Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35
A sixth-grade class is growing plants for their
science projects. Each student spent $1.00 for a
package of seeds and $2.50 for a container to
plant the seeds in. There are 30 students in the
class. How much money did the sixth-grade class
spend on seeds and containers in all?
Answer:
5.76
Step-by-step explanation:
Answer:
$105
Step-by-step explanation:
Each student buys one package of seeds and one container
s = Amount of students; p = price of seed package; c = price of container
s*(p+c)=30(1.00+2.50)=30(3.5)$105.
Hope This Helps!
11/10= x+2/5 Please Explain
Answer:
x=7/10
Step-by-step explanation:
2/5=4/10
11/10=x+4/10
11/10-4/10=x
7/10=x
Answer:
x=7/10 or 0.7
Step-by-step explanation:
I turned the fractions into decimals
so
1.1=x+0.4
subtract 0.4 from 1.1 to get 0.7
Turn it into a fraction which is 7/10
Rewrite 4 - 5 using the addictive inverse and display the expression on a number line
Answer:
d. (4) + (-5)
Step-by-step explanation:
We know that 4 is the positive value and 5 is the negative value, therefore if to be able to rewrite in it we will almost make a sum of these values without changing the meaning of each one of the values, therefore:
(+4) + (-5)
Which means that the correct option is the last option, that is, d. (4) + (-5). Furthermore, the representation is correct because the resulting arrow is the one corresponding to -1.
Select the correct answer.
What is the exact solution to the system of equations shown on the graph?
Answer:
Option (B)
Step-by-step explanation:
There are two lines on the graph representing the system of equations.
First line passes through two points (-3, 1) and (-2, 3).
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{3-1}{-2+3}[/tex]
m = 2
Equation of the line passing through (x', y') and slope = m is,
y - y' = m(x - x')
Equation of the line passing through (-3, 1) and slope = 2 will be,
y - 1 = 2(x + 3)
y = 2x + 7 ----------(1)
Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.
Let the equation of this line is,
y = mx + b
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-1}{-1-0}[/tex]
= -3
Here 'b' = 1
Therefore, equation of the line will be,
y = -3x + 1 ---------(2)
From equation (1) and (2),
2x + 7 = -3x + 1
5x = -6
x = [tex]-\frac{6}{5}[/tex]
x = [tex]-1\frac{1}{5}[/tex]
From equation (1),
y = 2x + 7
y = [tex]-\frac{12}{5}+7[/tex]
= [tex]\frac{-12+35}{5}[/tex]
= [tex]\frac{23}{5}[/tex]
= [tex]4\frac{3}{5}[/tex]
Therefore, exact solution of the system of equations is [tex](-1\frac{1}{5},4\frac{3}{5})[/tex].
Option (B) will be the answer.
Answer:
B. (-1 1/5, 4 3/5)
Step-by-step explanation:
Point A is at (-6,6) and point C is at (-6,-2). Find the coordinates of point B on Ac such that AB =3/4AC
Answer:
B(-6, 0)
Step-by-step explanation:
You want to find B such that ...
(B -A) = (3/4)(C -A) . . . . the required distance relation
4(B -A) = 3(C -A) . . . . . . multiply by 4
4B = 3C +A . . . . . . . . . . add 4A, simplify
Now, we can solve for B and substitute the given coordinates:
B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)
The coordinates of point B are (-6, 0).
Answer:
the answer your looking for is (-3,-3)
Step-by-step explanation:
Please answer this in two minutes
Answer:
∠ G ≈ 38.9°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos G = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{GH}{GI}[/tex] = [tex]\frac{7}{9}[/tex] , thus
∠ G = [tex]cos^{-1}[/tex] ([tex]\frac{7}{9}[/tex] ) ≈ 38.9° ( to the nearest tenth )
Which statements are true about the solution of 15 greater-than-or-equal-to 22 + x? Select three options. x greater-than-or-equal-to negative 7 x less-than-or-equal-to negative 7 The graph has a closed circle. –6 is part of the solution. –7 is part of the solution.
Answer:
[tex]x \leq -7[/tex]
The graph has a closed circle.
–7 is part of the solution.
Step-by-step explanation:
Given
[tex]15 \geq 22 + x[/tex]
Required
Select 3 options from the given list of options
[tex]15 \geq 22 + x[/tex]
Subtract 22 from both sides
[tex]15 - 22 \geq 22 - 22+ x[/tex]
[tex]-7 \geq x[/tex]
Swap positions of the expression; Note that the inequality sign will change
[tex]x \leq -7[/tex]
This means x less-than-or-equal-to negative 7
There are two options left to select;
The inequality sign in [tex]x \leq -7[/tex] implies that the graph has a close circle.
Inequality signs such as [tex]\leq[/tex] and [tex]\geq[/tex] signifies a close circle
There is only one option left to select;
Lastly;
Split the expression [tex]x \leq -7[/tex] into two
We have:
[tex]x < -7[/tex] or [tex]x = -7[/tex]
Because [tex]x = 7[/tex],
Then, -7 is also a part of the solution
Answer:
B) x less-than-or-equal-to negative 7
C) The graph has a closed circle.
E) –7 is part of the solution.
Step-by-step explanation:
Im not 100% sure but i am 95% sure they r
Please answer the following questions
Step-by-step explanation:
sorry I can only explain as there are no labels to each diagram
The first diagram is single and can solved using triangular formular given as 1/2 ×base × height
A = 1/2 × 5 × 12
A = 30cm^2..
as for the second one...it consist of 2 diagrams which will be solved separately before adding ...it can simply be done using Pythagoras theorem..
To get the smaller part ...out tita is 45degrees while our adjacent is 4 and opposite is x we are to find x which is the height...
using SOH CAH TOA...
WE HAVE TAN45= opp/adj
Tan45= x/ 4
Tan 45 =1 ...so
1 = x/ 4
and x= 4 ...
so...having our height as 4 and base as 4 ..
Area of smaller triangle become 1/2 × 4 × 4
A = 8cm^2 ...
......SOLVING FOR THE SECOND DIAGRAM ..
WE HAVE the height as ( dotted spot + undotted spot ) = 4 + 4 = 8cm
and our base can be gotten from
Tan45 = opp / adj
1 = 8/x ..
x = 8cm ....so the base is 8 and the height is 8
..
The Area becomes 1/2 × 8×8 = 32cm ...
Total area becomes 32cm + 8cm = 40cm^2
A newspaper article claimed: "The average cost of weekly groceries is $124.50." What
statistical measurement are they most likely claiming?
O A. median
B. mean
C. range
D. mode
The average cost of weekly groceries is $124.50." The statistical measurement are they most likely claiming is Mean
The correct option is (B)
what is Mean?The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:
Mean = Sum of all observations/Number of observations
MedianThe value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.
ModeThe value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.
As per the situation we have given average cost of groceries.
The mean is also the average sum of data divided by total number of data.
Hence, The statistical measurement is Mean.
Learn more about mean here:
https://brainly.com/question/15323584
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A particular geometric sequence has strictly decreasing terms. After the first term, each successive term is calculated by multiplying the previous term by $\frac{m}{7}$. If the first term of the sequence is positive, how many possible integer values are there for $m$?
Answer:
6 possible integers
Step-by-step explanation:
Given
A decreasing geometric sequence
[tex]Ratio = \frac{m}{7}[/tex]
Required
Determine the possible integer values of m
Assume the first term of the sequence to be positive integer x;
The next sequence will be [tex]x * \frac{m}{7}[/tex]
The next will be; [tex]x * (\frac{m}{7})^2[/tex]
The nth term will be [tex]x * (\frac{m}{7})^{n-1}[/tex]
For each of the successive terms to be less than the previous term;
then [tex]\frac{m}{7}[/tex] must be a proper fraction;
This implies that:
[tex]0 < m < 7[/tex]
Where 7 is the denominator
The sets of [tex]0 < m < 7[/tex] is [tex]\{1,2,3,4,5,6\}[/tex] and their are 6 items in this set
Hence, there are 6 possible integer
Solve the following: (1 point) x + 3y = 9 3x − 3y = −13
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(
−
1
,
10
3
)
Equation Form:
x
=
−
1
,
y
=
10
3
Tap to view steps...
image of graph
Tap to hide graph...
Which set of ratios could be used to determine if one triangle is a dilation of the other? A triangle has side lengths of 4, 6, 8.5. A second triangle has side lengths of 6, 9, 12.5. StartFraction 4 Over 6 EndFraction = StartFraction 6 Over 9 EndFraction = StartFraction 8.5 Over 12.5 EndFraction StartFraction 6 Over 4 EndFraction = StartFraction 6 Over 9 EndFraction = StartFraction 8.5 Over 12.5 EndFraction StartFraction 4 Over 6 EndFraction = StartFraction 9 Over 6 EndFraction = StartFraction 8.5 Over 12.5 EndFraction StartFraction 4 Over 6 EndFraction = StartFraction 8.5 Over 9 EndFraction = StartFraction 6 Over 12.5 EndFraction
Answer:
[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]
Step-by-step explanation:
Given
Let the two triangles be A and B
Sides of A: 4, 6 and 8.5
Sides of B: 6, 9 and 12.5
Required
Which set of ratio determines the dilation
To determine the dilation of a triangle over another;
We simply divide the side of a triangle by a similar side on the other triangle;
From the given parameters,
A ------------------B
4 is similar to 6
6 is similar to 9
8.5 is similar to 12.5
Ratio of dilation is as follows;
[tex]Dilation = \frac{4}{6}[/tex]
[tex]Dilation = \frac{6}{9}[/tex]
[tex]Dilation = \frac{8.5}{12.5}[/tex]
Combining the above ratios;
[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]
From the list of given options, the correct option is A,
Answer:
a
Step-by-step explanation:
1) In rectangle ABCD, AE is perpendicular on diagonal BD, BE=3DE and AC∩BD={O}.
1. DE/EO=?
2. If BD=8√2 inches, find out the lenght of AE
3. Calculate the measure of angle AOD.
2) In rectangle MNPQ, MA⊥NQ, A∈NQ, MA∩PQ={B}. If AN measures 12 inches, AQ=27 inches, calculate the lenght of MA and MB.
Please help me with these. Or at least with one of them.
Answer:
to be honest I'm not sure how to do
A group conducted a poll of 2022
likely voters just prior to an election. The results of the survey indicated that candidate A would receive 49
%
of the popular vote and candidate B would receive 46
%
of the popular vote. The margin of error was reported to be 5
%.
The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means.
Answer:
Step-by-step explanation:
number of likely voters = 2022
candidate A = 49%
candidate B = 46%
margin of error = 5%
using the concept of a confidence interval to explain
from the result of the poll conducted candidate A scored 49% of the votes while Candidate B scored 46% therefore the difference between the two voters is 3%.
also the margin of error is 5% which is higher than the 3% difference between the candidates. this margin error means that the 5% can vote for either candidate A or candidate B .which makes the results TOO CLOSE TO CALL
The quadrilateral shown is a (blank) x= (blank)
Answer:
The quadrilateral shown is a kite, because it has two non-congruent pairs of congruent sides
x = 3
Step-by-step explanation:
The vertex angles in a kite are bisected by the diagonals. Thus, 11x = 9x + 6.
11x=9x+6
2x=6
x=3
Hope it helps <3
Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. How many square meters could he make with 4 cloaks of fabric
Answer:
14 square meters of fabricStep-by-step explanation:
[tex]21\: square\:meters = 6 \:wizard \:cloak\\x\:square\:meters\:\:=4 \:wizard\:cloaks\\\\Cross\:Multiply\\6x = 84\\\frac{6x}{6} =\frac{84}{6} \\\\x = 14 \:square\:meters[/tex]
Answer:
14.0 square meters
Step-by-step explanation:
The sketch shows a triangle and its
exterior angles. Find the measure of
angle IAC.
