Given data:
The original cost of dinner C=$20.00.
The sale price is 80% of the original cost.
[tex]\begin{gathered} S=\frac{80}{100}(20)_{} \\ =0.8(20) \\ =16 \end{gathered}[/tex]Thus, the final sale price is $16.00.
over Thanksgiving break Joshua drove from Connecticut to Ohio which is 422 Mi this trip took Jason and his family 6 hours how fast was Joshua driving be sure to round your answer to the nearest whole number
In this case the answer is very simple. .
Step 01:
Data
total distance = 422 mi
total time = 6 hours
Step 02:
[tex]\frac{total\text{ distance}}{\text{total time}}=\frac{422mi}{6\text{ hour}}\text{ = }70.33\text{ mi / hour}[/tex]The answer is:
Joshua's speed was 70 mi/hours
In a video game, Connor scored 25% more points than Max. If c is the number of points that Connor scored and m is the number of points that Max scored. Write an equation that represents the situation.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Connor scored = c
Max scored = m
equation = ?
Step 02:
Connor scored =>>> + 25% Max scored
c = m + m * 0.25
c = m ( 1 + 0.25)
c = 1.25 m
The answer is:
c = 1.25 m
In the figure XYZ ~ ABC.Find cosB, tanB, and sinB.Round your answers to the nearest hundredth.
we have the following;
1. Cos B:
[tex]\begin{gathered} CosB=\frac{a}{h} \\ CosB=\frac{15.4}{17}=0.91 \end{gathered}[/tex]2. Tan B:
[tex]\begin{gathered} TanB=\frac{o}{a} \\ TanB=\frac{7.2}{15.4}=0.48 \end{gathered}[/tex]1. Sin B:
[tex]\begin{gathered} SinB=\frac{o}{h} \\ SinB=\frac{7.2}{17}=0.42 \end{gathered}[/tex]Erian's extended family is staying at the lake house this weekend for a family reunion. She is in charge of making homemadepancakes for the entire group. The pancake mix requires 2 cups of flour for every 10 pancakes.[a] Write a ratio to show the relationship between the number of cups of flour and the number of pancakes made.[b] Determine the value of the ratio.c Use the value of the ratio to fill in the following two multiplicative comparison statements..The number of pancakes made is.times the amount of cups of flour needed.The amount of cups of flour needed isof the number of pancakes made.(d If Erian has to make 70 pancakes, how many cups of flour will she have to use?
(a) The ratio is:
[tex]\frac{\text{ number of cups of flour}}{\text{ number of pancakes}}[/tex](b) This ratio is equal to:
[tex]\begin{gathered} \frac{\text{ number of cups of flour}}{\text{ number of pancakes}}=\frac{2}{10} \\ S\text{implifying} \\ \frac{\text{ number of cups of flour}}{\text{ number of pancakes}}=\frac{1}{5} \end{gathered}[/tex](c) Isolating "number of cups of flour":
[tex]\text{ number of cups of flour}=\frac{1}{5}\cdot\text{number of pancakes}[/tex]Isolating "number of pancakes":
[tex]5\cdot\text{ number of cups of flour}=\text{ number of pancakes}[/tex]The number of pancakes made is 5 times the amount of cups of flour needed.
The amount of cups of flour needed is 1/5 of the number of pancakes made.
(d) Substituting with "number of pancakes" = 70, we get:
[tex]\begin{gathered} \text{ number of cups of flour}=\frac{1}{5}\cdot\text{7}0 \\ \text{ number of cups of flour}=14 \end{gathered}[/tex]She will have to use 14 cups of flour
A community service group spent Planet summer planting trees in City park the table shows the total of number of trees after a certain number of weeks how many trees were already planted in the park before the community group started to plant?
If we consider the number of weeks equals 0 as the moment where the group started to plant, we can notice that at this point there were already 16 trees, then the answer is 16 trees
The cost in dollars of a class party is 59+13n, where n is the number of people attending. What is the cost of 44 people?
The function is:
C(n) = 59 + 13n
where n is the number of people, and C(n) is the cost of a class party.
