the solution to this system of equations is x=5 and y=16.
2x + 6 = 3x + 1
Subtract 2x from both sides:
6 = x + 1
Subtract 1 from both sides:
5 = x
Solve for y:
y = 3(5) + 1
y = 16
The substitution method is used to solve a system of equations by replacing one of the variables with an expression containing the other variable. In this system of equations, we have Y=3x+1 and 2x+6=y. To solve this, we start with the second equation and subtract 2x from both sides to get 6 = x + 1. Subtracting 1 from both sides gives us 5 = x. Now that we have x = 5, we can use this to solve for y. We substitute 5 for x in the first equation, giving us y = 3(5) + 1, which simplifies to y = 16. Therefore, the solution to this system of equations is x=5 and y=16.
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Factor the expression completely. X^4y^4+x^5y^2 x 4 y 4 +x 5 y 2
The expression [tex]x^4y^4+x^5y^2[/tex] can be factored to [tex](x^4y^2 + x^3y^2)(x + y^2).[/tex]
To factor [tex]x^4y^4+x^5y^2[/tex], we start by taking out the highest common factor, which is [tex]x^4y^2[/tex]. We then divide the expression by [tex]x^4y^2[/tex] to get [tex]x+y^2[/tex].
We can then rewrite the expression as ([tex]x^4y^2 + x^3y^2)(x + y^2).[/tex]
To verify this solution, we can multiply it out to get [tex](x^4y^2 + x^3y^2)(x + y^2) = x^5y^2 + x^4y^4[/tex], which is equal to the original expression. Therefore, the expression [tex]x^4y^4+x^5y^2[/tex] can be factored to [tex](x^4y^2 + x^3y^2)(x + y^2[/tex]).
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Tommy wants to use his 5.89 m long ladder against a wall, as shown below. The instructions state that the angle between his ladder and the ground should be in the range 74° to 77°. Calculate the maximum distance that the base of his ladder should be placed from the wall. Give your answer in metres to 2 d.p.
Answer:
1.49m
Step-by-step explanation:
Trigonometry:
cosθ = adjacent/hypotenuse
cos(74) = adjacent/(5.39)
adjacent = 5.39 × cos(74)
adjacent = 2.3125974152
1.49 (to 2 d.p.)
EXPONENTS AND SCIENTIFIC NOTATION
Date:
Pd:
MAZE #2 Instructions: Solve each of the problems below to make it correctly through the maze. Shade or
color your path as you go.
INDIC
1.25 x 107 +
63,000,000
7.55 x 107
9 x 10¹2 +
4.5 x 104
2 x 108
9.78 x 105-
732,000
ht
7.55 x 10¹4
2 x 106
2 x 103
2.46 x 103
2.46 x 105
12,000 +
7 x 104
2.86 x 10⁹
1.3 x 10³.
2,200
7 x 106
3.5 x 10².
2 x 104
8.2 x 104
8.2 x 10³
2.86 x 106
2.86 x 105
7 x 108
5.88 x 105-
3.44 x 105
7.5 x 104
6.3 x 104 +
1.2 x 104
2 x 10³
1.1 x 108 +
22,000
2.44 x 105
2.44 x 10³
7.5 x 108
6.8 x 106
5 x 103
6 x 108 +
120
5 x 106
3,400.
2 x 104
6.8 x 107
FINISH!
Maneuvering the Middle L
Each of the expressions has been simplified by using properties of exponents as shown below.
What is an exponent?In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.
n is referred to as a superscript or power.
By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:
(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷
12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴
5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵
6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶
9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸
1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶
(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴
3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷
9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵
3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶
1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.
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Is the data set approximately periodic? If so, what are its period and amplitude?
not periodic
periodic with a period of 4 and an amplitude of about 20
periodic with a period of 4 and an amplitude of about 30
periodic with a period of 5 and an amplitude of about 25
The supplied data collection has a periodic period of 4 and an amplitude of 25.
Let's study data points with a 4-day gap;
Data point 2 is [tex](2, 76)[/tex]
Data point 6 is[tex](6, 74)[/tex]
Data point 10 is[tex](10, 75)[/tex]
Every four day intervals, the readings are within the typical range. The points[tex](3, 91), (7, 88),[/tex] and (114) all support this same 4-day timeframe [tex](11, 92).[/tex]
As the data points at intervals of 4 days follow a pattern, we may infer that the period is 4 and the amplitude is around 25.
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Answer:
periodic with a period of 4 and an amplitude of about 30
Step-by-step explanation:
A pizza is divided into 16 equal pieces violet and sophie each ate 1/8 of the pizza on friday the next day sophie ate 1/2
of the pizza that was leftover how many of the pieces of the original pizza remain
Answer:
6 pieces of the original pizza remain.
Step-by-step explanation:
Initially, the pizza was divided into 16 equal pieces. Violet and Sophie each ate 1/8 of the pizza on Friday, so a total of 1/8 + 1/8 = 1/4 of the pizza was eaten on Friday.
This means that 3/4 of the pizza remained after Friday.
The next day, Sophie ate 1/2 of the remaining pizza. So she ate 1/2 * 3/4 = 3/8 of the original pizza.
Therefore, the amount of pizza that remains is 3/4 - 3/8 = 3/8 of the original pizza.
To convert this fraction to a number of pieces, we need to multiply it by the total number of pieces the pizza was divided into:
3/8 * 16 = 6 pieces
Anna has leaned a ladder against the side of her house. the ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. what length is the best approximation for the distance along the ground from the bottom of the ladder to the wall? responses 2 m 2 m 3 m 3 m 4 m 4 m 5 m
The most accurate estimate of the distance on the ground between the wall and the bottom of the ladder is 2 meters.
One approach to tackle this problem is to apply trigonometry to establish the connection between the angle, height, and distance. Specifically, we can utilize the cosine function, which relates the adjacent side and the hypotenuse of a right triangle. In this case, the adjacent side represents the distance between the wall and the ladder, and the hypotenuse corresponds to the ladder's length. The given angle is 72 degrees.
By employing the formula cos(angle) = adjacent/hypotenuse, we can input the known values and determine the unknown distance:
cos(72) = distance/6
distance = 6 * cos(72)
distance is approximately 1.9 m
Thus, the most accurate estimation for the ground distance from the ladder's bottom to the wall is 2 m.
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Answer:2m
Step-by-step explanation:
i took the test
answer pleaseeeeeeeeeeeee help
It is equal to (x-4)² - (x- 4) ⁶ = 0 to solve the quadratic equation u² - u - 6 = 0 where u = (x -4).
What is a formula?A numerical assertion known as a situation comprises of two mathematical articulations isolated by equivalent signs (=) on one or the other side.
It demonstrates that the printed statements on the left and right are in equal relationship.
In all formulas, the left side equals the right side. Equations can be solved to determine the values of unknown variables, which represent unknown quantities.
Without the equals sign, a statement is not an equation. A mathematical statement known as an equation will include the symbol "equal to" between two expressions that have the same value.
According to our question-
(x-4)² – (x − 4) − 6 = 0
Let (x - 4) = u
u² - u - 6 = 0
Hence, It is equal to (x-4)² - (x- 4) ⁶ = 0 to solve the quadratic equation u² - u - 6 = 0 where u = (x -4).
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Round 27,684,000 to the greatest place
(Will mark brainiest)
Answer: 30 mil
Step-by-step explanation:
Suppose that p partners equally share the profits from a sale of $3,600. Which algebraic expression represents this situation?
3600 + p
3600 minus p
3600 p
StartFraction 3600 over p EndFraction
3600/p is an algebraic expression that represents the Share of each partner.
What is the algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
Here, we have
Given: Suppose that p partners equally share the profits from a sale of $3,600.
Number of Partners = p
Total Profit = $ 3600
Profit of Each Partner = Total Profit/number of Partners
=> Profit of Each Partner = 3600 / p
Hence, 3600/p is an algebraic expression that represents the Share of each partner.
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32²-27
How do I solve equations like these?
You ask 120 randomly chosen people at a stadium to name their favorite stadium food. There are about 50,000 people in the stadium. Estimate the number of people in the stadium whose favorite stadium food is nachos.
The number of people in the stadium whose favorite stadium food is nachos is 10000.
What is random sample space?
