Answer: P = 2((49h²+42h+9)(64h²-64h+16))
Step-by-step explanation:
The price of a coat is reduced by 17% in a sale.
The sale price is £78.85.
What was the original price of the coat?
Give your answer in pounds (£).
The required original price of the coat is given as £95.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95
Hence, the cost of the coat before the sale is £95.
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The digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Explain how to correctly place the decimal point without knowing the other factor. Then Place place the decimal point in the product.
The decimal point is to be placed three places to the left.
What are decimal numbers?
When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.
If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.
Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.
The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.
The decimal point is to be placed three places to the left.
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What are the consecutive perfect cubes which added to obtain a sum of 100? PLEASE HELP!!!!!!!
Answer: 1, 2, 3, 4 are the consecutive perfect cubes which are added to obtain a sum of 100.
Step-by-step explanation:
Perfect cubes are the numbers that are triple product of same number.
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
1+8+27+64 = 100
Answer: 1, 2, 3, 4 are the consecutive perfect cubes which are added to obtain a sum of 100.
Explanation:
Perfect cubes are the numbers that are triple product of same number.
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
1+8+27+64 = 100
ray ab bisects CAT. if m< CAT =30 and m
(pls show how i did it)
Help please i can’t do the math right I’m not getting any of those 4 options right
it's B. 3,406 that the answer I now bye bye
Answer:
it's b
Step-by-step explanation:
Two of the coordinates representing the corners of Maya's rectangular driveway are (-1, 1) and (1 1\2, -8 1\2
9. Plot the other two coordinates of Maya's rectangular driveway. What are the ordered pairs that you plotted?
Answer:
the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
Step-by-step explanation:
To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).
Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.
We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.
We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:
y = -3/17 * x + (-3 3/4)
x = (y - (-3 3/4))/(-3/17)
Substituting the coordinates of the corner we found earlier, we get:
x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3
So, the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
boston thinks that the domain is all positive real numbers between 0-4 while caleb thinks it is all whole numbers between 0-4. who do you agree with, and why?
0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.
Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.
Let's understand what is positive real numbers.
That is all the real numbers that are greater than or equal to zero.
real numbers are numbers which include both rational and irrational numbers.
whole numbers are positive integers that mean only positive integers.
that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.
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suppose that, of people who undergo routine screening, for every two people who have colon cancer, there are 100 who do not. (that is, 2/102 people have it.) of those who undergo screening and do have colon cancer, all of them will have a positive test. of the people who undergo screening but don't have colon cancer, only 2 percent have a positive test. a random person undergoes routine screening and has a positive test. what is the probability (not odds) that this person has colon cancer? choose the range in which the answer lies.
The probability that a person has colon cancer given that they have a positive test result is approximately 0.98. The answer lies in the range [0.95, 1.00].
Let's call the probability that a person has colon cancer given that they have a positive test result "p". We can use Bayes' Theorem to find this probability.
Bayes' Theorem is: p(A|B) = (p(B|A) * p(A)) / p(B)
In this case, A is the event that the person has colon cancer, and B is the event that the person has a positive test result.
We are given that:
p(B|A) = 1 (all people who have colon cancer will have a positive test result)
p(B|~A) = 0.02 (2% of people who do not have colon cancer will have a positive test result).
We are also given that p(A) = 2/102 (2 out of 102 people who undergo routine screening have colon cancer) and p(~A) = 100/102 (100 out of 102 people who undergo routine screening do not have colon cancer).
Substituting these values into Bayes' Theorem, we get:
p(A|B) = (1 * (2/102)) / (1 * (2/102) + 0.02 * (100/102))
Simplifying, we get:
p(A|B) = 0.98
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Which is the midpoint of segment AB with A(-1,5) and B(6,-3)
Answer:
(2½,1)
Step-by-step explanation:
(-1+6/2,5+-3/2)
(5/2,2/2)
(2½,1)
Please help, thank you!
6. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the initial
height of the rocket before it is launched?
h(t) = -5t² +42t +54
Answer:
Step-by-step explanation:
The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:
h(0) = -5(0)² + 42(0) + 54
h(0) = 0 + 0 + 54
h(0) = 54
Therefore, the initial height of the rocket before it is launched is 54 meters.
Answer: 54 meters.
Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.
To confirm this, you can plug in t = 0 into the quadratic function to get:
h(0) = -5(0)² + 42(0) + 54 = 54 meters
This means that the initial height of the rocket before it is launched is 54 meters.
Solve. 3 x − 9 x 2 = − 10
Answer:
below
Step-by-step explanation:
9x^2-3x-10 = 0 Use quadratic Formula with a = 9 b = -3 and c = -10
to find the zeroes are x = 1/6 ± sqrt (41) / 6
I need help with these answeres. they are for geometry.
1) The two column proof for ΔLMN ≅ ΔLON is as developed below.
2) The two column proof for ΔGHJ ≅ ΔKLM is as developed below
How to carry out two column proof?A two-column proof is defined as a geometric proof that consists of a list of statements, and then the reasons that we know those statements are deemed to be true.
1) The two column proof showing that ΔLMN ≅ ΔLON is;
Statement 1: LN bisects ∠MLO and LM ≅ LO
Reason 1: Given
Statement 2: MN ≅ ON
Reason 2: Line segment bisector
Statement 3: ∠MLN ≅ ∠OLN
Reason 3: def. of angle bisector
Statement 4: LN ≅ LN
Reason 4: Reflexive property of congruence
Statement 5: ΔLMN ≅ ΔLON
Reason 5: SSS Congruency postulate
2) The two column proof is as follows;
Statement 1: ∠G ≅ ∠K, ∠J ≅ ∠M
Reason 1: Given
Statement 2: ∠H ≅ ∠L
Reason 2: 3rd angle theorem
Statement 4: ΔGHJ ≅ ΔKLM
Reason 4: ASA Congruency Postulate
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PLEASE HELP ASAP FOR MY FINALS
Answer:
A.86
is the answer will show how it's solved if necessary on comment.
hope it helps!!!
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 5 ≤ x ≤9.
7
8
9
6
x
4
5
f(x)
4
8
16
32
64
medically explained PAINL X
128
Deltal/ath
The average rate of change, in simplest form, is -2/5.
What is average rate ?
Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.
The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]
Using the coordinate points from the table (0,41) and (15,35)
Substitute the coordinate into the expression:
[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]
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Please help meee asap please !!!????
A right triangle has a leg length of √ and a trypolenuse length of 7. Determine the length of the other leg of the right triangle.
03
O √59
O√43
The length of the other leg is (c) √43
How to determine the length of the other legFrom the question, we have the following parameters that can be used in our computation:
Hypotenuse = 7
One leg = √6
The length of the other leg can be calculated using
The length of the other leg = √(Hypotenuse^2 - One leg^2)
So, we have
The length of the other leg = √(7^2 - √6^2)
Evaluate
The length of the other leg = √43
Hence, the length is (c) √43
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Complete question
A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.
show that 12cos30 + 2tan60 can be written in the form Vk where k is an integer
Answer:
√192
Step-by-step explanation:
12 cos 30° + 2 tan 60°
Substitute the trig functions of the special angles.
12 (½√3) + 2 (√3)
Simplify.
6√3 + 2√3
8√3
Move under the radical.
√(8² · 3)
√192
It takes 47 pounds of seed to completely plant a 5 -acre field. How many acres can be planted per pound of seed? (b)
Which is an expression for the derivative P(x) = f(x) / —f(x)
the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
given expression p(x)= f(x)/1-f(x)
The derivative of the given expression will be
p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²
Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
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the population of a city was 250,000 in 1980, and it was 310,000 in 2000. what was the average rate of growth over this period?
Average rate of growth over this period is 0.4%.
Average rate of growth over a period is given by:
A=P[tex]e^{rT}[/tex] where,
A- Population at time T
P- Initial population
r-average rate of growth
T-Time period
Now, P=250,000, A=310,000 and T=21 (2000-1980+1)
therefore, putting values in the equation, we get:
310,000=250,000[tex]e^{21r}[/tex]
⇒ [tex]e^{21r}[/tex] = 1.24
⇒ 21r = log(1.24)
⇒ r = 0.0044 or 0.4%.
so, the average rate of growth over this time period is 0.4%.
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The statement for the expression 4x-10 is
Subtract 3
2y + 2xy – x + 4 from 9 - 7x + 3xy - 4
2y
if you babysit for a year for 10hr every weekday how much did you make?
Answer:
Well, nothing because you didn't say how much money you make a day, a week, or a month.
Step-by-step explanation:
You tried to trick me haha <3
A line is parallel to y = 4x + 11 and
intersects the point (-2, 4). What is the
equation of this parallel line?
y = 4x + [?]
The equation of the line that is parallel to given line is y = 4x + 12
What is slope of Parallel lines:Parallel lines have an equal slope. The slope of parallel lines is identical because they are all equally inclined with respect to the positive x-axis.
If m₁ and m₂ are slopes of parallel lines then => m₁ = m₂
Here we have
A line is parallel to y = 4x + 11 ---- (1)
The given line is in form of y = mx + c [ where slope of line = m ]
On comparing both lines, Slope given line = 4
Let the required line with slope m₁ is y = m₁x + c --- (2)
As we know slope of parallel lines are equal or same
=> Slope of line (2), m₁ 4
Line (2) => y = 4x + c
Given that the line passes through (-2, 4)
=> 4 = 4(-2) + c
=> 4 = -8 + c
=> c = 12
Therefore,
The equation of the line that is parallel to given line is y = 4x + 12
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Point E has the same y-coordinate as point D, but the x-coordinate of point D. Plot point E and write the coordinates of point E. Then describe the type of reflection you plotted.
The coordinates of Point E are (-4,2) and Point E is a reflection of point D across the X-axis.
What is the coordinate about?Point E has the same y-coordinate as point D, which is 2. However, the x-coordinate of point E is the opposite of the x-coordinate of point D. The x-coordinate of point D is 4, so the x-coordinate of point E must be -4. Therefore, the coordinates of Point E are (-4,2).
As for the reflection, you can imagine a mirror placed on the x-axis (horizontally) and Point D and E being on the same side of that mirror.
Therefore, As Point D is reflected on the mirror, it will be flipped and the x-coordinate changes its sign and becomes -4. Therefore Point E is a reflection of point D across the X-axis.
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See full question below
Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x- coordinate of point D. Drag tiles to complete the statements. (4,2) (4,-2) (-4,2) (-4,-2) X-axis y-axis The coordinates of Point E are --- &Point E is a reflection of point D across the ---
Express cos E as a fraction in simplest terms.
Answer: cos E=
E
10
24
C
0
The trigonometric ratio, cos E of the right triangle is 5 / 13.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
A right triangle is a triangle that has one of its angles as 90 degrees.
The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;
opposite sideadjacent sidehypotenuse sideTherefore,
cos E = adjacent / hypotenuse
Hence,
let's find the hypotenuse side using Pythagoras theorem,
24² + 10² = c²
c = √576 + 100
c = √676
c = 26
cos E = 10 / 26
Therefore,
cos E = 5 / 13
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Complete these sentences by selecting the correct answers from the drop-down menus.
After one half-life,
% of the atoms will change to a stable isotope and
% will remain radioactive.
After three half-lives,
% of the atoms will change to a stable isotope and
% will remain radioactive.
Answer:
After one half-life,
50% of the atoms will change to a stable isotope and
50% will remain radioactive.
After three half-lives,
87.5% of the atoms will change to a stable isotope and
12.5% will remain radioactive.
Step-by-step explanation:
During the 1st half-life, 50% of the atoms change to a stable isotope, 50% radioactive left.
During the 2nd half-life, 50% of the left 50% radioactive change to a stable isotope, which is 25% of the total. 50% of 50% radioactive left, which is 25% of the total. Then 75% change to a stable isotope and
25% remain radioactive.
During the 3rd half-life, 50% of the left 25% radioactive change to a stable isotope, which is 12.5% of the total. 50% of 25% radioactive left, which is 12.5% of the total. Then 87.5% change to a stable isotope and
12.5% remain radioactive.
Angela is following this recipe to make biscuits.
Angela uses 0.9 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 10 biscuits
150 g margarine
180 g sugar
225 ml syrup
225 g oats
40 g sultanas
The amount of margarine needed in Kg for making biscuits is 0.6kg
What is proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
How to find the amount of margarine needed in KgThe amount of margarine needed in Kg is calculated using proportions
If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require
0.225 l = 0.15 kg
0.9 l = ?
cross multiplying
0.225 * ? = 0.9 * 0.15
? = 0.135 / 0.225
? = 0.6
Angela will require 0.6 kg of margarine
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2. Which of the following expressions has a
constant term of 4?
a. 4x² + 4x
b. x² + 3x - 4
C. 2x²-x+4
d. 4x²+2x - 10
e. x+ 5x + 8
Answer:
C would be the answer
Step-by-step explanation:
constants are the numbers with no terms.
given that e1 and e2 have a high spearman correlation, what can we say about the pearson correlation of e1 and e2?
Given that e1 and e2 have a high spearman correlation, what we can say about the Pearson correlation of e1 and e2 is; The Pearson correlation must be high
How to Interpret Correlation Coefficient?A correlation coefficient is defined as the measurement of the extent to which two variables tend to change together.
Now, the Pearson correlation is the type that evaluates the linear relationship that exists between two continuous variables. A relationship is said to be linear as a result of a change in one variable being associated with a proportional change in the other variable.
Meanwhile, the spearman correlation is one that evaluates the monotonic relationship between two continuous or ordinal variables.
If the relationship described above tells us that one variable increases when the other increases, but then the amount is not consistent, then it means that the Pearson correlation coefficient is positive but less than +1. However, the Spearman coefficient still equals +1 in this case.
Thus, we conclude that as the spearman correlation is high, then the Pearson correlation is also high.
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