Answer:
12
Step-by-step explanation:
6=a/4+2
L.C.M=4
4(6)=a+6(2)
24=a+12
24-12=a
a=12
A geometric sequence has first term 5 and common ratio 2. the sum of the first n terms of the sequence is 163 835. What is n ? [Answer format: integer, no units]
First term in a geometric sequence is 5, and common ratio is 2. The sum of the first n terms of the sequence is 163,835.
The following formula can be used to calculate the sum of the first n terms of a geometric sequence:
Sn = a (1 - rn) over (1 - r),
where
a is the first term,
r is the common ratio, and
n is the number of terms.
So, Sn = a (1 - rn) over (1 - r) => 163835 = 5 (1 - 2n) over (1 - 2).
Simplifying it, we have
163835 = 5 (1 - 2n) over (-1)
=> 163835 = -5 + 10n
=> 163840 = 10n
=> n = 16,384.
Therefore, the value of n is 16,384.
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57
Exhibit 18-2
Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early. In a sample of 150 students, 40 preferred a 10-minute break, 80 preferred to get out 10 minutes early, and 30 had no preference. We want to determine if there is a difference in students' preferences.
Refer to Exhibit 18-2. The test statistic based on the number of students who preferred to get out early equals
Group of answer choices
1.825
0.67
0.82
3.65
The test statistic based on the number of students who preferred to get out early equals 3.65.
What is a test statistic?A test statistic is a numerical summary of the sample data that is employed to determine the strength of the evidence for a hypothesis. It is a quantitative measure that compares the observed data to the hypothesis. The t-value, Z-score, F-value, and chi-squared value are examples of common test statistics. In statistical hypothesis testing, a test statistic is used to make decisions about whether or not to reject the null hypothesis.
Based on the given problem, the number of students who preferred to get out of class early is 80, while the number of students who preferred a 10-minute break is 40. Hence, the number of students who had no preference is 30.
Now, we will find the test statistic based on the number of students who preferred to get out of class early as follows:
Test Statistic = (Observed Value - Expected Value) / Standard Deviation
To find the observed value, we need to calculate the proportion of students who preferred to get out of class early in the sample as follows:
Proportion of students who preferred to get out of class early = 80 / (150-30)= 80 / 120= 0.67
Therefore, the observed value is 0.67.
To find the expected value, we need to assume that there is no difference in students' preferences, and the proportion of students who preferred to get out of class early is the same as the proportion of students who preferred a 10-minute break.
Expected value = Proportion of students who preferred to get out of class early * Total number of students= 0.5 * 150= 75
Therefore, the expected value is 75.
To find the standard deviation, we need to use the formula for the standard deviation of a proportion as follows:
Standard Deviation = √[(p*q) / n]
where p is the proportion of students who preferred to get out of class early, q is the proportion of students who preferred a 10-minute break, and n is the total number of students.
Standard Deviation = √[(80/120)*(40/120) / 150]= √(0.1778 / 150)= 0.048
Therefore, the standard deviation is 0.048.
Now, we will substitute the values in the formula for the test statistic as follows:
Test Statistic = (0.67 - 0.5) / 0.048= 3.65
Therefore, the test statistic based on the number of students who preferred to get out early equals 3.65.
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Which of the following statements most accurately describes the relationship between cultured yeast preparation conditions and fermented alcohol yield, based on passage data?Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield.A is correct. Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, with 10% glucose (not 12%, as in Broth C) and 8% yeast inoculate (not 10%, as in Broth B). Therefore, increasing neither glucose concentration nor percentage yeast inoculate led to more production of alcohol, so neither of those parameters showed a positive correlation with alcohol yield.
Based on the passage data, the most accurate statement describing the relationship between cultured yeast preparation conditions and fermented alcohol yield is: "Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield."
What this means is that increasing the concentration of glucose or percentage of yeast inoculate did not lead to more production of alcohol. The data in Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, which had 10% glucose and 8% yeast inoculation. Broth C, which had a higher concentration of glucose at 12%, did not result in a higher yield of alcohol. Similarly, Broth B, which had a higher percentage of yeast inoculate at 10%, did not lead to a higher yield of alcohol.
Therefore, it can be concluded that neither glucose concentration nor percentage of yeast inoculates was positively correlated with fermented alcohol yield.
