Answer:
[tex]cos(x)=\frac{\sqrt{5}}{5}[/tex]
Step-by-step explanation:
we have that
[tex]tan(x)=-2[/tex]
The angle x is in quadrant IV
That means ---> The value of cos(x) is positive and the value of sin(x) is negative
Remember that
[tex]cos^2(x)+sin^2(x)=1[/tex] ----> equation A
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
so
[tex]-2=\frac{sin(x)}{cos(x)}[/tex]
[tex]sin(x)=-2cos(x)[/tex] ----> equation B
substitute equation B in equation A
[tex]cos^2(x)+(-2cos(x))^2=1[/tex]
solve for cos(x)
[tex]cos^2(x)+4cos^2(x)=1[/tex]
[tex]5cos^2(x)=1[/tex]
[tex]cos^2(x)=\frac{1}{5}[/tex]
square root both sides
[tex]cos(x)=\pm\frac{1}{\sqrt{5}}[/tex]
but remember that the value of cos(x) is positive (IV quadrant)
[tex]cos(x)=\frac{1}{\sqrt{5}}[/tex]
simplify
[tex]cos(x)=\frac{\sqrt{5}}{5}[/tex]
What is the simple interest earned on $1,200 at 3.5% for five years?
A. $180.00
B. $210.00
C. $318.00
D. $201.00
Answer:
B
Step-by-step explanation:
210=1200*.035*5
The sum of the first three terms of a geometric progression is 126. If 14, 36, and 4 are added to each of these terms, respectively, then the new numbers form an arithmetic progression. Find the sixth term of the geometric progression
Answer:
if r=4:
[tex]\displaystyle a_6=6144[/tex]
if r=1/4:
[tex]\displaystyle a_6=\frac{3}{32}[/tex]
Step-by-step explanation:
Geometric and Arithmetic Progressions
We define a geometric progression when each term [tex]a_n[/tex] is defined as the previous term [tex]a_{n-1}[/tex] times a constant called the common ratio. The iterative formula is
[tex]\displaystyle a_n=a_1.r^{n-1}[/tex]
In an arithmetic progression, each term is found by adding a constant called common difference, to the previous term
[tex]\displaystyle a_n=a_1+(n-1).r[/tex]
We are given the condition that the sum of the three first terms of a geometric progression is 126
[tex]\displaystyle a_1+a_2+a_3=126[/tex]
Using the iterative formula, we have
[tex]\displaystyle a_1+a_1.r+a_1.r^2=126[/tex]
Taking a common factor
[tex]\displaystyle a_1(1+r+r^2)=126....[eq\ 1][/tex]
We also know that if 14, 36, and 4 are added to each term, respectively, the new numbers form an arithmetic progression. It means they will have a common difference. The new numbers will be
[tex]\displaystyle a_1'=a_1+14[/tex]
[tex]\displaystyle a_2'=a_2+36[/tex]
[tex]\displaystyle a_3'=a_3+4[/tex]
The common difference between term 2 and term 1 is
[tex]\displaystyle a_2'-a_1'=a_2+36-a_1-14[/tex]
Using the iterative formula again
[tex]\displaystyle a_2'-a_1'=a_1.r-a_1+22[/tex]
The common difference between term 3 and term 2 is
[tex]\displaystyle a_3'-a_2'=a_3+4-a_2-36[/tex]
Using the iterative formula again
[tex]\displaystyle a_3'-a_1'=a.r^2-a.r-32[/tex]
Both common differences must be equal
[tex]\displaystyle a_1.r-a_1+22=a_1.r^2-a_1.r-32[/tex]
Rearranging
[tex]\displaystyle 2a_1r-a_1r^2-a_1=-54[/tex]
Solving for [tex]a_1[/tex]
[tex]\displaystyle a_1=\frac{54}{1-2r+r^2}......[eq\ 2][/tex]
Replacing in eq 1
[tex]\displaystyle \frac{54(1+r+r^2)}{1-2r+r^2}=127[/tex]
