To find the answer, we have to find the LCM of 25 and 40.
To get LCM, we
Write each number as prime factors
take the prime factor that occurs greatest number of time
take the product of those
Thus,
25 = 5 * 5
40 = 2 * 2 * 2 * 5
2 occurs 3 times and 5 occurs 2 times (greatest).
hence,
LCM(25, 40) = 2 * 2 * 2 * 5 * 5 = 200
So,
200 mins will pass before the two buses meet
What is the simplified form of the expression square root of -64
What is the simplified form of the expression square root of -64
we have
[tex]\sqrt[]{-64}[/tex]Remember that
64=2^6
and
i^2=-1
substitute
[tex]\sqrt[]{-64}=\sqrt[]{(-1)(2^6)}=\sqrt[]{i^2\cdot2^6}=2^3i=8i[/tex]option BJamal built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box.
Okay, here we have this:
Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will first calculate the area of the base, the area of the short side and the area of the longest side, then we have:
Base area=6 in * 14 in=84 in^2
Short side area=8 in * 6 in = 48 in^2
Longest side area=8 in * 14 in=112 in^2
Total surface area=Base area+ 2(Short side area) + 2(Longest side area)
Total surface area=84 in^2+ 2(48 in^2) + 2 (112 in^2)
Total surface area=84 in^2+ 96 in^2 + 224 in^2
Total surface area=404 in^2
Finally we obtain that the total surface area in square inches of the toy box is 404 in^2.
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 12% vinegar. The chefwants to make 370 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
Assuming these are volume percentages and the volumes don't change when you mix them, we can calculate this using a system of equations.
But first we need to identify each equation and variable.
let x be the volume of 7% vinegar used and y be the volume of 12% vinegar used.
The total volume is the sum of those and it must be equal to 370 mL, so:
[tex]x+y=370[/tex]The amount of vinegar in the x volume of 7% vinegar can be calculated by multiplying x by the 7%, that is, by 0.07:
[tex]0.07x[/tex]Similarly, the amount of vinegar in y is:
[tex]0.12y[/tex]So, the total amount of vinegar after the mixture is:
[tex]0.07x+0.12y[/tex]Since the percentage of the final mixture is 8%, the amount after the mixture can also be calculated by taking 8% of the final volume of 370mL, that is:
[tex]0.08\cdot370=29.6[/tex]The two ways of calculating the amount of vinegar in the mixture must be the same, so we have got our second equation:
[tex]0.07x+0.12y=29.6[/tex]So, the system of equations is:
[tex]\begin{gathered} x+y=370 \\ 0.07x+0.12=29.6 \end{gathered}[/tex]We can solve this by substitution:
[tex]\begin{gathered} x+y=370 \\ x=370-y \end{gathered}[/tex]Thus:
[tex]\begin{gathered} 0.07x+0.12y=29.6 \\ 0.07(370-y)+0.12y=29.6 \\ 0.07\cdot370-0.07y+0.12y=29.6 \\ 25.9+0.05y=29.6 \\ 0.05y=29.6-25.9 \\ 0.05y=3.7 \\ y=\frac{3.7}{0.05} \\ y=74 \end{gathered}[/tex]And, going back to the first equation:
[tex]\begin{gathered} x=370-y \\ x=370-74 \\ x=296 \end{gathered}[/tex]give the answer as a mixed number and as an improper fraction (number 1)
Answer:
Jossie has filled 59/30 of the 3 baskets.
Step-by-step explanation:
If Jossie has filled 3/5 of one, 7/10 of another, and 2/3 for the last one. The proportion of the total baskets:
[tex]\frac{3}{5}*\frac{2}{2}+\frac{7}{10}+\frac{2}{3}=\frac{6}{10}+\frac{7}{10}+\frac{2}{3}[/tex]Compute.
[tex]\frac{13}{10}+\frac{2}{3}=\frac{39+20}{30}=\frac{59}{30}[/tex]Jossie has filled 59/30 of the 3 baskets.
Could I assistance receive some on this question it’s very confusing
We need to translate the vertex F of triangle BDF. When we translate it 2 units to the left and 4 units down, we obtain the point F'.
We know that triangle BDF has vertices B(4,3), D(6,3), and F(6,1).
