Answer:
2 \(\frac{3}{4}\)
Step-by-step explanation:
Substitute the given values into the expression
2 ( \(\frac{1}{16}\) + (\(\frac{1}{4}\) )² ) + 5(\(\frac{1}{2}\) )
= 2 ( \(\frac{1}{16}\) + \(\frac{1}{16}\) ) + \(\frac{5}{2}\)
= 2 (\(\frac{2}{16}\) ) + \(\frac{5}{2}\)
= 2 (\(\frac{1}{8}\) ) + \(\frac{5}{2}\)
= \(\frac{1}{4}\) + \(\frac{10}{4}\)
= \(\frac{11}{4}\)
= 2 \(\frac{3}{4}\)
How many solutions does this equation have? h² = -49
Answer:
The equation has no real solutions. It has 2 imaginary, or complex solutions.
Step-by-step explanation:
Good boy
Answer: 0
Step-by-step explanation:
none you can't take the square root of a negative number
Or if you square any number you can never get -49
7*7 = +49
(-7)(-7)=+49
It' only has 2 imaginary solution 7i
given: δabc is a right triangle. prove: a2 + b2 = c2
In a right triangle, the Pythagorean theorem states that the square of the length of the side opposite the right angle (side AB) plus the square of the length of the side adjacent to the right angle (side BC) is equal to the square of the length of the hypotenuse (side AC).
In a right triangle, one of the angles is a right angle, which measures 90 degrees. Let's label the sides of the triangle as follows: AB is the side opposite to the right angle, BC is the side adjacent to the right angle, and AC is the hypotenuse, which is the side opposite to the remaining acute angle.
According to the Pythagorean theorem, in any right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse. Mathematically, it can be expressed as:
A\(B^{2}\) + B\(C^{2}\) = A\(C^{2}\)
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Assume that the recovery time for an individual from an infectious disease can be modeled as a normal distribution. (a) Calculate the time, d, in days for an individual to recover from being initially infected, with a 95% confidence level, assuming that the likelihood of recovering at any time is modeled as a normal distribution with a mean of 5 days and a standard deviation of 0.5 days. (b) Use the SIR model that you constructed previously. Assume that a city of 10 million people is confronted with a potential infectious epidemic. A ship arrives at the international airport carrying 100 individuals who are infected, but are unaware that they are infected. While contagious, infected individuals come into transmission contact with another individual once every 2 days. The recovery process is modeled using the Poisson process from Part (a). Assume that recovered individuals that survive develop immunity to the disease. Plot the fraction of susceptible individuals, infected individuals, and recovered individuals as a function of time throughout the epidemic. (c) What fraction of the total population will have ultimately come down with the infectious disease once the epidemic is over? How many days after the ship docking did this number finally reach steady state (i.e.,the epidemic is completely over). (d) What is the basis for this structured model (i.e.,scale, time, etc.)? What is/are the major assumptions associated with the structure?
Upper
daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.
(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.
Given:
Mean (μ) = 5 days
Standard deviation (σ) = 0.5 days
The confidence interval can be calculated as follows:
Lower limit = Mean - (1.96 * Standard deviation)
Upper limit = Mean + (1.96 * Standard deviation)
Lower limit = 5 - (1.96 * 0.5)
= 5 - 0.98
= 4.02 days
Upper limit = 5 + (1.96 * 0.5)
= 5 + 0.98
= 5.98 days
Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.
(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.
(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.
(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:
Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.
Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.
Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.
No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.
These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.
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The ratio of males to females is 3:4. How many females are there if there are..
i. 3 males
ii. 6 males
Answer:
i) 4 females
ii) 8 females
Step-by-step explanation:
1. Ratio of males= 3x
3x = 3
Thus, x = 1
If there are 3 males, there will be 4 females
2.Rato of males= 3x
3x = 6
Thus x = 2 [6 divided by 3]
4x = 4 x 2 = 8
If there are 6 males, there would be 8 females.
7(x-2) = 3(x+4)? Please help soon!
Answer:
x=6.5
Step-by-step explanation:
7(x-2)=3(x+4)
Step 1. Distribute
7x-14=3x+12
Step 2. Combine like terms and calculate
4x=12+14
Step 3. Divide 4 on both sides
4x=26
Solution:
x=6.5
Hope this helps! :)
Solve the triangle. Round your answers to the nearest tenth.
Answer:
m∠A ≈ 43°
m∠B ≈ 55°
mBC ≈ 20
Step-by-step explanation:
Law of Sines: \(\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}\)
Step 1: Find m∠B
\(\frac{29}{sin82} =\frac{24}{sinB}\)
Step 2: Solve for ∠B
29sinB = 24sin82°
sinB = 24sin82°/29
B = sin⁻¹(24sin82°/29)
B = 55.038°
Step 3: Find m∠A
180 - (55.038 + 82)
180 - 137.038
m∠A = 42.962°
Step 4: Find BC
\(\frac{29}{sin82} =\frac{BC}{sin42.962}\)
Step 5: Solve for BC
29sin42.962° = BCsin82°
BC = 29sin42.962°/sin82°
BC = 19.9581
Jonah needs to determine the dimensions of a rectangular poster that will cover an area represented by
7x² + 3x - 10. Which of the following expressions is equivalent to the area of the rectangular poster?
A (x+1)(7x-10)
B (x-1)(-7x+10)
C(x-1)(7x+10)
D(x-7)(x+10)
E(7x-1)(x+10)
Answer:
The correct answer is A (x+1)(7x-10).
Step-by-step explanation:
To determine the dimensions of a rectangular poster that will cover an area represented by 7x² + 3x - 10, we need to find the factors of the expression 7x² + 3x - 10 that will give us the length and width of the poster.
One way to do this is to factor the expression 7x² + 3x - 10 using the difference of squares method. We can write the expression as follows:
7x² + 3x - 10 = (7x² + 3x) - 10
To factor (7x² + 3x) - 10, we can write the expression as the difference of squares:
(7x² + 3x) - 10 = (7x² + 3x + 10) - (10 + 10)
To simplify the expression, we can complete the square for the terms in parentheses:
(7x² + 3x + 10) - (10 + 10) = (7x² + 3x + 10) - 20
To complete the square, we need to add and subtract the square of half the coefficient of the x term, which is (3/2)² = 9/4. We can rewrite the expression as follows:
(7x² + 3x + 10) - 20 = (7x² + 3x + 10 + 9/4) - (20 - 9/4)
To simplify the expression, we can factor the terms in parentheses:
(7x² + 3x + 10 + 9/4) - (20 - 9/4) = [(7x² + 3x + 10 + 9/4) - (20 - 9/4)]
To simplify the expression further, we can factor out a common factor:
[(7x² + 3x + 10 + 9/4) - (20 - 9/4)] = (x + 1)(7x - 10)
From the given options, the expression that represents the area of the rectangular poster is (x+1)(7x-10), which is equivalent to 7x² + 3x - 10. We can verify this by multiplying (x+1)(7x-10) to get 7x² + 3x - 10. Therefore, the correct answer is A (x+1)(7x-10).
A package of 4 pairs of insulated gloves costs $31.16. What is the unit price of the pairs of gloves?
The unit price is $ per pair of gloves.
Answer:
$7.79 per pair of gloves
Step-by-step explanation:
divide
31.16÷ 4 = 7.79
the ability to order items in a sequence, such as longest to shortest, is known as:
The ability to order items in a sequence, such as longest to shortest, is known as Seriation.
Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.
Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.
Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.
Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.
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What helps find the volume of the figure? 6 × 6 × 7 8 × 6 × 6 6 × 7 × 8 6 × 6 × 7 × 8
The volume of the rectangular prism can be found using the 6x6x7 option (A) 6x6x7 is correct.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.
It is given that:
The volume of the rectangular prism is given by:
V = L×W×H
Here, V is the volume of the rectangular prism
L is the length of the rectangular prism
W is the width of the rectangular prism
H is the height of the rectangular prism
From the figure:
L = 6 cm
W = 7 cm
H = 6 cm
V = 6x7x6
or
V = 6x6x7
Thus, the volume of the rectangular prism can be found using the 6x6x7 option (A) 6x6x7 is correct.
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Identify the number of molecules in the chemical formula for Butane.
5C4H10
2
4
5
or 10
Answer:
the way you have the question on here is weird, but I'm pretty sure the answer is 5
Step-by-step explanation:
molecules are groups of bonded atoms, so one molecule of Butane would be C4H10 by itself, but if you have 5 of those, you have 5 molecules.
however, if you're talking about the number of ATOMS in one molecule of Butane, there would be 14 (4 carbon, 10 hydrogen)
find and solve a recurrence relation for the number of matches played in a tournament with n players, where n is a power of 2.
A recurrence relation for the number of matches is m = 2^n / 2.
What is recurrence relation?
A recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms.
If we have 2^n players, and m(n) is the number of matches, then the first tournament round will be m matches between m = (2^n / 2) pairs of players. The next round will be among the winners of those matches, and so on:
m(n = 1), there is 1 match between 1 pair \(2^{n} /2\) of players.
m(n = 2), there are 2 matches between 2 pairs \((2^2 / 2)\) of players, plus the match (as above) between the 2 winners.
m(n = 3), there are 4 matches between 4 pairs \((2^3 / 2)\) of players, plus the 2 matches (as above) between the 2 pairs of winners, and so on ...
So, for m(n), in a tournament of n players, m = \(2^n / 2\) matches in the first round of the tournament, plus the number of rounds required for \(2^{n-1}\) players.
Step 1: m(1) = 1
Step 2: m(n) = (2^n)/2 + m(n - 1)
A recurrence relation for the number of matches is m = 2^n / 2.
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Use inductive reasoning to predict the next month in the pattern: January, April, July...
A.) November
B.) August
C.) October
D.) September
Answer:
c.) October
Step-by-step explanation:
the pattern just skip two months
The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.
a. 10.6%
b. 89.4%
c. 39.4%
d. 78.8%
e. 68.27%
Using the normal curve to estimate the following percentages. The answer that is closes to being correct is 39.4%. So, the correct answer is C.
Since the distribution is approximately normal, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages.
a. 10.6%: This corresponds to the area under the curve that is more than 2 standard deviations below the mean. Using the rule, we know that about 2.5% of the area under the curve is more than 2 standard deviations below the mean. So 10.6% is too high. The answer is not a.
b. 89.4%: This corresponds to the area under the curve that is less than one standard deviation above the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 89.4% is too high. The answer is not b.
c. 39.4%: This corresponds to the area under the curve that is within one standard deviation of the mean. Using the rule, we know that about 68% of the area under the curve is within one standard deviation of the mean. So 39.4% is the closest to being correct. The answer is c.
d. 78.8%: This corresponds to the area under the curve that is less than two standard deviations above the mean. Using the rule, we know that about 95% of the area under the curve is within two standard deviations of the mean. So 78.8% is too high. The answer is not d.
e. 68.27%: This corresponds to the area under the curve that is within one standard deviation of the mean. This is the same as c. So e is not the correct answer.
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Evaluate 15 C5. 15 C5 (Simplify your answer. Type an integer or a fraction.)
The value of 15 C5 is 3003.
In combinatorics, "n choose r" (notated as nCr or n C r) represents the number of ways to choose r items from a set of n items without regard to the order of selection. In this case, we are calculating 15 C 5, which means choosing 5 items from a set of 15 items. The value of 15 C 5 is found using the formula n! / (r! * (n-r)!), where "!" denotes the factorial operation.
To evaluate 15 C 5, we calculate 15! / (5! * 10!). The factorial of a number n is the product of all positive integers less than or equal to n. Simplifying the expression, we have (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1 * 10 * 9 * 8 * 7 * 6). This simplifies further to 3003, which is the final answer.
15 C 5 evaluates to 3003, representing the number of ways to choose 5 items from a set of 15 items without regard to the order of selection. This value is obtained by calculating the factorial of 15 and dividing it by the product of the factorials of 5 and 10.
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A study of child care enrolled 1364 infants and followed them through their sixth year in school. Later, the researchers published an article in which they stated that "the more time children spent in child care from birth to age four-and-a-half, the more adults tended to rate them, both at age four-and-a-half and at kindergarten, as less likely to get along with others, as more assertive, as disobedient, and as aggressive." $^{31}$ (a) Is this an observational study or an experiment? Justify your answer. (b) What are the explanatory and response variables? (c) Does this study show that child care causes children to be more aggressive? Explain.
(a) Is this an observational study or an experiment?
ans=Observational study – no treatment was imposed
(b) What are the explanatory and response variables?
ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior
d) Does this study show that child care causes children to be more aggressive? Explain.
No. Observational studies cannot show cause-and-effect
Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.
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Write and simplify an expression for the ratio of the volume of the cylindrical tank to its surface area (including the bases).
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
Then the surface area of the cylinder will be
SA = 2πrh square units
Then the ratio of the volume of the cylindrical tank to its surface area will be
V / SA = π r²h / 2πrh
V / SA = r / 2
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
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What is the answer to y=-2/3x0+1
Answer:
1 is the answer to this question
(20 points) please help with this deltamath assigment
The sοlutiοn tο the system οf equatiοns -2x - 2y = -24 and -3x - 2y = -33 is x = -3 and y = 46/30 (οr simplified as y = 23/15).
What is the system οf equatiοns?In mathematics, a set οf simultaneοus equatiοns, alsο knοwn as a system οf equatiοns οr an equatiοn system, is a finite set οf equatiοns fοr which cοmmοn sοlutiοns are sοught.
Tο sοlve the system οf equatiοns -2x - 2y = -24 and -3x - 2y = -33 by cοmbining the equatiοns, we can eliminate οne οf the variables by adding οr subtracting the equatiοns. In this case, we can eliminate y by adding the twο equatiοns. The result is:
(-2x - 2y) + (-3x - 2y) = (-24) + (-33)
Simplifying this equatiοn, we get
-5x - 4y = -57
Nοw, we have a single equatiοn with οne variable, which we can sοlve fοr x.
-5x - 4y = -57
-5x = -57 + 4y
x = (-57 + 4y) / (-5)
We can substitute this expressiοn fοr x intο οne οf the οriginal equatiοns tο sοlve fοr y. Let's use the first equatiοn:
-2x - 2y = -24
-2((-57 + 4y) / (-5)) - 2y = -24
114/5 - 8y/5 - 2y = -24
-18y/5 = -114/5 - 24
-18y/5 = -138/5
y = 138/90
y = 46/30
Nοw we can substitute y = 46/30 intο οur expressiοn fοr x tο find the value οf x:
x = (-57 + 4(46/30)) / (-5)
x = -3
Hence, the sοlutiοn tο the system οf equatiοns -2x - 2y = -24 and -3x - 2y = -33 is x = -3 and y = 46/30 (οr simplified as y = 23/15).
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I need help on this. I need a really good explanation on how you got it.
Answer:
y = \(\frac{1}{7}\) x + 30
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (0, 30) and (x₂, y₂ ) = (70, 40) ← 2 points on the line
m = \(\frac{40-30}{70-0}\) = \(\frac{10}{70}\) = \(\frac{1}{7}\)
The line crosses the y- axis at (0, 30) ⇒ c = 30
y = \(\frac{1}{7}\) x + 30 ← equation of line
Which is an equation of the inverse of y=3/2x?
Answer:
y
=
3
2
x
Rewrite in slope-intercept form.
Tap for more steps...
y
=
3
2
x
Use the slope-intercept form to find the slope and y-intercept.
Tap for more steps...
Slope:
3
2
y-intercept:
(
0
,
0
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
Tap for more steps...
x
y
0
0
2
3
Graph the line using the slope and the y-intercept, or the points.
Slope:
3
2
y-intercept:
(
0
,
0
)
x
y
0
0
2
3
image of graph
Step-by-step explanation:
how many students are involved in the school music program but not school sports
Answer:
45% of the school because some will sign up
How rany metric toes (1 metric ton =10^3
kg ) of water fel on the city? (2 cm ^3 of water has a mass of 1gram=10^−1 kg) Express your answer using one significant figure. Khesy nuroom ompn 10 cm of tain en a oy 5 kin wide and 9 km lore in a 2.tu period PartB Expiess yeur answer using one significani figuee. How mary metic tons (1 metric ton =10 ^3 kg ) of water fell on the city? (1 cm^3 of water has a mass of 1gram=10^3 kg) Express your answer using one significant figure. A heovy rarttorm dumps 1.0 cm of rain on a city 5 kin whe and 9 km tong in a 2.h persed. Part 8 How man oalson of wame fel on the cry? (1 kal a 3 fas 1 ? I kgress youe anwwer using one significant tigure.
To know how many metric tons of water fell on the city, we'll solve the given questions step by step. In Part A, 2 cm^3 of water corresponds to 1 * 10^-4 metric tons. In Part B, 1 cm^3 of water corresponds to 1 metric ton.
In Part A, we are given that 2 cm^3 of water has a mass of 1 gram (10^-1 kg), and we need to determine the amount of water in metric tons. Since 1 metric ton is equal to 10^3 kg, we can convert the mass of water from grams to metric tons by dividing it by 10^3. Therefore, the amount of water that fell on the city is 1 * 10^-1 kg / 10^3 kg = 1 * 10^-4 metric tons.
Moving on to Part B, we are given that 1 cm^3 of water has a mass of 1 gram (10^3 kg). Similar to the previous calculation, we divide the mass of water by 10^3 to convert it to metric tons. Thus, the amount of water that fell on the city is 1 * 10^3 kg / 10^3 kg = 1 metric ton.
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The study of statistics rests on what two major concepts? A) Data and Context B) Variation and Number C) Variation and Data D) Average and Variation.
The study of statistics rests on two major concepts:
Variation and Data.
Correct option is C.
What is statistics?Statistics is simply defined as the study and manipulation of data. Statistics deals with the analysis and computation of numerical data.
Given,
The study of statistics rests on what two major concepts:
Variance and Data
The basics of statistics include the measure of central tendency and the measure of variation. The central tendencies are mean, median and mode and variation, comprise variance and standard deviation.
Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set.
Hence, Variation and Data are two major concepts, on which study of statistics rely.
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How do I solve this I need help
Answer:
h = -xy + r
r = xy + h
Step-by-step explanation:
Given the equation, \(x = \frac{r - h}{y}\)
Part A: To solve for h:
Multiply both sides by (y) to eliminate the denominator on the right-hand side:
\(x (y) = \frac{r - h}{y} (y)\)
\(x (y) = r - h\)
Next, subtract r from both sides:
\(xy - r = r - h - r\)
xy - r = - h
Finally, to solve for h, divide both sides by - 1:
\(\frac{xy - r}{-1} = \frac{-h}{-1}\)
h = -xy + r
Part B: To solve for r:
\(x = \frac{r - h}{y}\)
Multiply both sides by (y) to eliminate the denominator on the right-hand side:
\(x (y) = \frac{r - h}{y} (y)\)
\(x (y) = r - h\)
Add h to both sides of the equation to solve for r:
xy + h = r - h + h
xy + h = r
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I need help on these as well
Answer:
5. 2
6. -1
7. undefined
Step-by-step explanation:
An 11 ounce bottle of shampoo costs $2.97. What is the cost per ounce?
The total length of 3 boards was 21.35 m. If one board was 8.2 m long and another was 6.42 m long, how long was the third board? *
Answer:6.56
Step-by-step explanation:
Answer:
Step-by-step explanation:
Length of the third board = Total length - ( sum of other two boards)
= 21.35 - ( 8.2 + 6.42)
= 21.35 - 14.62
= 6.73 m
Tyrell had $73.25. He then spent $42.73 on a pair of shoes. Witch is the best estimate of the amount tyrell had left?
Answer:
I would estimate $30.52
Step-by-step explanation:
If you subtract his original total from the beginning from what he had spent on shoes, you would get the amount of what he has left.
Help me!!!!!!!!!!!!!!!
Answer:
A. 2.72
Step-by-step explanation: