Problem
0.8 divided 40
Solution
We can do the following:
[tex]\frac{0.8}{40}=\frac{0.8\cdot10}{40\cdot10}=\frac{8}{400}[/tex]and if we simplify we got:
[tex]\frac{8}{400}=\frac{4}{200}=\frac{2}{100}=\frac{1}{50}=0.02[/tex]If Erica teaches 15 fewerthan twice as many as Bo, how many classes does each instructor teach per week?
STEP - BY - STEP EXPLANATION
What to find?
The number each instructor teach per week.
Given:
Total number they teach per week =39
let e = number of classes Erica teaches per week and b = the number of classes Bo teaches per week.
e =2b - 15
Step 1
Form the linear equation.
[tex]b+e=39[/tex]Step 2
Substitute e=2b-15 into the above.
[tex]b+2b-15=39[/tex]Step 3
Collect like term.
[tex]b+2b=39+15[/tex][tex]3b=54[/tex]Step 4
Divide both-side of the equation by 3.
[tex]\frac{3b}{3}=\frac{54}{3}[/tex][tex]b=18[/tex]Step 5
Determine Erica's age.
[tex]\begin{gathered} b+e=39 \\ \\ e=39-b \\ \\ e=39-18 \\ \\ e=21 \end{gathered}[/tex]ANSWER
c. 18 Bo; 21 Erica
Noah bought 15 baseball cards for $9 assuming each baseball card cost the same amount answer the following questions one at this rate how much will the third 30 baseball cards cost explain your reasoning. At this rate how much will 12 baseball cards cost explain your reasoning. Do you think this information will be better represented using a table or a double number line explain your reasoning.
We know that 15 baseball costs $9.
We have to divide to find the unit cost.
[tex]\frac{9}{15}=0.6[/tex]Each baseball card cost 60 cents.
So, for 30 cards, it would cost
[tex]\begin{gathered} 0.6\cdot30=18 \\ 0.6\cdot12=7.2 \end{gathered}[/tex]Hence, 30 baseball cards cost $18, at the same unit price. And 12 baseball cards would cost $7.20.Observe that to get the answers, we just had to multiply the number of cards by the unit price.
There's no need for a table or a number double line because they are used when the amount of data is big enough. It is better to keep it simple.
Marge makes four payments each year of $175 for her auto insurance. Howmuch must she budget weekly to cover this fixed expense?a. $13.46b. $.84c. $58.33d. $ 700
Since she makes four payments each year, the total amount she pays in a year is
[tex]\$175\times4=\$700[/tex]Now there are 52 weeks in a year, divide the total amount of what she pays in a year by the number of weeks in a year.
[tex]\$700\div52=\$13.46[/tex]Therefore, she must budget weekly $13.46 to cover for this fixed expense.
refer to the figure to complete thus proportion. c/a = a/?
Here, we want to compare triangles and such write the equivalent ratio on both
Mathematically, if two triangles are similar, the ratio of their sides are fixed
In the triangle consisting of c and a, we can see that c is the hypotenuse( the side facing the right-angle) while a represents the base
Now, in the triangle where we have a as the hypotenuse, we can see that the measure r reresents the base of the triangle
Thus, we can complete the proportion as;
[tex]\frac{c}{a}\text{ = }\frac{a}{r}[/tex]question is in image
r-value being 0.9874, shows that the goodness of fit of the equation is close to 1. This implies that y = 65.18x + 21.43 properly approximates the data.
substitute 32 for x in the equation.
y = 65.18(32) + 21.43
y = 2107.19
Thus, the correct answer is $2107.19 (option A)
The values of x and y vary directly and one pair of values are given write an equation that relates x and y X=2 y=5
Given:
The values of x = 2 and y = 5
The relation between the values of x and y:
[tex]y=\frac{?}{\square}\text{x}[/tex]Now we need to have y = 5 for x = 2 so let us substitute 5/2 in place of blank space.That is,
[tex]y=\frac{5}{2}x[/tex][tex]\begin{gathered} y=\frac{5}{2}x \\ 5=\frac{5}{2}\times2 \\ 5=5 \end{gathered}[/tex]Hence, the relation gets satisfied.
Hence, the relation is :
[tex]y=\frac{5}{2}x[/tex]Jane earns £11 400 per year.90169 brs anottoB
After her pay rise she earns £12 198 per year.
What was her percentage pay rise?
The percentage rise of Jane= 7%.
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentage Increase/ Rise and Decrease/ Fall
The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
% increase = [(New number – Original number)/Original number] x 100
where,
increase in number = New number – original number
Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100.
% decrease = [(Original number – New number)/Original number] x 100
Where decrease in number = Original number – New number
So basically if the answer is negative then there is a percentage decrease.
In the given question , Jane earns initially = £11 400 per year
After rise Jane earns = £12 198 per year.
