I need help with this problem please and thank you :)
Answer:
a. P = 190t -373,930 . . . . . t=actual year number
b. P = 6640
Step-by-step explanation:
Given the two points (1991, 4360) and (1999, 5880) on a linear relation between years and moose population, you want a formula for the population (P) and an estimate of the population in 2003.
a. FormulaWe can use the point-slope form of the equation for a line to write the formula for moose population. To do that, we need to know the slope of the line.
The slope is given by the formula ...
m = (y2 -y1)/(x2 -x1) . . . . . . . . line through points (x1, y1) and (x2, y2)
Using the given point values, we have ...
m = (5880 -4360)/(1999 -1991) = 1520/8 = 190
The point-slope equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
Using the first ordered pair, we can write the equation as ...
y -4360 = 190(x -1991)
y = 190x -373,930 . . . . . . . where x is the actual year number
Using P and t for the variables, the formula is ...
P = 190t -373,930
b. Population in 2003Using t=2003, the above formula evaluates to ...
P = 190(2003) -373,930 = 380,570 -373,930
P = 6,640
The linear model predicts the 2003 population to be 6640 moose.
__
Additional comment
The formula above uses actual year number. The year value can be translated any way you might want. For example, using t = years after 1991, the formula would be ...
P = 190(t +1991) -373,930
P = 190t +4360
Then t=12 for year 2003.
The measure of Angle b is 40 degrees and the measure of angle c is 66 degrees. What is the measure of angle a?
Answer:
74
Step-by-step explanation:
All the angles of a triangle add up to 180
66+40 = 106
To find the missing angle...
180-106 = 74
Answer:
ANGLE A=74
Step-by-step explanation:
LET ANGLE A BE X
ANGLE B=40°
ANGLE C=66°
SUM OF ADJACENT ANGLE IS 180°
SO, WHEN:
40+66+X=180
X=180-106
ANGLE A=74°
HAVE A NICE DAY!!
Leo knows that each time a dight moves one place to the left in a whole number, the value of the dight is 10 times as much
Describe an example you would show to Leo to
demonstrate that this is true for decimal numbers also.
Help me if you may
The example regarding the values of digits is also true for decimal numbers, as we showed with 0.52.
How do values of digits work?For the integer part of a number, the unit digit is worth 1, and for each subsequent digit, moving left, the value of the digit is multiplied by 10. For example 22, 22 = 2 x 10 + 2 x 1 = 22.For the fractional part of a number, the first decimal digit is worth 0.1, and for each subsequent digit, moving right, the values is divided by 10.For example, for the decimal 0.52.
.52 = 5 x 0.1 + 2 x 0.01 = 0.52.
Hence, moving a digit one place to the left, the value is 10 times as much, as we saw with digits 5 and 2 in the number 0.52.
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What is the quotient of 3 and 1 over 5 divided by 1 over 3? SHOW WORK
The quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6
How to solve for the quotientWe we would start first by having the definition for the term quotient. This is defined as the value that is gotten when we divide on quantity by another quantity.
From the definition that we have gotten here, we would have to divide the values by themselves and get the final solution.
We have 3 and 1 over 5 divided by 1 over 3 to be represented as
[tex]3\frac{1}{5} / \frac{1}{3}[/tex]
This would be rewritten as
(16 /5) / (1/3)
= 16 / 5 x 3/1
= 48 / 5
= 9.6
Hence the quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6
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12. DIG DEEPER The sum of a three-digit
number and a one-digit number is 731.
The product of the numbers is 2,908,
What are the numbers?
The three digit number is 727 while the one digit number is 4
Given data
The sum of a three-digit number and a one-digit number is 731.
