Answer:
Step-by-step explanation:
divide through by the coefficient of [tex]x^{2}[/tex]
[tex]\frac{5x^{2} }{5}[/tex] + [tex]\frac{16x}{5} + \frac{-40}{5} = \frac{8}{5}[/tex]
[tex]x^{2} +\frac{16}{5}x -8 =\frac{8}{5}[/tex]
[tex]x^{2} +\frac{16}{5} x = \frac{8}{5} +8[/tex]
[tex]x^{2} + \frac{16}{5} x =\frac{48}{5}[/tex]
Add half of the square of the coefficient of x to both sides [tex](\frac{1}{2} X \frac{16}{5} ) ^{2}[/tex]
[tex]x^{2} + \frac{16}{5}x + (\frac{1}{2} X \frac{16}{5} )^{2} =[/tex] [tex]\frac{48}{5} +(\frac{1}{2} X \frac{16}{5} )^{2}[/tex]
[tex]x^{2} +\frac{16}{5} x +(\frac{16}{10}) ^{2} =\frac{48}{5} +\frac{64}{25}[/tex]
[tex](x +\frac{16}{10})^{2} =\frac{304}{25}[/tex]
[tex]x +\frac{16}{10} =[/tex]±[tex]\sqrt{\frac{304}{25} }[/tex]
[tex]x = -\frac{16}{10}[/tex] ± [tex]\sqrt{\frac{304}{25} }[/tex]
[tex]x=-\frac{16}{10} + \sqrt{\frac{304}{25} }[/tex] or[tex]-\frac{16}{10} - \sqrt{\frac{304}{25} }[/tex]
[tex]x = 1.89[/tex] or -5.09
Granola 6 cups rolled oats 2 cups mixed nuts 1 2 cup sesame seeds 1 cup dried cranberriesWhat is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to . 1 cup dried unsweetened coconut 1 2 cup honey
Answer:
2:11
Step-by-step explanation:
6 cups rolled oats, 2 cups mixed nuts, 1 /2 cup sesame seeds, 1 cup dried cranberries, 1 cup dried unsweetened coconut, 1 /2 cup honey. What is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to .
Solution
Rolled oats= 6 cups
Mixed nuts=2 cups
Sesame seeds=1/2 cup
Cranberries= 1 cup
Dried unsweetened coconuts=1
Honey =1/2 cup
The ingredients listed above are used to make granola
Total cups of granola= Rolled oats + Mixed nuts + Sesame seeds + Cranberries + Dried unsweetened coconuts + Honey
=6 + 2 + 1/2 + 1 + 1 + 1/2
=11 cups
The ratio of cups of mixed nuts to cups of granola= mixed nuts : granola
=2:11
Answer:
2 to 11
Step-by-step explanation:
The number of girls in a mixed school is 420. If the ratio of boys to girls in the school is 3:2, how many students are in the school? *
[tex] \huge{ \bf{ \underline{ \underline{ \pink{Solution:}}}}}[/tex]
Let,
Number of boys be 3xNumber of girls be 2xThen, Total number of students = 3x + 2x = 5xIt is given that,
➙ Number of girls = 420
Then,
➙ 2x = 420
➙ x = 420/2 = 210
No. of boys = 3x = 630
Then,
➙ Number of students = 5x
➙ Number of students = 5(210)
➙ Number of students = 1050
ANSWER - 1050━━━━━━━━━━━━━━━━━━━━
Answer:
3+2=5 2x=120
Step-by-step explanation:
x=420/2=210 boy=3=630 no of students =5 5(210)=2050
The height of the sail on a boat is 7 feet less than 3 times the length of its base. If the
The area of the sail is 68 square feet, find its height and the length of the base.
Answer:
Base=8 feet
Height=17 feet
Step-by-step explanation:
Let
Base=x
Height=3x-7
Area=68 square feet
Area of the sail boat=1/2 * base * height
68 = 1/2 * x * (3x-7)
Cross product
68 * 2 =(1) * (x) * (3x-7)
136 = 3x^2 - 7x
3x^2 - 7x - 136=0
Using quadratic formula
x= -b +or- √b^2 - 4ac / 2a
= -(-7) +or- √(-7)^2 - (4)(3)(-136) / 2(3)
= 7 +or- √49 - (-1632) / 6
= 7 +or- √49+1632) / 6
= 7 +or- √1681 / 6
=7 +or- 41 /6
x= 7+41 / 6 or 7-41 / 6
=48/6 or -34/6
=8 or -17/3
Answer:
Step-by-step explanation:
Let
Base=x
Height=3x-7
Area=68 square feet
Area of the sail boat=1/2 * base * height
68 = 1/2 * x * (3x-7)
Cross product
68 * 2 =(1) * (x) * (3x-7)
136 = 3x^2 - 7x
3x^2 - 7x - 136=0
Base of the boat can't be a negative value
Therefore,
Base = x = 8 feet
Height= 3x-7
=3(8)-7
=24-7
=17 feet
Find the mean distance (○｀ 3′○)
Answer:
10,724.3 mi
Step-by-step explanation:
The mean distance travelled daily by Ling is the sum of the distance travelled each day divided by the number of days travelled so far.
