Answer:
Ratio of the increase in value to the original value will be 1 : 5
Step-by-step explanation:
This question is incomplete; Here is the complete question.
A house with an original value to $150,000 increased in value to $180,000 in 5 years. what is the ratio of the increase in value to the original value of the house?
Original value of the house = $150000
Value of the house after 5 years = $180000
Appreciation in value of the house after 5 years = $180000 - $150000
= $30000
Now the ratio of the increase in value to the original value = [tex]\frac{\text{Increased value}}{\text{Original value}}[/tex]
= [tex]\frac{30000}{150000}[/tex]
= [tex]\frac{1}{5}[/tex] or 1 : 5
Therefore, ratio of the increase in value to the original value of the house is 1 : 5
Final answer:
To find the ratio of the increase in house value to the original value, subtract the original price from the increased price, then divide by the original price. For a house purchased at $200,000 and increased to $250,000, the ratio would be 0.25, or a 25% increase from the original value.
Explanation:
To calculate the ratio of the increase in value to the original value of a house, you must take the difference between the final value and the original value, then divide this by the original value. Suppose a house was bought for $200,000 and is now worth $250,000, this would be an increase of $250,000 - $200,000 = $50,000. The ratio of increase to original value would thus be $50,000 / $200,000 = 0.25 or 1:4. This indicates that, for every dollar of the original value, the house increased in value by 25 cents. If we wanted to express this as a percentage, we would multiply by 100, giving us a 25% increase in value. However, it's important to remember other factors such as transaction costs, market conditions, and loan repayment when considering the rate of return on a house.
Miss Alvarez has a piece of ribbon that is 2.65 feet long she cuts the ribbon into 5 equal pieces what is a good estimate of the length of each piece of ribbon
Final answer:
To find the length of each piece of ribbon, divide the total length of 2.65 feet by 5, resulting in 0.53 feet per piece, or approximately 6 inches after converting to a more convenient measurement.
Explanation:
The student's question involves the division of a length of ribbon into equal pieces. Miss Alvarez has a piece of ribbon that is 2.65 feet long and she cuts it into 5 equal pieces. To estimate the length of each piece, we would divide the total length of the ribbon by the number of pieces.
The calculation would be: 2.65 feet ÷ 5 pieces = 0.53 feet per piece. If we want a more convenient measure, we could convert feet to inches since there are 12 inches in a foot, resulting in approximately 6.36 inches per piece (0.53 feet × 12 inches/foot).
As an estimate and for ease of measurement, we might round this to the nearest whole number, suggesting that each piece of ribbon is approximately 6 inches in length.
if 60% of A is 20% of B, then B is what percent of A?
a. 3%
b. 30%
c. 200%
d. 300%
Answer:
d. 300%
Step-by-step explanation:
The given relation is ...
60%·A = 20%·B
Dividing by 20%, we see that ...
3·A = B
Of course, 3 = 3×100% = 300%, so B is 300% of A.
First, let's write the given condition in the form of an equation. If 60% of A is 20% of B, it can be written as:
60/100 * A = 20/100 * B
In order to proceed, we begin simplifying the equation by eliminating the fractions. This can be achieved by multiplying both sides of the equation by 100, turning our equation into:
60A = 20B
Following this, we can further simplify by solving for B. This involves dividing the equation through by 20A which yields:
B = 60A / 20
This simplification results in the following expression:
B = 3A
This means that B equals three times the value of A. However, we have been asked to express B in terms of what percent it is of A. Knowing that 'percent' may be understood as 'per hundred', this corresponds to converting the ratio to a percentage.
We can safely say therefore that B is 300% of A which corresponds to choice (d) among our original options.
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A company makes steel rods shaped like cylinders. Each rod has a radius of 4 centimeters and a height of 30 centimeters. If the company used 94,953.6 of steel, how many rods did it make
Answer:
Company made 63 rods with the given amount of steel.
