Answers
In order to determine the weighs of the boxes, name x as the larger box and y as the smaller one.
Then, based on the given situation, you can write the following equations:
3x + 2y = 86
8x + 4y = 209
Solve the previous system of equations as follow:
Multiply the first equation by -2 and add the result to the second equation:
(3x + 2y = 86)(-2)
-6x - 4y = -172
8x + 4y = 209
-6x - 4y = -172
2x = 37
Solve the previous equation for x by dividing by 2 both sides:
x = 37/2
x = 18.5
Next, replace the previous value of x into any of the equations of the system, for instance, into the first equation, and solve for y:
3x + 2y = 86
3(18.5) + 2y = 86
55.5 + 2y = 86
2y = 86 - 55.5
2y = 30.5
y = 30.5/2
y = 15.25
Hence, the weighs of the boxes are:
larger box = 18.5 kg
smaller box = 15.25 kg
Related Questions
A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which therewere 2153 class attendees. The data is summarized in the table below.Class Type and Member Status of ClassAttendeesClass TypeBarreBoot CampBoxingSpinningYogaMember207230291233239Non-Member196185180176216What is the probability that an attendee does not attend a barre class? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The total number associated to barre class is 207 + 196 = 403
Therefore, the probability that a attendee does not attend a barre class is given by 403/2153 = 0.1872
I only need the answer
THANK YOU!!
Answers
Formula for the trigonometry is y = b sin ( πx/2 - π/2) + 4
y = A sin( ωx + δ) + b
period: t = 4
ω = 2π/t = 2π/4 = π/2
A = 10 -(-2)/ 2
= 6
b = (10-2)/2
= 4
y = b sin (πx/2 + δ) + 4
x = 0, y = bsinδ + 4 = -2
sinδ = -1 => δ = -π/2
y = b sin( πx/2 - π/2) + 4
Therefore the formula for the trigonometry function is y = b sin(πx/2 - π/2) + 4.
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Charlotte has 41 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 204 square meters. List each set of possible dimensions (length and width) of the field.
Answers
Answer:
L x W = 8.5 x 24 or 12 x 17
Step-by-step explanation:
x (41 -2x) =204
-2x^2 + 41x -204 = 0 Use Quadratic Formula to find x = 8.5 or 12
(x-8.5)(x-12) = 0
two sides = 8.5 and river/third side = 24
or two sides 12 and river/thirdside = 17
Convert. 260 milliliters to centiliters.
Answers
Answer:
26 centilitres.
Explanation:
First, we start by recalling the standard conversion between millilitres and centilitres.
[tex]10\text{ milliliter = 1 centileter}[/tex]Let 260 milliliters = x centiliters
We express it as a ratio:
[tex]\frac{10\text{ }milliliters}{1\text{ centiliter}}=\frac{260milliliters}{x\text{ centiliters}}[/tex]Cross multiply to solve for x:
[tex]\begin{gathered} 10x=260\times1 \\ x=\frac{260}{10} \\ x=26\text{ centiliters} \end{gathered}[/tex]Therefore, 260 millilitres is 26 centiliters.
Jenna bought a coat on sale for $120 which was 2/3 of the original price what was the original price of the coat
Answers
Jenna bought a coat on sale for $120
The price of the coat is the 2/3of the original price
Let the original price is $x
So, the equation will be :
2/3 of x =120
[tex]\begin{gathered} \frac{2}{3}\text{ of x=120} \\ \frac{2}{3}\times x=120 \\ x=120\times\frac{3}{2} \\ x=60\times3 \\ x=180\text{ dollars} \end{gathered}[/tex]So, The original price of the coat is $180
At the bakery cupcakes are displayed in 12 rows with 6 cupcakes per row. If a
customer buys 24 cupcakes, how many cupcakes are left?