Dividing by 18 and cross-multiplying
[tex]\displaystyle 3+3r+3r^2=7-14r+7r^2[/tex]
Rearranging we have a second-degree equation
[tex]\displaystyle 4r^2-17r+4=0[/tex]
Factoring
[tex]\displaystyle (r-4)(4r-1)=0[/tex]
The solutions are
[tex]\displaystyle r=4\ ,\ r=\frac{1}{4}[/tex]
If r=4, and using eq 2
[tex]\displaystyle a_1=\frac{54}{1-8+16}=6[/tex]
Having [tex]a_1[/tex] and r, we compute [tex]a_6[/tex]
[tex]\displaystyle a_6=a_1.r^5=6.(4)^5[/tex]
[tex]\displaystyle a_6=6144[/tex]
If we use the other solution r=1/4
[tex]\displaystyle a_1=\frac{54}{1-\frac{1}{2}+\frac{1}{16}}=\frac{54}{\frac{9}{16}}[/tex]
[tex]\displaystyle a_1=96[/tex]
The sixth term is
[tex]\displaystyle a_6=96(\frac{1}{4})^5=\frac{96}{1024}[/tex]
[tex]\displaystyle a_6=\frac{3}{32}[/tex]
Both solutions are feasible
Final answer:
In this question, we explore geometric and arithmetic progressions to find the 6th term of a geometric progression given specific conditions.
Explanation:
Geometric Progression (GP): In a GP, the sum of the first three terms is 126. Let the first term be a and the common ratio be r. The sum of the first three terms can be represented as a + ar + ar^2 = 126.
Arithmetic Progression (AP): Adding 14, 36, and 4 to the terms of the GP forms an AP. The common difference of this AP is 36 - 14 = 22.
Finding the 6th Term: Using the formula for the nth term of a GP, the 6th term can be calculated as a * r^5.
Clare said that (4/3) ÷ (5/2) is (10/3). She reasoned: (4/3) ⋅ 5 = (20/3) and (20/3) ÷ 2 = (10/3). Explain why Clare's answer and reasoning are incorrect. Find the correct quotient.
Answer:
Correct quotient =
[tex]\dfrac{8}{15}[/tex]
Step-by-step explanation:
We are given he following in the question:
[tex]\text{Clare's calculation:}\\\\\dfrac{4}{3}\div \dfrac{5}{2} = \dfrac{10}{3}\\\\\text{Clare's reason:}\\\\\dfrac{4}{3}\times 5 = \dfrac{20}{3}, \dfrac{20}{3} \div 2 = \dfrac{10}{3}[/tex]
Clare's, reason is incorrect.
The correct quotient can be calculated in the following manner:
[tex]\dfrac{4}{3}\div \dfrac{5}{2}\\\\= \dfrac{4}{3}\times \dfrac{2}{5} = \dfrac{8}{15}[/tex]
Clare simply multiplied the fraction with 5 and divided the product with 2 which is incorrect. We have to multiply the fraction with the reciprocal of divisor.
Answer:
The answer is 8/15
Step-by-step explanation:
4/3 divided by 5/2 is the same as 4/3 times 2/5
4/3 times 2/5= 8/15
8/15 is the answer
She is wrong because if you want to do it you have to multiply the fraction with 5 and then MULTIPLY it by 2 not divide it by 2.
How do you do this problem?
Answer:
(2, 2)
Step-by-step explanation:
According to the distance formula, the distance between two points is:
d² = (x₂ − x₁)² + (y₂ − y₁)²
If one point is (x, y) and the other point is (1, 4), then:
d² = (x − 1)² + (y − 4)²
We know y² = 2x, so x = ½ y². Substituting:
d² = (½ y² − 1)² + (y − 4)²
The minimum distance is when dd/dy equals 0. We can either simplify first by distributing, or we can immediately take the derivative using chain rule.
