Answers:
Team A = 175 people
Team B = 150 people
This is before the 45 students transfer from A to B.
===========================================================
Explanation:
x = number of people in team A
y = number of people in team B
These counts are before the 45 pupils transfer from A to B.
The counts are in ratio 7:6, which means,
x/y = 7/6
6x = 7y
x = 7y/6
If we subtract 45 people from team A, we have x-45 people left. Those 45 people go to team B to have y+45 pupils there.
The quantities x-45 and y+45 are in ratio 2:3, so,
(x-45)/(y+45) = 2/3
3(x-45) = 2(y+45)
3x-135 = 2y+90
3(7y/6)-135 = 2y+90 .... plug in x = 7y/6
21y/6 - 135 = 2y+90
6*( 21y/6 - 135 ) = 6*(2y+90)
21y-810 = 12y+540
21y-12y = 540+810
9y = 1350
y = 1350/9
y = 150
x = 7y/6
x = 7(150)/6
x = 175
We have 175 people on team A, and 150 people on team B.
This is before the 45 students transfer from A to B.
-------------------
Check:
x/y = 175/150 = (7*25)/(6*50) = 7/6
This shows x and y are in ratio 7:6 to match the instructions.
x-45 = 175-45 = 130
y+45 = 150+45 = 195
(x-45)/(y+45) = 130/195 = (2*65)/(3*65) = 2/3
And we have the updated counts in the ratio 2:3, which matches the stated info in the instructions. The answers are fully confirmed.
Question 3 (2 points)
Find the area of the composite figure. Show work to get bonus points.
The area of the shaded portion of the composite figure could be easily 25*25 - 1/2*13*10 that is 625 - 65 = 560 feet
What is meant by the term Area?When referring to a two-dimensional space or points, in mathematics, the term "area" is used. It refers to a region's or a flat object's size, such a square or rectangle. The area of a form is determined in geometry by dividing the length by the breadth. For example, the area of a square with a side length of 4 units is 4 x 4 = 16 square units. Square units, such as square inches, square feet, or square meters, are used to measure area. Triangles (1/2 x base x height), circles ( x radius squared), and trapezoids (1/2 x (base 1 + base 2) x height) are other basic geometric forms with associated area calculations.
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What are the coordinates of B′ after the pentagon is rotated 90° about the origin?
Assuming that the rotation is anticlockwise (as it is not defined) the coordinates of B after the rotation are (-5, 1), so the correct option is C.
What are the coordinates of B' after the rotation?If the pentagon is rotated 90°, then all the vertices are also rotated 90° about the origin.
Here we don't know if the rotation is clockwise or anticlockwise, so we assume it is anticlockwise, as this is the standard rotation.
The orignal coordiates of point B are (1, 5)
This is on the first quadrant, a rotation of 90° anticlockwise will:
Interchange the x-value and the y-value.Add a negative sign to the new x-value.So we will go from a point (x, y) to (-y, x)
Then the new coordinates of B' are (-5, 1)
Thus, the correct option is C.
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I6
Researchers measured the data speeds for particular smartphone carrier at 50 airports. The highest speed measured was
75.5 Mbps. The complete list of 50 data speeds has a mean of ) 15.59 Mbps and a standard deviation of s = 23.85 Mbps.
What is the difference between carrier's highest data speed and the
mean of all 50 data speeds?
b. How many standard deviations is that [the difference found in part (a)]?
. Convert the carrier's highest data speed to a z score.
d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly high,
is the carrier's highest data speed significant?
Answer:
66 es pero que te ayude ■■♤♤
Mia is 1.65 meters tall. At 3 p.m., she measures the length of a tree's shadow to be
26.45 meters. She stands 21.4 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
The height of the tree to the nearest hundredth of a meter is 8.64 meters
What are equivalent ratios?"Two or more ratios that reflect the same relation or comparison of numbers are known as equivalent ratios," according to the definition of the equivalent ratio in mathematics. The idea of corresponding fractions is comparable. The term "proportion" also refers to the equivalence of two ratios. Even if the values of the antecedent and the consequent are different, if we simplify them, we will still arrive at the same value.
How to solve?
Mia's height=1.65 m
Tree's equivalent height=26.45m
Mia's height w.r.t. the tree's shadow=26.45-21.40 =5.05m
Ratio of the equivalent height w.r.t original height=5.05:1.65 =3.06
Tree's original height= tree's equivalent height: ratio of Mia's height
= 26.45:3.06 =8.64m
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What is always true about an isosceles triangle?
In an isosceles triangle, two angles and two sides are always equal.
What do we mean by an isosceles triangle?In geometry, an isosceles triangle is one with at least two sides of equal length.
It can be defined as having exactly two equal-length sides or as having at least two equal-length sides, with the equilateral triangle being an exception to the second definition.
Isosceles Triangle: A triangle is referred to as being isosceles if any of its two sides is equal.
if the triangle has X, Y, and Z as its three sides.
The triangle is isosceles when X = Y, X = Z, or Y = Z.
Scalene triangles are recognized as triangles without equal sides.
Therefore, in an isosceles triangle, two angles and two sides are always equal.
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Multiply and write a fraction or mixed numbers in its simplest form
2/5 x 6/7
Find the equation of the line that passes through the point (3, 28) and has slope 11. Simplify your equation to the following form.
=11+____
Answer:
y=11x-5
Step-by-step explanation:
y=mx+b
28=11(3)+b
28=33+b
b=-5
y=11x-5
2. A standard package of pencils contains 24
pencils.
# of
packages
# of
pencils
127
?
1
?
3
?
4
?
6
1
2
?
Answer:
12, 24,72,96,156
Step-by-step explanation:
1/2 package would be 1/2 of 24 which is 12
21 x 24 = 24
3 x 24 = 72
4 x 24 = 72
We know that 3 packages is 72 so 6 packages is double that at 144. We also know that have a package is 12. so 144 + 12 = 156
Answer:
1/2 package = 1/2 of 24 = 12 pencils
1 package = 24 pencils
3 packages = 24*3 = 72 pencils
4 packages = 24*4 = 96 pencils
6 1/2 packages = 24*6.5 = 156
Step-by-step explanation:
1 package = 24 pencils
1/2 package = 1/2 of 24 = 12 pencils
1 package = 24 pencils
3 packages = 24*3 = 72 pencils
4 packages = 24*4 = 96 pencils
6 1/2 packages = 24*6.5 = 156
Which ordered pair is a solution to the inequality y + 2 < 2x
The ordered pairs are of the form (x, y < 2x - 2), some examples of solutions are (0, -3) and (0, -4)
Which ordered pair is a solution of the inequality?An ordered pair will be a solution if, when we replace the values of the ordered pair on the inequality, the inequality becomes true.
Here the inequality is:
y + 2 < 2x
Isolating one of the variables we get:
y < 2x - 2
Now let's assume we impose x = 0, then the inequality becomes:
y < 2*0 - 2
y < -2
So y can be any value smaller than -2, then for example:
(0, -3), (0, -4)...
All of these are solutions of the inequality.
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Let
f(x)={x2+2xx+1if x≤−1if x>−1.
Evaluate the following:
1. f(−7) =
2. f(−1) =
3. f(0) =
Answer: [tex]35, -1, 1[/tex]
Step-by-step explanation:
[tex]-7 \leq -1 \implies f(-7)=(-7)^2 +2(-7)=35\\\\-1 \leq -1 \implies f(-1)=(-1)^2 +2(-1)=-1\\\\0 > -1 \implies f(0)=0+1=1[/tex]
Journee and her brother were arguing over who was responsible for the dishes. Journee explained to her brother that she had washed the dishes the last three nights
Her brother replied, "Sure, but that's just because you're a nerd with nothing better to do." Which logical fallacy has Journee's brother used?
