Because of this, we need to choose 15 integers in such a way that we can ensure that when they are divided by 14, at least two of them will provide the same residual.
In order to be sure that at least two of them have the same remainder when divided by 14.
Generally, If you divide a number by 14, the result is a fraction. There are 14 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and, 13.
So if we pick a number and divide it by 14, the remainder can be one of 14 (0 memory 13). So if we select 14 numbers, we have the option to select 14 unique memories ranging from 0 to 13.
Finally, if we choose another integer, we will have the same reminders according to the drawer principle, because there are only 14 reminders and 15 > 14.
Therefore, we should choose the number of 15 so that at least two numbers have the same remainder when divided by 14.
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Prove: ABD is congruent to CBD
The Proof for ABD is congruent to CBD is shown below.
What is Congruence Rule?The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
Two triangles are congruent by side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).
Given:
AB || CD, <CBD = <ADB
In ΔABD and ΔCDB
<CBD = <ADB {Given}
BD= BD {Common}
<ABD = <CDB {Alternate Interior Angle}
So, By ASA Congruence Rule ΔABD ≅ ΔCDB
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The booster club at NHS sells hot chocolate and coffee at high school football games. At the last game, they had sales of $182.50. They need to keep track of how many of each type drink was sold so that they can make predictions for future sales. Bruce knows that they used 275 cups that night. If the hot chocolate sells for 75 cents and coffee sells for 50 cents, how much of each type of drink was sold?
Answer:
180 cups of hot chocolate and 95 cups of coffee
Step-by-step explanation:
multiply the cups by the price and add them together and it adds up to the total sales they got
(6+3) to the power of 2 + (10-15 divide by 3 )
The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ (6 + 3)² + [10 - (15/3)]
Simplify the expression, then we have
⇒ (6 + 3)² + [10 - (15/3)]
⇒ (9)² + [10 - 5]
⇒ 81 + 5
⇒ 86
The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.
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a town has a population of 5000 and grows at 4% every year. what will be the population after 7 years, to the near test whole number?
Given that about 25% of the mammalian genome is associated with genes, including introns and regulatory sequence, what would be the approximate average length of dna per gene if the genome contained 20,000 genes?
The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.
Average gene length: just 2.5% of the human genome codes for proteins. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements. "The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes".
A DNA region from which an mRNA is transcribed is the de facto definition of a "gene" in mammalian genome annotation. Because one cannot deduce function from a genome sequence alone, the correct functional genetic definition of a gene—a segment of DNA that can complement a mutant phenotype—is lost.
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A man starts walking north at 2 feet per second from a point p. A minute later a woman starts walking south at 1 foot per second from a point 800 feet due east of p. At what rate are the people moving apart 3 minutes after the woman starts walking?.
The required rate are the people moving apart 3 minutes after the woman starts walking is 2.36 ft/S.
Explain the rate of change of distance.The rate of change of distance is speed ( not uprooting). Similar distance in different headings is alluded to as a similar distance.
According to question:Let x and y be the distance of the man and woman respectively.
We have,
dx/dt = 2 ft/s, dy/dt = 1 ft/s
Then, x = 2×6×60 = 720 ft
y = 1×5×60 = 300 ft
And in triangle which make by the locus of man and woman.
(x +y)^2 + (800)^2 = z^2
z = √(1020)^2+(800)^2
z = 1296.3 ft
So, people are 1296.3 ft apart,
Rate change
[tex]\frac{d}{dt}[/tex](x+y)^2 = [tex]\frac{d}{dt}[/tex]z^2
2(x+y)(dx/dt+dy/dt) = (2z)dz/dt
(720+300)+(2+1) = (1296.3)dz/dt
dz/dt = 3060/1296.3 = 2.36 ft/s
Thus, their moving rate is 2.36 ft/s
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nora invests $800 that pays simple interest at a rate of 6% per annum. what is her total annual interest on this investment?
Please solve with steps
Answer:
To calculate Nora's total annual interest on her $800 investment, we can use the following formula:
Interest = Principal x Rate x Time
In this case, the principal is $800, the rate is 6% per annum, and the time is 1 year. Plugging these values into the formula, we get:
Interest = $800 x 0.06 x 1
To convert the 6% rate to a decimal, we divide 6 by 100. This gives us 0.06. We then multiply the principal by the rate and the time to get the total annual interest. So the total annual interest on Nora's $800 investment is:
Interest = $800 x 0.06 x 1 = $48
Therefore, Nora will earn a total of $48 in interest on her $800 investment over the course of one year at a rate of 6% per annum.
