Answer: 3.375oz
Explanation
Given
• Reduce his daily soda intake by 25%.
,• Currently, he drinks 4.5oz. cans of soda per day.
,• Ounces of soda can the patient drink if he reduces his intake by 25%?
We have to build a relation, where 4.5 is our 100% and x is 75% (100 - 25 = 75%):
[tex]\frac{x}{75}=\frac{4.5}{100}[/tex][tex]x=\frac{4.5}{100}\cdot75[/tex]Solving for x:
[tex]x=4.5\cdot0.75[/tex][tex]x=3.375[/tex]<
An inequality is shown.
-2x+12<18
What is the solution to the inequality?
0x<3
x>3
Answer:
-3 < x
Step-by-step explanation:
first of all get the positive x on one side, so we have
12 < 18 + 2x ( positive x is easier to work with)
then, get only x on one side
-6 < 2x
simplify
-3 < x
Solve the quadratic equation using the quadratic formula or completing the square. Show exact answers in simplified, radical form; no rounded decimals 2x^2-4x+3=0
The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula
Given,
In the question:
The equation is :
2x^2-4x+3=0
To solve by using the quadratic formula :
Now, According to the question;
[tex]2x^2 -4x+3=0[/tex]
Identify the coefficients
a = 2, b = -4 , c = 3
Use the quadratic Formula :
x = (-b±√(b²-4ac))/(2a)
Substitute into values above formula :
x = -(-4) +√(-4)²-4x 2 x 3))/(2x2) or
x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)
Determine the sign for exponential or radical expressions
x = -(-4) -√(-4)²-4x 2 x 3))/(2x2)
x = 4 -√16-4x 2 x 3))/(2x2)
Calculate the product or quotient
x = 4 -√16-24/4
x = 4 -√-8/4
x = 4 - √-8 x √-1/ 4
x = [tex]\frac{4\sqrt{2^2.2 } }{4}[/tex] x [tex]\sqrt{-1}[/tex]
Simplify the radical expression:
x = [tex]\frac{4 - 2\sqrt{2} . \sqrt{-1} }{4}[/tex]
Rewrite by definition i = [tex]\sqrt{-1}[/tex]
x = [tex]\frac{4-2\sqrt{2i} }{4}[/tex]
x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex]
Hence, The value of x = x = 1 - [tex]\frac{2\sqrt{2i} }{4}[/tex] and x = 1 + [tex]\frac{2\sqrt{2i} }{4}[/tex] by using quadratic formula .
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Mia is deciding between two truck rental companies. Company A charges an initial fee of $30 for the rental plus $3 per mile driven. Company B charges an initial fee of $85 for the rental plus $2 per mile driven. Let AA represent the amount Company A would charge if Mia drives xx miles, and let BB represent the amount Company B would charge if Mia drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Mia needs to drive 80 miles with the rented truck.
Answer:
(a.): Company A: 3x + 30; Company B: 2x+85
(b.) Company B is cheaper as it would cost $245 for Mia to drive 80 miles
Step-by-step explanation:
The equations we need are linear and we can think of them as such. x represents the slope (cost per mile) and the initial fee represents our y-intercept or constant (amount paid before Mia ever drives)
(a.): Thus, for company A, we have y = 3x + 30 and for company B we have y = 2x + 85.
(b.) Since we know that Mia needs to drive 80 miles, we plug this into x for both companies and find which one is lower
Company A: 3(80) + 30 = $270
Company B: 2(80) + 85 = $245
Company B's price would be lower for Mia's needs.
The graph shown shows the supply and demand for a widget. What mappens if the price is set at $25.00? Include in your answer how retailers will react to a $25.00 price point.
From the graph, if the price increases to $25
The quantity demand will decrease
Quantity supply increases --------This is the reaction from the retailers
?
Find the Area of the figure below, composed of a rectangle and a semicircle. The
radius of the circle is shown. Round to the nearest tenths place.
Area of Irregular Shapes
Nov 03, 2-44:03 PM
Answer:
9
3
20 POINTS PLEASE HELP !!!!!
Area of irregular shape is 41.13m².
Define area.The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
Given,
Area of irregular shape = Area of rectangle + Area of semicircle
Area of rectangle = Length × Breadth
Area of rectangle = 9 × 3
Area of rectangle = 27 m²
Area of semicircle:
1/2πr²
1/2 × 3.14 × 3²
14.13 m²
Area of irregular shape = 27 + 14.13
Area of irregular shape = 41.13
Area of irregular shape is 41.13m².
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24. Find fl-1).For questions 24-27, use the graph below.25. Find f(4).26. Find f(-3).27. If f(x) = 9, find x.
Let's start by calculating the value for f(-1).
For this we go to the graph and count the number of squares to the left of the axis to be at -1. In this case f(-1) would be 5.
Now let's calculate f(4)
For this case the value of f(4) would be 0.
Similarly we calculate f(-3). As you can see in the graph it would be 6.
The last scenario would be for when f(x) = 9, we look for that value on the curve and realize that it corresponds to x = 1.
write and equation in slope-intercept form to represent each table x-3,6,9,12 y-5, -1, -7, -13
The equation that represents the table, in slope-intercept form, is: y = -2x + 11.
How to Write the Equation of a Line in Slope-intercept Form?The slope-intercept form of an equation that represents a line is expressed as y = mx + b, where:
m = slope = change in y / change in x.b = y-interceptUsing two pairs of values from the table, (6, -1) and (9, -7):
Slope (m) = (-7 -(-1)) / (9 - 6)
Slope (m) = -6/3
Slope (m) = -2.
Find the y-intercept, b, by substituting m = -2 and (x, y) = (6, -1) into y = mx + b:
-1 = -2(6) + b
-1 = -12 + b
-1 + 12 = b
b = 11
To write the equation, substitute m = -2 and b = 11 into y = mx + b:
y = -2x + 11
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In the figure, assume that angles that appear to be right angles are right angles.What is the area of the figure?Use 3.14 for π.The approximate area is ___ square units.Use 3.14 for π.
We can break apart the figure into a half-circle, rectangle, and a triangle.
Shown below:
We find the area of each region and sum it up to find the area of the total figure.
Area of Half CircleThe volume of the area of a half circle is
[tex]A=\frac{\pi r^2}{2}[/tex]Given, radius (r) = 3, we find the area:
[tex]\begin{gathered} A=\frac{\pi r^2^{}}{2} \\ A=\frac{\pi(3)^2}{2} \\ A=\frac{9\pi}{2} \\ A=\frac{9(3.14)}{2} \\ A=14.13 \end{gathered}[/tex]Area of RectangleThe area of a rectangle is found by multiplying the length and width.
Given,
Length = 8
Width = 6
The area is:
[tex]\begin{gathered} A=8\times6 \\ A=48 \end{gathered}[/tex]Area of TriangleThe area of a triangle is given by the formula,
[tex]A=\frac{1}{2}bh[/tex]Where
b is the base length and h is the height
Given,
b = 3
h = 6
The area of the triangle is,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(3)(6) \\ A=9 \end{gathered}[/tex]The total area of the figure >>>14.13 + 48 + 9
= 71.13 square units19. highlight where values show g(x) = 0 and what is the answer20. highlight where values show f(x) > g(x) and what is the answer
19) g(x)=0 is the value of x at points where the line cuts the x-axis
From the graph that is at:
x=-7, x=1, x=3, and x=9
20) f(x)>g(x) where the curve f(x) is higher than the curve g(x), and this is at:
x<-3, 07
I need help evaluating/answering this!
The value of the expression is equal to 6.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is [3(6-14)]/(-4). The value of the expression will be calculated below,
E = [3(6-14)]/(-4).
Simply the expression by using mathematical operations,
E = [3( -8)]/(-4).
E = 3 x 2
E = 6
Therefore, the value of the expression is equal to 6.
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27y over 15y in lowest terms
Given: 27y over 15y
The expression will be as following:
[tex]\frac{27y}{15y}=\text{?}[/tex]The result of the given expression will be:
[tex]\frac{27y}{15y}=\frac{27}{15}=\frac{3\cdot9}{3\cdot5}=\frac{9}{5}[/tex]The answer is 9/5
It can be written as a mixed number = 1 4/5
Jason is a high school basketball player. In a particular game, he made some free
throws (worth one point each) and some two point shots. Jason made a total of 13
shots altogether and scored a total of 20 points. Write a system of equations that
could be used to determine the number of free throws Jason made and the number of
two point shots he made. Define the variables that you use to write the system.
The total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.
First, let us understand the variables:
Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.
Let x and y be the quantity of shorts.
x is the number of attempts at the free throw line.
y is the quantity of two-point attempts.
According to the question, we have;
x + 2y = 20 ............equation 1
x + y = 13 ............equation 2
From equation 2 we can take out the value of x;
x = 13 - y ............equation 3
substituting the value of x in equation 1, we will get;
(13 - y) + 2y = 20
13 - y + 2y = 20
13 + y = 20
y = 20 - 13
y = 7
putting the value of y in equation 3, we will get
x = 13 - 7
x = 6
Thus, the total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.
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Rita is playing a game by rolling a rectangular prism made up of cubes. The prism is 6 cubes wide, 3 cubes high, and 4 cubes deep. Rita rolls the cube and says that the top view is a 6-unit by 4-unit rectangle.