Step-by-step explanation:
Given:
Radius of each rod =4 cm
height of each rod = 30 cm
Number of steel company used = 94953.6
We need to find how many rods company can make.
Solution:
First we will find the Volume of each rod.
Since rod is in cylindrical shape.
So we will use Volume of cylinder.
Now Volume of cylinder is given by π times square of the radius times height.
framing in equation form we get;
Volume of each rod = [tex]\pi r^2h= \pi \times4^2\times 30 = 1507.96 \ cm^3[/tex]
So we can say that steel used to make each rod = 1507.96
Number of steel company used = 94953.6 (given)
To find the number of steel rod company made we will divide Number of steel company used by number of steel used to make each rod.
framing in equation form we get;
number of steel rod company made = [tex]\frac{94953.6}{1507.96}= 62.96\approx63[/tex]
Hence Company made 63 rods with the given amount of steel.
The number of rods made using given data is approximately 63 rods .
To find out how many steel rods a company made based on the total volume of steel used, we need to calculate the volume of one rod and then divide the total volume of steel by this.
The volume of a cylinder (which is the shape of the rods) is calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Given that each rod has a radius of 4 centimeters and a height of 30 centimeters, the volume of one rod can be found as follows:
V = π(4²)(30)
≈ 3.14(16)(30)
= 1,507.2 cm³
Given the total volume of steel used is 94,953.6 cm³, the number of rods made can be calculated by dividing the total volume of steel by the volume of one rod:
Number of rods = 94,953.6 cm³ / 1,507.2 cm³
≈ 63
Therefore, the company made approximately 63 steel rods.
Martinez purchased a pair of shoes on a web site. The original price of the shoes was $75. She used a coupon code to receive a 20% discount? The website applied a 10% service fee to the discounted price. Martinez's shoes were less than the original price by what percent?
Answer:
Bb
Step-by-step explanation:
Final answer:
After applying a 20% discount and a 10% service fee to a pair of shoes originally priced at $75, Martinez ends up saving 12% from the original price.
Explanation:
Martinez is looking to calculate the final price of a pair of shoes after applying a 20% discount and a 10% service fee. She wants to know the overall percentage saved from the original price. First, let's calculate the discount: $75.00 × 0.20 = $15.00. Thus, the discounted price is $75.00 - $15.00 = $60.00. Next, we add the service fee on the discounted price: $60.00 × 0.10 = $6.00. Therefore, the total cost after the discount and service fee is $60.00 + $6.00 = $66.00.
To find the percent decrease from the original price, we can use the formula 'Percent Decrease = ((Original Price - Final Price) / Original Price) × 100%'. Substituting the respective values, we get: ((75 - 66) / 75) × 100% = 12%. Martinez saved 12% off the original price of the shoes after all the adjustments.
Miguel walked 1/2 mile to the library and then 3/5 mile to the post office.How can he write 1/2 and 3/5 as a pair of fractions with a common denominator?
Answer:
[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]
Step-by-step explanation:
Given:
The fractions are given as:
[tex]\dfrac{1}{2}\ and\ \dfrac{3}{5}[/tex]
The denominators of the first fraction is 2 and that of the second fraction is 5.
In order to find the common denominator for 2 and 5, we have to find the least common multiple of each of the numbers.
Multiples of 2 = 2, 4, 6, 8, 10, 12,....
Multiples of 5 = 5, 10, 15, 20, 25, 30,....
Therefore, the least common multiple of 2 and 5 is 10. So, the common denominator is 10.
Now, multiply the numerator and denominator of each fraction by the same suitable number such that the denominator becomes 10.
So, for the first fraction, 2 is in the denominator.
So, 2 when multiplied by 5 gives 10.
So, we multiply the numerator and denominator of first fraction by 5. This gives,
[tex]\dfrac{1}{2}=\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}[/tex]
Now, for the second fraction, 5 is in the denominator.
So, 5 when multiplied by 2 gives 10.
