60 POINTS!!!!
Your mother is 25 years older than you. Your father is 3 years older than your mother. The product of all three ages are 32,130. How old is your father?
Explanation would be appreciated!
Answers
If father is 3 years older than mother,
m +3 = f
The product of all three ages is 32130:
I-m.f = 32130
Substitute m with r+ 25:
m+3 =f r+ 25 + 3 = f r+ 28 = f
Substitute now f and m:
I- m.f = 32130 x(x+ 25)(x + 28) = 32130 (a2 + 25x)(x + 28) = 32130 3 + 28r2 + 25r + 700r = 32130 3 + 53r2 + 700r = 32130
Subtract 32130 from each side 3 + 53? + 700r – 32130 = 0
On the graph we can see that the only real solution is 17. > x = 17 m = 25 + 17 m = 42 f = m + 3 f = 42 + 3 f =|45
Our age is 17, Mother's age is 42 and father's age is 45.
Father’s age is 45
( sorry I know it’s too long but hope it helps )
My father is 42 years old as obtained from the cubic polynomial's real root.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
let my age be x years.
So, My mother is (x + 25) and my father is (x + 28) years.
∴ {x(x + 25)(x + 28) = 32130.
(x² + 25x)(x + 28) = 32130.
x³ + 53x² + 700x = 32130.
x³ + 53x² + 700x - 32130 = 0.
Now solving this has only one real solution x = 17.
So, My father is (17 + 25) = 42 years old.
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Related Questions
the first sheet of the spreadsheet linked above contains the scores of 50 students on 4 different exams. what is the mean exam score of student 2 for all four exams?
Answers
The mean exam score of student 2 for all four exams is 87.5. Based on the information provided, you have a spreadsheet containing the scores of 50 students on 4 different exams. To calculate the mean exam score for Student 2 across all four exams, you need to follow these steps:
1. Locate the scores for Student 2 on all four exams. They should be on the first sheet of the spreadsheet and likely in a row or column corresponding to Student 2.
2. Add the scores of Student 2 for all four exams together. For example, if their scores were 80, 85, 90, and 95, the total would be 80 + 85 + 90 + 95 = 350.
3. To calculate the mean, divide the total score (from step 2) by the number of exams (which is 4 in this case). Using the example scores above, the mean would be 350 / 4 = 87.5.
So, the mean exam score for Student 2 for all four exams is 87.5. Keep in mind that this example assumes hypothetical exam scores; you will need to replace them with the actual scores found in the spreadsheet to obtain the correct mean score for Student 2.
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im giving all my points away
Answers
Answer: thank u for the points thats kind of u
Step-by-step explanation: have a nice day buddy
Answer:
I-
Oop-
Step-by-step explanation:
A change that occurs as the result of new information or as additional experience is acquired is a: change in accounting principle. change in accounting estimate. change in reporting entity. correction of an error.
Answers
A change that occurs as the result of new information or as additional experience is acquired is a change in accounting estimate. The correct answer is option (B): change in accounting-estimate.
The change in accounting estimate is a type of change that involves revising a previous estimate of an amount or other relevant measurement based on new information or developments, such as changes in market conditions or project completion timelines. It is important to note that a change in accounting estimate is different from a change in accounting principle, which involves adopting a new accounting method for recognizing and measuring certain types of transactions or events.
Additionally, a correction of an error involves fixing an error in previously reported financial information, while a change in reporting entity involves a change in the company or organization that is being reported on. All of these terms are defined within the field of accounting and are important concepts to understand for accurate financial reporting.
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y=3x-1
Help pleaseeeeee
Answers
Answer:
y=3x-1
Step-by-step explanation:
Not enough context
Hope this helps!
:)
Something is said to be statistically significant if it is not likely to happen by chance.
True False
Answers
The statement "something is said to be statistically significant if it is not likely to happen by chance" is true.
Statistical significance is a measure used to determine the strength of evidence against the null hypothesis.