O Ad hominem
Oad populum
Answer: Ad Hominum
Step-by-step explanation:
It just attacks the person.
A radio is bought at 550 and sold at a profit of 35. What is the selling price?
The selling price of the radio with a cost price of 550 and sold at a profit of 35 is 585.
What is selling price?The selling price is how much a buyer pays for a product or service.
To calculate the selling price of the radio, we use the formula below.
Formula:
S.P = C.P+Profit............ Equation 1Where:
S.P = Selling Price of the radioC.P = Cost price of the radioFrom the question,
Given:
C.P = 550Profit = 35Substitute these values into equation 1
S.P = 550+35S.P = 585.Hence, the selling price of the radio is 585.
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How do you make an addend?
We can make addend just by adding a number to another number.
What is addend?
Addends in math can be defined as the numbers that we add together to get a sum. The numbers you use in addition are called addends; in multiplication, the analogous term is a factor. If you add 7 to 112, the 7 is an addend, and the second number is an augend, though you're unlikely to hear anyone other than a math teacher use either of these phrases. Addere, which means "to add to, join, or attach," is the Latin root of the word addend.
Any number that is added to another is referred to as an addend in mathematics. When you add 10 to 15, 10 is the addend. An addend can alternatively be referred to as a summand.
So in example 15 is an addend of 10.
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The prices of two radios are in the ratio x : y
When the prices are both increased by £20, the ratio becomes 5:2
When the prices are both reduced by £5, the ratio becomes 5:1
Express the ratio x : y in its lowest terms.
Prices of two ratios in the ratio is 4 : 1.
What do you mean by ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.
For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole.
For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.
Let us assume price of radios are x and y
According to the question
[tex]\frac{x + 20}{y+20} =\frac{5}{2}\\2x+40=5y+100\\2x-5y=60[/tex]-------------------------- eq(1)
and
[tex]\frac{x-5}{y-5} =\frac{5}{1}\\5y-x = 20[/tex]
5y-x = 20
multiplying this equation by 2
we get
10y-2x = 40 ------------------ eq(2)
adding eq 1 and 2
we get
5y=100
y=20
solving further we get x=80
Thus the ratio is 4 : 1.
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What should be the remainder of the polynomial function for the divisor to be a factor?
Answer:
zero
Step-by-step explanation:
You want to know the remainder of the polynomial function for the divisor to be a factor?
DivisionA divisor is a factor of the dividend in any division problem if and only if the remainder is zero (0).
The divisor will be a factor of a polynomial function if division of the function by that divisor has a remainder of zero.
Finding the multiplier to give a final amount after a percentage increase or decrease
With percent increase or decrease situations, you have to consider the starting point as being 100%. So if the account increased by 27%, it's now 100% + 27% or 127% of it's original value.
As a decimal, 127% = 1.27. So 1.27 is your multiplier in this example.
And 1.27 • 7600 = 9652, which is the ending balance.
This gets the same result as finding 27% of 7600 and adding it back on to 7600, but does it more efficiently.
25/24 as a decimal rounded to the nearest tenth
Answer:
1.0
Step-by-step explanation:
Hope this helps! :)
The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, we have,
given that, 25/24
now, we have to rounded to the nearest tenth
as decimal, so, we have to divide 25 by 24
i.e. 25/24 = 1.041
we get, 1.041 => 1.0
so, it is 1.0 a decimal rounded to the nearest tenth
Hence, The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .
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What is 1 * 2 * 3 * 4 * 5 all the way to 100?
9.332622e+157 or 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
What is Factorial?
The product of all positive integers less than or equal to a given positive integer, indicated by that integer plus an exclamation point, is known as Factorial in mathematics.
The approximate value of 100! is 9.3326215443944E+157.
The number of trailing zeros in 100! is 24.
The number of digits in 100 factorial is 158.
