1:4 is the ratio of the pigeon's aorta radius to that of the goose.
What do we mean by Ratio?A ratio in mathematics indicates how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio of 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), and the proportion of oranges to total fruit is 8:14. (or 4:7).A ratio's numbers can be any quantity, such as a count of people or objects, or measurements of lengths, weights, time, and so on. In most situations, both numbers must be positive.So,
The ratio will be 3:12.Canceling it to the simplest form:
3/12 = 1/4So, the ratio is 1:4.
Therefore, 1:4 is the ratio of the pigeon's aorta radius to that of the goose.
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Please, I'm desperate. 13 Questions. 1-11 have provided options, 12 and 13 are manual answers.
1. Perform the required operations on the following functions.
Given: f(x) = 3 - x; g(x) = -2x
Find g[f(x)].
Options:
A. -x - 6
B. 2x - 6
C. 2x + 3
2. Perform the required operations on the following functions.
Given: f(x) = 3 - x; g(x) = -2x
Find f[g(2)].
Options:
A. -1
B. 25
C. 7
3. Given: f(x) = 3 - x; g(x) = -2x
Find g[f(-1)].
Options:
A. -22
B. 8
C. -8
4. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find F[G(x)] - F(x).
Options:
A. 4x + 4
B. 4x
C. 4x + 2
5. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find G[H(1)].
Options:
A. 5
B. 35
C. 8
6. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x&2
Find F{G[H(2)]}.
Options:
A. 121
B. 27
C. 71
7. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find H(x + a) - H(x)
Options:
A. a^2
B. a^2 + 2ax
C. 2a
8. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x 2
Find [H(x + a) - H(x)] / a
Options:
A. 2x + a
B. a
C. a^2 + 2x
9. Given: F(x) = 2x - 1; G(x) = 3x + 2; H(x) = x^2
Find F(x) + G(x) + H(x).
Options:
A. 5x^3 + 1
B. x^2 + 5x + 3
C. x^2 + 5x + 1
10. If f(x) = 2x 2 - 3x + 1, find f(3) - f(2).
Options:
A. 0
B. 7
C. 17
11. If G(x) = 5x- 2, find G^-1 (x).
Options:
A. (x + 2)/5
B. (x/5) + 2
C. -5x + 2
12. What is the inverse of f(x) ? Show all work for full credit.
f(x) = 2 / [x - 6]
13. Use composition of functions to determine whether f(x) and g(x) are inverses of each other. Show all work for full credit.
f(x) = 4/5 x + 1
g(x) = [5x - 5] / 4
The evaluation of the given functions are as follows;
B. 2•x - 6C. 7C. -8A. 4•x + 4A. 5B. 27B. a² + 2•a•xA. 2•x + aC. x² + 5•x + 1B. 7A. (x + 2)/5(2/x) + 6The inverse of g(x) is f(x)How can the functions be evaluated?1. f(x) = 3 - x
g(x) = -2•x
Therefore;
g(fx) = -2 × f(x)
Which gives;
-2 × (3 - x) = -6 + 2•x = 2•x - 6
g(fx) = 2•x - 6
B. 2•x - 6
2. f(x) = 3 - x
g(x) = -2•x
f(g(x)) = 3 - (-2•x) = 3 + 2•x
f(g(x)) = 3 + 2•x
f(g(2)) = 3 + 2×2 = 7
The correct option is therefore;
C. 7
3. f(x) = 3 - x
g(x) = -2•x
Therefore;
g(fx) = 2•x - 6
g(f-1) = 2×(-1) - 6 = -8
C. -8
4. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(G(x)) = 2•(3•x + 2) - 1 = 6•x + 3
F(G(x)) - F(x) = 6•x + 3 - (2•x - 1) = 4•x + 4
A. 4•x + 4
5. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
G(H(x)) = 3•x² + 2
G(H(1)) = 3×1² + 2 = 5
A. 5
6. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(G(H(x))) = 2•(3•x² + 2) - 1 = 6•x² + 3
F(G(H(2))) = 6×2² + 3 = 27
B. 27
7. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
H(x + a) - H(x) = (x + a)² - x² = 2•a•x + a²
B. a² + 2•a•x
8. (H(x + a) - H(x))/a = (a² + 2•a•x)/a
(a² + 2•a•x)/a = a + 2•x = 2•x + a
A. 2•x + a
9. F(x) = 2•x - 1, G(x) = 3•x + 2, H(x) = x²
F(x) + G(x) + H(x) = 2•x - 1 + 3•x + 2 + x² = x² + 5•x + 1
C. x² + 5•x + 1
10. f(x) = 2•x² - 3•x + 1
f(3) - f(2) = 2×3² - 3×3 + 1 - (2×2² - 3×2 + 1) = 7
B. 7
11. G(x) = 5•x - 2
G^(-1)(x) = (G(x) + 2)/5
Which gives;
G^(-1)(x) = (x + 2)/5
A. (x + 2)/5
12. f(x) = 2/(x - 6)
The inverse is therefore;
(2/f(x)) + 6
The inverse of f(x) is therefore;
(2/x) + 6
13. g(x) = (5•x - 5)/4
(4•g(x) + 5)/5 = (4/5)•g(x) + 1
The inverse of g(x) is therefore;
(4/5)•x + 1 = f(x)
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Marline Was playing basketball and made 8⁄10Of the shots he took what decimal Number repeat Number repeat represents done fraction of shots Merlin made
The fraction ( 8/10 ) when converted into a decimal number is equal to 0.8.
The decimal number system is frequently used to express both integer and non-integer quantities. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system.
The number of shots fired by Marlin should be expressed as a decimal number.
We know that,
Marlin made 8 shots out of 10 shots which is in fraction, it is 8/10.
However, since we are dividing by 10, we shall shift the decimal point of 0.8 to the left (the zero is not really important as it only represents a place value )
Or,
( 8 /10) = ( 4 / 5 ) = 0.8
Therefore, the fraction of the shots Marlin made is 0.8.
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Angle relationships and triangles
Three angles make compose a triangle.
They'll be known as a°, b°, c°.
If we total everything up:
a° + b° + c = 180
The triangle's horizontal line may be drawn farther to the right, creating a new angle. Call this angle "d°" for short.
a° + b° Equals d°
Give this some values:
a° = 60° b° = 70°
c° = 50°
Do should be 130° since c and d create 180° with c° 50°.
Additionally, because:
A + B + C Equals 180, and C + D = 180.
Because the cremains in both cases are the same, a + b = d.
Any of these fit the bill.
Let's call this f° if you will just extend the triangle's horizontal line to the left.
So, b + c Equals f.
So, if a F Equals 120° since f = 60° and a + f = 180.
We established that b + c Equals f in this instance.
Let's now make the line longer and give it the name angle g°.
B being equal to 70°, the angle next to it is 110°.
Consequently, a + c = g.
All inner angles added together equal 180 degrees.
Additionally, the total of the other two inside angles is equal to the outer angles.
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F(x) = 5x + 6 evaluate f(-7)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{f(x) = 5x + 6}\\\mathsf{f(x) = 5(-7) + 6}\\\mathsf{f(x) = -35 + 6}\\\mathsf{f(x) = -29}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{f(x) = -29}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Determine the probability of following event.
In Armando's senior class of 100 students, 91% went to the senior prom. If two people are chosen at random from the entire class, what is the probability that at least one of them did not go to prom?
According to the question, the probability of the event in which all the students went to prom except one. For this, the probability of the complement rule is used.
Out of [tex]100[/tex] students, [tex]91[/tex] went to prom.
So, the probability that students went to prom = [tex]\frac{91}{100} =0.91[/tex]
Now, P(both went to prom) = [tex](0.91)(0.91)=0.8281[/tex]
Using standard probability formula:
P(at least one did not went to prom) = 1-P(both went to prom)
[tex]1-0.8281=0.1719=17.2%[/tex]
The probability that at least one student did not went is [tex]17.2[/tex] percentage.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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What is the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter?
The annual percentage rate on a loan with a stated rate of 2.75 percent per quarter is 11%.
How to calculate the loan?It was given that the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter.
It should be noted that quarter means that the value was divided by 4.
Therefore, the annual percentage will be:
= 2.75 × 4
= 11%.
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State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Line t is called the transversal for lines p and q .
The statement "Line t is called the transversal for lines p and q" is true
Given,
The statement "Line t is called the transversal for lines p and q"
In the figure we can see that line t cut two parallel line p and q
So the line t is transversal for lines p and q
So the given statement "Line t is called the transversal for lines p and q" is true
Hence, the The statement "Line t is called the transversal for lines p and q" is true
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Line t is called the transversal for lines p and q .
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Solve each system by elimination.
x + y = 12 , x - y = 2
By elimination, the solution of the system of equations, x + y = 12 and x - y = 2, is (7 , 5).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Adding the two equations will eliminate the variable y.
x + y = 12 (equation 1)
x - y = 2 (equation 2)
2x + 0y = 14
x = 7
Substitute the value of x to any of the two equation and solve for y.
x + y = 12 (equation 1)
7 + y = 12
y = 12 - 7
y = 5
Hence, the solution of the system of equations is (7 , 5).
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7x+ 6y=2
- 28x- 24y = -8
Answer:
x=2/7 - 6y/7
Step-by- explanation:
Find the measure of the missing angles h,g and m,k
Give the degrees 119 and 121
The missing angles in degrees are-
∠k = 61°∠m = 119°∠g = 29°∠h = 151°What is defined as the vertically opposite angles?Vertically opposite angles are produced by two straight intersecting lines that are exact reverse one another at a specific vertex. Angles that are vertically opposite each other are equal. These are sometimes referred to as vertical angles.In the given figure;
∠g = 29°, as ∠g and ∠29° are vertically opposite to each other. Both will be equal.
Similarly,
∠k = 61°, as ∠k and ∠61° re vertically opposite to each other. Both will be equal.
What is defined as the linear pair?When 2 lines intersect at a single point, a linear set of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is indeed 180°.From the linear pair;
∠h + ∠g = 180
∠h = 180 - 29
∠h = 151°
Similarly,
∠m + ∠k = 180
∠m = 180 - 61
∠h = 119°
Thus, the missing values of the angles are found.
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WHAT are the angle relationships formed when a third line
intersects two parallel lines?
the angles are the same as their pair
the pairs are
1 and 5
2 and 6
4 and 8
3 and 7
Point b is on line segment \overline{ac} ac . given ab=2x+10,ab=2x+10, bc=x,bc=x, and ac=5x,ac=5x, determine the numerical length of \overline{ac}. ac
The numerical length of line segment AC is 25.
A line segment refers to a straight line connecting two points.
If point B is on line segment AC, then point B divides the line segment into segments AB and BC.
AB + BC = AC
Given that AB =2x + 10, BC = x, and AC = 5x, substitute these expressions in the equation AB + BC = AC.
AB + BC = AC
2x + 10 + x = 5x
3x + 10 = 5x
5x - 3x = 10
2x = 10
x = 5
To determine the numerical length of line segment AC, substitute the value of x in the equation AC = 5x.
AC = 5x
AC = 5(5)
AC = 25
Hence, the numerical length of line segment AC is 25.
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The product of two rational numbers is -14/7 if one of the numbers be 7/9 find the other
Answer:
The other number is (-18/7)
Step-by-step explanation:
Let the other rational number be 'x'.
[tex]\sf x * \dfrac{7}{9}= \dfrac{-14}{7}[/tex]
[tex]\sf x = \dfrac{-14}{7} \div \dfrac{7}{9}[/tex]
Now, use KCF method.
Keep the first fractionChange the division to multiplicationFlip the second fraction
[tex]\sf x = \dfrac{-14}{7}*\dfrac{9}{7}\\\\x = -2* \dfrac{9}{7}\\\\x = \dfrac{-18}{7}[/tex]
Answer:
-18/7
Step-by-step explanation:
let the unknown no be y
7/9×y= -14/7
7y/9= -14/7
cross multiply
-14×9=7y×7
divide both sides by 7
-2×9=7y
-18=7y
divide both sides by the coefficient of y which is 7
y= -18/7
hope this helps
please give brainliest
Expand & simplify:
4(× + 5) - 2(x - 3)
The Simplification of 2x +26
simplify:
4(× + 5) - 2(x - 3)
4x + 20 - 2x +6
2x +26
Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.
Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.
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m/KLM = 135º.
Find the value of y and m/MLN
L
M
K
47°
(16y)⁰
N
Engineers evaluate the efficiency of the memory and speed of a computer. What does evaluate mean in mathematics?
To evaluate anything is to determine its monetary value. Finding all of the values of a variable or collection of variables necessary to make a statement true is what it means to solve something.
What does evaluate mean in mathematics?It is to figure out or compute a formula, function, or relation's value.Middle school math involves evaluating solely arithmetic expressions.It is like to evaluate the equation with a specific value of x or y or any variable.As opposed to solution, which essentially involves going backwards and undoing all of the changes made to the input.Evaluating the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.To evaluate anything is to determine its monetary value. Finding all of the values of a variable or collection of variables necessary to make a statement true is what it means to solve something.To learn more about evaluate, refer to:
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PLEASE HELP ME
The frequency distribution shows the widths, in inches, of available cell phones at a technology store.
What is the mean of the frequency distribution? Round answers to tenths place, if answer is a whole number
than put a zero in the tenths place so it will be counted correct.
For given data set, The value of mean is 6.02.
What is mean?The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.
The formula to calculate mean is = sum of all observations / total number of observations
x = 4 5 6 7 8
f = 12 1 8 18 4 ∑f = 43
fx = 48 5 48 126 32 ∑fx = 259
The formula of mean = ∑fx / ∑f
= 6.02
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Find the relationship between p and q if px*2+2x-q is a perfect square. please help me ASAP
[tex]\displaystyle\\Answer:\ p=-\frac{1}{q}[/tex]
Step-by-step explanation:
A perfect square has equal sides
Hence, px²+2x-q has equal roots (D(discriminant)=0)
[tex]\displaystyle\\D=2^4-4*p*(-q)\\D=2*2+4pq\\D=4+4pq\\D=0\\\Rightarrow\ 0=4+4pq\\Divide\ both\ parts\ of\ the \ equation\ by\ 4:\\0=1+pq\\0-1=1+pq-1\\-1=pq\\Divide\ both\ parts\ of\ the \ equation\ by\ q(q\neq 0):\\-\frac{1}{q}=p\\ Thus,\\p=-\frac{1}{q}[/tex]
Solve each equation using the Quadratic Formula. x(x-5)=-4 .
Answer:
x
2
−4x−5=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x
2
−4x−5=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−(−4)±
(−4)
2
−4(−5)
Square −4.
x=
2
−(−4)±
16−4(−5)
Multiply −4 times −5.
x=
2
−(−4)±
16+20
Add 16 to 20.
x=
2
−(−4)±
36
Take the square root of 36.
x=
2
−(−4)±6
The opposite of −4 is 4.
x=
2
4±6
Now solve the equation x=
2
4±6
when ± is plus. Add 4 to 6.
x=
2
10
Divide 10 by 2.
x=5
Now solve the equation x=
2
4±6
when ± is minus. Subtract 6 from 4.
x=
2
−2
Divide −2 by 2.
x=−1
The equation is now solved.
x=5
x=−1
At an electronics store, a smart phone is on sale for 35% off the original price of 679.if you use the store credit card,you can recive an additional 15% off the sale price.what is the final price of the smart phone if you use the store credit card?Round to the nearest cent.
The final price of the smart phone if you use the store credit card is $375.15.
What is the final price?A discount is when the price of an item is marked down. An item becomes cheaper when it is discounted.
Percentage is the fraction of an amount expressed as an amount out of 100. Percentage is a measure of frequency. The sign used to represent percentage is %.
Price of the smartphone after 35% is discounted : (1 - percentage decrease) x original price
(1 - 0.35) x 679
0.65 x 679 = $441.35
Purchase price after you buy with your credit card : (1 - percentage decrease) x discounted price
(1 - 0.15) x $441.35
0.85 x $441.35
= $375.15
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS Which expression is equivalent to 4 ^ 3
The expression that is equivalent to 4 ^ 3 would be an expression that equals 4 ^ 3
4 ^ 3 = 4 x 4 x 4 = 16 x 4 = 64
Answer:
4^3 =
4 x 4 x 4 x4 = 64
c. Will bought a tennis racket on sale for $24.60. If the sale was 20% off,
how much was the tennis racket originally?
Answer:
$30.75
Step-by-step explanation:
Since the sale was 20% off, the tennis racket is 80% of its original price.
[tex].8p = 24.60[/tex]
[tex]p = 30.75[/tex]
HELP HELP HELP HELP HELP 4/9×4/5=
Answer: 16/45
Step-by-step explanation:
[tex]\displaystyle\\\frac{4}{9}*\frac{4}{5}= \\\\\frac{4*4}{9*5}=\\\\\frac{16}{45}[/tex]
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The arithmetic mean of two numbers is the positive square root of the product of the numbers.
The statement "The arithmetic mean of two numbers is the positive square root of the product of the numbers." is False.
And the true sentence is "The geometric mean of two numbers is the positive square root of the product of the numbers."
Arithmetic Mean:
The arithmetic mean, is also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
Given,
Here they given the sentence, "The arithmetic mean of two numbers is the positive square root of the product of the numbers.".
We need to find this one is true or not and we also need to replace the underlined word or phrase to make a true sentence.
Based on the definition of arithmetic mean, the given statement is false.
And the correct sentence is
"The geometric mean of two numbers is the positive square root of the product of the numbers.".
Because geometric mean is average value or mean which signifies the central tendency of the set of numbers by finding the product of their values.
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A baker uses the equation y= 3.5x to find the number of cups ,y, of milk he needs to make a number ,x, of tres leches cakes. What is the constant of proportionality between y and x?
Answer:
Step-by-step explanation
Equation: y=3.5x
Constant of proportionality:
The constant ratio of one variable quantity to another to which it is proportional.
Answer: 3.5
The reason is for 3.5 cakes you need this amount of milk.
Find the value of x to the nearest tenth. tan x° = 90 89.9 89.6 89.4
Answer:
89.4
Step-by-step explanation:
89.9,89.6 are more than five so we'll be using the lowest number as the nearest thenth
(3x
3
+4x
2
)−(2x
3
+3x
2
−x
On simplifying, x(x2 + 7x + 1) is the final expression.
The provided simplification expression can be solved, per the question, by moving the variable terms to one side and the normal terms to the other.
As a result, the phrase may be expressed more succinctly as:
(3x^3+4x^2) - (2x^3 + 3x^2 -x)
x^3 + 7x^2 + x
x(x^2 +7x + 1)
Consequently, x(x2 + 7x + 1) is the right solution via simplification.
How does simplification work?A technique to make the phrase less complex is simplification. And the variables' calculations became simple. Problems with simplification can be resolved by using mathematical characteristics.
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Find the distance between the points (1, 6) and (9, 0).
Answer:
You have to use the distance formula
d=√(x2-x1)^2 + (y2-y1)^2
replace the points and get 10
A customer wants to buy 0.4 pounds of mulch that cost $5.20 per pound. If the customer has a coupon for $0.50 off the total cost, how much will they pay for the mulch?
$1.04
$1.58
$2.08
$4.16
The amount paid for 0.4 pounds of much after deducting $0.50 coupon is $1.58. option B
DiscountCost of each pound of mulch = $5.20Number of pounds of mulch bought = 0.4 Coupon = $0.50Cost of 0.4 pounds of mulch = xCost of mulch : pounds of mulch
5.20 : 1 = x : 0.4
5.20/1 = x/0.4
5.20 × 0.4 = 1 × x
2.08 = x
Cost of 0.4 pounds of mulch = x = $2.08
Amount paid for 0.4 pounds of much after deducting $0.50 coupon
= $2.08 - $0.50
= $1.58
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Answer:
b) $1.58
Step-by-step explanation:
Now we have to,
→ find the amount the customer must pay.
One pound of mulch costs,
→ $5.20
Then 0.4 pounds of mulch costs,
→ $5.20 × 0.4
→ 5.20 × 0.4
→ $2.08
Total cost after reducing $0.50,
→ 2.08 - 0.50
→ $1.58
Hence, customer must pay $1.58.
I think i know how to do this but i keep getting them wrong lol help
Answer:
no worry I'll help u out
Step-by-step explanation:
90+55=145
180-145=35
z=35°
also may I ask for u to mark brainlist?asking