So, we multiply the numerator and denominator of first fraction by 2. This gives,
[tex]\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2}=\dfrac{6}{10}[/tex]
Therefore, the new fractions after making the denominators same are:
[tex]\dfrac{5}{10}\ and\ \dfrac{6}{10}[/tex]
So, the miles covered in fraction with same denominators are:
[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]
Lily is five years old she has a younger brother leo her brothers age is represented by the expression 3x-14 where x represents lilys age how old is leo
Answer:
Leo is 1 year old.
Step-by-step explanation:
Given:
Lily's age = 5
Leo's age = [tex]3x-14[/tex]
we need to find the Leo's age.
Solution:
Leo's age = [tex]3x-14[/tex]
where x ⇒ Lilly age
But Lilly's age = 5 years (given)
So we will substitute the value of x as 2 in Leo's age expression.
On Substituting we get;
Leo's age = [tex]3x-14 = 3\times5-14 = 15-14 = 1\ year[/tex]
Hence Leo is 1 year old.
A packaging company is going to make open-topped boxes, with square bases, that hold 140 cubic centimeters. What are the dimensions of the box that can be built with the least material? (Round your answers to the nearest hundredth.)
Answer:
x = 6.54 cm
h = 3.27 cm
Step-by-step explanation:
Volume of open top box
V = 140 cm³
Dimensions of the box
It is a base square box then area of the base of side x is
A(b) = x²
And we will call h the height of the box then
V = 140 ⇒ 140 = x²*h ⇒ h = 140/ x²
We have to calculate the area of the 4 sides
Area of one side is As = x*h ⇒ total area of 4 sides = 4 x* 140/x²
Ats = 560/x
Then Total area of the box is
A(t) = Area of the base + Total area of sides
A(x) = x² + 560/x
Taking derivatives on both sides of the equation we get:
A´(x) = 2x - 560/x²
A´(x) = 0 ⇒ 2x - 560/x² = 0 ⇒ 2x³ - 560 = 0
x³ = 280 ⇒ x = 6.54 cm
And h h = 140/ (6.54)² ⇒ h = 140/ 42.77 h = 3.27 cm
Over three years ago Lucius a $550 $600 and $650 from Babysitting the polynomial 550 X to the 3rd+600 X squared +650 X represents her savings with interest after three years the annual interest rate equals X minus one find the interest needed so that she will have $200 after three years
Answer:
about 5.52%
Step-by-step explanation:
If Lucius wants an account value of $2000 after 3 years, she can find the interest rate by solving the polynomial ...
550x³ +600x² +650x -2000 = 0
This equation has one positive real root. It is irrational, so must be found using the rather complicated cubic solution formula or, more simply, a graphing calculator. The latter shows the root to be near 1.05516.
Lucius needs an interest rate of ...
(1.05516 -1)×100% = 5.516%
The interest rate needed for a balance of $2000 after 3 years is about 5.52%.
The pizza stand gives patrons a free pizza when they collect 8 coupons how many free pizzas can Mrs.Fowler get if she has 78 coupons?How many more coupons does she need for the next free pizza
Answer:
Mrs. Fowler will get [tex]9[/tex] free pizza. And she needs two more coupon for the next pizza.
Step-by-step explanation:
Given that pizza stand gives a free pizza for every [tex]8[/tex] coupons.
And Mrs. Fowler has [tex]78[/tex] coupons.
Part (a)
How many free pizzas can Mrs. Fowler get if she has [tex]78[/tex]coupons?
We will divide total number of coupons [tex]78[/tex] by [tex]8[/tex] coupons.
[tex]\frac{78}{8}=9\frac{6}{8}[/tex]
When we divide we get quotient as [tex]9[/tex], with a remainder of [tex]6[/tex]. So, Mrs. Fowler will get [tex]9[/tex] free pizza.
Now, part (b)
If Mrs. Fowler adds two more coupons that will turn remainder [tex]6[/tex] into [tex]6+2=8[/tex].
So, she can have next pizza.
State aid and state B or among the states with the most remaining and drive in movie screens state a has six more screen stay in state be there are 48 screens total in the two states how many drive-in movie screens remain in each state
Answer:
State A has 27 screens and state B has 21 screens.
Step-by-step explanation:
Let the number of screens in state B be 'x'.
Given:
Number of screens in state A is 6 more than state B
Total number of screens = 48.
Now, as per question:
Number of screens in state A = 6 more than state B.
Framing in equation form, we get:
Number of screens in state A = [tex]6+x[/tex]
Now, total number of screens is the sum of the screens in state A and number of screens in state B. Therefore,
Total number of screens = 48
Number of screens in state A + Number of screens in state B = 48
Substituting the given values, we get:
[tex]6+x+x=48\\\\6+2x=48\\\\2x=48-6\\\\2x=42\\\\x=\frac{42}{2}=21[/tex]
So, state B has 21 screens.
State A has = 6 + 21 = 27 screens.
Therefore, state A has 27 screens and state B has 21 screens.
Triangle ABC is congruent to triangle PQR, angle B equals 3v+4, and angle Q equals 8v-6, find the measurements of angles B, and Q. please show step by step, thank you.
Last week Stacy earned $24 for baby sitting for hours in her part time job at Burger city she work 12 hours and earned $78 how many total hours distese work last week?
Answer:
Last week she work [tex]3\frac{54}{78}\ hours[/tex].
Step-by-step explanation:
Given:
Last week Stacy earned $24 for baby sitting for hours in her part time job at Burger city she work 12 hours and earned $78.
Now, to find the total hours she work last week.
As, given she work 12 hours and earned $78.
So, to solve by using unitary method:
If she earned $78 in working 12 hours.
So, she earned $1 in working = [tex]\frac{12}{78}\ hour.[/tex]
Thus, she earned $24 in working = [tex]\frac{12}{78} \times 24[/tex]
[tex]=\frac{288}{78}[/tex]
[tex]=3\frac{54}{78}\ hours.[/tex]
Therefore, last week she work [tex]3\frac{54}{78}\ hours[/tex].
Jaimie paid $126 for 42 pretzels. He incorrectly calculates the rate per pretzel to be $84 per pretzel. Which statement identifies the error Jaimie most likely made in determining the rate per pretzel and describes the correct method for determining the rate per pretzel?
Answer:
see the explanation
Step-by-step explanation:
we know that
To determine the rate per pretzel or unit rate, divide the total paid by the number of pretzel
so
[tex]\frac{126}{42}=\$3\ per\ pretzel[/tex]
Jaimie's error
He subtracted 42 from $126 when he should have divided $126 by 42
Rosita can wax her car in 2 hours or 120 minutes. When she works together with Helga, they can wax the car in 45 minutes. How long would it take Helga, working by herself, to wax the car?
Step-by-step explanation:
Let w be the work of waxing.
Rosita can wax her car in 2 hours or 120 minutes.
Time taken by Rosita = 120 minutes
[tex]\texttt{Rate of Rosita = }\frac{W}{120}[/tex]
Let time taken by Helga be t,
[tex]\texttt{Rate of Helga = }\frac{W}{t}[/tex]
When she works together with Helga, they can wax the car in 45 minutes.
We have
[tex]\frac{W}{\frac{W}{120}+\frac{W}{t}}=45\\\\120t=45(120+t)\\\\120t=5400+45t\\\\t=72minutes[/tex]
Time taken by Helga to wax the car is 72 minutes
The mean weight of the seven linebackers was 236 pounds. The first six linebackers weighed 215lb, 305lb, 265lb, 196lb, 221lb, and 236lb, respectevily. What was the weight of the seventh linebackers?
Answer:
The weight of the seventh linebacker is = 214 lb.
Step-by-step explanation:
Given:
Mean of 7 linebackers = 236 lb
The weights of first 6 linebackers are:
215 lb, 305 lb, 265 lb, 196 lb, 221 lb and 236 lb
To find the weight of seventh linebacker.
