The correct option is A) With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution.
Explanation:Given:P(t > 1.96) = 0.0408P(t < -1.96) = 0.0408The t-distribution is different from the z-distribution because it has a thicker tail.The tail is thicker since the t-distribution is determined by the sample size, whereas the z-distribution is determined by the population size (the t-distribution is estimated with the standard error of the mean in this case).
A t-distribution with small degrees of freedom has a much thicker tail than a z-distribution with the same degrees of freedom. Because sample size is related to the degrees of freedom, it makes sense that t-distributions with smaller sample sizes will have thicker tails.
The population variance is replaced with the sample variance in the estimation of the t-distribution. As a result, the t-distribution has heavier tails than the z-distribution.
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Kira is choosing between two exercise routines.
In Routine #1, she burns 24 calories walking. She then runs at a rate that burns 15.5 calories per minute.
In Routine #2, she burns 52 calories walking. She then runs at a rate that burns 9.9 calories per minute.
For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2?
Use t for the number of minutes spent running, and solve your inequality for t.
For any value of inequality for t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.
What is inequality?
In mathematics, an inequality is a statement that compares two quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Let's start by calculating the total number of calories burned in each routine as a function of the number of minutes spent running:
Routine #1:
Total calories burned = 24 + 15.5t
Routine #2:
Total calories burned = 52 + 9.9t
To find the point where Routine #1 burns at most as many calories as Routine #2, we need to solve the inequality:
24 + 15.5t ≤ 52 + 9.9t
Simplifying this inequality, we get:
5.6t ≤ 28
Dividing both sides by 5.6, we get:
t ≤ 5
Therefore, for any value of t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.
So the answer is: t ≤ 5.
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5.
Ka'mya is planning a zoo which will be built on the Oregon coast. Each carnivore (a meat eating animal) will
cost $30 each week to feed, and each herbivore (a plant eating animal) will cost $10 each week to feed.
Her starting budget for feeding all of the animals is $360 per week. The location for the zoo will have
room for 24 animals. How many carnivores and how many herbivores should she plan on having in her zoo?
Answer:
6 carnivore's and 18 herbivore's
Step-by-step explanation:
It takes Rosita 32 hours to drywall a basement by herself and 18 hours if Paola helps her. How long would it take Paola to drywall the basement by herself? Round your answer to the nearest hour.
Lebo decided to rather buy a new lounge suite for R42 000. She paid a 15% cash deposit and the balance is paid through a hire purchase loan agreement. She repays the loan over 4 years at an interest rate of 19% p.a. on the full amount of the loan. Calculate her monthly instalments over the 4 year period.
Answer:
Step-by-step explanation:
First you need to find the balance amount that she paid in instalments which is 42000 * 15% which is equalled to 6300.
Then you need to minus 42000 - 6300 as 630l is the price she paid as cash deposit which is equalled 35700.
Now, to find the interest the formula is I = p * r/100 which equalled 7890 for a year. To calculate her monthly instalments, you have to divide 7890 divided by 12 months which equals 665.
what does the symmetric bell shape of the normal curve imply about the distribution of individuals in a normal population?
Answer:
Answer and Explanation: The symmetric bell shape of the normal curve implies that the skewness of the distribution of the data is 0, and most of the observation is located at the middle of the distribution. The shape of the normal distribution is not positive and negative skewed, the shape seems to be bell-shaped.
HOPE THIS HELPS!
Hello can you find the absolute value?
-3 2/3=
Answer:
Yes, I can find the absolute value of -3 2/3.
The absolute value of a number is the distance of the number from zero on the number line. It is always a positive number.
To find the absolute value of -3 2/3, we need to ignore the negative sign and just look at the magnitude of the number.
So, the absolute value of -3 2/3 is:
|-3 2/3| = 3 2/3
Therefore, the absolute value of -3 2/3 is 3 2/3.
using the rule of 72, how long will it take $100,000 to equal $200,000 if you can earn 14% annually? question 40 options: 5.1429 years 4.1529 years 2.78 years 1.38 years
The Rule of 72 is a simple mathematical formula that allows investors to quickly estimate the number of years required for an investment to double in value.
To use this formula, we divide the number 72 by the annual interest rate earned on the investment.
The result is an estimate of the number of years it would take for the investment to double in value. For example, if an investment earns an annual interest rate of 8%, it would take approximately nine years for the investment to double in value (72 divided by 8 equals 9).The Rule of 72 is a useful tool for investors who want to quickly estimate the potential growth of their investments.However, it is important to note that this formula provides only an estimate, and the actual time required for an investment to double in value will depend on a variety of factors, such as market conditions, investment fees, and taxes.
Nevertheless, the Rule of 72 can be a helpful starting point for investors who want to set realistic expectations for their investments.
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cindy and tom, working together, can weed the garden in 6 hours. working alone, tom takes three times as long as cindy. how many hours does it take cindy to weed the garden alone? round your answer to two decimal places, if needed.
The main answer is that it takes Cindy 4 hours to weed the garden alone, which was found using the equation 1/x + 1/(3x) = 1/6 where x is the time it takes Cindy to weed the garden alone.
Let x be the time it takes Cindy to weed the garden alone. Then, it takes Tom 3x time to weed the garden alone. Using the formula for the work done by each person, we can create an equation in terms of x:
1/x + 1/(3x) = 1/6
Solving for x, we get:
x = 4 hours
Therefore, it takes Cindy 4 hours to weed the garden alone.
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Evelyn buys bracelets thats cost $6 each and three purses that cost $12 each. The cost of evelyns total purchase is $60. Write and equation thar can be used to find n, the number of bracelets that evelyn buys
b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.
Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.
We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.
Using this information, we can create an equation:
6b + 12p = 60
Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:
b + 2p = 10
Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":
b + 2(2) = 10
b + 4 = 10
b = 6
So if Evelyn buys two purses, she also buys six bracelets.
In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.
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What is the product of (3x+2) and (x - 7) ?
you spin the spinner once.
what is p(less than 4)?
write your answer as a fraction or whole number
The equation used to obtain the probability of a number less than 4 on the spinner is given as follows:
P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Desired: number of regions with numbers that are less than 4.Total: total number of regions.Hence the probability is calculated as follows:
P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.
Missing InformationThe problem asks for the probability of spinning a number less than 4 on the spinner.
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How to elimination 18x-6y=-20 -9x+3y=15
The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10, which is a contradiction. This means that there is no solution to the system of equations.
What is an elimination?
To eliminate one of the variables, we need to manipulate one or both of the equations so that when we add them together, one of the variables is eliminated.
Let's start with the given equations:
18x - 6y = -20
-9x + 3y = 15
We can see that the coefficients of y in both equations are opposite, which means we can eliminate y by adding the two equations together. However, we need to make sure the coefficients of y have the same absolute value, so we'll multiply the second equation by 2:
18x - 6y = -20
-18x + 6y = 30
Now we can add the two equations together:
0x + 0y = 10
This equation simplifies to 0 = 10, which is a contradiction. This means that there is no solution to the system of equations. In other words, the two equations represent two parallel lines that never intersect.
Alternatively, we can recognize that the two equations represent the same line when simplified, since the second equation is simply half of the first equation. In this case, there are infinitely many solutions, since any point on the line satisfies both equations.
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Complete question is: The elimination of the equations 18x-6y=-20 and -9x+3y=15 is 0 = 10.
A line passes through the point (6, - 3) and has a slope of -2.
Write an equation in slope-Intercept form for thls line.