The first coordinate of each point represents its x-coordinate (the distance from the y-axis). And the second coordinate of each point represents its y-coordinate (the distance from the x-axis).
So, this triangle is shown below:
Now, we need to translate the point F 2 units to the left, to obtain the redpoint below. And then translate it 4 units down, to obtain F' (the yellow point):
Therefore, the F' has coordinates:
F'(4,-3)
find the area of the figure below, composed of a rectangle with two semicircles removed.
This is a composite shape composed of a rectangle with two semicircles removed. The area will be calculated by subtracting the area of the two semicircles from the area of the rectangle
The area of a rectangle is given by:
[tex]\begin{gathered} Area(rectangle)=length\cdot width \\ length=12 \\ width=6 \\ Area(rectangle)=12\cdot6=72 \\ Area(rectangle)=72 \end{gathered}[/tex]The area of the two semicircles is given by:
[tex]\begin{gathered} Area(2semicircles)=2(\frac{1}{2}\pi r^2) \\ Area(2semicircles)=\pi r^2 \\ r=\frac{diameter}{2}=\frac{6}{2}=3 \\ Area\mleft(2semicircles\mright)=\pi\cdot3^2=3.14\cdot9=28.26 \\ Area\mleft(2semicircles\mright)=28.26 \end{gathered}[/tex]Therefore, the area of the figure is:
[tex]\begin{gathered} Area(figure)=Area(rectangle)-Area(2semicircles) \\ Area(figure)=72-28.26 \\ Area(figure)=43.74\approx43.7 \\ Area(figure)=43.7 \end{gathered}[/tex]a quadratic function has its vertex at the point (4,6) the function passes through the point (-5,-2) find the quadratic and linear coefficients and the constant term of the function The quadratic coefficient is_____The linear coefficient is_______the constant term is_____
We have to find the equation of the quadratic function.
We know the vertex, located in (4,6), and one point (-5,-2).
The x-coordinate of the vertex (4) is equal to -b/2a, being a the quadratic coefficient and b the linear coefficient.
Now, we have 2 points to define the 3 parameters, so one of the parameters is undefined.
[tex]y=ax^2+bx+c[/tex]We start with the vertex, that we know that is:
[tex]\begin{gathered} x=-\frac{b}{2a}=4 \\ -b=4\cdot2a=8a \\ b=-8a \end{gathered}[/tex]Then, we can write the equation as:
[tex]y=ax^2-8ax+c=a(x^2-8x)+c[/tex]If we replace the point (-5,-2) in the equation, we get:
[tex]\begin{gathered} -2=a((-5)^2-8\cdot(-5))+c \\ -2=a(25+40)+c \\ -2=65a+c \\ c=-2-65a \end{gathered}[/tex]We replace the vertex coordinates and get:
[tex]\begin{gathered} 6=a(4^2-8\cdot4)+c \\ 6=a(16-32)+(-2-65a) \\ 6=-16a-2-65a \\ 6=-81a-2 \\ 81a=-2-6 \\ a=-\frac{8}{81}\approx-0.01 \end{gathered}[/tex]Then, the linear coefficient b is:
[tex]b=-8a=-8\cdot(-\frac{8}{81})=\frac{64}{81}\approx0.79[/tex]And the constant term is:
[tex]c=-2-65a=-2-65\cdot(-\frac{8}{81})=-2+\frac{520}{81}=\frac{-162+520}{81}=\frac{358}{81}\approx4.42[/tex]The quadratic coefficient is a=-0.01
The linear coefficient is b=0.79
the constant term is c=4.42
A store is having a sale on jelly beans and trail mix today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
please refer to the image
The required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
What is the equation?the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
According to the question,
6x + 5y = 28 - - - - (1)
2x + 3y = 14 - - - - (2)
Solving equations 1 and 2 by substitution method we get,
x = 7/4 = and y = 7/2
Thus, the required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
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Please get help with us for I am confused as to have should draw the rotation after a 90° clockwise rotation
In the given figure we can observe a triangle with vertices located at:
(-3,-2)
(-5,-4)
(1,-5).
We need to draw it after a 90° clockwise rotation.
We can apply the rule for 90° clockwise rotation, which is:
Each point of the given figure has to be changed from (x, y) to (y, -x) and then we need to graph the new coordinates.
By applying the rule to the given coordinates we obtain:
[tex]\begin{gathered} (x,y)\to(y,-x) \\ (-3,-2)\to(-2,3) \\ (-5,-4)\to(-4,5) \\ (1,-5)\to(-5,-1) \end{gathered}[/tex]Now we have to draw the new coordinates:
Which statement is true for all real values of θ? sin2θ − cos2θ = 1 cos2θ − sin2θ = 1 cos2θ = sin2θ − 1 cos2θ = 1 − sin2θ
The statement holds true for all true values of is cos²θ = 1 − sin²θ
What is meant by trigonometric identities?Trigonometric Identities are equalities that involve trigonometry functions and hold true for all variables in the equation. There are numerous trigonometric identities involving the side length and angle of a triangle. Trigonometry identities are trigonometry equations that are always true, and they are frequently used to solve trigonometry and geometry problems as well as understand various mathematical properties. Knowing key trig identities aids in the retention and comprehension of important mathematical principles as well as the solution of numerous math problems. Convert everything to sine and cosine terms. When possible, use the identities. Begin by simplifying the left side of the equation, then move on to the right side if you get stuck.To learn more about trigonometric identities, refer to:
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(4 to the 3rd power * 4 to the 6 power)to the 5th power
hello
if i'm right, what you're trying to ask is
Corbie earns $2750 paid once a month after taxes.
James gets paid every other week for tutoring at the
local library, and his smallest paycheck in the past six
months was $280.
Their monthly rent for their home is $925 and their most
expensive month for combined utilities last year cost
$325. Their smartphones cost $180 per month. They
spend $120 per week on groceries, $45 per week on
gas,and $620 per month for their car's payment,
insurance, and maintenance savings. James spends
$600 per semester (twice a year) for college tuition.
They each give themselves a $100 per week allowance
for personal expenses such as clothes, haircuts, dining
out, and entertainment.
Calculate their prorated monthly amounts, their monthly
totals, and their cash flow.
1. Corbie and James' total prorated monthly incomes are Corbie's $2,750 and James' $606.
2. Their combined monthly totals are:
Income = $3,356.
Expenses = $3,111.
3. Their monthly net cash flow is $245.
What is the net cash flow?The net cash flow is the cash surplus after paying all operating costs.
The net cash flow for Corbie and James is the difference between their total earnings per month and their total expenses per month.
For some income and expenses, there is a proration. Since 52 weeks make up the typical year, each month is considered 4.33 weeks.
1 year = 52 weeks
1 month = 4.33 weeks (52/12)
Monthly Income:
Corbie = $2,750
James = $606 ($280 x 26/52 x 4.333)
Total income = $3,356
Monthly Expenses:
Rent = $925
Utilities = $325
Phones = $180
Groceries = $520 ($120 x 4.33)
Gas = $195 ($45 x 4.33)
Tuition = $100 ($600 x 2)/12
Incidentals = $866 (200 x 4.33)
Total expenses = $3,111
Net Cash Flow = $245 ($3,356 - $3,111)
Thus, whereas, Corbie and James earn a combined and prorated monthly income of $3,356, their total monthly expenses of $3,111 leave them with a net cash flow of $245.
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the sum of three consecutive integers is 219. find The largest of the three integers.
Let n be the lesser number of the three. Therefore,
[tex]n+(n+1)+(n+2)=219[/tex]Solving for n,
[tex]\begin{gathered} \Rightarrow3n+3=219 \\ \Rightarrow3n=216 \\ \Rightarrow n=72 \end{gathered}[/tex]Then, the three numbers are 72, 73, and 74. The answer is 74
Define table represents grouped frequency distribution of the number of hours found computer per week for49 students. What is the value of the upper class limit of the fifth class
Sample unit: students
Sample size: 49
Variable: number of hours spent on the computer per week
There are 5 classes. The 5th class (the last one) of the table is:
14.0 - 17.4
Its upper-class limit of the 5th class is 17.4 hours
In a class of 6, there are 4 students who are secretly robots. If the teacher chooses 2 students, what is the probability that neither of them are secretly robots?i know how to get 2/6 but how do i get the other fraction?
The chance of the first student chosen not secretly being a robot is 2/6, but if the student is secretly a robot, then it doesn’t matter who the second student chosen is, because “neither” cannot be obtained.
So, 2/6th the time we care about the second student. There is in this case 1 non robot among the 5 remaining students, so the chance is 1/5 of picking that second non robot.
Hence;
2/6 x 1/5 = 2/30 = 1/15
V256 rational or irrational
First, in order to get to know if 256 it is a rational or irrational number we have to begin with the definition of what is rational and irrational number.
Rational numbers are all the number that can be represented as fractions, while the irrational numbers are all the numbers that can not be expressed as fractions.
In this case, then we can confirm that the number 256 can be considered as a rational number because it can be expressed as the quotient of the two integers: for example 256/1.
35* 35. Which of the following values for r suggests that one variable causes another? A. -0.7 B. O C. 0.9 D. None of the above
The correlation coefficient r indicates if two variables are or not dependent. If r is close to 1, then one variable causes the other one. From the options, a value of 0.9 suggests that one variable causes another
Question 1 of 10 - What is the value of the expression below when d= 5 and m = -2? d? + | dm|
Note the absolute value of any negative value is positive.
a.a + 0 = 0Additive Identityb. Multiplicative IdentityCommutative Property of Additiond. Associative Property of AdditionC.
Answer:
a. Additive Identity
Explanation:
Given the equation:
[tex]a+0=a[/tex]When zero(0) is added to 'a', the result is still 'a'.
The number 0 is the additive identity of 'a'.
Kirsten is driving to a city that is 400 miles away. When Kirsten left home, she had 15 gallons of gas in her car. Assume that her car gets 25 miles per gallon of gas. Define a function f so that f(x) is the amount of gas left in her car after she has driven x miles from home. What are intercepts for that function. What do they represent.
The equation that gives us the amount of gas left in her car, given the driven miles, is
[tex]f(x)=15-\frac{x}{25}[/tex]Notice that when x=25, there will remain 14 gallons of gas in the tank.
The x-intercept is
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow0=15-\frac{x}{25} \\ \Rightarrow x=15\cdot25=375 \end{gathered}[/tex](375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.
On the other hand, the y-intercept is
[tex]\begin{gathered} x=0 \\ \Rightarrow f(x)=15 \end{gathered}[/tex](0,15). This is the number of gallons in the tank when we have driven 0 miles.
You have to write 1/2 page for an assignment. You write 1/5 page. How many pages do you have left to write ?
To find the number of missing pages:
[tex]\frac{1}{2}-\frac{1}{5}=[/tex]rewriting the expression as homogeneous fractions:
[tex]\frac{1}{2}\times\frac{5}{5}-\frac{1}{5}\times\frac{2}{2}=[/tex]simplifying it:
[tex]\frac{5}{10}-\frac{2}{10}=\frac{3}{10}[/tex]ANSWER
you have left 3/10 page.
Please help me asap with both I’ll mark you brainly
1. The scholar made a mistake in the last step
where he said x=3.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14[/tex]
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS
[tex]lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4[/tex]
Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n
[tex]rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4[/tex]
FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.
I HOPE THIS HELPS.
Write an expression to show how much Gretchen paid for drama,action, and comedy videos if she paid $4 for each at a sale. Evaluate the expression
explanation
To determine how much Gretchen paid, we will have to list out the number of Video purchases made for drama, action, and comedy videos.
Let the Action videos be represented by A
Let the Comedy videos be represented by C
Let the Drama videos be represented by D
Also,
A has 3 purchases
C has 5 purchases
D has 2 purchases
Therefore, we will have the expression
[tex]3A+5C+2D[/tex]If she paid $4 for each, then
The total videos purchased = 3+5+2=10
Thus, the total amount paid will be
[tex]\begin{gathered} 10p \\ \text{where p is the price she paid for each video} \\ \text{Thus, } \\ \text{she paid} \\ 10(4)=\text{ \$40} \end{gathered}[/tex]Thus, Gretchen paid $40
May I please get help with this math. I have tried several times but still could not get the right answer
Given:
m∠3 = 63°
Let's find the m∠5 and m∠8.
• m∠5:
Angle 5 and angle 3 are alternate interior angles.
Alternate interior angles are angles formed on the opposite sides of the transversal.
To find the measure of angle 5, apply the Alternate Interior Angles theorem which states that when two parallel lines are cut by a transversal, the alternate interior angles are congruent.
The measure of angle 5 will also be 63 degrees.
Thus, we have:
m∠3 = m∠5 = 63°
m∠5 = 63°
• m∠8:
Angle 8 and angle 5 are linear pair of angles.
Angles that form a linear pair are supplementary.
Supplementary angles are angles that sum up to 180 degrees.
Thus, we have:
m∠8 + m∠5 = 180
m∠8 + 63 = 180
Subtract 63 from both sides:
m∠8 + 63 - 63 = 180 - 63
m∠8 = 117°
Therefore, the measure of angle 8 is 117 degrees.
ANSWER:
• m,∠,5 = 63°
,• m∠8 = 117°
You are trying to put together a chart depicting how many people by age group attended the most recent blockbuster movie What type of chart would best to use to display this Information and why-column graphs -line graphs-pie charts -bar graphs -Area charts -scatter charts
The first step will be to review all of the types of graphs or charts mentioned in the options.
The following diagram shows an example of each type of graph:
In this case, we need a graph to show the number of people by age group that attended the movie.
In this case, the line graph, the area chart, and the scatter chart will not represent the information in the best way, but a column graph, a bar graph, or a pie chart will give a better idea of the number of people by age group that went to see the movie.
Answer:
-Column graphs
-Pie charts
-Bar graphs
Solving a present makes your problem using a system of linear equations
Answer:
Explanation:
If it costs $1.50 for a pack of Starbursts at ShopRite, how much will 5 packs cost?
Answer : $7.5
1 pack of starbursts cost $1.50 at shoprite.
How much will 5 packs cost
Let the cost in dollars of 5 packs of starbursts be x
1 pack will cost $1.50
5 packs will cost $x
Mathematically,
1 pack ---------------- $1.50
5 packs -------------= $x
Cross multiply
1 * x = 5 x 1.50
x = $7.5
Hence, 5 packs of starbursts would cost $7.5
Mark is roofing an old gymnasium that measures 270’x390’, and needs to calculate how many “squares “ he will need.(1 “square=100 ft square). The gym’s roof is a standard gable roof with 3’ of overhang on all sides. The roof angle measures 22.55 degrees from horizontal. How many squares of roofing does mark need ?
First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.
Let's take a look at the situation:
Since we're on a right triangle, we can say that:
[tex]\cos (22.25)=\frac{G}{R}[/tex]Solving for R,
[tex]\begin{gathered} \cos (22.25)=\frac{G}{R}\rightarrow R\cos (22.25)=G \\ \\ \Rightarrow R=\frac{G}{\cos (22.25)} \end{gathered}[/tex]Since we already know that the lenght of the gym's floor is 390',
[tex]\begin{gathered} R=\frac{390^{\prime}}{\cos (22.25)} \\ \\ \Rightarrow R=421.38^{\prime} \end{gathered}[/tex]We get that the lenght of the surface we want to roof is 421.38'
Now, let's take a look at the surface we want to roof:
Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427
Our total roofing area would be:
[tex]427.38^{\prime}\cdot276^{\prime}=117956.88ft^2[/tex]We then divide this total area by the area of one of our "squares":
[tex]\frac{117956.88}{100}=1179.56[/tex]We round to the nearest integer from above, since we can't buy a fraction of a square.
(this is called ceiling a number)
[tex]1179.56\rightarrow1180[/tex]Therefore, we can conclude that Mark needs 1180 squares of roofing.
please help me with this question
The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x
Given,
The cost of a convention center to host an event = $300 + $45 per person attending
Number of attendees = x
We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.
Here,
Total cost for the event = Fixed cost + cost per person attending x number of person
Total cost = 300 + 45 × x
Total cost = 300 + 45x
Now,
The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x
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The Shoe Outlet bought boots for $60 and marks up the boots 55% on the selling price. What is the selling price of the boots?
If the markup is of the 55%, then the selling price will be the 155% of the original price, this means that the selling price is:
S = $93.
What is the selling price of the boots?If the original price is P, and the markup is given by a percentage X, then the selling price of the product will be:
S = P*(1 + X/100%).
In this case, the original price is $60 and the mark up is of 55%, then we have:
P = $60
X = 55%.
S = $60*(1 + 55%/100%) = $60*(1 + 0.55) = $93
The selling price is $93.
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