Solution:
Let the weight of the seventh linebacker be = [tex]x[/tex]
The mean of 7 line backers will be given as:
⇒ [tex]\frac{215+305+265+196+221+236+x}{7}[/tex]
The mean of the 7 linebackers is given = 236 lb
Thus, the equation to find [tex]x[/tex] will be :
[tex]\frac{215+305+265+196+221+236+x}{7}=236[/tex]
Simplifying.
[tex]\frac{1438+x}{7}=236[/tex]
Multiplying both sides by 7.
[tex]7.\frac{1438+x}{7}=236(7)[/tex]
[tex]1438+x=1652[/tex]
Subtracting both sides by 1438.
[tex]1438-1438+x=1652-1438[/tex]
∴ [tex]x=214[/tex]
Thus, the weight of the seventh linebacker is = 214 lb.
A bakery made 26 cherry pies, using 115 cherries for each pie. They threw away 36 cherries that were bad. If they used all the cherries they had, how many cherries did they start with?
Final answer:
To calculate the total number of cherries that the bakery started with, multiply the number of pies by cherries per pie and then add the ones thrown away, resulting in 3026 cherries.
Explanation:
The question asks how many cherries the bakery started with before making the cherry pies. To find the answer, we multiply the number of cherry pies by the cherries used per pie and then add the number of cherries thrown away.
Multiply the number of pies (26) by the number of cherries used for each pie (115).
The result from step 1 gives the number of cherries used to make the pies.
Add the number of cherries thrown away (36) to the result from step 2.
The sum from step 3 is the total number of cherries the bakery started with.
Let's do the calculations:
26 pies × 115 cherries per pie = 2990 cherries
2990 cherries + 36 bad cherries = 3026 cherries
Therefore, the bakery started with 3026 cherries.
You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr. your actual velocity is the vector sum of the stream's velocity and ytour swimming velocity. find your actual velocity?
Answer:
Step-by-step explanation:
You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr.
If your actual velocity is the vector sum of the stream's velocity and your swimming velocity, it means that your actual velocity is the resultant velocity. Let R represent the resultant velocity. It means that
R² = 3² + 5² = 9 + 25
R² = 34
Taking square root of the left hand side and the right hand side of the equation, it becomes
R = √34 = 5.83 km/hr.
Final answer:
To find the swimmer's actual velocity in a stream where the swimmer's velocity is 3 km/hr and the stream's velocity is 5 km/hr, we use the Pythagorean theorem, resulting in an actual velocity of approximately 5.83 km/hr.
Explanation:
The question involves calculating the actual velocity of a swimmer moving in a stream. The swimmer swims at a rate of 3 km/hr perpendicular to the stream, while the stream itself has a current of 5 km/hr.
To find the swimmer's actual velocity when these two vectors are combined, we use the Pythagorean theorem, as the velocities are perpendicular to each other.
Let the swimmer's velocity be represented by Vswimmer = 3 km/hr and the stream's velocity by Vstream = 5 km/hr.
The actual velocity (Vactual) is the vector sum of these two velocities. Since they are at right angles to each other, Vactual can be calculated as [tex]\sqrt{((Vswimmer)^2 + (Vstream)^2)[/tex] .
Substituting the values gives Vactual =[tex]\sqrt{(3^2 + 5^2)} = \sqrt{(9 + 25)} = \sqrt{(34),[/tex] which approximately equals 5.83 km/hr.
Therefore, the actual velocity of the swimmer, taking into account the stream's current, is approximately 5.83 km/hr.
A frequency distribution lists the _________ of occurrences of each category of data, while a relative frequency distribution lists the __________ type proportion number of occurrences of each category of data.
Answer:
A frequency distribution lists the number of occurrences of each category of data, while a relative frequency distribution lists the proportion of occurrences of each category of data.
Explanation:
A "frequency distribution" is one of the ways in organizing a data, either by listing the information, putting them in a table or showing them in a graph. The items in the list (distinct values) are then counted when it comes to the number of times they've occurred.
Thus, this explains the first answer, "number."
On the other hand, a "relative frequency distribution" refers to the proportion of the overall number of observations in a particular category. You can get this by dividing each frequency with the total number of data in a sample.
Thus, this explains the second answer, "proportion."
A frequency distribution lists the number of occurrences for each category of data, whereas a relative frequency distribution provides the proportion of occurrences for each category in relation to the total number of data points. Histograms are a common tool to visualize these distributions, with the heights of bars representing either frequency or relative frequency.
Explanation:The frequency distribution primarily deals with the number of occurrences of each category of data. For instance, in a class of 20 students, if the question is how many students scored in a particular range, the frequency distribution helps identify this - telling us how many students achieved each possible score.
In contrast, a relative frequency distribution showcases the proportion of the total number of data points that each category represents. So, instead of just telling you how many students achieved each score, it would express these amounts as a ratio or percent of the 20 total students, giving you a relative perspective of the categories.
An example of these principles might be visualized in a histogram: a type of graph that can express either frequency or relative frequency. The horizontal axis represents the categories of data (such as score ranges), while the vertical axis reflects frequency or relative frequency, displaying these values through the heights of bars along the graph.
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If there are 6 randomly selected digits in an automobile license tag, and each digit must be one of the 10 integers (0-9), then there are 106 possible license tags.A. TrueB. False
Answer: True.
Step-by-step explanation:
The total number of possible digits in the number system : 10 (from 0 to 9)
If there are 6 randomly selected digits in an automobile license tag, and each digit must be one of the 10 integers (0-9), then the choices for each digit in license tag = 10
Fundamental counting principle , the total number of ways to make 6-digits license tag where the choices for each digit in license tag is 10 will be :
[tex]10\times10\times10\times10\times10\times10=10^6[/tex]
Hence, there are [tex]10^6[/tex] possible license tags.
Therefore , the given statement is correct.
Final answer:
The statement is True because for each of the 6 digits in a license tag, there are 10 possible integers, giving us a total of 10^6 possible combinations.
Explanation:
The question relates to probability and combinatorics, which are branches of mathematics that deal with the likelihood of certain outcomes and the combination of different elements, respectively. If an automobile license tag consists of 6 randomly selected digits and each digit must be one of the 10 integers (0-9), then we must consider every digit independently.
Since there are 10 options for each digit, and there are 6 digits, we calculate the total number of possible license tags by multiplying the number of options for each digit. This is done by raising the number of options (10) to the power of the number of digits (6), which gives us: 10^6. Therefore, the statement is True as there are indeed 10^6 possible license tags.
What is the common factor of the numerator and denominator in the expression (2x+3)(x−4)/(x−4)(x+4)?
Answer:
(2x-3)/(x+4)
Step-by-step explanation:
Answer:
(x - 4).
Step-by-step explanation:
(x - 4) is common to to top and bottom of the fraction.
The fraction simplifies to (2x+3)/(x+4).
Suppose that a company ships packages that are variable in weight, with an average weight of 15 lb and a standard deviation of 10. Assuming that the packages come from a large number of different customers so that it is reasonable to model their weights as independent random variables, find the probability that 100 packages will have a total weight exceeding 1700 lb.
ANSWER= 0.9772
STEP-BY-STEP EXPLANATION:
We are assuming that there is an underlying distribution of package weights,even though we don´t speciify the shape of that distribution.
Letting [tex]x_{i}[/tex] denote the ith package weight and S=[tex]x_{1} +....x_{100}[/tex] we are trying to find P(S ≤ 1700)
We know that the distribution of S is approximately normal with mean nцХ and variance по²Х
S≈N( 100 * 15, 100 * 10² ) = N (1500.10000) (note that they gave us the standar deviation aove; variances add, so we need to square this). Finally,
P(S ≤ 1700) = P ([tex]\frac{S-1500}{\sqrt{10000} }[/tex] ≤ [tex]\frac{1700 - 1500}{\sqrt{10000} }[/tex])
≈P (Z≤2) = 0.9772
the standard deviation of duration times in seconds of the old faithful geyser is less than 40 sec. identify the null hypothesis and alternative hypothesis in symbolic form
Answer:
this is a left tailed test
Null hypothesis, [tex]H_{0} :[/tex] σ = 40 seconds
Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.