To find the equation of the line passing through the point (6, -3) with a slope of -2, we can use the point-slope form of the equation of a line:y - y1 = m(x - x1)where (x1, y1) is the given point and m is the slope.Substituting the given values, we get:y - (-3) = -2(x - 6)Simplifying, we get:y + 3 = -2x + 12Subtracting 3 from both sides, we get:y = -2x + 9So, the equation of the line is y = -2x + 9
two positive whole numbers greater than 1 multiply to 576 and have no common factors other than 1. what is the sum of those two numbers?
Thus, the two positive whole numbers that are greater than one multiply to 576 and share only the number one in common is 5.
Explain about the positive whole numbers?One of the categories that mathematicians have created for numbers is titled whole numbers, and it contains all of the numbers from 0 to infinity.
The specific class or collection of numbers known as whole numbers includes:
Are all positive numbers with no fractional or decimal parts, including zero.Positive numbers with no decimal or fractional portions are referred to as whole numbers, including zero. They are numerical representations of whole, unbroken things. The set of whole numbers is mathematically represented by the numbers 0 through 9.Two positive whole numbers greater than 1 are 2 and 3.
2 and 3 does not have any common factor except 1.
sum of 2 and 3 = 5
Thus, the two positive whole integers that are greater than one multiply to 576 and share only the number one in common is 5.
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your cousin says that if two fractions have the same numerator,then the fraction with the greater denominator is the greater fraction. is your cousin correct explain
It is not always true that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction.
The statement that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction is not always correct. This is because the value of a fraction is determined by both its numerator and denominator, and if the denominators of two fractions with the same numerator are different, then the fractions are not directly comparable.
Consider the fractions 3/4 and 3/5. Both have a numerator of 3, but the denominator of the first fraction is greater than the denominator of the second fraction. However, 3/5 is actually the greater fraction because it represents a larger portion of the whole.Consider the fractions 5/7 and 5/9. Both have a numerator of 5, but the denominator of the second fraction is smaller than the denominator of the first fraction. Therefore, 5/7 is the greater fraction because it represents a larger portion of the whole.
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help i will give alot of points
According to the information, the surface area of the prism is 3200 square meters.
How to find surface area of the prism?To find the surface area of the prism, we need to add up the areas of all its faces.
The prism has 2 triangle sides with a height of 15m and a base of 40m. The area of each triangle can be calculated using the formula A = 1/2 × b × h, where b is the base and h is the height of the triangle. So, the total area of these two triangles is:
A = 2 × 1/2 × 40m × 15mA = 600m^2The prism also has 2 triangle sides with a height of 25m and a base of 40m. The total area of these two triangles is:
A = 2 × 1/2 × 40m × 25mA = 1000m^2Finally, the prism has 2 rectangular sides with a height of 40m and a base of 40m. The area of each rectangle is simply the product of its height and base, so the total area of these two rectangles is:
A = 2 × 40m × 40mA = 1600m^2To find the total surface area of the prism, we add up the areas of all its faces:
Total surface area = 600m^2 + 1000m^2 + 1600m^2Total surface area = 3200m^2Therefore, the surface area of the prism is 3200 square meters.
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Order the angles from greatest to least
The side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:
angle Y > angle Z > angle X.
What is triangle ?
A triangle is a three-sided polygon, or a closed two-dimensional shape with three straight sides and three angles. The sum of the angles in a triangle always adds up to 180 degrees. The sides of a triangle can be of different lengths, and the angles can be acute (less than 90 degrees), right (equal to 90 degrees), or obtuse (greater than 90 degrees).
To order the angles from greatest to least in triangle XYZ, we need to determine which side is the longest. By the Law of Cosines, we know that:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
where c is the side opposite to angle C, and a and b are the other two sides.
So, let's calculate [tex]c^2[/tex] for each angle:
For angle X: [tex]c^2 = 25^2 + 27^2 - 2(25)(27)*cos(X)[/tex] ≈ 173.65
For angle Y: [tex]c^2 = 24^2 + 27^2 - 2(24)(27)*cos(Y)[/tex] ≈ 267.43
For angle Z: [tex]c^2 = 24^2 + 25^2 - 2(24)(25)*cos(Z)[/tex] ≈ 121.97
Therefore, the side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:
angle Y > angle Z > angle X
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Above, a right triangle is removed from a rectangle. What is the area of the remaining figure?
O 48 in²
O 136 in²
O 140 in²
O 160 in2
The correct option is (b) i.e. The area of the remaining figure is 136 in².
What is Right angled triangle?
A right angled triangle, also known as a right triangle, is a triangle in which one of the interior angles measures 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs or the adjacent and opposite sides. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the sum of the squares of the two legs is equal to the square of the hypotenuse.
Given : length = 20 and breadth = 8
The area of given rectangle = l × b
= 20 × 8
= 160 in²
Similarly, area of right angled triangle = 1/2 × b × h
= 1/2 × (20-8) × 4
= 1/2 × 12 × 4
= 24 in²
Hence, The area of remaining figure :
= The area of given rectangle - area of right angled triangle
= 160 - 24
= 136 in²
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H + i3 where i = 1 and h = 19 caculate please
Answer: 22
Step-by-step explanation:
Substitude 1 for i and 19 for H.
19+1(3) = 19+3 = 22
End of unit 4 assessment right triangle trigonometry
End of unit 4 assessment on right triangle trigonometry is an evaluation of a student's understanding of the basic concepts and applications of trigonometry involving right triangles.
This assessment may cover topics such as the trigonometric functions, Pythagorean theorem, special right triangles, and solving right triangles.
Trigonometry is the study of the relationships between the angles and sides of triangles, particularly right triangles. It is a branch of mathematics that has numerous applications in fields such as physics, engineering, and astronomy.
The trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions can be used to solve problems involving angles and sides of right triangles, such as finding the missing side or angle.
The Pythagorean theorem is another fundamental concept in right triangle trigonometry. It states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Special right triangles, such as the 30-60-90 triangle and the 45-45-90 triangle, have specific ratios of their side lengths that can be used to solve problems more easily.
Solving right triangles involves finding the measures of all the angles and sides of a right triangle given certain information, such as the length of one side and the measure of one angle.
In conclusion, the end of unit 4 assessment on right triangle trigonometry evaluates a student's understanding of the basic concepts and applications of trigonometry involving right triangles. This assessment is important for students to demonstrate their mastery of the subject and to prepare them for further studies in mathematics and related fields.
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End of unit 4 assessment right triangle trigonometry describe the importance of Side ratios in right triangles as a function of the angles ?
suppose 58% of recent college graduates plan on pursuing a graduate degree. thirteen recent college graduates are randomly selected. a. what is the probability that no more than four of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) b. what is the probability that exactly seven of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) c. what is the probability that at least six but no more than ten of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.)
The probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437. b. X= 7 = 0.2004.
What is binomial distribution?With a set number of independent trials, each of which has just two potential outcomes—success or failure—a binomial distribution defines the number of successes. The chance of success, represented by p, and the number of trials, denoted by n, are the two factors that define the distribution.
Given that, 58% of recent college graduates plan on pursuing a graduate degree.
Using the binomial probability formula we have:
[tex]P(X \leq 4) = \sum (i = 0 \to 4) (n C i) * p^i * (1 - p)^{(n-i)}\\\\[/tex]
Here, n = 13, p = 0.58.
[tex]P(X \leq 4) = Σ(i = 0 \to 4) (13 C i) * 0.58^i * (1 - 0.58)^{(13-i)}= 0.1437[/tex]
Hence, the probability that no more than four of the college graduates plan to pursue a graduate degree is approximately 0.1437.
b. For X = 7:
[tex]P(X = 7) = (13 C 7) * 0.58^7 * (1 - 0.58)^{(13-7)}= 0.2004[/tex]
Hence, the probability that exactly seven of the college graduates plan to pursue a graduate degree is approximately 0.2004.
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Alex used his grandmother’s recipe to make 11 3/7 pounds of granola. If he fills as many bags as he can with 2 2/3 pounds of granola in each bag, how many pounds will he have left over?
A 16/21 pound
B 2 20/21 pounds
C 4 2/7 pounds
D 8 16/21 pounds
The number of pounds that he will have left over from 11 3/7 pounds is 4 2/7
How many pounds will he have left over?To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.
We can convert 11 3/7 pounds to an improper fraction:
11 3/7 pounds = 80/7 pounds
Also, we have
2 2/3 pounds = 8/3 pounds
Now we can divide the total amount of granola by the amount in each bag:
(80/7) ÷ (8/3)
To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:
(80/7) × (3/8)
Simplifying, we get:
(80 x 3) / (7 x 8) = 30/7
Divide
(80 x 3) / (7 x 8) = 4 2/7
Hence, the bags is 4 2/7
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Colleen paid $13.70 to download 12 songs from an online music service. Some of the songs were on sale and cost $0.99 each. The rest were regularly priced at $1.25 per song. Let x represent the number of sale priced songs, and let y represent the number of regularly priced songs. This situation can be represented by the system x+y=12 and 0.99x+1.25y=13.7 . How many of each type of song did Colleen purchase?
Using equations, we can find that the number of sale-priced songs is 5 and the number of regularly priced songs is 7.
What exactly is an equation system?Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol.
As per the question, equation given are:
x + y = 12
x = 12 - y
Now, substituting the value in:
0.99x+1.25y = 13.7
= 0.99(12-y) +1.25y = 13.7
= 11.88 - 0.99y + 1.25y = 13.7
= 0.26y = 13.7 - 11.88
0.26y = 1.82
y = 1.82/0.26
y = 7
Now, substitute this value,
x = 12 - 7
x = 5
As a result, there are 5 songs on sale and 7 songs that are regularly priced.
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how mang triangles are possible given the following side maesurment: 3 feet , 5 feet, 4 feet
The answer is: 1 triangle is possible given the following side maesurment: 3 feet , 5 feet, 4 feet.
To determine how many triangles are possible with these side measurements, we can use the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
What is inequality theorem?
In this case, we have three side measurements: 3 feet, 5 feet, and 4 feet. Let's call these sides a, b, and c, respectively. Using the triangle inequality theorem, we can see that:
a + b > c
a + c > b
b + c > a
Substituting in the values of a, b, and c, we get:
3 + 5 > 4
3 + 4 > 5
4 + 5 > 3
All three of these inequalities are true, so it is possible to form a triangle with these side measurements.
To determine how many distinct triangles are possible, we can use the fact that any two triangles are distinct if and only if they have at least one side with a different length. In this case, all three sides have different lengths, so there is only one distinct triangle that can be formed with these side measurements.
Therefore, the answer is: 1 triangle.
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Complete question is: 1 triangle is possible given the following side maesurment: 3 feet , 5 feet, 4 feet.
Identify the two choices that best completes the statement below.
What is the sum of the first 10 terms of the series 1 + 2 + 4 + 8...?
The sum of the first 10 terms of the geometric progression that is given in the question is 1023.
What is geometric progression ?
Geometric progression, also known as geometric sequence, is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed constant. This fixed constant is called the common ratio.
The given series is a geometric progression, where each term is obtained by multiplying the preceding term by 2. The first term is 1, and the common ratio is 2.
The sum of the first n terms of a geometric progression is given by the formula:
[tex]S_n = a(1 - r^n) / (1 - r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
Using this formula, we can find the sum of the first 10 terms of the given series as:
[tex]S_{10} = 1(1 - 2^{10}) / (1 - 2)[/tex]
[tex]= 1(1 - 1024) / (-1)[/tex]
[tex]= 1023[/tex]
Therefore, the sum of the first 10 terms of the series 1 + 2 + 4 + 8... is 1023.