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1. If f = {(0,2), (-3,2), (2,5)} and g = {(3,4), (1,5), (-1,2)}, Find: f+g
Answer:
Step-by-step explanation:
F = (-1,9)
G = (-3,11)
It takes 120 unit cubes to completely fill a rectangular prism. The prism is 10 unit cubes high. What are the other possible dimensions of the rectangular prism?
the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:
V = l × w × 10
We are also given that the prism requires 120 unit cubes to fill completely, which means:
V = l × w × 10 = 120
Dividing both sides by 10, we get:
l × w = 12
Now we need to find pairs of positive integers l and w that multiply to 12. These are:
1 × 12
2 × 6
3 × 4
Therefore, the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.
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Understanding and Interpreting Confidence Intervals a Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college. She finds a 95% confidence interval for the mean systolic blood pressure to be (108.6, 120.3) mm Hg. Which statement below incorrectly conveys the meaning of the confidence interval? She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. O She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. Hint Assistance Used Use the definition of a 95% confidence interval.
The Statement 1: She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. This statement is accurate and conveys the meaning of a 95% confidence interval.
The confidence interval is the range of values within which a statistical parameter is estimated to be accurate with a certain level of confidence.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college.
Statement 2: She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. This statement is inaccurate because the confidence interval obtained from the sample cannot be generalized to the entire population of students.
The correct statement should mention that the confidence interval is only for the random sample.Statement 2 is the incorrect statement.
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A.14.5 square inches
B.29 square inches
c.20.5 square inches
d.32 square inches
Answer:
d. 32 in.²
Step-by-step explanation:
Bottom face: 6 in. × 0.5 inch
Side faces: 2 × 5 in. × 0.5 in.
Front and back faces: 2 x 6 in. × 4 in. / 2
surface area = 3 in.² + 5 in.² + 24 in.²
surface area = 32 in.²
I need help with this
Therefore , the solution of the given problem of function comes out to be he function's average rate of change over the range 3 x 4 is 4.
Describe function.There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.
Here,
Calculate the difference between the function values at
=> x = 4 and x = 3, then split by the difference in x-values,
which is 4 - 3 = 1, to determine the average rate of change of the function over the range 3 x 4.
We can see from the table that f(4) = -5 and f(3) = -9. As a result, the following function numbers are different:
=> f(4) - f(3) = (-5) - (-9) = 4
=> 4 - 3 = 1 represents the x-value disparity.
Therefore, the function's average rate of change over the period 3 x 4 is:
Average rate of change is equal to
=> (f(4)-f(3))/(4-3) = 4/1 = 4.
Consequently, the function's average rate of change over the range 3 x 4 is 4.
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Whatis the value of # y_ When y = 5 and x = 10?
The value of y when x=36 is 31/3.
According to the question,
x varies directly with 3y+5
Thus,
[tex]x = k(3y+5)[/tex]
where K is any positive integer.
Now, from the question,
y=5/3 when x=10
Thus,
[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]
Now we can use k to find the value of y when x=36:
[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]
In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.
Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.
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Complete Question:
If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36
Suppose the number of water people drink in a week is normally distributed with a mean of 50 and a standard deviation of 5 glasses of water. Find the value 1 standard deviation below the mean
Answer:
Step-by-step explanation:
.
8. Points P, Q, whose abscissae are 2 and 2+h, are taken on the curve y = 2x^2+1. Find the gradient of the chord PQ. To what value does this gradient approach as h decreases towards the value zero?
The gradient of the chord PQ is 2h + 8
What is the gradient of the chord?Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.
Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).
Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).
The gradient of the chord PQ is given by:
(m) = Δy /Δx
(m) = (2h^2+8h+9 - 9) / (2+h - 2)
(m) = (2h^2+8h) / (h)
(m) = 2h + 8
As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.
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Calvin ordered scissors. Each pair of scissors weighs 0. 34 kg. A box of scissors weighs
64. 6 kg. How many pairs of scissors come n each box?
190 pairs of scissors came in each box.
This is an example of a word problem. As a model, a word problem depicts circumstances from the actual world that may be converted into phrases.
Weight of each pair of scissors = 0.34 kg
Weight of a box of scissors = 64.6 kg
Therefore, pairs of scissors in each box = Weight of a box of scissors ÷
Weight of each pair
= 64.6 ÷ 0.34
= 190 pairs.
Hence, 190 pairs of scissors came in each box.
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An unfair coin with Pr[H]=23 is flipped. If the flip results in a head, then a marble is selected from an urn containing 6 red, 9 white, and 10 blue marbles. If the flip results in a tail then a marble is selected from an urn containing 10 red and 1 white marbles. If the marble selected is white, then what is the probability that a flip resulted in a head?
The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.
Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.
Using Bayes' theorem, we have:
Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]
Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.
Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:
Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]
= (9/25)*0.23 + (1/11)*0.13
= 0.0888 + 0.0118
= 0.1006
Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.
Therefore,
Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508
Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).
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(a) In the figure below, m CED=50° and m AB = 140°. Find m CD.
(b) In the figure below, m VYW=36 and m VX = 62. Find m VW
a) Measurement of arcCD is 40°
b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]
50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]
36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
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10 * x = 425
81729 / y = 898.12
What is X and Y?
I WILL GIVE BRAINLY IF U DONT USE CALCULATOR
The value of X is 42.5 and Y is 90.98.
How to solve equations?
To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:
Simplify both sides of the equation by combining like terms and following the order of operations.
Add or subtract the same value from both sides of the equation to isolate the variable term.
Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.
Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.
Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:
[tex]10x/10 = 425/10[/tex]
Simplifying the left side of the equation gives:
[tex]x = 42.5[/tex]
Therefore, X is 42.5.
To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:
[tex]81729 = 898.12 \times Y[/tex]
Simplifying the right side of the equation gives:
[tex]Y = 81729 / 898.12[/tex]
[tex]Y = 90.98[/tex]
Therefore, Y is 90.98.
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PLEASE HELP!!
20 POINTS
A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost f(m)
is a function of the number of miles m
that the car is driven.
Plan A: f(m)= 0.12+75
Plan B: f(m)+0.35
I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.
II. For each function, determine how the rate of change will affect the total cost of a car rental.
III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?
Answer: At 250 miles, plan B is the most cost effective.
Step-by-step explanation:
Answers are under the questions below.
I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.
Plan A will charge .12 per mile plus a one time fee of $75.
Equation is y = .12x + 75 with the $75 being the y intercept or one time fee.
Plan B will charge .35 per mile with no one time fee.
Equation is y = .35x with the y intercept being (0) zero.
II. For each function, determine how the rate of change will affect the total cost of a car rental.
Initially the Plan A will be more expensive because of the one time fee, even though the rate is .12 per mile, which is much less than Plan B.
Plan B charges .35 per mile, but will eventually catch up in cost.
At approximately 326 miles the cost of each plan will equal at $114.13.
After 326 miles, Plan B will cost more than Plan A.
III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?
Plan A, substitute 250 miles for x
Cost = .12 (250) + 75
Cost = $105
Plan B, substitute 250 miles for x
Cost = .35 (250)
Cost = $87.50
At 250 miles, plan B is the most cost effective, saving $17.50.
graph is attached.
Dakota earned $6.00 in interest in Account A and 30.00$ in interest in Account B after months. If the simple interest rate is 4% for Account A and 5% for Account B, which account has the greater principal? Explain.
the principal in Account B is 4.8 times the principal in Account A.
How to solve?
Let the principal in Account A be P and the principal in Account B be Q. Also, let n be the number of months.
From the given information, we have:
Interest earned in Account A = $6.00
Interest rate in Account A = 4%
Number of months = n
Using the formula for simple interest, we have:
Interest earned in Account A = (P × 4%× n) / 12
Substituting the given values, we get:
6.00 = (P × 4% × n) / 12
P× n = 150
Similarly, we have:
Interest earned in Account B = $30.00
Interest rate in Account B = 5%
Number of months = n
Using the formula for simple interest, we have:
Interest earned in Account B = (Q× 5% × n) / 12
Substituting the given values, we get:
30.00 = (Q× 5% ×n) / 12
Q × n = 720
To compare the principals, we can divide the equation for Account B by the equation for Account A:
(Q × n) / (P× n) = 720 / 150
Simplifying, we get:
Q / P = 4.8
Therefore, the principal in Account B is 4.8 times the principal in Account A.
Since the interest rate in Account B is higher than the interest rate in Account A, we can conclude that the principal in Account B is greater than the principal in Account A.
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A shopkeeper bought 26 apples from a fruit vendor for $37.70.How much did each apple cost?
Answer: 1.45 Cents per (Rounded to the nearest cent)
Step-by-step explanation:
26 apples = $37.70
We want what one apple costs individually. The best way to do this is to divide both sides by 26.
1 apple = 37.70/26
1 apple = 1.45 Cents
How do you work this out?
Anyone help please .
Answer:
x=5/4 or x=5/9
pls mark me brainliest
Answer:
x=5/4 (for the first x),x=5/9 (for the second x)
pls help find y. 4x+5y-y+3x
Answer:
7x+4y
Step-by-step explanation:
combine like terms
Answer:
4?
Step-by-step explanation:
Sleep researchers know that some people are early birds (E), preferring to go to bed by 10 P.M. and arise by 7 A.M., while others are night owls (N), preferring to go to bed after 11 P.M. and arise after 8 A.M. A study was done to compare dream recall for early birds and night owls. One hundred people of each of the two types were selected at random and asked to record their dreams for one week. Some of the results are presented below. Group Mean Median Standard Deviation No dreams 5 or more dreams Early birds 7.26 6.0 6.94 0.24 0.55
Night owls 9.55 9.5 5.88 0.11 0.69 A) The researchers believe that night owls may have better dream recall than do early birds. Use the data provided to carry out a test of the hypotheses about the mean number of dreams recalled per week. Do the data support the researchers' belief? (5 pts) B) Compute a 92% confidence interval about the mean number of dreams recalled per week. (You do NOT need to re check the conditions) (5pts)
The answer is: A) The data support the researchers' belief that night owls have better dream recall than early birds. B) we can be 92% confident that the true difference in mean number of dreams recalled per week between night owls and early birds is between 1.87 and 2.63.
A) These are the alternative and null hypotheses:
H0: μE = μN (the mean number of dreams recalled each week is the same for early birds and night owls) (the mean number of dreams recalled per week is the same for early birds and night owls)
Ha: μE < μN (the mean number of dreams recalled each week is smaller for early birds than for night owls) (the mean number of dreams recalled per week is lower for early birds than for night owls)
Using the following formula, we can run a two-sample t-test with unequal variances:
t = [(sN2 / nN) + (sE2 / nE)] / sqrt[(xN - xE)]
where nN and nE are the sample sizes for night owls and early birds, respectively, and xN and sN and xE and sE are the sample means and standard deviations for night owls and early birds, respectively.
When we enter the values, we obtain:
t = (9.55 - 7.26) / sqrt[(5.88^2 / 100) + (6.94^2 / 100)] = 5.01
The data are consistent with the researchers' hypothesis that night owls are more capable of remembering their dreams than early birds.
B) We can use the following formula to determine the confidence interval:
CI is equal to (xN - xE) t/2 * sqrt[(sN / nN) + (sE / nE)].
where t/2 is the t-value for the required level of confidence and degrees of freedom, and xN, xE, sN, sE, nN, and nE are the same as previously (198 in this case).
With a t-value of 1.75 and a 92% confidence level (from a t-distribution with 198 degrees of freedom), we get:
CI is equal to (9.55 - 7.26) 1.75 * sqrt[(5.88 - + 6.94 / 100)] = (1.87, 2.63) (1.87, 2.63)
The genuine difference between night owls and early birds in terms of the average number of dreams recalled per week is therefore between 1.87 and 2.63, with a 92% confidence interval.
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A circle with radius of 2 cm sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. 2 cm CH 4 cm
the area of the shaded region is approximately 37.68 cm².
define area of circleThe area of a circle is the amount of space that is enclosed by the circle in a two-dimensional plane. It is defined as the product of the square of the radius (r) of the circle and the mathematical constant pi (π), which is approximately equal to 3.14159.
The area of the larger circle is:
A1 = π(4 cm)² = 16π cm²
The area of the smaller circle is:
A2 = π(2 cm)² = 4π cm²
To find the area of the shaded region, we subtract A2 from A1:
A1 - A2 = 16π cm²- 4π cm² = 12π cm²
To round the final answer to the nearest hundredth, we can use the approximation π ≈ 3.14:
12π cm² ≈ 12 × 3.14 cm² ≈ 37.68 cm²
Therefore, the area of the shaded region is approximately 37.68 square centimeters.
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If John had 3 apples then Droped 2 then found 4 then gave one to his friend how many apples does he have now
Answer:
4 apples
Step-by-step explanation:
We know
John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.
How many apples does he have now?
3 - 2 + 4 - 1 = 4 apples
So, he has 4 apples now.
Answer:
4 apples
Step-by-step explanation:
We know that John had 3 apples
but then he had dropped 2 of them
he then found 4
then he gave 1 to his friend
3-2=1
1+4=5
5-1=4
The answer is 4
Hope this helps!
what is the equation for pattern 2
Therefore , the solution of the given problem of equation comes out to be the number of dots is filled in below table.
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a single formula that separates 12 into two parts and can be used to assess received from y + 7, normalization in this case yields b + 7.
Here,
Given : A table with number of dots can be filled by this:
Here are the number of dots in each pattern:
Pattern Number of dots
1 4
2 7
3 10
4 13
5 16
6 19
7 22
8 25
9 28
10 31
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Which conic section is formed when a plane intersects the central axis of a double-napped cone at a 90° angle?
