts.
What are parallel lines?Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.
The following key traits and qualities make it simple to recognize parallel lines:
They are usually parallel straight lines that are spaced equally apart.
These lines are coplanar.
No matter how far you extend them in any direction, they never come together.
All the statements mentioned are true.
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????What’s the answer??
Answer: d
Step-by-step explanation: -5 is the intercept since x is 0 above it.
using the y2-y1 / x2-x1 we will get 2/4 (1/2 when simplified).
MARKING BRAINLIEST!!!!! The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function below, where t represents time, in seconds. F(t) = 20cos (2pi/5)t, how many seconds does it take the pendulum to complete one full cycle?
According to the trigonometric function, F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.
What is a period in math?A period on a graph function is the distance between two repeating points.
The graph repeats itself as it advances along the x-axis, as you can see.
Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.
The equation is F(t) = 20 cos (2π/5)t
The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds
the period to complete an oscillation which is 2π
2π/5 * t = 2π
t = 2π * 5/2π
t = 5 seconds
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Which ordered pairs are solutions to the system of equations (-2,1.6)(0,3 3/5)(2,5 3/5) y=-0.5x+0.6
Y=x+3 3/5
The ordered pairs are solutions to the system of equations are (-2,1.6)
How to determine which ordered pairs are solutions to the system of equations?In order to determine which ordered pairs are solutions to the system of equations, you need to equate the two equations and solve for x:
y = -0.5x+0.6 and y= x+3 3/5
-0.5x+0.6 = x+3 3/5
-0.5x+0.6 = x+3.6
x+3.6 + 0.5x-0.6 = 0
1.5x + 3 = 0
1.5x = -3
x = -3/1.5
x = -2
y =-0.5x+0.6
y = -0.5(-2) + 0.6
y = 1.6
y = x + 3.6
y = -2 + 3.6
y = 1.6
Thus, the ordered pairs are (-2, 1.6)
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What are this graph's amplitude, period, horizontal shift, and equation? Write an equation that represents the curve in the form: y = a cos(k(x - b)) (Show Work!)
The features of the cosine function are given as follows:
Amplitude: 1/3.Period: π.Horizontal shift: π/3.The equation of the cosine function is given as follows:
y = 1/3cos(2(x - π/3)).
How to define the cosine function?The cosine function is defined as follows:
g(x) = acos(b((x+c))+d.
The coefficients have these following roles:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.The function oscillates between -1/3 and 1/3, hence the amplitude is of:
a = 1/3.
The period is of 2π/3 - (-π/3) = π, hence:
2π/B = π.
B = 2.
The horizontal shift is of -π/3, hence the equation is given as follows:
y = 1/3cos(2(x - π/3)).
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Factor
2x2 + 7x + 5.
The solution to the quadratic equation are x = 1 and -5/2
How to determine the valueWe have the quadratic function;
2x² + 7x + 5
Using the factorization method of solving quadratic equation. We need to multiply the coefficient of x² and the constant 5.
Then find the pair factors and substitute the values into the function.
Substitute the values, we have;
2x² + 2x + 5x + 5
Factor the expression in pairs
(2x² + 2x) + (5x + 5)
Factor the common terms, we get;
2x(x + 1) + 5( x+ 1)
We have the equations;
2x + 5 = 0
x = -5/2
And
x + 1 = 0
x = -1
Thus, the values are x = -5/2 and -1
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Ravi and Susan each opened a savings account today. Ravi opened his account with a starting amount of $650, and he is going to take out $40 dollars per month. Susan opened her account with a starting amount of $850 dollars, and she is going to take out $65 per month. Write an expression to show how much money will be in each account after 6 months, and also another to show when the two accounts would have the same amount of money.
The amount in Ravi account after 6 months will be $410.
The amount in Susan account after 6 months will be $460
How to illustrate the expression?From the information, Ravi and Susan each opened a savings account today. Ravi opened his account with a starting amount of $650, and he is going to take out $40 dollars per month. This will be:
650 - 40m
Susan opened her account with a starting amount of $850 dollars, and she is going to take out $65 per month. This will be:
850 - 65m
The amount in Ravi account after 6 months will be;
= 650 - 40(6)
= 410
The amount in Susan account after 6 months will be:
= 850 - 65(6)
= $460
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A cashier checks the price of a picnic basket that is marked $31, because it usually rings up at $36. What is the discount, as a percentage?
Round your answer to the nearest percent and include a percent sign (%).
HELP PLEASE
The discount as a percentage is 13.8%
How to calculate the discount as a percentage?The price of a picnic basket is marked as $31
The original price is $36
The discount percentage can be calculated as follows
36-31/36 × 100
= 5/36 × 100
= 0.138× 100
= 13.8%
Hence the percentage discount is 13.8%
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What is the value of
Answer:
1
Step-by-step explanation:
[tex](\frac{2}{3} )^{0} =1[/tex]
[tex](1)^{-3} =1[/tex]
Hope this helps
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable name x or y to describe the unknowns
5 times a number, divided by 6
Answer: The phrase "5 times a number, divided by 6" can be translated into the algebraic expression:
(5/6)x
This expression represents "5 times a number, divided by 6", where x is the unknown number.