Step-by-step explanation:
i) the standard deviation of duration times in seconds of the old faithful geyser is less than 40 sec. identify the null hypothesis and alternative hypothesis in symbolic form
ii) this is a left tailed test
Null hypothesis, [tex]H_{0} :[/tex] σ = 40 seconds
Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.
Morten Andersen played in NFL for 25 years write and solve an equation to find how many points he averaged each year
Answer:
[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]
So then we have that Morten Andersen scored on average 97.45 points per year in his career.
Step-by-step explanation:
Assuming the following table on the figure attached.
We see that the career points for Morten Andersen was 2437. That include all the points over alll the years the he played in the NFL.
Since the total years played by Morten Andersen was 25 we can write the following equation:
[tex] 25 r =2437[/tex]
Where [tex] r[/tex] represent the rate of points average per year.
If we solve for r from the last equation we can divide both sides of the equation and we got:
[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]
So then we have that Morten Andersen scored on average 97.45 points per year in his career.
triangle RSt is similar to triangle xyz with rs= 3 inches and xy= 2 inches. Of the area of triangle RST is 27 in^2, determine and state the area of triangle XYZ in square inches.
Answer: The area of triangle ΔXYZ is 12 square inches.
Step-by-step explanation:
Since we have given that
RS = 3 inches
XY = 2 inches
Area of ΔRST = 27 in²
Since ΔRST is similar to ΔXYZ.
So, using the "Area similarity theorem":
[tex]\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2[/tex]
Hence, the area of triangle ΔXYZ is 12 square inches.
The area of triangle XYZ is found by squaring the ratio of the corresponding sides of the similar triangles and multiplying it by the area of the larger triangle RST. With the side length ratio of 2:3, the area ratio is (2/3)², resulting in an area of 12 in² for triangle XYZ.
The student's question involves determining the area of a smaller similar triangle (XYZ) given the area of the larger similar triangle (RST) and the lengths of corresponding sides. To solve, we utilize the property that similar triangles' areas are proportional to the square of the ratio of their corresponding sides.
Given:
Length of RS in triangle RST = 3 inches
Length of XY in triangle XYZ = 2 inches
Area of triangle RST (A1) = 27 in²
We establish the ratio of their sides as 2 inches (XY) / 3 inches (RS), which simplifies to 2/3. The ratio of their areas would then be (2/3)² because the area of similar triangles scales with the square of the ratio of their corresponding linear dimensions. Hence, the Area of triangle XYZ (A2) will be A1 × (2/3)².
A2 = 27 in² × (2/3)2 = 27 × 4/9 = 12 in².
The area of triangle XYZ is 12 in².
Joan spend half of her paycheck going to the movies. She washed the family car and earned 7 dollars. What is her weekly paycheck if she ended up with 18 dollars?
Answer:
her weekly allowance is $16
Step-by-step explanation:
Let x represent Joan's weekly paycheck.
Joan spent half of her paycheck going to the movies. This means that the total amount that she spent at the movies is x/2. The amount that she is left with would be
x - x/2 = x/2
She washed the family car and earned 7 dollars. This means that the total amount left with her is
x/2 + 7
if she ended with 18 dollars, it means that
x/2 + 7 = 18
x/2 = 18 - 7 = 11
x = 2 × 11 = $22
What is 12 2/3 X 2 1/2
Answer:
31.67
Step-by-step explanation:
12 2/3 X 2 1/2
we begin by converting this into improper fractions,
= 38/3 * 5/2
= 95/3
= 31.67
Find a third-degree polynomial equation with rational coefficients that has the given numbers as roots. 1 and 3i
Answer:
x³ − x² + 9x − 9 = 0
Step-by-step explanation:
Imaginary roots come in conjugate pairs. So if 3i is a root, then -3i is also a root.
(x − 1) (x − 3i) (x − (-3i)) = 0
(x − 1) (x − 3i) (x + 3i) = 0
(x − 1) (x² − 9i²) = 0
(x − 1) (x² + 9) = 0
x (x² + 9) − (x² + 9) = 0
x³ + 9x − x² − 9 = 0
x³ − x² + 9x − 9 = 0
To find a third-degree polynomial equation with rational coefficients that has the given roots, we consider the conjugate of the complex root. The equation can be written as (x - 1)(x - 3i)(x + 3i) and simplified to x^3 - x^2 + 9x - 9.
Explanation:
To find a third-degree polynomial equation with rational coefficients that has the given roots of 1 and 3i, we need to consider the conjugate of 3i, which is -3i. Therefore, the roots of the equation are 1, 3i, and -3i.
To find the polynomial equation, we start by noting that the polynomials with rational coefficients will have complex conjugate pairs of roots. Thus, we can write the equation as (x - 1)(x - 3i)(x + 3i). Simplifying, we get (x - 1)(x^2 + 9). Expanding further, the equation is x^3 - x^2 + 9x - 9.
Therefore, the desired third-degree polynomial equation with rational coefficients is x^3 - x^2 + 9x - 9.
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ANSWER THIS MATH QUESTION
Answer:
The slope of the line tangent to the function at x = 1 is 2.01 ≅2.Step-by-step explanation:
Using the formula of derivative, it can be easily shown that, [tex]\frac{d f(x)}{dx} = 2[/tex] where [tex]f(x) = x^{2}[/tex].
Here we need to show that as per the instructions in the given table.
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = [tex](1 + 0.01)^{2} - 1^{2} = 0.0201[/tex].
In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.
Hence, dividing Δy by Δx, we get, [tex]\frac{0.0201}{0.01} = 2.01[/tex].
Let's examine this taking a smaller value.
If we take Δx = 0.001, then Δy = [tex]1.001^{2} - 1^{2} = 0.002001[/tex].
Thus, [tex]\frac{0.002001}{0.001} = 2.001[/tex].
The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
We can see here that the slope of the line tangent to the function at x = 1 is 2.001 ≅ 2.
How we arrived at the solution?We can use the formula of derivative: [tex]\frac{df(x)}{dx} = 2[/tex]
Looking at the instructions in the given table, we have:
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = (1 + 0.01)² - 1² = 0.0201
In the above written equation, x = 1 because we need to find the slope of the line tangent at x = 1.
Thus, Δy divided by Δx, we get, 0.0201/0.01 = 2.01
If we take Δx = 0.001, then Δy = 1.001² - 1² = 0.002001
So, we have: 0.002001/0.001 = 2.001
We can see here that the more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
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The depreciation of the value for the car is modeled by the equation Y equals 100,000 (.85)x or ask year since 2000. In what year was the value of the car was $61,412.50?
Answer:
Step-by-step explanation:
The car's value was $61,412.50 in the year 2006.
x = no. of years since 2000.
Acc. to ques,
100,000 × (0.85)ˣ = 61,412.50
(0.85)ˣ = 0.614125.
ln((0.85)ˣ) = ln(0.614125).
x × ln(0.85) = ln(0.614125).
x = ln(0.614125) / ln(0.85).
x = 5.832 ≈ 6
In an experiment, it is important that independent and dependent variables are given _____, which specify procedures for manipulating the independent variable and measuring the dependent variable.
Answer:
a relationship ( model equation)
Step-by-step explanation:
the relationship specifies how the dependent variable relies on the independent variable.This helps in manipulating of the variable to see its effect/outcome.The relationship can be mathematical or logical ; it can also be a set of algorithm (program) which can be worked on using the independent variables as inputs. Usually the independent variables influence the dependent variables.