You bought 17 pounds of rice for a group lunch at the neighborhood market the last time you went there for $12.75. This week, you'll need 38 pounds of rice to prepare another shared meal.
How do you find original price ?Step 1: Divide the percent discount by 100% to convert it to a decimal. Step 2: Construct the equation P=(1d)x P = (1 d) x where P is the sale price, d is the discount expressed as a decimal, and x is the original price of the item to get its original price.
A linear demand equation is written as Q = a - bP in standard form. The price is treated as a function of quantity required in the inverse demand equation (also known as the pricing equation): P = f(Q) (Q).
When you most recently visited the neighborhood market, you spent $12.75 on 17 pounds of rice for a communal lunch. You need 38 pounds of rice this week to create another communal supper.
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Can Someone Explain Sin Cos and Tan to me, My finals are coming up and I do not understand anything about them
Sine and cosine are the fundamental trigonometric functions associated to the sides of a right triangle and tangent is a derivate trigonometric function.
What are the sine, the cosine and the tangent of an angle?
Let be a right triangle, whose features are introduced in the figure attached below. The side with measure y is the side opposite to the angle θ, whereas the side with measure x is the side adjacent to the angle θ. The side with measure r represents the hypotenuse of the right triangle, which can be found by means of Pythagorean theorem:
r = √(x² + y²)
Trigonometric functions are trascendent functions that relates two sides of the right triangle. There are two fundamental trigonometric functions and four derivate trigonometric functions:
Fundamental
sin θ = y / r = (Opposite side) / (Hypotenuse)
cos θ = x / r = (Adjacent side) / (Hypotenuse)
Derivate
tan θ = sin θ / cos θ = y / x = (Opposite side) / (Adjacent side)
cot θ = 1 / tan θ = cos θ / sin θ = x / y = (Adjacent side) / (Opposite side)
sec θ = 1 / cos θ = r / x = (Hypotenuse) / (Adjacent side)
csc θ = 1 / sin θ = r / y = (Hypotenuse) / (Opposite side)
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2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of which type of reaction?
The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction
What is Redox reaction?Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.
The equation of the reaction is written as
2H₂O + 2K → 2KOH + 2H₂
The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor
The oxidizing agent is water which ended up as Hydrogen molecule
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Write a system of equations to describe the situation below, solve using substitution, and fill
in the blanks.
Aunt Emily is pricing cakes for a baby shower she is throwing. She wants one large cake
shaped like a duckling and also some cupcakes in pastel colors. Clarksville Bakery charges $3
for each cupcake, plus $50 for the large cake. Sebastian's Sweet Shoppe charges $34 for the
large cake and $4 for each cupcake. If Aunt Emily orders a certain number of cupcakes, the
cost will be the same at either bakery. How many cupcakes would that include? What would
the total cost be?
If Aunt Emily orders
cupcakes, it will cost s
at either shop.
The system of equations is y = 50 + 3x; y = 34 + 4x. The number of cups that Aunt Emily orders is 16. The cost of either shop for 16 cupcakes is $98.
What is substitution method?
The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.
Assume that x number of cups that ordered by Aunt Emily.
Given that, Clarksville Bakery charges $3 for each cupcake, plus $50 for the large cake.
Therefore, the cost of x cupcake is 50 + 3x.
y = 50 + 3x
Also, Sebastian's Sweet Shoppe charges $34 for the large cake and $4 for each cupcake.
Therefore, the cost of x cupcake is 34 + 4x.
y = 34 + 4x
The system of equations is
y = 50 + 3x ....(i)
y = 34 + 4x ...(ii)
To find the number of cupcakes that Aunt Emily orders, use substitution method to solve the system of equation.
Substitute y = 50 + 3x in equation (ii)
50 + 3x = 34 + 4x
Subtract 3x from both sides:
50 = 34 + x
x = 16
Putting x = 16 in equation (i)
y = 50 + (3 × 16) = 98
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What is the volume of the cylinder shown below?
A. 1112 units³
B. 132 units3
C. 121 units3
D. 1452 units3
Answer: 1452 units^3
The required volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.
What is volume?
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
The formula for the volume of a cylinder is given as:
V = πr²h
Where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.
Substituting the given values, we get:
V = π(11)²(12)
= π(121)(12)
= 1452π cubic units
Therefore, the volume of the cylinder with a height of 12 units and radius of 11 units is 1452π cubic units.
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Alex has $600 in her checking account. She wants to spend a part of this money on a computer.
She wants to have at least $250 left in her checking account after buying the computer. Write an
inequality that can be used to find t, the amount of money in dollars that Alex can spend on the
computer, and solve for t.
Answer: $350 = t
Step-by-step explanation:
might help); 600-250 = t
t + 250 ≤ 600 INEQUALITY
Answer: $350.
Explanation: if you do [tex]600 -250[/tex] you will end up with $350
find the length??????????
Answer:
√53 or 7.28
Step-by-step explanation:
To find the length of the line segment from the point (4, 2) to the point (-3, 4), you can use the distance formula, which is:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of the two points, you get:
distance = √((-3 - 4)^2 + (4 - 2)^2)
Simplifying this expression gives:
distance = √((-7)^2 + (2)^2)
Which simplifies to:
distance = √(49 + 4)
Which simplifies to:
distance = √53
So the length of the line segment from the point (4, 2) to the point (-3, 4) is approximately 7.28.
the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection.
For each binomial experiment described, find
A. the mean
B. the variance
C. the standard deviation
The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.
As given in the question,
Let success be defined by health department inspection is passed by restaurant
Probability of success rate 'p' = 0.94
Value of ' 1 - p ' = 1 - 0.94
= 0.06
Number of owners of restaurant which are surveyed 'n' = 58
For the given binomial experiments calculation of the following distributions are:
Mean 'μ' = np
= 58 × 0.94
= 54.52
Standard deviation 'σ' = √ np (1 - p)
= √ 58 × 0.94 × 0.06
= √3.2712
= 1.808
Variance 'σ²' = np( 1 - p )
= 58 × 0.94 × 0.06
= 3.2712
Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.
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Plsss help me with this !!
How can you check that 463 20/35 is the correct quotient for 10,920 divided by 25?
Answer: It is correct.
Step-by-step explanation:
Help please!! This is actually so confusing
Answer: [tex]\frac{\sqrt{55}}{8}[/tex]
This is the same as writing sqrt(55)/8 where the 8 is not inside the square root.
=====================================================
Explanation:
Draw a right triangle in the quadrant Q1, which is in the northeast corner.
We're given [tex]\cos(\theta) = 3/8[/tex]. Recall that cosine is the ratio of adjacent over hypotenuse.
[tex]\cos(\text{angle}) = \text{adjacent/hypotenuse}[/tex]
This right triangle will have an adjacent side of 3 and hypotenuse of 8.
Refer to the diagram below.
Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to find the missing side is exactly [tex]\sqrt{55}[/tex], which is the opposite side of angle theta.
Then as one last step, we would say:
[tex]\sin(\text{angle}) = \text{opposite/hypotenuse}\\\\\\\sin(\theta) = \frac{\sqrt{55}}{8}[/tex]
--------------
A very similar approach is to use the pythagorean trig identity
[tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex]
Solving for sine gets us
[tex]\sin(\theta)=\sqrt{1-\cos^2(\theta) }[/tex]
Sine is positive in Q1.
Then plug in [tex]\cos(\theta) = 3/8[/tex] and simplify. You should get the answer mentioned above.
convert 0.55 as a fraction.
Answer: 11 / 20
Step-by-step explanation:
A grocery store has small bags of apples for $5 each and large bags for $8 each. If you buy 15 bags and spend $93, how many of each size bag did you buy?
Answer:
There are 9 small $5 bags and 6 large $8 bags
Step-by-step explanation:
9 x 5 = 45
6 x 8 = 48
45 + 48 = 93
Rename 4/5 and 5/7 using the least common denominator.
Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?
22. What are the values of w and x in the triangle below? Round the answers to the nearest tenth.
(1 point)
The values of x and w on the triangle are given as follows:
w = 14.4, x = 11.2.
How to obtain the values of x and w?The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For the angle of 48º, we have that:
The adjacent side is w.The opposite side is of 16.Hence:
tan(48º) = 16/w
w = 16/tan(48º)
w = 14.4.
For the angle of 32º, we have that:
The adjacent side is 14.4 + x.The opposite side is of 16.Hence:
tan(32º) = 16/(14.4 + x)
tan(32º)(14.4 + x) = 16
x = (16 - 14.4tan(32º))/tan(32º)
x = 11.2.