Show all your calculations. Justify your
answer.
MDHA = 128"
MZHCA = 46°
Answer:
∠ IAC = 98°
Step-by-step explanation:
The sum of the exterior angle = 360°
∠ HCB = 180° - 46° = 134° ( adjacent angles )
Thus
∠ IAC + 128° + 134° = 360°, that is
∠ IAC + 262° = 360° ( subtract 262° from both sides )
∠ IAC = 98°
Answer:
<IAC=°98
Step-by-step explanation:
<DHA + CHA = 180 SUPPLEMENTARY ANGLE
128 +CHA=180
<CHA=52
<CHA + <HAC+<ACH=180 b/c it is triangle
46 +52+HAC= 180
<HAC= 180-98
<HAC= 82
<HAC + <IAC= 180. Supplementary angle
82+<IAC=180
<IAC=180-82
<IAC=98
Three metal cubes with edges 6 cm, 8 cm and 12 cm respectively are melted down and made into a single cube. Find the length of one edge of the resulting cube.
Answer: 13.5
Step-by-step explanation:
Find the total volume of the melted cubes:
V₁ = 6³ V₂ = 8³ V₃ = 12³
= 216 = 512 = 1728
So the new cube will have a volume of 216 + 512 + 1728 = 2456
Volume of the cube = side³
2456 = s³
[tex]\sqrt[3]{2456} = s[/tex]
13.5 = s
Algebra 2 help needed
Answer:
D
Step-by-step explanation:
From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.
the legnth of rectangular sheet decreases by 34.5 cm its width decreases proportionally that is by the same percentage. if the sheets original width was half of the legnth and the new (smaller) area was 1.2 m^2 what was original sheet's width
Answer:
The original width was 94.71 cm
Step-by-step explanation:
Given:
new smaller area = 1.2m^2
Decrease in length of the rectangular sheet = 34.5cm
Therefore:
1. the final width of the sheet is given as
2X^2 = 1.2 m^2
X^2 - 0.6 m^2
X^2 = 10000 * 0.6 cm
X = 77.46 cm (this is the width)
2. The length of the sheet
= 2 * 77.46
= 154.92 cm.
3. Initial length of the sheet
= 154.92 + 34.5
= 189.42 cm.
4. Initial width of the sheet ( original ).
= 189.42 / 2
= 94.71 cm.
5. Initial area of the sheet
= 94.71 * 189.92
= 17939.9 cm^2
New area of the sheet
= 79.46 * 154.92
= 12000.1 cm^2
Difference between the initial and new area
= 17939.9 - 12000.1
= 5939.86 cm^2
Percentage of area decrease
= 5939.86 ' 17939.9
= 33.1%
The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day. Which statements are true based on the model?
Answer:
Options (1), (2) and (5)
Step-by-step explanation:
Outcomes from the quadratic function given in the graph,
1). Negative y-intercept of the graph represents the loss to the store when x = 0 Or the loss when no clerk is working.
2). Peak of the parabola represents a point (vertex) with x-coordinate as number of clerks working = 4 and y-coordinate as maximum profit earned by the store = $400,000
3). x-intercept of the graph shows the number of clerks working at store when profit earned by the store is zero.
Graph reveals that the store is in loss when number of clerks is zero and 8.
Summarizing these outcomes from the graph,
Options (1), (2), (5) are the correct options.
The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.
Which statements are true based on the model?
Where is the function decreasing?
Answer:
the function is decreasing at the domain values: (-∞,1)
Step-by-step explanation:
the function is decreasing in the domain values from -∞ until 1, the lowest point with no increase or decrease:
which in interval notation can be written as: (-∞,1)
I hope this helps, but if I didn't answer the question or answered wrongly I will try again.
Please help WILL GET REPORTED IF ANSWERS NONSENSE FOR POINTS I am really struggling and need help It is a lot of points so try answering as much
Answer:
301.59
Step-by-step explanation:
your answer was almost right you just forgot to multiply by 9
A rectangular solid has edges whose lengths are in the ratio 1:2:3. If the volume of the solid is 864 cubic units, what are the lengths of the solid's edges?