If we distribute and then take the derivative:
d² = ¼ y⁴ − y² + 1 + y² − 8y + 16
d² = ¼ y⁴ − 8y + 17
2d dd/dy = y³ − 8
If we use chain rule instead without distributing:
2d dd/dy = 2(½ y² − 1) (y) + 2(y − 4)
2d dd/dy = y³ − 2y + 2y − 8
2d dd/dy = y³ − 8
Setting dd/dy equal to 0:
0 = y³ − 8
y = 2
x = ½ y²
x = 2
(2, 2) is the point on the parabola closest to (1, 4).
Graph: desmos.com/calculator/m4apqwsduk
Find the exponential function that satisfies the given conditions: Initial value = 64, decreasing at a rate of 0.5% per week
f(t) = 0.5 ⋅ 0.36t
f(t) = 64 ⋅ 1.005t
f(t) = 64 ⋅ 0.995t
f(t) = 64 ⋅ 1.5t
Answer:
Step-by-step explanation:
An exponential function is of the form
[tex]y=ab^x[/tex]
where a is the initial value and b is the growth/decay rate. Our initial value is 64. That's easy to plug in. It goes in for a. So the first choice is out. Considering b now...
If the rate is decreasing at .5% per week, this means it still retains a rate of
100% - .5% = 99.5%
which is .995 in decimal form.
b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1. .995 is less than 1 so it is a rate of decay. The exponential function is, in terms of t,
[tex]f(t) = 64(.995)^t[/tex]
Answer:
f(t) = 64 ⋅ 0.995t
Step-by-step explanation:
Add me on S n a p c h a t :) yofav_tai
Write an equation of the line containing the given point and perpendicular to the given line.
(7, -4); 9x+7y=4
please try to help i'm really struggling with this one:)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y on the vertical axis) / (change in the value of x on the horizontal axis)
The equation of the given line is
9x+7y=4
7y = 4 - 9x = -9x + 4
y = -9x/7 + 4/7
Comparing with the slope intercept form, slope = -9/7
If the line passing through the given point is perpendicular to the given line, it means that its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (7,-4) is 7/9
To determine the intercept, we would substitute m = 7/9, x = 7 and y = - 4 into y = mx + c. It becomes
- 4 = 7/9×7 + c = 49/9 + c
c = - 4 - 49/9
c = - 85/9
The equation becomes
y = 7x/9 - 85/9
There was a dog and a cat they both had walked 2 miles in the morning and in the afternoon the dog walked 3 miles how many miles did the cat and dog walk.
Step-by-step explanation:
In the morning cat and dog walked 2 miles.
Total distance traveled in the morning = 2 x 2 = 4 miles
In the afternoon the dog walked 3 miles
Total distance traveled in the afternoon = 3 miles
We need to find how many miles did the cat and dog walk.
Total distance traveled by cat and dog = Total distance traveled in the morning + Total distance traveled in the afternoon
Total distance traveled by cat and dog = 4 + 3
Total distance traveled by cat and dog = 7 miles
Identify which value represents the sample mean and which value represents the claimed population mean.A) American households spent an average of about $52 in 2007 on Halloween merchandise such as costumes, decorations and candy. To see if this number had changed, researchers conducted a new survey in 2008 before industry numbers were reported. The survey included 1,500 households and found that average Halloween spending was $58 per household.B) The average GPA of students in 2001 at a private university was 3.37. A survey on a sample of 203 students from this university yielded an average GPA of 3.59 in Spring semester of 2012.
Answer:
A) the average value of Halloween spending of $52 in 2007 is claimed population mean and the value of Halloween spending $58 per household found out through survey done in 2008 is the sample mean
B) the average GPA 3.37 in 2001 is the claimed population mean and the average GPA through survey of 203 students is sample mean.
Step-by-step explanation:
'Claimed population mean' means the average value not taken through a survey of a sample size therefore in both options the average value is Claimed population mean
'Sample mean' is taken from a group of population therefore the value in both options taken through a survey of a sample population is Sample mean
A sample is a portion of a whole group. We use sample to predict data about the whole group(called population).