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He turns 110 degrees and walks 270 yards until he arrives at the other end of the lake. Approximately how long is the lake?
The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.
Given : b = 245 yards, c= 270 yards,
To find: The length of the lake which is the value of x
To find [tex]\angle A[/tex], we know that [tex]110^o\, and\, \angle A[/tex] lie on straight line. So
[tex]110^o + \angle A = 180^o\\\\\angle A = 180^o - 110^o = 70^o[/tex]
Using law of cosines
[tex]a^2 = b^2 +c^2 - 2bc\cdot cosA[/tex]
Plugging the values of b , c and A into the equation, we get
[tex]a^2 =245 ^2 +270^2 - 2\times 245 \times 270 \times \cos 70^o \\[/tex]
The value of [tex]\cos 70^o[/tex] is 0.342 approximately
On substituting this in the equation, we get
a = 296.1 yards
What is law of cosines?Every triangle has three vertices and three sides. If in a triangle, the three vertices are A, B, and C, then, the sides opposite these vertices are a, b, and c, respectively. The angle at each vertex is given the same name as the vertex. Therefore, the three angles are also named A, B, and C. To solve such a triangle is to find the lengths of each of its sides and all its angles.
The sine rule or law of sines is used when we are given either
a) two angles and one side
or
b) two sides and the angle that is not included between these two sides.
[tex]\frac{\sin A}{a} =\frac{\sin B}{b} =\frac{\sin C}{c}[/tex]
The cosine rule or law of cosines is used when we are given either
a) three sides (SSS)
or
b) two sides and the included angle (SAS)
[tex]c^2=a^2+b^2-2ab\cdot\ cosC \\ b^2=a^2+c^2-2ac\cdot\ cosB\\ a^2=b^2+c^2-2bc\cdot\ cosA\\[/tex]
The measurement of the length of two sides and the included angle are given. Hence, using law of cosines, the approximate length of the lake is found to be 296.1 yards.
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3x+9-7=c+10+x
-4x+9=2x+10
determine if law of sines or law on cosines is the best choice substitute the values into the appropriate formula and solve
Answer:
Hi again, use the sine rule for length. answer: 82.42
Step-by-step explanation:
An investor invested a total of $2900in two mutual funds. One fund earned a 8% profit while the other earned a 6% profit. If the investor's total profit was $194, how much was invested in each mutual fund?
The amount invested at 8% and 6% is 1000 and 1900 respectively.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, The person invested $2900 in two mutual funds and the total profit is $194.
Let the amount invested at 8% is x, then the amount invested at 6% is:
2900-x
Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194
8x/100 + 6(2900 - x)/100 = 194
8x + 17400 - 6x = 19400
2x = 19400 - 17400
2x = 2000
x = 1000
The amount invested at 6% is:
2900 - 1000
= 1900
Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.
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what would you expect to see in a residual plot if the linearity assumption is correct? select all that apply.
In a residual plot if the linearity assumption is the points are scattered and there is no obvious pattern.
Residual plot:
in statistics, residual value is a measure of how much a regression line vertically misses a data point.
Given,
Here we need to find what would you expect to see in a residual plot if the linearity assumption is correct.
As per the definition of residual plot, there is no obvious pattern for this plot and the positive and negative values are evenly spread across the whole range.
Therefore, in the regression line there are some points are misses the line on the vertical base.
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Question 4
A seller at a farmer's market sells trays of large eggs and extra large eggs.
They sold a total of 75 trays of eggs in the past month.
•
They sold twice as many trays of large eggs as extra large eggs.
4.1. If they sold x trays of large eggs and y trays of extra large eggs, write
down two linear equations for the results above.
Answer:
They would have sold 8.2 eggs
Step-by-step explanation:
^
The sum of two (2) prime numbers is 85. What is the product of these two prime numbers?
Answer: 166
Step-by-step explanation:
The sum of two odd numbers is an even number.
85 is odd, and so is the sum of an odd number and an even number.
2×83=166
Write down the inequality shown on the
number line below.
For the given number line the inequality equation would be -10 < x ≤ 20.
What is inequality?
