on a map 1 inch equals 18.4 miles. If two cities are 4.5 inches apart on the map, how far are they actually apart?
5m-1=4m+5 what is m.
The correct answer is 6. In other words, the value of m that satisfies the solving linear equation is m = 6.
In the given equation, we are asked to find the value of m. The equation states that the quantity 5m minus 1 is equal to the quantity 4m plus 5.
To solve this equation, we can use algebraic methods. The goal is to isolate the variable m on one side of the equation.
First, we combine like terms. By subtracting 4m from both sides of the equation, we eliminate the term with m on the right side. This results in the equation m - 1 = 5.
Next, we isolate the variable m by adding 1 to both sides of the equation. This cancels out the -1 term on the left side and gives us m = 6.
Therefore, the correct answer is 6. In other words, the value of m that satisfies the solving linear equation is m = 6.
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How many comparisons are required to merge these pairs of lists using algorithm 10?
a.1, 3, 5, 7, 9; 2, 4, 6, 8, 10
b.1, 2, 3, 4, 5; 6, 7, 8, 9, 10
c.1, 5, 6, 7, 8; 2, 3, 4, 9, 10?
Carlos has 5/8 pound of pumpkin seeds. He puts the seeds evenly into 20 envelopes. How much pumpkin seed is in each envelope?
Question Help Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 45 in. by 24 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.
Answer:
The dimensions are [tex]35\times 14\times 5[/tex] and the volume is 2450 inches³.
Step-by-step explanation:
Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 45 in. by 24 in. by cutting congruent squares from the corners and folding up the sides.
To find : The dimensions and the volume of the open rectangular box ?
Solution :
Let the height be 'x'.
The length of the box is '45-2x'.
The breadth of the box is '24-2x'.
The volume of the box is [tex]V=L\times B\times H[/tex]
[tex]V=(45-2x)\times (24-2x)\times x[/tex]
[tex]V(x)=4x^3-138x^2+108x[/tex]
Derivate w.r.t x,
[tex]V'(x)=4(3x^2)-138(2x)+108[/tex]
[tex]V'(x)=12x^2-276x+108[/tex]
[tex]V'(x)=12(x^2-23x+90)[/tex]
The critical point when V'(x)=0
[tex]12(x^2-23x+90)=0[/tex]
[tex]x^2-23x+90=0[/tex]
[tex](x-18)(x-5)=0[/tex]
[tex]x=18,5[/tex]
18 is not possible we reject.
So, the height is 5 inches.
Derivate again w.r.t x,
[tex]V''(x)=24x-276[/tex]
[tex]V''(5)=24(5)-276[/tex]
[tex]V''(5)=120-276[/tex]
[tex]V''(5)=-156<0[/tex]
i.e. V(x) is maximum at x=5.
The dimensions are
Height = 5 inches
Length = 45-2(5)=35 inches
Breadth = 24-2(5)=14 inches.
The maximum volume is
[tex]V=35\times 14\times 5[/tex]
[tex]V=2450[/tex]
So, The dimensions are [tex]35\times 14\times 5[/tex] and the volume is 2450 inches³.
Prakrit bought a pack of paper for $5.69 and printer toner for $9.76. He paid with a $20 bill. What was his change?
Find the exact circumference of a circle with the given radius. 5 inches C = 2.5 in. 10 in. 25 in.
Answer: The exact circumference of the circle is [tex]10\pi[\tex] in.
Step-by-step explanation:
Since, the circumference of a circle is,
[tex]C=2\pi r[/tex]
Where, r is the radius of the circle,
Here, r = 5 inches,
Hence, the circumference of the circle is,
[tex]C = 2\pi(5) = 10\pi\text{ in}[/tex]
Thus, The exact circumference of the circle is [tex]10\pi[\tex] in.
round to the nearest tenth 10.357
A text message plan costs $3 per month pulse $0.32 per text. find the monthly cost for x text messages
Why would a bank charge a fee to noncustomers who use it’s ATM?
ANSWER: Charging a noncustomer helps pay for the cost of keeping the ATM running and supplied with cash. Customers of the bank already cover the ATM costs with regular fees or by allowing the bank to loan out their money.
Answer:
Bank charges fee to non customers while using ATM. ATM's frequently charge fees to users who are not account holders from that same bank whose ATM you are operating.
This fee goes towards the compensation for the costs associated with owning and operating the machine.
Same bank persons pay many types of fee yearly to their banks, so same bank ATM do not charge any fee.
When using other banks, your bank has to pay some interchange amount to that bank, this is also the reason why banks charge fee, basically they recoup the money that they will have to pay to other banks for interchange.
what is the absolute value of the complex number -4-sr2i
If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n
The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.
Given :
If m and n are two positive real numbers whose product is 10.
Given that m and n are two positive real numbers whose product is 10 that is:
mn = 10
[tex]\rm m= \dfrac{10}{n}[/tex] ---- (1)
The minimum value of (m + 2n) can be determined by using the following calculation.
Put the value of m in the given expression.
[tex]\rm = \dfrac{10}{n}+2n[/tex] ---- (2)
Now for minimum value differentiate the above expression with respect to n.
[tex]\rm =-\dfrac{10}{n^2}+2[/tex]
Now equate the above equation to zero.
[tex]\rm \dfrac{10}{n^2}=2[/tex]
[tex]\rm n = \sqrt{5}[/tex]
Now, put the value of n in equation (2).
[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]
= 8.95
The minimum value of (m + 2n) is 8.95.
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how many times greater is the value of the digit 2 in the 23.876 than the value of the digit 2 in 3.254?
(3x-3)° [6{x-10)]° what is the value of x
The actual answer to this equation is x=19 not x=1 or n=0
Find all points on the circle x 2 + y 2 = 100 where the slope is 3 4
The points on the circle x² + y² = 100 where the slope of the tangent is ¾ are (6, -8) and (-6, 8). This is found by taking the derivative of the circle equation, setting it equal to the slope, solving for y, substituting this into the original circle equation, and solving for x.
Explanation:The equation of the circle is x² + y² = 100. To find the points on this circle where the slope of the tangent is ¾, we need to find the derivative of this equation. The derivative of y with respect to x is dy/dx = -x/y. Set this equal to ¾ and solve for y, which gives y = -4x/3. Substitute this into the original circle equation to solve for x, which yields x = ± 6. Then substitute these x-values back into the equation y = -4x/3 to get y = ± 8. Therefore, the points on the circle where the slope of the tangent is ¾ are (6, -8) and (-6, 8).
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Final answer:
To find points on the circle x² + y² = 100 where the slope is 3/4, differentiate the circle's equation and set the derivative equal to 3/4. Solve the system of equations involving the circle's equation and the line's equation derived from the slope criteria. This process typically yields two points of intersection due to the geometrical properties of circles and lines.
Explanation:
To find all points on the circle x2 + y2 = 100 where the slope is 3/4, we first acknowledge that the given circle is centered at the origin (0,0) with a radius of 10 units. Since the slope of a tangent to the circle at any point can be found using implicit differentiation, let's differentiate the given equation with respect to x. Doing so, we get 2x + 2yy' = 0 where y' denotes the slope of the tangent to the circle at (x,y). Solving for y', we get y' = -x/y. Setting this equal to the given slope of 3/4, we have -x/y = 3/4.
By cross-multiplying and rearranging, we get 4x + 3y = 0. To find the points of intersection between the line and the circle, we substitute x2 + y2 = 100 into this equation. Solving the system of equations will yield the points on the circle where the slope of the tangent is 3/4.
Note: The exact points of intersection would require solving a resulting quadratic equation, which can give two possible points since a line with a given slope (except vertical) will typically intersect a circle at two points.
Solve for x. 9x = 3x -36
Amira sells balloon animals. She uses the same number of balloons for each animal she makes. The table compares the number of balloon animals sold and the remaining number of balloons on a certain day.
Animals Balloons
15 200
24 164
33 128
How many balloons does Amira use for each balloon animal?
Answer:
4 balloons for each balloon animal.
Step-by-step explanation:
Amira sells balloon animals. The given table compares the number of balloon animals sold and the remaining number of balloons on a certain day.
Animals Balloons
15 200
24 164
33 128
When she sold 15 animals the leftover balloons were 200.
then she sold 24 animals the number of leftover balloons were 164.
The difference of the number of items = 24 - 15 = 9 more animals sold
The difference of the leftover balloons = 200 - 164 = 36 balloons used
Now the number of her sold animals was = 33
and the left over balloons = 128
The number of sale was increased by 24 to 33 = 33 - 24 = 9 more animals
and the leftover balloons now 164 to 128 = 164 - 128 = 36 used
Therefore, we can see each sale of 9 balloon animals she used 36 balloons.
so Amira used for each balloon animal = [tex]\frac{36}{9}[/tex]
= 4 balloons.
Amira used 4 balloons for each balloon animal.
Answer:
The most she can sell is 65
Step-by-step explanation:
"How many balloon animals at most can Amira sell?"
Prove: the sum of four consecutive integers is never divisible by 4 g
[tex]n+n+1+n+2+n+3=4n+6[/tex]
4n is divisible by 4, but 6 is not, so the sum 4n+6 is not divisble by 4.
drag and drop the correct numbers into the boxes to complete the table. amounts may be rounded to the nearest cent
A painter made the table below to show the amount of paint it takes to cover a certain amount of square feet. The amount of paint varies directly with the area of each wall.
Answer:
Option A.
Step-by-step explanation:
The table made by the painter shows the amount of paint required to cover a certain amount of area of the wall.
