Since we used x and x+2 as consecutive odd integers. "x" to represent Henry's age, Henry's age is 27. Since we used the expression "x+2" to represent Cameron's age, Cameron's age is "27+2" which is just 29.
How to do age sums?So the consecutive odd integers, just means they're separated by a value of 2. This can be generally expressed as "a and a+2" where the these two values would be consecutive odd integers assuming "a" is an integer.
So let's express the Henry's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive odd integer, Cameron's can be expressed as "x+2"
So the equation we need to set up is 2(Cameron's age) + (Henry's age) = 85
So we can substitute variables we defined to express Cameron and Henry's age:
2(x+2)+x= 85
Distribute the 2:
2x+4+x
Add like terms:
3x+4=85
Subtract 4 from both sides:
[tex]3x= 81[/tex]
Divide both sides by 3:
x=27
Since we used "x" to represent Henry's age, Henry's age is 27. Since we used "x+2" to represent the Cameron's age, Cameron's age is "27+2" which is just 29.
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Leroi is using coordinate geometry to prove this theorem.
Theorem: The diagonals of a parallelogram bisect one another.
Given: AD//BC; AB//CD; AC and BD intersect at M.
Prove: M bisects AC and BD.
Which of these is the BEST strategy for this proof?
A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
B) Use the equations of line AC and line BD to find the coordinates of M, then use the Distance Formula to verify that AC= BD
C) Use the equations of line AC and line BD to find the coordinates of M, then use the midpoint Formula to verify that M is the midpoint of both AC and BD
D) Use the Distance Formula to find the coordinates of M, then use the Midpoint Formula to verify that M is the midpoint of both AC and BD
The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
How to determine the best strategy for the proof?The theorem is given as
Theorem: The diagonals of a parallelogram bisect one another.
Also, we have the following given parameters
AD//BC; AB//CD;
AC and BD intersect at M.
The above means that:
Lines AD and BC are parallel lines, and AB and CD are parallel lines
The statement AC and BD intersect at M implies that
AM = MC and BM = MD.
The above means that we need to calculate the lengths of the above segments, and then make comparison
The lengths of the segments can be calculated using the distance formula
Other than that, the coordinate of the point M needs to be calculated
The option that satisfies the above conditions is (a)
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PLS HELP I WILL GIVE LOTS OF POINTS PLS HELP
Answer:
21 kilograms
Step-by-step explanation:
Every hour she produces 3 kilograms of dough. 9/3 = 3. So, in 7 hours, she can produce 21 kilograms of dough
Answer:
I want points
Step-by-step explanation:
e
a group of people are waiting in line for a movie premier. every 14th person in line will win a free movie ticket . every 10th person will receive a gift card of 30 dollars. which person is the first to win both prizes.if there are 200 people in line how many will receive both prizes?
In order to determine which person is the first to win both prizes, you have to find the least common multiple to both numbers 14 and 10.
To determine what is the least common multiple number you proceed as follow:
You list different multiples of each number 14 and 10.
For 14: 14 28 42 56 70 84 98 112
For 10: 10 20 30 40 50 60 70 80
The least common multiple is 70, becasue is the first common number in each list.
Hence the 70th person in the line will win both prizes.
HELP! 100 POINTS!!!
A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.
Recipe A Recipe B
Sample #1 26 67
Sample #2 48 89
Sample #3 22 56
A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.
B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?
Answer:
Question A: They should add product B because it has a 69% rate of approval. They can be 69% confident that the addition of product B will be successful.
Question B: 31% of people would prefer cookie A over cookie B
Step-by-step explanation:
Rectangle ABCD is shown with the dimensions given in units. The length of AB is greater than the length of AD which inequality represents this situation?
A: 9x-16<1.5+42
B: 9x-16>1.5x+42
C: 10.5x<26
D: 10.5x>26
Answer:
B
Step-by-step explanation:
it is simple.
because AB > AD, their size representations must have the same relationship.
therefore,
9x - 16 > 1.5x + 42
that could be simplified to
7.5x > 58
The inequality that represents AB > AD is B: 9x - 16 > 1.5x + 42.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, In Rectangle ABCD the length of AB is greater than the length of AD.
∴ The inequality that represents this is AB > AD which is,
9x - 16 > 1.5x + 42.
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Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual
mean of 53.2 degrees.
Low Temperature (o F)
Frequency
40-44 45-49 50-54 55-59
1
6
9
6
The mean of the frequency distribution is
(Round to the nearest tenth as needed.)
degrees.
...
60-64
3
Answer:
7777777777777777777777770
Step-by-step explanation:
7777777777777777777777770
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.
Maximum heightGiven equation:
y = 88t - 16t²
Maximum height dy/dt = 0
88-32t = 0
32t = 88
t = 88/32sec
t = 2.75sec
Hence,
Maximum height attained by the ball :
Maximum height attained by the ball = 88(2.75)-16(2.75)²
Maximum height attained by the ball = 242 - 121
Maximum height attained by the ball = 121 feet
Therefore the maximum height is 121 feet.
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A certain standardized test has a mean of 421 and a standard deviation of 18. For a student to score higher than 30.85% of those who took the exam, what score would be necessary?
The score required for the exam so that the score is higher than 30.85% is 412 for certain standardized test.
What is defined as the z-score?A Z-Score is a measurable statistic of a score's connection to the mean among a set of scores.A Z-score can tell a trader whether a value is characteristic for a given data set or atypical.In overall, a Z-score of less than 1.8 indicates that a company may be on the verge of bankruptcy, whereas a score nearer to 3 indicates that a company is in good financial standing.The formula for finding the z-score is;
z = (x - μ)/σ
x = sample size
μ = mean of the population
σ = standard deviation of the population.
The given values are-
μ = 421
σ = 18
Probability = 30.85% = 0.3085
Check the z-score from the negative z table for 0.3085
z score = -0.5
Put the values in z formula and find x.
z = (x - μ)/σ
-0.5 = (x - 421)/18
Simplifying;
x = -9 + 421
x = 412
Thus, the score required for the standardized test is found as 412.
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The numbers of trading cards owned by 9 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
352, 409, 424, 471, 497, 503, 515, 525, 561
Send data to calculator
Suppose that the number 561 from this list changes to 768. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
OOO
It decreases by
It increases by
It stays the same.
It decreases by .
0.
It increases by 0.
It stays the same.
X
S
The mean increases by 23 and the median stays the same.
What are the mean and median?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the middle value.
Given the data set: 352, 409, 424, 471, 497, 503, 515, 525, 561
(a) Mean = [tex]\frac{352+409+424+471+497+503+515+525+561}{9}[/tex]
Mean = [tex]\frac{4257}{9}[/tex]
= 473
The number 561 from this list changes to 768.
New mean = [tex]\frac{352+409+424+471+497+503+515+525+768}{9}[/tex]
= [tex]\frac{4464}{9}[/tex]
= 496
Thus, the mean increases by 496 - 473 = 23.
(b) Median = mid value
= 497
When the number 561 changes to 768, still the mid value will remain the same i.e. the median remains the same.
Therefore, the mean increases by 23 and the median stays the same.
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HELP ME QUICK!! I’LL MARK YOU BRAINLIEST!!
3-8. Find the distance between each pair of points if they were graphed on a number line. Represent your work
using absolute value symbols.
a. -10 and 10
b. -15 and -7
find all real and complex zeros for f(x)=x^3-x^2+3x-3
The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively
How to determine the zeros of the function?The equation of the function is given as
f(x) = x³ - x² + 3x - 3
Group the terms of the function in two's
So, we have the equation
f(x) = (x³ - x²) + (3x - 3)
Factor each group in the function
f(x) = x²(x - 1) + 3(x - 1)
Factor out x - 1
f(x) = (x² + 3)(x - 1)
Set to 0
(x² + 3)(x - 1) = 0
This gives
x² = - 3 and x = 1
Evaluate the roots
x = ±i√3 and x = 1
Hence, the zeros of the equation are x = ±i√3 and x = 1
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Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)
Hello! So...
We are given the following to solve:
Solve for x.
