John drank 18 fluid ounces of juice. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
We know that 1 cup is equivalent to 8 fluid ounces. Then, we can establish the following rule of three:
[tex]\begin{gathered} 8\text{ fluid ounces ----- 1 cup} \\ 18\text{ fluid ounces ------ x} \end{gathered}[/tex]Then, by cross multiplying these quantities, we have
[tex]x\times8\text{ fluid ounces= 1 cup}\times\text{ 18 ounces}[/tex]By dividing both sides by 8 fluid ounces, we get
[tex]x=\frac{1\text{ cup}\times18\text{ ounces}}{8\text{ fluid ounces}}[/tex]which gives
[tex]x=\frac{18}{8}\text{ cups}[/tex]Now, we need to convert this simple form to a mixed form, that is,
Then, by simplifying this mixed form, the answer is:
[tex]2\frac{1}{4}\text{ cups}[/tex]
Related Questions
collin noticed that various combinations of the nickels and dimes could add uo to $0.75 let x equal the numver of nickles let y equal the number of dimes what is the domain where y is a function of x and the total value is $0.75
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Input data
nickles = 5 cents
dimes = 10 cents
x = number of nickles
y = number of dimes
determine the degree of the polynomial[tex] - 65b + {53x}^{3}y[/tex]
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Determine the degree of the polynomial
656+ 3x^3 y
Degree of the polynomial = 4 = (3 + 1)
3x^3 grade (3)
y grade (1)
________________
The degree of the polynomial is 4
picture with question
Answers
In order to determine if the given triangles are similar, it is necessary to find the values of the missing angles.
Take into account that the sum of the interior angles of a triangle is equal to 180°, the for the missing angles you have:
180° - 90° - 46° = 44°
180° - 38° - 46° = 96°
AS YOU CAN NOTICE THE THREE ANGLES ARE NOT EQUAL.
Then, the triangles are NOT similar because it is necessary that the three angles are equal.
How do you write 1.9 x 102 in standard form?
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We are given the following number in scientific notation.
[tex]1.9\times10^2[/tex]We are asked to write this number in standard form.
Method 1:
Simply multiply 1.9 by 10²
[tex]1.9\times10^2=1.9\times(10\times10)=1.9\times100=190[/tex]Method 2:
Simply move the decimal point to the right by 2 places (since the exponent is 2
y=-2xy=x-8how do you do this
Answers
Separate
y =- 2xy
-2xy = x - 8
Now solve first equation
and then second equation
PART2
y = -2x
y= -4x + 10
Is solved by , substracting both equations
Then
(y - y) = -2x - ( -4x + 10)
0 = -2x + 4x - 10
10 = 2x
10/2= xx
A plane has a speed of 400mi/h. On a windy day, theplane could fly 75 mi with thewind in the same time it tookto fly 65mi against the samewind. What is the rate of thewind?
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The plane has a top speed of 400 miles per hour. That means if it travelled at this same speed on a windy day, it would cover
[tex]undefined[/tex]18/10 [blank] x/12 x =
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18/10 = x/12
(18/10)* 12 = (x/12)* 12
18*12/ 10 = x (12/12)
216/ 10 = x
x= 108/5
x = 21.6
What is the system of inequalities associated with the following graph?A) {y<−1x {+y>1 B) {y>−1 {x+y≥1 C) {y<−1 {x+y≥1 D) {y < -1 {x + y <1
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
What is the system of inequalities associated with the following graph?
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
C) {y<−1
{x+y≥1
Please please please help me
Answers
The lines l, m, and n are parallel to each other and the value of x is 8.34.
What are parallel lines?Parallel lines are lines that are equidistant from each other and do not meet no matter how far they extend in either direction. Parallel lines form angles when crossed by a transversal and show some significant properties.
Angles that correspond are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that are opposite each other are equal.On the same side of the transversal, a pair of interior angles are supplementary.For the given question, we can see that lines l ║m ║n.