Which statement explains whether Rita could be correct?
Rita could be correct because the cube could land so the 3-cube height and the 4-cube depth make up the top face of the cube.
Rita could be correct because the cube could land so the 6-cube width and the 4-cube depth make up the top face of the cube.
Rita could not be correct because the top face of the cube is made up of the 6-cube width and the 4-cube depth.
Rita could not be correct because the top face of the cube is made up of the 6-cube width and the 3-cube height.
Answer:
Step-by-step explanation:
Answer:
Option B: Rita could be correct because the cube could land so the 6-cube width and the 4-cube depth make up the top face of the cube.
Step-by-step explanation:
We are told the dimensions of the prism are;
Width = 6 cubes wide
Height = 3 cubes high
Depth = 4 cubes deep.
Circle O shown below has a radius of 25 inches. To the nearest tenth of an inch,determine the length of the arc, x, subtended by an angle of 137°.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
[tex]Length\text{ of Arc =}\frac{\theta}{360^0}\text{ x 2}\pi\text{ r}[/tex][tex]\begin{gathered} where\text{ }\theta\text{ = 137}^0 \\ radius\text{ = 25 inches} \end{gathered}[/tex][tex]Length\text{ of arc = }\frac{137^0}{360^0}\text{ x 2 x }\pi\text{ x 25}[/tex][tex]Length\text{ of arc =}\frac{137^0}{360^0}\text{ x }\frac{50\pi}{1}[/tex][tex]Length\text{ of Arc = }\frac{21,519.90968}{360}[/tex][tex]Length\text{ of Arc = 59.77752688 inches}[/tex][tex]Length\text{ of Arc }\approx\text{ 59. 8 inches \lparen to the nearest tenth \rparen}[/tex]Tim buys a torch and a battery
The torch costs eleven times as much as the battery
Tim pays with a £10 note and gets £4.84 change
How much does the battery cost?
The cost of battery is £0.43.
Given,
In the question:
Tim buys a torch and a battery
The torch costs eleven times as much as the battery and
Tim pays with a £10 note and gets £4.84 change.
To find the how much does the battery cost?
Now, According to the question:
Let cost of battery = £ x
So, Cost of torch = £ 11x
Based on the given conditions :
=> x + 11x = £ 10 - £ 4.84
=> 12x = £ 5.16
=> x = £ 5.16/ 12
=> x = £ 0.43
Hence, The cost of battery is £0.43.
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number 8 State how you know each pair of triangles are congruent
trianglesPairs of congruent triangles
Triangles A is congruent since UV = WX
Triangle Δ KLJ = Δ MNO and are congruents
Triangle Δ UGI ≠ Δ MNO ≠ ΔKLJ is congruent
what is evaluate 5-(6/3)
3 times x increased by 20 as a algebraic expression
Answer:
3x+20
Step-by-step explanation:
Which of the following shows a graph of a tangent function in the form y = atan(bx − c) + d, such that b equals one half question markgraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative 3 times pi over 2 comma negative 2 and negative pi comma negative 1 and negative pi over 2 comma 0 to the right asymptotic to the line x equals 0 and another piece that increases from the left in quadrant 4 asymptotic to the line x equals 0 passing through the points pi over 2 comma negative 2 and pi comma negative 1 and 3 times pi over 2 comma 0 to the right asymptotic to the line x equals 2 times pigraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative pi comma negative 2 and 0 comma negative 1 and pi comma 0 to the right asymptotic to the line x equals 2 times pigraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 2 times pi passing through the points negative 3 times pi over 2 comma 1 to the right asymptotic to the line x equals negative pi and another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative pi passing through the point negative pi over 2 comma 1 to the right asymptotic to the line x equals 0 and continuing periodicallygraph of tangent function with one piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 7 times pi over 4 passing through the point negative 3 times pi over 2 comma negative 1 to the right asymptotic to the line x equals negative 5 times pi over 4 and another piece that increases from the left in quadrant 3 asymptotic to the line x equals negative 5 times pi over 4 passing through the point negative pi comma negative 1 to the right asymptotic to the line x equals negative 3 times pi over 4 and continuing periodically
In general, given
[tex]y=a*tan(bx-c)+d[/tex]b is related to the period of the function, such that, in the case of the tangent function,
[tex]period=\frac{\pi}{b}[/tex]Remember that the period of tan(x) is equal to pi.
Therefore, in our case,
[tex]\begin{gathered} b=\frac{1}{2} \\ \Rightarrow period=\frac{\pi}{\frac{1}{2}}=2\pi \end{gathered}[/tex]The period of the function is 2pi, which means that it repeats every 2pi units.
Thus, the answer is the first graph, the one shown below.How many times larger is 6 × 108 than 3 × 10-4?
Answer:
About 24.9 or 25 (if rounded to the nearest whole number or tenth).
HELP QUICK 30 POINTS!!!!
What equation is graphed in this figure?
A. y−4=−2/3(x+2)
B. y+2=−3/2(x−2)
C. y+1=−2/3(x−3)
D. y−3=3/2(x+1)
Answer:
B is correct. The slope is -3/2.
Answer:D
Step-by-step explanation:
Which table shows a function that is decreasing only over the interval (-1, infinity)
The last table shows the function that is decreasing only over the interval [tex](-1, \infty)[/tex].
From given tables we clearly see that in below table, the functions are decreasing as 'x' increases
x f(x)
-3 -5
-1 -1
-1 -1
0 0
1 -4
2 -8
We need to find interval [tex](-1, \infty)[/tex].
In first table,f(x)=-5,-2,-1,2. Here the functions are in increasing order
In second table, f(x)=-7,-6,1,-1. Here the functions does not follow a specific order
in third table, f(x)=-1,2,1,-6, Here also the functions does not follow a specific order.
In fourth table, f(x)=1,0,-4,-8. Here the functions are in decreasing order.
Hence, the fourth table shows the function that deceases over interval [tex](-1, \infty)[/tex].
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Torren deposits $4500 in an account earning 2% interest, compounded annually. The equation that represents this situation is:A(n) = 4500(1 + 0.02) - 1How much will he have in the account at the beginning of year 8? Round youranswer to the nearest dollar.A. $5169B. $32,130C. $16,124D. $5272
Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
The following formula can be used to calculate the compound interest.
[tex]A(n) = P(1 + r)^{(t- 1)}[/tex]
where,
A(n) denotes the final sum.
P stands for the initial deposit.
r denotes the interest rate (in decimal).
t denotes the time (in year).
The compound interest will be C.I = A - P in this case.
We are given in the question;
The account's initial deposit is $4500, and the term is 8 years.
As a result,
A = 4500 and
t = 8
As we all know, interest is compounded once a year.
We shall divide the interest rate in percentage form by 100 to convert it to decimal form.
r = 2% = 2/100
⇒r = 0.02
The given equation is
[tex]A(n) = 4500(1 + 0.02)^{(n- 1)}[/tex]
Substituting the given values in the above equation, we will get,
[tex]A(n) = 4500(1 + 0.02)^{(8- 1)}[/tex]
[tex]A(n) = 4500(1 + 0.02)^{7}[/tex]
[tex]A(n) = 4500 \times 1.14868[/tex]
[tex]A(n) = 5169.06[/tex]
[tex]A(n) = 5169[/tex]
Thus, Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
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Attendance at october fest was 15% more than last year. this year's attendance was 1785 people. find the number of people who attended the festival last year. rounded to the nearest person
Using the concept of equations, 1552 people attended the festival last year.
What are algebraic equations?Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.
An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.
Let the number of people who attended the festival last year =x
Then, we can write an equation as
1785=1.15 × x
x = 1785/1.15
=1552 people
So, last year's attendance = 1552
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What is the value of x in the triangle?
a 30-60-90 triangle with long leg length x and shorter leg length of 7 times the square root of 3
Answer:
sin 30 = 7 *3^1/2 / c
sin 60 = x / c definition of 30-60-90 -
sin 30 / sin 60 = 7 * 3^1/2 / x = .5 / .866 = .577
x = 7 * 3^1/2 / .577 = 21
Check: tan 30 = 7 * 3^1/2 / 21 = .577 = tan 30
which value represents between 11% and 17%?
which value of x below will solve equation 3/4x+10=4
3/4x+10=4
Then solve for x
3/4x = 4 - 10
x = (4-10)/(3/4)
. = -6/3/4
. = -24/3
. = -8
In consecuence , answer IS
x= -8
Vivian has $535 in her stavings account and she has to pay $5.00 each month for her cell phone Reza has $145 and he saves $25 each month for his job walking the dogs at this rate when will they had the same amount of money and how much will they have
Answer: $456
Step-by-step explanation: They will both have the same amount of money at 7 months
According to the rules of significant figures:1.25 × 200 = 300True orFalse
According to the rules of significant figures:
1.25 × 200 = 300
the answer is
TRue
Multiply binomial by polynomials
In this case the answer is very simple . .
We must apply the distributive property of multiplication.
[tex](d^2+3)\cdot(d^2\text{ + 2d + 1) }[/tex][tex]d^2\cdot d^2+d^2(2d^{})+d^2+3(d^2\text{) + 3(2d) + 3}[/tex][tex]d^4\text{ + }2d^3+d^2+3d^2+6d+3[/tex][tex]d^4+2d^3+4d^2+6d+3^{}[/tex]That is the solution. .