Percentage rise = [(New number – Original number)/Original number] x 100
Percentage rise = [( 12198 – 11400)/11400] x 100
= [( 798)/11400] x 100= 0.07 × 100 = 7%
So the percentage rise of Jane= 7%.
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The length of a rectangle is 4 in longer than its width. If the perimeter of the rectangle is 362 in, find it's area.
The length of a rectangle is 4 in longer than its width, which means
Length = 4 in + width
P = 362 in = 2L + 2W
362in = 2(4 in + W) + 2W = 8in+2W+2W = 8in + 4W
362in = 8in + 4W
Solve for W
362 in - 8in = 4W
354 = 4W
354/4 = W
88.5 = W
Replace W in the Length
Length = 4 in + W
Length = 4 in + 88.5in
Length = 92.5in
The formula for the area is A = Length * Width = L * W
Replace the values and find the area
A = L* W
A = 92.5in * 88.5in
A = 8186.25 in²
A boat is heading towards a lighthouse, where Dalvin is watching from a vertical distance of 138 feet above the water. Round your answer to the nearest tenth of a foot if necessary.
To find the first distance we use:
[tex]\begin{gathered} tan13=\frac{138ft}{x} \\ x=\frac{138ft}{tan13º} \\ x=\frac{138ft}{0.23} \\ x=\text{ 600ft} \end{gathered}[/tex]For the second distance, we change 13º to 45º and 77º to 45º as well.
So:
[tex]\begin{gathered} tan45=\frac{138ft}{x} \\ 1=\frac{138ft}{x} \\ x=138ft \end{gathered}[/tex]So the distance from point A to B is=600ft - 138ft = 462ft
write word problem1- correct variable term for the left side2-correct constant term for the left side 3-correct operation between the terms of the left side 4-correct equal sign or inequality symbol 5-correct variable term for the right side6-correct constant term for the right side 7-correct operation between the terms of the right side58×+170>42×+320
For the equation
[tex]58x+170>42x+320[/tex]A word problem could be the following.
Suppose we have a coin whose value we do not know and let us call the value of this coin x. All we know that 58 of these coins plus $170 is greater than 42 of these coins plus $320. This information, when converted into a word problem, gives the above inequality.
1. Which of the following is the value of -13 - 51 – 3? (A) -5 (B) -1 (C) 0 (D) 1 M
The value of -|3-5|-3 is,
[tex]\begin{gathered} -|3-5|-3=-|-2|-3 \\ =-2-3 \\ =-5 \end{gathered}[/tex]Hence, Option A is right.
A. Show all of your work to solve each equation and to check for extraneous solutions:4. [√(2x^2 - 1)]=x
ANSWER:
x = 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{2x^2-1}=x[/tex]We solve for x:
[tex]\begin{gathered} 2x^2-1=x^2 \\ \\ 2x^2-x^2=1 \\ \\ x^2=1 \\ \\ x=\sqrt{1}=\pm1 \\ \\ \text{ we check:} \\ x=1 \\ \\ \sqrt{2\left(1\right)^2-1}=1 \\ \\ \sqrt{2-1}=1 \\ \\ 1=1 \\ \\ x=-1\rightarrow\text{ true} \\ \\ \sqrt{2\left(-1\right)^2-1}=-1 \\ \\ \sqrt{2^-1}=-1 \\ \\ 1=-1\rightarrow\text{ false} \end{gathered}[/tex]Therefore, the solution of the equation is x = 1
What graph is the function of the table shown ?
Answer:
Explanation:
The table contains corresponding values of x and y
We would look at the points in the graph that contains these corresponding values of x and y. Looking at the graphs,
A baseball player went up to bat 500 times in a season. He hit the ball 150 times. Find the rate of balls hit to times at bat. Express as a ratio.
To find the answer, we just divide
[tex]\frac{150}{500}=0.30[/tex]As ratio would be
[tex]\frac{150}{500}=\frac{15}{50}=\frac{3}{10}[/tex]Hence, his rate is 3/10, three hits every 10 attempts.Karina purchased 5 yard a fabric costing $7.99/yard, two spools of thread at $1.25/spool and a pattern costing $5.25 . what was the total amount of her purchase before tax?
Given:
She purchased:
5 yard of fabric at $7.99/yard
2 spools of thread at $1.25/spool
1 pattern at $5.25
We can calculate the total amount of her purchase before tax by summing the cost of each item without tax.
The total amount:
[tex]\text{Total amount = cost of yard }\times\text{ number of yards purchased + cost of thread }\times\text{ number of spools + cost of pattern }\times Number\text{ of pattern}[/tex]Substituting we have:
[tex]\begin{gathered} \text{Total amount = 7.99}\times\text{ 5 + 1.25}\times2\text{ + 5.25 }\times\text{ 1} \\ =47.7 \end{gathered}[/tex]Hence, the total amount of her purchase before tax is $47.7
Answer: $47.7
Roseanna, Kennedy and Guadalupe had a super mean Math teacher who made them come up with a probability game where the chances of winning was 1/7. Roseanna’s idea was to have 5 red blocks and 30 blue blocks all in a bag. Each player gets one chance to pull out a block and if they pull out a red one they win Kennedy’s idea was the same as Roseanna’s except to have 1 red block and 7 blue blocks.Guadalupe’s idea was to have a seven sided die with a number 1 through 7 on each side. Each player rolls the die once and wins if they get a 3Whose game has a 1/7 chance of winning? Whose game doesn’t? For each game that doesn’t, show one way to change it so that it does have a 1/7 chance.
We are asked to determine which games have a 1/7 chance of winning. -
In the case of Roseanna's game, we have that there are 5 red blocks and 30 blues blocks. If the winner is the person that pulls out a red block then to determine the probability we must determine the quotient between the number of red blocks and the total number of blocks, like this:
[tex]P(red)=\frac{5}{5+30}[/tex]Solving the operations:
[tex]P(red)=\frac{5}{35}=\frac{1}{7}[/tex]Therefore, Roseanna's game has a 1/7 probability.
In the case of Kennedy's game, there are 1 red block and 7 blue blocks, therefore, the probability of getting a red block is:
[tex]P(red)=\frac{1}{7+1}=\frac{1}{8}[/tex]Therefore, Kennedy's game has not a chance of 1/7 but 1/8 of winning.
For Kennedy's game to have a probability of 1/7 he could remove one of the blue blocks, that way the probability is:
[tex]P(red)=\frac{1}{6+1}=\frac{1}{7}[/tex]In the case of Guadalupe's game, we have that there is a dice with 7 sides numbered from 1 to 7. This means that the probability of getting a 3 is:
[tex]P(3)=\frac{1}{7}[/tex]Therefore, Guadalupe's game has a probability of 1/7.
Juanita is eight years older than her brother hector. If Juanita is nineteen years old this year, how old is hector
juanita: 19
hector:?
[tex]h+9=j[/tex][tex]h+9=19[/tex][tex]h=19-9=10[/tex]Hector is 10 years
While hiking manuel descended 400 meters if manuel started at 1000 meters above sea level which integer represents his elevation now
Let me explain this with the following drawing:
If Manuel started at 1000 meters above sea level and he descended 400 meters, his elevation after this, is 600m above sea level.
So the integer that represents his elevation now is 600.
find the slope of the line passing through the points (-6,4) and (2,4)
To find the slope, we will use the formula below:
[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]x₁= -6 y₁=4 x₂=2 y₂=4
substitute the values into the formula
[tex]\text{slope =}\frac{4-4}{2+6}[/tex][tex]\text{slope}=\frac{0}{8}[/tex][tex]\text{slope = 0}[/tex]Find the distance between the points (-5,4) and (-2,-1)
Answer
√34
Step-by-step explanation
Distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
• d: distance between two points
,• (x₁, y₁): coordinates of the first point
,• (x₂, y₂): coordinates of the second point
Substituting into the formula with the points (-5,4) and (-2,-1), we get:
[tex]\begin{gathered} d=\sqrt{(-2-(-5))^2+(-1-4)^2} \\ d=\sqrt{3^2+(-5)^2} \\ d=\sqrt{9+25} \\ d=\sqrt{34} \end{gathered}[/tex](3m - 2n)³ = (9m² -12mn + 4n²)
For this expression (3m - 2n)³ = (9m² -12mn + 4n²)
1)Let's remember the difference of two cubes
(a -b)³ = a³ -3a²b +3ab²-b³
(3m - 2n)³ = (3m)³ -3 (3m)²(-2n) +3(3m)(-2n)²-(2n)³ = 27m³ -54m²n +36mn²-8n³
27m³ -54m²n +36mn²-8n³ = 9m² -12mn + 4n²
2) Combining Like terms:
27m³ -54m²n +36mn²-8n³ -9m² +12mn+4n² =0
Since we can't get a simpler version of it. Let's keep with that.
(2,-1)(-3,5)1:2find the point that partitions the segment with the two given endpoints with the given ratio
We are given two points
A = (2, -1)
B = (-3, 5)
Ratio = 1:2
Let the ratio be P
Therefore, P is 1:2
Slope = Rise / Run
Rise = y2 - y1
Run = x2 - x1
x1 = 2, y1 = -1, x2 = -3 and y2 = 5
P = 1 / 1+ 3
P = 1/3
The horizontal distance is the same as run
Run = x2 - x1
=-3 - 2
Run = -5
Therefore we have
P x run
1/3 x -5
= -5/3
The distance between P and A on the x - axis is
-5/3 - 2
= -11/3
Rise = y2 - y1
5 - (-1)
= 5 + 1
Rise = 6
1/3 x 6
6/3 = 2
The distance between A and P on the y axis is
2 -(-1)
=2 + 1
= 3
The points are -11/3 and 3
The answer is (-11/3, 3)
5x - 2 + 10 = 20 - 32
In this case the answers is very simple. .
We must apply algebraic rules to find the solution.
5x - 2 + 10 = 20 - 32
5x = 20 - 32 + 2 - 10
5x = (20 + 2) + (- 32 - 10)
5x = 22 - 42
5x = -20
x = -20 / 5
x = -4
The answers is:
x = -4
Last year. Kareem deposited into an account that paid 4% interest per year and $6000 into an account that paid 9% interest per year. No with withdrawals were made from either account. No rounding needed What was the total interest earned at the end of 1 year? What was the percent interest for the total deposited?
Vectors u = −10i + 3j and v = −3i − 7j. What is u − v?
In order to calculate the subtraction of the vectors, we can do the following steps:
[tex]\begin{gathered} u-v\\ \\ =(-10i+3j)-(-3i-7j)\\ \\ =-10i+3j+3i+7j\\ \\ =(-10i+3i)+(3j+7j)\\ \\ =-7i+10j \end{gathered}[/tex]Therefore the correct option is the first one.
It costs $350 to repair a refrigerator compressor. Compute the QLF for losses incurred as a result of a deviation from a target setting with a nominal tolerance of 60 amps, where a 2-amp variation is acceptable. The mean squared deviation is 1/5
The Quality loss function QLF incurred as a result of a deviation from a target setting is $17.5
How to determine the QLF for the lossesQLF is acronym for quality loss function, this solved using the formula
= kv^2
where
k = constant
v = mean square deviation = 1/5
the constant k is solved by the formula
= c/T^2
where
c = cost of item = 350
T = variation acceptable = 2
= 350 / 2^2
= 87.5
QLF = kv^2\
= 87.5 * 1/5
= 17.5
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Use the formula t= ln2 over k that gives the time for a population, with growth rate k, to double, to answer the following questions. The growth model A=6e^0.001t describes the population, A, of a country in millions, t years after 2003. A. What is the country's growth rate? B. (After answering A I will assistance for question B following question A)
Answer:
A. k = 0.001
B. 693 years
Explanation:
An exponential function has the following form:
[tex]y=a\cdot e^{kt}[/tex]Where a is the initial value and k is the growth or decay rate.
So, if the equation is:
[tex]A=6e^{0.001t}[/tex]Therefore, the growth rate is 0.001.
Now, to know how long will it take the country to double its population, we can use the equation:
[tex]t=\frac{\ln 2}{k}[/tex]Where k is the growth rate. So, replacing k by 0.001, we get:
[tex]\begin{gathered} t=\frac{\ln 2}{0.001} \\ t=693.14\approx693\text{ years} \end{gathered}[/tex]Therefore, the country will double its population 693 years after 2003
Write the phrase as an algebraic expression8. the quotient of eight and a number h
the quotient of eight and a number h
we have that
quotient is a division
where
eight is the numerator and h is the denominator
so
8/h
the answer is 8/h
How many routes does this function have Y= -2x^2+12x-10
We have that the equation is equal to
[tex]-2(x-1)(x-5)[/tex]So the equation have two roots, x = 1 and x = 5.
Point P(4,-2) undergoes a translation given by (x, y) - (x+3, x-a) , followed by another translation (x, y) - (x-b, x+7) to produce the image of P”(-5,-8). Find the values of a and b and point P’.
Assuming x - a = y - a and x + 7 = y + 7
Original Point P (4, -2)
Translated to Point P' (x + 3, y - a) = (4 + 3, -2 - a) = (7, -2 - a)
Translated to next point P'' = (x - b, y + 7) = (7 - b, -2 - a + 7) = (7 - b, 5 - a) = (-5, 8)
From the above changes, we can see that 7 - b = -5 and 5 - a = 8. Therefore:
[tex]\begin{gathered} 7-b=-5 \\ 7+5=b \\ 12=b \end{gathered}[/tex][tex]\begin{gathered} 5-a=8 \\ 5-8=a \\ -3=a \end{gathered}[/tex]The value of a = -3 and b = 12.
The point P' (7, -2 - a) = (7, -2 - (-3)) = (7, 1). Point P' is at (7, 1).
To check if this is right, let's look at the original point again and its transformations.
P (4, -2) translated to (x + 3, y - a) = (4 + 3, -2 - (-3)) = (7, 1).
P' (7, 1) is then translated to ( x - b, y + 7) = (7 - 12, 1 + 7) = (-5, 8).
As mentioned in the question, P'' is indeed found at (-5, 8).