While at college orientation, Kate is buying some cans of juice and some cans of soda for the dorm. The juice is $0.60 per can while the soda is $0.75. Kate has $24 of dorm funds all to be spent. What is an equation that represents all the different combinations of juice and soda Kate can buy for $24 and how many different combinations of drinks are possible?
From the question the following can be derived:
(a)
Let x cans of juice and y cans of soda be purchased for the dorm. Then the cost of the juice and soda is 0.60x + 0.75y. The equation of all the combinations of juice and soda is 0.60x + 0.75y = 24.
(b)
The cost of exactly 24 cans of juice is $24 * 0.60 = $14.40. After this purchase, the remaining sum of money available is $24 - $14.40 = $9.60. This will suffice to buy 12 cans of soda, leaving a balance of $0.80. Thus. the entire money cannot be spent if exactly 24 cans of juice are purchased.
(c)
Below is a graph of the line 0.6x + 0.75y = 24 or 4x + 5y = 160 is plotted. All possible cimbinations of juice and soda will lie on this line. The x-intercept is 40 and the y-intercept is 32. Since neither of x and y can be negative, hence the lower and upper bounds for x are 0 and 40 and the lower ad upper bounds for y are 0 and 32. Also , x has to be multiple of 5 and y has to be a multiple of 4. As may be observed from the graph, only 9 combinations are possible which are (x, y):
(0, 32), (5, 28), (10, 24), (15, 20), (20, 16), (25, 12), (30, 8), (35, 4), (40, 0).
Graph:
Can you evaluate 3 + (a + 4)(8- b ) when a= 5 and b=6
The expression to evaluate is:
[tex]3+a+4\mleft(8-b\mright)[/tex]When
a = 5 and b = 6
We simply plug in the values of 5 and 6, into a and b respectivly. And do algebra to get our answer. The process is shown below:
[tex]\begin{gathered} 3+a+4\mleft(8-b\mright) \\ 3+5+4\mleft(8-6\mright) \\ 3+5+4(2) \\ 3+5+8 \\ 16 \end{gathered}[/tex]The answer is 16.
Franklin is drawing a model of a rectangular swimming pool. He marks two points, A and B, on the coordinate plane and connects them to represent one side of the pool. Points C and D are reflections of B and A, respectively, across the x- axis. Each unit in the coordinate plane represents 1 meter. Draw a rectangle in the coordinate plane yo model the swimming pool. What is the area of the swimming pool?
Area = base x height
A = 8 x 6 = 48 m²
a relationship between decimal, fraction, or 3 Three students wrote percentage. Maggie wrote 75% = Bieber wrote 0.05 = 50% Lee Yung wrote == 0.375 Whích students wrote a correct equation? A. All the above B. None of the above C. Beiber and Lee Yung only D. Lee Yung only 8
To change decimal or fraction to percent multiply them by 100
Example: 1/4 x 100% = 25%, 0.2 x 100% = 20%
Let us check the answer of the 3 students
Maggie wrote 75% = 3/5
Since
[tex]\frac{3}{5}\times100=\frac{300}{5}=60[/tex]Then 3/5 = 60%, not 75%
Maggie is wrong
Bieber wrote 0.05 = 50%
Let us check
0.05 x 100% = 5%, not 50%
Bieber is wrong
Yung wrote 3/8 = 0.375
Let us check
[tex]\begin{gathered} \frac{3}{8}\times100=\frac{300}{8}=\frac{\frac{300}{2}}{\frac{8}{2}}=\frac{150}{4} \\ \frac{150}{4}=\frac{\frac{150}{2}}{\frac{4}{2}}=\frac{75}{2}=37.5 \end{gathered}[/tex]Since 0.375 x 100% = 37.5%
Yung is right
The answer is Lee Yung only
The answer is D
I inserted a picture of the question Please don’t ask tons of questions. & please state whether it’s a b c or d
As given by the question
There are given that the graph of the triangle.
Now,
According to the properties,
If the point (x, y) or (-x, y) rotated about the origin by the angle of 360 degrees.
That means,
There is no difference between rotating 360 degrees clockwise or anti-clockwise around the origin.
Then,
From the vertices of the triangle ABC is:
[tex]\text{A is (-6, 3), B is (-5, 7) and C is (-4, 3).}[/tex]Since the triangle map onto itself
[tex]\begin{gathered} A=A^{\prime} \\ B=B^{\prime} \\ C=C^{\prime} \end{gathered}[/tex]So, the triangle is rotated 360 degrees about the origin
Hence, the correct option is D.
