The first term of an A.P is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the A.P is 70/11.
The first term of an A.P is 14. Let the common difference be d. Then the second term of the A.P is given by 14 + d. Similarly, the third term of the A.P is given by 14 + 2d.
The third term of the A.P.Solution:
Sum of the first 5 terms of the A.P can be expressed as:
5/2 [2a + (5 - 1) d] = 5/2 [2(14) + 4d] = 35 + 10d
Sum of the first 10 terms of the A.P can be expressed as:
10/2 [2a + (10 - 1) d] = 10/2 [2(14) + 9d] = 70 + 45d
According to the question, the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. It can be written as follows: 35 + 10d = - (70 + 45d)
Simplifying the above equation, we get:
55d = -105⇒ d = -105/55 = -21/11
Substituting the value of d in 14 + 2d, we get:
14 + 2d = 14 + 2(-21/11) = 14 - 42/11= 112/11 - 42/11= 70/11
Hence, the third term of the A.P is 70/11.
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It takes 8 workers 12 days to complete a job. How long would 6 workers take?
Answer:
It would take 6 workers 16 days to complete the job.
This is because the number of workers and the number of days are inversely proportional. This means that if the number of workers increases, the number of days will decrease, and vice versa.
In this case, the number of workers has decreased from 8 to 6. This means that the number of days will increase from 12 to 16.
Here is the formula for calculating the number of days it would take 6 workers to complete the job:
Number of days = (Number of workers x Number of days) / (New number of workers)
Plugging in the values, we get the following:
Number of days = (8 x 12) / 6 = 16
Therefore, it would take 6 workers 16 days to complete the job.
Step-by-step explanation:
Answer:
It will take 6 workers 16 days
Step-by-step explanation:
8 workers at 12 days = 96 work days
We have 6 workers
96/6 = 16 days
It will take 6 workers 16 days
one pipe can fill a pool in 10 hours. another pipe can fill the same pool in 30 hours. how long would it take to fill the pool if both pipes were used at the same time?
Answer:
7,5 hours
Step-by-step explanation:
1/10+1/30=2/15
HELPP PLEASE THANK YOUUUU
The estimate of the horizontal distance traveled by a ball hit at an angle of 55º is given as follows:
348.9 feet.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
From the table, the points in this problem are given as follows:
(15, 157.2), (20, 189.2), (24, 220.8), (30, 253.8), (34, 269.2), (40, 284.8), (45, 285).
Inserting these points into a calculator, the line of best fit is given as follows:
y = 4.42x + 105.8.
Hence when x = 55 the output is given as follows:
y = 4.42(55) + 105.8
y = 348.9 feet.
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a store keeper wants to mix two types of flour to gett 300 lbs so he can sell it by 2.05 per lbs . if he uses flour worth 2.40 pr lbp with another flr work 3$ pers lob how many lbs of each didhe use
The store keeper used 125 pounds of flour worth $2.40 per pound and 175 pounds of flour worth $3 per pound to get 300 pounds of mixed flour.
What is equation?The assertion that two expressions are equal when they are connected by the equals sign ("="), is the mathematical definition of an equation. As an example, 2x - 5 = 13. The equations in this example are 2x - 5 and 13. The symbol "=" links these two expressions together.
Let x be the number of pounds of the flour worth $2.40 per pound, and y be the number of pounds of the flour worth $3 per pound. Since the store keeper wants to end up with 300 pounds of flour, we have:
x + y = 300
We also know that the store keeper wants to sell the mixed flour for $2.05 per pound. This means that the total cost of the flour (x pounds at $2.40 per pound, plus y pounds at $3 per pound) must be equal to:
300 pounds × $2.05 per pound = $615
In other words:
2.40x + 3y = 615
Two equations with two unknowns are now present:
x + y = 300
2.40x + 3y = 615
We can find x and y using algebra. One way to do this is to solve the first equation for x:
x = 300 - y
We can then substitute this expression for x into the second equation:
2.40(300 - y) + 3y = 615
Expanding the parentheses and simplifying, we get:
720 - 2.4y + 3y = 615
0.6y = 105
y = 175
So, the store keeper used 175 pounds of flour worth $3 per pound. To find the amount of flour worth $2.40 per pound, we can substitute y = 175 into the equation x + y = 300:
x + 175 = 300
x = 125
Therefore, the store keeper used 125 pounds of flour worth $2.40 per pound and 175 pounds of flour worth $3 per pound to get 300 pounds of mixed flour.
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The coordinates of point J are (1.75,3)
What are the coordinates of point K?
The coordinates of point K can be given by (-1/4, 5/8).
What are cartesian coordinates?
Cartesian coordinates are the values on a graph that can be used to show the location of a point on the graph.
The coordinates of point K can be found as follows:
There are 4 lines between 0 and -1 on the x-axis which divide it into 4 equal parts.
Point K lies on the first line. This means that the x-coordinate of the point is -1/4.
There are 8 lines between 0 and 1 on the y-axis which divide it into 8 equal parts.
Point K lies on the fifth line. This means that the y-coordinate of the point is 5/8.
From this, we can understand that the coordinates of the point K on the graph can be given by (-1/4, 5/8).
Therefore, the coordinates of point K can be given by (-1/4, 5/8).
Choose the INCORRECT statement below.
#4: The transformation can be represented by (x, y - 8).
Use the formula to find the volume of the figure. Show your work.
Hello !
Answer:
[tex]\boxed{\sf V{cone} \approx 2408.55 m^3}[/tex]
Step-by-step explanation:
To find the volume of a cone with the radius of its base and its height, we will apply the following formula:
[tex] \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} [/tex]
Where r is the radius of its base and h is its height.
Given:
r = 10 mh = 23 mLet's substitute our values into the formula:
[tex]\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}[/tex]
Have a nice day ;)
Bars cost $4. 50 after a 10% discount, what was the price before the discount
To find the price before the discount, we can use the information given.
Let's assume the original price before the discount is "P."
After a 10% discount, the price becomes $4.50. This means that the discounted price is equal to 90% of the original price:
0.90P = $4.50
To find the original price "P," we divide both sides of the equation by 0.90:
P = $4.50 / 0.90
P = $5.00
Therefore, the price before the discount was $5.00.
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leslie used some of her allowance money to buy a stack of 300 baseball trading cards at a yard sale. she randomly looks at 24 cards and sees 8 outfielders, 7 pitchers, 4 catchers, and 5 infielders. based on the data, what is the probability that the next card leslie looks at will be a pitcher?
the probability of picking a pitcher from the remaining cards is still 7/24. The probability that the next card Leslie looks at will be a pitcher is 7/24.
Leslie randomly looked at 24 cards out of 300, and she saw that 7 of them were pitchers. So, the probability of picking a pitcher from those 24 cards is 7/24. Since the remaining cards are still part of the same deck, and Leslie did not replace any of the cards she looked at, the probability of picking a pitcher from the remaining cards is still 7/24. Therefore, the probability that the next card Leslie looks at will be a pitcher is 7/24.
Step 1: Determine the total number of cards Leslie looked at, which is 24 (8 outfielders + 7 pitchers + 4 catchers + 5 infielders).
Step 2: Identify the number of pitchers, which is 7.
Step 3: Calculate the probability of picking a pitcher by dividing the number of pitchers by the total number of cards: 7 pitchers / 24 cards = 0.2917, or 29.17% when expressed as a percentage.
So, based on the data, the probability that the next card Leslie looks at will be a pitcher is approximately 29.17%.
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(b)In the sequence the sum of the third and fourth term is -12, the sum of the third and fifth term is 60 and the sum of the fourth and fifth term is 24. Show that the term form geometric progression. Find the sum of the first ten terms of the sequence.
The sum of the first ten terms of the sequence is approximately -22.17.
Let the first term of the sequence be a, and let the common ratio be r. Then the third term is ar², the fourth term is ar³, and the fifth term is ar⁴.
We are given:
ar² + ar³ = -12
ar² + ar⁴ = 60
ar³ + ar⁴ = 24
Subtracting the first equation from the second gives:
ar⁴ - ar³ = 72
Subtracting the first equation from the third gives:
ar⁴ -ar²= 36
Dividing these two equations gives:
r - 1/r = 2
Multiplying both sides by r gives:
r² - 1 = 2r
r² - 2r - 1 = 0
Using the quadratic formula, we find:
r = 1 + √2 or r= 1- √2
Since the terms of the sequence must be real numbers, we can discard the second solution. Therefore, the common ratio is:
r = 1 + √(2)
To find the first term a, we can use the equation:
ar² + ar³ = -12
Substituting r and simplifying, we get:
a = -12 / (3 + 2√(2))
So, The sum of the first ten terms of the sequence is:
a(1 - r¹⁰) / (1 - r)
=-22.1666... (rounded to the nearest hundredth)
Therefore, the sum of the first ten terms of the sequence is approximately -22.17.
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the new jersey renewable energy incentive program provides incentives for the use of photovoltaics, solar hot water, and other renewable energy sources. during the last few years it was assumed that approximately 20% of families in new jersey are interested in the program. however, it is now suspected that this figure has increased. in order to test this, a random sample of 1200 families is selected, and it is found that 360 of them are interested in the program. what are the null and alternative hypotheses that should be used (h0
The sample proportion (360 out of 1200) can be used to estimate the population proportion, and statistical tests such as a one-sample proportion test or a Z-test can be applied to evaluate the hypotheses and determine the significance of the results.
The null and alternative hypotheses that should be used in this scenario are as follows:
Null Hypothesis (H₀): The proportion of families interested in the program is still 20% or less.
Alternative Hypothesis (H₁): The proportion of families interested in the program has increased, i.e., it is greater than 20%.
Symbolically, we can represent the hypotheses as:
H₀: p ≤ 0.20 (proportion is 20% or less)
H₁: p > 0.20 (proportion is greater than 20%)
In this case, "p" represents the population proportion of families in New Jersey interested in the renewable energy program.
To determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, a hypothesis test can be conducted using appropriate statistical methods.
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(PLEASE ANSWER! WILL GIVE BRAINLIEST)
Determine if the given set of lengths could be those
of the sides of a triangle.
(a) 2 cm, 3 cm, 4 cm
(b) 6 m, 7 m, 10 m
(c) 21 m, 21 m, 21 m
(d) 20 m, 20 m, 4 m
(e) 8 cm, 12 cm, 3 cm
(f)(x-2) cm, (x + 1) cm, 2x cm
Answer:
(a) yes
(b) yes
(c) yes
(d) yes
(e) no
(f) no--2x - 1 > 2x, so -1 > 0 (not true)
Suppose that you were offered a lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing or a guaranteed payoff of $300. If you choose the lottery, you would be considered O a risk taker O a risk-neutral individual O a risk avoider O a risk-creator
If you choose the lottery, you would be considered a risk taker.
By opting for the lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing, you are demonstrating a willingness to take a chance and accept the uncertainty associated with the potential outcomes. A risk taker is someone who is willing to engage in risky or uncertain situations for the possibility of gaining a favorable outcome. In this case, you are accepting the risk of potentially winning nothing in exchange for the chance to win a larger amount.
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Which of the following is equivalent to sinθcosec wherever sinθcosec is defined? A. −1. B. 0.5. C. tanθ. D. −tanθ.
The expression sinθcosec is equivalent to 1 wherever it is defined, since cosecθ is the reciprocal of sinθ. Therefore, none of the given options are correct.
The expression sinθcosec is equivalent to 1 wherever it is defined, not any of the given options. To show this, recall that cosecθ is defined as the reciprocal of sinθ, i.e., cosecθ = 1/sinθ. Therefore, sinθcosec = sinθ(1/sinθ) = 1, whenever sinθ is not equal to 0 (since division by 0 is undefined).
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Answer Immeditely Please
The length of AC is given as follows:
AC = 70 units.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude of a triangle is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The altitude segment for this problem is given as follows:
21.
The bases for this problem are given as follows:
AD and 7.
Hence the length AD is obtained as follows:
7AD = 21² -> Geometric mean definition
AD = 21 x 21/7
AD = 21 x 3
AD = 63.
Applying the segment addition postulate, the length AC is obtained as follows:
AC = AD + DC
AC = 63 + 7
AC = 70 units.
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a warehouse has x cases containing 13 boxes of product and x 12 cases containing 21 boxes of product. write a simplified expression to represent the total number of boxes of product in the warehouse
The simplified expression to represent the total number of boxes of product in the warehouse is 13x + 21x12.
The warehouse has two types of cases: one type containing 13 boxes of product and the other containing 21 boxes of product. Let x be the number of cases containing 13 boxes of product.
Step 1: Identify the terms given in the problem. We have x cases with 13 boxes of product and x cases with 21 boxes of product.
Step 2: Write expressions for each group of cases. For the first group, the expression is 13x. For the second group, the expression is 21x.
Step 3: Add the expressions together to represent the total number of boxes of product. So, the combined expression is 13x + 21x.
Step 4: Simplify the expression by combining like terms. The final simplified expression is 13x + 21x = (13 + 21)x = 34x.
So, the simplified expression representing the total number of boxes of product in the warehouse is 34x.
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How do I solve this?
The expression tan²θ-Sin²θ = tan²θsin²θ is proven that the left hand side is equal to the right hand side.
How to prove an expression?To prove the expression, tan²θ-Sin²θ = tan²θsin²θ, start from the left-hand side and use the trigonometric identity tan²θ = sin²θ/cos²θ and the Pythagorean identity sin²θ + cos²θ = 1.
Starting from the left-hand side:
tan²θ - sin²θ = (sin²θ/cos²θ) - sin²θ
= sin²θ (1/cos²θ - 1)
= sin²θ ((1-cos²θ)/cos²θ)
= sin²θ (sin²θ/cos²θ)
= tan²θ sin²θ
Thus, it is shown that the left-hand side is equal to the right-hand side: tan²θ - sin²θ = tan²θ sin²θ.
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pls help i really need it
The total surface area of the prism is 684.15 m²
How to find the surface area?We can decompose the prism into 3 rectangles and two triangles.
The area of a rectangle is equal to the product between its dimensions, now let's find the areas of the rectangles from top to bottom.
a₁ = 15m*13m = 195m²
a₂ = 15m*9m = 135m²
a₃ = 15m*15.81m = 237.15 m²
And the area of a triangle of base B and height H is:
A = B*H/2
Here we have two triangles of height of 13m and a base of 9m, then the area of each triangle is:
A = 13m*9m/2 = 58.5m²
Then the total area of the prism is:
area =195m² + 135m² + 237.15 m² + 2* 58.5m²
area = 684.15 m²
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Everett runs 1. 5 fewer miles than skylar. Everett runs 7. 64 miles. How many miles does skylar run?
To find how many miles Skylar runs, we need to use the information given that Everett runs 1.5 fewer miles than Skylar and that Everett runs 7.64 miles. Let x be the number of miles Skylar runs. Then, we know that x - 1.5 is the number of miles Everett runs.
We can set up an equation:
x - 1.5 = 7.64
To solve for x, we add 1.5 to both sides:
x = 9.14
Therefore, Skylar runs 9.14 miles.
In summary, to find the number of miles Skylar runs, we can use the fact that Everett runs 1.5 fewer miles than Skylar and that Everett runs 7.64 miles. We can set up an equation and solve for x, which represents the number of miles Skylar runs. The answer is 9.14 miles.
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To find how many miles Skylar runs, we need to use the information given that Everett runs 1.5 fewer miles than Skylar and that Everett runs 7.64 miles. Let x be the number of miles Skylar runs. Then, we know that x - 1.5 is the number of miles Everett runs.
We can set up an equation:
x - 1.5 = 7.64
To solve for x, we add 1.5 to both sides:
x = 9.14
Therefore, Skylar runs 9.14 miles.
In summary, to find the number of miles Skylar runs, we can use the fact that Everett runs 1.5 fewer miles than Skylar and that Everett runs 7.64 miles. We can set up an equation and solve for x, which represents the number of miles Skylar runs. The answer is 9.14 miles.
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IF YOU SOLVE THIS CORRECTLY WITH EXPLANATION U WILL GET BRAINILEST
-2r(8r+5)
Answer:
-16r^2 - 10r
Step-by-step explanation:
To simplify the expression -2r(8r+5), you can use the distributive property of multiplication over addition.
-2r(8r+5) = -2r * 8r - 2r * 5
First, let's simplify -2r * 8r:
-2r * 8r = -16r^2
Next, let's simplify -2r * 5:
-2r * 5 = -10r
Putting it all together, the simplified expression is:
-2r(8r+5) = -16r^2 - 10r
what is the answer, i am having trouble solving this and i need to see an example
Answer:
m∠B = 11°
Step-by-step explanation:
When two angles are complementary, the sum of the measures equals 90° (the two angles form a right angle together)
Step 1: Therefore, we can find x by making the sum of the measures of angles A and B equal to 90:
m∠A + m∠B = 90
4x - 13 + x - 12 = 90
5x - 26 = 90
5x = 115
x = 23
Step 2: Now, we can plug in 23 for x in the equation representing m∠B:
m∠B = x - 12
m∠B = 23 - 12
m∠B = 11°
Other Examples: There are many ways to have two complementary angles, where none of the two angles are 0 or 90, including (1° + 89°), (2° + 88°) (3° + 87°), ..., (44° + 46°)
Let's say that m∠X = 1° and m∠R = 89°. The two angles are complementary since 1 + 89 = 90°
Use the product rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. The derivative is (x-50+(x+1)。 A. B. The derivative is (x-5)(x + 1) C. The derivative is (x-5) O D. The derivative is (x(1x+1) OE. The derivative is (x-5 1x+1)+
The correct answer is B. The derivative is 2x - 49.
To find the derivative of the function (x - 50 + (x + 1)), we can apply the product rule, which states that the derivative of the product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.
Let's break down the given function into its components:
f(x) = (x - 50) + (x + 1)
To differentiate this function, we can consider each term separately:
Term 1: (x - 50)
Term 2: (x + 1)
Now, applying the product rule, we differentiate each term and combine the results:
Derivative of Term 1 = 1 (since the derivative of x is 1)
Derivative of Term 2 = 1 (since the derivative of x is 1)
Using the product rule, the derivative of the function is:
f'(x) = (x - 50) * 1 + (x + 1) * 1
f'(x) = x - 50 + x + 1
f'(x) = 2x - 49
Therefore, the correct answer is B. The derivative is 2x - 49.
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arbitron media research incorporated conducted a study of the ipod listening habits of men and women. one facet of the study involved the mean listening time. it was discovered that the mean listening time for a sample of 8 men was 39 minutes per day. the standard deviation was 12 minutes per day. the mean listening time for a sample of 10 women was also 39 minutes, but the standard deviation of the sample was 16 minutes. at the 0.10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women?g
There is no significance difference in the variation in the listening times for men and women.
In this study conducted by Arbitron Media Research Incorporated, the iPod listening habits of men and women were examined. One aspect of the study focused on the mean listening time for both genders. The objective is to determine if there is a significant difference in the variation of listening times between men and women. To do so, statistical analysis will be conducted using the given data.
To determine if there is a significant difference in the variation of listening times between men and women, we can perform a hypothesis test. Let's denote the mean listening time for men as μ₁, the mean listening time for women as μ₂, the standard deviation for men as σ1, and the standard deviation for women as σ₂.
Null Hypothesis (H₀): There is no difference in the variation of listening times between men and women. In mathematical terms, H₀ : σ₁ = σ₂.
Alternative Hypothesis (H₁): There is a difference in the variation of listening times between men and women. In mathematical terms, H₁ : σ₁ ≠ σ₂.
We will use a significance level of 0.10, which indicates that we are willing to accept a 10% chance of rejecting the null hypothesis when it is true.
To test this hypothesis, we can use the F-test for comparing variances. The F-test compares the ratio of the variances between two independent samples. In this case, the samples are the listening times of men and women. The F-test statistic is calculated as follows:
F = (s₁²) / (s₂²)
where s₁ and s₂ are the sample variances. In this case, the sample variances are the square of the standard deviations provided.
Let's calculate the F-test statistic using the given data:
For men:
Sample size (n₁) = 8
Sample standard deviation (s₁) = 12 minutes/day
Sample variance (s₁²) = (12²) = 144 minutes²/day²
For women:
Sample size (n₂) = 10
Sample standard deviation (s₂) = 16 minutes/day
Sample variance (s₂²) = (16²) = 256 minutes²/day²
Calculating the F-test statistic:
F = (s₁²) / (s₂²) = 144 / 256 ≈ 0.5625
Next, we need to determine the critical value for the F-test statistic at a significance level of 0.10. This critical value can be found in the F-distribution table. Since the sample size is small, we will use the F-distribution table.
With a sample size of 8 for men and 10 for women, the degrees of freedom for the numerator (df₁) is 7 (n₁ - 1) and the degrees of freedom for the denominator (df₂) is 9 (n₂ - 1).
Looking up the critical value from the F-distribution table with df₁ = 7 and df₂ = 9, at a significance level of 0.10, we find the critical value to be approximately 2.76.
Now, we compare the calculated F-test statistic with the critical value. If the calculated F-test statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
In this case, the calculated F-test statistic (0.5625) is less than the critical value (2.76). Therefore, we fail to reject the null hypothesis. This means that there is no enough evidence to conclude that there is a significant difference in the variation of listening times between men and women at the 0.10 significance level.
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how do you convert other bases to base ten in binary
To convert other bases to base ten in binary, we multiply the base to the exponent of the position of the number and take the sum
Converting other bases to base ten in binaryFrom the question, we have the following parameters that can be used in our computation:
Numbers in other bases to base ten
To do this we use the product rule
Where each number is multipled by the base to the exponent of the position of the numberAnd the sum of each product is takenTake for instance, we want to convert the binary number 1011 to base ten.
This means that we are converting from base 2 to base 10
Using the above as a guide, we have the following:
1011₂ = 1 * 2³ + 0 * 2² + 1 * 2¹ + 1 * 2⁰
Evaluate
1011₂ = 13
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Factorise completely:
ax-bx+by+cy-cx-ay
Answer:
x(a-b-c)+y(-a+b-c)
Step-by-step explanation:
If you ride a pterodactyl for 3 hours at 10mph and then ride a spinosaurus for 1 hour at 2mph, what would be our average speed?
Answer:
To compute the average speed, multiply the total distance travelled by the whole time spent. There's a formula for speed, time and distance
Travel distance aboard the pterodactyl = 10 mph x 3 hours = 30 miles
Distance travelled on the spinosaurus = 2 miles x 1 hour = 2 miles
30 miles + 2 miles = 32 miles total distance travelled
Total time required = 3 hours + 1 hour = 4 hours
Average speed = total distance travelled divided by the total time taken = 32 miles divided by 4 hours = 8 mph
As a result, our average speed is 8 mph.
someone help
please and asap and show steps
Answer:
44 yd^2
Step-by-step explanation:
Area of trapezium = ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
= 1/2 (12 + 5.6) × 5
= 44yd^2
A rectangular prism-shaped display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall.
What is the volume of the display case in cubic inches?
Responses
73 1/4 in³
73 and 1 fourth, in³
320 1/4 in³
320 and 1 fourth, in³
10,328 1/16 in³
10328 and 1 sixteenth, in³
28,372 5/8 in
The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.
Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:
Volume = Length * Width * Height
Using the given measurements:
Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches
To simplify the calculation, we can convert the mixed numbers to improper fractions:
Volume = (21/2) inches * (61/2) inches * (129/4) inches
Next, we multiply the fractions:
Volume = (21/2) * (61/2) * (129/4) = 17289/8
The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:
Volume = 2161 1/8 in³.
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Find the solution point(s) for the system of equations given by y = 2x^2 + 5x – 10 and 4x – y = –11
Answer:
the solution points for the system of equations are (3, 25) and (-7/2, -7).
Step-by-step explanation:
We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:
Substitute y = 2x^2 + 5x - 10 into the second equation:
4x - (2x^2 + 5x - 10) = -11
Simplifying the left side of the equation:
4x - 2x^2 - 5x + 10 = -11
Rearranging the terms:
2x^2 - x + 21 = 0
Using the quadratic formula:
x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)
x = (1 ± sqrt(169)) / 4
x = (1 ± 13) / 4
Simplifying:
x = 3 or x = -7/2
Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:
For x = 3:
y = 2(3)^2 + 5(3) - 10 = 25
So one solution point is (3, 25).
For x = -7/2:
y = 4(-7/2) + 11 = -7
So the other solution point is (-7/2, -7).
Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).
Danny and Ariana are buying a commercial building for their new business. The assessed value of the building is $500,000 and the market value is $457,350. They will put a down payment of 20%.
a. What will the property taxes be on the assessed value of the building if the taxes are 2.415%?
b. What will their monthly payment be if they take a 30-year mortgage at a 4.55%?
c. How much interest will they pay on the 30-yr mortgage for the life of the loan?
d. What will be the range for their closing costs?
e. If they take a balloon mortgage instead at a 3.5%, what is the monthly payment, before paying off the balloon?
For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term.
a. Property Taxes:
The assessed value of the building is $500,000, and the property tax rate is 2.415%. To calculate the property taxes, we multiply the assessed value by the tax rate:
Property taxes = Assessed value * Tax rate
Property taxes = $500,000 * 2.415% (convert percentage to decimal)
Property taxes = $500,000 * 0.02415
Property taxes = $12,075
Therefore, the property taxes on the assessed value of the building will be $12,075.
b. Monthly Mortgage Payment:
To calculate the monthly mortgage payment, we need to consider the loan amount, interest rate, and loan term. The down payment is 20%, so the loan amount will be 80% of the market value of the building:
Loan amount = Market value * (1 - Down payment percentage)
Loan amount = $457,350 * (1 - 20%) (convert percentage to decimal)
Loan amount = $457,350 * 0.8
Loan amount = $365,880
We can now use this loan amount, along with the mortgage interest rate and loan term, to calculate the monthly payment using the formula for a fixed-rate mortgage:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))
The monthly interest rate is the annual interest rate divided by 12, and the total number of months is the loan term multiplied by 12.
Annual interest rate = 4.55% (convert percentage to decimal)
Monthly interest rate = 4.55% / 12
Loan term = 30 years
Total number of months = 30 * 12
Now, let's calculate the monthly payment:
Monthly payment = ($365,880 * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))
c. Total Interest Paid:
To calculate the total interest paid over the life of the loan, we multiply the monthly payment by the total number of months and subtract the loan amount:
Total interest paid = (Monthly payment * Total number of months) - Loan amount
d. Closing Costs:
The closing costs can vary, but a common range is between 2% and 5% of the purchase price. To calculate the range for closing costs, we'll use these percentages:
Minimum closing costs = Purchase price * 2%
Maximum closing costs = Purchase price * 5%
e. Balloon Mortgage Payment:
For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term. To calculate the monthly payment for the balloon mortgage, we'll use the loan amount, interest rate, and loan term:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))
Now, let's calculate the monthly payment for the balloon mortgage.
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