Answer: 5.24 units, 10.48 units , 15.72 units
Step-by-step explanation:
Volume of a rectangular solid is given by :-
V = lwh, where l = length , w= width and h = height
Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.
Let lengths of the rectangular solid x , 2 x, 3x.
volume of the solid is 864 cubic units
Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]
[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]
Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units
= 5.24 units, 10.48 units , 15.72 units
solve the equation by using substitution method X + 2 Y equal to 8 equation first 2 x minus 2 equal to 10 equation second
Answer:
(6, 1)
Step-by-step explanation:
x + 2y = 8
1. subtract 2y to get x alone -- x = -2y + 8
2. insert (-2y + 8) as x
2x - 2 = 10
2(-2y + 8) -2 = 10
3. distribute the 2
-4y + 16 - 2 = 10
4. combine like terms
-4y + 14 = 10
5. subtract 14 from both sides
-4y = -4
6. divide by -4
y = 1
7. plug y into any of the two original equations
x + 2(1) = 8
8. simplify
x + 2 = 8
x = 6
9. check answer with second equation
2(6) - 2 = 10
12 - 2 = 10
Find the slope of the line that contains (6, 2) and (6,-3).
Find the slope of the line through the points (-4,-7) and (4, 3).
Answer:
A. Undefined slope (no slope)
B. [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
A slope is rise over run.
The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.
However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.
Hope this helped!
Which expressions are equivalent to -56z+28 A 1/2*(-28z+14) B (-1.4z+0.7)\* 40 C (14-7z)*(-4) D (8z-4)*(-7) E-2(-28z-14)
Answer:
D (8z-4)*(-7)
Step-by-step explanation:
Given:
-56z+28
D (8z-4)*(-7)
-56z+28
Therefore, option D is the equivalent expression
Finding the equivalent expression by solving each option and eliminating the wrong option
A 1/2*(-28z+14)
=-28z+14/2
=-14z+7
B (-1.4z+0.7) /* 40
Two signs ( division and multiplication)
Using multiplication,we have
-56z+28
Using division, we have
0.035z + 0.0175
C (14-7z)*(-4)
-56+28z
D (8z-4)*(-7)
-56z+28
E -2(-28z-14)
56z+28
Answer:
B and D
trust me
Una compañía sabe que si produce "x" unidades mensuales su utilidad "u" se podría calcular con la expresión: u(x)=-0.04x^2+44x-4000 donde "u" se expresa en dólares. Determine la razón del cambio promedio de la utilidad cuando el nivel de producción cambia de 600 a 620 unidades mensuales. Recuerde que la pendiente de la recta secante a la gráfica de la función representa a la razón de cambio promedio.
Answer:
The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.
Step-by-step explanation:
The question is:
A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.
Solution:
The expression for the utility is:
[tex]u (x) = - 0.04x ^ {2} + 44x-4000[/tex]
It is provided that the slope of the secant line to the graph of the function represents the average rate of change.
Then the ratio of the average change in profit when the level of production changes is:
[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]
Compute the values of u (x₁) and u (x₂) as follows:
x₁ = 600
[tex]u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000[/tex]
[tex]= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000[/tex]
x₂ = 620
[tex]u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000[/tex]
[tex]= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904[/tex]
Compute the average rate of change as follows:
[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]
[tex]=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5[/tex]
Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.
plssssssss helppp 3x – 5 = 1
Answer:
x = 2
Step-by-step explanation:
Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:
3x – 5 + 5 = 1 + 5
Simplify: 3x=6
Divide each side by 3 to isolate and solve for x:
3x/3=6/3
Simplify: x=2
Please answer it now in two minutes
Answer:3.2 ft
Step-by-step explanation:
sin 32°=[tex]\frac{yz}{6}[/tex]
cross multiply
sin 32° x 6=yz
0.5299 x 6 =yz
yz=3.1795
≅3.2ft