A) The sample mean is: average Halloween spending was $58 per household (survey in year 2008)
The population mean is: American households spent an average of about $52 in 2007
B) The sample mean is: average GPA of 3.59 (survey in 2012)
The population mean is: average GPA of students in 2001 at a private university was 3.37
What is sample mean and sample, and population mean and population?Sample is a portion researchers or any interested person or community takes out from a big group(called population) so as to predict properties of that big group.
We work on sample because big groups are sometimes too big that we can't cover it all in normal time. There are some other reasons too because of which we work on samples instead of population.
Sample mean is the mean obtained in the sample taken.
Population mean is hypothesized mean of population(since we don't know real mean of population, that's why hypothesized).
Thus, for given condition, we have:
A) The sample mean is: average Halloween spending was $58 per household (survey in year 2008)
The population mean is: American households spent an average of about $52 in 2007
B) The sample mean is: average GPA of 3.59 (survey in 2012)
The population mean is: average GPA of students in 2001 at a private university was 3.37
Learn more about sample mean and population mean here:
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A baseball game is scheduled for Saturday. If it rains on Saturday, the game will be moved to Sunday. If it rains on Saturday and Sunday, the game will be cancelled. There is a 30% chance that it will rain on Saturday and a 60% chance that it will rain on Sunday. What is the probability that it will rain on both days and the game will be cancelled?
A. 18
B. 28
C. 30
D. 55
E. 90
Answer:
A. 18%
Step-by-step explanation:
For independent events:
P(A and B) = P(A) × P(B)
P = 0.30 × 0.60
P = 0.18
There is an 18% probability that it will rain on both days and the game will be canceled.
The amount of turn between two straight lines that have a common end point is called __________.
Answer:
Angle
Step-by-step explanation:
In the image I added you can observe that the common endpoint is called a vertex, and the "turn" or aperture formed between the two straight lines (or arms) that converge in the vertex, is the angle and it can be measured on degrees.
I hope you find this information usefun and interesting! Good luck!
Final answer:
The amount of turn between two straight lines that have a common end point is referred to as an angle. This concept is central to the study of geometry and aids in measuring the difference in direction where two lines meet. Angles are typically measured in degrees as a part of spherical trigonometry and other geometric calculations.
Explanation:
The amount of turn between two straight lines that have a common end point is called an angle. An angle measures the difference in direction between two lines that extend from the same point. The concept of angle is found in the principles of geometry, where it is foundational to understanding shapes and their properties.
In more mathematical terms, the angle between two intersecting lines can also be seen as the distance between their poles when conceptualized on a sphere, a concept from advanced geometry and spherical trigonometry. The measurement of this angle is generally given in degrees, where a full circle is 360 degrees, and this system of measurement allows us to apply the angle measure to various geometric constructions and theorems, such as determining the sum of the angles of a triangle.
Using the dot plots provided, what is the mean absolute deviation of the height of basketball players, rounded to the nearest tenth?
Answer:
[tex] MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0[/tex]
Step-by-step explanation:
Previous concepts
The mean absolute deviation or MAD "is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values)". And is given by this formula:
[tex] MAD= \frac{1}{n} \sum_{i=1}^n |x_i -\bar X|[/tex]
Solution to the problem
Assuming the info from the picture. So then the data is this one:
66,69,70,70,71,72,72,72,73,73,74,75,75,75
So the first step is find the mean for the dataset with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And if we replace the values we got:
[tex]\bar X = \frac{66+69+70+70+71+72+72+72+73+73+74+75+75+75
}{14}=71.929[/tex]
And now we need to subtract for each value the mean like this:
Data [tex] X_i -\bar X[/tex]
66 5.929
69 2.929
70 1.929
70 1.929
71 0.929
72 0.0714
72 0.0714
72 0.0714
73 1.0714
73 1.0714
74 2.0714
75 3.0714
75 3.0714
75 3.0714
Now we need to add the deviations and divide by the the number of data values and we got:
[tex] MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0[/tex]
A student wants to find point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4. Point A is at -6 and point B is at 2. The student's work is shown .
Answer: A No, the student should have added 3 + 4 to get the total number of sections, and used the fraction Three-sevenths instead of Three-fourths.
