Answer:
The largest term is 52.---------------------------------
Given sequence:
t(n) = 60 - 8nThis is decreasing sequence since the common difference is negative, d = - 8.
Therefore the first term is the largest one:
t(1) = 60 - 8*1 = 60 - 8 = 52There are 1000 students at a college. In January, æ of these students had passed
their driving test.
Between January and April, the number of students who had passed their driving
test increased by 20%, and the number of students who had not passed
decreased by 5%. No one left or joined the college during this time.
a) Explain why the number of students who had not passed their driving test yet
was 0.95(1000 - x) in April.
b) Hence explain why 1.2x +0.95(1000-x) = 1000.
c) How many students had passed their driving test in January?
a) In April, the number of students who had not passed their driving test decreased by 5%.
b) The equation is 1.2x + 0.95(1000 - x) = 1000.
c) 200 students passed their driving test in January.
a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).
In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
b)
The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).
The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.
c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.
Expanding the equation, we get:
1.2x + 950 - 0.95x = 1000
0.25x = 50
x = 200
Therefore, 200 students passed their driving test in January.
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A student scored 80% on a test. If the test had 50 questions worth one point each, how many questions did the student answer correctly?
Answer:
40
Step-by-step explanation:
All questions are worth the same, 1 point each.
80% of 50 = 0.8 × 50 = 40
Answer: 40
Answer:
40
Step-by-step explanation:
80/100*50 = 40
Eight fourths is proportional to what value?
Eight fourths is proportional to the value of 2/1
What is proportionality of values?Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.
A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.
Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1
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A triangle has sides with lengths of 13 meters, 18 meters, and 8 meters. Is it a right triangle?
Answer:
The Pythagorean Theorem describes the relationship among the three sides of a right triangle
[tex]a^{2} +b^{2} = c^{2} \\8^2+13^2=c^2=208 \\\sqrt{208}=14.4\\ 14.4 \neq 18[/tex]--> not a right triangle
There is a multiple choice quiz with six questions and five possible answers and only one choice is correct what is the probability you get your first and only incorrect answer on the fourth question?n
Answer:1/1875
Step-by-step explanation:
the probability of getting any one question correct is 1/5, and the probability of getting any one question incorrect is 4/5.
The probability of getting the first three questions correct and the fourth question incorrect can be calculated as follows:
(1/5) * (1/5) * (1/5) * (4/5) = 4/3125
Since there are six possible positions for the incorrect answer to occur (first, second, third, fourth, fifth, or sixth), the probability of getting the first and only incorrect answer on the fourth question is 4/3125 * 1/6 = 1/1875.
Find the surface area and volume of the for fire. Round to the nearest tenth
The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A
How to determine the valuesThe formula for calculating the surface area of a cone is expressed as;
SA = πr² + πrl
Such that the parameters are;
r is the radius l is the lengthSubstitute the values, we have;
Surface area= 3.14 × 16 = 3.14 × 4 × 8
Multiply the values
Surface area = 50.24 + 100.48
Add the values
Surface area = 150.8 in²
Volume of the cone is;
Volume = 3.14 × 4² × 6.9/3
Volume = 3.14 × 16 × 6.9/3
Volume =116. 1in³
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In triunghiul ABC ,A este de 75 grade si B este de 45 grade. Daca AD perpendicular BC, D apartine BC si BE perpendicular AC, E apartine AC iar AB=12 Radical din 6 cm calculati lungimile AD si BE si Perimetrul ABC
Answer:
just start scamming
Step-by-step explanation:
what is the probability of spinning a blue, then green
The probability of getting Blue then Green while spinning the wheel is
3 / 32
Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.
From the given figure we can find out the following information
The probability of getting Blue While spinning the wheel = 3/8
The probability of getting Green While spinning the Wheel = 2 / 8
The probability of getting Blue then Green while spinning the wheel
= 3/8 * 2/8
= 6/64
= 3/32
Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32
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Pierre produces wedges of aged cheddar cheese and sells them for $12 each. The table below shows the labor productivity
forPierre's cheese-making business. Fill in the missing values. Assume this is a perfectly competitive market.
Instructions: Round your answers to one decimal place.
Pierre's Cheese Business and Revenues
Labor
0
2
4
6
8
10
12
14
Total Product (wedges
of cheese)
(workers)
0
———
48
66
82
———
———
114
Marginal Product
(wedges of cheese)
/
12
——-
9
——-
7
5
4
Price
(dollars)
$12
12
12
12
12
12
12
12
Total Revenue
(dollars)
$0
288
———
792
984
———
1,272
———
Marginal Revenue
Product (dollars)
/
———
144
108
———
84
———
48
Answer: To fill in the missing values, we can use the formulas for marginal product and marginal revenue product:
Marginal Product = Change in Total Product / Change in Labor
Marginal Revenue Product = Price x Marginal Product
Using the given information, we can fill in the missing values as follows:
Labor Total Product Marginal Product Price Total Revenue Marginal Revenue Product
0 0 - $12 $0 -
2 48 24 $12 $288 $288
4 66 9 $12 $792 $108
6 82 7 $12 $984 $84
8 96 5 $12 $1,152 $60
10 114 9 $12 $1,368 $108
12 132 9 $12 $1,584 $108
14 150 9 $12 $1,800 $108
So the missing values are:
Total Product for labor = 0 and 14: 0 and 150, respectively.
Marginal Product for labor = 0, 8, and 14: -, 5, and 9, respectively.
Total Revenue for labor = 4, 6, and 8: $792, $984, and $1,152, respectively.
Marginal Revenue Product for labor = 0, 4, and 6: -, $84, and $60, respectively.
Step-by-step explanation: :)
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A basketball player guesses her team will score 54 points during the game. The player's team actually scores 60 points.
What is the percent error in the player's guess?
A: 5%
B: 10%
C: 12%
D: 15%
Answer:
6 divide by 60 into 100
Step-by-step explanation:
is 10
The length of timber cuts are normally distributed with a mean of 95 inches and a standard
deviation of 0.52 inches. In a random sample of 30 boards, what is the probability that the
mean of the sample will be between 94.7 inches and 95.3 inches?
O 0.998
O 0.436
O 0.002
O 0.950
The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
How to find the probability that the mean of the sample will be between 94.7 inches and 95.3 inchesUsing the Central Limit Theorem.
The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.
Calculate the standard error of the mean (SEM):
SEM = σ / √n
SEM = 0.52 / √30
SEM ≈ 0.095
Calculate the z-scores for the lower and upper limits:
z1 = (94.7 - μ) / SEM
z2 = (95.3 - μ) / SEM
z1 = (94.7 - 95) / 0.095 ≈ -0.526
z2 = (95.3 - 95) / 0.095 ≈ 0.316
Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.
Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.
Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
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8 cosθ-1=0 to the nearest 0.1°
Answer:
82.8°
Step-by-step explanation:
We can solve for θ by first isolating cosθ:
8 cosθ - 1 = 0
8 cosθ = 1
cosθ = 1/8
We can find the inverse cosine of 1/8:
θ = cos⁻¹(1/8) = 82.8191°
Rounding to the nearest 0.1°, we get:
θ ≈ 82.8°
1. An isosceles triangle has a base with a length of 14 inches and base angles that measure 68° each. Which
expression below correctly calculates the area of this isosceles triangle?
(1) 7²-tan (68°)
(2) 14²-sin (68°)
(3) 7²-cos (68°)
(4) 14-7-sin (68°)
None of the given expressions (1), (2), (3), or (4) correctly calculates the area of the isosceles triangle. The correct expression is (1/2) * 14 * (7 * tan(44°)).
To calculate the area of an isosceles triangle, we need the base length and the height of the triangle. In this case, the base length is given as 14 inches, but the height is not provided.
However, we can use trigonometry to find the height of the triangle by using one of the base angles. Since the triangle is isosceles and the base angles are each 68°, we know that the remaining angle (at the top of the triangle) is 180° - 68° - 68° = 44°.
We can then use the trigonometric function tangent (tan) to find the height. The formula is: tan(angle) = opposite/adjacent.
tan(44°) = height/7, where 7 represents half of the base length.
Rearranging the equation, we have: height = 7 * tan(44°).
Now, we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Substituting the given values, we get:area = (1/2) * 14 * (7 * tan(44°)).
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Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?
A. 20
B. 26
C. 32
D. 36
HELPPP
Instructional Item I
A research group is trying to determine how many alligators are in a particular area. They
tagged 30 alligators and released them. Later, they counted 12 alligators who were tagged out
of the 150 they saw. What can the research group estimate is the total population of alligators
in that area?
Instructional Item 2
The local grocery store is going to donate milk and cookies to an upcoming middle school
event. They surveyed 150 students in the school to determine which type of milk they prefer
and recorded the results below.
Cow's Milk Soy Milk
82
25
Almond Milk
43
If there are 950 students in the school, how much soy milk should the store plan to donate?
The total population of alligators will be 375.
The amount of soy milk that the grocery store should plan to donate is: 158.
How to calculate the total population of alligators in the areaTo calculate the total population of alligators in the area, we will assign the following variables:
30 Tagged alligators = m
12 Counted alligators = k
150 alligators seen = n
The total population size (N bar) of alligators is calculated with the formula:
N bar = mn/k
= 30 * 150/12
= 4500/12
375
For the amount of soy milk, we can say that if 25 out of 150 students preferred soy milk, then the number that would prefer soy milk out of 950 will be: 950 * 25/150 = 158.
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Directions: Transformations from the parent function y = x² are described
below. Write an equation to represent the function.
13, translated 2 units right
14. translated 5 units up
15. translated 3 units left and 4 units
down
17. reflected over the x-axis, then
translated 3 units down
16. translated 7 units right and 4
units up
18. reflected over the x-axis, then
translated 5 units right and 2 units
down
19. vertically compressed by a factor 20. vertically stretched by a factor
of 1/3, then translated 8 units up
of 2, reflected over the x-axis,
then translated 4 units left
The result of the transformation of the parent function y = x² are;
13. y = (x - 2)²
14. y = x² + 5
15. y = (x + 3)² - 4
16. y = (x - 7)² + 4
17. y = -(x²) - 3
18. y = -(x - 5)² - 2
19. y = (1/2)x²
20. y = (3x²) + 8
What are the results of the transformations?The transformations on the parent function y = x² can be described as;
13. Translated 2 units right:
The equation will be y = (x - 2)²
14. Translated 5 units up:
The equation will be y = x² + 5
15. Translated 3 units left and 4 units down:
The equation will be y = (x + 3)² - 4
16. Translated 7 units right and 4 units up:
The equation will be y = (x - 7)² + 4
17. Reflected over the x-axis, then translated 3 units down:
The equation will be y = -(x²) - 3
18. Reflected over the x-axis, then translated 5 units right and 2 units down:
The equation will be y = -(x - 5)² - 2
19. Vertically compressed by a factor of 2:
The equation will be y = (1/2)x²
20. Vertically stretched by a factor of 1/3, then translated 8 units up:
The equation will be y = (3x²) + 8
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How much less would Maria have to spend to have $70 per month available for saving?
A. $45.95
B. $75.95
C. $25.95
D. $24.05
Maria have to spend $ 45.95 less than what she spends now in order to save $ 70 per month.
Hence the correct option is (A).
From the given Maria's Income Statement we can see that,
Her total income from Fast food Restaurant = Gross Pay + Allowance = $ 580 + $ 50 = $ 630.
Total deductions by taxation = Federal Income Tax + State Income Tax + Social Security Tax = $ 58 + $ 16 + $ 24.36 = $ 98.36
So here net income = $ (630 - 98.36) = $ 531.64.
Here total expenses = Auto + Clothing + Food + Entertainment + Other = $ 290.02 + $ 92.29 + $90.28 + $ 32 + $ 3 = $ 507.59
So Her Savings = Net Income - Total Expenses = $ 531.64 - $ 507.59 = $ 24.05.
Now in order to save $ 70 per month Maria has to spend = $ 70 - $ 24.05 = $45.95 less than she spend now.
Hence the correct option will be (A).
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Suppose that a safety deposit box at your bank costs $45/month to rent. How much would
it cost for you to rent the box for 15 years?
<
Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3 7/8, 5 1/4, 4, 6 1/8, 4 1/2, 5 1/4, 3 1/2, 5 3/8, 4 3/4, 5
The students will make a line plot of the data. They will use only one fraction in their scale. They must be
able to plot all of the data above a label. Which should this fraction be?
A. tenths
B. eighths
C. fourths
D. halves
The required, the students use eighths as their scale, they will be able to plot all of the data points above the label. Option B is correct.
To make a line plot, the students will mark a number line with a scale that includes all the data points. Since the given data includes fractions with denominators of 2, 4, and 8, it would be best to choose a fraction that is a factor of all of these denominators. The only option that satisfies this condition is B. eighths.
To see why, note that 1/8 is a factor of 1/2 (4/8), 1/4 (2/8), and 1/8 (1/8). Therefore, if the students use eighths as their scale, they will be able to plot all of the data points above the label. Using any other fraction would require rounding some of the data points, which could lead to a loss of information.
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Byron worked fewer than 20 days last month. Write an inequality for d, the number of days Byron worked last month.
Answer:
[tex]d < 20[/tex]
Step-by-step explanation:
The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.
Which best describes the solution set for the compound inequality below?
2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
no solution
x = 1
all real numbers except x = 1
all real numbers
The statement that best describes the solution to the inequality in this problem is given as follows:
all real numbers except x = 1.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
The solution to the first inequality is given as follows:
2(x + 7) – 1 > 15
2x + 14 > 16
2x > 2
x > 1.
The solution to the second inequality is given as follows:
3(x + 2) < 2x + 7
3x + 6 < 2x + 7
x < 1.
The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:
all real numbers except x = 1.
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(05.03 MC)
A regular heptagon with 7 sides is inscribed in a circle with radius 8 millimeters. What is the area of
the figure? (3 points)
O 25.019 mm.2
O 150.112 mm.2
O 175.130 mm.²
205.639 mm.2
Answer:
i think 25.019mm2 is the correct answerrrrrrrr.
Answer:
175.130 mm^2
Step-by-step explanation:
Took the test.
If ΔABC is dilated from point A by a scale factor of one half, which of the following equations is true about segment D prime E prime?
segment D prime E prime = one half segment DE
segment D prime E prime = two segment DE
segment D prime E prime = segment DE
segment D prime E prime = three segment DE
An equation that is true about segment D prime E prime include the following: A. segment D prime E prime = one half segment DE
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.
In this scenario and exercise, we would dilate the coordinates of the vertices of triangle ABC (ΔABC) by applying a scale factor of 1/2 that is centered at point A as follows:
D'E' = 1/2 × DE
In conclusion, line segment D'E' is equal to one half line segment DE.
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Use the Law of Sines to solve (if possible) the triangle: A = 25° 4', a = 9.5, b = 22? Round answer to two decimal places.
The measure of the angle B of the triangle is 78.15 degrees
How to determine the possible solutions from the triangleFrom the question, we have the following parameters that can be used in our computation:
A = 25 degrees
a = 9.5 units
b = 22 units
Using the law of sines, the angle B is calculated as
sin(A)/a = sin(B)/b
So, we have
sin(25)/9.5= sin(b)/22
This gives
sin(b) = 22 * sin(25)/9.5
Evaluate
sin(b) = 0.9787
Take the arc sin of both sides
b = 78.15
Hence, the measure of the angle is 78.15 degrees
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Los estudiantes de la escuela organizan reuniones del equipo verde para planear maneras de proteger el medioambiente. Esta semana hay 144 miembros en la reunión, que es ek 90% del total del grupo
¿Cuál es el número total de miembros en el equipo verde?
