When the rule reads, "Add 12, Subtract 3," and the pattern begins at 41, the sixth number in the pattern is 71.
What is pattern?A pattern is defined in mathematics as a sequence of repeated objects, forms, or numbers. A pattern can be associated with any form of event or object. A pattern has a rule that informs us which items belong to the pattern and which objects do not. Patterns are items that repeat logically, such as vertical stripes on a shirt. They can take the form of numbers, pictures, or forms. A pattern constructed of plastic animals, for example, can alternate between two and four legged creatures, or animals that swim and animals that fly.
Here,
pattern begin at 41,
=41+12
=53
=53-3
=50
=50+12
=62
=62-3
=59
=59+12
=71
The 6th number in the pattern is 71 when the rule says, "Add 12, Subtract 3." and pattern start at 41.
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how do u solve x+5y=20 and -2x+7y=45 by elimination
Answer:
x = -5; y = 5
Step-by-step explanation:
x + 5y = 20
-2x + 7y = 45
Multiply both sides of the first equation by 2 to get 2x. Write the second equation below it and add the equations. 2x and -2x add to zero eliminating the x terms.
2x + 10y = 40
-2x + 7y = 45
-----------------------
17y = 85
y = 85/17
y = 5
Now use substitution in the first original equation to find x.
x + 5y = 20
x + 5(5) = 20
x = -5
Answer: x = -5; y = 5
Jiya’ mother i 12 year more than twice her age. After 8 year, her mother’ age will be 20 year le than three time her age. Find Jiya’ age and her mother’ age
The present age of Jiya whose mother 12 year more than twice her age., is sixteen years and her mother present age is fourty-four years.
We have, Jiya's mother is 12 year more than twice of her age. Let "x years" and "y years" be the present age of Jiya and her mother respectively.
According to problem, 12 + 2x = y --(1)
After 8 years, her mother age = 20 years less then three times of her age.
After 8 years, age of Jiya = (x+8) years.
i.e y + 8 = 3( x+8) - 20 --(2)
we have to calculate the present ages of both. Simplify the equation (2),
y + 8 = 3x + 24 - 20
=> y + 8 = 3x + 4 => y = 3x -4 --(3)
eqution (1) and (3) represent the linear equations so, we solve these linear equations by substitution,
plugging the value of y from( 1) to (3),
12 + 2x = 3x -4
=> 3x - 2x = 12+4
=> x = 16 then y = 12 + 2×16 = 44
Hence, Jiya's age is 16 years and her mother is about 44 years.
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Determine the sign of the solution of ax+b=cx+d in each situation. Justify your reasoning with a graph.
a. 0 < b < d and a < c b. d < b < 0 and a < c
The sign change of the expression ax + b = cx + d in the conditions are solved to be
a. 0 < b < d and a < c
negative solutionb. d < b < 0 and a < c
positive solutionHow to determine the sign changeThe given expression is
ax + b = cx + d
comparing the conditions
a. 0 < b < d and a < c
here b is non negative number and less than d a is also less than c. hence
ax + b = cx + d
ax - cx = d - b
ax - cx will be negative
d - b will be positive
this will lead to a negative solution since positive divided by negative give negative
b. d < b < 0 and a < c
ax + b = cx + d
ax - cx = d - b
d - b = negative
ax - cx = negative
negative dividing negative is positive hence a positive solution
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A COMPANY THAT MANUFACTURES BATTERIES GURANTEE THEM A LIFE OF 24 MONTHS
1 THE AVERAGE LIFE HAS BEEN FOUND IN TESTS TO BE 33 MONTHS AND A S. D OF 4 MONTHS HOW MANY WILL HAVE BE REPLACED UNDER GURRANTEE IF A NORMAL DISTRIBUTION IS ASSUMED FOR BATTER LIFETIMES
According to the standard normal distribution table, the area under the curve that is 2.25 standard deviations below the mean is approximately 1.22%.
What is standard deviation?Standard deviation is a measure of the spread or dispersion of a set of data. It tells you how much the individual values in the set differ from the mean (average) of the set.