Therefore, (6x - 2)° = 52° [Vertically opposite angles are equal]
6x = 52 - 2
6x = 50
x = 50/6
x = 8.34
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Find the slope of the line shown on the graph to the right.What is the slope of the line? The slop of the line is ___
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The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of initial and final points on the line
x1 and x2 are the x coordinates of initial and final points on the line
From the graph,
when x1 = - 4, y1 = 0
when x2 = 2, y2 = 4
slope = (4 - 0)/(2 - - 4) = 4/(2 + 4) = 4/6
Simplifying 4/6 to its lowest term
slope = 2/3
Completing the square to find the zeros3. a^2+2a-3=0
Answers
Answer:
1 and -3.
Explanation:
Given the quadratic polynomial:
[tex]a^2+2a-3=0[/tex]To use the completing the square method to find the zeros, follow the steps below:
Step 1: Take the constant to the right-hand side.
[tex]a^2+2a=3[/tex]Step 2: Divide the coefficient of a by 2, square it and add it to both sides.
[tex]a^2+2a+(1)^2=3+(1)^2[/tex]Step 3: Write the left-hand side as a perfect square.
[tex](a+1)^2=4[/tex]Step 4: Take the square root of both sides.
[tex]a+1=\pm\sqrt[]{4}[/tex]Step 5: Solve for a.
[tex]\begin{gathered} a=-1\pm\sqrt[]{4} \\ a=-1\pm2 \\ a=-1+2\text{ or }a=-1-2 \\ a=1\text{ or }a=-3 \end{gathered}[/tex]The zeros of the quadratic equation are 1 and -3.
What is a discrete set?Is option d and e and possibly c?
Answers
Discrete sets are sets which members are countable and distinct.
That is, they are separable and can only have a certain value.
For example, the number of players in a rugby team is discrete because they are countable.
Hence, options C, Dare applicable.
Wyatt's eraser box is shaped as a rectangular prism. His erasers are cubes with 1-centimeter sides. The
bottom of the box can hold 14 erasers, and the box is 6 centimeters tall. How many erasers can Wyatt fit
in his box?
Answers
Each eraser has the shape of a cube with a side length of 1 cm.
The eraser box is a rectangular prism (a rectangular box).
We know the bottom of the box can hold 14 erasers. If we lay 14 more erasers on top of it, we would have used 2 cm of the box's height.
We can do it a total of 6 times until we top up the box, thus the total number of erasers that fit the box is 6*14 = 84 erasers
SI unit conversion Could you please help me with exercise number 12 please and explain the process? I copied exercise 11 from the board and trued to solve #13 but not sure if it’s correct
Answers
Given:-
[tex]9468mg=\ldots kg[/tex]To find the required solution.
So we use the formula,
[tex]1\operatorname{kg}=1000000mg[/tex]So now we substitute,
[tex]\frac{9468}{1000000}=0.009468[/tex]So the required solution is 0.009468 kg.
A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
Answers
The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
Explanation:The given functions are:
[tex]\begin{gathered} f(\theta)=2\cos \theta+\sqrt[]{3} \\ g(\theta)=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal when both functions coincide
That is;
[tex]\begin{gathered} f(\theta)=g(\theta) \\ \Rightarrow2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]Solving the equation, we have:
[tex]\begin{gathered} 2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \\ Subtract\sqrt[]{3}\text{ from both sides} \\ 2\cos \theta=1-\sin ^2\theta \end{gathered}[/tex]Note the identity below:
[tex]\begin{gathered} \cos ^2\theta+\sin ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \end{gathered}[/tex]This means
[tex]\begin{gathered} 2\cos \theta=\cos ^2\theta \\ \cos ^2\theta-2\cos \theta=0 \\ \cos \theta(\cos \theta-2)=0 \\ \cos \theta=0 \\ \Rightarrow\theta=\cos ^{-1}(0)=1 \\ \\ OR \\ \cos \theta-2=0 \\ \cos \theta=2 \\ \theta=\cos ^{-1}(2)=0.9994 \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
-3x + 5y = -155x - 2y = -101. Find the solution2. Write an equation to replace the second equation so that the system will have infinitely many solutions.