Step-by-step explanation:
Simplify √192
√83
√106
√643
√824
Answer:
[tex]\displaystyle 8\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\displaystyle \sqrt{3 \times 64} = 8\sqrt{3}[/tex]
I am joyous to assist you anytime.
Answer:
the answer is: [tex]8\sqrt{3}[/tex]
good luck
As a prize a contest winner get to draw out one bill at a time from a box containing 10 five dollar bills 10 ten dollar bills and 10 twenty dollar bill the drawing end when 3 bill of the same denomination are drawn and of course the contest winner keeps whatever he was drawn. What is the largest sum of money that can be won under these condition?
The largest sum of money that can be won under these condition is $90.
To start finding the maximum able to be drawn, they contest winner would draw 3 [tex]\times[/tex] $20 bills = $60.
Prior to drawing the 3rd $20 bill, the contest winner could draw 2 of the $5 bills and 2 of the $10 bills.
This added to the $20 bills they had drawn would give:
(2 [tex]\times[/tex] $5) = $10
(2 [tex]\times[/tex] $10) = $20
Add all the ability to win the contest.
$10 + $20 + $60 = $90
Thus, the largest sum of money that can be won under these condition is $90.
Mailing on a weekly salary of $385 plus a 70% commission on a sale at a gift shop how much would she make in a work week if she had sold for 4300 worth of merchandise
Answer:
Total Amount made by Mailing in a week is $3395.
Step-by-step explanation:
Given:
Fixed Salary = $385
Percentage of Commission on Sale = 70%
Total Sale = 4300
we need to find Total amount made by Mailing in a week.
We will first find the amount made on commission.
Amount made on commission = [tex]\frac{70}{100} \times 4300 = \$3010[/tex]
Now Total Amount made by Mailing in a week is equal to sum of Fixed Salary and Amount made on commission.
Framing in equation form we get;
Total Amount made by Mailing = $385 + $3010 = $3395.
Hence Total Amount made by Mailing in a week is $3395.
T.J. Had a car loan for $5800. Over the course of the loan, he paid a total of $1508 in interest at a rate of 6.5%. Over how many months did T.J. Pay of the car loan?
Answer: it took T.J. 48 months to pay the car loan.
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P = principal or amount loaned
R = interest rate
T = time in years.
I = interest
From the information given,
P = $5800
R = 6.5%
Over the course of the loan, he paid a total of $1508 in interest. Therefore,
I = $1508 Therefore,
1508 = (5800×6.5×T)/100
1508 = 377T
T = 1508/377 = 4 years
Assuming there are 12 months in a year, the number of months in 4 years would be 4×12 = 48 months
40 points!!
What's the equation for this ellipse?
Answer:
(x +5)²/4 +(y +8)²/36 = 1
Step-by-step explanation:
The equation of an ellipse with center (h, k) and semi-axes "a" and "b" (where "a" is in the x-direction and "b" is in the y-direction) can be written as ...
((x -h)/a)² +((y -k)/b)² = 1
Here, the center is at (h, k) = (-5, -8), and the semi-minor axis is a=2, while the semi-major axis is b=6.
The equation can be written as ...
((x +5)/2)² +((y +8)/6)² = 1
More conventionally, it is written ...
(x +5)²/4 +(y +8)²/36 = 1
Answer:
The answer to your question is [tex]\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1[/tex]
Step-by-step explanation:
From the graph we know that the center = (-5, -8) and a= 6 and b = 2.
See the picture below
Here, we have a vertical ellipse so the equation is
[tex]\frac{(x - h)^{2} }{b^{2} } + \frac{(y - k)^{2} }{a^{2} } = 1[/tex]
Substitution
[tex]\frac{(x + 5)^{2} }{2^{2} } + \frac{(y + 8)^{2} }{6^{2} } = 1[/tex]
[tex]\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1[/tex]
PLEASE PLEASE HELP ASAP
Answer: basically just set them equal and solve
Step-by-step explanation: vertical angles are xongruent
Lizzie solve you equation 2+3x+3=3(x+3)+2x rand got an answer of x=2. Without solving the equation, determine whether or not Lizzy's answer is correct. Show all work and provide reasoning for your answer.