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The length of one of the legs of a right triangle is 7. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides (the second leg).
Answer: 24
Step-by-step explanation:
Write out problem using Pythagorean Theorem: [tex]7^2+x^2=(x+1)^2[/tex]
Simplify and expand right side: [tex]49+x^2=x^2 + 2x + 1[/tex]
Subtract [tex]x^2[/tex] from both sides: [tex]49 = 2x + 1[/tex]
Subtract 1 from both sides: [tex]48=2x[/tex]
Divide by 2 on both sides: [tex]24 = x[/tex]
[tex]x = 24[/tex]
PLEASE HURRY !! I NEED HELP!!!
Answer:$10
Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?
He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.
Solve for x,
using the secant lines.
6 cm
3 cm
x = [?] cm
X
15 cm
Remember a b = c d
W
Enter
Answer: 3
Step-by-step explanation:
Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.
Explain about the secant lines?A straight line connecting two points on such a function is known as a secant line. The average change rate or just the slope across two locations can also be used to describe it.
The slope between two points and the average rate of shift in a function among two points are interchangeable terms.
Given data:
AE = 6 cm, AB = 3 cm, ED = x cm, BC = 15 cm
Now,
AD = AE + ED
AD = 6 + x ...eq 1
AC = AB + BC
AC = 3 + 15
AC = 18 ....2
As the given two chords are intersecting internally,
AC x AB = AD x AE
18 x 3 = (6 + x) x 6
6 + x = 18 x 3 / 6
6 + x = 9
x = 3
Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.
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Complete question:
Solve for x, using the secant lines.
AE = 6 cm, AB = 3 cm,ED = x = [?] cm, BC = 15 cm
Remember a.b = c.d
The diagram is attached.
What function is represented by the graph
The function [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.
What is graph?
A graph is a visual representation of data or a mathematical function, usually plotted on a coordinate plane. It is a way to display information in a clear and concise manner, making it easier to analyze and interpret.
From the graph, it can be observed that the function intersects the x-axis at three points, namely x=-1, 2, and 5. Therefore, these values are considered to be the zeros of the function.
According to the definition, if c is a zero of a function f(x), then (x-c) is a factor of f(x). Applying this definition, we can infer that (x+1), (x-2), and (x-5) are the factors of the given function.
In summary, the zeros of the function are -1, 2, and 5, and the corresponding factors of the function are (x+1), (x-2), and (x-5).
Therefore the function [tex]f(x)=(x-5)(x-2)(x+1)[/tex] represents the graph.
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johnny read 30 pageson monday. opn tuesday he read 1/8 of the book. on wednesday he read the remaining 1/4. how many pages
Johnny read 30 pages on Monday. On Tuesday he read 1/8 of the book. On Wednesday he read the remaining 1/4. How many pages did he read in total?To find out how many pages Johnny read in total, we need to first determine the total number of pages in the book. We know that he read 1/8 of the book on Tuesday and the remaining 1/4 on Wednesday. So we can add these two fractions to find out the total fraction of the book that he read:1/8 + 1/4 = 3/8Now we know that Johnny read 3/8 of the book. We can use this information to set up a proportion to find out how many pages he read in total:3/8 = x/total number of pagesTo solve for x, we can cross-multiply and simplify:3/8 * total number of pages = xMultiply both sides by 8/3:total number of pages = x * 8/3Now we need to find out what x is. We know that Johnny read 30 pages on Monday, which is 1/8 of the total number of pages. So we can use this information to set up another proportion:1/8 = 30/total number of pagesTo solve for the total number of pages, we can cross-multiply and simplify:1/8 * total number of pages = 30Multiply both sides by 8:total number of pages = 240Now we can substitute this value for the total number of pages in our previous equation to find out how many pages Johnny read in total:total number of pages = x * 8/3240 = x * 8/3Multiply both sides by 3/8:x = 90Therefore, Johnny read a total of 30 + 90 = 120 pages.