The conic section that formed when a plane intersects the central axis of a double-napped cone at a 90° angle is circle
When a plane intersects the central axis of a double-napped cone at a 90° angle, the resulting conic section is a circle.
To understand why this is the case, we can first consider the properties of a double-napped cone. A double-napped cone is formed by rotating a straight line, called the generatrix, around an axis that intersects the line at a fixed point, called the vertex. The resulting surface consists of two parts, each of which is a circular cone.
Now, let us imagine a plane that intersects the central axis of the double-napped cone at a 90° angle. Since the central axis of the cone is perpendicular to the base, the plane must intersect both cones at their widest point, which is also their center. At this point, the cone has a circular cross-section, which means that the plane intersects the cone in a circle.
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Answer:
circle
got it right on edg
Don bought the furniture listed below he paid $500 and will make monthly payments of $85 for the remaining amount how long will it take to pay for the furniture
Answer:
it will take approximately 5.88 months for Don to pay off the remaining amount of $R = $85t = $85(5.88) = $499.80
Step-by-step explanation:
Don paid $500 upfront and will make monthly payments of $85 for the remaining amount. Let's assume the remaining amount he needs to pay is $R. The total cost of the furniture is the sum of the amount paid upfront and the remaining amount:
Total Cost = $500 + $R
Since he will be paying $85 per month, we can set up an equation to determine the time it will take to pay off the remaining amount:
$R = $85t
where t is the number of months it will take to pay off the remaining amount.
Substituting $R = $85t in the total cost equation, we get:
Total Cost = $500 + $85t
Since we want to find the time it will take to pay off the furniture, we need to solve for t. We can equate the total cost to the amount Don will pay at the end of the payment period, which is:
Total Cost = Amount Paid
$500 + $85t = $500 + $85t + $R
$85t = $R
$500 + $85t = $500 + $85t + $85t
$500 + $170t = $500 + $R
$170t = $R
Substituting $R = $85t, we get:
$170t = $85t
t = $500/$85
t = 5.88 (rounded to two decimal places)
A triangle has a base that measures 6.4 feet. Its height measures 5 feet. How many square feet is the area of the triangle?
Answer:
16 feet
Step-by-step explanation:
Area of triangle = 1/2(a x b)
A = 1/2(6.4 x 5)
A = 32/2
A = 16 feet
Select THE TWO values of that are solutions to the equation (* - 5) (7x - 21) = 0.
A package is delivered 3 hours 25 minutes after it is collected, it is collected at 15:39
at what time is the package delivered
Given the data in the question we calculate that the package is delivered at 18:44.
If the package is collected at 15:39 and delivered 3 hours and 25 minutes later, we can add that amount of time to the collection time to find the delivery time.
First, we need to convert 3 hours and 25 minutes to just minutes. To do this, we multiply 3 by 60 (to convert hours to minutes) and then add 25:
3 hours and 25 minutes = (3 × 60) + 25 = 185 minutes
Now we can add 185 minutes to the collection time of 15:39:
15:39 + 185 minutes = 18:44
Therefore, the package is delivered at 18:44. The delivery time of a package is the time it takes for the package to be transported from the sender to the receiver. In this case, the package was collected at 15:39 and delivered 3 hours and 25 minutes later. To find the delivery time, we added the duration of 3 hours and 25 minutes to the collection time. It is important to keep track of delivery times to ensure timely and efficient shipping, especially for time-sensitive or perishable items. Timely delivery is crucial for businesses that rely on shipping to meet customer expectations and maintain customer satisfaction.
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Step 1 of 3
a.
About 180,000 terawatts of solar power reaches Earth’s surface.
Out of which about 0.06% is used by plants for photosynthesis.
Thus 108 terawatts of solar power is used by plants for photosynthesis.
Of this energy, about ends up stored in plant matter
Thus 1.08 terawatts of energy get stored in plant matter.
Consider the following facts
Therefore,
Therefore joules of energy get stored in plant matter each second.
The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
Step 1: Calculation of joules of energy stored in plant matter each secondGiven that, 1.08 terawatts of energy gets stored in plant matter for photosynthesis in a second.Therefore, 1.08 × 1012 watts of energy gets stored in plant matter each second. Also, the energy stored in plants matter in Joules = Watts × seconds (Joule is the unit of energy)1.08 × 1012 watts of energy stored in plant matter in a second.1 watt-second = 1 JouleEnergy stored in plant matter in a second = 1.08 × 1012 watts × 1 second = 1.08 × 1012 Joules Answer: The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
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