Lizzie's answer is not right as two sides are not equal.
Step-by-step explanation:
Given equation is;
2+3x+3=3(x+3)+2x
Lizzy got;
x=2
We will put this value of x in Equation to determine if the sides are equal or not.
[tex]2+3(2)+3=3(2+3)+2(2)\\2+6+3=3(5)+4\\11=15+4\\11\neq 15[/tex]
Lizzie's answer is not right as two sides are not equal.
Keywords: linear equation, addition
Learn more about addition at:
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Payment history is ____ of your credit score. 30% 35% 10% 15% Descrip
Answer:35%
Step-by-step explanation:
Tom is saving for his new motorcycle. He has already saved $450 and continues to save $75 each month. How many months will it take to save at least 2,175?
Answer:
Tom required 23 months to save at least $2175.
Step-by-step explanation:
Given:
Money already Saved = $450
Money Needs to be saved = $2,175
Each month saving = $75
We need to find the Number of months required to save at least $2,175
Solution:
Let the number of months be 'x'.
Now We can say Total Money which is already save plus Each month saving multiplied by number of months should be equal to Money Needs to be saved.
Framing in equation form we get;
[tex]450+75x=2175[/tex]
Solving the equation we get;
We will Subtract both side by 450 we get;
[tex]450+75x-450=2175-450\\\\75x=1725[/tex]
Now By dividing 75 on both side we get;
[tex]\frac{75x}{75}= \frac{1725}{75}\\\\x= 23\ months[/tex]
Hence Tom required 23 months to save at least $2175.
Fifty numbers are rounded to the nearest integer and then summed. if the individual round-off errors are uniformly distributed between -0.5 and 0.5, what is the approximate probability that the resultant sum differs from the exact sum by more than 3?
Answer:
0.0414
Step-by-step explanation:
Each error is uniform between -0.5 and 0.5, so the mean error is 0, and the variance is (b-a)²/12 = (0.5-(-0.5))²/12 = 1/12
If we sum 50 numbers, the errors will sum with each other, and the resultant mean and variance will be summed, because the errors are independent. The mean of the sum of 50 number is 0*50 = 0, and the variance in 50/12.
The central limit theorem states that the sum of identically distributed random variables has distribution approximately normal. In this case, if we call X the sum of the 50 random numbers, then X has distribution approximately N(μ = 0,σ = √(50/12)). If we divide X with its standard deviation √(50/12), we obtain (approximately) a standard normal random variable. Lets call Y = X/√(50/12). Y distribution is approximately N(0,1). Y is called the standarization of X.
The values of the cummulative distribution of the standard Normal random variable, denoted by Ф, are tabulated; you can find those values in the attached file. We want the error to be greater than 3. We will calculate the complementary event: the probability for the error to be between -3 and 3, and substract from 1 that result
P(-3 ≤ X ≤ 3) = P( -3/√(50/12) ≤ X/√(50/12) ≤ 3/√(50/12)) = P(-3/√(50/12) ≤ Y ≤ 3/√(50/12)) = Ф(3/√(50/12)) - Ф(-3/√(50/12))
Since the density function of a normal random variable centered at 0 is symmetric, then Ф(-3/√(50/12)) = 1- Ф(3/√(50/12)), as a result
P(-3 ≤ X ≤ 3) = Ф(3/√(50/12)) - Ф(-3/√(50/12)) = 2 Ф(3/√(50/12)) - 1 = 2 * Ф(2.04) - 1 = 2*0.9793 - 1 = 0.9586
hence, the probability for the error to be greater thar 3 is 1-0.9586 = 0.0414
If a lift takes 40 seconds to go to the fourth floor from the ground floor then how much time will it take to go to sixteenth floor from the fourth floor
Answer:
120 seconds
Step-by-step explanation:
if the elevator is moving at a constant rate, then it takes 10 seconds to move up one floor, to travel from the 4th to the 16th floor, it will take 120 seconds total to travel 10 floors
Some coconuts fall out of a tree. Mercy is greedy and takes half, Joe grabs what he can, and gets five more than Frank. Frank gets one coconut. How many fell off the tree
Answer:
Total Number of Coconuts which fell from tree are 14.