Amount of paint is directly proportional to the area covered
In other words Amount of paint (y) ∝ Area covered (x)
y ∝ x
As we know when proportionality sign is removed, a constant known as proportionality constant is multiplied with the variable.
So y = k(x) where k is the proportionality constant
Now from the table to cover the area of 64 square feet, 4 pints of paint is required.
Now from the formula
4 = 64x
x = [tex]\frac{4}{64}=\frac{1}{16}[/tex]
Now we have to calculate the amount of paint required to cover the area of 256 square feet.
y = [tex]\frac{1}{16}\times 256[/tex]
y = 16 pints
Therefore, 16 pints of the paint will be required to cover 256 square feet.
Option A is correct.
Answer:
Just Pick 16 Pints
Step-by-step explanation:
Min Jee wants to build a small patio using either brick or paver stones. It will be 70 inches long and 49 inches wide. Each brick covers an area of 3 1/2 inches by 7 1/2 inches, and cost $0.59. Each paver covers an areas 8.4 inches by 8.4 inches and costs $1.88. What would be less expensive to use, and by how much?
A lender estimates the closing costs on a home loan of $50,000 as listed below.
Closing Cost
Charge
Loan origination
$200
Title insurance
$530
Attorney’s fees
$600
Appraisal
$265
Inspection
$575
Recording fees
$130
Escrow
$800
If the lender's good faith estimates are accurate, are they a reasonable amount for closing costs? Why or why not?
a.
Yes, because the lender esitmated 3.08% of the home loan in closing costs which falls between 3 - 5%.
b.
Yes, because the lender estimated 4.6% of the home loan in closing costs which does not fall between 3 - 5%.
c.
No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%.
d.
No, because the lender estimated 17.7% of the home loan in closing costs which does fall between
Answer:c.
No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%
Step-by-step explanation:
Summation of the cost of loan =200+530+600+265+575+130+800
=3100
Now percentage of the estimate=
(3100/50000)*100%
=6.2%
C- The lender should not consider them as reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3-5%.
The lender cannot be accepting these costs as this will lead to the lender incurring losses over a longer period after doing all the necessary calculations.
The lender has disbursed a home loan of $50000 on which he has estimated certain closing costs and are considered to be true and accurate. The costs are loan origination, title insurance, attorney's fees, appraisal, inspection, recording fees, escrow, etc.The amounts will add up as a summation of all the fees and charges as titles above are mentioned which will end up totaling to $3100[tex]200+530+600+265+575+130+800=3100[/tex]
The calculation of of costs in to the percentage of total home loan is calculated as dividing the cost with total loan amount which will be totaled as 6.2%.[tex]\frac{3100}{50000} *100= 6.2[/tex]
The costing of this home loan is way above the ideal range of 3-5% and is not worth disbursing and may be called back.Hence, the correct option is C that the amounts of $3100 are not a reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between the range of 3-5%.
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Describe or show two ways to find the following product: 1/4 x 2/3.
Albert thought of a number, added 5, multiplied the result by 2, took away 6 and then divided by 2 to give an answer of 8
If A game is played using one die. If the die is rolled and shows 2 the player wins 40. If the die shows any number other than 2 the player wins nothing
Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.
Which statement is true about lines a and b?
They are parallel lines.They are perpendicular lines.They are skew lines.They will intersect.The use of the normal probability distribution as an approximation of the sampling distribution of p̄ is based on the condition that both np and n(1 – p) equal or exceed _____.
a. .05
b. 5
c. 15
d. 30
The use of the normal distribution as an approximation for the sampling distribution of[tex]\( \bar{p} \)[/tex] requires both [tex]\( np \)[/tex] and [tex]\( n(1 - p) \)[/tex] to be at least 5. So, the answer is (b) 5.
The normal approximation for the sampling distribution of [tex]\( \bar{p} \),[/tex] the sample proportion, relies on the conditions that both[tex]\( np \)[/tex] and [tex]\( n(1 - p) \)[/tex] are greater than or equal to 5. Here, [tex]\( n \)[/tex] represents the sample size, and [tex]\( p \)[/tex] is the probability of success in a binary outcome. These conditions ensure that the distribution of[tex]\( \bar{p} \)[/tex] is approximately normal, allowing for the application of statistical techniques based on the normal distribution. When[tex]\( np \)[/tex]and [tex]\( n(1 - p) \)[/tex]are both at least 5, the central limit theorem asserts that the distribution of [tex]\( \bar{p} \)[/tex] is sufficiently close to normal, facilitating the use of standard normal tables and z-scores for making probability calculations and inferences about the population proportion. This approximation is pivotal in hypothesis testing and confidence interval construction for proportions in statistical analyses.
How to find the factor for the expression
4x-6y
2.8y+6+0.2y=5y-4 what is the solution to the linear equation
What is 65 3/5 - 24 1/3
Does anyone know a rule that work for all of these