What is the formula to calculate standard deviation?The formula for calculating the standard deviation of a set of n data points:
Standard deviation = sqrt(((x1 - mean)^2 + (x2 - mean)^2 + ... + (xn - mean)^2) / n)
First, we need to calculate the number of standard deviations that the guarantee period of 24 months is from the mean of 33 months. We can do this by subtracting the mean from the guarantee period and dividing by the standard deviation:
(24 - 33) / 4 = -9 / 4 = -2.25
Since we are assuming that the distribution of battery lifetimes is normal, we can use the standard normal distribution table to look up the area under the curve that is 2.25 standard deviations below the mean. This area represents the proportion of batteries that will have to be replaced under the guarantee.
According to the standard normal distribution table, the area under the curve that is 2.25 standard deviations below the mean is approximately 0.0122. This means that approximately 1.22% of the batteries will have to be replaced under the guarantee.
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Yochanan walked from home to the bu top at an average peed of
mph. He immediately got on hi chool bu and traveled at an average peed of
mph until he go to chool. The total ditance from hi home to chool i
mile, and the entire trip took
hour. The following ytem of equation repreent thi:
Distance covered by Yochanan by walking = 5 km
Distance covered by Yochanan by bus = 30 km
Given the values in the question,
The average speed of Yochanan when he walked to the bus stop from home = 5 km/h
The average speed of the bus till Yochanan reached his school = was 60 km/h
The total distance between his school from home = is 35 km
Time is taken by the entire trip = 1.5 hours
Relation between Distance, Time, and speed,
⇒ Average Speed = [tex]\frac{Distance}{Time}[/tex]
Let us consider that Yochanan walked = a km
The bus travelled = 35 - a
We know that the total time is constant so,
⇒ T = T1 + T2
⇒ 1.5 = [tex]\frac{x}{5} + \frac{35-a}{60}[/tex]
Solving for a,
⇒ 1.5 = [tex]\frac{12a + 35 - a}{60}[/tex]
⇒ 11 a + 35 = 90
⇒ 11 a + 55
⇒ a = 5
The distance covered by Yochanan by walking = a = 5 km
Distance covered by bus = 35 - a
= 35 - 5
= 30 km
Therefore, the distance covered by Yochanan by walking = is 5 km, distance covered by Yochanan by bus = is 30 km
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Yochanan walked from home to the bus stop at an average speed of 5 km/h he immediately got on his school bus and traveled at an average speed of 60 km/h until he got to school. the total distance from his home to school is 35 kilometers, and the entire trip took 1.5 hours. how many kilometers did Yochanan cover by walking, and how many kilometers did he cover by traveling on the bus? Yochanan walked kilometers and traveled kilometers on the bus.
relationship between f(x) , f’(x) , f’’(x) at x
Refer to the photo taken.
if a country has a natural increase rate of 2.0 percent, how long will it take to double its population?
It will take 35 years to double the population
What is Percent ?Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it. For instance, if you properly answered 68 out of 100 questions on a test, you would have received a 68% grade (68/100).
According to the given information
Let [tex]P(0)[/tex] be initial population
and K be the growth rate
Then Population of the country after t years
[tex]P = P(0)e^{Kt}[/tex]
Let x be the present population
2x will be the double of present population
And we know
The growth rate K = 0.02%
So
The value of t could be determined as follows
[tex]xe^{0.02t}=2x[/tex]
[tex]e^{0.02}=2[/tex]
[tex]0.02t=ln(2)[/tex]
Multiply both sides by 1000
0.02t × 1000 = ln(2) × 1000
Refine
20t = ln(2) × 1000
Divide both sides by 20
[tex]\frac{20t}{20}=\frac{ln(2).1000}{20}[/tex]
t = [tex]ln(2).500[/tex]
t = 0.693×50
t = 34.65 years
t = 35 years
It will take 35 years to double the population
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Antonio's dad bought gas for their family's ATV two weeks in a row. Last week, he bought 12 gallons for $35.40. This week, he bought 9 gallons for $25.83. How much more did Antonio's dad pay per gallon last week?