Find an equation of the line.Write the equation in the standard form.Through (8,4); parallel to 7x-y= 2.
Answer:
7x-y=53
Explanation:
Given the line
[tex]7x-y=2[/tex]Making y the subject of the equation, we have:
y = 7x-2
Therefore, the slope of the line, m=7
• If two lines are parallel, their slopes are equal.
Therefore, the slope of the parallel line = 7
The equation of the parallel line through (8,4) will then be:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=7(x-8) \\ y-4=7x-57 \\ 7x-y=-4+57 \\ 7x-y=53 \end{gathered}[/tex]Jake and Joshua have new jobs selling gift cards at a local convenience store at the cash register, but their pay is different. Jake earns a foundational wage of $6 per hour, as well as $8 for each gift card sold. Joshua gets $4 for each gift card sold and earns a foundational wage of $6 per hour. If they each sell a certain number of gift cards in one hour, they will end up earning the same amount of pay. How many gift cards would that make up to?Write a system of equations, graph them, and type the solution.
Let x be the number of cards Jake and Joshua sell within one hour. Therefore, their earnings are given by the following expressions,
[tex]\begin{gathered} Ja=6+8x \\ Jo=6+4x \end{gathered}[/tex]Then, set Ja=Jo (both earn the same amount),
[tex]\begin{gathered} Ja=Jo \\ \Rightarrow6+8x=6+4x \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow8x=4x \\ \Rightarrow4x=0 \\ \Rightarrow x=0 \end{gathered}[/tex]Then, they will earn the same within one hour only if both sell zero cards within the hour.
Graphing the system of equations,
As one can see, the intersection point is (0,6), which stands for 0 cards and $6
In the diagram, m/ACB = 55°.
E
What is mZECD?
90°
O 55°
180°
D
O 125°
C
B
80
Answer:
55°
Step-by-step explanation:
Angle ACB and angle ECD are alternate exterior angles and alternate angles have same angle measurements:
If angle ACB = 55°
then angle ECD is also = 55°
calculated the slope (5,-14),(-14,0) help
the slope can be calculated using the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(5,-14)=(x1,y1)
(-14,0)=(x2,y2)
then we substitute the values
[tex]m=\frac{0+14}{-14-5}=\frac{14}{-19}=-\frac{14}{19}[/tex]the answer is -14/19
Brody received a $13.25 tip on a meal that cost $109. What percent of the meal costwas the tip?Round answer to the nearest whole percent.
Explanation
To find the percentage of the tip we will use the formula below.
[tex]\text{\%Tip}=\frac{\text{Tip(\$)}}{Cost\text{ of meal}}\times100[/tex][tex]\begin{gathered} \text{ \%Tip =}\frac{\text{13.25}}{109}\times100 \\ =13\text{\%} \end{gathered}[/tex]Answer: 13%
Select the correct answerVector u has its initial point at (15, 22) and its terminal point at (5, 4). Vector v points in a direction opposite that of u, and its magnitude is twicethe magnitude of u. What is the component form of v?OA V=(-20, 36)OB. V=(-20, 52)Ocv = (20, 36)ODV= (20, 52)
Answer
Option C is correct.
v = (20, 36)
Explanation
If the initial and terminal points of a vector are given, the vector itself is obtained, per coordinate, by doing a terminal point coordinate minus initial point coordinate.
u = [(5 - 15), (4 - 22)]
u = (-10, -18)
Then, we are told that vector v points in the opposite direction as that of vector u and its magnitude is twice that of vector u too.
In mathematical terms,
v = -2u
v = -2 (-10, -18)
v = (20, 36)
Hope this Helps!!!
Graph the line y = -4 on the graph below.
we have the equation
y=-4
This is a horizontal line (parallel to the x-axis) that passes through the point (0,-4)
see the graph below to better understand the problem
The bacteria in a dish triples every hour. At the start of the experiment therewere 400 bacteria in the dish. When the students checked again there were32,400 bacteria. How much time had passed? (Write your equation and solve forx; y= a • bx).