[tex]6(x+3)-8=4x+2(4+x)[/tex]
_______________________________________________________
1. Expand both sides of the equation.
[tex]6(x+3)-8=6x+10[/tex]
[tex]4x+2(4+x)=6x+8[/tex]
[tex]6x+10=6x+8[/tex]
______________________________
2. Subtract 10 from both sides.
[tex]6x+10-10=6x+8-10[/tex]
_______________________________
3. Simplify.
[tex]6x=6x - 2[/tex]
_______________________________
4. Subtract 6x from both sides.
[tex]6x-6x=6x-2-6x[/tex]
_______________________________
5. Simplify.
[tex]0=-2[/tex]
^Notice, the sides are not equal in the solution. This being said, there would be no solution.
___________________________________________________
Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!
the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?
Answer:
The new price of the article is $270
Step-by-step explanation:
270-240/240
x 100% = 12.5%
12.5x240/100
= 30
Find the value of (-3/8) x (+8/15)
A. -1/5
B. -1/3
C. 11/15
D. 11/23
Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]
Step-by-step explanation:
Given expression
[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]
Combine the fractions
[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]
Cancel out the 8 on both the numerator and denominator
[tex]=\dfrac{-3}{ 15}[/tex]
Divide 3 on both the numerator and denominator
[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]
[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What is the sum of the first 7 terms for the geometric sequence with first term 3, seventh
term 46,875, and common ratio 5?
A. 58,593
B. 19,531
C. 35,154
The sum of the first 7 terms for the geometric sequence with first term 3, seventh term 46,875, and common ratio 5 is 58,583.
A geometric progression is a sequence where each and every succeeding term is formed by multiplying the preceding term by a constant number. That constant number is called common ratio.
The common ratio is provided to be 5. While the first term is 3.
The seventh term is 46875.
The formula for sum of n terms of a GP is,
Sn = a(rⁿ-1)/(r-1)
We have to find sum of seven terms,
Sn = a(r⁶.r - 1)/(r-1)
Putting,
a = 3
r = 5
n =6
Sn = 3(5⁶.5 - 1)/(5-1)
Sn = (3.5⁶.5 - 3)/4
Sn = (46875×5 - 3)/4
Sn = (234375-3)/4
Sn = 234372/4
Sn = 58593.
The sum is 58593.
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find the answer to this problem (15/16) - ( -3/16)
A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8
let y=ln(x^2+y^2) determine y prime at the point -(e^4-16)^1/2
dy/dx = -2√e⁴ - 16/e⁴ - 8 is differential equation .
The meaning of a differential equation?
An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics.y = In( x² + y² )
now doing implicit differentiation
dy/dx = d/dx In( x² + y² )
dy/dx = 1/(x² + y² ) × d/dx ( x² + y² )
dy/dx = 1/x² + y² × ( 2x + 2y dy/dx)
(x² + y² )dy/dx = 2x + 2y dy/dx
dy/dx (x² + y² - 2y) = 2x
dy/dx = 2x/(x² + y² - 2y)
we need to calculate dy/dx at ( - √e⁴ - 16 , 4 )
dy/dx = [tex]\frac{2 * ( - \sqrt{e^{4} - 16} }{-\sqrt{(e^{4 - 16)^{2} }+ ( 4)^{2} - 2 * 4 } }[/tex]
dy/dx = - 2√e⁴ - 16/e⁴ - 16 + 16 - 8
dy/dx = -2√e⁴ - 16/e⁴ - 8
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go fast if you are smart.
see attachment beloww.
[tex]3x + x + (x + 12) = 152[/tex]
<AOD =<COB(VERTICAL OPPOSITE ANGLES)
[tex]3x + x + x = 152 - 12 \\ 5x = 140 \\ \frac{5x}{5} = \frac{140}{5} \\ x = 28[/tex]
x=28°
be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT
i.e <COE,<EOF AND <FOB
Answer:x=28°
Step-by-step explanation:
152=3x+x+x+12
152=5x+12
140=5x
x=28
Rylie ate 12 of the 20 grapes that her mom packed in her lunch which decimal is equivalent to the fraction of grapes Riley ate?
Answer: 0.6
Step-by-step explanation: To find the decimal you seek, you put 12 over 20, 12/20. That means you divide it, so 12 divided by 20 is 0.6, or 60%.
help meeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
2320 is what percent of 2000
[tex]3-\sqrt{x} 5[/tex]
The value of the expression given as 3 - √x⁵ is 3 - x^2√x
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
3 - √x⁵
Express 5 as the sum of 4 and 1
So, we have the following equation
3 - √x⁵ = 3 - √x^(4 + 1)
Apply the law of indices to expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √(x^4 * x)
Next, we expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √x^4 * √x
Evaluate the square root of x^4
So, we have the following equation
3 - √x⁵ = 3 - x^2 * √x
Evaluate the product
So, we have the following equation
3 - √x⁵ = 3 - x^2√x
Hence, the value of the expression is 3 - x^2√x
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Which complex number has an absolute value of 5?
What is an equation in slope-intercept form for the line
perpendicular to y = 3x + 9 that
contains (-6, 3)?
An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.
What is slope-intercept form?The most "popular" type of a straight line is one with a slope-intercept. Due to its simplicity, this is helpful to a lot of students. The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.
The equation for a line written in slope-intercept form
y = mx + b
Where,
m is the slope, and b is the y-intercept.
We know that the slope of a line perpendicular to given equation becomes reciprocal with opposite sign.
So, here slope is 3 and in perpendicular line it will become -1/3.
Now we will go with slope-intercept form and put the values (-6, 3) as x and y in y = mx + b
⇒ 3 = -1/3(-6) + b
Lets solve for b
⇒ b = 3 - ( -1/3(-6))
= 3 - (2)
= 1
Now we have the desired equation
3 = -1/3(-6) + 1
Thus, An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.
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What is a different common Denominator you could use in problem 2
Answer:
what is the problem ???
Step-by-step explanation:
Make x the subject of m=n+x/p
mp=n+x the P on the right side cancels out now you want to shift the n to the left side by subtracting it from both sides x=mp-n so that leaves us with the solution. m=n+x/p first you want to move the P over to the left side by x P so that leaves us with the answer. ...
mp=n+X X=mp-n, where m=n+x/p multiplies p on both sides.
How can you change the formula so that x is the subject?
To change x to the subject:Identify the variable by:Arrange the terms in the equation so that they are all on the same side of the equal sign, or =.If more than one term contains x, factorization may be required. ...Make a change to ensure that there is only one x variable remaining to serve as the subject.To learn more about m=n+x/p refer to:
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x = mp - n ( x as the subject of m= n+ x/p)
How to make x the subject of m = n +x/p ?
[tex]m =\frac{n+x}{p} \\\\mp = n+ x\\\\mp - n = x\\\\x= mp -n[/tex]
What is making x the subject?
Making x the subject of a formula or equation requires rearranging the formula or equation such that we have a single x variable that is equal to the other variables in the formula.The equation should be rearranged so that each term containing x is on the same side of the equation.If more than one term contains x, factorization may be required.Only one x must be displayed at the end in order to make it the subject. A number or variable can have a positive or negative result when we square root it as an inverse operation.To learn more about making x the subject, refer:
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on a highway there are billboards located every 1 1/2 km there are 14 billboards in that highway how long is the highway
Answer:
1 1/2 = 3/2
3/2 x 14
= 42/2
=21
Step-by-step explanation:
Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x
It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.
Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.
Now let's analyze the functions from the problem.
[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.
Use these rules to find whether each function is increasing or decreasing.
Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.
Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10
As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.
A straight angle in radians is π radians.
Then, the minute hand rotates π radiansm=85kg, a=4.29m/s^write an expression for the magnitude of the force, F
The magnitude of force is 364.65 Kg / ( m/s²)
What is force?An influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate.
given:
m = 85 Kg
a= 4.29 m/s²
We know
Force = mass x acceleration
F= 85 x 4.29
Force = 364. 65
Hence, the magnitude of force is 364.65 Kg / ( m/s²)
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