Answers
Problem
-3x + 5y = -15
5x - 2y = -10
Solution
For this case we can solve x from the first equation and we got:
3x = 5y +15
x= (5y+15)/3
Now we can replace this value into the second equation and we got:
5((5y+15)/3) -2y = -10
25/3y +25 -2y= -10
And solving for y we got:
(25/3 -2)y =-10-25
19/3 y = -35
y= -105/19
And then we can solve for x and we got:
x= (5*(-105/19) +15)/3 = -80/19
Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.
Answers
Answer:
[tex]84.3\text{ cm}^2[/tex]Explanation:
Here, we want to calculate the area of the regular heptagon
Mathematically, we use the formula below:
[tex]A\text{ = a}^2n\text{ tan\lparen}\frac{180}{n})[/tex]where:
a is the length of the apothem which is 5 cm
n is the number of sides of the polygon which is 7 (heptagon is a 7-sides polygon)
Substituting the values, we have it that:
[tex]\begin{gathered} A\text{ = 5}^2\times7\text{ }\times\text{ tan }\frac{180}{7} \\ \\ A\text{ = 84.3 cm}^2 \end{gathered}[/tex]Find the radius of the circle with a circumference of 39 yards. Round your answer to the nearest hundredth of a yard.the radius of the circle is blank yards
Answers
Answer:
6.207
Explanation:
The circumference C of the circle is given by
[tex]C=2\pi r[/tex]where r is the radius.
Now we are given that C = 39 yd; therefore,
[tex]39=2\pi r[/tex]dividing both sides by 2pi gives
[tex]\frac{39}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]r=\frac{39}{2\pi}[/tex][tex]r=6.207yd[/tex]Hence, the radius of the circle is 6.207 yards.
A given circle has an approximate area of 78.5 square units. How long is the circles diameter?
Answers
Remember that
The area of a circle is equal to
[tex]A=\pi\cdot r^2[/tex]we have
A=78.5 unit2
I will assume pi=3.14
substitute in the formula
[tex]\begin{gathered} 78.5=3.14\cdot r^2 \\ r^2=\frac{78.5}{3.14} \\ r=5\text{ units} \end{gathered}[/tex]the diameter is two times the radius
so
D=2(5)=10 units
therefore
The diameter is 10 unitsWhat function best represents the perimeter of the orange boxes? *
Answers
The formula used to calculate the perimeter of a rectangle is given to be:
[tex]P=2l+2h[/tex]FIRST BOX
For the first orange box, we have that:
[tex]\begin{gathered} l=x+x=2x \\ h=2 \end{gathered}[/tex]Note that the box is divided into 2 parts.
Therefore, this perimeter is:
[tex]P_1=2(2x)+2(2)=2(2x)+4[/tex]SECOND BOX
For the second orange box, we have that:
[tex]\begin{gathered} l=x+x+x=3x \\ h=2 \end{gathered}[/tex]Note that the box is divided into 3 parts.
Therefore, the perimeter is:
[tex]P_2=2(3x)+2(2)=2(3x)+4[/tex]Using the associative property of multiplication, we have that:
[tex]P_2=3(2x)+4[/tex]Since x = 5, we have:
[tex]\begin{gathered} P_1=2(10)+4 \\ P_2=3(10)+4 \end{gathered}[/tex]where 2 and 3 are the number of divisions of the boxes.
If we represent the number of divisions with x, we have the perimeter's function to be:
[tex]P=10x+4[/tex]ANSWER
The correct option is the THIRD OPTION.
which inequality best represents that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C
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that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C:
[tex]-3C^{\circ}<1C^{\circ}[/tex]Suppose that y varies jointly with w and x and inversely with z and y = 24 when w = 8, X= 9 and z = 6. Write the equation that models the relationship. Then find y when w = 2, X= 20 and z = 8.