Step-by-step explanation:
Solving linear equations, mixture problem pls help
61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.
This is a mixture problem that can be solved using algebra. We can set up a system of equations to represent the amount of each solution being used and the final acid concentration.
Let x be the amount of 55% acid solution and y be the amount of 30% acid solution used.
We can set up the following system of equations:
(55/100)x + (30/100)y = (43/100)(x + y) (Equation 1) represents the final acid concentration.
x + y = 100 (Equation 2) represents the total amount of solution mixed
We can solve for one variable in equation (1) by isolating it and substituting it into equation (2).
Solving for x in equation (1) we get: x = (100*43/100 - y30/100)/55/100
Substituting this value into equation (2) we get: (10043/100 - y30/100)/55/100 + y = 100
Solving for y we get: y = (100*100 - 100*43)/30 = 33.33 oz
And then substituting this value back into the equation x = (100*43/100 - y30/100)/55/100 we get x = 61.67 oz
So, 61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.
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Multiply.
8×35
Enter your answer as a mixed number in simplest form by filling in the boxes
PLS HELP
Answer:
280
Step-by-step explanation:
Answer:
8×35=280.
This is the best I can give to you
Let f(x) and g(x) be polynomials as shown below f(x)=a 0 +a 1 x+a 2 x^ 2 ...+a n x^ n; g(x)=b 0 +b 1 x+b 2 x^ 2 ...+b m x^ m Which of the following is true about f(x) and g(x) ? . f(x) and g(x) are not closed under addition because when added, the result will be a polynomial B. f(x) and g(x) are not closed under addition because when added, the result will not be a polynomial_ f(x) and g(x) are closed under addition because when added, the result will not be a polynomial . D. f(x) and g(x) are closed under addition because when added , the result will be a polynomial
Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m
D. f(x) and g(x) are closed under addition because when added , the result will be a polynomialWhat is closure under property?In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.
A set therefore either possesses closure for a given mathematical operation or it does not.
Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number
In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.
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please help quickly!!!A shuffled deck of cards is placed face-down on the table. It contains 5 hearts, 6 diamonds, 4 clubs and 3 spades. What is the probability that the top two cards are both spades?.
The probability of getting two spades when two cards are drawn from the deck is 1/17.
What is probability?Probability branch of mathematics the deal with the likewood of an event occouring. It is the measure of how likely it is something will happen or be the case. Probabilities expressed as a number between zero and one 00 indicates impossibility and one indicus certainity. Probability can be used to calculate the chances of certain outcome based on a state condition or data. Probability can also be used to make decision and prediction about the future.
The probability of getting two spades when two cards are drawn from a shuffled deck of cards is 3/52 x 2/51, or 1/17.
This is because there is a 3/52 chance of getting the first spade and a 2/51 chance of getting the second spade (since there is one less card in the deck).
Therefore, the probability of getting two spades when two cards are drawn from the deck is 1/17.
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h is defined by the rule
h(x)=2x-3
The complete function table using the defined function rule is as shown below.
How to solve function tables?We are given the function rule as;
h(x) = 2x - 3
From the function table attached, we will need to find the value of the function h(x) at x = -3, -2, 1, 3, 5
Thus;
Plugging in the value of -3 for x in the given function rule gives us the output as;
h(-3) = 2(-3) - 3
h(-3) = -9
Plugging in the value of -2 for x in the given function rule gives us the output as;
h(-2) = 2(-2) - 3
h(-2) = -7
Plugging in the value of 1 for x in the given function rule gives us the output as;
h(1) = 2(1) - 3
h(1) = -1
Plugging in the value of 3 for x in the given function rule gives us the output as;
h(3) = 2(3) - 3
h(3) = 3
Plugging in the value of 5 for x in the given function rule gives us the output as;
h(5) = 2(5) - 3
h(5) = 7
Thus, the complete function table is;
x h(x)
-3 -9
-2 -7
1 -1
3 3
5 7
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A soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
121 over 7 cm
121 over 14 cm
121 over 28 cm
121 over 56 cm
The length of the label is 121 over 28. (option C)
What is the length of the label?The length of the label is equivalent to the circumference of the cylinder. The circumference of an object is the distance round the object.
The formula for circumference of a cylinder = 2πr
Where:
π = 22/7
r = 2 3/4 = 11/4
2 x 22/7 x (11/4) = 121/28 cm
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Answer: 121/7
Step-by-step explanation: I got it correct :)
Freddy had two of the brownies from a large pan. His friend said he ate 1/8 of the brownies in the pan. Tell why you agree or disagree.
