[tex]3\sqrt{2} - 4 * (\sqrt{2})^2 = 3\sqrt{2} - 8[/tex]
Answer = [tex]3\sqrt{2} - 8[/tex]
HELPP‼️‼️
21. Out of 500 people in a room, 200 of them are
wearing red shirts. Of the people wearing red
shirts, 15% are wearing red pants. What percentage of the people in the room are wearing both red shirts and red pants?
500 people
200 people wearing red shirts
200x15%= 30 people
30 =6% of 500
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas.During
one particular week, the two cars went a combined total of 1400 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week
20 gallons is consumed from the first car and 25 gallons is consumed from the second car.
What is an Equation ?A mathematical statement that relates two algebraic expression using an equal sign is called an equation.
It is given that
Fuel Efficiency of the first car is 20 miles per gallon of gas
Fuel Efficiency of the second car is 40 miles per gallon of gas
Total miles travelled = 1400 miles
Total gas consumption = 45 gallons
Let the gallons consumed from the first car is x
then the gallons consumed by the second car is (45 - x)
The equation formed will be
20* x + 40 * (45 -x) = 1400
20x +1800 - 40x = 1400
-20x = -400
x = 20
Therefore 20 gallons is consumed from the first car and
45-20 = 25 gallons is consumed from the second car.
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Ten friends want to play a game. They must be divided into three teams with three people in each team and one field judge. In how many ways can they do it?
Using the combination formula, it is found that there are 16,800 ways for them to do it.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
For the judge, one is taken from a set of 10.For the first team, 3 are taken from a set of 9.For the second team, 3 are taken from a set of 6.For the third team, 3 are taken from a set of 3.Hence the number of ways is:
[tex]N = C_{10,1}C_{9,3}C_{6,3}C_{3,3} = \frac{10!}{1!9!} \times \frac{9!}{3!6!} \times \frac{6!}{3!3!} \times \frac{3!}{3!0!} = 16800[/tex]
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Quick factorisation question… can someone pls help and also provide a step by step explanation? Thank you!
Hello,
Answer:
C. (b - c)(a + b)
Step-by-step explanation:
A = (b - c)(a - c)
A = ba - bc - ac - c² ≠ ab + b² - ac - bc
B = (b + a)(b + c)
B = b² + bc + ab + ac ≠ ab + b² - ac - bc
C = (b - c)(a + b)
C = ba + b² - ca - cb
= ab + b² - ac - bc
→ That is answer C
An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?
2 < s < 18
6 < s < 12.8
s < 2 or s > 18
s < 6 or s > 12.8
Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.
What is the Triangle Inequality Theorem?According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.
Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:
10 - 8 < s > 8 + 10
2 < s > 18
The range of values for the third side is: A. 2 < s < 18.
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Answer: A. 2 < s < 18.
Step-by-step explanation:
Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.
Explain in your own words why you think a tangent of a circle is always perpendicular to the radius at the point of tangency
Explain in your own words why you think angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle
A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;
i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.
ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.
A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.
A diameter is a line from one point on the circumference of a circle to another through its center.A radius is a line drawn from the center of a circle to its circumference. Thus a radius is half of the diameter.A tangent is an external line drawn to meet the circumference of a circle at a point,Thus the reasons required in the question are given as;
i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.
ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.
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Which of the following options is a polynomial with a root 2i and exactly 2
real roots?
A. F(x)=x²-x²³ +2x² - 4x-8
B. F(x)=x²-x² + 4x-4
C. F(x)=x²-x³-6x² +4x+8
OD. F(x)= x³ + x² + 4x+8
The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
Factorizing polynomial functionsGiven the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
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CAN ANYONE HELP PLEASE
Answer:
x = 8
Step-by-step explanation:
Every angle in an EQUILATERAL triangle = 60°
so 9x -12 = 60
9x = 72
x = 8
Step-by-step explanation:
[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]
[tex]9x = 60 + 12[/tex]
[tex]9x = 72[/tex]
[tex]x = \frac{72}{9} \\ [/tex]
[tex]x = 8[/tex]
hence the value of x is 8...
Julie bought 5 bottles of water for $5.35. Which of the following have the same unit rate? (Click all that apply.)
1 bottle for $1.07
3 bottles for $3.15
8 bottles for $8.56
6 bottles for $6.42
Answer: 1 bottle, 6 bottle, 8 bottle
Answer: 1 bottle for $1.07, 8 bottles for $8.56 and 6 bottles for $6.42
Could you guys help meee
1. y= 2x
2. (0, 5)
3. y = 3x + 12
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
1. let us take (0,0) and (1, 2)
m= 2-0/1-0
m= 2
So equation of line
y- 0 = 2(x-0)
b
2. y= 3x+5
passes through (0, 5)
3. y= 3x+5
m = 3
We need the equation of a line with slope 3 that passes through point (0, 12).
y - y1 = m(x - x1)
y - 12 = 3(x - 0)
y - 12 = 3x
y = 3x + 12
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9. The length of a rectangle is 2p cm and its breadth is p cm. When the length of the rectangle is increased by 25% and the breadth is decreased by 25%, determine the percentage change in (i) its perimeter, (ii) its area.
Answer:
The answers are:
(i) 108.33%
(ii) 93.75%
Step-by-step explanation:
The original area and perimeter are as follow:
Perimeter = 2l + 2w
= 2(2p) + 2(p)
= 4p + 2p
= 6p cm
Area = l * w
= 2p * p
= 2p^2 cm^2
A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm
A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm
Perimeter = 2l + 2w
= 2(2.5p) + 2(0.75p)
= 5p + 1.5p
= 6.5p cm
Area = l * w
= 2.5p * 0.75p
= 1.875p^2 cm^2
Now that we have found the changes, let's calculate the percentage changes
Percentage change of perimeter:
x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33
Percentage change of area:
x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75
Answer:
i = 8 1/3%
ii = -6 1/4%
Step-by-step explanation:
The previous answer is wrong this is the correct one:
Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm
i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm
The percentage change is
65-60/60 x 100
= 5/60 x 100
= 500/60
= 8 2/6% simplified 8 1/3%
ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2
The percentage change is
187,5-200/200x 100
= - 12,5/200 x 100
= - 1250/200 = - 6 1/4 %
That is the Correct answer. Hope that help
which is a stretch of an exponential decay function ?
Using translation concepts, a stretch of a decay exponential function is given by:
[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
An exponential decay function is given by:
[tex]y = ab^x[/tex]
In which |b| < 1.
A stretch means that the function is multiplied by a factor with absolute value greater than 1, hence the function would be given by:
[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]
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3,
Which expression is equivalent to
56x7y5, if x #0 and y# 0?
Answer:
1960
Step-by-step explanation:
1960
times 56 times 7 time 5 = 1960
A ferris wheel has 32 passenger cabins. if you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?
Answer:
30Step-by-step explanation:
A ferris wheel has 32 passenger cabins. if you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?
from the top to the base you have a semicircle, so 16 cabins, if at the top there is the 14 below you will have the 30.
32 : 2 + 14 = 30
Answer:
Number of the cabin at the bottom of the wheel is 30
Step-by-step explanation:
Since there are 32 passenger cabins, each half of the wheel has:
32/2 = 16 cabinsIt means the opposite cabins on the Ferris wheel have number difference of 16.
If one of the cabins has a number 14, the opposite cabin has number of:
14 + 16 = 30Work out the mean for the data set below: 3 , 5 , 4 , 3 , 5
Answer:
4
Step-by-step explanation:
The mean is the average of the numbers.
if you rearrange the data, you will get the order, 3,3,4,5,5.
you add all of them together to get the number twenty, then you divide 20 by the total number of data plots which is five. Then you get the number 4 which is your answer
3+3+4+5+5 = 20
20/5 = 4
Aria is paddling a canoe at a constant speed. She starts a timer when she is 40 feet from her starting position. After 30 seconds, Aria is 130 feet from her starting position. Write a linear equation in slope-intercept form to find the distance d of Aria from her starting position after t second.
Answer:
[tex]y = 3x + 40[/tex]
Step-by-step explanation:
The slope-intercept equation takes the form
[tex]y = mx + c[/tex]
Where m is the gradient, and c is the y-intercept.
If we assume we are plotting a graph where the X axis is time, and the y axis is distance, and we know our time value starts at 40, then we can say that our y intercept value is 40.
Next, let's figure out how far she has travelled. 130-40 = 90, and she has travelled this distance in 30 seconds, so dividing 90 by 30, we know that she is travelling 3 feet a second. This leaves us with a gradient of 3.
Putting these two values together, we can find the final form of the equation to be:
[tex]y = 3x + 40[/tex]
Answer:
d = 3t + 40
Step-by-step explanation:
So, since you have a constant speed you're going to have a linear equation, which was also stated in the question. So it's asking for slope-intercept form which is expressed as: y=mx+b, where m=slope, and b=y-intercept. So it's important to know what these two things mean in certain contexts. In every single case, the slope is how much the y-value is changing as x increases by 1, and in this specific case, the distance is what is changing as time goes by. So this means that the distance would be the y-value, and x would be the t variable (time). And remember how it mentioned "constant speed", this means as one second passes, the distance increases by a constant distance. We can solve for this by using the given information.