Step-by-step explanation:
Given:
Some coconuts fall out of a tree.
Mercy is greedy and takes half,
Joe grabs what he can, and gets five more than Frank.
Frank gets one coconut.
We need to find Total number of coconuts fell from tree.
Number of Coconuts franks has = 1
Now Given that Joe grabs what he can, and gets five more than Frank.
Number of Coconuts Joe has = Number of Coconuts franks has + 5 = 1 + 5 = 6
Also Given Mercy is greedy and takes half.
It means mercy took half of coconuts and rest half were took by Frank and Joe
Hence Number of Coconuts Mercy has = Number of Coconuts franks has + Number of Coconuts Joe has = 6 + 1 = 7
Now Total Number of Coconuts is equal to sum of Number of Coconuts Mercy has and Number of Coconuts Joe has and Number of Coconuts frank has.
Total Number of Coconuts = 7 + 1 + 6 = 14
Hence Total Number of Coconuts which fell from tree are 14.
Mrs. Bailey gives a test, and her students’ scores range from 30 to 70. She decides to curve the scores, so that they range from 65 to 95. Let "x" be an original score, and "y" be a curved score. Using the ordered pairs (30,65) and (70,95), write the equation in slope/intercept form that she should use to curve the test scores.
Answer:
f(x) = x*3/4 + 42.5
Step-by-step explanation:
The original difference between the pair is 70 - 30 = 40
The new difference between the pair is 95 - 65 = 30
Since the differences are not the same, Mrs Bailey must first perform a (slope) multiplication by a factor of 30/40 or 3/4
Then 30 * 3/4 = 22.5
Then she can shift the scores up by 65 - 22.5 = 42.5 in order to get the range from 65 to 95
Therefore, f(x) = x*3/4 + 42.5. We can test that
f(30) = 30*3/4 + 42.5 = 65
f(70) = 70*3/4 + 42.5 = 95
Which statements about triangle JKL are true? Select two options.
M is the midpoint of line segment KJ.
N is the midpoint of line segment JL.
MN = One-halfKJ
MN = 4.4m
MN = ML
Answer: 2nd and 3rd statement
Step-by-step explanation:
From the diagram, the 1st statement is wrong, the 2nd statement is correct
To know which of the rest of the statement is correct we have to find the value of MN
So we use the cosine rule to find the angle inside the triangle at point L
c2 = a2+b2-2abcosC
For our triangle
c= 12.8
b= 5.9+5.9=11.8
a= 3.7+3.7=7.4
C = ?
(12.8)2 = (7.4)2 + (11.8)2 - 2x11.8x7.4cosC
163.84 = 54.76+739.24 - 174.64cosC
163.84 = 194 - 174.64cosC
163.84-194 = -174.64cosC
-30.16 = -174.64cosC
-30.16/-174.64 =cosC
cosC = 0.1727
cos-1(0.1727) = 80.06
C = 80.06 degrees
So we use this value to find length MN with also cosine rule from the triangle NML
c2 = a2+b2-2abcosC
c = ?
a = 5.9
b = 3.7
C = 80.06
c2 = (5.9)2 + (3.7)2 - 2x5.9x3.7cosC
c2 = 34.81 + 13.69 - 43.66x0.1727
c2 = 48.5 - 7.54
c2 = 40.96
c = root(40.96)
c = 6.4
Which is half of KJ
So therefore, the third statement is correct
Answer:
b,c
Step-by-step explanation:
i did the test:)
Barbara is converting 78°F to degrees Celsius. First, she subtracts 32 from 78. What is the next step?