Step-by-step explanation:
100 points crown if you answer all of these and explain your answer
The angles of a triangle are equal to 5x + 10, 8x − 20 and 3x + 30. Find the value of x
The acute angles of a right triangle measure (48 − x ) and (3x − 10). What is the value of
Triangle ABC is a right scalene triangle. If ∠ = 72°, what is the measure of ∠A?
An obtuse isosceles triangle contains an angle that measures 162°. What is the measure of another interior angle within this triangle?
The angles of a triangle are equal to 5x, 2x + 8, and 3x + 12. What is the measure of the smallest angle of the triangle?
The angles of a triangle are equal to x, x + 4 and 20. What is the measure of the largest angle of the triangle?
Answer:
Step-by-step explanation:
Answer: He will need 49 tiles.
Step-by-step explanation:
Given: The patio will measure 13.5 feet by 43 feet.
Area of patio = 13.5 feet x 43 feet [Area = length x width]
= 580.5 sq. feet
Since area of each concrete tile = 12 sq. inch
Number of concrete tiles required to cover patio = (Area of patio) ÷ (area of each concrete tile)
= 580.5 ÷ 12
= 48.375 sq. inch ≈49
Is 250% of 44 less than 100, greater than 100 but less than 150, or greater than 150? Explain your reasonine.
The required value is evaluated as 110. The correct option is (B).
How to find percent value of a number?The percent value can be found by multiplying the given number with the percent divide by 100.
For example, 10% of 20 is 20 × 10/100 = 2.
The given expression for percentage is found as follows,
250% of 44
= 250/100 × 44
= 2.5 × 44
= 110
It can be written as 100 < 110 < 150.
Hence, the value of the given expression is 110 which is greater than 100 but less than 150 as 110 lies between the two numbers.
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Which is a graph of the following?
The graph of the function f(x) = [x² if x ≤ 2] [x + 4 if x > 2]
How to determine the graph of the function?From the question, we have the following parameters that can be used in our computation:
f(x) = [x² if x ≤ 2] [x + 4 if x > 2]
The above function is a piecewise function, and it can be split as follows:
f(x) = [x² if x ≤ 2]
f(x) = [x + 4 if x > 2]
The domain x ≤ 2 in f(x) = [x² if x ≤ 2] means that:
The x values stop at 2 (i.e. 2 inclusive)
The domain x > 2 in f(x) = [x + 4 if x > 2] means that:
The x values starts at a value greater than 2 (i.e. 2 exclusive)
This is represented by the graph (d) with the open and closed circles
Hence, the graph is graph d
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A man of height 1.8 m observes the angle of elevation of the top of a building of height 107 m from the roof of a house and it is found to be 30°. If the distance between the house and the building is 25√3 m, find the height of the house..
Answer:
sorry
Step-by-step explanation:
idrk
The height of the house is approximately 29.43 meters.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
We can use the tangent function to solve this problem.
The tangent of an angle is equal to the opposite side (the height of the house) divided by the adjacent side (the distance between the house and the building). In this case, the angle is 30 degrees and the opposite side is the height of the house, so we can write the following equation:
tan(30°) = height of house / 25√3
We can use a calculator or look up the value of tangent 30° to find that tangent 30 is approximately 0.577. Therefore, the equation becomes:
0.577 = height of house / 25√3
Multiplying both sides of the equation by 25√3 gives us:
height of house = 0.577 × 25√3
Plugging in the values and simplifying, we get:
height of house = 29.43 m
Therefore, the house's height is approximately 29.43 meters.
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Find the 64th tent of the arithmetic sequence -3, -14 -25.
The 64th term of the arithmetic sequence -3, -14 -25, will be - 696.
What is Arithmetic sequence?An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.
Given that;
The arithmetic sequence is,
⇒ -3, -14 -25.
Now,
Since, We know that;
⇒ nth term = a + (n - 1)d
Where, 'a' is first term, 'd' is common difference.
Here, The arithmetic sequence is,
⇒ -3, -14 -25.
First term (a) = - 3
Common difference (d) = - 14 - (-3)
= - 14 + 3
= - 11
So, We get;
⇒ 64th term = - 3 + (64 - 1) (-11)
= - 3 + 63 × - 11
= - 3 - 693
= - 696
Thus, 64th term = - 696
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arc ABC=___ for number 2 witch is actually labeled number 3
What is the measure of angle D?​
If the angle C is 15 degree and angle D is complementary then the measure of angle D is 75 degree .
In the question ,
it is given that ,
the measure of angle C is = 15 degree ,
we have to find the measure of angle D in the question,
and the angle C and angle D are complementary ,
that means ; angle C + angle D = 90°
Substituting the values ,
we get ,
15° + ∠D = 90°
subtracting 15° from both the sides ,
we get ,
∠D = 90° - 15°
Simplifying further ,
we get,
∠D = 75°
Therefore , the measure of angle D is = 75° .