To determine the value of C(n) where n = 44, just replace this value of n into the previous formula, and simplify the expression, just as folow:
C(44) = 59 + 13(44)
C(44) = 59 + 572
C(44) = 631
Hence, the cost for 44 people is 631 dollars.
Could you please help me out with this question ??
Given the polynomial function:
[tex]x^3-2x^2-x+2[/tex]Group the functions:
[tex](x^3-2x^2)-(x-2)[/tex]Factor out the greatest common factor from the parenthesis
[tex]\begin{gathered} x^2(x-2)-1(x-2) \\ (x^2-1)(x-2) \end{gathered}[/tex]Simplify fully to have:
[tex]\begin{gathered} (x^2-1)(x-2) \\ \lbrack(x^2-1^2)\rbrack(x-2) \\ (x+1)(x-1)(x-2) \end{gathered}[/tex]This gives the factored form of the given polynomial.
A fashion designer makes and sells hats. The material for each had cost three dollars. The hats sell for $13.50 each. The designer spends $2121 on fixed cost: advertising, Power, water, rent . How many hats mustard designers sell to break even
The designer spends $2121 and $3 each for hat and he can sell it for $13.50 each.
If there are x number of hats, it will cost him (2121 + 3x) and he can gain 13.50x
The break even is when the cost and sales are equal.
Equating both expressions :
[tex]\begin{gathered} 2121+3x=13.50x \\ 2121=13.50x-3x \\ 2121=10.50x \\ x=\frac{2121}{10.50}=202 \end{gathered}[/tex]The answer is 202 hats
What are the magnitude and direction of w = ❬–5, –14❭? Round your answer to the thousandths place.
To solve the question, we will have to determine the quadrant within which the point falls
Since both values are negative
[tex](x,y)=(-5,-14)[/tex]So the values are in the third quadrant
So we will have to get the magnitude first
[tex]\begin{gathered} \text{Magnitude}=\sqrt[]{x^2+y^2} \\ \text{Magnitude}=\sqrt[]{(-5)^2+(-14)^2} \\ \text{Magnitude}=\sqrt[]{25+196} \\ \text{Magnitude}=221 \\ \text{Magnitude}=14.866 \end{gathered}[/tex]Next, we will have to get the direction
[tex]\begin{gathered} \text{direction}=\tan ^{-1}(\frac{y}{x}) \\ \text{direction}=\tan ^{-1}(\frac{-14}{-5}) \\ \text{direction}=\tan ^{-1}(2.8) \\ \text{direction}=70.346^0 \end{gathered}[/tex]So, since we know that the point is on the third quadrant, then
We will add 180 degrees (90 degrees from first and 90 degrees from the second quadrant)
So we will have
[tex]180^0+70.346^0=250.346^0[/tex]Thus the answer is
[tex]\mleft\Vert w\mleft\Vert=\mright?\mright?14.866,\theta=250.346^0[/tex]PLSS HELP Find a formula for the exponential function passing through the points (-3, 3/8) and (3,24)
The exponential function is of the form:
[tex]y=ab^x[/tex]Given the two points, we can plug each point into the equation and see:
1.
[tex]\begin{gathered} y=ab^x \\ \frac{3}{8}=ab^{-3} \end{gathered}[/tex]2.
[tex]\begin{gathered} y=ab^x \\ 24=ab^3 \end{gathered}[/tex]Let's divide the the 2nd equation by the 1st one:
[tex]\begin{gathered} \frac{24}{\frac{3}{8}}=\frac{ab^3}{ab^{-3}} \\ 24\times\frac{8}{3}=\frac{b^3}{b^{-3}} \\ 64=b^{3+3} \\ b^6=64 \end{gathered}[/tex]Note: we used the property of exponents, 1/a^x = a^ -x to simplify it.
Now, we can solve for b:
[tex]\begin{gathered} b^6=64 \\ b=\sqrt[6]{64} \\ b=2 \end{gathered}[/tex]The second equation, now, becomes:
[tex]\begin{gathered} 24=ab^3 \\ 24=a(2)^3 \end{gathered}[/tex]Now, we can easily find a:
[tex]\begin{gathered} 24=a(8) \\ a=\frac{24}{8} \\ a=3 \end{gathered}[/tex]We know b = 2 and a = 3.
So, the final equation will be:
[tex]\begin{gathered} y=ab^x \\ y=3(2)^x \end{gathered}[/tex]
1. Given triangle ABC, what is the length of the line segment connecting the midpoints of AC and BC?
A = (1,6)
B = (3,1)
C = (8,3)
The length of the line segment connecting the midpoints of AC and BC is 2.69 units.
We are given a triangle. The vertices of the triangle are A, B, and C. The coordinates of the vertices are A (1, 6), B (3, 1), and C (8, 3). We need to find the length of the line segment connecting the midpoints of AC and BC.
Let the midpoints of AC and BC be E and F.
The coordinates of the midpoint E are calculated below.
E = [(1 + 8)/2, (6 + 3)/2] = (4.5, 4.5)
The coordinates of the midpoint F are calculated below.
F = [(3 + 8)/2, (1 + 3)/2] = (5.5, 2)
The length of the line segment EF can be calculated by using the distance formula. Let the length of EF be represented by "L".
L = √[(4.5 - 5.5)² + (4.5 - 2)²]
L = √(1 + 6.25)
L = √7.25
L = 2.69
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PLEASE HELP!!!! Explain in depth!!! In a geometry course, the grade is based on the average score on six tests, each worth 100 points. W. Orrier has an average of 88.5 on his first four tests. What is the lowest average he could obtain on his next two tests and still receive an A (an average of 90 or better)?
Answer:
93 marks
Step-by-step explanation:
If he has an average of 88.5 marks on the first four tests then the total score for these four tests is:
[tex]\implies 88.5 \times 4=354[/tex]
To obtain an average of at least 90 marks on each test the total number of marks needed for the six tests is:
[tex]\implies 90 \times 6=540[/tex]
So the minimum total marks he needs to obtain an A is 540.
To find the lowest average he could obtain on his next two tests to still receive an A, subtract the total for the first four tests from the total needed for the six tests and divide by two:
[tex]\implies \dfrac{540-354}{2}=\dfrac{186}{2}=93[/tex]
Therefore, he needs to score an average of at least 93 marks on his next two tests to still receive an A grade.
What is the value of 2x in this equation?3(2x-5)-4x+8=-2x+1a. 8 b. -1c. 4d. -4
The value of (2x) after the solving the equation
[{3(2x-5) - 4x + 8} = (-2x + 1)] for the variable "x" will be 4.
As per the question statement, we are provided with an equation:
[{3(2x-5) - 4x + 8} = (-2x + 1)],
And we are required to calculate the value of (2x) from the solution of the above mentioned equation.
Given, [{3(2x-5) - 4x + 8} = (-2x + 1)]
Or, [{(6x - 15) - 4x + 8)} = (-2x + 1)]
Or, [{(6x - 4x) + (8 - 15)} = (-2x + 1)]
Or, [(2x - 7) = (-2x + 1)]
Or, [(2x + 2x) = (7 + 1)]
Or, (4x = 8)
Or, [x = (8/4)]
Or, (x = 2)
Or, [2x = (2 * 2)]
Or, (2x = 4)
Equation: An equation is a mathematical statement that determines the relation of equality among two or more expressions, by a connector "equal to" sign in between.To learn more about Equations, click on the link below.
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James and Susan wish to have $10,000 available for their wedding in 2 years.
How much money should they set aside now at 6% compounded monthly in
order to reach their financial goal?
They need to set aside $8871.86
I need help quick please i have to turn this in tomorrow it’s 4am.
Answer:
sitting in his highchair modifies baby
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function =ht−80t16t2. After how long will it reach its maximum height?
A group of people were asked "What time do you prefer to see a movie? The two way tablebelow represents the results by their age.Morning 4 2 12 25 4316-20 21-25 26-30 Over 30 TotalsAfternoon 8 12 18 32 70EveningTotals28 34 28 11 101Late Night 34 18 21 4 7774 66 79 72 291What the approximate probability that a person will be over 30 given they prefer afternoonmovies?
From theinformation given,
total number of people = 291
Number of persons over 30 that prefer afternoon movies = 32
Number of persons that prefer afternoon movies = 70
This is a conditional probability.
Recall, Probability of event A given event B = P(A and B)/P(B)
Thus,
Probability that a person will be over 30 given that they prefer afternoon movies = 32/70
By multiplying by 100, it becomes
32/70 x 100
= 46%
Probability that a person will be over 30 given that they prefer afternoon movies = 46%
What is the positon of the letter E on the number line and how can i write it as a fraction or mixed number
We are asked to identify the position of the letter E on the number line.
First of all, count the total number of spacings between 2 and 3.
There are a total of 7 spacings.
The letter E is at the 6th spacing.
So, we can write the position of the letter E in the mixed form as
[tex]2\frac{6}{7}[/tex]We can also re-write the above mixed number as a fraction
[tex]2\frac{6}{7}=\frac{2\times7+6}{7}=\frac{14+6}{7}=\frac{20}{7}[/tex]So, the position of the letter E on the number line as a fraction is 20/7
Reflect the vector (-3,5) acrossthe x-axis.([?],[])
1) When we reflex across the x-axis we must follow this rule:
Pre-image Image
(x, y) ----------------> (x,-y)
2) Since we have a vector <-3,5> then reflecting it across the x-axis we'll have
Pre-image Image
<-3,5>---------> <-3, -5>
3) So the vector after the reflection is < -3,-5>
- Which subsets of the real number system does -2.8 belong? A.Rational and Integer.B.Irrational and Integer.C.Irrational onlyD. Rational only.
Answer:
D. Rational only.
Step-by-step explanation:
-2.8 is only rational.
It is not irrational because it is rational(decimal numbers are rational).
It is not integer because there is a decimal part.
So, the correct answer is:
D. Rational only.
Drag the preimage to the correct location on the graph.
Quadrilateral 2 is a reflection of a quadrilateral across line m. Where is the preimage for quadrilateral 2 located and what is its orientation?
It is true that the preimage of the quadrilateral labeled 1 is reflected across line M to produce 2. The preimage for quadrilateral 2 is located at exactly below the position of quadrilateral 2 as indicated in the attached image. Its orientation is °180 the current location of image 2.
What is a preimage?Preimage refers to a collection of some input set items that are handed to a function to get some output set elements. It is the opposite of the Image. Domain = all valid independent variable values. This is the input set of a function, also known as the set of departure.
The orientation (that is angular position or attitude or bearing, or direction) of an object, such as a line, plane, or rigid body, is described in geometry as part of how it is positioned in the space it inhabits.
Hence quadrilateral 2 is 180° reflected from the preimage, given that it was reflected across line m.
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took me an hour to figure it out
Step-by-step explanation:
Identify a benchmark you can use to find an equivalent percent for eachratio. Then find the equivalent percent. (Example 1)13. Lo Benchmark: 4. Benchmark:6105.Benchmark:
The benchmark of a fraction a/b is 1/b. Then, for the given:
To find the equivalent percent: find the a/b of 100 :
6/10:
[tex]\frac{6}{10}\cdot100=60[/tex]6/10 =60%___________________
2/4:
[tex]\frac{2}{4}\cdot100=50[/tex]2/4=50%___________________
4/5:
[tex]\frac{4}{5}\cdot100=80[/tex]4/5 = 80%Type the equation for the graphbelow.Pi/3 2piy = [?] sin([ ]x)
To find the equation of the graph, what we do is to recognize some characteristics of a sine function:
- Amplitude: The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In this case, the amplitude is 1.
- Period: The period of a sine function is defined as the length of one complete sine wave or one complete cycle of the curve. It can be found using the equation: P=2pi/B.
Why are these characteristics important?
Because the sine function has the following general form:
In this problem, we have A=1 and we know that the period equals 2pi/3. So,
Therefore, the equation of the graph is:
A dilation by a scale factor od 2 centered at (2,-1) is performed on the triangle shown draw the resulting triange
Explanation:
The vertices of the triangle are:
• (2, -1)
,• (-3, -1)
,• (1,2)
The triangle is dilated by a scale factor of 2 with the center of dilation at (2, -1).
The coordinates of the image triangle are (-2,1), (0,5) and (-8, -1).
Answer:
The triangle and its image are attached below:
I need help number 7
The population at the beginning of 1950 was 2600 thousand people.
Then it started increasing exponentially 23% every decade.
The general form of any exponential function is:
[tex]f(x)=a(b)^x[/tex]Where
a is the initial value
b is the growth/decay factor
x is the number of time periods
y is the final value after x time periods
a. To calculate the growth factor of an exponential function, you have to add the increase rate (expressed as a decimal value) to 1:
[tex]\begin{gathered} b=1+r \\ b=1+\frac{23}{100} \\ b=1.23 \end{gathered}[/tex]b. Considering the initial value a= 2600 thousand people and the growth factor b=1.23, you can express the exponential function in terms of the number of decades, d, as follows:
[tex]f(d)=2600(1.23)^d[/tex]c. Considering that the time unit is measured in decades, i.e d=1 represents 10 years
To determine the corresponding value of the variable d for 1 year, you have to divide 1 by 10
[tex]1\text{year/10years d}=\frac{1}{10}=0.1[/tex]Calculate the growth factor powered by 0.1:
[tex]\begin{gathered} b_{1year}=(1.23)^{0.1} \\ b_{1year}=1.0209\approx1.02 \end{gathered}[/tex]d. Use the factor calculated in item c
[tex]g(t)=2600(1.0209)^t[/tex]what is the area of a square with side of 14 millimeters
The formula for determining the area of a square is expressed as
Area = length^2
If the length of each side of the given square is 14 millimeters, then
Area = 14^2
Area = 196 mm^2
in the figure below, points D, E, and F are the midpoints of sides ABC. suppose AC =58, DF =26, and AB =38. find the following lengths. DE, BC, and CE
The values of the lengths DE, BC, and CE are 29, 52, and 26 respectively which can be found out by using the relations for mid-points of triangle.
In the figure, it is given to us that -
Points D, E, and F are the midpoints of sides AB, BC, and AC of the ΔABC respectively.
AC = 58
DF = 26
and, AB = 38
We have to find out the values of the lengths DE, BC, and CE.
Now, AC = 58 is parallel to the mid-segment DE
=> The mid-segment DE is half of the AC.
=> DE = AC/2
=> DE = 58/2
=> DE = 29
Similarly, the mid-segment DF = 26 is parallel to BC
=> BC = Twice the mid-segment DF
=> BC = 2*26
=> BC = 52
Now, E is the midpoint of BC of the ΔABC.
=> CE = BC/2
=> CE = 52/2
=> CE = 26
Through the formulas for mid-points of triangle, we find out that the values of the lengths DE, BC, and CE are 29, 52, and 26 respectively.
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Writing rational numbers as a decimal
2. Let's convert the rational number as a decimal
[tex]-2\frac{4}{5}[/tex]The given number is a mixed number, so we need to convert it to rational.
[tex]-2\frac{4}{5}=-2+\frac{4}{5}=-\frac{6}{5}[/tex]Then: To convert -6/5 into a decimal number, divide 6 by 5:
6 divide by 5
5*1 = 5, then 6-5 = 1
6 l 5
1
--------------
6 l5
5 1
-------------
1 l 5
1
We add
Solve the equation. 6x = 96a16b576c90d102
Answer
Option A is correct.
x = 16
Explanation
We are asked to solve the equation
6x = 96
Divide both sides by 6
(6x/6) = (96/6)
x = 16
Hope this Helps!!!
Quadrilateral QRST with vertices Q (1,2), R(3,4), S(5,6) and T(2,7), is dilated by a factor of 2 with the center of dilation at the origin. what are the coordinates of the quadrilateral QRST
SOLUTION
Now, since the center of dilation is at the origin, to get the new coordinates of the vertices of the quadrilateral, we will simply multiply the coordinates by a the scale factor of 2. This becomes
d
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