Given
The bacteria in a dish triples every hour. At the start of the experiment there
were 400 bacteria in the dish. When the students checked again there were
32,400 bacteria. How much time had passed? (Write your equation and solve for
x; y= a • bx)
Solution
([20 + 10.4^2 - 116,870) / (20/ 1/3 x 15 - 10.4/ (116,870/6808))] ^-1
Answer:
[tex]8\frac{875730264}{8491541359}[/tex]Explanation:
Given the values of the variables below:
• D = 116,870
,• E=1/3
,• L =15
,• M = 20
,• O = 10.4
,• Y = 6,808
We are required to evaluate:
[tex]\begin{gathered} \lbrack(M+O^2-D\div Y)\div(M\div E\cdot L-O\div(D\div Y))\rbrack^{-1} \\ =\mleft(\frac{(M+O^2-D\div Y)}{(M\div E\cdot L-O\div(D\div Y))}\mright)^{-1} \end{gathered}[/tex]Substitute the given values:
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div(116,870\div6,808)}\mright)^{-1}[/tex]We simplify using the order of operations PEMDAS.
First, evaluate the parentheses in the denominator.
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, evaluate the exponent(E): 10.4²
[tex]=\mleft(\frac{20+108.16-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, we take multiplication and division together:
[tex]\begin{gathered} =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{20\times3\times15-10.4\times\frac{6808}{116,870}}\mright)^{-1} \\ =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{900-\frac{13616}{22475}}\mright)^{-1} \end{gathered}[/tex]Finally, take addition and subtraction and then simplify.
[tex]\begin{gathered} =\mleft(\frac{9445541}{85100}\div\frac{20213884}{22475}\mright)^{-1} \\ =(\frac{9445541}{85100}\times\frac{22475}{20213884})^{-1} \\ =(\frac{8491541359}{68808061136})^{-1} \\ =1\div\frac{8491541359}{68808061136}=1\times\frac{68808061136}{8491541359} \\ \\ =\frac{68808061136}{8491541359} \\ =8\frac{875730264}{8491541359} \end{gathered}[/tex]The result of the evaluation is:
[tex]8\frac{875730264}{8491541359}[/tex]1 mile= 1,760 yards.1 kilometer= 1,000 metersIf Jose walked 2 miles this morning, about how many kilometers did he walk?
1 mile= 1.609 km
Then,
2*1.609=3.218 km
He walked 3.218 kilometers
Could you please help with
The angle measures
m WXZ = 180 - 90 - 24
mWXZ = 66°
In the figure shown, what is mzA? Explain.57°; AABC is an isosceles triangle with base angles A and C. m2A = mc.B. 66; AABC is an isosceles triangle with base angles B and C. m2B = m_C = 57, and m2A + m2B + m2 = 180.C. 57. AABC is an equilateral triangle.
Since ABC is an isosceles triangle with sides AB=AC, then the angle ABC is the same as ACB, an it's equal to 57º.
Since all three internal angles should add up to 180º, then the angle BAC should have a measure of 180-2(57)=66º.
A table is in the shape of a regularhexagon. The perimeter of the table is 12 ftfeet. What is the length of each side ofthe tableA 1 ftB 2 ftC 3 ftD 4 ft
Solution:
Given the shape of a hexagon;
The perimeter, P, of a hexagon is;
[tex]\begin{gathered} P=6s \\ \\ \text{ Where }s=side\text{ length} \end{gathered}[/tex]Given;
[tex]\begin{gathered} P=12ft \\ \\ s=\frac{12}{6}ft \\ \\ s=2ft \end{gathered}[/tex]CORRECT OPTION: B
QuestionGiven that cot(0)- 1 and 0 is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.Provide your answer below:sin (O)=
Given:
The trigonometric ratio is given as,
[tex]\cot \theta=-\frac{1}{2}[/tex]The value of θ lies in the second quadrant.
The objective is to find the value of sinθ.
Explanation:
The formula of cotθ is,
[tex]\cot \theta=\frac{\text{adjacent}}{\text{opposite}}=-\frac{1}{2}[/tex]Since, the value of θ lies in second quadrant, the triangle formed for cotθ will be,
Then, the value of x can be calculated as,
[tex]\begin{gathered} x^2=2^2+(-1)^2 \\ x=\sqrt[]{4+1} \\ x=\sqrt[]{5} \end{gathered}[/tex]To find the value of sinθ:
The value of sinθ can be calculated as,
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=\frac{2}{\sqrt[]{5}} \\ \sin \theta=\frac{2}{\sqrt[]{5}}\times\frac{\sqrt[]{5}}{\sqrt[]{5}} \\ \sin \theta=\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]Hence, the value of sinθ is (2√5)/5.
Please Help!!
Karen was computing the volume of a rectangular prism where v=lwh. In her case w=h. After she multiplied l and w she realized she made w 1/3 larger than it should have been. Since w=h, she lowered the third number by 1/3 of itself and continued to multiply to get the final answer. Betty, who did the same problem with the correct numbers, showed that Karen was off by 12 cubic yards. The correct volume of the prism is __ cu. yds.
The correct volume of the rectangular prism as calculated by Betty is 108 cubic yards
What is a rectangular prism?A rectangular prism is cuboid and an hexahedron that has 6 faces.
The formula for finding the volume of the rectangular prism is V = l•w•h
Where;
l = Length
w = Width
h = Height
The measurement of the prism, for which Karen is calculating the volume gives;
w = h
The amount larger Karen found that she made the width, which gives;
Width of the cube Karen used = (1 + 1/3) × w
Therefore;
h = (1 + 1/3) × w
The volume becomes;
V' = l × (1 + 1/3) × w × (1 - 1/3) × w = l•w²•(1²-1/3²)
V' = l•w²•(8/9)
The amount by which the volume increased, dV = 12 yd³
Which gives;
l•w²•(8/9) = l•w•h - 12 = l•w² - 12
l•w²•(8/9) - l•w² + 12 = 0
l•w²•(8/9) - l•w² + 12 = 0
l•w²/9 = 12
V = l•w² = 12 × 9 = 108
The correct volume of the prism is 108 cubic yards
Learn more about finding the volume of solids here:
https://brainly.com/question/20284914
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Pats normal pulse rate is 80 beats minute. How many times does it beat in 3/4 of a minute?
The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given,
Pat's normal pulse rate is 80 beats per minute.
So, 80 beats → 1 minute
Multiply both sides by 3/4
80 × 3/4 beats → 1 × 3/4 minute
(3/4) minute → 60 beats.
Hence "The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times".
For more information about ratios and proportions,
brainly.com/question/26974513
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Calculate the slope (2,-5) and (4,3)
Answer:
Slope = 4
Step-by-step explanation:
The slope of a line can be calculated using the following formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
From the question can put the points as:
(2, -5) as (x1, y1)
and
(4, 3) as (x2, y2)
Therefore, we can put in the values into the formula to solve for the slope.
[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]
Indicate the transformation that has occurred.2.A. (x,y)-->(-x+3.y-5) C. (x,y) --> (-x,y-5)B. (x,y) --> (x +3,y-5) D. (x,y) --> (x-1,-y)
So we have a transformation that maps a triangle into another one. This is made by transforming the points X, Y and Z into X', Y' and Z'. In order to find out which of the four options is the correct one we must verify that points X, Y and Z actually transform into X', Y' and Z'.
We have:
[tex]X=(2,5)\rightarrow X^{\prime}=(1,0)[/tex]Let's see which of the four transformations do this. So for A:
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x+3,y-5)=(-2+3,5-5) \\ X^{\prime}=(1,0) \end{gathered}[/tex]So transformation A is a possible answer, let's see the rest.
For C:
[tex]\begin{gathered} (x,y)\rightarrow(-x,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x,y-5)=(-2,5-5) \\ X^{\prime}=(-2,0)\ne(1,0) \end{gathered}[/tex]So the X' that we calculate with transformation C is different that the one we are looking for so we discard this option.
For option B we have:
[tex]\begin{gathered} (x,y)\rightarrow(x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x+3,y-5)=(2+3,5-5)=(5,0) \\ X^{\prime}=(5,0)\ne(1,0) \end{gathered}[/tex]Like what happened with C, transformation B is discarded.
Let's see what happens with D:
[tex]\begin{gathered} (x,y)\rightarrow(x-1,-y) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x-1,-y)=(2-1,-5)=(1,-5) \\ X^{\prime}=(1,-5)=(1,0) \end{gathered}[/tex]So D is also discarded. This would mean that A is the correct option but just in case, let's check if it tansform points Y=(0,2) and Z=(3,1) into Y'=(3,-3) and Z'=(0,-4):
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ \text{If} \\ Y=\mleft(0,2\mright) \\ \text{Then} \\ Y^{\prime}=(-0+3,2-5)=(3,-3) \\ \text{If} \\ Z=\mleft(3,1\mright) \\ \text{Then} \\ Z^{\prime}=(-3+3,1-5)=(0,-4) \end{gathered}[/tex]So Y' and Z' are (3,-3) and (0,-4) which definetely means that option A is the correct one.
A production applies several layers of a clear acrylic coat to outdoor furniture to help protect it from the weather. If each protective coat is 2/27 inch thick, how many applications will be needed to build up 2/3 inch of clear finish.
We know that
• Each protective coat is 2/27 inches thick.
,• We need to fill 2/3 inches of this protective coat.
To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression
[tex]\frac{2}{27}x=\frac{2}{3}[/tex]We solve for x
[tex]x=\frac{2\cdot27}{3\cdot2}=\frac{27}{3}=9[/tex]Therefore, we need 9 applications in total.Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
Answer:
A. 83 1/3 miles
B. Less than 9/10 of the way there
Step-by-step explanation:
A.
2/3 of the way. "of" means to multiply, so multiply 2/3 and 125.
[tex]\frac{2}{3}[/tex] × [tex]\frac{125}{1}[/tex] = [tex]\frac{250}{3}[/tex]
Simplify by dividing 250 and 3.
250 ÷ 3
[tex]83 \frac{1}{3}[/tex] miles
B.
Multiply 125 by 9/10 then compare the answer to 110 to see if she is more or less than 110 miles.
[tex]\frac{125}{1}[/tex] × [tex]\frac{9}{10}[/tex] [tex]= \frac{1125}{10}[/tex]
Divide 1125 by 10
1125 ÷ 10 = 112.5
Since 9/10 of the distance is 112.5 miles, 110 miles is less than 9/10 of the way there.
Shandar rents a pickup truck for her house move. She has to pay $96 for the first day, $88 for each additional day she keeps the truck, and 45 cents for each mile she drives. She will also be able to use a $25 coupon. Write an expression that represents the total cost when Shandar keeps the truck for h days and travels a total of p miles.Simplify the expression completely.List the terms in your expression.For each term, identify the coefficient and variable.
96 first day
88 for each additional day (h)
0.45 for each mile driven (p)
$25 coupon
Expression
Total cost = 96 + 88h + 0.45p - 25
Simplify:
Combine like terms:
TC = 96 - 25 + 88h + 0.45p
TC = 71 + 88h + 0.45p
Terms:
71 = constant
88h = coefficient 88 , variable h
0.45p= coeficcient 0.45 , variable p
The test results for 4 students are 96 83 78 and 83. If one more student's test score of 87 is added, what would increase?A. median B. meanC. modeD. range
Mean will increase because 87 is greater than 83 and 78, then the eman will be greater
So I joined a ged class and this is apparently a “high school level” math problem, maybe for people in advanced classes but not regular. Anyway, I need help with solving this. Also the greater than sign with the problem that I’m doing has like an underline under it, which I think means greater than or equal to 3x + 9 > - x + 19
Given the inequality:
[tex]3x+9\ge-x+19[/tex]Solve for x:
[tex]\begin{gathered} 3x+x\ge19-9 \\ 4x\ge10 \\ x\ge\frac{10}{4} \\ \\ x\ge\frac{5}{2} \end{gathered}[/tex]so, the answer will be:
[tex]\begin{gathered} x\ge\frac{5}{2} \\ x\in\lbrack\frac{2}{5},\infty) \end{gathered}[/tex]the question is y=4m=2x=3solve for b
y=mx+b
replacing y=4, m=2, x=3 in the equation:
4=2(3)+b
then
b=4-2(3)=4-6=-2b=-2Which systems of inequalities represents the number of apartments to be built
Given that:
- The office building contains 96,000 square feet of space.
- There will be at most 15 one-bedroom units with an area of 800 square feet. The rent of each unit will be $650.
- The remaining units have 1200 square feet of space.
- The remaining units will have two bedrooms. The rent for each unit will be $900.
Let be "x" the number of one-bedroom apartments and "y" the number of two-bedroom apartments.
• The words "at most 15 one-bedroom units" indicates that the number of these apartments will be less than or equal to 15 units:
[tex]x\leq15[/tex]• You know that the remaining units are two-bedroom apartments. And the number of them is greater than or equal to zero. Then, you can set up the second inequality to represent this:
[tex]y\ge0[/tex]• You know the area of each one-bedroom apartment, the area of each two-bedroom apartment, and the total area that the office building contains. The sum of the areas of the apartments must be less than or equal to the total area of the office building.
Then, the inequality that represents this is:
[tex]800x+1200y\leq96,000[/tex]• Therefore, you can set up this System of Inequalities to represent that situation:
[tex]\begin{gathered} \begin{cases}x\leq15 \\ \\ y\ge0 \\ \\ 800x+1200y\leq96,000 \\ \end{cases} \\ \end{gathered}[/tex]Hence, the answer is: Last option.