Proportions are created when we set two ratios equal to each other. They help us convert between rates.
Example:
[tex]\dfrac{4\hspace{3}stars}{8\hspace{3}hearts}=\dfrac{6\hspace{3}stars}{x\hspace{3}hearts}[/tex]⇒ In this example, we are solving for x.
⇒ Question example: For every 4 stars, there are 8 hearts. How many hearts will there be for 6 stars?
To solve proportions, we can cross multiply. This means multiplying the numerator of one fraction by the denominator of the other fraction.:
[tex]\dfrac{4\hspace{3}stars}{8\hspace{3}hearts}=\dfrac{6\hspace{3}stars}{x\hspace{3}hearts}\\\\4x=6*8[/tex]
Solving the QuestionWe're given:
8 minutes of jogging = 96 calories burned14 minutes of jogging = ? calories burnedSet up a proportion:
[tex]\dfrac{8\hspace{3}minutes}{96\hspace{3}calories}= \dfrac{14\hspace{3}minutes}{x\hspace{3}calories}[/tex]
⇒ Let x be equal to the number of calories the jogger would burn in 14 minutes.
Cross multiply:
[tex]8x=14*96\\8x=1344\\x=168[/tex]
AnswerTherefore, the jogger would burn 168 calories in 14 minutes of jogging.
What's the circumference of a circle with a diameter of 7 feet Use 3.14 for pi.
Answer:
21.98
Step-by-step explanation:
Formula for Circumference of a Circle:
C=2πr
1. We find r, which is basically the diameter divided by 2, aka half of the diameter:
d/2 = r
Fill in:
7/2 = r
r = 3.5
2. We fill in the Formula:
C = 2πr
C = 2(3.14)(3.5)
3. Multiply it all
3.14 x 3.5 = 10.99
10.99 x 2 = 21.98
Hence, the circumference of the circle is 21.98.
write balanced chemical equation for the process of photosynthesis giving the physical state of all the substances involved in the conditions of the reaction
Answer:
The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.
Step-by-step explanation:
help please
1.) Write in words the decimal 123.0047.
Write in fractional notation and simplify.
2.) 0.91 3.) 2.769
Write in decimal notation.
4.) 74 over 1000 5.) 37047 over 10000 6.) 756 9 over 100
Which decimal number is greater?
7.) 0.07 or 0.162 8.) 8.049 or 8.0094
Round the next decimal number, 5.6783, to the indicated decimal place.
9.) To the Unit 10.) To the Thousandth 11.) To the Tenth
Rewrite in simplest radical form
X^5/6 / X^1/6
Answer:
[tex]\sqrt[3]{x^2}[/tex]
Step-by-step explanation:
The rule of exponents says that we must use subtraction for [tex]\frac{5}{6}[/tex] and [tex]\frac{1}{6}[/tex] since we are dividing.
Thus, we have [tex]\frac{x^\frac{5}{6} }{x^\frac{1}{6} }\\\\\frac{5}{6}-\frac{1}{6}=x^\frac{4}{6}=x^\frac{2}{3}[/tex]
When dealing with fractions and radicals, we can find the simplest radical form by using the saying [tex]\frac{exponent}{index}[/tex]
Thus we have [tex]\sqrt[3]{x^2}[/tex]
if an item regularly cost d dollars and is discounted 12 percent, which of the following represents the discounted price?
If an item usually costs d dollars a 12% discount can be represented as 0.88d.
What is a discount?This refers to a deduction in the regular price of a product or service that is usually represented using a percentage.
How can the discounted price be represented?Considering 12% is being deducted from 100% (100-12 = 88). The final price can be represented as 0.88d or 0.88 multiplied by the regular price (d).
For example, if the regular price is $100, 0.88 x 100 = $88.