She's already 40 feet from her starting position, and after 30 seconds she's 130 feet from her starting position. This means she traveled (130 - 40) feet, because she was already 40 feet away from her starting position. This means she traveled 90 feet. Now to find how much she travels in a second, divide it by the time which is 30 seconds, and you get: 90 feet / 30 seconds = 3 ft/s, this is her constant speed. This is the slope of the equation. So now we have the equation: d = 3t + b. Now all we need to find is the y-intercept
The y-intercept in this context, is how far away she is from her starting position initially. This is given in the problem, it's 40 feet. She's already 40 feet away when 0 seconds have passed. So this gives us the equation: d = 3t + 40
Divide 54 into the ratio 11:7
Answer:
33:21
Step-by-step explanation:
The way I look at it is that 11:7 is 18 parts of 54. So I divide 54 by 18 and get 3 per. Then multiply, 11 * 3 is 33 and 7 * 3 is 21.
The expression is 12 x 2 / 7 will be 24/7. And the number 54 into the ratio 11:7 will be 33 and 21.
What is the ratio?The utilization of two or more additional numbers that compares is known as the ratio.
The expression is given below.
⇒ 12 x 2 / 7
⇒ 24 / 7
Divide 54 into the ratio 11:7.
⇒ 54 x 11 / (11 + 7)
⇒ 594 / 18
⇒ 33
⇒ 54 x 7 / (11 + 7)
⇒ 378 / 18
⇒ 21
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Find the surface area. Round your answer to the nearest hundredths, if necessary. Leave your answer in terms of for answers that contain .
Answer:
I don't know how to answer this, sorry!
Step-by-step explanation:
A survey was conducted to determine which type of lunch was more popular among the school’s football team. For this purpose, the number of each type of lunch sold to the players was tracked. How many more pizza lunches than hot dog lunches were sold? A. 3 B. 4 C. 7 D. 5
The number of pizza lunches sold more based on the survey is 5.
How to compute the value?The information is incomplete and an overview will be given.
Let the number of pizza lunches sold be 24.
Let the number of hot dog lunches be 19.
Therefore, the number of pizza lunches sold more will be:
= 24 - 19
= 5
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Answer: C, 7
Step-by-step explanation:
Logarithmic Functions
Can anyone help?
The equation [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex] has x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞). Thus Option A,B and C are correct.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.
Given function,
= [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex]
Domain of the above function is grater than -2 because at -2 system goes to infinity. Domain can be given as(-2, ∞).
Given function has x intercept at (14, 0) and y intercept at (0, 6).
Thus, the given function of log has following characteristic i.e.
x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞).
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Pls, can someone help me with this problem?
Answer:
1 ÷ 3
Step-by-step explanation:
You want 1/3 written as a quotient.
QuotientThe quotient of A and B is "A divided by B." There are two ways to write this using math symbols:
A/B
A÷B
The fraction 1/3 is already written as a quotient. This set of symbols can be read as either of ...
"one-third""one divided by three".The other way to write the quotient is ...
1 ÷ 3
__
Additional comment
When you learn about exponents, you learn another way to write the quotient of A and B is ...
A·B⁻¹
<95141404393>
The area of a square is 64 n Superscript 36square units. What is the side length of one side of the square?
8 n Superscript 6 units
8 n Superscript 18 units
64 n Superscript 6 units
64 n Superscript 18 units
The correct answer is option D which is the side length will be (64n)¹⁸.
What is the area of the square?The square is defined as a quadrilateral having all four sides equal to each other and the area of the square is the product of its sides.
Given that:-
The area of the square is given as- A = (64n)³⁶.The sides of the square will be calculated as follows:-
A = (64n)³⁶
a² = (64n)³⁶ Here a = Side of the square.
a = √ (64n)³⁶
a = 64n¹⁸
Therefore the correct answer is option D which is the side length will be (64n)¹⁸.
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Question 4(Multiple Choice Worth 2 points)
(02.04 MC)
Beginning with the graph of f(x) = x², what transformations are needed to form g(x) = 3(x + 2)2-1?
The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
Transformation of functionsTransformation is the technique used to change the position of a figure on an xy-plane.
Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units
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A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the direction 30° south of east. what is the plane’s drift angle?
Lets simplify the given problem,
The speed with which the plane flies = 350 mph
The direction of flight of the plane = N 40° E
The speed with which the wind blows = 40 mph
The direction in which the wind blows = S 40° E
Therefore, we have;
The resolution of the components of the motion of the plane, given as follows;
= 350 × sin(40°)·i + 350 × cos(40°)·j
The resolution of the components of the motion of the wind, given as follows;
= 40 × sin(40°)·i - 40 × cos(40°)·j
The resultant motion of the plane is given as follows;
= 262.563·i + 254.435·j
The direction of motion of the plane = tan⁻¹(262.563/254.435) ≈ N 45.9° E
Therefore, the plane's drift = Plane's Track - Plane's Heading = N 45.9° E - N 40° E ≈ 5.9° ≈ 5.89°
Drift Angle of the plane is 5.89 degree.
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Answer: A 5.9
Step-by-step explanation:
cuz i said so
In a recent survey of 1002 people, 701 said that they voted in a recent presidential election. voting records show that 61% of eligible voters did not vote. how would the confidence interval change if we increased the confidence level to 99%? find the 99% confidence interval estimate to support your answer.
The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).
Given sample size=1002 and confidence level of 99%.
In a sample with a number n of people surveyed with a probability of a success of π and a confidence level of 1-α, we have the following confidence interval of proportions.
π±z[tex]\sqrt{}[/tex]π(1-π)/n
in which z is the z score that has a p value of 1-α/2
n=1002,π=701/1002
So α=0.01, z is the value of Z that has a p value of 1-0.01/2=0.995, so Z=2.575.
Lower limit=π-[tex]z\sqrt{}[/tex]π(1-π)/n
=0.6996-2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]
=0.6623
Upper limit=π+[tex]z\sqrt{}[/tex]π(1-π)/n
= 0.6996+2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]
=0.7369
Hence the 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).
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Find the area of the trapezoid
Answer:
337.5Ft
Step-by-step explanation:
please assist me wit this question
Answer: 65
Step-by-step explanation:
By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]
So, by the Pythagorean theorem,
[tex]x=\sqrt{60^2 + 25^2}=65[/tex]
Complete the statement to describe the expression a b c + d e f abc+defa, b, c, plus, d, e, f. the expression consists of terms, and each term contains factors.
The statement of expressions is two terms and three factors.
The statement and expressions:According to the question, the statement that teaches us about expression is made up of two terms, each of which has three factors.
The ABC and DEF expressions define the expression of two terms, each of which comprises two elements.
As a result, the answer is two terms and three factors.
The terms of the expressions are connected by mathematical signs like addition and subtraction. Variables are combined using multiplication signs to form the factor.The three components are found in each word. Looking at the first term ABC, we can see that it has three variables, a, b, and c, which is multiplied together.Therefore, the answer is two terms and three factors.
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For what values of x is the expression below defined?
√x+4÷√1-x
Answer:
x=1
Step-by-step explanation:
(a) Find the three-digit number that increases by 30% when each of its
digits are increased by 1.
(b) Show that no three-digit number increases by 40% when each of its
digits are increased by 1.
Step-by-step explanation:
So a three digit number can be expressed as: [tex]100a + 10b + c[/tex] where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:
[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)[/tex]
Distribute the multiplication on the left side:
[tex]100a+100+10b+10+c+1=1.30(100a+10b+c)[/tex]
Distribute the multiplication on the right side:
[tex]100a+100+10b+10+c+1=130a+13b+1.3c[/tex]
Add like terms on the left side:
[tex]100a+10b+c+111=130a+13b+1.3c[/tex]
Subtract 100a, 10b, and c from both sides
[tex]111=30a+3b+0.3c[/tex]
So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.
So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value
111 = 30(3) + 3b + 0.3c
111 = 90 + 3b + 0.3c
Now subtract the 90 from both sides
21=3b+0.3c
Well 3 can fit into 21, 7 times!
21 = 3(7) + 0.3c
21 = 21 + 0.3c
subtract 21 from both sides
0 = 0.3c
and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant
c = 0
This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!
part b:
So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.
So let's start with the same equation except this time instead of 1.3 it's 1.4
[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)[/tex]
Distribute on the left side;
[tex]100a+100+10b+10+c+1=1.40(100a+10b+c)[/tex]
Distribute on the right side:
[tex]100a+100+10b+10+c+1=140a + 14b + 1.4c[/tex]
Add like terms on left side:
[tex]100a + 10b + c + 111 = 140a + 14b + 1.4c[/tex]
Subtract 100a, 10b, and c from both sides:
[tex]111 = 40a + 4b + 0.4c[/tex]
Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.
So only 2 40's can fit in 111 without going over the value
111 = 40(2) + 4b + 0.4c
Subtract 80 from both sides
[tex]31=4b+0.4c[/tex]
4 can fit into 31, 7 times
31 = 4(7) + 0.4c
31 = 28 + 0.4c
subtract 28 from both sides
3 = 0.4c
divide both sides by 0.4
7.5 = c.
Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.