If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.
If 144 members represent 90% of the total group, we can set up the equation:
144 = 0.9x
where x is the total number of members on the green team.
To solve for x, we can divide both sides of the equation by 0.9:
144 ÷ 0.9 = x
This simplifies to:
160 = x
To check our answer, we can verify that 144 is indeed 90% of 160:
144 ÷ 160 = 0.9
which confirms that our answer is correct.
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Be sure to round the mileage to nearest whole mile
The miles you drive must be greater than or equal to 183 miles in order for Plan B to save you money.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.For the mileages, we have that:
The slope is the cost per mile.The intercept is the daily cost.Hence the functions are given as follows:
Plan A: A(x) = 30 + 0.14x.Plan B: B(x) = 50.Cost B is the better plan when:
A(x) > B(x)
Hence:
30 + 0.14x > 50
0.14x > 20
x > 20/0.14
x > 142.9 miles -> rounded to 143.
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Can you guys help me with this please
Step-by-step explanation:
Using rules of logs :
9 loga x = loga x^9
Then using another rule:
loga x^9 + loga y = loga (x^9 * y )
Is the inverse of the function shown below also a
function? Explain your answer.
DONE ✔
AY
y
4
We can see here that it is true that the inverse of the function shown is also a function. This is true because the graph of the inverse of the function shown by reflecting the red graph about the line y = x.
What is a function?A function in mathematics is a unique connection between a group of inputs and their results. A function is a rule that specifically assigns one element from another set to each element in a set.
The set of inputs is referred to as the function's domain, while the set of outputs is referred to as the function's codomain.
From the given graph, we can deduce that the resulting graph is true for all x values and for all y values; it passes the vertical line test.
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What is the value of x in the given triangle, in inches?
The numerical value of side length x in the right triangle is 8.
What is the numerical value of x?The figures in the image are two similar right triagles.
Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.
x/6 = (x + 4)/9
Cross multiply and solve for x:
6( x + 4 ) = x × 9
Apply distributive property:
6 × x + 6 × 4 = x × 9
Simplifying, we get:
6x + 24 = 9x
Subtract 6x from both sides:
6x - 6x + 24 = 9x - 6x
24 = 9x - 6x
24 = 3x
3x = 24
Divide both sides by 3:
x = 24/3
x = 8
Therefore, the value of 8.
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What are the first five terms of the sequence a_{n} = - 11 * (1/2) ^ (n - 1)
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
B) -11/2 - 11/4 - 11/16 - 11/32 - 11/8
C) -11, 5, - 9/4 - 4/3 - 7/8
D) -11, - 11/2 - 11/3 - 11/4 - 11/5
All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
We have to given that;
Rule for sequence is,
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Now, WE can find first five terms of sequence as;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Put n = 1;
⇒ a (1) = - 11 × (1/2)¹⁻¹
⇒ a (1) = - 11
Put n = 2;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (2) = - 11 × (1/2)²⁻¹
⇒ a (2) = - 11 × (1/2)¹
⇒ a (2) = - 11 / 2
Put n = 3;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (3) = - 11 × (1/2)³⁻¹
⇒ a (3) = - 11 × (1/4)
⇒ a (3) = - 11 / 4
Put n = 4;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (4) = - 11 × (1/2)⁴⁻¹
⇒ a (4) = - 11 × (1/2)³
⇒ a (4) = - 11 / 8
Put n = 5;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (5) = - 11 × (1/2)⁵⁻¹
⇒ a (5) = - 11 × (1/2)⁴
⇒ a (5) = - 11 / 16
Thus, All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
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