The factorial of 100 is calculated, through its definition, this way:
100! = 100 • 99 • 98 • 97 • 96 … 3 • 2 • 1
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4x+8y-3z=1 -5x-2y+6z=-6 9x+3y-10z=10
The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2
The width and the length of the slab are 2 meters and 12 meters, respectively
How to determine the dimensions of the slab?From the question, we have the following parameters that can be used in our computation:
Width of a rectangular slab of concrete = 10m less than the length.
Area = 24 m²
These parameters can be represented as
Width = Length - 10
Area = Length * Width
So, we have
w = l - 10
A = lw
Also, we have
A = 24
Substitute w = l - 10 in A = lw
A = l(l - 10)
So, we have
l(l - 10) = 24
Expand
l² - 10l = 24
This gives
l² - 10l - 24 = 0
Expand
l² + 2l - 12l - 24 = 0
Factorize
(l + 2)(l - 12) = 0
So, we have
l = -2 and l = 12
The length cannot be negative
So, we have
l = 12
Recall that
w = l - 10
So, we have
w = 12 - 10
Evaluate
w = 2
Hence, the dimensions are 2 meters and 12 meters, respectively
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Possible question
The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2
Compute the dimensions of the slab
12. The hourly temperatures at Eppley Airfield Airport in Omaha, Nebraska, in May 2014 are approximately normally distributed with a mean of 64.4˚F and a standard deviation of 12.2 ˚F. The z-score of the lowest temperature is −2.49. What is the lowest temperature? Round your result to the one’s place.
The lowest temperature with a z score of of -2.49 is 24.0 ˚F
How to find the temperature with a z score of -2.49Z scores, measures the amount of standard deviation sample X is from mean. the formula is below
z = (X - μ) / σ
Definition of variables
mean, μ = 4.4˚F
standard deviation, σ = 12.2 ˚F
X = lowest temperature
z = -2.49
substituting into the formula
-2.49 = (X - μ) / σ
-2.49 = (X - 64.4) / 12.2
-2.49 * 12.2 = X - 64.4
-30.378 + 64.4 = X
X = 34.022
X = 34.0 (to one decimal place)
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A right triangle has side lengths 9,40, and 41 as shown below . Use these lengths to find tanY, Sin Y, and cosY
Using the trigonometric ratio of sin, cos and tan of Y, the values are 12.7, 12.7 and 12.4 degrees respectively
Trigonometric RatioThis involves using ratios of sine, cosine, tangent, cot, cosec, sec to find the missing sides of a right angle triangle.
In the triangle given;
Using angle Y as a reference point;
hypothenuse = 41opposite = 9adjacent = 40Sin Y = opposite / hypothenuse
sin Y = 9 / 41
Y = sin⁻¹ (9/41)
Y = 12.7°
The cosine value of Y
cos Y = adjacent / hypothenuse
cos Y = 40 / 41
Y = cos⁻¹(40 / 41)
Y = 12.7°
The tangent value of Y is
tan Y = opposite / adjacent
tan Y = 9 / 41
Y = tan⁻¹(9/41)
Y = 12.4°
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how many solutions are there to this nonlinear system
There is only one solution to the nonlinear system.
What is Nonlinear system?
A nonlinear system is a system in which the change of the output is not proportional to the change of the input.
The solutions of a nonlinear system of equations are in the form of x and y values and these are the points at which the graphs intersect. Such systems have no solution, or one or more solutions.
So, here function 1 is a parabola and function 2 is a straight line. The parabola is touching the straight line at one point only, so this has one solution.
Hence the answer is there is only one solution to the nonlinear system.
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Find x.
Finding an angle measure given extended triangles
Answer:
108 degree
Step-by-step explanation:
the angle x is equals to 108 degree
(a)In a certain board game, players spin a spinner to determine how many spaces they advance. The odds in favor of advancing five spaces are 3/10. Find the probability of advancing five spaces.
(b)Ravi has a box of candies with different flavors. He will randomly choose one piece of candy. The probability that he chooses a strawberry-flavored piece is 6/19. What are the odds against him choosing a strawberry-flavored piece?
The probability of advancing five spaces is 0.2307.
Given that, the odds in favor of advancing five spaces are 3/10.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
The probability of advancing five spaces can be obtained as:
P =Odds/1+Odds
= [tex]\frac{\frac{3}{10} }{1+\frac{3}{10} }[/tex]
= [tex]\frac{\frac{3}{10} }{\frac{13}{10} }[/tex]
= 3/13
= 0.2307
Therefore, the probability of advancing five spaces is 0.2307.
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Find the distance CD rounded to the nearest tenth.
C=(7,-4) and D=(-8,-5)
CD=?
HINT: Use the distance formula:
d=√(x2-x1)²+(y2-y1)²
Round your answer to the tenths place.
The distance of CD is 15.0 units
How to calculate distance CD?By using a Distance formula calculator, we can determine the distance between various sets of points. The correct formula to determine the distance between two points (a, b) is therefore (c - a)2 + (d - b)2.
The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.
The distance between two points A (a,b) and B (c,d) is given by :-
AB = √[(d-b)² +(c - a)²]
Given ,
C=(7 -4)
D=(-8,-5)
Now, the distance between two points C=(7 -4) and D=(-8,-5) will be :-
CD = √[(-5-(-4))²+(-8-7)²
CD= √[(-5+4)²+(-15)²
CD = √[(-1)²+(-15)²
CD = √[1+25]
CD = √226
= 15.0332963784 approximately
=15.0
Therefore the Distance of CD is 15.0 unit
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are the triangles congruent why or why not brainly
∠C is not congruent to any angle in DEF. Hence, option C is the correct answer.
From the given figure below,
In ΔABC,
∠A=33° and ∠C=88°
By angle sum property of triangles,
∠A+∠B+∠C=180°
33°+∠B+88°=180°
∠B=180°-33°-88° [subtracting 33° and 88° from both sides]
∠B=59°
Now, In ΔDEF,
∠D=33° and ∠E=58°
By angle sum property of triangles,
∠D+∠E+∠F=180°
33°+58°+∠F=180°
∠F=180°-33°-58° [subtracting 33° and 58° from both sides]
∠F=89°
Thus, ΔABC is not congruent to Δ DEF as∠C and ∠B are not congruent to any angle of the Δ DEF .
Hence, ∠C is not congruent to any angle in DEF."
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The complete question is -
Are the triangles congruent? Why or why not?
A) Yes, ∠A ≅∠D and AB ≅ DE.
B) Yes, they are congruent by either AAS or ASA.
C) No,∠C is not congruent to any angle in ΔDEF.
D) No, the congruent sides do not correspond.
Line a is parallel to line b. If the
measure of 47 is 114°, what is the
measure of <1?
21
34
65
114 78
Answer:
66 degrees
Step-by-step explanation:
By the Corresponding Angles Theorem, Angle 7 is equal to Angle 2. This means that the measure of Angle 2 is 114.
Since Angle 1 is supplementary to Angle 2:
[tex]114 + x = 180\\x = 66[/tex]
Angle 1 is 66 degrees
for a fishing trip, debra is going to choose lures to put in her tackle box. she has 4 lures that are jigs and 9 that are spinnerbaits. In how many waits can she choose 6 lures if more than 4 must be spinnerbaits?
Answer:
1680
Step-by-step explanation:
If TU = 4x, UV = x + 2, and TV = 7, what is TU?
===========================================================
Explanation:
Assuming points T, U, and V are all on the same straight line, then we can say the following:
TU + UV = TV
(4x) + (x+2) = 7
5x+2 = 7
5x = 7-2
5x = 5
x = 5/5
x = 1
Now we can determine the length of each piece.
TU = 4x = 4*1 = 4UV = x+2 = 1+2 = 3as a check: TU + UV = 4+3 = 7 which matches perfectly with TV = 7. The answer is confirmed.
Once again, this assumes that points T, U, and V are collinear (i.e. on the same straight line). It also assumes that U is between T and V.