Answers
We would have the following:
[tex]24=\frac{8\cdot9}{6}\cdot2[/tex]From this, we will have the following expression:
[tex]z=2\cdot\frac{w\cdot x}{y}[/tex]Now, we determine the values after replacing the ones given:
[tex]8=2\cdot\frac{2\cdot20}{y}\Rightarrow y=\frac{4\cdot20}{8}\Rightarrow y=10[/tex]The value of y is 10.
in the diagram ,EF and AB are parallel .Line CD is a transversal PartA:Describe the transformation that will take
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The described transformation is a translation and a reflection that is dilation.
By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made.
The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation. A function can be moved in one direction or another by translation, rotated around a point by rotation, reflected in its mirror image by reflection, and scaled by dilation.
The dilation is the transformation that causes the 2-d shape to stretch or contract vertically or horizontally by a fixed amount. The equation y = a.f. yields the vertical stretch (x). The function stretches in relation to the y-axis if a > 1.
Hence we get the required answer.
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Can decimals be constants?
Answers
Constants refer to a number and a decimal is a number expressed in decimal notation, therefore, decimals can be constants.
What is a decimal?A decimal number is the expression of a fraction in terms of the quotient of the fraction, for example, 1/4 in decimal form is 0.25.
The standard form or system for representing numbers that are integers and numbers that are non integers is the decimal number system which is based on the Hindu-Arabic number system.
When numbers (integers and non integers) are expressed as decimals, the numbers are cited as being in decimal notation.
The location of a number in decimal notation is between the ones and tenth place of the number.
A constant is a value in an expression or equation that remains the same in an equation.
A constant is therefore expressed quantitatively as a number.
Therefore, decimals, which are also numbers can be constants.
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convert the following from degrees to radians (use × 180/pi)(-2pi)/7
Answers
Use the conversion 180/pi
[tex]-\frac{2\pi}{7}\cdot\frac{180}{\pi}=-\frac{360}{7}=-51.43[/tex]An investment of R2000 is made at 10 %per year simple interest for 3 years. The amount earned is there invested for 5 years at 16 %simple interest calculator the value of the investment at the end of 8 year
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Explanation
We are asked to calculate the value of the investment at the end of 8 years
For the first part, we will find how much R2000 will yield after 3 years
[tex]\begin{gathered} A=P(1+rt) \\ P=2000 \\ r=10\text{ \% =0.1} \\ t=3 \\ \\ A=2000(1+0.1\times3) \\ A=2000(1+0.3) \\ A=2000(1.3) \\ \\ A=R2600 \end{gathered}[/tex]For the second part, we will have to know how much R2600 will yield after 5 years
[tex]\begin{gathered} P=2600 \\ t=5\text{ years} \\ r=16\text{ \%=0.16} \\ \\ A=2600(1+0.16(5)) \\ A=2600(1+0.8) \\ A=R4680 \\ \end{gathered}[/tex]At the end of the 8 years, the value of the investment will be R4680
What is the component form of resultant of 4b⃗ −2aa = (7 , -5)b = ( -4 , 4)
Answers
1) Since we have this expression, let's do it in parts.
[tex]\begin{gathered} 4\langle-4,4\rangle-2\langle7,-5\rangle \\ x-component=4(-4)-2(7)=-16-14=-30 \\ y-component=4(4)-2(-5)=16+10=26 \\ \end{gathered}[/tex]Note that since each vector has two components x, and y. The resultant will be the vector:
[tex]\langle-30,26\rangle[/tex]33. A coin is tossed and a die with numbers 1-6 is rolled. What is P(head and 3)a. 1/12b. 1/4C.1/3d. 2/334. Two cards are selected from a deck of cards numbered 1 - 10. Once a card isselected, it is replaced. What is P(two even numbers)?a. 1/4b. 2/9c. 1/2d. 135. Which of the following in NOT an example of independent events?a. rolling a die and spinning a spinnerb. tossing a coin two timesc. picking two cards from a deck with replacement of first cardd. selecting two marbles one at a time without replacement36. A club has 25 members, 20 boys and 5 girls. Two members are selected atrandom to serve as president and vice president. What is the probability that bothwill be girls?b. 1/25c. 1/30d. *a. 1/537. One marble is randomly drawn and then replaced from a jar containing twowhite marbles and one black marble. A second marble is drawn. What is theprobability of drawing a white and then a black?b. 2/9c. 3/8a. 1/3d. 1/638. Maria rolls a pair of dice. What is the probability that she obtains a sum that iseither a multiple of 3 OR a multiple of 4?a. 5/9b. 7/12c. 1/36d. 7/3639. Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What isP(A and B)?c. 4/15d. 2/15b. 1/5a. 2/5
Answers
SOLUTION
(33) The question says a coin is tossed and a die with 6 faces is rolled, what is the probability of getting a head and a 3.
Probability is given as
[tex]Probability=\frac{expected\text{ outcome}}{total\text{ outcome }}[/tex]Now, a coin has two faces, a head and a tail. So, total outcome is 2 faces.
We want to get the probability of getting a head. This becomes
[tex]\begin{gathered} Probability\text{ of head = }\frac{expected\text{ outcome}}{total\text{ outcome}}=\frac{1\text{ head}}{2\text{ faces}} \\ =\frac{1}{2} \\ P(head)=\frac{1}{2} \end{gathered}[/tex]So, probability of getting a head is 1/2
A die has 6 faces labelled 1, 2, 3, 4, 5 and 6
Probability of getting a 3 should be
[tex]\begin{gathered} Probability\text{ of getting 3 = }\frac{one\text{ face showing 3}}{6\text{ faces}} \\ that\text{ is }\frac{1}{6} \end{gathered}[/tex]So, probability of getting a 3 is 1/6
Now probability of getting a head and a 3, that is P(head and 3), means we multiply both probabilities, we have
[tex]\begin{gathered} P(head\text{ and 3\rparen = }\frac{1}{2}\times\frac{1}{6} \\ =\frac{1}{12} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{12}[/tex]a smmall rectangular tray measures 16 cm by 18 cm determine the length of the diagonal . round you're answer to the nearest tenth.m
Answers
Given the dimension of the rectangle:
16 cm by 18 cm
We have the image of the rectangle below:
To find the length of the diagonal AC, use pythagorean theorem since ACD form a right triangle.
Thus, we have:
[tex]\begin{gathered} AC^2=AD^2+DC^2 \\ \\ AC=\sqrt[]{AD^2+DC^2} \end{gathered}[/tex]Input values into the formula:
[tex]\begin{gathered} AC=\sqrt[]{18^2+16^2} \\ \\ AC=\sqrt[]{324+256} \\ \\ AC=\sqrt[]{580} \\ \\ AC=24.08\approx24.1\text{ cm} \end{gathered}[/tex]Therefore, the length of the diagonal is 24.1 cm
ANSWER:
24.1 cm
Tina babysits and cuts lawns to earn money. For one week, she babysits for 5 hours. She earns $8.25 per hour babysitting If Tina earns $92 this week, how much does tina earn cutting lawns? 1) $10.152) $16.753) $41.254( $50.75
Answers
Answer:
[tex]\text{ \$50.75}[/tex]Explanation:
Here, we want to calculate how much Tina earns cutting lawns
From the question, she earns $8.25 per hour for 5 hours cutting lawns
What she earned in totality that week would be:
[tex]\text{ 5 }\times\text{ \$8.25 = \$41.25}[/tex]What she earned cutting lawns would be the total earned minus what she earned cutting lawns
Mathematically, we have that as:
[tex]\text{ \$92 - \$41.25 = \$50.75}[/tex]