$
per gallon
Answer: $0.08
Step-by-step explanation:
First, let's find last week's price
Take 35.40 divided by 12 = $2.95 per gallon
Next, find this week's price
Take 25.83 divided by 9 = $2.87 per gallon
Then take 2.95 - 2.87 = $0.08
is this parallel, perpendicular, or neither?
If line BG⃡ and CF⃡ are parallel, then LD→ i proportional to MD→. I thi tatement correct? Explain your anwer
Yes, this statement is correct because in quadrilaterals if two lines are parallel, then the other two sides have to be equal in length.
Triangles that are equal in all ways and interchangeable are typically described as being congruent.
A triangle with equal legs, such as an isosceles triangle, may have equal legs that are also equal to the two equal legs of another triangle with equal legs, but if the included angle is different, the triangles are not congruent.
Two sides are simply equal if their lengths are the same.
When it comes to parallelograms, both opposite side pairs are equal and parallel.
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Evelyn Everest gave property to her mother Sharon when the adjusted basis of the property was $12,000 and the fair market value was $80,000. Sharon died eight months later when the property was valued at $85,000 and she left the property to Evelyn. What is Evelyn’s basis? If Sharon had died more than a year after receiving the gift when the fair market value was $85,000, what would the basis have been to Evelyn?
Evelyn basis is the adjusted market value of the property and the basis would have been to Evelyn as profit
What is adjusted basis?We should know that adjusted basis is the value of a property after deducting all expenses and taxes from the property.
The Adjusted basis of the property was $12,000
It was given to Sharon at fair value of $80,000
After death of Sharon, the property was worth $85,000
Based on these figures, the basis is a gain of $(85000-80000) to to Evelyn
In conclusion, Evelyn has gained the sum of $(85000-12000)=$73000
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Multiple choice math
I believe it would be the first answer choice
a.5n^2
n^2 being "the square of a number"
5n^2 is just multiplying 5 and n^2
in other words the product of the square of a number and 5
You want to apply the filter() function to the variables Cocoa. Percent and Rating. Add the code chunk that lets you filter the data frame for chocolate bars that contain at least 75% cocoa and have a rating of at least 3. 9 points. Filter(Cocoa. Percent >= 75, Rating >= 3. 9)What value for cocoa percent appears in row 1 of your tibble? a. 80% b. 75% c. 88% d. 78%
Answer:
A
Step-by-step explanation: here ya go <3
HELP ME PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!
In the first circle, the measure of angle ABC is 24°
In the second circle, the measure of angle ABC is 20°
Circle Geometry: Calculating the measure of anglesFrom the question, we are to determine the measure of angle ABC
In the first diagram,
The measure of the arc is 48°
From one of the circle theorems, we have that
The angle subtended by an arc in a circle is twice the angle subtended at the circumference.
Then, we can write that
2 × ∠ ABC = 48°
∠ ABC = 48°/2
∠ ABC = 24°
Question 5
Using the same theorem,
The angle subtended by an arc at the center of the circle is twice the angle subtended at the circle
∠ ABC = 1/2 × 40°
∠ ABC = 20°
Hence, the measure of the angle is 20°
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The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
The scale factor will be 1/4.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The right triangle on the right is a scaled copy of the right triangle on the left.
Now,
Since, The right triangle on the right is a scaled copy of the right triangle on the left.
Hence, The ratio of their similar sides is equal to the scale factor.
So, We get;
⇒ 2 / 8 = 1 / 4
And, 2 / 8 = 1 / 4
Thus, The scale factor = 1/4.
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Please help me, it’s asap
The price that is 3rd standard above the mean, if the mean is $10000 and the standard deviation is $500 is $18500.
What is mean?Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
The mean, m = $17000,
The standard deviation, σ = $500
Calculate the 3rd standard deviation as shown below,
3rd standard deviation = mean + 3 × standard deviation
3rd standard deviation = 17000 + 3 × 500
3rd standard deviation = 17000 + 1500
3rd standard deviation = $18500
Therefore, the price that is 3rd standard above the mean, if the mean is $10000 and the standard deviation is $500 is $18500.
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Given a
system,
3y=x+21
y+2/3x = 10
a. Solve graphically.
Be sure to state the
exact coordinates.
b. Check the solution by substituting into
both equations.
The solution to the system of linear equations 3y = x + 21 and y + 2/3x = 10
is (x, y) = (3, 8)
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
From the question, we have the following parameters that can be used in our computation:
In this case, the system of equations is given as
3y = x + 21
y + 2/3x = 10
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (3, 8)
Hence, the solution is (3, 8)
Checking the solutionIn (a), we have
The lines intersect at (3, 8)
This means that
(x, y) = (3, 8)
So, we have
3 * 8 = 3 + 21 = 24
y + 2/3 * 3 = 10
The above equations are true
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Suppose that you are rolling a six sided dice. Let A-get a 3 What is P(A^C)? 2/6
4/6 5/6 1/6 3/6
Answer:
5/6 (option 3)
Step-by-step explanation:
[tex]P(A^C)[/tex] is asking what the complement of A is. This means we are asking what the probability of NOT getting A is. This would be 1 - P(A).
P(A) = The probability of getting a 3 = 1/6
We can solve for the probability of the complement of the A and get:[tex]P(A^C) = 1 - P(A) = 1 - \frac{1}{6} = \frac{5}{6}[/tex]
Thus, the answer is 5/6 (which I believe is the 3rd option you are given)
Identify the type of angle shown
A. Alternate exterior angles
B. Same side interior angles
C. Corresponding angles
D. Alternate interior angles
Help!!!
Answer:
A. Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are congruent angles that are outside the parallel lines. That is why their name is alternate exterior angles since they are exterior from parallel lines.
A translation 5 units right and 3 units down, then a reflection across x = 0 is applied to the point (5, –1). Where is the image in the coordinate system?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
Answer:
it would be quadrant |||
so answer choice C
Step-by-step explanation:
What value of x is in the solution set of the inequality 9(2x 1) < 9x – 18? –4 –3 –2 –1
The value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18 is -4.
Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
9(2x + 1) < 9x - 18
18x + 9 < 9x - 18
18x - 9x < -18 - 9
9x < -27
x < -3
x = (-∞, -3)
Hence, the solution set of the given inequality is the set of numbers less than -3. Among the given choices, only -4 is less than -3. Therefore, the value of x is -4.
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Answer: -4
Step-by-step explanation: edge2020
A construction company is building a roof on a house. The horizontal distance from the edge of the
roof to the peak is 25 feet. The vertical distance from the edge of the roof to the peak is 6.25 feet. What is the slope of
the roof? Write in the simplest form.
The slope of the roof is 0.25
What is a slope ?
A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. And b is the value of b at the y-intercept (0, b).
To find slope
= 6.25 / 25
= 0.25
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Kansas City and Denver are 600 mi
apart. Two cars start from these cities.
traveling toward each other. They meet
after 6 hr. Find the rate of each car if one
travels 30 mph slower than the other.
Answer:
65 mph; 35 mph
Step-by-step explanation:
let x = rate of car 1
x-30 = rate of car 2
distance = rate x time
6x = 600 - 6(x-30)
6x = 600 - 6x + 180
6x = 780 - 6x
12x = 780
x = 780/12 = 65 mph
x - 30 = 65 - 30 = 35 mph
Challenge A large university accepts 40% of the students who apply. Of the students the university accepts, 50% actually
enroll. If 30,000 students apply, how many actually enroll?
students would actually enroll.
Help me please
Answer: 6000 students
Step-by-step explanation:
First, we find the 40% that the university accept
40% = 0.4
Take 30000 times 0.4 = 12000 students got accept
Now we find the 50%
50% = 0.5
Take 12000 times 0.5 = 6000 students
6000 students would actually enroll
Translate the sentence into an inequality. The sum of 8 and y is greater than or equal to 17.
Answer:
8+y[tex]\geq[/tex]17
Step-by-step explanation:
Jaon went hopping
He bought a watch and a pair of trainer for a total price of £53. 55
Thi price include a 15% loyalty dicount
Before the dicount, the trainer were priced at £38
Work out the price of the watch before the dicount
The price of the watch before the discount is calculated to be £24.44.
