Answer:
Steps to find the equation of a line from two points:
Find the slope using the slope formula. ...
Use the slope and one of the points to solve for the y-intercept (b). ...
Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Step-by-step explanation:
Answer:
[tex]y=-2x+30[/tex]
where y is the weight of the cat (in pounds) and x is the number of months.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value when x is zero, so the initial value.
If the cat initially weighs 30 pounds, the y-intercept is 30.
The slope is the rate of change.
If the cat lost 2 pounds per month, then the rate of change is -2.
Therefore, the equation the models the given word problem is:
[tex]\boxed{\begin{minipage}{7 cm}\phantom{ww}\\$y=-2x+30$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is the weight of the cat (in pounds). \\ \phantom{ww}$\bullet$ $x$ is the number of months.\\\end{minipage}}[/tex]
Kari wins 1,282 tickets at an arcade. For each group of 65 tickets, she will receive a prize. Kari solves the problem 1,282 ÷ 65 and determines that she has enough tickets right now for 19 prizes. What is the least number of additional tickets that Kari needs to win to have enough tickets for a 20th prize?and i need a step by step explanation.
Answer:
18 more tickets
Step-by-step explanation:
What we know:
We know that 65 Tickets is 1 Prize.
We know we have 1,282 tickets.
So if 65 tickets is one prize
then to figure out how many for twenty then we:
65 x 20 = 1300
Now to figure out how many more she needs at the least we:
1300 - 1282 = 18
So for 1 more prize she needs 18 more tickets.
Mr. Anderson decides to visit a childhood friend. His car gives him 24.23 miles to the gallon. Mr. Anderson has 4 gallons of fuel. Which of the following is true?
A: Mr. Anderson can travel 48.46 miles.
B: Mr. Anderson can travel 112.92 miles.
C: Mr. Anderson can travel 96.92 miles.
D: Mr. Anderson can travel 80.92 miles.
Answer:
C
Step-by-step explanation:
multiply 24.23 by 4
You are one of the retirement counselors at the Valley View Bank. You have been asked to give a presentation to a class of high school seniors about the importance of saving for retirement. Your boss has designed an example for you to use in your presentation. The students are shown five retirement scenarios and are asked to guess which yields the most money. Note: All annuities are ordinary annuities. Also, although some people stop investing, the money remains in the account and receives 10% interest compounded annually. Look over each scenario and make an educated guess as to which investor will have the largest accumulation of money invested at 10% over the next 40 years. Then for your presentation, calculate the final value for each scenario, how much each person actually contributed, and how much interest was earned. • Adam invests $1,200 per year and stops after 15 years (remember, the balance will remain in this account, earning 10% interest compounded annually for the remaining 25 years. • Becky waits 15 years, invests $1,200 per year for 15 years, and then stops (balance will earn int • Clare waits 15 years, then invests $1,200 per year for 25 years. • David waits 10 years, then invests $1,500 per year for 15 years, and then stops (balance will earn interest for the remaining 15 years). • Ellen waits 10 years, then invests $1,500 per year for 30 years.
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
[tex](1+10)^{15}[/tex]Venus invests $1,200 per year and stops after 15 years.
He can get money : [tex]1200*[/tex] [tex](1+10)^{15}[/tex] at the first year,
We can use ,
Compound interest formula, S = [tex]P*(1+i)^{n}[/tex]
Where,
P means the Principal
I means the interest
n means the year
S means the principal and interest
At the second year he can get,
= 1200 * [(1+[tex]\frac{10degrees}{1}[/tex]) + ([tex]1+[\frac{10degrees}{1} ]^{2}[/tex])
The money of first year has two years interest,
The money of second year has one year interest.
So, we can calculate the 15th year he can get :
= 1200 * [[tex](1+\frac{10degrees}{1}] ^{1}) +(1+(\frac{10degrees}{1} )^{2} )+......(1+(\frac{10degrees}{1})^{15} )[/tex]
= 1200 * [tex]\frac{(1*1)*(1-1*1^{15} )}{1-1*1}[/tex]
The sum of geometric progression,
[tex]S_{n} =\frac{a*(1-q)^{n} }{1-q}[/tex] , q≠1
= $ 41939.67
The rest of years he can get money :
= 41939.67 * ([tex](1+10percent))^{40-15}[/tex]
= $ 454404.053
Kevin can get money 1200* [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{15} )[/tex]
= 41939.67 at 30th year
Finally he can get money = 41936.67 [tex](1+\frac{10degrees}{1}) ^{40-15*0}[/tex]
= $ 108780.71
Rafael can get money : 1200 * [[tex](1+(\frac{10degrees}{1}) ^{1} )+.......(1+(\frac{10degrees}{1} )^{25} )[/tex]
= $ 129818.11
$454404.05 > $129818.11 > $108780.71
Therefore,
The retirement counselors at the Valley View Bank$454404.05 > $129818.11 > $108780.71, then the Venus have the largest accumulation.
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express the final answer in terms of log x, and log y
log x^3y^2
The logarithmic function log ( x³ y² ) when expressed in terms of log x and log y is 3 log ( x ) + 2 log( y).
The opposite of exponentiation is the logarithm. In other words, the exponent to which a fixed number, the base a, must be raised in order to create a specific number x, is represented by the logarithm of that number.
Consider the logarithmic function log x³ y⁴
Using the logarithmic formula,
log ( a b ) = log (a) + log (b)
We have,
log( x³ y² ) = log ( x³ ) + log( y² )
By applying the logarithmic property:
log ( xⁿ ) = n log x
We have,
log x³ y² = log ( x³ ) + log( y² )
log x³ y² = 3 log ( x ) + 2 log( y)
Therefore, the function log ( x³ y² ) in terms of log x and log y is 3 log ( x ) + 2 log( y).
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help meeeeeeeeeeeeee
Answer:
74.44
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]
If the ratio of red objects to blue objects is 3 : 1, what precent of the objects are red?
Answer:
75%
Step-by-step explanation:
If the ratio of red:blue is 3:1, then there are 4 (some multiple of 4) in all.
The ratio of red:total is 3:4
3/4 is .75, times by 100 to convert to a percent.
.75 × 100 is 75%
BAсThe sum of m AB and mBC is equal to:O 360° - MAC240" - MAC180т АС120
The sum of mAB and mBC is equal
360 - mAC
which makes otion A the correct answer
Find the sample standard deviation.
15 42 53 7 9 12 14 28 47
The answer to your question is s. sqrt (316.9) = 17.8 when you take the square root of that number. As a result, the correct response is 17.8.
This is further explained below.
What is the sample standard deviation?Generally, Because you need to calculate the sample standard deviation to answer the question, use the following formula:
[tex]s = \sqrt {{ \sum of x - \bar x}{(n - 1} }[/tex]
There are 9 numbers, there, so n - 1 = 8
find the mean
[tex]\bar x[/tex]: 15 + 42 + 53 + . . . + 47 = 227. 227 / 9
x= 25.2
After that, deduct one from each number and then square the output, as seen here:
(15 - 25.2) = 104.0 (42 - 25.2)²
= 282.2 (53 - 25.2)²
= 772.8
After that, total up all of those values. The response to this, using this illustration as an example, is
[tex]x=\frac{ 2,535.2}{ 8}[/tex]
x= 316.9.
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What 2 2/4 x 3 5/6
I need an answer quick because i need this answer.
[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]
ATTACHED IS THE SOLUTION
log 2 8 = 3 can be written in the form 2 A = B where
The equation written in exponential form is (a) 2³ = 8
What are exponents?A symbol used to denote the action of raising to a power that is written above and to the right of a mathematical phrase.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given equation is
㏒₂ 8 = 3
㏒ₐx = b
x = aᵇ
㏒₂8 = 3
8 = 2³
Hence, (a) 2³ = 8
Therefore, the equation written in exponential form is (a) 2³ = 8.
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Find the scale factor from triangle A to triangle B:
Answer:
Step-by-step explanation:
x=3?
Answer:
3
Step-by-step explanation:
If you multiply 1 by 3 it gives you 3, the side of triangle B. Using that scale factor. you can then take the side of triangle B that is 9 and divide it by 3. That gives you the missing side of triangle A.
Hope this helps! :)
How many
inches are in 3.5 miles
Answer:
221 760 inches
Step-by-step explanation:
So, 3.5miles * 63360= 221760 inches.
Formula: multiply the value in miles by the conversation factor '63360'.
PLS ANSWER THIS MATH PROBLEM!!
Answer:
48[tex]units^{2}[/tex]
Step-by-step explanation:
i needed help with the problem. didn't understand it.
Answer:
a
Step-by-step explanation:
as all the other points had inflection
I would appreciate it if anyone could help?
:)
The most appropriate choice for corrosponding angle will be given by-
x = 2 is the correct answer
What is corrosponding angle?
At first we need to understood what is angle, parallel lines and transversal
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Parallel lines
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal
Transversal is a line that intersects two or more parallel lines
Corrosponding angle
The angles formed in the same position on the same side of transversal when a transversal cuts two or more parallel lines
Here,
(7x + 3)° and (8x + 1)° are corrosponding angles.
Lines m and n are parallel.
So corrosponding angles are equals
By the problem,
(7x + 3) = (8x + 1)
8x - 7x = 3 - 1
x = 2
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A set of average city temperatures in April are normally distributed with a mean of 19.7 Celsius in a standard deviation of two Celsius the average temperature of Kabul is 15 Celsius what proportion of the average city temperatures are lower than that of Kabul?
Answer:
There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Step-by-step explanation:
In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.
Firstly, we shall calculate the z score
Mathematically;
z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35
so we are to calculate the probability of; P(z< -2.35) = 0.0094
This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
The area of a rectangular pool is 8217m2. If the Length of pool is 99m, what is its width
The width of rectangle is 83 meter.
What is the area of rectangle?
By dividing the rectangle's length by its breadth, we may determine the area of a rectangle.
Formulas for rectangles.
Formula for the perimeter of a rectangle. Rectangle Area Formula: P = 2 (l + b). A = l × b, where l is length of rectangle and b is width of rectangle.
Given area of rectangle is 8217m^2
length l = 99 m
Let width of rectangle be b meter
Therefore,
99 x b = 8217
=> b = 8217/99
=> b = 83
Therefore, the width of rectangle is 83 m.
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In exercises 11-14 ,find m<1,m<2, and m<3.explain your reasoning ?
The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.
The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.
For 11. part:
Considering a transversal p that cuts two parallel lines l and m,
Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.
m∠1 + 80° = 180°
m∠1 = 180° - 80°
m∠1 = 100°
Similarly, m∠1 + m∠2 = 180°
⇒ 100° + m∠2 = 180°
⇒m∠2 = 180° - 100°
⇒m∠2 = 80°
and also, m∠2 + m∠3 = 180°
⇒ 80° + m∠3 = 180°
⇒m∠3 = 180° - 80°
⇒m∠3 = 100°
Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.
For 12. part:
m∠3 + 133° = 180°(interior angles are supplementary)
m∠3 = 180° - 133°
⇒m∠3 = 47°
m∠2 = 133°(alternate interior angles)
The angle vertically opposite to 133° would also be 133°.
So, 133° + m∠1 = 180°( interior angles are supplementary)
m∠1 = 47°
Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.
For 13. part:
m∠3 = 100° (vertically opposite angle)
Let's assume the angle adjacent to ∠3 is x.
m∠3 + m ∠x = 180° (Linear pair property)
100° + m ∠x = 180°
m ∠x = 180° - 100°
m ∠x = 80°
Therefore, m∠1 = m∠2 = m ∠x = 80°(Corresponding angles are equal.)
For 14. part:
m∠1 + 86° = 180°(co-interior angles are supplementary)
m∠1 = 180°- 86° = 94°
The angle vertically opposite to m∠1 is also equal to 94°.
94° + m∠1 = 180°(co-interior angles are supplementary)
m∠2 = 86°
Similarly, the angle vertically opposite to m∠2 is also equal to 86°.
86° + m∠3 = 180°(co-interior angles are supplementary)
m∠3 = 94°
Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.
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A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 153 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)
b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.
Given:
Confidence level,c = 90% = 0.90
Number of successes, x = 153
Sample size,n = 434 + 153 = 587
a) The sample proportion is the number of successes divided by the sample size is,
p = x/n
p = 153/587
p ≅ 0.2606
For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix
[tex]z_{\alpha /2} = 1.64[/tex]
The margin of error is calculated as:
[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]
E ≅ 0.0297
Therefore, the boundaries of the confidence interval are:
p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%
p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%
We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.
b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.
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Write an equation for the function graphed below. The y intercept is at (0,0.2)
Equation for the function graphed is f(x) = -0.6 (x - 1)² ÷ (x + 1)(x + 3)
Given, the y-intercept is at (0, 0.2).
From the given graph, it can be deduced the vertical asymptotes are at x = -1, x = 1 and x = -3.
Which implies denominator is 0 and the function is undefined for x = -1, x = 1 or x = -3.
So, -1 and -3. are the roots of the denominator. As a result, the denominator equation has the form: (x + 1)(x + 3).
For finding the equation of the function f(x) = a(x - 1)² ÷ (x + 1)(x + 3)
Put f(0) = 0.2
f(0) = a(0 - 1)² ÷ (0 + 1)(0 + 3) = 0.2
a = - 0.6
∴ Equation is f(x) = -0.6(x - 1)² ÷ (x + 1)(x + 3) for y-intercept is at (0,0.2).
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equations with parenthesis
Answer:b=6
Step-by-step explanation:
State the slope of each line-without rewriting the equation in y = mx + b form:
a. Given the expression of the form Ax + By + C = 0, the slope is
[tex]\text{slope}=\frac{-A}{B}[/tex]In this case: A = -2 and B = 3.
[tex]\text{slope}=\frac{-(-2)}{3}=\frac{2}{3}[/tex]Answer: 2/3
b. A = -4 and B = 1, so
[tex]\text{slope}=\frac{-(-4)}{1}=4[/tex]Answer: 4
c. A = 5 and B = -7, so
[tex]\text{slope}=\frac{-5}{-7}=\frac{5}{7}[/tex]Answer: 5/7
d. A = 5 and B = -8, so
[tex]\text{slope}=\frac{-5}{-8}=\frac{5}{8}[/tex]Answer: 5/8
Write an equation in slope-intercept form for the line with slope -4/3 and y-intercept 3
I got that but I’m not sure if it’s right.
Answer:
[tex]y=-\frac{4}{3}x+3[/tex]
Which value of xis in the domain of f(x) = √x – 7?
We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root
[tex]x-7\geq 0\\x\geq 7[/tex]
The domain of the function is all the real numbers greater or equal to 7 .
x≥7 ε R
Multiply using the FOIL method.
(8z + 7)(9z-1)
Answer: [tex]72z^{2} +55z-7[/tex]
Step-by-step explanation:
We multiply each component with each other:
8z * 9z = 72z^2
8z * -1 = -8z
9z * 7 = 63z
7 * -1 = -7
We then add it all together, 63z + -8z = 55z and get
[tex]72z^{2} +55z-7[/tex]
Pls help with number 20
The lengths 8 cm, 14 cm, 15 cm can form a triangle
Explanation:Given 8 cm, 14 cm, 15 cm
These can form a triangle if the sum of any two sides of the triangle is greater than the third side.
8 + 14 > 15
14 + 15 > 8
8 + 15 > 14
Since all the above are true, we conclude that they can form a triangle
what is the equation of a line that goes through the points 2, -2 and 0,2
it is vital that we first find the gradient/slope between the points .
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]
The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.
[tex]2=-2(0)+c\\\\c=2[/tex]
⇒This tells us that the equation of the line is y=-2x+2
Need help for this
Answer:
[tex]1. a=-10[/tex]
[tex]2. b=-0.2[/tex]
[tex]3. c=0.25[/tex]
Step-by-step explanation:
1. 1/5a = -2
a=-10
2. 8+b=7.8
b=-0.2
3.-0.5=-2c
c=0.25
:]
(Brainliest would help a lot) Tell me if this is incorrect!
Is 47/8 less then 23/4
Answer:
no
Step-by-step explanation:
Generally you can't really compare two functions with a different denomination, and you want to multiply the fractions by some fraction: [tex]\frac{a}{a}[/tex] which simplifies to one so we're not changing the value of the fraction at all but it helps so we have the same denominator.
You'll notice we can multiply 4 by 2 to get 8, which would give us the same denominator as 8.
[tex]\frac{23}{4}*\frac{2}{2}=\frac{46}{8}[/tex]
Now it's much easier to compare: [tex]\frac{47}{8}\text{ and }\frac{46}{8}[/tex] and here all we have to compare is the numerators, and obviously 47 is greater than 46 so the 47/8 is greater than the 23/4. This means 47/8 is not less than 23/4
Find the length of the third side. If necessary, write in simplest radical form.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{2}\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 2^2}\implies c=\sqrt{16 + 4}\implies c=\sqrt{20}[/tex]