The given question is incomplete , the complete question is
If Angle C = 15 degrees and Angle D is complementary to Angle C, what is the measure of Angle D ?
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Complete the statement
Answer:
B
Step-by-step explanation:
Lines that are both perpendicular to a given line are parallel.
when performing the steps of checking the abcs during the survey of the victim, the two most vital body systems are checked. which systems are those? (choose two.)
The two most vital body systems that are checked when performing the steps of checking the ABCs are the Circulatory and Respiratory Systems.
Blood veins in the circulatory system are responsible for moving blood away from and back toward the heart. Arteries carry blood out from the heart while veins carry it back. Oxygen, nutrients, and hormones are delivered to cells by the circulatory system, which also eliminates wastes like carbon dioxide.
The respiratory system refers to the network of tissues and organs in your body that facilitates breathing. It includes your lungs, blood vessels, and airways. The lungs' moving muscles are a part of the respiratory system. Together, these elements circulate oxygen throughout the body and remove waste gases like carbon dioxide.
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Which action by x develops the theme of the struggle between self-identity and perception by others?.
The action by X that develops the theme of the struggle between self-identity and perception by others is: He wears special clothing to show people that he has superpowers.
Self-identity: It defines the combining of the various roles individuals fulfill throughout their lives. It also tells about awareness and beliefs about the self as an object or being.
The second is people are viewed that the individual as internalized roles, also called role identity.
Today, our identities encompass memories, experiences, relationships, and values, these components, help to create our identities and the sense of ourselves.
There are some aspects that will contribute to the development of different types of identities. They are race/ethnicity, gender, age, and class.
Social identity can be represented in terms of three factors:
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a domino is a rectangular tile composed of two squares. an integer is represented on both squares, and each integer 0-9 is paired with every integer 0-9 exactly once to form a complete set. a double is a domino that has the same integer on both of its squares. what is the probability that a domino randomly selected from a set will be a double? express your answer as a common fraction.
The probability that a domino randomly selected from a set will be a double = 2 / 11
what is probability?
A thing's probability indicates how probable it is to happen. When we are uncertain about the result of a given event, we can talk about the probabilities of several outcomes—how likely they are. Statistics refers to the study of events that have a probability component.
When 'n' is the largest integer in the set, the total number of dominoes in the set is given by the following formula:
(n + 1) (n + 2) / 2
This means that (9 + 1) (9 + 2) / 2 =
(10)(11)/ 2 =
110/2 =55
10 of these dominoes will be "doubles"
So....the probability that a domino randomly selected from a set will be a double = 10 / 55 = 2 / 11
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2.
How many solutions does the following equation have?
8.5m +8 = 8.5m
infinitely many solutions
O exactly one solution
Ono solutions
O exactly two solutions
The given equation has no solution. Option B is correct.
As mentioned, the solution of the equation 8.5m +8 = 8.5m is to be determined.
What are equations?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given expression,
8.5m + 8 = 8.5m
Now,
8.5m - 8.5m = 8
0 ≠ 8
Thus, the given equation has no solution. Option B is correct.
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Systems of Equation Task
Answer:
Priya: S=20w+50
Vanessa: S=25w+20
6 weeks
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Part aDefine the variables:
Let w be the number of weeks.Let S be the total savings (in dollars).Given that Priya starts with $50 in her bank account, the y-intercept of the linear equation modelling her savings will be 50.
If she then deposits $20 each week for 12 weeks, the slope will be 20.
Therefore, the linear equation that models Priya's savings is:
[tex]S=20w+50[/tex]Given that Vanessa starts with $20 in her bank account, the y-intercept of the linear equation modelling her savings will be 20.
If she then deposits $25 each week for 12 weeks, the slope will be 25.
Therefore, the linear equation that models Vanessa's savings is:
[tex]S=25w+20[/tex]Part bCreate a table for each linear equation from part a.
Priya Vanessa
[tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&70 \\\cline{1-2} 2& 90\\\cline{1-2} 3&110 \\\cline{1-2} 4&130 \\\cline{1-2} 5& 150\\\cline{1-2} 6&170 \\\cline{1-2} 7&190 \\\cline{1-2} 8&210 \\\cline{1-2} 9&230 \\\cline{1-2} 10&250 \\\cline{1-2} 11& 270\\\cline{1-2} 12& 290\\\cline{1-2} \end{aligned}[/tex] [tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&45 \\\cline{1-2} 2& 70\\\cline{1-2} 3& 95\\\cline{1-2} 4& 120\\\cline{1-2} 5& 145\\\cline{1-2} 6& 170\\\cline{1-2} 7& 195\\\cline{1-2} 8& 220\\\cline{1-2} 9& 245\\\cline{1-2} 10& 270\\\cline{1-2} 11& 295\\\cline{1-2} 12&320 \\\cline{1-2} \end{aligned}[/tex]
Create a graph for each linear equation (see attachment).
Part cThe week in which Priya and Vanessa will have the same amount of savings is the week where the S-values in the tables are the same, and the point of intersection of the graphed lines.
Therefore, from inspection of the tables and graphs from part b, Priya and Vanessa will have the same amount of savings in week 6.
Triangle
X
Y
Z
XYZX, Y, Z is similar to triangle
P
Q
R
PQRP, Q, R.
35
35
30
30
X
X
Y
Y
Z
Z
Slice for n
Answer:
Step-by-step explanation:
Find all real zeros of the function
Determine the domain of the following graph
circle $c$ has radius 10 cm. how many square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle $c$?
100 square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Base = 2r = 2*10 = 20 cm
Height = r= 10 cm
Area = 1/2 * base * height
= 1/2 * 20 * 10
= 100 square centimeters
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which type of rigid transformation is the equivalent of two reflections across intersecting lines?
Rotation is the type of rigid transformation which is equivalent of two reflections across intersecting lines.
Define rigid transformation
A rigid transformation is a transformation that persists the original size or shape of a given figure. Examples of rigid transformations are rotation, reflection etc;
In mathematics a rigid transformation is also known as Euclidean Isometry or Euclidean transformation. Euclidean Isometry deals mainly with transformation of any figure. But, doesn't changes the length, shape or size of a given figure.
The concept of of two reflections across intersecting lines is equivalent to single rotation transformation of the original figure.
Therefore the rigid transformation or Euclidean isometry which is similar to two reflections across intersecting lines is rotation.
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the robinson family and the wong family each used their sprinklers last summer. the water output rate for the robinson family's sprinkler was per hour. the water output rate for the wong family's sprinkler was per hour. the families used their sprinklers for a combined total of hours, resulting in a total water output of . how long was each sprinkler used?
Robinson's time is 25 minutes and Wrong' time is 40 minutes.
Equation of Time:
x + y = 65 -------------------------- (1)
Total usage amount:
15x + 35y = 1775 -----------------------------(2)
There are several ways to answer this question. I will teach we how to create two equations from the given information. First we need to set some variables (or unknowns). we need to set up a sprinkler time variable for each household. Let's call the time of the Robinson family "x" and the time of the Wrong family "y". The total time used was 65, so the first formula is x + y = 65 ( Robinson's time plus Wrong's time gives total time).
Now,
We use the other hourly water information (remember we already have time variables for each family, x and y). We can set the following equation as 15x + 35y = 1775 (15 liters x the amount of time the Robinson's use water plus 35 liters x the amount of time the use water gives equal to total usage).
Now,
We can solve for one of the variables (x or y). It doesn't matter which one we start with. Also, it doesn't matter which formula you start with. I used
x + y=65 . On the other hand, subtracting x gives y = 65 - x.
Now,
Replace y in the other formula. 15x + 35y = 1775 turns into
15x + 35(65-x) = 1775.
Distribute 35 to each term in brackets. By isolating the x variable: x=25
Recall that x means how long the Robinson's have been using sprinklers.
Now,
We can plug x into the other equation: 25 + y = 65
Therefore,
Subtract 25 on the other side to isolate y: y= 40
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A school gives every student a sandwich for a picnic on the last day of school. The school has 1,821 students. Each sandwich has 2 slices of bread, and there are 21 slices of bread in a loaf. How many loaves of bread are needed for all the sandwiches?
Answer:
86
Step-by-step explanation:
pleassee I need this as soooonnn as possible
At the grand opening of a store, the first 18 customers will randomly draw a gift certificate from a box which contains twelve $10 coupons, two $50 coupons, and four $20 coupons. How many $20 coupons would need to be added so that the probability of drawing a $20 coupon is 1/3 ????
Answer:
70
Step-by-step explanation:
20+20
The table below shows the number of students gaining certificates for outstanding achievements:
What is the modal number of certificates?
6
4
2
5
3
Examining the table showing number of students gaining certificates for outstanding achievements the modal number is 4
What is modal number in math?The most frequent number, or the one that appears the most frequently.
In a frequency table the frequency shows the number of times a the data measured appears
Looking at the table the number that has most frequency is 4. This means that the people that collected 4 certificates are more than any other set of people.
The next is two which have a frequency of two while the least the people that collected 6 certificates. they have a frequency of 2 which means they are only tow people
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What is 3x+y=-3 and 3x+y=-4
Answer:
The equations 3x+y=-3 and 3x+y=-4 are both linear equations in the standard form. The standard form of a linear equation is ax+by=c, where a and b are coefficients, and c is the constant term.
Step-by-step explanation: