Final answer:
To calculate the amount of chemical in the pond after a very long time, multiply the rate at which the chemical flows in per hour by the number of hours that have passed.
Explanation:
To find out how much of the chemical will be in the pond after a very long time, we can first calculate the amount of chemical that flows into the pond per hour. Since 0.01 g of chemical flows in per gallon, and the rate of flow is 300 gallons per hour, the amount of chemical added per hour is 0.01 g/gal * 300 gal/hr = 3 g/hr.
Since the amount of water in the pond remains constant, the concentration of the chemical will also remain constant. Therefore, after a very long time, the amount of chemical in the pond will be the amount added per hour multiplied by the number of hours that have passed. So, if time is represented by 't', then the amount of chemical in the pond after a very long time is given by 3 g/hr * t.
Angie wants to purchase mulch for her tulip garden. The dimensions of her garden are 6 feet by 8 feet. If mulch is sold by the square yard, determine how many square yards of mulch she must purchase and how much it costs. The price of the mulch is 1.50 per square yard.
Answer:
72 dollars
Step-by-step explanation:
Puppy B weighs 8 pounds which is about 75% of its adult weight what will be the adult weight of puppy B
The adult weight of puppy B is estimated to be around 11 pounds, as we learned by understanding percentages and using a mathematical formula to determine the total from a known percentage.
Explanation:
The subject is Mathematics and it involves a commonly used concept known as ratios and percentages. From the question, we know that puppy B weighs 8 pounds which is about 75% of its adult weight. This means that the adult weight will be greater than 8 pounds.
To find the adult weight, we know that the puppy's current weight represents 75% of it. So, we use the formula to find the total when we know the percentage:
Weight = percentage / 100 * total Weight = 8 pounds, Percentage = 75 Then we rearrange to find the total: Total = Weight / (Percentage / 100) = 8 / (75 / 100) = 8 / 0.75 = 10.67 pounds approximately
Therefore, we can estimate that the adult weight of puppy B will be around about 11 pounds.
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The adult weight of Puppy B will be approximately 10.67 pounds.
To find the adult weight of Puppy B, we can set up a simple proportion based on the given information that 8 pounds is 75% of its adult weight. Let's denote the adult weight as A .
We can express the relationship as:
[tex]\[ 8 \text{ pounds} = \frac{75}{100} \times A \][/tex]
To solve for [tex]\( A \)[/tex], we can multiply both sides of the equation by [tex]\( \frac{100}{75} \)[/tex] to isolate [tex]\( A \)[/tex]:
[tex]\[ A = 8 \text{ pounds} \times \frac{100}{75} \][/tex]
Now, we calculate the value of A:
[tex]\[ A = 8 \times \frac{4}{3} \][/tex]
[tex]\[ A = \frac{32}{3} \][/tex]
[tex]\[ A \approx 10.67 \text{ pounds} \][/tex]
Therefore, the adult weight of Puppy B is approximately 10.67 pounds.
Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14) as follows. m = StartFraction 14 minus (negative 2) Over 3 minus (negative 5) EndFraction = StartFraction 16 Over 8 EndFraction = 2. y = 2 x + b. Negative 2 = 2 (negative 5) + b. Negative 2 + 10 = negative 10 + b + 10. b = 8. What is the equation of the line in slope-intercept form?
Solution:
Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14)
To find: Equation of the line in slope - intercept form
The equation of line in slope intercept form is:y = mx + c ------ eqn 1
Where, "m" is the slope of line and "c" is the y intercept
Find the slope of line[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From given,
[tex](x_1, y_1) = (-5, -2)\\\\(x_2, y_2) = (3, 14)[/tex]
Therefore,
[tex]m = \frac{14-(-2)}{3-(-5)}\\\\m = \frac{14+2}{3+5}\\\\m = \frac{16}{8}\\\\m = 2[/tex]
Thus slope of line is 2
Find the y intercept:Substitute m = 2 and (x, y) = (-5, -2) in eqn 1
-2 = 2(-5) + c
-2 = -10 + c
c = -2 + 10
c = 8
Thus the equation of line is:Substitute c = 8 and m = 2 in eqn 1
y = 2x + 8
Thus the equation of line is found
Answer:
the answer is y=2x+8
Step-by-step explanation:
Identify the Pythagorean triple. A) 3, 6, 12 B) 8, 16, 32 C) 12, 34, 30 D) 28, 45, 53
Answer:
D, 28, 45, 53
Step-by-step explanation:
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a2 + b2 = c2; thus, Pythagorean triples describe the three integer side lengths of a right triangle.
The product of 10 and half of A
Answer:
Step-by-step explanation:
Selma is buying a cell phone for business. The regular price of the phone is $179. If she buys the phone at 20% discount how much will she save?
Answer:
[tex]\large \boxed{\$35.80}[/tex]
Step-by-step explanation:
Discount = Regular price × % discount
[tex]\text{Discount} = \text{\$179 regular price} \times \dfrac{\text{\$20 }}{\text{\$100 regular price}} = \textbf{\$35.80}\\\text{Selma will save $\large \boxed{\mathbf{\$35.80}}$}[/tex]
Selma will save $35.8 after getting 20% discount on regular price.
What is Discount?" Discount is the deduction amount from the regular price assigned to any product."
Formula used
Discount = Regular Price × discount %
According to the questions,
Regular price = $179
Discount% = 20%
Substitute the value in the formula we get,
Discount = 179 × 20%
= 179 × (20 / 100)
= $ 35.8
Hence, Selma will save $35.8 after getting 20% discount on regular price.
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(-4.7)^0 Does anyone have the answers to the Exponents and Exponential Functions Unit test
The answer to (-4.7)⁰ is 1
How to solve the exponent
We have a rule of thumb that Any non-zero number raised to the power of 0 is equal to 1.
This is a fundamental rule in mathematics and is consistent across all real numbers.
So, when you have (-4.7)⁰, you're essentially raising the number -4.7 to the power of 0.
Even though -4.7 is negative, it's still a non-zero number. Therefore, according to the rule, (-4.7)⁰ equals 1.
Solve for x in the equation x squared minus 8 x + 41 = 0.
x = negative 4 plus-or-minus StartRoot 37 EndRoot i
x = –4 ± 5i
x = 4 plus-or-minus StartRoot 37 EndRoot i
x = 4 ± 5i
Answer:
Option 4 - The solution of x is [tex]x=4\pm5i[/tex].
Step-by-step explanation:
Given : Equation [tex]x^2-8x+41=0[/tex]
To find : Solve for x in the equation ?
Solution :
Solving a quadratic equation [tex]ax^2+bx+c=0[/tex] solution is given by, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1, b=-8 and c=41
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(1)(41)}}{2(1)}[/tex]
[tex]x=\frac{8\pm\sqrt{-100}}{2}[/tex]
[tex]x=\frac{8\pm10i}{2}[/tex]
[tex]x=4\pm5i[/tex]
Therefore, the solution of x is [tex]x=4\pm5i[/tex].
Answer:
D
Step-by-step explanation:
trust meh
The system crosses (3,4). How many solutions will the system have?
Answer:
the system would have crossed one solution
scientific notation of .313
Answer:
3.13 * 10^-1
Step-by-step explanation:
Question is in the picture, please help
Answer:
18.9 units to 1 decimal Place
Step-by-step explanation:
You need the diameter so do 3 X 2 = 6
Circumference is pi X diameter so
Do 6 X pi = 6pi or 18.9 to 1 dp
20 blocks 6 are shaded what percent are shaded?
The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
Age: 25-34. 35-44. 45-54. 55-64
Number 22.1. 31.5. 37.7. 25.3
(Millions)
Answer:
Mean = 45.178
Standard Deviation = 10.33
Step-by-step explanation:
class m frequency, f m [tex]\times[/tex] f f [tex]\times[/tex] [tex]m^{2}[/tex]
25 - 34 29.5 22.1 651.95 19232.525
35 - 44 39.5 31.5 1244.25 49147.875
45 - 54 49.5 37.7 1866.15 92374.425
55 - 64 59.5 25.3 1505.35 89568.352
116.6 5267.7 250323.15
mean = [tex]\frac{5267.7}{116.6} = 45.178[/tex] standard deviation = [tex]\sqrt{\frac{250323.15 - \frac{(5267.7)^2}{116.6} }{(116.1 - 1)} } = 10.33[/tex]
The mean of a distribution is the average of the distribution ; it is the sum of observation divided by the count of the observation.
The mean age is 45.18The standard deviation is 10.29
Given that:
[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64\\{Number}&22.1&31.5&37.7&25.3\end{array}[/tex]
First, we calculate midpoint of each class.
This is the sum of the class interval divided by 2.
So, we have:
[tex]x_1 = \frac{25+34}{2} = 29.5[/tex]
[tex]x_2 = \frac{35+44}{2} = 39.5[/tex]
And so on...
The table becomes:
[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64&{Number(f)}&22.1&31.5&37.7&25.3&{x}&29.5&39.5&49.5&59.5\end{array}[/tex]
The mean of the distribution is:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{29.5 \times 22.1 + 39.5 \times 31.5 + 49.5 \times 37.7 +59.5 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}[/tex]
[tex]\bar x = \frac{5267.7}{116.6}[/tex]
[tex]\bar x = 45.18[/tex]
The standard deviation is calculated as follows:
[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
[tex]\sigma= \sqrt{\frac{(29.5 - 45.1)^2\times 22.1 + (39.5 - 45.1)^2 \times 31.5 + (49.5 - 45.1)^2 \times 37.7 + (59.5 - 45.1)^2 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}}[/tex]
[tex]\sigma= \sqrt{\frac{12342.176}{116.6}}[/tex]
[tex]\sigma= \sqrt{105.85}[/tex]
[tex]\sigma= 10.29[/tex]
Hence:
The mean age is 45.18The standard deviation is 10.29Read more about mean and standard deviation at:
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4(a+5) in distributive form
Answer:
4a+20
Step-by-step explanation:
Answer:4a + 20
Step-by-step explanation:
Amanda is at a store for apples and bananas. if she buys 6 apples and 5 bananas, it will cost $8.00. is she buys 5 apples and 7 bananas, it will cost $9.50. write and solve a system to determine how much the apples cost
Answer:
Therefore the cost of each apple is $ 0.50 and each banana is $1.
Step-by-step explanation:
Given , Amanda buys 6 apples and 5 bananas , it will cost $8.00 and if she buys 5 apples and 7 bananas it will cost $9.50.
Let the cost of one apple be =$ x
and the cost of one banana be =$y
According to the problem,
6x+5y=8.........(1) 5x+7y= 9.50............(2)
Equation (1)×5 - equation (2) × 6
30x +25 y-(30x+42y)= 40-57
⇔30x+25y -30x-42y= -17
⇔-17y =-17
⇔y=1
putting the value of y in equation (1)
6x+5×1=8
⇔6x = 8-5
⇔6x=3
⇔[tex]x =\frac{3}{6}[/tex]
⇔x = 0.50
Therefore the cost of each apple is $ 0.50 and each banana is $1.
What is 3/2+2/3 in fraction form
Answer:
[tex]\frac{13}{6}[/tex] or [tex]2\frac{1}{6}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:3/2 x 3= 9/6
2/3 x 2= 4/6
9/6 + 4/6 = 13/6
13/6=2 1/6
Which data set is the most spread from its mean?
14,26, 24, 28
22, 16, 18, 36
22, 28, 20, 22
21, 19, 27, 25
Answer 22,16,18,36
Step-by-step explanation:
Second data set 22, 16, 18, 36 is the most spread from its mean
What is Mean?" Mean is defined as the ratio of the sum of the all the numbers of data set to the total numbers of number present in data set."
Formula used
Mean = [tex]\frac{Sum of all the numbers in data set}{Total number of numbers}[/tex]
According to the question,
Given data set,
14,26, 24, 2822, 16, 18, 3622, 28, 20, 2221, 19, 27, 25Mean of first data set,
Substitute the values in the formula we get,
Mean = [tex]\frac{14 +26 + 24 + 28}{4}[/tex]
[tex]=\frac{92}{4}\\ =23[/tex]
Mean of second data set,
Substitute the values in the formula we get,
Mean = [tex]\frac{22 +16 + 18 + 36}{4}[/tex]
[tex]=\frac{92}{4}\\ =23[/tex]
Mean of third data set,
Substitute the values in the formula we get,
Mean = [tex]\frac{22 +28 + 20 + 22}{4}[/tex]
[tex]=\frac{92}{4}\\ =23[/tex]
Mean of fourth data set,
Substitute the values in the formula we get,
Mean = [tex]\frac{21 +19 + 27+ 25}{4}[/tex]
[tex]=\frac{92}{4}\\ =23[/tex]
Hence, second data set 22, 16, 18, 36 is the most spread from its mean.
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The rectangles in the figure below are similar. Find the value of x.
A. 2.4
B. 2.7
C. 6
D. 6.7
Answer: the answer is 6
Step-by-step explanation:
The value of x is 6.
What is Similarity?Two triangles are comparable if the measurements of their corresponding sides are proportionate. The same is true if the lengths of two sides in one triangle are proportional to the lengths of the corresponding sides in another triangle and the included angles are congruent.
Given:
As, the rectangles in the figure below are similar.
Using the property of similarity
x/(x+ 4) = 3/5
5x = 3x + 12
5x - 3x = 12
2x = 12
Divide both side by 2
2x /2 = 12/2
x = 6
Hence, the value of x is 6.
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Name the property the equation illustrates.
-4x-1/4=1
Answer:
Distrbutive Property
Step-by-step explanation:
The equation -4x - 1/4 = 1 illustrates the addition property of equality.
Explanation:The property illustrated by the equation -4x - 1/4 = 1 is the addition property of equality. According to this property, if you add the same number to both sides of an equation, the equality of the equation is maintained. To isolate the variable, we need to get rid of the constant term (-1/4) on the left side of the equation by adding 1/4 to both sides. This simplifies the equation to -4x = 1 + 1/4. Then, divide both sides by -4 to solve for x.
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Answer part A and part B and explain how you got your answers please ❤️
Part a: Option c: [tex]3x+90+x-14=180[/tex]
Part b: The value of x is 26
Explanation:
Part a:
Option a: [tex]3x+x-14=180[/tex]
Since, adding all the angles in the straight line results in 180°, and only two of the three angles were added in the equation to find the value of x.
Thus, the equation [tex]3x+x-14=180[/tex] cannot be used to determine the value of x.
Hence, Option a is not the correct answer.
Option b: [tex]3x+90+x-14=90[/tex]
Adding all the angles in the straight line results in 180°.
Thus, adding all the angles does not equals to 90°
Hence, the equation [tex]3x+90+x-14=90[/tex] cannot be used to determine the value of x.
Hence, option b is not the correct answer.
Option c: [tex]3x+90+x-14=180[/tex]
Since, the straight line is 180° and thus adding the angles in this straight line will result in 180°
Thus, the angles in this straight line are 3x, 90° and x-14.
Hence, adding these angles will result in 180°
Thus, the equation becomes
[tex]3x+90+x-14=180[/tex]
Hence, the equation used to determine the value of x is [tex]3x+90+x-14=180[/tex]
Thus, Option c is the correct answer.
Option d: [tex]4x+90=360[/tex]
Adding all the angles in the straight line results in 180°.
Since, not all the three angles were added in this equation and the equation equals to 180°
Hence, the equation [tex]4x+90=360[/tex] cannot be used to determine the value of x.
Thus, Option d is not the correct answer.
Part b:
To determine the value of x, we shall add all the angles of the equation [tex]3x+90+x-14=180[/tex]
Thus, we get,
[tex]4x+76=180[/tex]
Subtracting both sides by 76,
[tex]4x=104[/tex]
Dividing both sides by 4, we get,
[tex]x=26[/tex]
Thus, the value of x is 26.
What is the algebraic expression for three more cookies than are in the jar
Answer:
x+3
Step-by-step explanation:
Since the number of cookies in the jar could be anything we'll use a variable to represent it, x. so three more than x is what?
Well, what's thee more than 5? 8, so you add 3.
So x+3
Can someone please answer this question please answer it correctly please show work please
Answer:
3) A
4) D
Step-by-step explanation:
3)
Find any four points where y intersects with x on graph A
(-4 , 2) (-2 , 1) (4, - 2) (2 , -1)
Find the relationship(s) between x and y
(-4 , 2) (-2 , 1) (4, - 2) (2 , -1)
x = -2y x = -2y x = -2y x = -2y
It is shown that there is a direct proportional relationship between x and y, (x = -2y)
Repeat for graphs B, C, and D
Find any four points where y intersects with x on graph B
(3 , 2) (5 , 4) (-3 , -4) (-4 , -5)
Find the relationship(s) between x and y
x = 1.5y x = 1.25y x = 0.75y x = 0.8y
As you can see, there is not a constant direct proportional relationship between x and y. B is not the correct answer
Graph C
Find any four points where y intersects with x on graph C
(-5 , -3) (-1 , -3) (1 , -3) (5 , -3)
Find the relationship(s) between x and y
x = 1.67y x = 0.3y x = -0.3y x = -1.67y
Once again, there is not a constant direct proportional relationship between x and y, so C is not the correct answer
Graph D
Find any four points where y intersects with x on graph D
(2 , 1) (2 , 2) (2 , 3) (2 , 4)
Find the relationship(s) between x and y
x = 2y x = y x = 0.67y x = .5y
There is no direct constant relationship between x and y in this graph either.
Graph A is the only graph with a direct proportional relationship between x and y.
4) Allison wants to know whom seventh-grade students will vote for in the upcoming class president election.
A) Every member of the student council
Asking every member of the student council who they are voting for will not help Allison, because it is likely that there are multiple grades involved in the student council, when Allison just wants to know the opinions of seventh-graders. The student council also might have a different opinion than the general seventh-graders.
B) All 12 girls in Allison's homeroom class
It is likely that the girls at Allison's school have a very different opinion than the boys at her school, making this a bad data set.
C) Every tenth student who arrives at school on Monday
Allison only want to know the opinions of seventh-graders, not every tenth student at her school, which would consist of more than seventh-graders.
D) Every tenth name on a roster of all of the seventh-graders at the school
This data set would be the most useful to Allison because it is multi-gender, only seventh-grade, and consists of the general seventh-graders (not part of a special group).
D
Hope this helps :)
Y’all I need help on this what is this
Answer:
200
Step-by-step explanation:
Your answer should be a polynomial in standard form.(x-5)(x-4)
Answer: x^2-9x+20
Step-by-step explanation:
Answer:
x² - 9x + 20
Step-by-step explanation:
Given
(x - 5)(x - 4)
Each term in the second factor is multiplied by each factor in the first factor, that is
x(x - 4) - 5(x - 4 ) ← distribute both parenthesis
= x² - 4x - 5x + 20 ← collect like terms
= x² - 9x + 20
At ulrich 45% of the seventh graders ride the school bus to school if there are 360 seventh graders how many ride the bus
Basically 45% of 360.
45/100 * 360
45/360 * 100
16,200 / 100
162
Answer:
162
Step-by-step explanation:
There are 360 seventh graders and 45% of this 360 ride the school bus
All we need to do is find 45% of 360
we have;
45 / 100 X 360
= 162
Hence 162 seventh graders ride the school bus
Solve the inequality for #5 Please! (Ignore my horrible handwriting im a lefty lol)
Question:
Solve the inequality:
5.1 – r ≥ 5
Answer:
r ≤ 0.1
Solution:
Step 1: Given inequality:
5.1 – r ≥ 5
Step 2: Subtract 5.1 from both sides of the inequality
⇒ 5.1 – r – 5.1 ≥ 5 – 5.1
⇒ – r ≥ – 0.1
Step 3: To reverse the inequality, multiply both sides by –1.
⇒ (–r) × (–1) ≥ – 0.1 × (–1)
Negative × Negative = Positive
⇒ r ≤ 0.1
Hence the solution to the given inequality is r ≤ 0.1.
Connie's dog fido weighs 35 pounds. Her vet placed fido on a diet. What inequality can you write to find the average number of pounds Fido must lose monthly to reach a healthier weight of 28 pounds or less within 6 months? Write the inequality and solve.
Please give inequality, solution, and show work
Fido's dog must lose 1.17 pounds each month to reach healthier weight.
Step-by-step explanation:
Given,
Weight of fido's dog = 35 pounds
Time period = 6 months
Goal weight to reach = 28 or less pounds
Let,
m be the weight to be lose each month.
Weight of dog - Time period * Weight to lose each month ≤ Goal weight
[tex]35-6m\leq 28\\-6m\leq 28-35\\-6m\leq -7[/tex]
Dividing both sides by -6
[tex]\frac{-6m}{-6}\leq \frac{-7}{-6}\\\\m\leq 1.17[/tex]
Fido's dog must lose 1.17 pounds each month to reach healthier weight.
Keywords: division, subtraction
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helppppppppppppppppp
Answer:
C
Step-by-step explanation:
Note that (f + g)(x) = f(x) + g(x)
f(x) + g(x)
= 4x + 1 + x² - 5 ← collect like terms
= x² + 4x - 4 → C
If 4/5x is -16, what is the value of -2x-15?
Answer:
25
Step-by-step explanation:
Given data
(4/5)x = -16
x = -16 (5/4)
x = -20
Now,
-2x-15 = ?
putting the value of x
-2(-20)-15 = 25
Steve is buying a new car at the dealership. The price tag on the car reads $17,000.00. However, the salesman offers to sell him the car for 15% off the price tag. If sales tax is 8%, how much does the car cost after tax?
Answer:
$15606000
Step-by-step explanation:
17,000,000*.15 (15% off)
$ 2550000 off
17,000,000
-2550000
$14450000 (15% off)
*1.08 (sales tax)
$15606000
sorry if it is incorrect
Answer:
if the sale tax comes first before the 15% off,
Sales Tax: 1360
so the price became 18360
Price Off: 2754
18360 - 2754 = 15606
if the sale tax comes after the 15% off,
Price Off: 2550
17000-2550 = 14450
eight percent of 14450 is 1156
14450+1156 = 15606
anyways, the price is the same no matter if the sales tax comes first or the discount comes first