The formula for moose population, P, in terms of t, the years since 1990 would be P(t) = -110t + 4730.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Let's consider x on the graph to be years since 1990 and y on the graph to be the number of Moose.
We have two points on the graph as (4, 4290) and (8, 3850)
Now we can find the slope of this line:
m = (y2 - y1)/(x2 - x1)
Substitution;
m = (3850 - 4290)/(8 - 4)
Solve the subtraction in the parenthesis;
m = -440/4
m = -110
Then we have the slope of the line, we can use the point-slope formula to find the equation for the line.
y - y1 = m(x - x1)
Substitution;
y - 4290 = -110(x - 4)
y - 4290 = -110x + 440
y - 4290 + 4290 = -110x + 440 + 4290
y = -110x + 4730
Since the formula that is being sought is supposed to be in terms of P and t, we will replace y with P and x with t.
P(t) = -110t + 4730
To predict the population in 2006, we have to determine the years from 1990 to 2006.
2006 - 1990 = 16
P(16) = -110 (16) + 4730
P(16) = -1760 + 4730
P(16) = 2970
Hence, The formula for moose population, P, in terms of t, the years since 1990 would be P(t) = -110t + 4730.
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ffewessdt whats aowpwbe be du
Answer: I'm assuming you want our favorite so shaggy
Step-by-step explanation:
Find the perimeter of the following polygon. Be sure to include the correct unit in your answer.
Answer:
38 yd
Step-by-step explanation:
Definition:
the perimeter of a polygon is equal to the sum of all sides’ lengths.
Let P be the perimeter.
Then
P = 8 + 9 + 5 + 7 + 9 = 38
Write the following decimal in three different ways using unit form 3.754
please explain as much as you can.
Step-by-step explanation:
remember : to convert a fraction of one denominator into a fraction of another denominator, we need to multiply both (numerator and denominator) by the same factor, so that the denominator changes to the desired number, and the overall value of the fraction remains unchanged.
4 1/3 - 8
first I convert the mixed number into a full fraction :
4 1/3 = (4×3 + 1)/3 = 13/3
then, to be able to subtract 8, I need to convert 8 into a fraction with the same denominator as 13/3 :
8 = (8×3)/3 = 24/3
so, now I can do the subtraction :
13/3 - 24/3 = -11/3
-11/3 = -3 remainder 2 = -(3×3 + 2)/3 = -3 2/3
5 2/5 - (-2 4/15)
again, we convert all mixed numbers into full fractions :
5 2/5 = (5×5 + 2)/5 = 27/5
2 4/15 = (2×15 + 4)/15 = 34/15
now we need to bring both to the same denominator, and because 5 is a factor or 15, we can bring both to fractions of 1/15, for which we only need to transform the first fraction :
27/5 = 27/5 × 3/3 = 81/15
so, the subtraction is actually
81/15 - (-34/15) = 81/15 + 34/15 = 115/15 = 23/3
23/3 = 7 remainder 2 = (7×3 +2)/3 = 7 2/3
Berno deposits $30,000 into an account paying 3.25% annual interest,
compounded quarterly. How much will be in the account after fifteen years?
Based on the amount deposited by Berno and the annual interest on the account, the amount in the account after fifteen years is $49,012.91.
How to find the deposited amount?The interest is said to compound quarterly which means that the periodic interest rate is:
= 3.25% / 4
= 0.8125%
The number of periods is:
= 15 x 4
= 60 quarters
The amount in the account after 15 years is:
= 30,000 x (1 + rate) ^ number of periods
= 30,000 x (1 + 0.8215%)⁶⁰
= $49,012.91
In conclusion, the amount in the account after 15 years would be $49,012.91.
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Solve the problem.
Suppose a necklace is made from 18-karat gold and weighs 54 grams. Find the weight, in grams, of the pure gold in the necklace.
Select one:
A.
54 grams
B.
40.5 grams
C.
6 grams
D.
18 grams
Based on the karats on the gold necklace, the weight in grams of the pure gold in the necklace is B. 40.5 grams
What is the amount of pure gold in 18 karats?When something is said to be 18 karats of gold, it means that there is about 75% pure gold and then 25% of other materials.
If the necklace has 75% gold, the pure gold in grams is:
= 75% x 54
= 40.5 grams
In conclusion, the pure gold weighs 40.5 grams.
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Express x% of 6 plus y%of 6 as a percentage of 11.
x% of 6 plus y% of 6 can be expressed as x + y = 1.83.
A percentage is a quantity or ratio that is expressed as a fraction of 100. The symbol "%" is used to denote percentage. The percentage is denoted by the abbreviations "pct" or "pc". In other words, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
The sum of x% of 6 and y% of 6 is 11%.
Therefore,
x% of 6 + y% of 6 = 11%
x% × 6 + y% × 6 = 11%
[tex]\frac{x}{100} \times 6 + \frac{y}{100} \times 6 = \frac{11}{100}[/tex]
Taking [tex]\frac{6}{100}[/tex] common.
[tex]\frac{6}{100}(x+y)=\frac{11}{100}[/tex]
6( x + y ) = 11
Dividing each side by 6.
[tex]x + y = \frac{11}{6}[/tex]
x + y = 1.83
Therefore, the equation x + y = 1.83 expresses the statement x% of 6 plus y% of 6.
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2-7
please geometry chapter 1
The values of the indicated lengths.
We are given a number line with points A, B, C, D and E on it.
We need to find the lengths of:
DE
AB
AC
BD
CE
BE
Now, we are also given that:
AD = 18 units
AE = 27 units
DE = 27 - 18 = 9 units
AB = 18 / 3 = 6 units ( As AB = BC = CD)
AC = 12 units ( as AB + BC)
BD = 12 units
CE = 6 + 9 = 15 units
BE = 15 + 6 = 21 units.
Therefore, we get the values of the indicated lengths.
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The overtime rate of pay at "time and a half"
corresponding to a rate of 36 cents is
A. 18cents
B. 36 cents
C. 54 cents
D. 72 cents
Solve the following inequality for m.
−15+ 6 |2m − 1| < 3
A<m<B
A=
B=
The solution for the inequality is given by: -1 < m < 2 .
In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly. Size comparisons between two numbers are commonly made on the number line. Various types of inequalities can be represented using various notations, such as:
a is smaller than b, as shown by the symbol a<b.
When the expression a > b is employed, it means that an is larger than b.
In no circumstance is a the same as b. These relationships are referred to as strict inequalities since a is strictly less than or strictly greater than b. Equivalence isn't taken into account.
The given inequality is of the form:
−15+ 6 |2m − 1| < 3
Now let us solve the inequality :
or , 6 |2m − 1| < 3 + 15
or , 6 |2m − 1| < 18
or, |2m − 1| < 3
or, -3 < 2m-1 < 3
or, -3+1 < 2m < 3 + 1
or, -2 < 2m < 4
or, -1 < m < 2
Hence the solution of the inequality is -1 < m < 2 .
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the date of the second Wednesday of a month is a square number what is the date of the last Monday of this month
Answer:
28th
Step-by-step explanation:
There will be a wednesday in the first week
Wed 2nd Wed
1 8
2 9 <===== this is the Wednesday in question
Monday would be 2 days earlier at 7th
then every 7 days there is another Monday
7 14 21 28 <===== this would be the last one
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,7) and perpendicular to 2x+7y=1.
The line in standard notation is 2y - 7x = 7 and in slope-intercept form it is:
y = (7/2)*x + 7/2
How to find the linear equation?We want our line to be perpendicular to 2x + 7y = 1
Rewriting that line, we get:
y = (1 - 2x)/7 = 1/7 - (2/7)*x
So the slope is (-2/7), then the slope of a perpendicular line is 7/2.
So our equation is something like:
y = (7/2)*x + b
To find the value of b we replace the values of the point (1, 7), it gives:
7 = (7/2)*1 + b
7 = 7/2 + b
7 - 7/2 = b
7/2 = b
Then the linear equation in slope-intercept is:
y = (7/2)*x + 7/2
And the standard form is:
y - (7/2)*x = 7/2
2y - 7x = 7
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the bottom of a rectangular swimming pool is 23 meters wide and 29 meters long. What is its perimeter
Answer:
104m
Step-by-step explanation:
23+23+29+29=104m
find the slope of the line through (0,20) and (4,36)
Answer:
4
Step-by-step explanation:
Slope formula: y2 - y1/ x2 - x1 (this means the second y minus the first 1 divided by the second x minus the first x)
36 - 20 = 16
4 - 0 = 4
16/4 = 4
The slope of the line is 4
Ian's math teacher finds that there's roughly a linear relationship between the
amount of time students spend on their homework and their weekly quiz scores. This
relationship can be represented by the equation y = 60+ 6.9x, where y represents
the expected quiz score and a represents hours spent on homework that week. What
is the meaning of the x-value when y = 83?