The product of the numbers is 2,908
How to solve for the numberslet three digit number be x, y, and z
let the one digit be w
The sum
xyz + w =731
xyz * w = 2,908
making xyz the subject of formula
xyz = 731 - w
plugging in xyz into xyz * w = 2,908
( 731 - w ) * w = 2908
731w - w^2 = 2908
w^2 - 731w + 2908 = 0
solving the quadratic equation gives
w = 727 or 4
since w is a one digit number then w = 4
plugging in w = 4 into xyz + w =731 we have
xyz + w =731
xyz + 4 =731
xyz =731 - 4
xyz = 727
Hence the three digit number is 727 while the one digit number is 4
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A doctor was interested in the blood pressure of all 16-year-olds in the state of Colorado. She gathered data from a random sample of 10 pediatricians in the state and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for her data?
The graphical representation in the sample that would be best for her data is a bar graph.
How to illustrate the information?It should be noted that based on the information, the doctor gathered data from a random sample of 10 pediatricians in the state and wanted to create an appropriate graphical representation for the data.
It should be noted that the bar graph will be applicable. This is because it will display the categories of data with a bar to represent the blood pressure of the children.
This can then be used to analyze the needed information.
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What is the estimate of 827 times 4 ?
Answer:
3,308
Step-by-step explanation:
the internet said that 3,308 was the answer.
[tex]827 \times 4 \approx820 \times 4[/tex]
[tex]820 \times 4 = 800 \times 4 + 20 \times 4 \\ 820 \times 4 = 3200 + 80 \\ 820 \times 4 = 3280[/tex]
[tex]827 \times 4 \approx3280[/tex]
In reality it's just that additional 4 sevens,so
[tex]827 \times 4 = 820 \times 4 + 4 \times 7 \\ 827 \times 4 = 3280 + 28 \\ 827 \times 4 = 3308[/tex]
Please help, and explain why answer is correct
Answer:
AD
Step-by-step explanation:
It is the only segment that meets a side of triangle ABC at a right angle.
Suppose 3 < a < 4 and 4 < b < 5. find all possible values of each expression. 1/a+1/b
9/29 < 1/a + 1/b < 7/12
Here we have two expression
3 < a < 4 and 4 < b < 5
We have to find the value of the expression
1/a + 1/b
The lower bound of the expression is when we take the maximum value of both the expression a and b
a = 4 and b = 5
From this we get
= 1/ 4 + 1/5
= 5 + 4 / 20
9/ 20
In the same way, we get the higher bound of the expression taken by taking the minimum value of both the expression a and b
a = 3 and b = 4
By putting the value of a and in the expression we get:
1/ 3 + 1/4
= 4+3 / 12
= 7/12
Thus we get the possible value of the expression :
9/20 <1/a + 1/b < 7/12
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Given f (x) = 10x and g (x) = 2x – 1, find (f /g) (x).
Then evaluate the division when x = 3
Answer:
6
Step-by-step explanation:
(f / g)(x)
= [tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{10x}{2x-1}[/tex] ← substitute x = 3
= [tex]\frac{10(3)}{2(3)-1}[/tex]
= [tex]\frac{30}{6-1}[/tex]
= [tex]\frac{30}{5}[/tex]
= 6
Multiply. (√5+√11)(√5-√11)
The multiplication of the expression ( √5 + √11 )( √5 - √11 ) is - 6.
Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.
Consider the expression,
y = ( √5 + √11 )( √5 - √11 )
Using the distributive property,
a( b + c ) = ab + ac
y = (√5 + √11 )( √5 - √11 )
y = √5( √5 - √11 ) + √11( √5 - √11 )
y = ( √5 )² - √5 × √11 + √11 × √5 - ( √11 )²
y = 5 - √55 - √55 - 11
y = 5 - 11
y = - 6
The value of the expression (√5 + √11 )( √5 - √11 ) when simplified is - 6.
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Which of the following numbers is a factor of 63?
A 8
B 2
C 6
D 3
Answer:
The correct answer is D) 3.
Step-by-step explanation:
Since the number 63 is a composite number, 63 has more than two factors. Thus, the factors of 63 are 1, 3, 7, 9, 21 and 63.