The set of all potential outcomes for an experiment is referred to as the sample space S in a random experiment. The results of a random experiment, also known as sample points, are incompatible (i.e., they cannot occur simultaneously).
Here, we have
Given: You ask 120 randomly chosen people at a stadium to name their favorite stadium food. There are about 50,000 people in the stadium.
We have to estimate the number of people in the stadium whose favorite stadium food is nachos.
24/120 = x/50,00
x = 1200000/120
x = 10000
Hence, the number of people in the stadium whose favorite stadium food is nachos is 10000.
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a small school has three foreign language classes, one in french, one in spanish, and one in german. how many of the 34 students enrolled in the spanish class are also enrolled in the french class?
The number of students enrolled in the Spanish class who are also enrolled in the French class is 0.
Let the number of students enrolled in French class be F
Let the number of students enrolled in Spanish class be S
Let the number of students enrolled in German class be G
From the given information, we have
S + F + G = Total number of students...... (1)
Total number of students = 34S = 34 - F - G...... (2)
Now, we need to find out how many students are enrolled in both Spanish and French classes. So, let us assume that x students are enrolled in both Spanish and French classes.
So, the total number of students in Spanish and French classes will be S + F - x (as x students are enrolled in both the classes).
But we are given that there are 34 students enrolled in the Spanish class. Hence, the above expression will be equal to 34.
Therefore, S + F - x = 34
Now, substituting the value of S from equation (2) we get,
34 - F - G + F - x = 34 or, - G - x = 0 or, x = - G
But x represents the number of students enrolled in both Spanish and French classes, which cannot be negative.
Hence, there are no students enrolled in the Spanish class who are also enrolled in the French class.
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Rachael has a life insurance
policy that will pay her family
$45,000 per year if she dies.
Rachael's insurance company
expects that it would have to pu
$2,500,000 into a bank account
so that it could make the
payments. What does Rachael's
insurance company expect the
interest rate to be?
The insurance company expects the interest rate to be around 4.16%.
How to find determine Rachael's insurance company expect the interest rate to be?To find the expected interest rate, we can use the formula for present value of an annuity:
PV = PMT x (1 - (1 + r)^(-n)) / r
Where:
PV = present value of the annuity, which is the amount the insurance company needs to deposit
PMT = payment per period, which is $45,000
r = interest rate per period, which is what we need to find
n = total number of periods, which is unknown
We know that the insurance company needs to deposit $2,500,000 to make the payments, so we can set:
PV = $2,500,000:
$2,500,000 = $45,000 x (1 - (1 + r)^(-n)) / r
To solve for r, we can use trial and error or an iterative method. Here, we'll use trial and error.
Let's assume n = 20, which is a reasonable number of years for an insurance policy. Then we can solve for r:
$2,500,000 = $45,000 x (1 - (1 + r)^(-20)) / r
$2,500,000r = $45,000 x (1 - (1 + r)^(-20))
(1 + r)^(-20) = 1 - ($45,000 / $2,500,000) x r
1 + r = (1 - ($45,000 / $2,500,000) x r)^(-1/20)
r ≈ 0.0416 or 4.16%
Therefore, the insurance company expects the interest rate to be around 4.16%.
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whats 1 4/6 as a improper fraction
Answer:
1 4/6 as an improper fraction is 5/3
Step-by-step explanation:
What is an improper fraction?
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
How do you convert a mixed number to an improper fraction?
To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. Then, you put that sum over the denominator.
For example, 1 4/6 can be converted to an improper fraction as follows:
1 x 6 + 4 = 10
10/6 = 5/3
So, 1 4/6 as an improper fraction is 5/3.
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 46.8°?
The lake activity with a central angle of 46.8° is waterskiing, since it is the lake activity chosen by 13% of the campers.
what is central angle ?
A central angle is an angle formed by two radii of a circle that intersect at its center. The central angle is measured in degrees and is used in circle graphs or pie charts to represent the proportion or percentage of each category in the data.
In the given question,
To find out which lake activity has a central angle of 46.8°, we first need to calculate the total number of campers who participated in the survey:
Total number of campers = 15 + 11 + 7 + 13 + 54 = 100
Next, we need to find the percentage of campers who chose each lake activity:
Percentage of campers who chose kayaking = (15/100) x 100% = 15%
Percentage of campers who chose wakeboarding = (11/100) x 100% = 11%
Percentage of campers who chose windsurfing = (7/100) x 100% = 7%
Percentage of campers who chose waterskiing = (13/100) x 100% = 13%
Percentage of campers who chose paddleboarding = (54/100) x 100% = 54%
Now we can use the formula for calculating the central angle of a circle graph:
Central angle = (Percentage/100) x 360°
For the lake activity with a central angle of 46.8°, we can set up the following equation:
(Percentage/100) x 360° = 46.8°
Solving for Percentage, we get:
Percentage = (46.8°/360°) x 100% = 13%
Therefore, the lake activity with a central angle of 46.8° is waterskiing, since it is the lake activity chosen by 13% of the campers.
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The weight of a compact car is approximately 1,354 kilograms. Express the weight of the car in grams
The weight of the compact car, which is approximately 1,354 kilograms, can be converted to 1,354,000 grams.
In the metric system, "kilo" means thousand, so 1 kilogram is equal to 1000 grams. To convert from kilograms to grams, we simply multiply the weight in kilograms by 1000.
In this case, the weight of the compact car is given in kilograms as 1,354. To convert to grams, we multiply by 1000 to get:
1,354 kg x 1000 g/kg = 1,354,000 g
Therefore, the weight of the compact car in grams is approximately 1,354,000 grams.
The weight of an object is a measure of the force with which gravity pulls on the object. The unit of weight in the metric system is the newton (N), but kilograms (kg) are commonly used as a unit of mass and weight in everyday life. The conversion between mass and weight depends on the local acceleration due to gravity, which is approximately 9.81 m/s^2 at the Earth's surface.
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the difference between a sample statistic and the corresponding population parameter is known as the ?
The difference between a sample statistic and the corresponding population parameter is known as the sampling error.
What is sampling error?Sampling error is the disparity between a statistic from a sample and a corresponding parameter from a population. Statistic and parameter are two crucial words in inferential statistics that are used to describe data. A statistic is used to calculate a parameter, which is a calculated value from the population, which is a large group of people or objects.
The variance between the mean of the population and the sample's mean is known as sampling error. The sample statistic that is used to estimate the population parameter may not be the same as the population parameter.
The discrepancy between these two values is referred to as sampling error. When a small sample is chosen from a larger population, a sampling error is created.
Therefore, The sampling error is the discrepancy between a sample statistic and the equivalent population parameter.
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Help With This Please!!!!
a. True: We need to know the size of the pizza in order to calculate the unit price per square inch. Pi times the radius squared, or approximately 78.5 square inches, is the area of a 10-inch pizza.
If the 16 -inch pizza is sold by the slice at per slice, the restaurant will make a profit. True or False?b. False: We need to know the price of the entire pizza as well as the price per slice in order to determine if the restaurant would turn a profit by selling the 16-inch pizza by the slice. The cost is not specified in the problem, so we are unable to determine the profit.
A tray with a circumference of 32 inches is big enough to hold the personal-sized pizza. True or False?c. False: The circumference of a circle is the distance around the edge, which is not directly related to the size of the pizza. To determine if the tray is big enough to hold the personal-sized pizza, we need to know the diameter or radius of the pizza. The radius of the personal pizza is 5 inches, which means the diameter is 10 inches. Therefore, the tray with a circumference of 32 inches is not big enough to hold the personal-sized pizza.
The area of the large pizza is 2 square inches more than the area of the small pizza. True or False?d. False: The area of the large pizza is pi times the radius squared, which is approximately 254.5 square inches. The area of the small pizza is pi times the radius squared, which is approximately 201 square inches. The difference between the areas is 254.5 - 201, which is approximately 53.5 square inches, not 2. Therefore, the statement is false.
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A contractor is building a deck around a
15 x 20 rectangular swimming pool. He is going to build a 2 foot deck around the pool.
a) Write the length of the sides of the deck and pool together.
b) What is the total area of the deck and pool together?
c) What is the total area of just the deck?
The answer is in the picture below
HELPP!!! Find the value of x
Therefore, the length of the x is 24.04.
What is triangle?A triangle is a geometric shape that consists of three sides and three angles. It is a closed shape with three straight sides that connect at three vertices (corners). Triangles can be classified based on the lengths of their sides or the measures of their angles. For example, a triangle with three sides of equal length is called an equilateral triangle, while a triangle with two equal sides is called an isosceles triangle. Triangles can also be classified based on their angles, such as acute, obtuse, or right triangles. Triangles have a variety of properties and applications in mathematics, physics, and engineering.
by the question.
So, in this case, we have:
[tex]21 > x+7[/tex]
Where x is the length of the third side.
Simplifying the expression, we get:
[tex]21 > x+7[/tex]
Therefore, the length of the third side must be less than 28.
We can also use the Pythagorean theorem to determine if this triangle is a right triangle.
If a triangle is a right triangle, then the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, we have:
[tex]21^2 - 7^2 = x^2[/tex]
Simplifying, we get:
[tex]441 - 49 = x^2[/tex]
[tex]392 = x^2[/tex]
Taking the square root of both sides, we get:
x ≈ 19.79
Again, If a triangle is a right triangle, then the sum of the squares of the two shorter sides is equal to the square of the longest side.
[tex](x+3)^2 = (19.79)^2-(4)^2\\(x+3)^2= 391.64-16\\(x+3)^2= 225.64\\(x+3)= \sqrt225.64\\(x+3)= 15.021\\x = 15.021-3\\x = 12.021[/tex]
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The triangles are similar.
LM = ___ units
Using the concept of the ratio of similar triangles, we can say that the length of LM is: 12 units
How to find the ratio of similar triangles?
Similar triangles are defined as triangles that have the same shape, but then their sizes may very well vary. This means that we can say that, if two triangles are said to be similar triangles, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.
Looking at the given image, we can see that:
LM is similar to PN and LM is similar to QP
Thus:
LN/PN = LM/QP
(x + 3)/(x - 1) = 18/12
2(x + 3) = 3(x - 1)
2x + 6 = 3x - 3
3x - 2x = 6 + 3
x = 9
LM = 9 + 3
LM = 12
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help asap will give brainliest!!!!
Answer:
36
Angle LON is a right angle so it equals 90 degrees.
the Midpoint for the coordinates (3, -8) and (-9, -11)
Find the cost price of an Article when SP=Rs.1980 and loss%=10%
Answer:
Loss = Rs. 198
Step-by-step explanation:
[tex]{ \sf{\%loss = \frac{loss}{cost \: price} \times 100\%}} \\ \\ { \sf{10 = \frac{loss}{1980} \times 100}} \\ \\ { \sf{loss = \frac{10 \times 1980}{100} }} \\ \\ { \sf{loss = 198}}[/tex]
Let ABC be an isosceles triangle at A, altitude AH
a) Prove that ∆AHB = AHC. From that, deduce the remaining equal factors of the two triangles.
b) Draw the medians BM and CN, they intersect at G. Prove that the three points A,G,H are collinear, prove that ∆GBC is equal
c) On the opposite ray of ray MH take point D such that M is mid point of HD, prove BC=2AD
For isosceles triangle we have proved a) ∆AHB = AHC b) AH is the median of ∆ABC c) BC = 2AD
a) To prove that ∆AHB = AHC, we need to show that the two triangles have equal sides and angles. Since ABC is an isosceles triangle at A, we know that AB = AC. Also, since AH is the altitude of the triangle, we know that it is perpendicular to BC. Therefore, angle AHB and angle AHC are both right angles.
Now, to prove that the triangles have equal sides, we need to show that HB = HC. Since AB = AC, we have:
[tex]AB^{2} = AC^2\\AB^2 - AH^2 = AC^2 - AH^2\\BH^2 = CH^2[/tex]
Therefore, HB = HC, and we have proved that ∆AHB = AHC.
From this, we can deduce that angle BHA = angle CHA, as they are opposite angles in congruent triangles. Also, we know that angle ABC = angle ACB, as it is an isosceles triangle. Therefore, angle ABH = angle ACH, and we have proved that ∆ABH = ∆ACH.
b) To prove that A, G, and H are collinear, we need to show that AH is the median of ∆ABC. Since ∆AHB = AHC, we know that HB = HC. Therefore, BG and CG are medians of the triangle, and they intersect at G.
Now, to prove that ∆GBC is equal, we can use the fact that medians of a triangle divide it into six equal triangles. Therefore, we have:
Area(∆GBC) = 2/3 * Area(∆BGC)
Area(∆GBC) = 2/3 * Area(∆ACG)
Area(∆GBC) = 2/3 * Area(∆ABG)
Since ∆ABH = ∆ACH, we know that the altitude from A to BC passes through H, which is the midpoint of BC. Therefore, AH is also the median of ∆ABC.
c) Let E be the midpoint of BC. Since AE is the median of the triangle, we know that it divides BC into two equal parts, so EC = EB. Let X be the midpoint of AD. Since M is the midpoint of HD, so:
HX = (1/2) * HD
HX = (1/2) * (2AD)
HX = AD
AX is parallel to DE so:
AB/AD = AE/AX
2 = AE/AX
Since EC = EB and HX = AD, so:
AE = EC + HX
AE = EB + HX
AE = 2HX
Therefore, substitute, simplify:
2 = 2HX/AX
2AX = 2HX
AX = HX
Since AX = HX, DX is also equal to HX, so:
AD = DX
Also, since AE = 2HX, so:
BC = 2AE
Substitute in HX = AD and AE = 2HX, so:
BC = 2AE
BC = 2(2HX)
BC = 4HX
BC = 4AD
Therefore, we have proved that BC = 2AD.
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which graph best represents y=-x^2+6 x-1
Answer:
Step-by-step explanation:
The gas tank in Karla’s car holds 12 gallons of gas. Can Karla drive 360 miles without having to stop and buy more gas?
Answer:
she would have to go 30 miles per hour or less to make this possible
Step-by-step explanation:
if it went over 35 31 miles per hour they would run out of gas before they got there
How do you do this step by step please thank uu
The value for the given expression is 60.
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The exercise asks the value of the given expression a²-4a, for a=10. Thus, you should replace the variable a with the number 10. See below.
a²-4a
10²-4*10
100-40=60
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assume that the number of calories in a mcdonald's egg mcmuffin is a normally distributed random variable with a mean of 290 calories and a standard deviation of 14 calories. what is the probability that a particular serving contains fewer than 300 calories? more than 250 calories? between 275 and 310 calories?
The probability that a particular serving contains fewer than 300 calories is 0.71, more than 250 calories is -2.86, between 275 and 310 calories is 0.7186.
To solve this problem, we need to use the normal distribution and the corresponding z-scores. We can find the z-score for a particular value of x (number of calories) using the following formula:
z = (x - μ) / σ
where μ is the mean, σ is the standard deviation, and x is the specific value we are interested in.
Probability of serving containing fewer than 300 calories:
z = (300 - 290) / 14 = 0.71
Using a standard normal distribution table or calculator, we find that the probability of a z-score being less than 0.71 is 0.7611. Therefore, the probability of a serving containing fewer than 300 calories is 0.7611.
Probability of serving containing more than 250 calories:
z = (250 - 290) / 14 = -2.86
Using a standard normal distribution table or calculator, we find that the probability of a z-score being greater than -2.86 is 0.9977. Therefore, the probability of a serving containing more than 250 calories is 0.9977.
For 275 calories:
z = (275 - 290) / 14 = -1.07
For 310 calories:
z = (310 - 290) / 14 = 1.43
Next, we use a standard normal distribution table or calculator to find the probability of z falling between -1.07 and 1.43. For example, using a standard normal distribution table, we can find that the probability of z falling between -1.07 and 1.43 is approximately 0.7186.
Therefore, the probability that a particular serving of McDonald's Egg McMuffin contains between 275 and 310 calories is approximately 0.7186, or 71.86%.
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Trisha is running a marathon race. She runs the race at a steady pace. She makes a graph to show how far from the finish line she will be as she runs the race.
Answer:
Step-by-step explanation:trisha is running a marathon race she runs th erace at a steady pace she makes a graph to show how far from the finsh line she will be as she runs the race
=2