In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
In the given number line, a hollow circle represents that the number is excluded and solid circle represents that the number is included in the range
and the range lies between -10 to 2.
Let's take a variable to describe the relationship,
By using inequality we can prepare the inequality equation as
-10 < x ≤ 20
Hence, for the given number line the inequality equation would be -10 < x ≤ 20.
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helpppp me please!!!
Answer:
Step-by-step explanation:
17-8=9 but if 18-7=11 then 19-8=7
Heather works as a waitress at her family's restaurant she works every 2 hours every morning during the breakfast shift and returns to work each evening for the dinner shift in the last 4 days she worked 28 hours if Heather works the same number of hours each evening how many hours did she work during each dinner shift?
Heather worked 5 hours every evening during each dinner shift.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
Let morning shift = m
evening shift = e
Representing the word problem in an equation;
4(m + e) = 28
Diving both sides by 4
m + e = 7
but she always works 2 hours in th morning shift
2 + e = 7
e = 7 - 2
e = 5
Therefore she worked 5 hours in the evening shift for 4 days.
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the standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. a standard dartboard is 18 inches in diameter. suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left. brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor. does brian's dart land on the dartboard? drag the choices into the boxes to correctly complete the statements.
The question is an illustration of equation of circles.
The equation of the dartboard circle is: [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.
Given that,
h = 5 feet 8 inches ---- the height at which the dartboard was hung
d = 18 inches in diameter ---- the diameter of the dartboard
B = 12 feet --- the bull's eye
D = 11.5 feet , 5 feet --- Brian's dart
Equation of the circle
First, we convert all units to feet
This is done by dividing inches units by 12
h = 5 feet 8 inches
h = 5 ft + 8/12 ft
h = 5 ft + 2/3 ft
Take LCM
h = [tex]\frac{15+2}{3}[/tex] ft
h = [tex]\frac{17}{3}[/tex] ft
d = 18 inches
d = [tex]\frac{18}{12}[/tex] ft
d = [tex]\frac{3}{2}[/tex] ft
Divide by 2 to calculate radius
r = [tex]\frac{3}{2*2}[/tex] ft
r = [tex]\frac{3}{4}[/tex] ft
To find the equation of a circle when you know the radius and centre, use the formula as [tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex] , where represents the centre of the circle, and is the radius.
The equation of the circle is represented as:
[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]
In this case:
a = B = 12 feet -- the distance between the bull's eye and the wall
b = h = [tex]\frac{17}{3}[/tex] ft ---- the height at which the dartboard was hung
So, we have:
[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]
[tex](x-12)^{2} +(y-\frac{17}{3}) ^{2} = (\frac{3}{4}) ^{2}[/tex]
Evaluate the exponents
[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Hence, the equation of the circle is:
[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Does Brian’s dart land on the dartboard?
Yes her dart lands on the dartboard because
D = 11.5 feet , 5 feet is within the circumference of the dartboard
Therefore,
The question is an illustration of equation of circles.
The equation of the dartboard circle is: [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.
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what simplify. 5x + 3 (x + 2) + 3
Answer:
8x + 9
Step-by-step explanation:
5x + 3x + 6 + 3
8x + 9
if 15 and 9 are two members of a
Pythagorean triple, what is the third
member?
Answer: 12
Step-by-step explanation:
hope this helps
In Jillian's garden, there are 3 rows of carrots, 2 rows of string beans, and 1 row of peas.There are 8 plants in each row. How many plants are in the gradenn?
the capacity of an elevator is either 20 children or 15 adults. if 17 children are currently in the elevator, how many adults can still get in?
Two more adults can board the elevator if there are 17 children present inside.
Explain the concept of capacity of an elevator?The point when 20 children or 15 adults can enter an elevator is considered the elevator's capacity. The number of adults who can still enter the elevator when there are 17 children inside must be determined.A linear equation can be created to resolve the aforementioned issue.The number of adults who can still enter will be determined by the linear equation solution.
let
c is equal to a child's weight.a is equal to 1 adult's weight.20c = 15a ; 5 divided by both sides
4c = 3a
Another 3 kids can enter the elevator if there are already 17 in it.
The fact that;
3c = 9/4 a
3c = 9/4 a
3c = 2.25 a
3c = 2 a (no fraction)
Thus, two more adults can board the elevator if there are 17 children present inside.
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