I'm failing Geometry right now please help
Answer:
x = 61
Step-by-step explanation:
2x + 6 + x - 9 = 180
3x - 3 = 180 add 3 to the side
3x = 183 Divide the sides by 3 And you get 61 for x
a) Select all of the fractions below that are smaller than 1/9 1/8 1/3 1/10 5/9 1/90
Rearrange the Fraction in the order of least to largest:
1/8 > 1/91/3 > 1/9 1/10 < 1/95/9 > 1/91/90 < 1/9What is Fraction?A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator.
What is the significance of fraction?Fractions are significant because they indicate what percentage of a whole you require, have, or desire. In baking, fractions are used to indicate how much of an ingredient to use.
Why is it necessary to study fractions?Fractions are a vital basis for studying more advanced math's. As a student's first introduction to abstraction in mathematics, fractions give the greatest foundation for algebra.
According to the given data:Rearrange the items in the order of least to largest.: 1/8 > 1/9
Rearrange the items in the order of least to largest.: 1/3 > 1/9
Rearrange the items in the order of least to largest.: 1/10 < 1/9
Rearrange the items in the order of least to largest : 5/9 > 1/9
Rearrange the items in the order of least to largest.:1/90 < 1/9
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7 times the difference between a number and 5 Algebra expression
Step-by-step explanation:
so first just think about the question 7(x + 5)
Kayla and Shawna are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Kayla sold 7 small boxes of tangerines and 4 large boxes of tangerines for a total of $166. Shawna sold 7 small boxes of tangerines and 3 large boxes of tangerines for a total of $ 149. Find the cost each of one small box of tangerines and one large box of tangerines.
The price of small box of tangerines is $14.43 approx. and price of large box of tangerines is $ 17
Let the price of small boxes be x and the price of large boxes be y
we need to form a linear equation in two variable
So, Kayla's equation is
7x + 4y = 166
and Shawna's equation is
7x+ 3y = 149
Subtracting equation 2 from equation 1
7x + 4y = 166
(-) 7x +3y = 149
we get y = 17
Now substituting the value of y in equation 1
7x + 4(17) = 169
7x +68 = 169
7x = 101
x= 14.428
Hence, The price of small box of tangerines is $14.43 approx. and price of large box of tangerines is $ 17
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A rectangle has a length 6 meters more than six times the
width. The area of the rectangle is less than 72 meters².
Using the variable x, write an expression that represents all
possible widths of the rectangle. Write your answer as an
inequality in the form a
The required expression or inequality for possible widths of the rectangle is -4 < x < 3.
Given:
A rectangle has a length 6 meters more than six times the width.
The area of the rectangle is less than 72 meters squared.
We have to find,
The expression or inequality that represents all possible widths of the rectangle.
Let x be the width of the rectangle.
Length of the rectangle is 6 meters more than six times the width.
length = 6x + 6
Area of rectangle is:
Area = length × width
Area = (6x + 6) × x
Area = 6x² + 6x
The area of the rectangle is less than 72 meters squared.
6x² + 6x < 72
6x² + 6x -72 < 0
Divide both sides by 6.
x² + x - 12 < 0
x² + 4x - 3x - 12 < 0
x(x + 4) - 3(x + 4) < 0
(x + 4) (x - 3) < 0
It is true if one factor is negative and other is positive. So,
x - 3 < 0 ⇒ x < 3 ...(i)
x + 4 > 0 ⇒ x > -4 ...(ii)
Using (i) and (ii), we get
-4 < x < 3
Therefore, the required expression or inequality for possible widths of the rectangle is -4 < x < 3.
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What is the area of the figure? step by step please
Answer:
*A = 60 sq units
Step-by-step explanation:
Area(*A) = Length(*l)×breath (*b)
split the shape in two such that you get two rectanglesrectangle(*rec) 1 dimensions being *l=2,*b=18*rec 2 dimensions being*l=2 *b=12*A of *rec1 = 2 × 18 = 36*A of *rec2 = 2× 12 =24*A of the total shape = *A of *rec1 + *A of *rec1*A of the total shape = 36 +24*A of the total shape = 60 sq units
Answer:
Area = 60
Step-by-step explanation:
First make the rectangle 12 and 4 and a square 6 and 2.
12*4=48
6*2=12
48+12=60
3/
A and B are two similar solids.
15 cm
10 cm
A
B
The volume of A is 400 cm³.
Work out the volume of B.
+
25 students are going on a field trip and each student have to pay 10$ for lunch in addition to their ticket.write an expression that could represent the total cost for the students going on the trip.
Answer:
(10+t)*25
Step-by-step explanation:
25 students so the cost for 1 student needs to be multiplied by 25 for all the students
If lunch costs $10 by itself not including the ticket, we don't know how much the ticket costs so lets say ticket cost = t
$10+t = the cost for ONE student
but there are 25 students so, ($10+t)*25 could work
Expressions don't have equal signs so the total is (10+t)*25
For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=4 when x=3
After direct variation y = -4 when x = -3.
What exactly do we mean by "direct variation"?Direct variation equations use the same phrase, to give the reader a hint.Either "directly proportional" or "directly varies" is the phrase.The area of a square, for example, is proportional to the square of its side.If y varies directly as x and y = 6 when x = 2, the variational constant is k = 3.As a result, the direct variation equation is y = 3x.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ 4/3That is y = kx ⇒ y = 4/3 × xWhen x = -3:
y = 4/3 × -3 ⇒ y = -4Therefore, y = -4 when x = -3.
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What is the value of m in the equation 1/2m - 3/4n when n = 8?
Answer:
m = 12Step-by-step explanation:
What is the value of m in the equation 1/2m - 3/4n when n = 8?
1/2m - 3/4*8 =
1/2m = 6
m = 12
--------------------
Please help will give great points
The sample space is 0, 1, 2, 3, 4, 5, 6, 7.
Set A is {0, 1, 2, 3, 4}
Set B is {1, 2,3, 4, 5, 6, 7}
The probability of selecting a number less than 5 is 5 / 8.
The probability of spinning a natural numbers is 7/8
The probability of spinning natural numbers and numbers less than 5 is 1/2
A and B is {1, 2, 3, 4}
A' and B = {5, 6, 7}
The probability of spinning a number not less than 5 or a natural number is 1 3/8
What is the sample space?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. The relationship that is being illustrated with this Venn diagram is the relationship between natural numbers and numbers less than 5.
A natural number includes all positive numbers from 1 to infinity. Natural numbers does not include zero (0). The sample space represents all the possible sets of outcome. In mathematics, a set can be described as a collection of objects whose elements are fixed and cannot be changed.
The probability of selecting a number less than 5 = numbers less than 5/ total numbers
5 / 8
The probability of spinning a natural numbers = all natural numbers / total numbers
7/8
The probability of spinning natural numbers and numbers less than 5 = 4/8 = 1/2
A' = 5,6,7
B = 1, 2, 3, 4, 5, 6, 7
A' and B - 5, 6, 7
The probability of spinning a number not less than 5 or a natural number= ( 4/8) + (7/8) = 11/8 = 1 3/8
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NEED HELP ASAP WILL GIVE U BRAINLIEST
Based on the formulas given for PR and QR, the length of PR is 19.8 units.
How to find the length of PR?The shape that is given is an equilateral triangle. What this means is that all the sides of the triangle are equal.
This means that PR and QR are therefore equal:
PR = QR
This can help us to find the value of n by equating both formulas:
2n + 9 = 7n - 18
The value of n can then be found as:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR can then be solved by substituting n into the formula:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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Write 3.73 x 10^-2 in standard form.
Answer:
0.0373
Step-by-step explanation:
move the decimal over 2 spots to the left
when the power is negative, move left
when the power is positive, move right
What is each product or quotient in simplest form?
b. √x³ / ³√x²
Converting the given radicals into their exponential forms, √x³ / ³√x² = ⁶√x⁵
When work with radical numbers, sometimes it is easier to express them in exponential form first.
[tex]\sqrt[n]{a^{b}}=a^{\frac{b}{n}[/tex]
Recall the rules of exponent operations:
Product. [tex]a^{b}.a^{c}=a^{b+c}[/tex]Quotient. [tex]a^{b}:a^{c}=a^{b-c}[/tex]Power. [tex](a^{b})^{c}=a^{b.c}[/tex]Power of a product. [tex](a.b)^{c}=a^{c}.b^{c}[/tex]Zero power. a⁰ = 1Negative exponent. [tex]a^{-b}=\frac{1}{a^{b}}[/tex]Note that the first 3 rules use the same base. If there are more than 1 base number, then group the exponent that have the same base first.
Example:
[tex](2^{3}.3^{-2}) : (2^{-3}.3^{2})=( 2^{3}:2^{-3}).(3^{-2}:.3^{2})[/tex]
Tips: To simplify exponent numbers, sometimes it is useful to modify the base whenever possible.
Example:
8².2⁻⁵ = (2³)². 2⁻⁵ = 2⁶. 2⁻⁵ = 2⁶⁻⁵ = 2¹ = 2
The given problem:
Simplify √x³ / ³√x²
[tex]\sqrt{x^{3}}=x^{\frac{3}{2}}[/tex]
[tex]\sqrt[3]{x^{2}} =x^{\frac{2}{3}[/tex]
Using quotient rule of exponent:
[tex]x^{\frac{3}{2}}:x^{\frac{2}{3}}=x^{(\frac{3}{2}-\frac{2}{3}) }=x^{\frac{5}{6} }=\sqrt[6]{x^{5}}[/tex]
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Mrs. Ferreria asked her students to write a number in scientific notation that is greater than 500 but less than 5,000. circle the name of any student who correctly completed the task.
What are the slope of the two lines?
Answer:
- 3/4 for line passing through AB
- 2/3 for line passing through CD
Step-by-step explanation:
Slope = rise/run = (y2-y1)/(x2-x1) for any two points (x1, y1) and (x2, y2)
Line Passing through AB
Take points (0, 6) and (8, 0)
Slope = (0-6)/(8-0) = - 6/8 = -3/4
For line passing thru CD
take points (0, 2) and (3, 0)
Slope = (0 - 2)/(3 - 0) = -2/3
The slope of the two lines - 3/4 for line passing through AB
- 2/3 for line passing through CD
What is a meaning of a slope?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises.two points (x1, y1) and (x2, y2)
Slope [tex]m = \frac{y_{2}- y_{1} }{x_{2} - x_{1} }[/tex]
Line Passing through AB
Take points (0, 6) and (8, 0)
Slope = (0-6)/(8-0) = - 6/8 = -3/4
For line passing through CD
take points (0, 2) and (3, 0)
Slope = (0 - 2)/(3 - 0) = -2/3
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Solve the equation t − 5 = 12 for t.
17
7
−7
−17
Step-by-step explanation:
t - 5 = 12 | add 5 to both sides
t = 17
and that is it. that's all we needed to do.
The bakery at Oaktown Grocery Store sells two types of bread, white and wheat. Last week, the store sold 4 loaves of white bread for every 5 loaves of wheat bread. If the store sold 117 loaves of bread in all last week, how many loaves of white bread did they sell?
The number of white bread sold is 65.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
We have,
Let the White bread be M
Let the Wheat bread be N
4 loaves of white bread for every 5 loaves of wheat bread can be written as:
4M = 5N _____(1)
Total number of bread sold = 117
M + N = 117 _______(2)
The number of white bread sold:
From (1)
N = 4M / 5 Putting in (2)
M + 4M/5 = 117
(5M + 4M) / 5 = 117
9M = 117 x 5
M = 13 x 5
M = 65
Thus the number of white bread sold is 65.
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Answer:
52 i just did the test
Step-by-step explanation: