Answer: The largest number of groups they can be split into and have the same number of boys and girls on each team is 6 groups with 2 boys and 2 girls in each group.
Someone please help me out
The figures for this problem are not scale drawings, as the ratios between the equivalent side lengths are different.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Hence, when a figure is a dilation of another figure, the two figures are scale drawings.
For this problem, the ratio between the bases of the rectangles is given as follows:
12/6 = 2.
The ratio between the height of each rectangle is given as follows:
6/2 = 3.
As the ratios are different, the two figures are not scale drawings of one another.
For them to be scale drawings, it would be needed either a ratio of 2 for the heights or a ratio of 3 for the bases.
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What's the equation and solution?
Observing the given figure , It is a balanced balance which signifies both side should be equal, The answer is 2=-8-x and x=-10.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination method2=-8-x is the required balanced equation.
-x = 2 + 8
x= -10
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Question 4 of 10
Find the difference. Enter your answer in the box below as a fraction, using
the slash mark (/) for the fraction bar.
8-7
14 14
There is a 2/17 difference between 16/17 and 14/17 as 17 is the shared denominator of both fractions.
what is fractions ?A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.
Given,
To get the difference between 16/17 and 14/17, discover their common denominator first.
17 is the shared denominator of both fractions.
To solve, multiply the result by the numerator of the fractions, then divide the sum by the common denominator:
16 - 14/17 (16 - 14) = 2/17 is the solution.
Therefore, there is a 2/17 difference between 16/17 and 14/17.
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How much is the monthly amortization on an automobile loan of ₱ 900,000 to be amortized over a 5-year period at a rate 9.5% compounded monthly?
The monthly amortization on the automobile loan, given the loan amount, the period, and the compounding frequency, is ₱ 18, 901.68
How to find the amortization ?The monthly amortization is constant so it will be an annuity. Seeing as we have the loan amount, this means that the present value of an annuity formula can be used to find the monthly amortization.
First, find the period in months:
= 5 x 12 months a year
= 60 months
The interest in months :
= 9 . 5 % / 12 months per year
= 9.5 / 12 %
The monthly amortization is:
= Loan amount / ( Present value interest factor of annuity, 60 periods, 9.5 / 12 %)
= 900, 000 / 47.614827336156
= ₱ 18, 901.68
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S= pi^2(b^2-a^2)
b=8
a=10
work out the value of S and give the answer to 3 significant figure
Answer:
S = pi^2 * (8^2 - 10^2)
= pi^2 * (-4)
= -12.57 pi^2
The value of S is approximately -12.57 * pi^2. To express this value to three significant figures, we would round it to -13 * pi^2, which is the same as -12.6 * pi^2. So the final answer is -12.6 * pi^2.
Convert the following component vectors to a linear combination:
< 20 , 14 , -23 >
The component vectors to a linear combination is given by the equation
A = 20 i^ + 14 j^ - 23 k^
What is the product of vectors?The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by
u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃
An equivalent definition, typically used in physics, is
u ⋅ v = ∣u∣ ∣v∣ cos θ,
where θ is the angle between u and v
Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero
Given data ,
Let the component vectors be represented as A
The value of A is
< 20 , 14 , -23 > be equation (1)
On simplifying the equation to the linear combination , we get
< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^
So , the linear combination of the vectors is given by the equation ,
A = 20 i^ + 14 j^ - 23 k^
Hence , the equation is 20 i^ + 14 j^ - 23 k^
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Will mark brainliest!
In 2-4, write yes or no to indicate whether the expressions are equivalent. Grade 6 math, please help
Britney bought 4 apples, 5 bananas, and 8 oranges at the grocery store.
Which is the ratio of apples to oranges written as a decimal?
A.
1.6
B.
0.4
C.
0.8
D.
0.5
Answer:
Step-by-step explanation:
The question asks for apples to oranges.
So put the number of apples as a numerator and the number of oranges as a denominator. Simply put 4 on top and 8 on the bottom:
4/8 then divide: 4 divided by 8 = .5
There is the ratio as a decimal.
0.5
Option D
Determine if each of the following statements are true or false (HELP!!! ARE MY ANSWERS CORRECT?)
Answer:
yes
Step-by-step explanation:
Anthony wants to buy a CD for $400 that earns 2.5% APR and is compounded
quarterly. The CD matures in 3 years. He will be paid the interest he earns
each quarter. How much interest will Anthony have earned on this CD after
the first quarter?
A. $10.00
B. $3.25
c. $1.25
D. $2.50
Answer:i think A
Step-by-step explanation:
How do I solve 6,000-5,258
Answer:
742
Step-by-step explanation:
6000
-5258
742
What is the answer to 156 x 13
Answer:
2028
Step-by-step explanation:
156 x 13 = 2028
Carlos measures an angle x. He then finds that the complement of the angle is 35 degrees. A. What is the measure of angle x? B. What is the supplement of angle x?
Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.
Describe complimentary angles.A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way
Here,
Given : complementary angle one of the angle is 35°
=> x+ 35° = 90°
=> x = 55°
Let y be the supplement of angle x
=> x+ y = 180°
=>55° + y =180°
=>y =125°
Therefore , the solution of the given problem of angle comes out to be
x = 55° and y =125°.
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Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give __ mL
Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give 1.74 mL
What is the Neupogen calculations about?To calculate the appropriate dosage of Neupogen to give to the patient, we need to convert the patient's weight from pounds to kilograms and then use the dosage provided in the order (10 mcg/kg/d IV).
First, we have to convert the patient's weight from pounds to kilograms:
115 pounds = 52.16 kg
Now we can use the dosage provided in the order (10 mcg/kg/d IV) to calculate the appropriate dosage for the patient:
10 mcg/kg/d IV
= 10 mcg/kg/day * 52.16 kg
= 521.6 mcg/day
Then, since the Neupogen is available in a solution of 300 mcg/ml, we can use the following formula to calculate the required volume of solution to give to the patient:
Volume = Dosage / Concentration
= 521.6 mcg / 300 mcg/ml
= 1.74 ml
So, the education order reads 24 hours after bone marrow transfusion, give 1.74 mL of Neupogen at a concentration of 300 mcg/mL IV.
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The odometer of a car reads 35,467.219 the 5 stands for 5 x1,000 miles. Use expanded form to show what each of the other digits in the odometer reading means.
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
What is expanded form?A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.
Define Decimal Numbers.The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.
5 stands for 5 x 1,000 miles
3 stands for 3 x 100 miles
4 stands for 4 x 10 miles
6 stands for 6 x 1 miles
7 stands for 7 x 1/10 of a mile
2 stands for 2 x 1/100 of a mile
1 stands for 1 x 1/1000 of a mile
9 stands for 9 x 1/10000 of a mile
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
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Which of the following is the slope of the line y - 3x =0
Answer:
-3
Step-by-step explanation:
Answer: The slope whould be 3
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope: 3
y-intercept:
(0,0)
x|y
----
0|0
1|3
Jorge gives 3 chocolate bars to his friend. HE GIVES 1/12 OF CHOCOLATE BAR TO EACH FRIEND. HOW MANY FRIENDS DOES HE GIVE A PIECE OF CHOCOLATE TO
compare the function rule f(x) = 3x +2 and the graph of g(x)
which statements are true? select two that apply.
-g(x) increases at a faster rate over the interval (-1,0)
-g(x) increases at a faster rate over the interval (1,2)
-g(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (2,3)
-f(x) increases at a faster rate over the interval (0,1)
-f(x) increases at a faster rate over the interval (1,2)
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x)
[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]
from the graphs n f (x) and g( x) are 1 and 5 .
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I’m confused HELP pls
On solving the equation n = za the value of a is obtained as a = n/z.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
To solve for a in the equation n = za, isolate a on one side of the equation.
Do this by dividing both sides by z:
n/z = (za) / z
On the right side, the z's cancel out, leaving -
n/z = a
So the solution is -
a = n/z
Therefore, the value of a that satisfies the equation n = za is equal to n divided by z.
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Select ALL composite numbers with their correct prime factors(I need help)
Answer:
The answer would be the second and fourth options.
Step-by-step explanation:
This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!
Solve the following mentally 65% of 100
Answer: 65
Step-by-step explanation:
A project requires you to figure out the area of a triangular lot. You take measurements and find that the lot has a base of 32 ft., while the altitude of the triangle, or height is 24 ft. What's the area of this lot?
A case of tomato cans weighs 563 dekagrams. A case of soup cans weighs 458 dekagrams. How much do the two cases weigh together in decigrams? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
1,021 decigrams
10,210 decigrams
102,100 decigrams
1,021,000 decigrams
Answer:
102200
Step-by-step explanation:
564+458= 1022
1 decagram=100 decigram
So multiply the sum by 100
1022*100=102200
Solve the equation Sin(X)=-1 on the interval [0,360)
Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).
