We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.
Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.
We can use the combination formula to find the total number of possible combinations:
C(4, 3) = 4! / (3! * 1!) = 4
This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.
Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:
C(6, 4) = 6! / (4! * 2!) = 15
This means that we can form a total of 15 different 4-digit numbers using the given digits.
Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.
To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:
C(3, 1) * C(5, 3) = 3 * 10 = 30
This means that we can form a total of 30 different 4-digit even numbers using the given digits.
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As part of a school project students will be randomly sampling from the students in the class. The assignment is to estimate the proportion of students who play on a sports team. Each student will randomly select 7 students. One student found out that 2 of the 7 play a sport. The teacher has collected data from all students and found that out of the 31 students in the class 20 of them played sports.
On solving the provided question, we can say that percentage terms is 41.93%
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fraction of 100. The abbreviatiοns "pct.," "pct," and "pc" are also occasionally used. It is frequently denοted using the percent symbol "%," though. The amount of percentages has nο dimensions. With a denominator of 100, percentages are basically fractiοns.
To show that a number is a percentage, place a percent symbol (%) next tο it. For instance, if yοu correctly answer 75 out of 100 questions on a test (75/100), yοu receive a 75%. To cοmpute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
total no. of students = 31
no. of students play sports = 13
percentage terms = 13/31 × 100= 41.93%
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write a formula for f(x)=1x1 shifted up one unit and right 3 units
Y = (1/x-3) has been moved 3 units to the right and up one unit. If it is moved to the right, it should look like this: (x-3). It should show up as (x+3) if it were moved to the left. If the result were moved ahead, the outcome would be (1/x-3).
How is the calculation for switching functions done?The original function f is horizontally shifted into the new function g(x)=f(xh), where h is a constant. Given a function f. The graph will shift to the right in a positive h situation. If h is negative, the graph will slide to the left.
How is a function moved to the left and right?To move a function left in function notation, add within the function's argument: f(x + b) moves f(x) b units left. In the same way, shifting to the right moves f(x) b units to the right.
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How many litters is 182.5 gallons
Answer:
689.85 liters
Step-by-step explanation:
1 gallon = about 3.78 liters
182.5 gallon = ? liter
We take
182.5 times 3.78 = 689.85 liters
So, 182.5 gallons is about 689.85 liters
Help, Solve the system of linear equations by Elmination.
Answer:
See the explanation below
Which expression is equivalent to x2 + 10x + 24?
A-(x + 12)(x - 2)
B-(x + 8)(x + 2)
C-(x + 6)(x + 4)
D-(x + 8)(x + 3)
Answer: the answer is C just did it
someone pls help with this question
a² y² - 2aby + b²
please help me as quick as possible
Answer:
try this
Step-by-step explanation:
Find the area of the figure below, round to the nearest whole number.
The area of the triangle with side lengths 28 and 21 and an angle of 118 degrees is 260 squared unit.
What is the area of the given triangle?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
The area of a triangle can be determine using the formula;
A = ( a × b × sin( C ) ) / 2
From the diagram;
Side a = 28side m = 21Angle R = 118Area A = ?Plug the given values into the above formula.
A = ( a × b × sin( C ) ) / 2
A = ( a × m × sin( R ) ) / 2
A = ( 28 × 21 × sin( 118° ) ) / 2
A = ( 588 × sin( 118° ) ) / 2
A = ( 588 × 0.8829 ) / 2
A = 519.17 / 2
A = 260 square unit.
Therefore, the area of the triangle is 260 square unit.
Option D) 260 is the correct answer.
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The area of the figure to the nearest whole number is 260
Calculating the area of a triangle involving angles.The area of a triangle is the region contained by the triangle's sides. The length of the sides and internal angles affect a triangle's area differently from one triangle to the other.
From the given triangle:
The required area of a triangle is:
[tex]A = a*b * \dfrac{sin \gamma}{2}[/tex]
where;
a and b are the two sides givenγ = the given angle[tex]A = 28*21 * \dfrac{sin \ 118}{2}[/tex]
A = 14 × 21 × sin 118
A = 14 × 21 × 0.8830
A = 259.602
A = 260
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Factorise: 16x4 - y4
Answer:
= (4x^2 + y^2)(2x + y)(2x - y).
Step-by-step explanation:
16x^4 - y^4
= (4x2)^2 - (y^2)^2
= (4x^2 +y^2)(4x^2 - y^2)
=(4x^2 + y^2)( (2x)^2 -y^2)
= (4x^2 + y^2)(2x + y)(2x - y).
Answer:
Step-by-step explanation: [tex]16x^{4} -4y^{4} = (4x^{2} )^{2} -(2y^{2} )^{2}= (4x^{2} + 2y^{2} )(4x^{2} - 2y^{2})[/tex]
identity used =
[tex](a^{2} -b^{2} ) = (a+b)(a-b)[/tex]
5. Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00. What was the price per dozen?
In a casee whereby Annette bought 8 dozen eggs from Mr. Joseph's Farm Store for $2,800.00 the price per dozen is $350 per dozen
How can the price per dozen be calculated?The concept that will be use here is division. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
The total dozen = 8 dozen eggs
The total price of the 8 dozen eggs $2,800.00
The price per dozen = $2,800.00/ 8 dozen
=$350 per dozen
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Find the compound interest and future value. Round your answers to the nearest cent.
Principal Rate Compounded Time
4.29% Weekly 34 years
$116,000
The compound interest is $348,966.97 and the future value is $464,966.97.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We can use the formula for compound interest to calculate the future value of the investment:
[tex]FV=P(a1+r/n)^{nt}[/tex]
where:
P = the principal amount (the initial investment)$116,000
r = the annual interest rate (as a decimal)=0.0429
n = the number of times the interest is compounded per year=52
t = the number of years=34
Plugging in these values, we get:
FV = $116,000(1 + 0.0429/52)¹⁷⁶⁸
FV = $464,966.97
So the future value of the investment after 34 years is $464,966.97.
Compound interest = $464,966.97 - $116,000 = $348,966.97
Therefore, the compound interest is $348,966.97 and the future value is $464,966.97.
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Which of the following sequences are geometric?
Check all that apply.
Answer:
A and C are the correct answers
Step-by-step explanation:
Answer:
And C is the answer to the question
Label each figure correctly. Area is understood to be square feet and perimeter is understood to be feet.
1. Area of the figure = 702 square feet.
Perimeter = 114 feet
2. Area of the figure = 20 square inches.
Perimeter = 24 inches.
How to Find the Area and Perimeter?Area of a rectangle = length * width
Perimeter of a shape = length of all the surrounding of a figure.
1. Area = area of rectangle 1 + area of rectangle 2 = 27 * 24 + 9 * 6
= 702 square feet.
Perimeter = 30 + 27 + 24 + 18 + 6 + 9 = 114 feet
2. Area = area of rectangle 1 + area of rectangle 2 = 7 * 2 + 3 * 2
= 20 square inches.
Perimeter = 7 + 2 + 3 + 3 + 2 + 3 + 2 + 2
= 24 inches.
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Triangle XYZ is shown on the coordinate plane.
A triangle on the coordinate plane with vertices X at 0 comma 5, Y at 10 comma 3, and Z at 4 comma negative 1.
If triangle XYZ is translated using the rule (x, y) → (x + 2, y + 3) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Z″?
(2, −8)
(6, −2)
(8, −2)
(12, −6)
The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;
(6, -2)What is a reflection transformation?A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.
The coordinates of the vertices of the triangle are;
X(0, 5), Y(10, 3), Z(4, -1)
The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;
(x, y) → (x + 2, y + 3)The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;
The coordinates of the point (x, y) following a reflection across the x-axis is the point (x, -y)Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))
(x, -y) → (x + 2, -(y + 3))The coordinates of the point Y(4, -1) following the composite transformation is therefore;
Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)
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The lengths of nails produced in a factory are normally distributed with a mean of 6.13
centimeters and a standard deviation of 0.06
centimeters. Find the two lengths that separate the top 7%
and the bottom 7%
. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
The two lengths that Bottom 7%: L= 6.04 cm
Top 7%: L= 6.22 cm
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.
The level of variability within a particular data collection is effectively reflected in the standard deviation.
Mean length of the population (μ) = 6.13 cm
Standard deviation (σ) = 0.06 cm
The z-score for any given length 'X' is
Z = X - μ/σ
What we want to know is the length at the 7-th percentile and at the 93-rd percentile.
According to a z-score table, the 7-th percentile has a correspondent z-score of -1.476 and the 93-rd percentile has a z-score of 1.476. Therefore, the bottom 7% and top 7% are separated by the following lengths
Z(Xb) = Xb - μ/σ
- 1.476 = Xb - 6.13/0.06
Xb = 6.04
z(Xt ) = Xt - μ/σ
1.476 = Xt - 6.13/0.06
Xt = 6.22
Bottom 7%: L= 6.04 cm.
Top 7%: L= 6.22 cm.
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keeps saying ive gotten it wrong yet its an easy question.. help me? (probability)
Answer:
Pole Vault, Discus, 200m, Long Jump
Step-by-step explanation:
Once putting them all as decimals can’t you just sort it our from there? From what I can see, your answers are incorrect, but they might have reset.
A group of friends wants to go to the amusement park. They have no more than $295
to spend on parking and admission. Parking is $11.50, and tickets cost $39
person, including tax. Which inequality can be used to determine x, the maximum
number of people who can go to the amusement park?
Answer:
295>_ 39x+11.50
Step-by-step explanation:
the >_ means less than or equal to.
According to government data 22 percent of children in the United States under the age of 6 years live in households with incomes that are closed a pincome A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood if the government data are correct, which of the following best approximates the probability that at 27 percent of the children in the sample live in households that are closed at the particulo income level o represents a standard normal random variable)
Answer: [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300} } } )[/tex]
Step-by-step explanation:
[tex]P=\frac{22}{100} =0.22, n=300[/tex] [tex]q=1-p=0.78[/tex]
[tex]p' = \frac{27}{100}=0.27[/tex]
[tex]p(z > \frac{p'-p}{\sqrt{\frac{p*q}{n} } } )[/tex]
[tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300}} }[/tex]
Rowan was collecting seashells she collects 4 more than three times the number of seashells Maribel collects if Maribel collects X seashells select the expression of represents the number of seashells Rowan collects
Answer:
Rowan collects
3x + 4
Step-by-step explanation:
Maribel collects x sea shells.
Rowan collects 4 more (this is the +4)
than 3 times Maribels (this is the 3x)
Maribel = x
Rowan = 3x + 4
Answer:
its actually 4x + 3
Step-by-step explanation:
A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4. 9 letters and 0. 15 letter, respectively.
Based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.
The reading specialist is trying to estimate the population mean word length of an elementary school history textbook, but it is not practical or possible to measure the word length of every single word in the book. So, instead, the specialist takes repeated random samples of 100 words from the book and calculates the mean word length of each sample. Based on these repeated samples, the specialist estimates that the mean word length of the book is 4.9 letters. This means that, on average, the words in the book are about 4.9 letters long. The specialist also calculated the standard deviation of the sampling distribution, which is a measure of the variability of the sample means. In this case, the standard deviation of the sampling distribution is estimated to be 0.15 letters. This means that the mean word length of each random sample is expected to vary by about 0.15 letters from the population mean. It is important to note that these estimates are based on a specific set of samples and are subject to sampling variability. If the specialist were to take different random samples, the estimates may be slightly different. However, based on the information given, the estimated mean word length of the book is 4.9 letters and the estimated standard deviation of the sampling distribution is 0.15 letters.
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How do I solve for side a and b and angle B when when side c equals 968m, angle a is 33 degrees abs 25 minutes and angle c is 90 degrees
Answer:
Step-by-step explanation:
Calculated based on 2 given angles and 1 given side.
∠B = 180° - A - C = 0.99484 rad = 57°
∠B = 57°
a = c·sin(A)/sin(C) = 527.21059
b = c·sin(B)/sin(C) = 811.83311
The table shows the number of 6th grade students who prefer each kind of juice at lunch time. Draw a circle graph to display the information. 6th Grade Juice Choices: Grape Juice 8, Orange Juice 6, Fruit Punch 6, Apple Juice 20.
A circle graph representing the data presented will show half of the students prefer apple juice; while grape, orange juice, and fruit punch are preferred by a lower ratio of students.
What is a circle graph?A circle graph also known as a pie graph is a visual representation of data based on a circle and its fractions of it. In this way, if 20 out of the 40 students prefer apple juice this means in the circle graph half of it would be for students preferring apple juice.
Based on this, a possible circle graph that represents the data is shown below:
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In the figure, m1-m22-22 and m23-m24-123. From this, you can conclude that mZTSK-
45.
33.
35.
The measure of angle TSK is given as follows:
m < TSK = 35º.
How to obtain the measure of angle TSK?On a triangle, the sum of the measures of the internal angles is of 180º.
For triangle TSK, the internal angle measures are given as follows:
m < 1 = 22.m < 3 = 123º.m < TSK.Then the measure of angle TSK is obtained as follows:
m < TSK + 22 + 123 = 180
m < TSK = 180 - 145
m < TSK = 35º.
Meaning that the last option is correct.
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Consider the system of equations.
y = -5x-1
y = 2x+6
Choose the correct answer to each question.
What is the slope of the first line?
What is the slope of the second line?
How many times do the lines intersect?
C
How many solutions does the system have?
C
John can jog twice as fast as he can walk. He was able to jog the first 3.5 miles to
his grandmother's house, but then he tired and walked the remaining 3.5 miles. If the
total trip took 1.75 hours, then what was his average jogging speed?
miles per hour
Solve 2x − 1 = 5.
A . x = 1
B . x = 2
C . x = 3
D . x = 4
C
The answer to the question is C
Answer:
D is the answer cuz 2x-1=5
2x=5-1
2x=4
X=2
We divide both side by two
Write the inequality shown by the shaded region in the graph with the boundary line −5x+2y=−2
Answer:
Step-by-step explanation:
The boundary line of the shaded region in the graph, which is represented by the equation -5x + 2y = -2, can be used to write the inequality that represents the shaded region. To do this, we first need to determine which side of the boundary line the shaded region is on.
If the shaded region is on the same side of the line as the open half-plane that contains the y-axis, then the inequality is given by:
-5x + 2y > -2
If the shaded region is on the same side of the line as the closed half-plane that does not contain the y-axis, then the inequality is given by:
-5x + 2y ≥ -2
So, the inequality that represents the shaded region depends on the specific context and requirements of the problem, as well as the interpretation of the graph.
Quick and Simple Algebra 2 question
Write the equation based on 2 points
The equation of line is y = 1.5x + 5.5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
We have the reference point as (-2, 2.5) and (-1, 4)
so, slope
= (4- 2.5)/ (-1 + 2)
= 1.5
and, the equation of line is
y- 2.5 = 1.5 (x+ 2)
y- 2.5 = 1.5x + 3
y = 1.5x + 5.5
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Help me with this question….
Answer:
A. 513 cubic units
Step-by-step explanation:
trust me bro.
Find the 52nd term of the arithmetic sequence
−
3
,
12
,
27
The 52nd term of the arithmetic sequence -3, 12, 27, ..... is equal to 762.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 12 - (-3)
Common difference, d = 12 + 3
Common difference, d = 15
Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;
a₅₂ = a₁ + (52 - 1)d
a₅₂ = -3 + (51)(15)
a₅₂ = -3 + 765
a₅₂ = 762.
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