Answer:
∠ I = 60°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan I = \(\frac{opposite}{adjacent }\) = \(\frac{HJ}{IJ}\) = \(\frac{3\sqrt{30} }{3\sqrt{10} }\) = \(\frac{\sqrt{30} }{\sqrt{10} }\) = \(\sqrt{\frac{30}{10} }\) = \(\sqrt{3}\) , then
∠ I = \(tan^{-1}\) (\(\sqrt{3}\) ) = 60°
Answer:
60°
Step-by-step explanation:
You want the measure of angle I in right triangle HIJ, given that the side opposite is 3√30 and the side adjacent is 3√10.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
In this triangle, ...
tan(I) = (3√30)/(3√10) = √(30/10) = √3
Then the angle is ...
I = arctan(√3) = 60°
The measure of angle I is 60°.
__
Additional comment
The trig functions of 30° and 45° and their relationships to each other are based on the side relationships of the two "special" right triangles:
30°-60°-90° triangle has side ratios 1 : √3 : 2
45°-45°-90° triangle has side ratios 1 : 1 : √2
Of course, side lengths are in the same order as their opposite angles.
The mnemonic SOH CAH TOA can help you remember the necessary relationships:
Sin = Opposite/HypotenuseCos = Adjacent/HypotenuseTan = Opposite/AdjacentSimplify the linear expression.
−2x+3(−5x+1)
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
Let's simply the given expression ~
\( - 2x + 3( - 5x + 1)\)\( - 2x - 15x + 3\)\( - 17x + 3\)name the values of digit in each number 2s in 2,265
Given the number 2,265
The value of each digit beginning from the left is given below:
• Place value of 2 = 2 Thousand
,• Place value of 2 = 2 Hundred
,• Place value of 6 = 6 Tens
,• Place value of 5 = 5 units
Therefore, the place value of the 2s are:
• Place value of 2 = 2 Thousand
,• Place value of 2 = 2 Hundred
Can someone plz help plzzzzz
J. Lo’s Clothiers has forecast credit sales for the fourth quarter of the year: September (actual) $ 70,000 Fourth Quarter October $ 60,000 November 55,000 December 80,000 Experience has shown that 30 percent of sales are collected in the month of sale, 60 percent are collected in the following month, and 10 percent are never collected. Prepare a schedule of cash receipts for J. Lo’s Clothiers covering the fourth quarter (October through December)
The preparation of a schedule of cash receipts for J. Lo's Clothiers covering the fourth quarter from October through December is as follows:
Fourth Quarter Cash Receipts October November December
Month of sale (30%) $18,000 $16,500 $24,000
Following month (60%) 42,000 36,000 33,000
Total cash receipts $60,000 $52,500 $57,000
What is a schedule of cash receipts?A cash receipts schedule is a financial document that specifies how a business expects to collect cash from its credit sales customers based on the sales budget.
The cash collection formula can be established using the company's past collection patterns.
September
Credit Sales (actual) $ 70,000
Fourth Quarter October November December
Credit Sales $60,000 $55,000 $80,000
Cash Receipts:
Month of sale (30%) $18,000 $16,500 $24,000
Following month (60%) 42,000 36,000 33,000
Total cash receipts $60,000 $52,500 $57,000
Cash receipts in October = $60,000 ($60,000 x 30% + $70,000 x 60%)
Cash receipts in November = $52,500 ($55,000 x 30% + $60,000 x 60%)
Cash receipts in December = $57,000 ($80,000 x 30% + $55,000 x 60%)
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Amelia grabbed 50% of the M&M's from a bowl. Then, Jess took 50% of what was left. Dominick takes 50% of the remaining M&M's. There were 3 left. How many M&M's were in the bowl before Amelia arrived.
The number of M&M's that were in the bowl before Amelia arrived is; 12
How to solve Percentage problems?Let the original amount in the bowl be x. Thus;
If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x
Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x
Now, we are told that there were finally 3 left after all the deductions. Thus;
0.25x = 3
x = 3/0.25
x = 12
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what is 999.09344471 rounded to the nearest square kilometer?
The nearest kilometers to 999.09344471 km is 1000 km.
Given value is 999.09344471 Km.
We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.
Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only the value after the decimal (934) is to be rounded off which is (900).
So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.
Again rounding off 999.900 km to nearest km so it becomes 1000 km.
The nearest kilometers to 999.09344471 km is 1000 km.
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B cubed equals 8. Solve for b
Answer:
b=2
Step-by-step explanation:
You are given:
\(b^{3} =8\)
What does \(b^3\) mean?