I agree that Freddy ate 1 / 8 of the brownies in the pan because two brownies represents 1 / 8 of the brownies in the pan.
How to find the proportion of brownies eaten ?The large pan is said to have been used to make 16 brownies which means that if Freddy ate 2 brownies out of this, the proportion that he would have eaten of the cookies in the pan is:
= Number of brownies Freddy ate / Number of total brownies in the large pan
= 2 / 16
= 1 / 8
This therefore shows that Freddy's friend was right in saying that Freddy ate 1 / 8 of the brownies in the pan.
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Full question is:
A large pan is used to make 16 brownies. Freddy had two of the brownies from a large pan. His friend said he ate 1/8 of the brownies in the pan. Tell why you agree or disagree.
Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys?
The number of toys is 5 in each container.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Let x be the number of toys in each container.
Weight of one toy car = 6 pounds
Weight of the container in which toy cars shipped = 5 pounds
Weight of x toy cars = 6x
Total weight of the container when toy cars are placed = 6x + 5
Weight of one toy truck = 3 pounds
Container weight = 20 pounds
Weight of x toy trucks = 3x
Total weight of the container when toy trucks are place = 3x + 20
Given that both containers have same weight.
6x + 5 = 3x + 20
6x - 3x = 20 - 5
3x = 15
x = 5
Hence the number of toys in each container is 5.
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5x-y=54 x=10 what is the answer
Answer:
Y = 4
Step-by-step explanation:
5x-y=54
50-y=54
circle y and subtract 50 from itself then subtract 50 from 54.
after subtracting you should have y=4
write an equation of the line that passes through (4,3) and is parallel to the line y=1/4x+10
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 1/4 and that it passes through (4 , 3)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \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}{3}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=\cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+2 \end{array}}[/tex]
(04.05 HC)
An applicant receives a job offer from two different companies.
Offer A is a starting salary of $55,000 and a 5% increase for 5
years. Offer B is a starting salary of $56,000 and an increase of
$2,000 per year.
Part A: Determine whether offer A can be represented by an
arithmetic or geometric series and write the equation for An, that
represents the total salary received after n years. Justify your
reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an
arithmetic or geometric series and write the equation for B, that
represents the total salary received after n years. Justify your
reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after 5
years? Show all necessary math work. (4 points)
On solving the provided question of arithmetic , we can say that after five years, Offer A will offer a higher total income.
What is arithmetic sequence?Every subsequent pair of terms in an arithmetic sequence has a constant difference. This resembles linear functions with the formula y=mx+b. There is a fixed ratio between every pair of subsequent terms in a geometric sequence. This would produce a constant multiplier effect.
Given that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:
Offer A = Arithmetic
55000.r1.055 X
70, 195.48 — x
Offer B = Geometric
56000+ (5a•2000) X
56000+ 10000 = x
66,000 = x
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Ok so I need help with this
Answer:
Step-by-step explanation:
1 Wanderer
2 moves on its own orbits the sun
3 Saturn
4 saturn
You or your parents purchased a car for 28,125+7. 5% sales tax the down payment is 3125 your fair credit rating what is your new principal balance at the beginning of the second month if you pay $529.75 at the end of the first month
26,706.08 nearest to 26,706.14
What is purchase?
Purchasing is the set of functions associated with acquiring the goods and services that an organization requires. Purchasing is a small subset of the broader procurement function.
The 6 key steps of the purchasing process are:
Identification of the need The description of the product characteristics Drafting the specifications. Is it necessary to issue a tender Supplier sourcing Preparing for the negotiation In-depth analysis of applicationsFair secured apr: 5.60% = 0.4666% for 1 month
28,125 x 1.075 = 30,234.38 - 3125 = 27,109.38
27,109.38 x 1.004666 = 27,235.87 - 529.79 = 26,706.08
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1. The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch?
19.75 meters is the rocket's height when it has 0.5 seconds after launch
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1
h(t) is their rocket's height in meters.
we have to find the rocket's height in meters 0.5 seconds after launch
Put t=0.5 in the above function.
h(0.5)=-5(0.5)² + 40(0.5)+ 1
=-5(0.25)+20+1
=-1.25+20+1
=19.75
Hence, 19.75 meters is the rocket's height when it has 0.5 seconds after launch
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for f(x)=3x-2 and g(x)=x^2+1 find (f+g)(x)
For the polynomial functions f(x) = 3x - 2 and g(x) = x² + 1, then function (f + g)(x) is calculated to be
x² + 3x - 1What is a polynomial function?A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation or the cubic equation.
The equation in the problem has integers as below
f(x) = 3x - 2: integer value here is 1
g(x) = x² + 1 integer value here is 2
In both conditions, the integer values are positive hence both are polynomial functions
(f + g)(x) is addition of the two polynomials
f(x) = 3x - 2 + g(x) = x² + 1
= 3x - 2 + x² + 1
= x² + 3x - 1
hence (f + g)(x) = x² + 3x - 1
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