As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;
discount on a pair of trainers = 15/100 × 38 = £5.7
cost of trainers after discount = £38 - 5.7 = £32.3
Now the price of the watch after the discount can be calculated by subtraction as follows;
price of watch after discount = total price - price of trainers after discount
price of watch after discount = £53. 55 - £32.3
price of watch after discount = £21.25
Now the price of the watch before the discount can be calculated as follows;
price of watch before discount = £21.25 × 15/100
price of watch before discount = £21.25 + £3.1875
price of watch before discount = £24.44
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A tree, which i approximately 80% of it full height, i preently 60 feet tall. How tall will the tree be when it i fully grown?
The tree will be 75 feet tall when it will be fully grown.
The total tree height is the distance between the tree's base and its highest point on the ground. A yardstick provides a quick and relatively accurate way to gauge the height of a tree.
If the tree is currently 60 feet tall and is approximately 80% of its full height, we can assume that the tree will be 100% of its full height when it is fully grown. To determine the full height of the tree, we can use the proportion:
60 feet / 80% = X feet / 100%
We can then cross-multiply to solve for X:
X = (60 feet * 100%) / 80%
= 75 feet
So, when the tree is fully grown, it will be approximately 75 feet tall.
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what is the value of the t score for a 99% confidence interval if we take a sample of size 18?
The value of the Confidence interval will be 2.898
The number of standard deviations from the t-mean distribution's is equal to a t-score. The test statistic used in t-tests and regression testing is the t-score. When the data follow a t-distribution, it may also be used to represent how distant an observation is from the mean.
The t-score formula is written as follows:t=¯¯¯x−μS√n t = x ¯ − μ S n , where ¯¯¯x, is the sample mean, is the population mean, S n is the sample size, and x is the standard deviation of the sample. Square root n must be included in the formula.
using tables of t distribution we have
alpha = 1 - 0.99 = 0.01
alpha / 2 = 0.005
df = 17
critical value or value of t score is = 2.898
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The value of the t score is 2.898 for a 99% confidence interval if we take a sample of size 18.
As per the details share in the above question are as bellow,
Confidence level = 99%
Now the significance level will be 100% - Confidence level
Substitute the value in above equation we get,
Thus, Significance level = (100% - 99%)
Significance level= 1%
Significance level=1/100= 0.01
Now the Sample size (n) = 18
Further the degrees of freedom = (n - 1)
Substitute the value in above equation we get,
Degrees of freedom= (18 - 1) = 1
Where, the t score for a 99% confidence interval is given by,
t({0.01/2},17)=2.898
Now calculating the critical value from t table we get,
Critical value or value of t score is = 2.898
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If a hypothesis test is significant at level α = 0.05, then what is known for the P-value?P-value > 0.01P-value ≤ 0.05P-value ≤ 0.01P-value > 0.05
If a hypothesis test is significant at level α = 0.05, then the P-value is less than or equal to 0.05 or P-value ≤ 0.05.
The P-value is a measure of the strength of the evidence against the null hypothesis. It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. If the P-value is less than or equal to the significance level α, it means that the observed evidence is unlikely to have occurred by chance under the null hypothesis, and we can reject the null hypothesis in favor of the alternative hypothesis.
For example, if the P-value of a hypothesis test is 0.03, it means that there is a 3% chance of obtaining the observed test statistic (or a more extreme one) if the null hypothesis is true. Since this is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.
Hence, if a hypothesis test is significant at level α = 0.05, then P-value ≤ 0.05.
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The larget taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. The total weight of thee two ingredient wa 617. 3 kg. How many kilogram of each ingredient were ued?
The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg
What is a unit amount in math?
When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio
1 k + 6.6 k = 617.3
Where “k” is a constant value, a multiplier.
Solving for k:
7.8 k = 617.3
k = 617.3 /7.8
k= 79.17
So:
Amount of onion used:
1 (79.17) = 79.17 kg
Amount of grilled steak used:
6.6 (79.17) = 538.356 kg
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