It is simply, b·b·b
Therefore:
b·b·b=8
What number could be multiplied by itself three times and equal 8?
...
2
Yay! That's great!
-8b=-14 solve for b please
Step-by-step explanation:
-8b =-14
8b= 14
b=14÷8
b=7÷4 or 1.74
hope it helps
Answer:
b= 7/4
Step-by-step explanation:
− 8 = − 1 4 -8b=-14 −8b=−14 − 8 − 8 = − 1 4 − 8 \frac{-8b}{{\color{#c92786 {-8}}}=\frac{-14}{{\color{#c92786}{-8}}} −8−8b=−8−14 2
=7/4 b=\frac{7}{4} b=47
Solution = 7/4
Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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1. Yale economist Robert J. Shiller and Wellesley economist Karl Case created the Case-Shiller
index of American housing prices that tracks the value of housing back to 1890 in consistent
terms, factoring out the effects of inflation. The 1890 benchmark is 100 on the chart. If a
standard house sold in 1890 for $100,000 (inflation-adjusted to today's dollars), an equivalent
house would have sold for $66,000 in 1920 (66 on the index scale) and $220,000 in 2006 (220 on
the index scale).
Use the following graph, based on the Case-Shiller index, to write a 60-second summary about
home values in the United States since 1890. You can use the Internet to find the current value
of homes and see if these projections are accurate.
A History of Home Values
130
120
110
100
90
80
70
60
PROJECTION
WORLD
GREAT WORLD
WARI DEPRESSION WAR II
for
1890
1900
1910
1920
1930
1940
1950
CURRENT JULY 2006
BOOM
1970'S 1980'S
BOOM BOOM
M
200
190
180
170
160
150
140
130
120
110
100
According to the chart, homes in the United States have fluctuated between $90,000 and $130,000 most of the time between 1890 and 2010 and then rise to more than $200,000.
What does the graph show?The graph shows the changes in the value of homes in the United States from the year 1890 to the year 2010. An important aspect of this graph is the influence that international events such as the world wars, the great depression, the boom of the 70s and 80s and the great boom.
How do home prices change?According to the graph, the price of houses varies as follows:
In 1890 it starts with a standard value of $100,000.Between 1890 and 1900 it has had two moments of increase in which it reached prices of 125,000 and 110,000. On the other hand, in 1900 it reaches the lowest point of this period with 90,000.Between 1900 and 1910 it peaks at 110,000, but closes the decade with a price of 95,000.Between 1910 and 1920, the effects of the First World War caused its value to fall to 65,000.Between 1920 and 1930 the Great Depression causes prices to not exceed 80,000 and closes the decade with a value of 75,000.Between 1930 and 1940 prices increase until reaching 80,000 at the end of the decade.Between 1940 and 1950 the effects of World War II cause prices to fall again to 70,000. However, the second half of the decade marks a recovery that reaches 110,000.Between 1950 and 1960 prices increase in the middle of the decade but close the period at 110,000.Between 1960 and 1970 prices remain stable. However, they close the decade with a minimal decrease.Between 1970 and 1980 there is a significant increase that raises prices to 120,000 at the end of the decade.Between 1980 and 1990 prices fall again in the middle of the decade to 105,000 but at the end of the period they exceed 120,000.Between 1990 and 2000 prices fall below 110,000.Between 2000 and 2010 prices increase exorbitantly and reaches more than 200,000.Learn more about house prices in: https://brainly.com/question/17021793
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write 16.76 correct to the nearest whole number
Answer:
17
Step-by-step explanation:
because they are both above 5 so add 1
what is the solution to the equation below? sqrt 2-3x / sqrt 4x =2
The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.
To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.
After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.
However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.
Therefore, this is the solution to the equation.
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Graph the equation y=−3x−4
Answer:
Look Down
Step-by-step explanation:
Which of the following is not true about reflections
Answer:
The image faces the same direction as the pre-image.
Step-by-step explanation:
These are TRUE statements
*An image created by a reflection will always be congruent to its pre-image.
*Corresponding angles and segments are always congruent in a reflection of a figure.
*Reflections can only be constructed across horizontal or vertical lines.
*Reflections may change the size of a pre-image
Hope that helps!
Can some help with this and maybe explain
Answer:
Step-by-step explanation:
81 = m/9
Divide both sides by 9
9 = m
h ÷ 3 = 12
h = 12/3 = 4
In this way you have to solve the other questions
Determine if the statement is true or false. A system in echelon form can have more variables than equations. True False
Answer:
True.
Step-by-step explanation:
A system of a mathematical expression such as a matrix is said to be in echelon form when it has many variables.
There are two (2) forms of echelon matrices and these includes;
I. Reduced row echelon form (RREF)
II. Row echelon form (REF)
Hence, a system in echelon form can have more variables than equations.
\(\left[\begin{array}{ccc}1&2&3\\0&0&1\\0&7&5\\0&0&0\end{array}\right]\)
Considering only the values of α and β for which cos(α−β)cosαcosβ is defined, which of the following expressions is equivalent to cos(α−β)cosαcosβ?
Select the correct answer below:
tanα−tanβ
1+tanαtanβ
cotαcotβ−1
cotα+cotβ
According to the given condition, the correct expressions is:
cotαcotβ−1
What is trigonometric equations?Trigonometric equations are mathematical equations that involve trigonometric functions, such as sine, cosine, tangent, cotangent, secant, or cosecant, and their variables. Trigonometric equations typically involve finding the values of the unknowns that satisfy the given equation, subject to certain restrictions or conditions on the domain of the trigonometric functions.
According to the given information:
Using trigonometric identities, we can simplify the expression cos(α−β)cosαcosβ:
cos(α−β)cosαcosβ = cos(α−β) * (cosα * cosβ)
Next, we can use the identity cos(α−β) = cosαcosβ + sinαsinβ to substitute into the expression:
cos(α−β)cosαcosβ = (cosαcosβ + sinαsinβ) * (cosα * cosβ)
Now, we can distribute and simplify:
cos(α−β)cosαcosβ = cosα² * cosβ² + sinαsinβ * cosα * cosβ
Finally, using the identity cotα = 1/tanα, we can rewrite the expression as:
cos(α−β)cosαcosβ = cotαcotβ - 1
So, the equivalent expression is cotαcotβ - 1.
Therefore, according to the given condition. The correct answer is:
cotαcotβ−1
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In the diagram, the parallel lines are cut by transversal BC−→−.If BD−→− bisects ∠ABC and m∠3 = 80, what is m∠ABD?
The value of m ∠ABD will be;
⇒ ∠ ABD = 50°
What are Parallel lines?Parallel lines are those lines that are equidistance from each other and never intersect each other.
Given that;
In the diagram, the parallel lines are cut by transversal BC.
And, BD bisects ∠ABC and m∠3 = 80.
Now,
Since, The parallel lines are cut by transversal BC.
Hence, We get;
⇒ ∠ 3 + ∠ 2 = 180°
⇒ 80° + ∠ 2 = 180°
⇒ ∠ 2 = 180 - 80
⇒ ∠ 2 = 100
And, We have;
⇒ ∠ 2 = ∠ ABC
⇒ ∠ ABC = 100°
Since, BD bisects ∠ABC.
Hence, We get;
⇒ ∠ ABD = 100 / 2
⇒ ∠ ABD = 50°
Thus, The value of m ∠ABD = 50°
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Which expression is equivalent to 8x - 12y + 32
Answer:
C
-16(0.5x-0.75y+2)
Step-by-step explanation:
I got it right on edge 2022 Hope it helps <3
Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha’s songs were played on 2 more commercials than movies, and her total earnings on the royalties from all the commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha’s songs were played. Define the variables that you use to write the system
The equations that Nakeishia can use to determine the number of commercials and the number of movies on which Nakeisha’s songs were played include:
30m + 110(m + 2) = 760
How to illustrate the information?Let the movies be represented by m
Since Nakeisha’s songs were played on 2 more commercials than movies, this will be m + 2.
Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. This will be:
30m + 110(m + 2) = 760
This represents the equation.
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need some help thanks ;)
Answer:
137
Step-by-step explanation:
sum of angle in a circle = 360°
105 + 118 + x = 360
223 + x = 360
x = 360 - 223
x = 137
The sample space, S, of a coin being tossed three times is shown below, where H and T denote the coin landing on heads and tails respectively.
Answer:
The probability distribution for the number of heads occurring in three coin tosses are P(X1) = 1, P(X2)= 2/3, P(X3)= 2/3, P(X4)= 1/3, P(X5)= 2/3, P(X6)= 1/3, P(X7)= 1/3 and P(X8)= 0
Step-by-step explanation:
The question is incomplete. Here is the complete question;
The sample space, S, of a coin being tossed three times is shown below, where Hand T denote the coin
landing on heads and tails respectively.
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let X = the number of times the coin comes up heads. What is the probability distribution for the number of heads occurring in three coin tosses?
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome/total outcome of event
From the question given, the total number of sample space will be our total outcome during each toss = 3
If X is the number of times the coin comes up heads, the number of times the coin turn up all heads will be the expected outcome during each throw.
Probability distribution P(Xi)= \(\frac{n(Xi)}{n(S)}\)
Xi is the probability that the head turns up at each throw.
n(Xi) is the expected outcome during each toss
n(S) is the total outcome during each toss
During the first throw, the head turns up three times (HHH), the probability that heads turns up ia 3/3 = 1
P(X1) = 1
During the second, third and fifth throw, the head turns up two times, the probability that heads turns up during this times will be 2/3
P(X2)= 2/3
P(X3)= 2/3
P(X5)= 2/3
During the fourth, sixth and seventh throw, the head turns up just once, the probability that heads turns up during this times will be 1/3
P(X4)= 1/3
P(X6)= 1/3
P(X7)= 1/3
Since no head turns up during the eight throw, the probability that heads turns up during this time will be 0/3 which is 0.
P(X8)= 0
The probability distribution for the number of heads occurring in three coin tosses are P(X1) = 1, P(X2)= 2/3, P(X3)= 2/3, P(X4)= 1/3, P(X5)= 2/3, P(X6)= 1/3, P(X7)= 1/3 and P(X8)= 0
Answer:
The guy who answered on top meant B if you didn't understand what he said
Step-by-step explanation:
:)
Un viajero ha recorrido la tercera parte de su trayecto y sabe que si cubre 65 km más completa la mitad del recorrido. Determine la distancia recorrida.
The travelled distance of the traveller is equal to 195 kilometers.
How to find the travelled distance by a traveller
According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:
x = d / 3
x + 65 = d / 2
Where:
d - Travelled distance, in kilometers.x - Initial travelled distance, in kilometers.Now we proceed to determine the travelled distance:
d / 3 + 65 = d / 2
d / 2 - d / 3 = 65
3 · d - d = 390
2 · d = 390
d = 195
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Match the expected time interval (in seconds) between the beginning of one stimulus and the beginning of the next to the correct frequency in Hz, Do the math using the formula 1/Hz = seconds where Hz = cycles/s 1 Hz [Choose) 4 Hz Choose 10 Hz [Choose 20 Hz Choose
The beginning of one stimulus and the beginning of the next to the correct frequency in Hz is 0.25, 1, 2.5 and 5 seconds.
In the field of science and engineering, frequency is a vital concept that helps in understanding many phenomena. It is the measure of the number of cycles that occur per second in a repeating waveform. The unit of frequency is Hertz (Hz).
The frequency of a waveform represents the number of cycles that occur per second. So, if we want to find the time interval between two stimuli, we can use the formula 1/Hz = seconds. This formula helps us to calculate the time interval between two stimuli.
Similarly, if we have a waveform with a frequency of 1 Hz, then the time interval between two stimuli would be 1/1 = 1 second. This means that every 1 second, a new stimulus is generated in the waveform.
In this exercise, we need to match the expected time interval between two stimuli to their corresponding frequencies.
If the time interval is 0.25 seconds, then the corresponding frequency would be 1 Hz (0.25/0.25 = 1 Hz).
If the time interval is 1 seconds, then the corresponding frequency would be 4 Hz (1/0.25 = 4 Hz).
If the time interval is 2.5 seconds, then the corresponding frequency would be 10 Hz (2.5/0.25 = 10 Hz).
If the time interval is 5 seconds, then the corresponding frequency would be 20 Hz (5/0.25 = 20 Hz)
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Show Work! A warehouse worker shipped 289 boxes of notebooks. Each box contained 36 notebooks. What was the total number of notebooks shipped?
(A) 2, 601
(B) 9, 404
(C) 10, 404
(D) 10, 413
Answer:
(c) 10, 404.
Step-by-step explanation:
Step 1.
To multiply 289 by 36, set them up as shown by arranging the two numbers in columns. We usually put the number with the smaller number of digits at the bottom.
Step 2.
Firstly, work out 6 × 289. The smaller figures in green are the tens figures carried over. Working from right to left:
6 × 9 = 54
Put the 4 in the appropriate column and carry the 5.
6 × 8 + 5(carried) = 53
Put the 3 in the appropriate column and carry the 5.
6 × 2 + 5(carried) = 17
Put the 7 in the appropriate column and carry the 1.
Step 3.
Lastly, work out 30 × 289.
This can be written as 3 × 289 × 10.
Because we are multiplying by 10, we place 1 zero to the right and then work out 3 × 289.
3 × 9 = 27
Put the 7 in the appropriate column and carry the 2.
3 × 8 + 2(carried) = 26
Put the 6 in the appropriate column and carry the 2.
3 × 2 + 2(carried) = 8
Step 4. Finally, the 2 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.
0 + 4 = 4
7 + 3 = 10
Put the 0 in the appropriate column and carry the 1.
6 + 7 + 1(carried) = 14
Put the 4 in the appropriate column and carry the 1.
8 + 1 + 1(carried) = 10
Put the 0 in the appropriate column and carry the 1.
1 (carried) = 1
So: 289 × 36 = 10404
Mathematics done on paper should look something like this; ( Did the best I can on PC)
2 8 9
................. 3....6....×
1 7 3 4
1 5 5
8 6 7 0
....... 2......2.........
1 0 4 0 4
1 1 1
Hope this helped!
Suppose that $6000 is placed in a savings account at an annual rate of 4%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the account to grow to $8670?
The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.
Given the amount of money that is the principal = $6000
Rate = 4% compounded quarterly.
Time = t
Amount = $8670
Now we know that the amount is calculated by the formula:
A = P(1+r/4)ⁿ
8670 = 6000(1+0.01)ⁿ
Hence
log 1.445 = n log 1.01
or, n = 36.99
Number of years = 36.99 / 4 = 9.24 years.
The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.
If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.
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A system of inequalities is shown.
The graph shows a dashed upward opening parabola with a vertex at negative 1 comma negative 4, with shading inside the parabola. It also shows a dashed line passing through the points negative 2 comma negative 1 and 0 comma 3, with shading above the line.
Which system is represented in the graph?
y > x2 + 2x – 3
y > 2x + 3
y < x2 + 2x – 3
y < –2x + 3
y ≥ x2 + 2x – 3
y ≤ 2x + 3
y > x2 + 2x – 3
y < –3x + 4
Because of this, the right response is (d) y > x² + 2x - 3 and y -3x + 4.
What exactly is a math graph?In mathematics, "graph" can refer to (at least) two different things. In basic mathematics, the term "graph" designates a diagram or a function graph. A graph is, in the language of mathematicians, a group of points and the connections between some selection of those points (which may be empty).
The graph's representation of the inequality system is as follows:
(d) y > x² + 2x - 3
y < -3x + 4
Let's break down each inequality and see how it relates to the graph:
y > x² + 2x - 3 represents the equation of an upward opening parabola with vertex (-1,-4) and the shaded region inside the parabola. The parabola is dashed, indicating that the boundary is not included in the solution set.
y < -3x + 4 represents the equation of a line passing through the points (-2,-1) and (0,3) with the shaded region above the line. The line is also dashed, indicating that the boundary is not included in the solution set.
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Consider the NASCAR race, the Indianapolis 500. Its name refers to the total race distance of 500 miles. There are 44 cars are racing (all of them also finish), and they all have an average mileage of 6.78 miles per gallon. If the fuel cost is $1.63 per gallon, what is the total fuel cost, in dollars, for all cars finishing the entire race?
Answer: $5289.35
Step-by-step explanation:
Since the cars have an average mileage of 6.78 miles per gallon and the race is 500 miles, the number of gallons each car will take will be:
= 500/6.78
= 73.75 gallons
Since they're 44 cars, the total gallons of fuel will be:
= 44 × 73.75
= 3245 gallons
Since the fuel cost is $1.63 per gallon, the total fuel cost, will be:
= $1.63 × 3245
= $5289.35
HELP ME OUT PLEASE!!!!
Which description BEST describes the correlation?
A) no correlation
B) prime correlation
C) positive correlation
D) negative correlation
Answer:
I believe the correlation is positive, because the dots are all clustered together and they are going upwards.
Step-by-step explanation:
Hope this helps you :)
The factored form of 30.8n+8.4 is a(11n+3) . What is the value of a?
After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We are given that the factored form of 30.8n+8.4 is a(11n+3).
To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.
Expanding a(11n+3), we get:
a(11n+3) = 11an + 3a
Equating this to 30.8n+8.4, we have:
11an + 3a = 30.8n + 8.4
We can factor out an "a" from the left-hand side:
a(11n + 3) = 30.8n + 8.4
Now we can see that this is the same as the given factored form, so we can equate the two expressions:
a(11n + 3) = a(11n + 3)
This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):
a = 30.8/(11n+3)
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