Answers
If a customer buys 24 cupcakes there are 48 cupcakes left. (72-24=48)
There are 100 centimeters (cm) in 1 meter (m) Choose the correct answers from the drop-downs lists to complete the sentence. To convert 4 m to centimeters Choose 4 by C
Answers
given: 100 cm = 1 meters
We need to convert 4 m to cm
so,
[tex]4m=4\cdot100\operatorname{cm}=400\operatorname{cm}[/tex]I need help with this practice problem from my ACT prep guideIt is trigonometry It asks to graph the function yourself, on paper, or on desmos
Answers
If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:
[tex]f(x)\to f(x+\frac{\pi}{6})[/tex]That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:
question is in image
Answers
The expresion for the correlation coefficient is :
[tex]r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\mleft\lbrace n\Sigma x^2-(\Sigma x)^2\}\mleft\lbrace n\Sigma y^2-(\Sigma y)\mright?^2\mright\rbrace}}[/tex]summation of x = 5 + 7 + 10 + 15 + 19
Summation of x = 56
Summation of y = 19 + 17 + 16 + 12 + 7
Summation of y = 71
Summation of prodcut xy
[tex]\begin{gathered} \Sigma xy=5\times19+7\times17+10\times16+15\times12+19\times7 \\ \Sigma xy=687 \end{gathered}[/tex]Summation of x^2 = 25 + 49 + 100 + 225 + 361
Summation of x^2 = 760
Summation of y^2 = 361 + 289 + 256 + 144 + 49
Summation of y^2 = 1099
Substitute tha value in the expression of correlation coefficient
[tex]\begin{gathered} r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt[]{\mleft\lbrace n\Sigma x^2-(\Sigma x)^2\}\mleft\lbrace n\Sigma y^2-(\Sigma y)\mright?^2\mright\rbrace}} \\ r=\frac{5(687)-56\times71}{\sqrt[]{\mleft\lbrace5(760)-(56)^2\}\mleft\lbrace5(1099\mright)-(71\mright)^2}} \\ r=\frac{541}{\sqrt[]{\begin{cases}3800-3136\}\mleft\lbrace5495-5042\mright\rbrace\end{cases}}} \\ r=\frac{541}{\sqrt[]{300792}} \\ r=\frac{541}{548.44} \\ r=0.985 \end{gathered}[/tex]Answer: A) Correlation coefficient is 0.985
Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually. How much would Montraie need to invest, to the nearest ten dollars, for the value of the account to reach $1,610 in 15 years?
Answers
If Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years
The interest rate = 4.6%
The final amount = $1610
The time period = 15 years
The compound interest
A = [tex]P(1+\frac{r}{100})^{t}[/tex]
Where A is the final amount
P is the principal amount
r = interest rate
t is the time period
Substitute the values in the equation
1610 = [tex]P(1+\frac{4.6}{100})^{15}[/tex]
1610 = P×1.96
P = 1610/1.96
P = $820.06
Hence, if Montraie is going to invest in an account paying an interest rate of 4.6% compounded annually, then she has to invest $820.06 for the value of the account to reach $1610 in 15 years
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Malcolm's Bakery Shop sells gourment cupcakes. The shop's cost for making 3 cupcakes is $6.75, and the cost of making 5 cupcakes is $9.75 . What is the shop's cost per minute?
A. $1.50
B. $1.95
C. $2.25
D. $3.00
Answers
The average cost per minute which the shop runs is $1.50
Shop's Cost per MinuteTo find the shop's cost per minute, we can write down equations and proceed to solve.
In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.
But we were not given the average cost per cupcake.
To do that, let's write an equation for this.
[tex]y = mx + c[/tex]
Let's find the slope to this equation which determines the average cost per minute.
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]
The shop's cost per minute was calculated to be $1.50.
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Tonya spends 55% of her savings on a new dress. If she saved $120, how much was the dress? mathematical representation.
a50/23 = b
b.0.55 x 120 = d
c.190x = 45; change the decimal to a %
d.x/45 = 190; change the decimal to a %
e.55d = 120
f.23 x 50 = b
g.23/50 = b
h.2.50/45 = p
i.2.50p = 45
j..23 x 50 = b
k..45 x 190 = x
l..55d = 120
Answers
The coat of the dress based on the percentage is $66.
How to calculate the value?From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.
Let the cost of the dress be represented as x
Therefore, the appropriate information given I'll be expressed as:
= 55% × 120 = x
0.55 × 120 = x
Multiply
x = 66
The amount spent is $66.
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Which values are solutions to the inequality below? √x≤=12 check all that apply: A. 143 B. 125 C. 20736 D. 144 E. 12 F. 145
Answers
Given data:
[tex]\sqrt[]{x}\leq12[/tex]First squaring both sides we get,
[tex]x\leq144[/tex]Therefore, the value for the solution which satisfies the above equation are
[tex]\begin{gathered} a)\text{ 143}<144 \\ b)\text{ 125}<144 \\ d)\text{ 144}\leq144 \\ e)\text{ 12}<144 \end{gathered}[/tex]Thus, the ans is (a) , (b) , (d) , (e)
3. Select all expressions that are equivalent to (2n + 6)(n + 3)a. 2(n? + 6n +9)b. 2n? + 6n + 18c. 2n2 + 12n + 18d. 12n + 18e. 2(n + 3)(n + 3)f. 2(n + 3)?
Answers
Select all expressions that are equivalent to (2n + 6)(n + 3)
we have
(2n + 6)(n + 3)
apply distributive property
2n^2+6n+6n+18
2n^2+12n+18
Verify each option
option A
2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok
option B
is not correct
option C
is correct
option D
is not correct
option E
2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct
option F
2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok
therefore
answers areA, C, E, FThe width of a room is 7 feet, and the area of the room is 77 square feet. Find the room's length.
...
Answers
Answer:
11
Step-by-step explanation:
A = lw
l = A/w
l = 77/7
l = 11
Hope that helps
For each relation, decide whether or not it is a function.
Answers
Top left: Yes, each input corresponds to only one output.
Top right: Yes, each input corresponds to only one output.
Bottom left: Yes, each input corresponds to only one output.
Bottom right: No, the input of -1 corresponds to three different outputs.
In a recent awards ceremony, the age of the winner for best actor was 38 and the age of the winner for best actress was 51. For all best actors, the mean age is 46.8 years and the standard deviation is 5.7 years. For all best actresses, the mean age is 31.9 years and the standard deviation is 10.8 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Answers
Given
the age of the winner for best actor was 38 and the age of the winner for best actress was 51.
For all best actors, the mean age is 46.8 years and the standard deviation is 5.7 years.
For all best actresses, the mean age is 31.9 years and the standard deviation is 10.8 years.
Find
who had the more extreme age when winning the award, the actor or the actress
Explanation
the Z- score is given by
[tex]Z=\frac{X-\mu}{\sigma}[/tex]Best Actor
X = 38
mean = 46.8 years
standard deviation = 5.7 years.
so ,
[tex]\begin{gathered} Z=\frac{38-46.8}{5.7} \\ \\ Z=-1.54385964912\approx-1.54 \end{gathered}[/tex]Best Actress
X = 51
mean = 31.9 years
standard deviation = 10.8 years.
so ,
[tex]\begin{gathered} Z=\frac{51-31.9}{10.8} \\ \\ Z=1.76851851852\approx1.77 \end{gathered}[/tex]the best actress's age is farther from the mean so he has the more extreme age when the winning the award.
Final Answer
Hence , the z- score for best actor is -1.54 and for best actress = 1.77
Actress has more extreme age
a line perpendicular to y = 2x +4 through (4.2) slope of the new line equationequation of the new line
Answers
y= 2x+4
Slope-intercept form
y=mx+b
Where:
m= slope
b= y-intercept
y=2x+4
Slope = m= 2
Perpendicular lines have negative reciprocal slopes.
So, the slope of the new line = -1/2
New equation:
y= -1/2x+b
Replace x,y by the point (4,2) and solve for b:
2 = -1/2(4)+b
2= -2 + b
2+2 = b
4 = b
New line equation:
y= -1/2x+4
Determine if it has a minimum of maximum and what that value is whilst also Identifying the domain and range
Answers
Hello!
First, let's rewrite the expression here:
[tex]f\mleft(x\mright)=-2x^2+12x-15[/tex]We will have to find the coefficients a, b and c:
• a ,= -2;
,• b ,= 12;
,• c ,= -15;
As we can see, coefficient a is negative. It means that the parabola will face downwards and have a maximum value.
We can obtain this point by using the two formulas below to calculate the coordinates (x, y) of this point, look:
[tex]\begin{gathered} X_V=\text{ }-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \end{gathered}[/tex]As we know the coefficients, let's replace the values in the formulas:
Xv:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{12}{2\cdot(-2)}=-\frac{12}{-4}=-(-3)=+3 \\ \\ X_V=3 \end{gathered}[/tex]Now let's find Yv:
[tex]\begin{gathered} Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{12^2-4\cdot(-2)\cdot(-15)}{4\cdot(-2)}=-\frac{144-120}{-8}=-\frac{24}{-8}=-(-3)=+3 \\ \\ Y_V=3 \end{gathered}[/tex]Doing this, we obtained the coordinate of the maximum point (x, y) = (3, 3).
As it doesn't have any restrictions, the domain will be: [-∞, +∞].
[tex]-\infty\: We have one restriction in the range, do you remember which?The maximum value will be when y = 3, so the range is [-∞, 3].
Look at the graph of this function below:
Simplify 4 - 2y +(-8y) +7.3.4-2y+ ( 8y) +7.3=Q(Simplify your answer. Use integers or decimals for any numbers in theWhat is 4-2y+(-8y)+7.3
Answers
In order to simplify an equation we want to add all the terms with the same unkowns.
In the equation
4 - 2y + (-8y) + 7.3
we can see that there are terms with y and numbers alone.
We combine like terms:
Terms with y: -2y,
The side lengths in yards of a triangle and a square are shown in the diagram. (4x - 2) yd 2x yd 2(x + 7) yd 2.5x yd The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?
Answers
(4x -2) yd, 2x yd, 2(x + 7) yd, 2.5x yd. The triangle's perimeter is the same as the square's perimeter. The value of x=6
Given that,
The graphic displays the yards-long sides of a triangle and a square. The triangle's perimeter is the same as the square's perimeter.
We have to find the value of x in the given side.
In the picture we can see the triangle and square.
The perimeter of the triangle is sum of the three sides of the triangle.
The perimeter of the square is 4 times the side of the square.
4x-2+2x+2(x+7)=4×2.5x
4x-2+2x+2x+14=10x
8x+12=10x
10x-8x=12
2x=12
x=12/2
x=6
Therefore, the value of x=6
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The current in a resistor is inversely proportional to the resistance. By what factor will the current change if the resistance increases 10%.
Answers
The factor by which the current changes if the resistance increases 10% is; 90.9% reduction
How to Interpret Ohms' Law?
Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;
I = V/R
Now, we are told that the resistance increases by 10%.
Thus, New value of resistance = 1.1R
Thus, new current/old current = 1/1.1 = 0.909 = 90.9%
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What property is used in theses math problems
1: If AB=CD, then CD=AB
2: 5(x-4) = 5x-20
3: 3x-17=8, then 3x=25
4: 22m=440, then m=20
5:(2a+3a)-4a=7a+55, then (5a)-4a=7a+55
6:If GH=2x+17, and 2x+17=JK, then GH=JK
7:2b+(b-7)=17, then (2b+b)-7=17
8:(x+7)/3=13, then x+7=39.
9:m
10:4+x=13, then x+4=13
Answers
The various algebraic properties used for each of the given expressions are;
1) Symmetric property of equality.
2) Distributive property of equality.
3) Addition property of equality.
4) Division property of equality.
5) Addition property of equality.
6) Transitive property of equality.
7) Associative property of equality.
8) Multiplication property of equality
9) Commutative property of equality.
What is the Property of Algebra that is used?
There are different properties of equality or algebra such as;
Commutative PropertyAssociative PropertyDistributive PropertyInverse propertyTransitive PropertyReflexive PropertySymmetric propertySubstitution propertyAddition propertySubtraction property1) If AB=CD, then CD=AB; Property used here is Symmetric property of equality because it suits the definition.
2) 5(x-4) = 5x-20; Property used here is Distributive property of equality because it suits the definition.
3) 3x - 17 = 8, then 3x = 25; Property used here is Addition property of equality because it suits the definition.
4) 22m=440, then m=20; Property used here is Division property of equality because it suits the definition.
5) :(2a+3a)-4a=7a+55, then (5a)-4a=7a+55; Property used here is Addition property of equality because it suits the definition.
6) If GH=2x+17, and 2x+17=JK, then GH=JK; Property used here is Transitive property of equality because it suits the definition.
7) 2b+(b-7)=17, then (2b+b)-7=17; Property used here is Associative property of equality because it suits the definition.
8) (x+7)/3=13, then x+7=39.; Property used here is Multiplication property of equality because it suits the definition.
9) m 10:4+x=13, then x+4=13; Property used here is Commutative property of equality because it suits the definition.
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3. Which of the following quadratic functions has a maximum point?
Answers
The general form of a quadratic equation is given by the expression:
[tex]ax^2+bx+c=0[/tex]A quadratic equation having a maximum value or point is one that has its value of a to be lesser than zero
(a < 0). Such a graph opens downwards
Therefore, any quadratic equation that has the a-value to be lesser than zero has a maximum point
Mathematically expressed as:
[tex]\begin{gathered} y=-x^2 \\ \Rightarrow a=-1 \end{gathered}[/tex]find the equatuon of the line y=_x+_
Answers
Answer: y = -2x + 5
Step-by-step explanation:
y = _x + 5
(5,0) (3,4)
(y2 - y1) / (x2 - x1)
(4 - 0 ) / (3 -5)
4 / -2
-2
y = -2x + 5
4.5(8-x) -36 = 102 - 25 (3x + 24)
Answers
Let's simplify the following equation
You wish to program an LED strip containing n LEDs . Each individual LED can be lit in red, green, blue, or white. How many length-n
colour sequences have at least one pair of adjacent LEDs that light up with the same colour?
Hint: Find a recurrence relation. Order matters, (GGR and RGG are different). Also need to consider for the intersection of probabilities.
Answers
Using the Fundamental Counting Theorem, the number of length-n sequences that have at least one pair of adjacent LEDs that light up with the same color is:
[tex]N = 4 - 4 \times 3^{n - 1}[/tex]
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In the context of this problem, there are n LEDs, each with 4 possible colors, hence he total number of sequences is:
[tex]T = 4^n[/tex]
For sequences with no repeating LEDs, we have that:
The first LED can have 4 outcomes.Any of the following LEDs can have 3 outcomes. (except the color of the previous one).Hence the number is:
[tex]T_n = 4 \times 3^{n-1}[/tex]
(n - 1) as the first LED is not included on those with 3 possibilities.
Having at least one repeating and no repeating are complementary events, hence the number of sequences is:
[tex]N = 4 - 4 \times 3^{n - 1}[/tex]
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Suppose a basketball player has made 359 out of 449 free throws. If the player makes the next 3 free throws, I will pay you $39. Otherwise you pay me $43.
Step 1 of 2 : Find the expected value of the proposition
Answers
The expected value of the proposition is $22.6
How to determine the expected value?The given parameters are
Proportions of free throws = 359 out of 449Amount paid for making a throw = $39Amount collected for losing a throw = $43Represent the proportion as a fraction
So, we have
p = 359/449
The expected value is then calculated as
E(x) = p * Amount paid for making a throw - (1 - p) * Amount collected for losing a throw
Where p represents the proportion defined above
So, we have
E(x) = 359/449 * 39 - (1 - 359/449) * 43
Evaluate the difference
E(x) = 359/449 * 39 - 90/449 * 43
So, we have
E(x) = 22.6
Hence, the proposition has an expected value of $22.6
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Answer:
-1.09
The problem requires one to calculate the win payoff and win probability as well as the lose payoff and probability. You would then do a calculation like this:
[(Win Payoff) x (Win Probability)] + [(Lose Payoff) x (Lose Probability)]
stionsUse the graph at the left to answer the questions in thetable.Your AnswerQuestionIdentify the x-intercept. Usean ordered pair to answer thequestionIdentity the y-intercept. Uzean ordered pair to answer thequestionWhat is the rate or slope ofthe graph?10What is the domain of thegraph?What is the range of thegraph?
Answers
Answer:
x-intercept: (-0.5,0)
y-intercept: (0,1)
Slope: 2
Domain: All real values
Range: All real values
Step-by-step explanation:
x-intercept:
The x-intercept is the value of x when y = 0. In this graphic, we have that when y = 0, x = -0.5. So the x-intercept is given by: (-0.5,0)
y-intercept:
The y-intercept is the value of y when x = 0. In this graphic, we have that when x = 0, y = 1. So the y-intercept is given by: (0,1).
Slope:
To find the slope, we select two points. The slope is given by the division of the change in y by the change in x.
Two points: (-0.5, 0) and (0,1)
Change in y: 1 - 0 = 1
Change in x: 0 - (-0.5) = 0 + 0.5 = 0.5
Slope: 1/0.5 = 2
Domain and range:
In a line, the domain is all real values, the same for the range.
the sum of the interior angles of an octagon is 1080 degrees. each angle is six degrees larger than the angle just smaller than it. what is the measure of the fourth angle?
Answers
The measure of the fourth angle that is x and the value is 133°
What is an octagon?A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.
Let the 8 interior angles of the octagon be:
x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.
Their sum = 8x+16 = 1080, or
this implies 8x = 1080–16 = 1064
thus on further solving we get x = 133
Hence the sixth angle = x+8 =141 degrees.
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