The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-
E = 3h(n) + 2g(n)
E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)
E = 12n + 6 + 2n³ + 10 -4n
E = 2n³ + 8n + 6
Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.
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The fish in a hatchery tank have mean length = 9.7 inches, with standard deviation = 1.2 inches. If a random sample of 40 fish is taken from the tank, what is the probability that their average length is less than 10 inches?
The probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
What is probability ?
Probability is a metric used to determine how likely an event or result is to occur. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.
A group of potential possibilities is referred to as an event in probability theory. By dividing the number of positive possibilities by the total number of possible outcomes, the probability of an event happening is determined.
The fish in the hatchery tank are distributed in length according to a normal distribution, with a mean length of 9.7 inches and a standard deviation of 1.2 inches.
With a mean that is equal to the population mean and a standard deviation that is equal to the population standard deviation divided by the square root of the sample size, the distribution of the sample means will also follow a normal distribution.
The formula to calculate the z-score for the sample mean is:
z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] )
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we want to find the probability that the sample mean is less than 10 inches. So we need to calculate the z-score for a sample mean of 10 inches:
z = (10 - 9.7) / (1.2 /[tex]\sqrt{40}[/tex]) = 1.21
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.21 is approximately 0.8869. This means that there is an 88.69% chance of getting a sample mean less than 10 inches.
Therefore, the probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.
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Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.
How much fruit drink and soda does he need?The system of equations that represents the question is:
f + s = 168 equation 1
2.41f + 1.57s = (1.66 x 168)
2.41f + 1.57s = 278.88 equation 2
Where:
f = number of gallons of fruit drink s = number of gallons of sodaThe elimination method would be used to determine the required values
Multiply equation 1 by 2.41
2.41f + 2.41s = 404.88 equation 3
Subtract equation 2 from equation 3
126 = 0.84s
s = 126 / 0.84
s = 150
Substitute for s in equation 1
f + 150 = 168
f = 168 - 150
f - 118 gallons
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A boat has a top speed of 26 knots and a displacement of approximately 81000 tons. (1 knot= 1 nautical mile per hour; 1 metric ton =1000 kilograms)
Express the top speed in miles per hour and the displacement in metric tonnes.
(1 knot=1 nautical mile per hour; 1 metric tonne=1000 kilograms)
On solving the provided question we can say that 2 decimal places =29.92 miles per hour
what is decimal?Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the
top speed is 26 knots,
1 knot = 1.15078 miles per hour
26 knots = 26 * 1.15078
= 29.92028 miles per hour
2 decimal places
=29.92 miles per hour
boat has a displacement of 96000 tons
1 ton = 0.907185 metric tonnes
96000 tons = 0.907185 * 96000
= 87,089.76 metric tonnes
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Construction each spatial figures
Blue pyramid
Black cown
Yellow cube
Green rectangular prism
Red silendar
Violet sphere
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a common point. The height of a pyramid is the perpendicular distance from the base to the apex.
How to explain the shapesA cube is a three-dimensional shape that has six square faces of equal size. All angles of a cube are right angles, and all edges have the same length. The volume of a cube is given by the formula V = s³ where s is the length of one edge.
A rectangular prism is a three-dimensional shape that has six rectangular faces. The opposite faces are congruent and parallel, and all angles are right angles. The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the lengths of the three perpendicular edges.
A sphere is a three-dimensional shape that is perfectly round and has no edges or corners. It is defined as the set of all points in three-dimensional space that are equidistant from a given point called the center. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
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Help me with this question…..
Answer:
In order from least to greatest, the numbers would be organized as such: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex]. So C is the correct answer.
Step-by-step explanation:
At first glance, these numbers are not the simple whole and decimal numbers one might be used to. However, we can find their approximate values and order them correspondingly. [tex]\frac{2}{3}[/tex] is a fraction that is less than one, so on a number line it would be between 0 and 1, making it the smallest number out of the four. [tex]\sqrt{5}[/tex] and [tex]\frac{5}{2}[/tex] are both between 2 and 3, but [tex]\sqrt{5}[/tex] is approximately equal to 2.24, while [tex]\frac{5}{2}[/tex] is equal to 2.5. Therefore, we can conclude that [tex]\frac{5}{2}[/tex] is greater than [tex]\sqrt{5}[/tex]. Lastly, [tex]\pi[/tex] is a constant number that is the ratio of a circle's circumference to its diameter that equals approximately 3.14, so we can conclude that [tex]\pi[/tex] is the greatest number out of the four.
Now that we have the four numbers in an easier and visually more clear way to find their exact values, we know that the order of these numbers from least to greatest would be choice C: [tex]\frac{2}{3}[/tex] , [tex]\sqrt{5}[/tex] , [tex]\frac{5}{2}[/tex] , [tex]\pi[/tex] .
Have a great day! Feel free to let me know if you have any more questions :)
A
B
C
D
Pick a letter
Answer: D
Step-by-step explanation:
1 in.=1488 milesx5=7440 miles.
Area= pi x r^2
=pi x (7440)^2 or option D.
Hope this helps :)
BRAINLIEST
QUICKLY HELPP
Answer:
BEF
What is an angle?An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.
What types of angles are there?There are right angles (exactly 90 degrees), acute angles (less than 90 degrees), obtuse angles (more than 90 degrees), and reflex angles (more than 180 degrees).
Looking at the following answers provided, we can see that BEF is a proper angle, because it is made up of two rays in the proper order.
KGH on the other hand, is not. KGH would be a proper angle if it was in the correct order (GHK or KHG), but because it is not in the right order, it is not a proper angle. LEA is not a proper angle either. We know that an angle is made up of two rays, but LEA isn't, and it's the same with ADE.
Answer:
BEF and ADE
Step-by-step explanation:
These points when connected make and angle. The others do not as they sinply dont make sense or have the points in a way that makes the whole statement false.
Simplify.
(-32)^-9/5
Answer: undefined
Step-by-step explanation: can’t raise a negative number to a integer exponent
A water reservoir is shaped like a rectangular solid with a base that is 40 yards by 40 yards, and a vertical height of 30 yards. At the start of a three-month period of no rain, the reservoir was completely full. At the end of this period, the height of the water was down to 5 yards. How much water was used in the three-month period?
In response to the above question, we may state that in the rectangle [tex]4,241,455[/tex] gallons [tex]= 4,570,000[/tex] Cubic feet[tex]x 7.48052[/tex] Gallons/cubic foot.
What is rectangle?In the geometry of the Euclidean plane, a rectangle is a quadrilateral having four right angles. You may also refer to it as an equiangular quadrilateral, meaning that all of its angles are equal. A straight angle could also be present in the parallelogram.
Rectangles with four evenly sized sides are called squares. Four 90-degree vertices and equal parallel sides make up a quadrilateral with the shape of a rectangle.
As a result, it's also known as an equirectangular rectangle. A rectangle is also referred to as a parallelogram, since its opposite sides are parallel and equal.
Volume of rectangular solid is L × W × H
[tex]50 × 30 × 20 = 30000[/tex] cubic yards
[tex]50 × 30 × 6 = 9000[/tex]cubic yards
[tex]30000–9000 = 21000[/tex]cubic yards
This needs to be converted to gallons of water. We are given the conversion factor between a gallon of water and cubic feet, therefore even though we have cubic yards rather than cubic feet, we must first convert the [tex]21,000[/tex] Cubic yards to cubic feet.
A cubic yard has a volume of 27 cubic feet.27 cubic feet per cubic yard times [tex]21,000[/tex]cubic yards equals 567,000 cubic feet.
7.48052 gallons make up 1 cubic foot.
Therefore, 4,241,455 gallons are equal to 567000 cubic feet times 7.48052 gallons/cubic foot.
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Part B
Landon thinks that the answer is
12 guests. He says, "10+ 4 = 14, and
14 rounds to 10. Then 10 X 12=120."
Do you agree with his reasoning? Explain
why or why not.
The number of guests that shared one platter is 10.
How to solve thisA. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.
If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.
B. Landon's reasoning is incorrect.
While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.
Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.
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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning
A right rectangular prism has a square base with sides 1/2 in. Long. The volume of the prism is 3/8 in to the third power. What is the prism?
Answer:
If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.
Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:
V = Bh
3/8 = (1/4)h
Multiplying both sides by 4, we get:
3 = h
So the height of the prism is 3 inches.
Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.
You paid $29.75 in tax when you bought a $350 bike. What is the percent tax?
The percent tax you paid when you bought the bike is approximately 8.493%.
What is percentage ?
Percentage can be defined as the product of ratio of given value, total value and hundred.
given ,
You paid $29.75 in tax when you bought a $350 bike
To find the percent tax, we can divide the amount of tax by the total cost (including tax) and multiply by 100 to express the result as a percentage.
tax = 29.75
total = 350
percent tax = (tax / total) * 100
So the percent tax would be
percent tax = (29.75 / 350) * 100
= 8.493%
Therefore, The percent tax you paid when you bought the bike is approximately 8.493%.
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< Question 4, 1.2.23 >
points
O Points: 0 of 1
Use the method of successive differences to determine the next number in the given sequence.