Mean distance = [tex] \frac{10,150 + 10,211 + 10,424 + 10,769 + 10,884 + 11,155 + 11,477}{7} [/tex]
Mean distance = [tex] \frac{75,070}{7} = 10,724.3 mi [/tex] (approximated to nearest tenth)
what is the product of 45.and 15
Answer:
675 In other words, we find the product of 45 and 15 by simply calculating 45 times 15 which equals 675.
Answer:
The product of 45 and 15 is 675.
Step-by-step explanation:
You can do it mentally this way:
45 * 15 = 45(10 + 5) = 450 + 225 = 675.
Explain how to find the decimal approximation of an irrational square root using perfect squares.
Step-by-step explanation:
say if the irrational sqrt was the sqrt of 5. to find the approximation you would figure out what two perfect squares the sqrt of 5 lies between. which is sqrt of 4 and the sqrt of 9. then find the sqrt of those perfect squares which is 2 and 3. now you know that the sqrt of 5 will lie somewhere between 2 and 3.
Convert 100 yards into meters (1 yd = 3 ft and 1 meter = 3.28 feet)
Answer:
91.46 m
Step-by-step explanation:
3 ft 1 m
100 yards x ----------- x ------------ = 91.46 m
1 yard 3.28 ft
The required solution is 100 yard is equal to 91.46 meter.
It is required to find the required solution.
What is length?Length is defined as the measurement or extent of something from end to end. The greater of two or the greatest of three dimensions of an object. It can be measured in different units like centimeters, inches, meters, etc.
Given:
From the dimension we know that given,
1 yard = 3 feet
100 yard =3*100 feet
100 yard = 300 feet.
Also,
1 meter = 3.28feet
3.28feet= 1 meter
1 feet=1/3.28 meter
1 feet=0.304 meter
300 feet= 0.304*300 meter
300 feet= 91.46 meter
Therefore, the required solution is 100 yard is equal to 91.46 meter.
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According to Nasa, when the International Space Station (ISS) is at an altitude of 385 kilometers, it travels at about 17,178 miles per hour. After how many hours of travel will the ISS reach a star that is 1.8 lightyears away? Recall that 1 light year = 9.5 ∙ 1012 kilometers and 1 kilometer = 0.62 miles. In your final answer, include all of your calculations.
Answer:
Supposing the ISS travels at a constant speed, then use the relation,
t=space/velocityt=space/velocity
Then you will obtain,
t=1.65\cdot 10^9\ hourst=1.65⋅109 hours
between which two consecutive integers is the negative square root of 5
Answer: Between the numbers -2 and -3
Step-by-step explanation:
The negative square root of 5 will be slightly greater than 2 because the square root of 4 is 2 and 5 is greater than 2. The negative square root of 5 will not be greater than -3 because 3 squared is 9. So it has to be between -2 and -3.
Answer:
-2 and -3
Step-by-step explanation:
So in a simple way we can look at it as what is square root of positive 5.
This is between 2 and 3 but since we are looking for Negative 3, our answer is between -2 and -3
Hope this helps!
a child's toy train collection contains 5 engines, 5 red cars, 7 blue cars, and 2 cabooses. What is the probability of randomly selecting pieces to make a three-part train of engine, red car, caboose?
Answer:
25/2907Step-by-step explanation:
Probability = Expected outcome/Total outcome of events
If a child's toy train collection contains 5 engines, 5 red cars, 7 blue cars, and 2 cabooses, the total collection will be 5+5+7+2 = 19 total collection
Note that if we are choosing this parts to make part engine, his car parts will no longer be replaced. Hence this is a problem of probability without replacement
If we randomly select pieces to make a three-part train of engine, red car and caboose, this can be chosen in that order and the following ways;
Probability of choosing an engine = 5/19
Probability of choosing a red car = 5/18 (note that the total collection has reduced by 1 since we didn't replace the engine)
Probability of choosing a carboose= 2/17 (the car chosen was not replaced as well)
Therefore the probability of randomly selecting pieces to make a three-part train of engine, red car, caboose is the product of the three probability calculated above i.e 5/19 * 5/18 * 2/17 = 50/5814
= 25/2907
How many pounds are in 2 tons 1, 920 ounces?
A.4, 240 pounds
B.5,920 pounds
C.4, 120 pounds
D.02, 120 pounds
Answer:
c. 4,120 pounds
Step-by-step explanation:
2 tons = 4000 pounds
1920 ounces = 120 pounds
The amount in pounds of 2 tons 1, 920 ounces by unit conversion will be 4,120 pounds thus, option (C) is correct.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
It is known that,
1 tone = 2000 pounds
2 tons = 4000 pounds
It is also known that,
1 ounce = 0.0625 pounds
1, 920 ounces = 120 pounds.
Total = 4000 + 120 = 4, 120 pounds
Hence "The amount in pounds of 2 tons 1, 920 ounces by unit conversion will be 4,120 pounds".
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please help:) which answer represents 4.72 times 10 to the 10th power? A. 472,000,000,000 B. 4,720,000,000 C. 47,200,000,000 D. 472,000,000
Answer:
C
Step-by-step explanation:
4.72×10^10
4.72×1000000000
move the point(.) ten times to your right. after first two movements
you'll have 472 remaining 8 digits to make
47200000000
4. Describe how you can tell by looking at the graph of a function
which variable is the input variable and which is the output variable.
Answer: The variable in the vertical axis (or y-axis) is the output
The variable in the horizontal axis (or x-axis) is the input.
Step-by-step explanation:
Usually, a graph of a function y = f(x) is represented in an X-Y coordinate axis.
An X-Y coordinate axis is conformed by two perpendicular lines, one vertical (y-axis) and one horizontal (x-axis)
The vertical axis (or the y-axis) is the output, and the horizontal axis (or the x-axis) is the input.
This method will work almost always, as is standardized that the x-axis corresponds to the input, and the y-axis corresponds to the output.
If n = 2 + 6m and p = 2/n, what is the value of p when m = -1/2?
Answer:
p = - 2
Step-by-step explanation:
Given
n = 2 + 6m ← substitute m = - [tex]\frac{1}{2}[/tex] into the expression
n = 2 + 6(- [tex]\frac{1}{2}[/tex] ) = 2 - 3 = - 1
Thus
p = [tex]\frac{2}{n}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2
3/12 simplified version
Answer:
1/4
Step-by-step explanation:
divide numerator and denominator by 3
A roulette wheel has 38 slots total, 36 of which are numbered 1 through 36, and 2 green slots labeled "0" and "00." For any spin of the wheel, what is the probability of the roulette ball NOT landing on red?
Answer:
Probability (Roulette ball not landing on red) = 10 / 19
Step-by-step explanation:
Given:
Number of total slots = 38
Number of red slots = 18
Number of black slots = 18
Number of green slots = 2
Find:
Probability (Roulette ball not landing on red)
Computation:
Probability (Roulette ball not landing on red) = 1 - Probability (Roulette ball landing on red)
Probability (Roulette ball not landing on red) = 1 - (18 / 38)
Probability (Roulette ball not landing on red) = 20 / 38
Probability (Roulette ball not landing on red) = 10 / 19
In a High School, 60% of the boys play baseball and 24% of the boys play baseball and football. What is the percent of those that play football given that they
also play baseball? Record your answer and fill in the bubbles on the answer document (Enter only a number for your answer.)
Answer:
i play baseball mark me as brainliest thank my answer and rate me as a 5 because im white
Step-by-step explanation:
Can you decimal that has repeating digits after the decimal point be converted into a fraction?
Answer:
Any Rational Number can become a fraction, which is what a repeating decimal is.
Step-by-step explanation:
PLEASE HURRY Pump it Up gym's daily revenue each can be modeled by R(x) = 5x where x represents the number of customers that visit the gym each day. The gym's daily costs can be modeled by the function C(x) = 2x + 150. Find the profit function P(x) if: P(x) = R(x) - C(x)
Answer:
P(x) = 3x - 150
Step-by-step explanation:
● P(x) = R(x) - C(x)
We khow that:
● R(x) = 5x
● C(x) = 2x + 150
● P(x) = 5x -(2x+150)
● P(x) = 5x - 2x -150
● P(x) = 3x - 150
The profit function of P(x) is 3x - 150.
It is required to find profit function of P(x).
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given :
Daily revenue
R(x) = 5x where x represents the number of customers that visit the gym each day.
C(x) = 2x + 150
P(x) = R(x) - C(x)...(i)
Put the value of R(x) and C(x) in equation ..(i)
P(x) = 5x -(2x+150)
P(x) = 5x - 2x -150
P(x) = 3x - 150
Therefore, the profit function of P(x) is 3x - 150.
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What is the perimeter of the given figure?
A.19pie inches
B. 24 + 5pie inches
C. 29pie inches
D. 14 + 5pie inches
Answer:
D.
Step-by-step explanation:
The length of the unmarked side of the triangle is found by using Pythagoras:
x sqrt (10^2 - 6^2)
= sqrt 64
= 8.
The length of the curved part = 1/2 * pi * 10 = 5pi
Perimeter = 8 + 6 + 5pi
= 14 + 5pi
Answer:
D. 14 + 5π inches
Step-by-step explanation:
1. solve for the side of a triangle using Pythagorean = [tex]\sqrt{(10^2 - 6^2)}[/tex] = 8 in.
2. circumference of a half circle = πd /2 = π*10 / 2 = 5π in.
3. total perimeter = (8 + 6) + 5π = 14 + 5π
therefore, the answer is D. 14 + 5π inches
Which expression is equivalent to 4(23)?
Answer:
92
Step-by-step explanation:
Multiply 4 and 23:
4 * 23 = 92
solve for k k/6 = 4/3
Answer:
k = 8
Step-by-step explanation:
Given
[tex]\frac{k}{6}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )
3k = 24 ( divide both sides by 3 )
k = 8
I am really confused
Answer:
GHC 33.50
Step-by-step explanation:
Pens: 6.50*.15=.975
.975*20=19.50
Pencils: 4.00*.10=.40
.40*35=14
Total=19.50+14=
33.50
-84+39
Negative 84 plus 39 equals
Answer:
The answer is -45 but why are you asking such a easy question you can use your calculator or mobile to get the answer.Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------
Answer: -45~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~please help! thank you <33
Answer:
14
hope this helps!
4x-7y=8 and -2x+5y=-1
Answer:
x=11/2 and x=2
Step-by-step explanation:
i took the test
Calculate the distance between the points H=(3,-1) and E=(8,-5) in the coordinate plane. Give an exact answer (not a decimal approximation).
Answer: [tex]\sqrt{41}[/tex]
===========================================
Work Shown:
Use the distance formula.
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-1-(-5))^2+(3-8)^2}\\\\d = \sqrt{(-1+5)^2+(3-8)^2}\\\\d = \sqrt{(4)^2+(-5)^2}\\\\d = \sqrt{16+25}\\\\d = \sqrt{41}\\\\[/tex]
Or you could use the pythagorean theorem, which is how the distance formula is set up.
Add or subtract.
1.-5+ (-2)
negative 5 plus negative 2
mathematically ,-5-2=-7
Five times the sum of a number and 6 equals 8.
Answer:
Algebraic expression = 5(x+6)=8
x = -22/5
Step-by-step explanation:
Let the unknown number be x
Translate into Algebraic expression ;
[tex]5(x+6)=8[/tex]
Solve the equation
[tex]5\left(x+6\right)=8\\Divide\: both \:sides \:by \:5\\\frac{5\left(x+6\right)}{5}=\frac{8}{5}\\\\Simplify\\x+6=\frac{8}{5}\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\x+6-6=\frac{8}{5}-6\\\\\mathrm{Simplify}\\x=-\frac{22}{5}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]\Huge \boxed{5(x+6)=8}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
Let the number be x.
The sum is the result from adding two or more values together.
The sum is multiplied by 5. The result is equal to 8.
[tex]5* (x+6) =8[/tex]
[tex]5(x+6)=8[/tex]
[tex]\rule[225]{225}{2}[/tex]
The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.a. Suppose you learn that 5% of American households spend less than $1000 for dailytransportation. What is the standard deviation of the amount spent?b. What is the probability that a household spends between $4000 and $6000?c. What is the range of spending for the 3% of households with the highest daily transportationcost?
Answer:
(a) The standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.
Step-by-step explanation:
We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.
(a) It is stated that 5% of American households spend less than $1000 for daily transportation.
Let X = the amount spent on daily transportation
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312
[tex]\sigma[/tex] = standard deviation
Now, 5% of American households spend less than $1000 on daily transportation means that;
P(X < $1,000) = 0.05
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05
In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;
[tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]
[tex]\sigma=\frac{-\$5312}{-1.645}[/tex] = 3229.18
So, the standard deviation of the amount spent is $3229.18.
(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)
P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)
P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)
= 1 - 0.5359 = 0.4641
P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex]
= 1 - 0.7642 = 0.2358
Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.
(c) The range of spending for 3% of households with the highest daily transportation cost is given by;
P(X > x) = 0.03 {where x is the required range}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03
In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;
[tex]\frac{x-\$6312}{3229.18}=1.88[/tex]
[tex]{x-\$6312}=1.88\times 3229.18[/tex]
x = $6312 + 6070.86 = $12382.86
So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.