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Simplify and write the trigonometric expression without any fractions: tan(u)+cot(u)
Answer:
[tex]\csc(u).sec(u)[/tex]
Step-by-step explanation:
[tex] \tan(u)+ \cot(u) \\ \\ = \frac{ \sin(u)}{ \cos(u)} + \frac{ \cos(u)}{ \sin(u)} \\ \\ = \frac{ { \sin}^{2} (u) + {\cos}^{2} (u)}{ \sin(u). \cos(u)} \\ \\ = \frac{1}{ \sin(u). \cos(u)} \\ ( \because \: { \sin}^{2} ( \theta) + {\cos}^{2} ( \theta) = 1) \\ \\ = \frac{1}{\sin(u)} \times \frac{1}{\cos(u)} \\ \\ = \csc(u).sec(u) \\ \\ \implies \: \purple{ \bold{ \tan(u)+ \cot(u) = \csc(u).sec(u)}}[/tex]
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
(Sin²u + Cos²u) = 1
The final expression of the trigonometric expression tan(u) + cot(u) is
Cosec(u) x Sec(u)
What are trigonometric identities?
There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
Tan (u) + Cot (u)
We know that,
Tan x = sin x / cos x
Cot x = cos x / sin x
Now,
Tan (u) + Cot (u)
= {Sin (u) / Cos (u) + Cos (u)}/ Sin (u)
Simplify by forming into a fraction.
= (Sin²u + Cos²u) / Sin(u)Cos(u)
[ sin² + cos² = 1 ]
So,
(Sin²u + Cos²u) = 1
= 1 / Sin(u)Cos(u)
= 1/Sin(u) x 1/Cos(u)
= Cosec(u) x Sec(u)
Thus,
The final expression of the trigonometric expression tan(u) + cot(u) is
Cosec(u) x Sec(u)
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give me list of letter arrangement and number arangement
Answer:
what the heck question is this
Find the area of the parallelogram.
3 cm
5 cm
Answer:
Area = Base ×Height
Step-by-step explanation:
Area = Base × Height
Area = 3cm × 5cm
Area = 15cm
Area of the parrallelogram is 15cm
[tex] \rm \frac{ {10}^5 }{ {e}^{ \sqrt{e} } } \left( \int^{1}_0 {e}^{ \sqrt[]{ {e}^{x} } } \: dx + 2 \int_{e}^{ {e}^{ \sqrt{e} } } ln( ln(x) ) \: dx\right) \\ [/tex]
In the first integral, substitute [tex]x \to e^{\sqrt{e^x}}[/tex]:
[tex]\displaystyle I = \int_0^1 e^{\sqrt{e^x}} \, dx = 2 \int_e^{e^{\sqrt e}} \frac{dx}{\ln(x)}[/tex]
In the second integral, integrate by parts:
[tex]\displaystyle J = \int_e^{e^{\sqrt e}} \ln(\ln(x)) \, dx = \dfrac12 e^{\sqrt e} - \int_e^{e^{\sqrt e}} \frac{dx}{\ln(x)}[/tex]
It follows that
[tex]\dfrac{10^5}{e^{\sqrt e}}(I+2J) = \dfrac{10^5}{e^{\sqrt e}} \times e^{\sqrt e} = \boxed{10^5}[/tex]
I need help with this question please
Answer:
Step-by-step explanation:
As ABCD is a rectangle, ∠A = 90°.
Diagonal BD will be the hypotenuse.
[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]
Length = AB = 33.8 cm
[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]
Width = 25.5 cm
An airline is planning its staffing needs for the next year. If a new route is approved, it will hire 837 new employees. If a new route is not granted, it will hire only 199 new employees. If the probability that a new route will be granted is 0.37, what is the expected number of new employees to be hired by the airline?
Considering a discrete distribution, it is found that the expected number of new employees to be hired by the airline is of 446.16.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, considering the situation described in the text, the distribution is given by:
P(X = 837) = 0.37.P(X = 199) = 0.63.Hence, the expected value is given by:
E(X) = 0.37(867) + 0.63(199) = 446.16.
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two-digit natural numbers are formed, with replacement, from 0 through 9. how many two-digit odd numbers are possible?
Let's solve this step by step:
The first digit has 9 choices --> 1 through 9The second digit has 10 choices --> 0 through 9*the first digit cannot have '0' as its first digit since it would make the
number one-digit
Total Choice: 9 choices * 10 choices = 90 choices
Hope that helps!
What expression is equivalent to 12x^4/4x^16 helpppp
Answer: 48x/64
Work (assuming ^ is multiplication):
12x^4/4x^16
12x ^ 4x = 48x
4 ^ 16 = 64
Change 75m to decimeters
Answer:
750 decimeters
Step-by-step explanation:
1 meter is equal to 10 decimeters.
so 75 times 10 equals your answer: 750 decimeters
Hope that helps!