The null hypothesis states that there is no relationship or effect between two variables, and it is tested against the alternative hypothesis, which proposes that there is a relationship or effect.
To determine statistical significance, researchers use a p-value, which represents the probability that the observed results occurred by chance alone.
A lower p-value indicates stronger evidence against the null hypothesis. A common threshold for statistical significance is a p-value less than 0.05, meaning that there is less than a 5% chance that the observed results happened by chance alone.
If the p-value is less than the predetermined threshold (e.g., 0.05), the results are considered statistically significant, and the null hypothesis is rejected in favor of the alternative hypothesis.
This means that the observed relationship or effect is likely not due to chance and has practical significance in the real world.
In summary, when something is statistically significant, it indicates that the results are unlikely to be a result of chance alone, providing evidence for a true relationship or effect between the variables being studied.
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GIVING 10
POINTS FOR CORRECT ANSWER!
Answers
Answer:
Step-by-step explanation: Since both the numerator and the denominator have a minus (-), they even each other out and the minus signs can be removed. Then we are left with this:
13
23
Now that both the dividend and divisor are positive numbers, we can simply divide 13 by 23 as follows:
13 ÷ 23 = 0.565217391304348
Which means that this is the answer to "What is negative 13 divided by negative 23?":
(-13) ÷ (-23) = 0.565217391304348
Answer:
t = -299
Step-by-step explanation:
\(\frac{t}{-13} = 23\\\\ t = 23 * -13\\\\t = -299\\\\Check:\\-\frac{-299}{-13} = 23\)
PLEASE HELP !! parallelogram rstu has vertices as shown below. the figure undergoes a series of transformations. it is reflected over the x-axis and then translated according to the rule x,y -> (x+2,y-1). determine the coordinates for R’, S’, T’, and U’
Answers
The coordinates for R', S', T', and U' after the transformation are (3,-3), (7,-3), (7,-7), and (3,-7) respectively.
What is coordinates?Coordinate is a pair of numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.
Parallelogram RSTU is a quadrilateral with four sides and four vertices. The coordinates for the vertices R, S, T, and U are (1,-1), (5,-1), (5,-5), and (1,-5) respectively.
When the figure is reflected over the x-axis, the coordinates of the vertices become (1,1), (5,1), (5,5), and (1,5). This is because a reflection over the x-axis is a transformation where the y values of the points change sign.
After the reflection, the figure is translated according to the rule x,y -> (x+2,y-1). This is a transformation where the x- and y-coordinates of the vertices are increased by 2 and decreased by 1 respectively. This means that the coordinates for R', S', T', and U' after the transformation are (3,-3), (7,-3), (7,-7), and (3,-7) respectively.
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Assume there is a sample of n
1
=4, with the sample mean
X
1
=35 and a sample standard deviation of S
1
=4, and there is an independent sample of n
2
=5 from another population with a sample mean of
X
ˉ
2
=31 and a sample standard deviation S
2
=5. In performing the pooled-variance t test, how many degrees of freedom are there? There are degrees of freedom. (Simplify your answer.)
Answers
There are 7 degrees of freedom.
In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)
Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7
Therefore, there are 7 degrees of freedom.
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There are 7 degrees of freedom for the pooled-variance t-test.
To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:
\(\[\text{{df}} = n_1 + n_2 - 2\]\)
where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.
In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:
\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)
In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.
To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.
In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.
Therefore, there are 7 degrees of freedom for the pooled-variance t-test.
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I haven't done this for a while and completely forgot how to do it
Answers
Answer:
SinC = 7/25
CosC = 24/25
TanC = 7/24
12.
Find x and y in trapezoid TRAP below.
Answers
Answer:
x = 115 , y = 40
Step-by-step explanation:
in a trapezoid
• each lower base angle is supplementary to the upper base angle on the same side.
∠ ART = 40° + 25° = 65°
then
∠ PAR = 180° - ∠ ART = 180° - 65° = 115° , so
∠ PAR = x = 115
the sum of the 3 angles in Δ PAR = 180° , that is
x + y + 25 = 180
115 + y + 25 = 180
140 + y = 180 ( subtract 140 from both sides )
y = 40
: If A is a set, then | P(A) is strictly larger than A. (That is, |A|S|P(A) , but |A| # | P(A) |) Select one: a. True if A is finite b. True if A is countable. If A is already uncountable, then |P(A)| = |A| True for any set A O d. False C.
Answers
The statement "If A is a set, then |P(A)| is strictly larger than A" is false.
The power set P(A) of a set A is defined as the set of all subsets of A, including the empty set and A itself. The cardinality of a set A, denoted as |A|, represents the number of elements in A.
In general, the cardinality of the power set P(A) is larger than the cardinality of A, which means |P(A)| > |A|. This holds true for both finite and countable sets A. However, when A is already uncountable (such as the set of real numbers), the statement |P(A)| = |A| is true.
Therefore, the correct answer is option d. False. The statement is false because it claims that |A| # |P(A)|, implying that the cardinality of A is not equal to the cardinality of P(A).
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Use the figure.
A circle has a radius labeled thirty-five inches.
Find the circumference. Round your answer to the nearest hundredth. Use 3.14
for π
.
Enter the correct answer in the box.
about
a
in.
Formula keypad has been closed. Press Control + Backslash to open it again.
Answers
Answer:
220 inches
Step-by-step explanation:
Formula for the circumference of circle is
2πr
Replacing it with the given values
2 x 3.14 × 35 = 219.8 inches
or 220 inches rounded
Find the radius of convergence, R, of the series (-1)nx" n-1 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Need Help? RaItTalk to a Tutor Read It 5. + --2 points scalc8 11.8.007 MI Find the radius of convergence, R, of the series. xn+ 5 R= Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Watch ItMaster It Talk to a Tutor Need Help? Read it Submit Answer Save ProgressPractice Another Version
Answers
The radius of convergence, R, of the series (-1)nx^n-1 can be found using the ratio test the interval of convergence is (-1, 1) in interval notation. .
We have
lim |(-1)^(n+1)x^(n) / (-1)^nx^(n-1)| as n approaches infinity
= lim |x|
Since the limit exists only when |x| < 1, the radius of convergence is R = 1.
To find the interval of convergence, we need to check the endpoints x = -1 and x = 1.
When x = -1, the series becomes (-1)^n(-1)^n-1 = (-1)^2n-1 which diverges.
When x = 1, the series becomes (-1)^n1^n-1 = (-1)^(n-1) which also diverges.
Therefore, the interval of convergence is (-1, 1) in interval notation.
Note that the endpoints are not included in the interval of convergence because the series diverges at those points.
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The radius of convergence is R = 1 and the interval of convergence is (-1, 1).
To find the radius of convergence, we can use the ratio test:
lim┬(n→∞)|(-1)^(n+1)x^n|/|(-1)^(n)x^(n-1)| = lim┬(n→∞)|x|/1 = |x|
The series converges if |x| < 1 and diverges if |x| > 1. So the radius of convergence is R = 1.
To find the interval of convergence, we need to test the endpoints x = -1 and x = 1. When x = -1, the series becomes (-1)^n(-1)^n = 1, which is a divergent series. When x = 1, the series becomes (-1)^n, which is an oscillating series that does not converge.
Therefore, the interval of convergence is (-1, 1), where -1 is excluded and 1 is included, since the series converges for -1 < x < 1 and diverges for x ≤ -1 and x ≥ 1.
In summary, the radius of convergence is R = 1 and the interval of convergence is (-1, 1).
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Covert 132 inches to feet
Answers
Answer:
11
.......................................
You have 4 blue shirts, 6 white shirts,
2 green shirts, and 6 red shirts.