A.) multiply 46 by 5/9
B.) multiply 46 by 9/5
C.) add 273 to 46
D.) subtract 273 from 46
Answer:
A.) Multiply 46 by 5/9
Step-by-step explanation:
The formula to convert Fahrenheit degrees to Celsius degrees is as follows:
[tex]\\ C = \frac{5}{9}*(F-32) [/tex]
So, converting 78°F to °C, according this previous equation is:
[tex]\\ C = \frac{5}{9}*(78-32) [/tex] [Barbara subtracts 32 from 78]
[tex]\\ C = \frac{5}{9}*(46) [/tex] [Barbara multiplies 46 by 5/9]
[tex]\\ C = \frac{5*46}{9} [/tex]
[tex]\\ C = \frac{230}{9} = 25.56 [/tex] or 25.56°C
Answer:
A) multiply 46 by 5/9
Step-by-step explanation:
Multiplying by number is the same as?
Multiplying is simply the same as repeated addition. For example:
[tex]5 \times 3 = 5 + 5 + 5[/tex]
Or:
[tex]4 \times 7= 4 + 4 + 4 + 4 + 4 + 4 + 4[/tex]
Answer:
Below.
Step-by-step explanation:
Adding the number the same number of times as the multiplier.
For example
2 * 3 = 2 + 2 + 2.
Quick movers charges $50 a day and $0.50 per mile . ABC movers charges $45 a day and $0.75 a mile at how many miles Is the cause the same for both companies?
Answer:
At 20 miles both companies cost will be same.
Step-by-step explanation:
Let Number of miles be 'x'.
Given:
Quick movers charges $50 a day and $0.50 per mile .
So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.
framing in equation form we get;
Quick movers charges = [tex]50+0.5x[/tex]
Also Given:
ABC movers charges $45 a day and $0.75 per mile .
So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.
framing in equation form we get;
ABC movers charges = [tex]45+0.75x[/tex]
We need to find the number of miles at which both companies cost are are same.
Solving to find the same we get;
[tex]50+0.5x=45+0.75x[/tex]
Combining like terms we get;
[tex]0.75x-0.5x=50-45\\\\0.25x=5[/tex]
By Division property of equality we will divide both side by 0.25 we get;
[tex]\frac{0.25x}{0.25} =\frac{5}{0.25} \\\\x= 20 \ miles[/tex]
Hence at 20 miles both companies cost will be same.
Final answer:
By setting up an equation to equate the charges of Quick Movers and ABC Movers, it is determined that at 20 miles, the costs for both companies will be the same.
Explanation:
To find at how many miles the cost for both Quick Movers and ABC Movers is the same, we set up an equation where the cost of each company is equal. Quick Movers charges $50 a day plus $0.50 per mile, and ABC Movers charges $45 a day plus $0.75 per mile. Let's use m to represent the miles.
The equation based on the costs given will be:
50 + 0.50m = 45 + 0.75m
To solve the equation, we first bring all the m terms to one side and the constants to the other:
0.50m - 0.75m = 45 - 50
This simplifies to:
-0.25m = -5
Dividing both sides by -0.25, we find:
m = 20
Therefore, the cost for both companies is the same at 20 miles.
Julia’s frogs are 2 5 of the amount of Rimma’s frogs. If Rimma gives 1 2 of her frogs to Julia, what will be the ratio of Julia’s frogs to Rimma’s frogs?
Answer:the ratio of Julia’s frogs to Rimma’s frogs is 1.8 : 1
Step-by-step explanation:
Let x represent the total number of frogs that Rimma had.
Julia’s frogs are 2/5 of the amount of Rimma’s frogs. This means that the number of frogs that Julia had is
2/5 × x = 2x/5
If Rimma gives 1/2 of her frogs to Julia, the number of frogs that Julia gets from Rimma would be
1/2 × x = x/2 frogs. Total number of frogs that Julia would have becomes
2x/5 + x/2 = (4x + 5x)/10 = 9x/0
The number of frogs that Rimma has left would be 1/2 × x = x/2
The ratio of Julia’s frogs to Rimma’s frogs would be
(9x/10) / (x/2) = (9/5)/1
= 1.8 : 1