Final answer:
The expanded form of 38,072 is 30,000 + 8,000 + 70 + 2, where each term represents the digit's value as a product of its place value.
Explanation:
The expanded form of the number 38,072 is written by separating each digit according to its place value and expressing it as the digit multiplied by the power of ten that represents its position. Therefore, the correct expanded form is:
30,000 + 8,000 + 70 + 2
To understand this, we can consider the place value of each digit in the number 38,072. The '3' is in the ten-thousands place, so it is 3 times 10,000, which is 30,000. The '8' is in the thousands place, so it is 8 times 1,000, which is 8,000. The '0' stands for no hundreds, so we skip it. The '7' is in the tens place, so it is 7 times 10, which is 70. Finally, the '2' is in the ones place, which is just 2.
If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)
For a better understanding of the explanation provided here, please go through the graphs in the attached files. The first file contains the explanations to the first part of the question and the second file contains the three graphs required to explain the second part (the y intercept part) of the question.
It has been given to us that the pH concentration equation is:
[tex] p(t)=-log_{10}t [/tex]
where, The variable t represents the amount of hydronium ions and p(t) gives the resulting pH level.
As can be seen from the first graph, pH is 1 when the amount of hydronium ions, t is 0.1. This is as expected, because, from the concept of logarithms we know that:
[tex] log_{10}(0.1)=log_{10}(\frac{1}{10})=log_{10}(10^{-1})=-1\times log_{10}10=-1\times 1=-1 [/tex]
Thus, [tex] p(0.1)=-1\times-1=1 [/tex]
Again, the value of pH, p(t) is 0 when the concentration of the Hydronium ions, t is 1. This, again, is as expected, because, from the concept of logarithms we know that [tex] log(1)=0 [/tex].
If the pool maintenance man uses our graph and needs to find the the pH level if the amount of hydronium ions is raised to 0.50, then to do so, the pool maintenance man must draw a vertical line from t=0.5 and check the x coordinate of the point where this vertical line intersects the p(t) graph. As we can see from the graph this roughly comes out to be the horizontal line y=0.3.
Let us now move on to the second part of the question. For a better understanding of this part please go through the second graph which has been attached. This graph contains all translations on the original graph and the explanation to each one of them is provided below:
Let us start with the last one, -p(t). We know that, since, [tex] p(t)=-log_{10}(t) [/tex], therefore, [tex] -p(t)=log_{10}(t) [/tex], simply a vertical "flip" or reflection of the original graph. And because the original graph did not have a y intercept, this graph too will not have a y intercept.
Let us now move on to the first one. Here, [tex] p(t)+1=-log(t)+1 [/tex]. This graph will simply move the original graph vertically up by 1 unit and that will not have any bearing on the y intercept and thus, the graph of p(t)+1 will again, not have a y intercept.
Finally, let us move on to the graph of the equation p(t+1). As can be seen, this graph has a y intercept at the origin when t=0. This is because:
[tex] p(t+1)=log_{10}(t+1) [/tex]
and when t=0, [tex] p(t+1)=p(0+1)=log_{10}(0+1) [/tex]
[tex] p(1)=log_{10}(1)=0 [/tex]
Thus, when t=0, p(t+1)=0 too and thus we have a y intercept.
Therefore, out of the three transformations, only the middle transformation results in a y-intercept, the explanation for which has been provided.
1. Which of the following expressions is not equal to 0.00055?
55 • 10^-5
5.5 • 10^-4
5.5 • 10^4
0.55 • 10^-3
2. A satellite can move at 17,000 miles per hour. How many hours will it take to reach a star that is three light years away? Recall that 1 light year = 9.5 ∙ 10^12 kilometers and 1 kilometer = 0.62 miles. Show your work.
. At a local bakery, all loaves of wheat bread come with 19 slices, while all loaves of rye bread come with 20 slices. If Grayson bought the same number of slices of each type of bread, what is the smallest number of slices of each type that Grayson could have bought?
Simplify the imaginary number square root of -12
The square root of -12, an imaginary number, can be simplified to 2i√3. This involves breaking -12 into -1 * 12 and taking the square root of both parts to get 'i' and 2i√3 respectively.
Explanation:The question asked is to simplify the imaginary number square root of -12. Imaginary numbers are those numbers whose square is less than or equal to zero. They are expressed in the form of 'i' where 'i' is the imaginary unit with the property i^2 = -1. When we take square root of a negative number, 'i' is involved in the solution.
To simplify the square root of -12, we can express -12 as -1 * 12. In this case, square root of -1 is 'i' and square root of 12 is 2 * square root of 3 (since 12= 4*3 and square root of 4 is 2).
Therefore, square root of -12 can be written as 'i' * 2 * square root of 3 or simply 2i√3.
Learn more about Imaginary Numbers here:https://brainly.com/question/6748860
#SPJ12
a survey asked 50 students if they play an instrument and if they are in band. 25 students play an instrument 20 are in a band and 30 are not in a band. which table shows these data correctly entered in a two way frequency table?
Answer:
Option 4th is correct.
Step-by-step explanation:
We have been the information 25 students play an instrument 20 are in a band 30 are not in a band.
We need to create a two way table:
Band Not in Band Total
Play instrument 20 5 25
Do not play instrument 0 25 25
Total 20 30 50
Option 4th is correct.
In a game played with a standard deck of cards, each face card has a value of 10 points, each ace has a value of 1 point, and each number card has a value equal to its number. two cards are drawn at random. it at least one card is an ace, what is the probability that the sum of the cards is 7 or less?
Jonas jogged up the hill at an average rate of of a mile per minute and then walked down the hill at an average rate of of a mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill?
if the xy-plane, the graph of y=x^2 and the circle with center (0,1) and radious 3 have how many points of intersection?
A. none
b. one
c, two
d. three
e. more than three
The answer could be A or c but idk which one is the right one please help
What is the answer plz help
A triangular bandana has an area of 70 square inches.The height of the triangle is 8 3/4 inches. Write and solve an equation to find the length of the base of the triangle.
The required equation is 70 = (1/2) × base × 8.75, resulting in a base length of 16 inches.
To find the length of the base of a triangle when given the area and the height, we use the formula for the area of a triangle: Area = (1/2) × base × height. In this problem, the area is 70 square inches and the height is 8 3/4 inches.
First, convert the height from a mixed number to an improper fraction or decimal. We have:
8 3/4 inches = 8 + 3/4 = 8.75 inches
Next, write the equation based on the area formula:
70 = (1/2) × base × 8.75
To solve for the base, first multiply both sides of the equation by 2 to eliminate the fraction:
140 = base × 8.75
Then, divide both sides by 8.75 to isolate the base:
base = 140 / 8.75
Calculating this gives:
base = 16 inches
Therefore, the length of the base of the triangle is 16 inches.
16. For quadrilateral ABCD, determine the most precise name for it. A (-2, 3), B (9, 3), C (5, 6) and D (2, 6). Show your work and explain.
Answer:
Trapzoid
Step-by-step explanation:
Given: A (-2, 3), B (9, 3), C (5, 6) and D (2, 6)
We will find the slope of each line.
Formula:
[tex]\text{Slope, m}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Slope of AB, m}_1=\dfrac{3-3}{9+2}=0[/tex]
[tex]\text{Slope of BC, m}_2=\dfrac{6-3}{5-9}=-\dfrac{3}{4}[/tex]
[tex]\text{Slope of CD, m}_3=\dfrac{6-6}{2-5}=0[/tex]
[tex]\text{Slope of AD, m}_4=\dfrac{6-3}{2+2}=\dfrac{3}{4}[/tex]
Slope of AB = Slope of CD = 0
[tex]m_1=m_3=0[/tex]
Thus, AB is parallel to CD
Slope of BC ≠ Slope of AD
[tex]m_2\neq m_4[/tex]
Thus, BC is not parallel to AD
The quadrilateral ABCD has two sides are parallel and two are not parallel.
Hence, The quadrilateral is trapzoid
Leah has a piece of cloth that is 3 ft 8 in long. She decides to cut 2/11 of the cloth off. How long is the cloth now?
Dan bought a home theater system for $178.99 on the installment plan. The term of the contact said that he would pay $35 a month for 6 months. How much are his total payment.
$30.01
$210
$178.99
$35
2. How much is Dan's finance charge?
$31.01
$210
$178.99
$35
Hey
Please someone help me!!!!!
Asap
Please help i will medal
y = 192(.25) + .25x
75 = 192(.25) + .25x
27 = .25x
x = 108
Jenny has been saving quarters in a piggy bank since she was born. She currently has 192 quarters in her piggy bank. She wants to save $75 to buy a new Ipod, so she decides to add 2 quarters every day.
She sets up and solves the equation shown. What does her solution mean?
A) She needs to save an additional $108.
B) She needs to save 216 more quarters.
C) She needs to save for 108 more days.
D) She needs to save an additional 108 quarters,
Is the inequality always, sometimes or never true?
9(x+2) > 9(x-3)
answer is 2>3 and i said it's never true, right?
2. 6x-13 < 6(x-2)
answer is 6x-13 < 6x-12 my answer is sometimes
3. -6(2x-10) + 12x less than or equal to 180. im stuck.,
A regular n-gon has an interior angle and an exterior angle with equal measures. What is the value of n?
Solve 2x2 + 3x = −8.
Solving the quadratic equation 2x² + 3x = - 8 for x, x = - 3/4 ± i√55/4
To solve 2x² + 3x = - 8, we proceed as follows.
Since we have the quadratic equation 2x² + 3x = - 8, to solve by completing the square, we rewrite the equation as
2x²/2 + 3x/2 = - 8/2
x² + 3x/2 = - 4
Next, we add the square of half the coefficient of x to both sides. So, we have that
x² + 3x/2 + (3/2 ÷ 2)² = - 4 + (3/2 ÷ 2)²
x² + 3x/2 + (3/2 × 1/2)² = - 4 + (3/2 × 1/2)²
x² + 3x/2 + (3/4)² = - 4 + (3/4)²
(x + 3/4)² = - 4 + 9/16
(x + 3/4)² = (-64 + 9)/16
Now, taking the square root of both sides, we have that
(x + 3/4)² = -55/16
√(x + 3/4)² = ±√(-55/16)
x + 3/4 = ±√-55/4
x + 3/4 = ±i√55/4
x = - 3/4 ± i√55/4
So, the value of x = - 3/4 ± i√55/4
The sum of three consecutive odd integers is 327. find the integers
Final answer:
To find the three consecutive odd integers whose sum is 327, we set up an equation with n as the first odd integer, resulting in the integers being 107, 109, and 111.
Explanation:
The question asks for the three consecutive odd integers whose sum is equal to 327. To solve this, we can represent the first integer as n, the second as n+2, and the third as n+4 because odd numbers are two units apart. We can then set up the following equation to find the value of n:
n + (n + 2) + (n + 4) = 327
Simplifying this equation, we get:
3n + 6 = 327
Subtracting 6 from both sides gives us:
3n = 321
Dividing both sides by 3, we find that n = 107. Therefore, the three consecutive odd integers are 107, 109, and 111.
Simplify the expression below. (xy)^8
calculate the length of the circumference of a circle with diameter of 9cm
how do you solve "z+ma=ba" solve for a
Final answer:
To solve the equation for a, subtract z from both sides, factor out a, and then divide by (m - b), resulting in a = -z / (m - b), assuming m and b are not equal.
Explanation:
To solve the equation z + ma = ba for a, we need to isolate a on one side of the equation. We can rewrite the equation, moving all terms involving a to one side and all other terms to the opposite side. This process is called collecting like terms.
Here are the steps to isolate a:
Subtract z from both sides of the equation to get ma = ba - z.
Since both terms on the right hand side involve a, factor a out: a ( m - b ) = -z.
Finally, divide both sides of the equation by (m - b) to solve for a: a = -z / (m - b), assuming that m ≠ b.
This algebraic manipulation gives us the value of a in terms of z, m, and b.
Solve for x. x/2 = -5
The population of current statistics students has ages with mean mu and standard deviation sigma. samples of statistics students are randomly selected so that there are exactly 48 students in each sample. for each sample, the mean age is computed. what does the central limit theorem tell us about the distribution of those mean ages?
What is the value of this expression when z = 36?
10 - /z
4
6
-8
-26
The provided expression with 'z = 36' is incomplete and lacks an operation or additional numbers, making it impossible to calculate its value. The student is advised to provide the full expression for proper assistance.
Explanation:The student asked: What is the value of this expression when z = 36?
Unfortunately, there is a typographical error in the expression provided. It seems to be missing an operation or additional numbers. Given the format '/z', it seems like it should have been a mathematical operation involving the variable 'z'. However, without an operator such as '+' (plus), '-' (minus), '*' (multiply), or '/' (divide), we cannot determine what the expression is supposed to be or calculate its value given z = 36.
If this is an expression from a specific textbook or sheet, I recommend double-checking the source material for the correct expression. If it's a part of a larger problem or context, please provide the full details so that an accurate computation can be made.
Chris is building a large deck for the community center. The deck is shaped as a rectangle. The width of the deck is 29 ft. The perimeter of the deck is to be at least 134 ft. (please answer both questions)
1) Write an inequality that represents all possible values for the length of the deck.
2) Solve algebraically to find all possible values for the length of the deck.
helppppppppppppppppppppppppppp
The population density of ground crickets at oldmill farm is about 15 per square meter. assuming that the crickets are randomly distributed, about how many crickets would you expect to find in a rectangular section of land that is 6 meters × 2 meters?
In the diagram the figures are similar. What is x
A. 2.6ft
B. 3.4ft
C. 0.4ft
D. 2.3ft