What is the probability of selecting a BLUE
shirt from your dresser?
Please help me!! I’ll give you brainliest if you give me a good answer :(
Answers
Answer:
4.5%
Step-by-step explanation:
What is the answer to this?
Answers
use the venn diagram to compare and contrast the definitions of the linnaean class answers
Answers
The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.
By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.
The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.
First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.
Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.
Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.
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if tan (x+y)=4/3 and tan x=5/13. evaluate tan y
Answers
tan(x + y) = (tan x + tan y) / (1 - tan x * tan y)
Substituting the given values, we get:
4/3 = (5/13 + tan y) / (1 - 5/13 * tan y)
Multiplying both sides by the denominator and simplifying, we get:
52/3 - 20/3 * tan y = 5/13 + tan y
Multiplying both sides by 3/20 and simplifying, we get:
tan y = (52/3 - 5/13) / (20/3 + 1)
tan y = (1699/39) / (23/3)
tan y = 221/299
Therefore, tan y is approximately 0.7391 (rounded to four decimal places).
In a museum, Nick is looking at a famous painting through a mirror at an angle of 58 degrees. Find the angle the painting makes with the mirror. Also, find m
Answers
Answer:
58°
Step-by-step explanation: Nick was able to view the museum painting through the mirror due to reflection. The painting was reflected after hitting the plane mirror. According to the law of reflection, the angle of incidence is equal to the angle of reflection. The incident angle is the angle which the incident ray( the ray which strikes or hits the plane mirror) makes with the normal(line perpendicular to the tangent).
Thus, the angle which the painting makes with the mirror is equal to the angle at which the painting is being viewed = 58°.
Find the area of the triangle. 7 in. 18 in. The area is square inches.
Answers
(7 x 18) / 2 = 63
. Describe how to get the mixed number answer to 19÷6 from the
whole-number-with-remainder
answer. By considering a simple word problem, explain why the
method you describe makes
sense."
Answers
To obtain the mixed number answer to 19 ÷ 6 from the whole-number-with-remainder answer, divide the numerator (19) by the denominator (6).
To find the mixed number answer to 19 ÷ 6, we divide 19 by 6. The whole-number quotient is obtained by dividing the numerator (19) by the denominator (6), which in this case is 3. This represents the whole number part of the mixed number answer, indicating how many complete groups of 6 are in 19. Next, we consider the remainder. The remainder is the difference between the dividend (19) and the product of the whole number quotient (3) and the divisor (6), which is 1. The remainder, 1, becomes the numerator of the fractional part of the mixed number.
This method makes sense because it aligns with the division process and provides a clear representation of the result. It shows the whole number part as the number of complete groups and the fractional part as the remaining portion. This representation is helpful in various real-world scenarios, such as dividing objects or quantities into equal groups or sharing items among a certain number of people.
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Find the equation of the parabola with its focus at (6, 2) and its directrix y = 0
Answers
Answer:
y= 1/4 x-62+1
Step-by-step explanation:
x^2=-49
Solve quadratic equation using square root
Answers
Answer:
x = 7i,-7i
Step-by-step explanation:
We are given x² = -49.
Using the square root - square root both sides.
√x² = √-49
Cancel the square and write plus-minus beside √-49.
x = ± √-49
Using the imaginary unit, i = √-1.
x = ± √49√-1
x = ± √49i
The square root of 49 is 7.
x = ±7i
Therefore, x = 7i,-7i but these solutions are in complex plane so in real plane, they do not exist.
At a constant speed, a car travels 75 miles in 60 minutes. How far does
the car travel in 18 minutes? If you get stuck, consider using the table.
Answers
Answer:
22.5 miles
Step-by-step explanation:
75/60 = x/18
60x = 1350
x = 22.5
S=(1,2,3,4,5,6); A=(1,2,3,4); B= (3,4,5) c = (6). Solve P (A U C)
Answers
Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.
The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.
P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.
There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.
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Angles A and B together create a 90° angle. ∠A = 4x −10 and ∠B = 2x − 20. Find the angle measures (what will
Answers
Answer:
see below
Step-by-step explanation:
A+ B = 90
4x-10 + 2x-10 = 90
Combine like terms
6x -20 = 90
Add 20 to each side
6x -20+20 = 90+20
6x = 110
Divide by 6
6x/6 = 110/6
x = 55/3
A = 4x-10 = 4(55/3) -10
A=63 1/3
B = 2x-10 = 2(55/3) -10
26 2/3
can anyone help me with this problem? Please it would be great.
Find the missing side of the triangle.
Answers
Answer:
\(\displaystyle 45 = x\)
Step-by-step explanation:
Use the Pythagorean Theorem to define the hypotenuse:
\(\displaystyle a^2 + b^2 = c^2 \\ \\ 36^2 + 27^2 = x^2 \hookrightarrow 1296 + 729 = x^2 \hookrightarrow \sqrt{2025} = \sqrt{x^2} \\ \\ \boxed{45 = x}\)
I am joyous to assist you at any time.
PLEASE HURRY PLEASE I WILL MARK BRAINLIEST!!!!!!!
Answers
Step-by-step explanation:
the first , second one and the last one
\( - 7 \frac{3}{4}x - 7(3) \\ 7( - \frac{3}{4} x) - 7(3) \\ - 5 \frac{1}{4} - 21\)
Suppose a manufacturer knows from previous data that 3. 5% of one type of
lightbulb are defective. The quality control inspector randomly selects bulbs
until a defective one is found. Is this a binomial experiment? Why or why not?
O A. Yes, because the situation satisfies all four conditions for a
binomial experiment.
B. No, because the trials are not independent.
C. No, because each trial cannot be classified as a success or failure.
O D. No, because the number of trials is not fixed.
Answers
The answer is A. Yes, because the situation satisfies all four conditions for a binomial experiment.
In a binomial experiment, there are four conditions that need to be met:
There are a fixed number of trials: In this case, the manufacturer's quality control inspector continues selecting bulbs until a defective one is found. Although the number of trials is not predetermined, it is still a fixed number determined by the occurrence of the first defective bulb.Each trial has only two possible outcomes: Each bulb can either be defective or non-defective, which qualifies as two distinct outcomes.
The probability of success remains the same for each trial: The manufacturer knows from previous data that the probability of a defective bulb is 3.5%. This probability remains constant for each trial.
The trials are independent: The selection of each bulb does not affect the selection of subsequent bulbs, assuming that the bulbs are chosen randomly. Therefore, the trials are independent.
Since the given situation satisfies all four conditions for a binomial experiment, the correct answer is A. Yes, it is a binomial experiment.
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Given that log_{a}(3) = 0.477 and
log_{a}(5) = 0.699, evaluate log_{a}(0.6) .
*The answer is -0.222 but I'm not sure how to do the steps.
Answers
Given:
\(\log_{a}(3) = 0.477,\log_{a}(5) = 0.699\)
To find:
The value of \(\log_{a}(0.6)\).
Solution:
We need to find the value of:
\(\log_{a}(0.6)\)
It can be written as
\(\log_{a}(0.6)=\log_a\left(\dfrac{6}{10}\right)\)
\(\log_{a}(0.6)=\log_a\left(\dfrac{3}{5}\right)\)
By using the property of logarithm, we get
\(\log_{a}(0.6)=\log_a(3)-\log_a(5)\) \([\because \log \dfrac{a}{b}=\log a-\log b]\)
\(\log_{a}(0.6)=\log_a(3)-\log_a(5)\)
On substituting the given values, we get
\(\log_{a}(0.6)=0.477-0.699\)
\(\log_{a}(0.6)=-0.222\)
Therefore, the values of \(\log_a(0.6)\) is -0.222.