What is trigonometry?The mathematical field of trigonometry investigates relationships between triangle sides and angles. Because every straight-sided form may be reduced to a collection of triangles, trigonometry is a fundamental concept in all of geometry. The relationships between trigonometry and other branches of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly intricate.
Here,
[tex]e^{x}[/tex] is a function that increases across all of space (d[[tex]e^{x}[/tex] ]/dx = [tex]e^{x}[/tex] which is never negative), it must be that so it must be that [tex]e^{u}[/tex] crosses y=1 just once, or at u = 0. To demonstrate this:
In[tex]e^{sinx}[/tex]= In 1
sin x = 0
And when x = "0, 0", "2", we would have that sin x = 0 in [0, 2"]. In general, we would then have that x = n, where n Z, because of the periodicity of sin (where n is an integer).
Therefore , the solution of the given problem of trigonometry comes out to be x = nπ where nЄ Z (where n is an integer).
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If c = d, then a + c = d + a true or false
Answer:
True
Step-by-step explanation:
First, you need to subtract a then that would make a 0
Answer: true
Step-by-step explanation: c and d are the same, so a+c and a+d will be the same
correct 0.00798516 to three significant figures
Explanation:
The zeros in 0.00798516 are not considered significant because they are not between nonzero values.
If we had something like 1.207, then that zero would be considered significant.
The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.
Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.
Answer: 0.00799
0.00798516 rounded off to three significant figures is 0.00799
hope that helps...
NEED HELP ASAP DUE TMR
1. The length of the altitude is 15 units.
2. The perimeter of trapezoid ABCD is 132 units.
Perimeter of a trapezoid.An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.
The perimeter of a trapezoid is the sum of all its sides.
From the question;
1. To determine AE,
DE = (DG - EF)/ 2
= (22 - 6)/ 2 (since AB = EF = 6)
= 8
DE = 8 units
The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;
/hyp/^2 = /opp/^2 + /adj/^2
AD^2 = DE^" + AE^2
17^2 = 8^2 + AE^2
289 = 64 + AE^2
AE^2 = 225
AE = 15
Thus the length of the altitude is 15 units.
2. To determine the perimeter of the trapezoid, we have;
AE = (AD - EF)/ 2
= (58 - 16)/ 2 (since BC = EF = 16)
= 21
AE = 21 units
So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;
/hyp/^2 = /opp/^2 + /adj/^2
AB^2 = BE^2 + AE^2
= 20^2 + 21^2
AB = 841^1/2
AB = 29
Perimeter of the trapezoid = 29 + 16 + 29 + 58
= 132 units
Thus, the perimeter of the trapezoid is 132 units.
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There is a pair of parallel sides in the following shape.
Answer:
A = 38.5 units²
Step-by-step explanation:
the figure has one pair of parallel sides and is therefore a trapezium.
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
b₁ and b₂ are the parallel bases and h the perpendicular height between them.
here h = 7 , b₁ = 5 , b₂ = 6 , then
A = [tex]\frac{1}{2}[/tex] × 7 × (5 + 6) = 3.5 × 11 = 38.5 units²
Add 1.8m, 77cm, 210mm and give your answer in cm
The total length is 2.077m (2177 cm).
What is length?Length is a measurement of size, distance, or duration. It can refer to physical size (length of a field, length of an object, etc.), distance (length of a journey, length of a river, etc.), or duration (length of a movie, length of a school day, etc.). Length can also refer to the duration of time it takes to complete something (length of a task, length of a process, etc.). Length is typically measured in units such as meters, feet, inches, miles, kilometers, and seconds.
The given measurements can be added together to calculate a total length. The addition of 1.8m, 77cm, and 210mm can be expressed in the form of a sum equation. The equation would be 1.8m + 77cm + 210mm = ?.
To solve this equation, the measurements need to be converted to the same unit of measurement. In this case, all measurements can be converted to cm. 1.8m is equal to 1800cm, 77cm is equal to 77cm, and 210mm is equal to 21cm.
Therefore, the sum equation becomes 1800cm + 77cm + 21cm = ?. To find the total length, the numbers can be added together.
The total length is 1977cm. However, since the measurements are expressed in decimals, the answer must also be expressed in decimals. Therefore, the total length is 2.077m (2177 cm).
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