7; 35; 173; 771; 2529; 6667; 15,095
Assuming that the pattern continues, the eighth term would be
The pattern does not have a consistency to get the differences
How to find the patternThe method of successive differences involves finding the difference between each consecutive term in a sequence, and then using those differences to find the next term.
Here's how the method would work for the sequence given:
7; 35; 173; 771; 2529; 6667; 15,095
Difference between terms:
28; 138; 598; 1758; 4138; 8428
Second difference between terms:
110; 460; 1160; 2380; 4290
Third difference between terms:
350; 700; 1220; 1910
Fourth difference between terms:
350; 520; 690
There is no consistency between the patterns.
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In which quadrant does the point (-21 , 13) lie?
Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of Planes are Green?
There are 29% of the Planes are Green.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of green vehicles = 870
The percent of green planes = (number of green planes/number of total green vehicles) x 100
The percent of green planes = (250/870) x 100
The percent of green planes = 0.2873 x 100
The percent of green planes = 28.73
Round to the nearest percent, and we get
The percent of green planes = 29%
Thus, 29% of Planes are Green.
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Solve for x and simplify answer
4
\x=-18
3
The value of the variable is x = -6/9
What is a fraction?A fraction is defined as the part of a whole number.
The different types of fractions are;
Mixed fractionsSimple fractionsComplex fractionsImproper fractionsProper fractionsWe are given the equation:
4/x = -18/3
To make 'x' the subject, cross multiply
-18x = 12
Now, divide both sides by the coefficient of x, we get;
x = 12/-18
x = -6/9
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Figure ABCD is a kite.
Find the value of x.
A
X =
= [?]
14x - 22
H
B
C
The value of x is equal to 8, in the equation 14x -22.
What is equation?An equation is a mathematical statement consisting of two expressions joined by an equal sign.
Solution:
The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.
setting the displayed dimensions correspond to 90° angular dimensions.
14x -22 = 90
You can solve this two-level linear equation in the usual way.
14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x
x = 112/14 = 8 . . . Step 2, divide by the factor of x
Hence, the value of x is 8.
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19. The mass of a radioactive element is 35
milligrams. The mass of the element decreases by
12.9% every year.
a. Write a function that represents this situation.
b. Predict the mass of the element in 4 years. Round
your answer to the nearest tenth.
c. Will the mass of the radioactive element ever be 0
milligrams? Explain.
a) The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
b) For 4 years, the mass of the element is, 19.95 milligrams
c) No, the mass of the radioactive element will never be 0 milligrams.
What is expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
Now, For 4 years, the mass of the element is,
⇒ y = 35 (1 - 12.9%)ⁿ
⇒ y = 35 (1 - 12.9%)⁴
⇒ y = 35 (1 - 0.129)⁴
⇒ y = 35 (0.87)⁴
⇒ y = 35 × 0.57
⇒ y = 19.95 milligrams
No, the mass of the radioactive element will never be 0 milligrams.
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Find the area of the figure. Round to the nearest tenth, if necessary.
The perimeter is 30cm.
Work out the lengths of all the sides.
3x + 2
X
4x - 6
Answer: To solve for the length of all sides, we need to set the perimeter equal to the sum of the lengths of the three sides:
30 cm = 3x + 2 + x + 4x - 6
30 cm = 8x + 2
Now we can solve for x:
30 cm = 8x + 2
28 cm = 8x
x = 28/8
x = 3.5
So each of the sides is 3.5 cm long, and the lengths of the three sides are:
3x + 2 = 3 * 3.5 + 2 = 11.5 cm
x = 3.5 cm
4x - 6 = 4 * 3.5 - 6 = 11.5 cm
Therefore, the lengths of the sides are 11.5 cm, 3.5 cm, and 11.5 cm.
Step-by-step explanation:
Answer:
(3x+2+4x-6)2=30
7x-4=30
7x=34
x=34/7
To find the side lengths of the rectangle;
3x+2=116/7. and. 4x-6=94/7
A magician has a magic trick that uses an 18" length of string that is cut into two pieces. One piece is two inches longer that the other. Find the length of each piece. Use algebraic equations.
The length of each piece is 10 in and 8 in.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total length of the string = 18 in
One piece = x + 2
Another piece = x
Now,
Solve for x.
x + 2 + x = 18
2x + 2 = 18
2x = 18 - 2
2x = 16
x = 8
Now,
One piece = 8 + 2 = 10 in
Another piece = 8 in
Thus,
The length of each piece is 10 in and 8 in.
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While on a camping trip with his friends, Finn made a pot of stew over the campfire. He
divided it equally among their 6 bowls. Each bowl had more than 2.5 cups of stew.
Let x represent how much stew Finn made. Which inequality describes the problem?
≥2.5
>2.5
Solve the inequality. Then, complete the sentence to describe the solution.
Finn made more than
cups of stew.
Submit
The inequality which describes the problem about the pot of stew Finn made is x/6 > 2.5
Which inequality describes the problem?Number of bowls= 6
Quantity of stew in each bowl > 2.5
Quantity of stew Finn made = x
The inequality
Quantity of stew Finn made / Number of bowls > Quantity of stew in each bowl
x/6 > 2.5
Therefore, x divided by 6 greater than 2.5 is the inequality which describes the situation.
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(SAT Prep) Find the value of x.
Answer: 36˚
Step-by-step explanation:
180 - 3x = 2x
180 = 5x
.: x = 36˚
Trigonometry question
The value of sin(tetha/2) is ±√½(1-8/√113)
What are half angles?In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45°), and so on. If θ is an angle, then the half angle is represented by θ/2.
if tan(tetha) = 7/8
this means that 7 is the opposite and 8 is the adjacent
hyp² = opp² +adj²
hyp² = 49+64
hyp = √113
sin(tetha/2) = ±√1-cos(tetha))/2
= ±√1-(8/√113))/2
therefore the value is sin(tetha)/2
= ±√1-(8/√113))/2 or ±√½(1-8/√113)
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SAQ-18. The firm provides the following information: Annual requirement Cost per unit ........ Rent, tax, and insurance Insurance per order...... Required: a. EOQ ..... Rs. 20 Rs. 2 per unit ..Rs. 200 ...............100,000 units Carrying cost per unit per year ...........10% of unit price Cost per order...... ...........Rs. 300 b. Total Cost of EOQ c. Number of order
Note that the Economic Order Quantity is given as approximately 4,472.13 Units.
Economic Order Quantity, also known as Economic Purchasing Quantity, is the order quantity in inventory management that minimizes overall holding costs and ordering expenses. It is one of the most ancient traditional production scheduling models.
EOQ = √[(2 * AR* OC)/CC]
Were AR = Annual Requirement = 100,000 units
OC = Ordering Cost = Rs 20 per unit
CC = Carrying Cost = 10% of Per Unit Cost
Per Unit Cost = Rs. 2
Thus,
EOQ = √[(2 * 100,000* 20)/10% * 2]
EOQ = √[(4000000)/0.2]
EOQ = √20000000
EOQ = 4472.135955
EOQ [tex]\approx[/tex] 4,472.13 Units.
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10x³•2 √5x4 I need help
Answer:
20√5x7
Step-by-step explanation:
Complete the Recursive formula.
Answer:
[tex]-13[/tex]
Step-by-step explanation:
The common difference of the arithmetic sequence is [tex]-13[/tex].
How do you solve the problem: 5/8 * a/b = - 1/4?
Answer:a=-2
b=5
Step-by-step explanation:
[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]
A bag contains 2 gold marbles, 7 silver marbles, and 29 black marbles. The rules of the game are as follows: you randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss of you play this game?
Total number of marbles is 5 + 7 + 29 = 41.
Your expected profit or loss of you play this game $0.17 loss?
The given parameters are
2 gold marbles,
7 silver marbles,
and 29 black marbles
Also you win $4, if it is silver, you win $2. If it costs $1 to play
Event P(Event) Net Winnings P(Event) * Net Winnings
Gold 5/41 4 - 1 = 3 15/41
Silver 7/41 2 - 1 = 1 7/41
Black 29/41 -1 -29/41
sum -7/41 = $0.17 loss
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A fruit juice recipe calls for 5 parts orange juice and 6 parts pineapple juice. Which proportion can be used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice?
30 over 21 equals j over 100
6 over 5 equals j over 21
6 over j equals 5 over 21
5 over 6 equals j over 21
For given ratio of orange juice and pineapple juice i.e. 5/6, proportion used to find the amount of orange juice, j, that is needed to add to 21 L of pineapple juice will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
What exactly is a ratio?
Fractions are commonly used to describe ratios and proportions. A ratio is demonstrated when a fraction is expressed as a:b, whereas a percentage indicates that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.
We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.
As a result, when b is larger than zero, the ratio, such as a:b, defines the relationship between two variables. For example, the 2:4 ratio is expressed as 2:4 = 1:2.
Now,
Given that In recipe ratio of orange juice / pineapple juice =5/6
then to make a recipe with 21 L of pineapple juice, the orange juice (j)
needed will be
5/6=j/21
j=17.5 L
hence,
proportion used to find the amount of orange juice, j will be 5 over 6 equals j over 21 i.e. 5/6=j/21.
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Answer: its D
Step-by-step explanation:
pls i belieive most of yall are npcs
