Answer:
The letter t occurs more than 26 times on approximately 420 of these pages.
Step-by-step explanation:
1 standard deviation below mean = M - SD
= 44 - 18 = 26
This implies that that "26" is 1 s.d. below the mean, which is at the 16th percentile.
Thus, there is a 0.16 chance that "t" will occur less than 26 times on any single page.
consequently, there is a 0.84 chance that it will occur more than 26 times on any single page.
there are 75 animals on a farm 48 of them are sheep what percentage of the animals are sheep
What is the pattern of the numbers 1,3,6,10,15,21,28,36. What is the 5857th triangular number?
the pattern of the numbers 1,3,6,10,15,21,28,36. What is the 5857th triangular number: The unit digit of the 5857th triangular number is 8.
A series of numbers known as triangular numbers might be demonstrated as the amount of a series of positive whole numbers. The condition Tn = (n(n+1))/2 yields the nth triangular number. The initial not many triangular numbers, for example, are 1, 3, 6, 10, 15, etc. Numerous numerical and non-numerical applications exist for triangular numbers. They can be found, for example, in the investigation of math, combinatorics, and number hypothesis. They are used in calculations for information looking and arranging in fields like software engineering, where they have reasonable applications.
The nth triangular number is given by the recipe:
Tn = (n(n+1))/2
For the given arrangement 1,3,6,10,15,21,28,36, the units digit are:
1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, ...
The worth of 5857 is compatible with 7 modulo 10.
Consequently, the unit digit is the seventh number in the cycle above, which is 8.
Thus, the unit digit of the 5857th triangular number is 8.
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the complete question is:
Here is the sequence of numbers called triangular numbers: 1,3,6,10,15,21,28,36, Notice the pattern -the numbers increase by one more each time. What is the unit's digit of the 5857th triangular?
Andariel went for a ride on her dune buggy in the desert. She rode east for 6 km, then turned 125° to the left for the second stage of her ride. After 5 minutes riding in the same direction, she turned to the left again, and from there travelled the 5.5 km straight back to her starting position.
How far did Andariel travel in the second section of her ride, correct to 2 decimal places?
Applying the laws of cosine, in the second section of her ride, Andariel traveled about 3.012 km, as rounded to 2 decimal places.
What is the law of cosines?The law of cosines is a mathematical formula used to determine the unknown length or angle of a triangle when two sides and an angle or all three sides are known.
Hence, we can think of it as trying to know Andariel's travel distance around a big triangle.
Thus to calculate, using the law of cosines, we have:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
Where in our case:
a = 6 km (distance traveled east)b = x km (distance traveled in the second section)C = 180 - 125 = 55 degrees (angle between a and b)c = 5.5 km (distance traveled straight back to the starting position)If we substitute the values above into the cosine formula, we get:
[tex](5.5)^2 = (6)^2 + (x)^2 - 2(6)(x)*cos(55)[/tex]
[tex]30.25 = 36 + x^2 - 12.0627x[/tex]
Simplifying and rearranging the equation further:
[tex]x^2 - 12.0627x + 5.75 = 0[/tex]
Applying the quadratic formula to simply:
[tex]x = (12.0627 ± sqrt(12.0627^2 - 415.75))/2[/tex]
x = 9.05 or x =3.012.
Remember, we are told Andariel turned left twice and ended up at her starting position, we know that she traveled in a closed loop.
Therefore, the distance she traveled in the second section of her ride must be less than 6 km (the distance she traveled east in the first section). Thus, the distance she traveled last or second section of her ride was 3.012 km.
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QUESTION 1
If we enter 6 debits of $25 each, the net effect on our account is how many
dollars (indicate if this is negative or positive amount by using a negative sign if the answer is negative).
A triangle has a 50° angle and two sides that are each 4 centimeters in
Select True or False for each statement about this triangle.
True False
0
One of the angles in the triangle might be 65º.
The triangle might be an equilateral triangle.
Two of the angles in the triangle must measure 50°.
One of the angles in the triangle might be 60°.
C
0
Answer:
1.True
2.False
3.True
4.False
I NEED HELP ON THIS ASAP! PLEASE IT'S DUE TODAY!!!
a. Midpoint of AB, BC, CD, DA is (4,4), (0,-4), (-4,-4),(-4,4) respectively. b. polygon formed by connecting the consecutive midpoints. c. get a smaller square inside the square.
Describe Midpoint?In geometry, the midpoint refers to the point that is exactly halfway between two given points, lines, or line segments. It is the point that divides a line segment into two equal parts. The midpoint is also known as the half-way point.
The midpoint can be found using a variety of methods, but the most common one is by using the midpoint formula, which is:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Where (x1, y1) and (x2, y2) are the coordinates of the two points.
The midpoint is an important concept in many mathematical and scientific fields, including physics, engineering, and computer graphics. It is often used to determine the center of mass, the point of balance, or the halfway point in a process or journey.
a. We can use the midpoint formula to find the midpoint of each side of the square:
Midpoint of AB: ((0+8)/2, (8+0)/2) = (4,4)
Midpoint of BC: ((0+0)/2, (-8+0)/2) = (0,-4)
Midpoint of CD: ((-8+0)/2, (0-8)/2) = (-4,-4)
Midpoint of DA: ((-8+0)/2, (0+8)/2) = (-4,4)
b. Connecting the consecutive midpoints of each side of a square creates a smaller square inside the original square. We can see this by observing that the midpoints of opposite sides of a square form the vertices of a smaller square.
The polygon formed by connecting the consecutive midpoints of each side of the square is a square.
c. If we repeat the process of connecting consecutive midpoints one more time, we will get a smaller square inside the square formed in part (b). This smaller square will have vertices at the midpoints of the sides of the square formed in part (b). We can see this by observing that the midpoints of the sides of a square form the vertices of a smaller square inside that square.
So the polygon that would result from connecting the consecutive midpoints of each side of the polygon determined in part (b) is another square.
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3 |x+7| - 18=0 Determine the solutions to the absolute value equation. (List the smallest number first).
Answer: -25 and 11
solution:
|x+7| - 18 = 0
|x+7| = 18
±x = 18 ± 7
x = -25, 11
Using what you know and learned about angles and triangles over the past few weeks, what is the measure of angle 6?
Answer:
158degrees
Step-by-step explanation:
2 = 68 ( vertically opposite)
4 = 90 (Vertically opposite)
6= 68 +90 = 158( exterior angle is sum of its opposite interior)
From her house, Celine could drive due north to get to her parents' house or she could drive due east to get to her grandparents' house. It is 68 kilometers from Celine's house to her parents' house and a straight-line distance of 85 kilometers from her parents' house to her grandparents' house. How far is Celine from her grandparents' house? kilometers 0
Answer: /
Step-by-step explanation:
Notebooks at the school store were on sale for $3 off the regular price. Sam bought 4
notebooks on sale and paid a total of $28. Write an equation to find the regular
price of one notebook.
Answer: (28 / 4) + 3 = x; x = the regular price of a notebook not on sale.
Step-by-step explanation: The price of the notebook on sale is $7 and the price of a notebook regularly is $10 (not on sale). Therefore, the equation "(28 / 4) + 3 = x" explains how to come to that value.
is y=10(1−0.04)x growth or decay
When b > 1, the function f (x) = bx represents exponential development. If 0 b 1, then the function f (x) = bx depicts exponential decay.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, Exponential growth and decay are the two different kinds of exponential functions.
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Amari gathered a random sample of oranges in her town. She calculated data on different variables. For one of the variables that she collected, she constructed a bar graph.
Which of the following variables did she use?
Type of orange
Diameter of the oranges
Number of navel oranges
Price per pound of oranges
Answer:
no. four
Step-by-step explanation:
Price of the oranges per pound..
Answer:
Step-by-step explanation:
Type of orange
Select all the shapes below that show rotations of shape X
Answer:
A/C/E/F/G/H
Step-by-step explanation:
all of them have the same rotations there just have been turned around
What number is 24% of 1/8
Answer:
0.03
Step-by-step explanation:
Answer:
.03
Step-by-step explanation:
x = .24(1/8)
x = .24/8
x = .03
Helping in the name of Jesus.
during certain periods of time at an airport, passengers arriving at a security checkpoint have waiting times that can be modeled by a uniform distribution on the interval from 0 to 15 minutes. find the probability that a randomly selected passenger has to wait more than 10 minutes during one of these time periods.
There is a 1/3 chance, or around 0.333, that a randomly chosen passenger will have to wait longer than 10 minutes during one of these times.
What is probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
Since waiting times follow a uniform distribution on the interval from 0 to 15 minutes, the probability density function (PDF) is:
f(x) = 1/15, for 0 ≤ x ≤ 15
The probability that a randomly selected passenger has to wait more than 10 minutes is:
P(X > 10) = ∫10¹⁵ f(x) dx
P(X > 10) = ∫10¹⁵ 1/15 dx (since f(x) = 1/15 for 0 ≤ x ≤ 15)
P(X > 10) = [x/15]10¹⁵
P(X > 10) = (15 - 10)/15
P(X > 10) = 5/15
P(X > 10) = 1/3
Therefore, there is a 1/3 chance, or around 0.333, that a randomly chosen passenger will have to wait longer than 10 minutes during one of these times.
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Find the surface area of the triangular prism.
A drawing of a triangular prism. The base is a right triangle with base 9 inches, height 12 inches, and third side 15 inches. The height of the prism is 29 inches.
The surface area is
square inches.
The surface area of the triangular prism is 1152 inches square.
How to find the surface area of a triangular prism?The triangular prism has the base as a right triangle with base of 9 inches, height of 12 inches and third side of 15 inches. The height of the prism is 29 inches.
Therefore,
surface area of a triangular prism = bh + l(s₁ + s₂ + s₃)
where
b = base of the right triangleh = height of the right trianglel = height of the prisms₁, s₂ and s₃ are the sides of the right trianglesurface area of a triangular prism = 9 × 12 + 29(9 + 12 + 15)
surface area of a triangular prism = 108 + 29(36)
surface area of a triangular prism = 108 + 1044
surface area of a triangular prism = 1152 inches
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Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided.
Lower bound = 0. 123,
upper bound = 0. 607,
n = 1000
The point estimate of the population proportion, the margin of error is 0.365.
Margin of error is a statistic that expresses the amount of random sampling error in survey results. The larger the margin of error, the less confident people are that the poll results will reflect the overall census results. When the population is incompletely sampled and the resulting measure has a positive variance, the margin of error will be positive, i.e. the measures differ. The term margin of error is often used in non-survey contexts to refer to the error observed in the reporting of measured quantities.
According to the Question:
Given that:
Lower bound = 0.123,
Upper bound = 0.607,
n = 1000
P = Lower Bound + Upper Lower /2
= 0.123 + 0.607/2
= 0.73/2
= 0.365
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Every year, Martha and her sister attend 'The Nutcracker' at the Greenpoint Ballet. Last year, orchestra seating cost $60 per ticket. This year, each ticket was 15% cheaper. What was the cost of each ticket this year?
Answer:119.7
Step-by-step explanation:60 divided by 15%
The function t relates the age of a plant fossil, in years, to the percentage, c, of carbon-14 remaining in the fossil relative to when it was alive.
Use function t to complete the statements.
A fossil with 47% of its carbon-14 remaining is approximately
years old.
A fossil that is 7,000 years old will have approximately
of its carbon-14 remaining.
it is known that carbon-14 has a half-life of approximately 5,700 years. This means that after [tex]5,700[/tex] years, half of the original carbon-14 in a sample will have decayed.
What is the half-life?Assuming that t is a function that relates the age of a plant fossil to the percentage of carbon-14 remaining, it can be expressed as:
[tex]t(c) = (ln(c/100) / ln(1/2)) \times 5,700 years[/tex]
where ln represents the natural logarithm.
Using this function, we can complete the statements as follows:
A fossil with 47% of its carbon-14 remaining is approximately 11,323 years old.
[tex]t(47) = (ln(47/100) / ln(1/2)) \times 5,700 ≈ 11,323 y[/tex] years
A fossil that is [tex]7,000[/tex] years old will have approximately 28% of its carbon-14 remaining.
[tex]t-1(7,000) = (ln(100/1) / ln(1/2)) \times 5,700 - 7,000 ≈ 23,200[/tex] years remaining
[tex]t-2(c) = (ln(c/100) / ln(1/2)) * 5,700[/tex]
[tex]c = 100 * e^(-7,000 / 5,700) ≈ 28% remaining.[/tex]
Therefore, In the second statement, we are using the inverse of the function t to find the percentage of carbon-14 remaining for a given age. We can write this as [tex]t-1(7,000) = c,[/tex] where c is the percentage of carbon-14 remaining for a fossil that is [tex]7,000[/tex] years old.
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PLS HELLL ILL MARK U BRAINLIST IF U EXPLAIN UR ANSWER
Answer:
Should be A
Step-by-step explanation:
find the compound interest on birr 5006 at 5% for 4 years compounded annvally
The compound interest on birr 5006 at 5% for 4 years compounded annually is $1,078.82.
What is compound interest?Compound interest is a type of interest that is calculated not only on the initial principal amount but also on the accumulated interest of previous periods.
In other words, the interest earned during each period is added to the principal amount, and the interest for the next period is calculated on the sum of the principal and the accumulated interest.
Given that:
Principal = 5006Annual Interest rate = 5%Time (t) in years = 4First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)^(nt)
A = 5,006(1 + 0.05/1)^(1*4)
A = 5,006(1 + 0.05)^(4)
A = $6,084.82
Compound interest =Amount - Principal
Compound interest = 6084.82 - 5006
Compound interest = $1,078.82
Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $5,006.00 at a rate of 5% per year compounded 1 time per year over 4 years is $6,084.82.
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You randomly select a seashell from a collection and record the type of shell. The types of the first 90 shells you select are shown.
What is the experimental probability that you select a Moon Snail?
The experimental probability of selecting a Moon Snail is approximately 0.16.
What is probability?Probability is the branch of mathematics concerned with measuring the likelihood or probability of an event occurring.
It is a numeric value from 0 to 1, with 0 indicating that the event is not possible and 1 indicating that the event is certain to occur.
The experimental probability of selecting a Moon Snail can be calculated by dividing the number of Moon Snails by the total number of seashells selected.
The total number of seashells selected is:
33 + 14 + 8 + 15 + 20 = 90
The number of Moon Snails selected is 14.
So the experimental probability of selecting a Moon Snail is:
14/90 = 0.155 or approximately 0.16
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i need help to this homework
The value of cosec ( Ф/2 ) obtained using the double angles formula and half angle identity is : cosec ( Ф/2 ) = 5/√2.
Explain about the double angles formula?In trigonometry, the double angles for trigonometric functions are dealt with via the double angle formulas. Other significant double angle formulas include:
sin 2A = 2 sin A cos Acos 2A = cos2A - sin2Atan 2A = (2 tan A) / (1 - tan2A)cos Ф = 3/5
By using half angle identity:
cos( Ф/2 ) = ± √(1 + cosФ)/2
cos( Ф/2 ) = ± √(1 + 3/5)/2
cos( Ф/2 ) = ± √8/10
cos( Ф/2 ) = ± √2/5
In first quadrant:
cos( Ф/2 ) = +√2/5
Using reciprocal identity:
cosec ( Ф/2 ) = 1/ cos( Ф/2 )
cosec ( Ф/2 ) = 1/√2/5
cosec ( Ф/2 ) = 5/√2
Thus, the value of cosec ( Ф/2 ) obtained using the double angles formula and half angle identity is : cosec ( Ф/2 ) = 5/√2.
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question 1 of 10: over the last week, you had 100 customers who bought a total of 75 hotdogs at $2.00, 23 grilled cheeses at $4.00, and 28 cheeseburgers at $6.00. what was the average price paid per customer?
Answer:
150+92+168=410
Step-by-step explanation:
Dena and Joey share a 18-ounce box of cereal. By the end of the week, Dena has eaten 1/6 of the box, and Joey has eaten 2/3 of the box of cereal. How many ounces are left in the box?
There are 8 ounces of cereal left in the box.
Dena ate 1/6 of the cereal, leaving 5/6 of the box for Joey.
Joey then ate 2/3 of the box, which is equivalent to (2/3) × (5/6) = 10/18 of the box.
The amount of cereal left in the box is therefore 18 - 10 = 8 ounces.
Therefore, there are 8 ounces of cereal left in the box.
HELPPP PLEASEEE MARK BRAINLIEST ALGEBRA 2 3 variable problem
The number of touchdowns are 4, field goals are 2 and safeties are 2 for the given system of equation.
What is system of equation?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A collection of equations fulfilled by the same set of variables is called a system of linear equations." Finding the values of the variables employed in a system of equations entails solving the set of equations. By keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the provided equations true is the primary goal when solving an equation system.
Let us suppose touchdowns = x.
Let us suppose field goals = y.
Let us suppose safeties = z.
Given that, they score point 8 times, thus:
x + y + z = 8
The total points scored are 38 thus,
7x + 3y + 2z = 38
Also,
x = (y + z)
Substituting the value of y + z in equation 1 we have:
x + x = 8
2x = 8
x = 4
Substitute the value of x in second equation:
7(4) + 3y + 2z = 38
28 + 3y + 2z = 38
3y + 2z = 10
Now, using x = (y + z). we have:
4 - z = y
Substitute the value of y:
3y + 2z = 10
3(4 - z) + 2z = 10
12 - 3z + 2z = 10
-z = -2
z = 2
Substitute the value of x and z:
x = (y + z)
4 = y + 2
y = 2
Hence, the number of touchdowns are 4, field goals are 2 and safeties are 2 for the given system of equation.
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!!!TIMED!!! !!!Please help as fast as possible!!!
Find the value of a.
In right triangle LMN, angles L and M are complementary.
Find the mesure of angle L.
Answer:
Step-by-step explanation:
y2= -13x+102 as an irrational equation
To write the equation y = -13x + 102 in irrational form, we need to isolate x on one side of the equation.
First, let's subtract y from both sides to get:
-y + y2 = -13x + y2 + 102
Next, let's divide both sides by -13 to get:
x = (-1/13)y2 + (1/13)y - (102/13)
Therefore, the irrational equation of y2 = -13x + 102 is:
x = (-1/13)y^2 + (1/13)y - (102/13)
7+3p2Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.
What is the polynomial equation?
A polynomial equation is an equation in which the variable(s) are raised to non-negative integer powers and the coefficients are constants. In other words, it is an equation in which the terms involve only addition, subtraction, multiplication, and positive integer exponents.
The expression is 7 + 3p²
To write the polynomial in standard form, we need to arrange the terms in descending order of degree:
3p² + 7
hence, The degree of the polynomial is 2, and the leading coefficient is 3. The polynomial has two terms, so we classify it as a binomial.
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Which of the following are subsets
Therefore , the solution of the given problem of number line comes out to be D, {-6}, {-3}, {5}, {-6, -3}, {-6, 5}, {-3, 5}.
What is number line?The number line, a representation of real numbers in visual form, is a tool for teaching arithmetic. An energy line is depicted by it. Every actual number is used to represent a integer in the genuine number, or every exact number is used to represent a position. The separations between increments on a number line are identical. The numbers in a line can only be replied in the manner indicated by those numbers.
Here,
The set D = "-6, -3, 5" can be divided into a wide variety of subgroups, including:
Since the empty set is a subset of every set, D is a subset of the empty set.
The set D is a subgroup of itself.
=> Because -6 is an element of D, the collection "{-6}" is a subset of D.
=> Because -3 is an element of D, the collection "{-3}" is a subset of D.
=> Because 5 is an element of D, the collection "{5}" is a subset of D.
Due to the fact that both -6 and -3 are components of D, the set "{-6, -3}" is a subset of D.
=> Because both -3 and 5 are elements of D, the collection "{-3, 5}" is a subset of D.
Consequently, the subgroups of D are:, D, {-6}, {-3}, {5}, {-6, -3}, {-6, 5}, {-3, 5}.
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