If Ian wants to get an expected quiz score of 83, then he needs to spend 3.33 hours in homework that week.
What is the meaning of the x-value when y = 83?We know that the situation is modeled by the linear equation:
y = 60+ 6.9x
Where y represents the expected quiz score and x the hours spend on homework that week.
If we define y = 83, the value of x will be the number of hours that the students need to do homework such tath the expected quiz score is 83.
Solving the linear equation:
83 = 60 + 6.9*x
(83 - 60)/6.9 = x
23/6.9 = x
3.33 = x
So to get an expected quiz score of 83, they need to spend 3.33 hours in homework that week.
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Answer: The number of hours a student should spend on their homework to expect a score of 83 on the quiz.
Step-by-step explanation: just did it!
LESSON 7.4
THERE ARE 4 DIFFERENT QUESTIONS PLEASE ANSWER ALL 4 TO GET THE POINTS THANK YOU
1. Find the value of the trig function indicated.
For the given right triangle, the tangent of theta is equal to 4/3 so the correct option is D.
How to find the value of the trigonometric function indicated?
Here we have a right triangle, and we want to find the tangent of one shown angle.
Remember that the trigonometric relation for a tangent is:
tan(a) =(opposite cathetus)/(adjacent cathetus).
On the image, we can see that the adjacent cathetus to the given angle has a measure of 6 units, while the opposite cathetus has a measure of 8 units, then we can replace that in the general relation to write:
tan(θ) = 8/6
Now we just can simplify that fraction if we divide both numerator and denominator by 2, we will get:
tan(θ) = 8/6 = 4/3
Then we conclude that the correct option is D.
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Solve the inequality.
-3s+7 ≤ 8 or -2s+4212
The solution for given inequality is s ≥ -1/3 or s ≤ -4
What is an inequality ?In mathematics, an inequality can be taken as a relation which makes a comparison which is non-equal between two specific numbers or the variables or other mathematical symbols and expressions. It is used mostly when we have to compare two numbers by their size on the number line.
The are various operators which are used while showing the inequality such as the signs of greater than (>) , less than (<), greater than or equals to (≥) , and less than or equals to (≤).
In the given question the inequality is:
-3s+7 ≤ 8 or -2s+4 ≥ 12
solving the equations
=> -3s ≤ 8-7 or -2s ≥ 12-4
=> -3s≤ 1 or -2s ≥ 8
=> -s ≤ 1/3 or -s ≥ 4
=> s ≥ -1/3 or s ≤ -4.
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The complete question is:
Solve the given inequality.
-3s+7 ≤ 8 or -2s+4 ≥ 12
Classify angle 5
Please help me
Answer:
It is an acute angle
Step-by-step explanation:
You can tell by looking at it that it is less than 90 degrees, making it an acute angle.
Find the domain of the function. f(x)=2/9x+4 Write in interval notation.
Answer: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{2}{9}x+4[/tex] has a domain of all real numbers since it is a polynomial function.
I need help with these math problems
Using proportions, it is found that:
3. Due to the lower cost per pound, the twelve-pack is the better value.
4. Due to the lower cost per cup, the Pacific Coast Coffee is the better value.
5. Lettuce and Asparagus cost the same per pound.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item 3, the cost per pound is the proportion of the cost by the weight, hence:
6 pack: 1.75/6 = $0.292 per pound.12 pack: 3/12 = $0.25 per pound.Due to the lower cost per pound, the twelve-pack is the better value.
For item 4, we follow the same procedure, hence:
Pacific: 12.88/80 = $0.161 per cup.Down South: 9/50 = $0.18 per cup.Due to the lower cost per cup, the Pacific Coast Coffee is the better value.
In item 5, we have that:
Lettuce: 8.75/3.5 = $2.5 per pound.Snap Peas: 11.25/3 = $3.75 per pound.Asparagus: 6.25/2.5 = $2.5 per pound.Lettuce and Asparagus cost the same per pound.
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Write the number 13 ones 2 hundreds 7tens
Answer:
283
Step-by-step explanation:
Please answer, will give brainliest to accurate answer.
-1 + 9y > -73 and y-4/-3 < 2
Answer:
Step-by-step explanation:
Rewrite
y − 4 − 3 >. y − 4 (−3>)
Need help please show work ThankYou
Will give a lot of points
Answer:
[tex]3 { \times }^{2} - 5 \times - 2[/tex]
help me pleaseeeeeeeeeee
Since the forces are directly opposing each other, we can subtract their magnitude to obtain the net force on the system.
Assume the positive direction is to the left:
[tex]f_{net} = f_{left} - f_{right} \\ f_{net} = 15 - 10 \\ f_{net} = + 5 \: newton[/tex]
5 Newtons to our assumed positive direction, which is to the left, so 5 newtons to the left is the answer.
CPLEASE HELP GIVING BRAINLIEAST
Answer:
Important Ideas:
Led American troops in War
Led Constitutional Convention
Served as first US President
Minor Details:
Had a $25,000 yearly salary
Had problems with teeth
Had a brother named Lawrence
Write the quadratic equation whose roots are −2 and −6, and whose leading coefficient is 3.
Answer:
3x² + 24x + 36 = 0
Step-by-step explanation:
A quadratic equation has the standard form ax² + bx + c = 0.
a, b and c are constants.
The roots of a quadratic equation represent the two solutions to the quadratic equation
Given that the roots are -2 and -6 we have
x = -2 and x = -6 as the solutions
Add 2 to both sides of x = -2 ==> x + 2 = 0
Add 6 to both sides of x = -6 ==> x + 6= 0
So (x+2)(x+6) = 0 is the factored representation of this equation. We have to multiply by a leading coefficient of 3
So the quadratic equation is
3(x+2)(x+6) = 0
Using the FOIL method
(x + 2)(x + 6) = x² + 6x + 2x + 12 = x² + 8x + 12
The leading coefficient is the coefficient of x² and is given as 3
So the quadratic equation in standard form is
3(x² + 8x + 12) = 0
==> 3x² + 24x + 36 = 0
If you solve this equation on a quadratic equation calculator you will get the solutions x = -2 and x=-6
A company sells Apple, Cherry, and Walnut
Mix. The ingredients are listed below for one
batch. They make large batches in order to
fill 250 bags. Determine how many pounds of
each ingredient should be used to make a
large batch. Decide how much the company
should charge for each bag of Apple, Cherry
and Walnut Mix, and explain how you made
your decision.
Apple, Cherry and Walnut Mix Recipe
3/4 pounds of dried apples
½ pounds of dried cherries.
½ pound of walnuts
Prices
dried apples: $2.80 per pound
dried cherries: $4.48 per pounds
walnuts: $3.96 per pound
Answer:
Step-by-step explanation:
1/4 of all of it
Mrs. McMinn loves Vanilla Coke. It has been difficult to find in stores but now she is at HEB and sees a full shelf of Vanilla Coke drinks! Every 12-pack of Vanilla Coke is $7. She also remembered she has to get a roll of paper towels, which is $2. Which equation best represents her total cost (y) after purchasing Vanilla Coke 12-packs (x)?
Her total cost after purchasing 12x packs of Vanilla Coke is given by the following linear function:
y = 2 + 7x.
What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, we have that:
The cost of the paper towel is constant, of $2, and only one is bought, hence the intercept is of b = 2.Each 12-pack of Vanilla Coke costs $7, hence the slope is of m = 7.Hence her total cost after purchasing 12x packs of Vanilla Coke is given by the following linear function:
y = 2 + 7x.
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If two angles are vertical angles, then they are congruent.
Which is the hypothesis of the conditional?
A. Two angles are not vertical angles.
B. The angles are congruent.
C. The angles are not congruent.
D. Two angles are vertical angles.
When two angles are vertical angles, then they are congruent, the hypothesis of the conditional is that D. Two angles are vertical angles.
What is vertical angles?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.
It should be noted that if p and q are statements, the conditional of q by p is “if p then q” denoted p → q. We call p the hypothesis of the conditional and q the conclusion.
Therefore, if two angles are vertical angles, then they are congruent, the hypothesis of the conditional is that the two angles are vertical angles.
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HELP PLS ASAP I DONT WANT TO FAIL THIS ASSIGMENT
Answer:
Step-by-step explanation:
3rd one