PLEASE HELP! Match the steps to find the equation of the parabola with focus (-1, -8) and directrix y = - 12.
Answer:
3,2,1,6,5,4
Step-by-step explanation:
Hope this helps!!!
All the correct steps to find the equation of the parabola with focus (-1, -8) and directrix y = - 12 are,
1. 2p + (- 8) = - 12 Find p
2. Since the focus is at - 1, Find the x - coordinates for the vertex.
then, vertex is at - 1
3. y = - 8 - 2 Find the x - coordinates for the vertex.
4. (- 1, - 10) Vertex coordinates
5. (x + 1)² = 4(-2) (y+10) Write the formula for the parabola.
6. (x + 1)² = -8 (y+10) Simplify the formula.
Given that,
In a parabola,
Focus = (-1 , - 8)
And, Directrix =; y = - 12
The standard equation of a parabola is,
[tex]y = - p (x - h)^2 + k[/tex]
Where, (h, k) is the vertex of the parabola.
Now, the Statement with reason to find the equation of a parabola is,
Statement Reason
1. 2p + (- 8) = - 12 Find p
p = - 2
2. Since the focus is at - 1, Find the x - coordinates for the vertex.
then, vertex is at - 1
3. y = - 8 - 2 Find the x - coordinates for the vertex.
y = - 10
4. (- 1, - 10) Vertex coordinates
5. (x + 1)² = 4(-2) (y+10) Write the formula for the parabola.
6. (x + 1)² = -8 (y+10) Simplify the formula.
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Help!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
53
Step-by-step explanation:
[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]
5/6 of a number is 65.
Find the number.
Answer:
78 is the number
Step-by-step explanation:
(65*6)÷5 = 78.
5/6 of a number is 65.
And the number is 78.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A phrase: 5/6 of a number is 65.
To find the number:
Let the number be n.
Applying multiplication operation,
5/6 of n is 65.
(5/6)n = 65.
Applying cross multiplication,
n = 65 x 6/5
n = 390/5
n = 78.
Therefore, the number is 78.
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What is the value if X? and how to find exterior angles.
The movie theater sold 50 buckets of popcorn last Wednesday. 60 people watched movies that day, and 40 of those people ate popcorn. Do you see a fraction that you could use to create a division problem?
Answer:
70
Step-by-step explanation:
60/40Ⅹ50=70
I hope this helps
CAN SOMEBODY HELP ME SOLVE THIS EQUATION
Examine the equation and solution method shown below. Indentify the error and then solve the equation using a valid solution method.
1. Find and explain the error in the solution method.
2. Solve the equation 3(3x+6+x)=1 using a valid solution method.
3. Explain each step in your solution method. Why is your method valid?
Pls Help. 100 points
3 ( 3x + 6 + x ) = 1
Step 1, apply distributive method.
9x + 18 + 3x = 1
Step 2, simplify the following
12x + 18 = 1
Step 3, Change side
12x = -17
Final answer
x = -17/12
The error/mistake was in step 2 where [ 9x +3x = 12x ]
Recheck the answer
3 ( 3x + 6 + x ) = 1
3 ( 3(-17/12) + 6 + -17/12 ) = 1
1 = 1
Hence proved our solution is correct.
Answer:
Question 1
The error is in step 2. They have subtracted [tex]3x[/tex] from the left side of the equation, yet only subtracted 3 from the right side.
Questions 2 & 3
Solve:
[tex]3(3x + 6 + x) = 1[/tex]
Apply the distributive law [tex]a(b + c) = ab + ac[/tex] :
[tex]\implies 9x + 18 + 3x = 1[/tex]
Collect and combine like terms:
[tex]\implies 9x + 3x+ 18 = 1[/tex]
[tex]\implies 12x + 18 = 1[/tex]
Subtract 18 from both sides:
[tex]\implies 12x + 18 - 18 = 1 - 18[/tex]
[tex]\implies 12x = -17[/tex]
Divide both sides by 12:
[tex]\implies \dfrac{12x}{12}=-\dfrac{17}{12}[/tex]
[tex]\implies x=-\dfrac{17}{12}[/tex]
Easy math 3 pictures
Answer:
1. 52yard²
2. $54
3. 30.5
Step-by-step explanation:
1. area of square shape = lenght x breadth
= 4 * 4
= 16
area of rectangle shape = lenght x breadth
= 9 * 4 = 36
tatal area = 16 + 36
= 52yard²
2. let the cost = c
thus 9% * c = 4.86
c = 4.86 * 90%
c = $54
3.area of length traingle=1\2 *base * height
= 1\2 * 3 * 7
= 10.5
area of right quadrilateral= legnth*bredth
= 4 * 3
= 12
area of right traingle = 1\2 * base * height
= 1\2 * 4 * 4
= 8
total area of shape = 10.5+12+8
= 30.5
DO MARK BRAINLIEST
Answer:52 54 30.5
Step-by-step explanation:
what is 4 1/8 x 1/4 equal to?
Answer:1.03125
Step-by-step explanation:
(a) A color page prints 20 pages in 7 minutes. How many pages does it print per minute?
(b) it takes 55 pounds of seed to completely plant a 7- acre field. How many acres can be planted per pound of seed?
If needed round to nearest hundredth.
Answer:
A. 20 / 7 = 3 (or 2.85)
B. 55 / 7 = 8 (or 7.85)
Brainliest is appreciated!
_ daintysword.mp4
Answer:
A.3
B.8
Step-by-step explanation:
this is the answer
Find the LCM of 20, 35 & 50.
Answer:
Answer: LCM of 20,35 and 50 is 1400
Step-by-step explanation:
pls help me in this math problem
Answer:
cUse the following equation
Step-by-step explanation:
Because of the way these angles are positioned, they must be equal to 180 together
(2x + 5) + (0.5x + 150) = 180
2.5x + 155 = 180
- 155 - 155
2.5x = 25
2.5x/2.5 = 25/2.5
x = 10
Put x into the original equations and solve
Find the equation of a line that contains the points (2,1) and (8,7). Write the equation in slope-intercept form.
Answer:
y = x - 1
Step-by-step explanation:
First find the slope. Subtract the y's and put that on top of a fraction. Then subtract x's and put that on the bottom. Simplify if possible.
7-1 is 6 goes on top.
8-2 is 6 goes below.
6/6 is 1 when simplified.
Slope is 1.
Slope-intercept form is y = mx + b.
m is slope, so fill that in.
y = (1)x + b
Now we need to find b.
Use either one of the given points; they will give you the same answer no matter which one you choose. Let's use (2,1) because smaller numbers.
y is 1 and x is 2.
y= (1)x + b
1 = (1)2 + b
1 = 2 + b
-1 = b
Now fill in both m and b. Leave x and y as letters (variables)
y = (1)x + -1
Final answer:
y = x - 1
Martina is ordering an ice cream dessert. She must order a size and a flavor of ice cream. There are 4 sizes and 2 flavors to choose from. How many different
cream desserts could she order?
Answer: 8.
Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large. There are 2 flavors, so let's say that the flavors are chocolate and vanilla. The possible combinations are below:
Small chocolateMedium chocolateLarge chocolateExtra large chocolateSmall vanillaMedium vanillaLarge vanillaExtra large vanillaAs you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.
Have a great day! :)
2. A student wanted to find the height h of a statue of a pineapple
in Nambour, Australia. She measured the pineapple's shadow
and her own shadow. The student's height is 5 feet 4 inches.
What is the height of the pineapple?
Using proportions, it is found that the height of the pineapple is of 280 inches = 23 ft 4 in.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, considering that a feet has 12 inches, the measures in inches, and applying the similarity of triangles, the proportions are as follows:
[tex]\frac{h}{64} = \frac{105}{24}[/tex]
Applying cross multiplication:
24h = 64 x 105
h = 64 x 105/24
h = 280
The height of the pineapple is of 280 inches = 23 ft 4 in.
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A laptop computer is purchased for $2350. After each year, the resale value decreases by 35% . What will the resale value be after 4 years?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2350\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=years\dotfill &4\\ \end{cases} \\\\\\ A=2350(1 - 0.035)^{4}\implies A=2350(0.965)^4\implies A\approx 2037.87[/tex]