The side length of the pyramid's base is approximately 0.7071 inches, and it is an irrational number.
To find the side length of the pyramid's base, we need to use the formula for the volume of a pyramid, which is given by:
[tex]\[ V = \frac{1}{3}Bh \][/tex]
where V is the volume, B is the area of the base, and h is the height of the pyramid.
Given that the volume V is 0.734 cubic inches and the height h is 4.41 inches, we can rearrange the formula to solve for the area of the base B :
[tex]\[ B = \frac{3V}{h} \][/tex]
Substituting the given values:
[tex]\[ B = \frac{3 \times 0.734}{4.41} \] \[ B = \frac{2.202}{4.41} \] \[ B \approx 0.5 \text{ square inches} \][/tex]
Now, assuming the base is a square (since we are looking for the side length), the area of the base B is also equal to the side length squared:
[tex]\[ B = s^2 \][/tex]
where \( s \) is the side length of the base. Therefore:
[tex]\[ s^2 = 0.5 \][/tex]
Taking the square root of both sides:
[tex]\[ s = \sqrt{0.5} \] \[ s \approx 0.7071 \text{ inches} \][/tex]
The side length of the pyramid's base is approximately 0.7071 inches.
To determine if this number is rational or irrational, we consider the definition of rational numbers. A rational number is one that can be expressed as the quotient of two integers. The square root of 0.5 can be rewritten as:
[tex]\[ s = \sqrt{0.5} = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1}{\sqrt{2}} \][/tex]
To rationalize the denominator, we multiply the numerator and the denominator by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ s = \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} \][/tex]
Since [tex]\( \sqrt{2} \)[/tex] is an irrational number, the side length s is also irrational because it cannot be expressed as the quotient of two integers.
A family has an annual income of $30,600. Of this, 1/4 is spent for food, 1/5 for housing 1/10 for clothes, 1/9 for savings, 1/4 for taxes, and the rest for other expenses. How much is spent for housing?
To find out how much is spent on housing from an annual income of $30,600, calculate 1/5 of the amount which equals $6,120.
Explanation:The student is seeking to determine how much money is spent for housing from a family's annual income of $30,600, given that 1/5 of this income is allocated for housing expenses. To find the amount spent on housing, we need to calculate 1/5 of the family's annual income.
Here's a step-by-step explanation:
Start with the family's annual income: $30,600.Calculate the fraction of this income that goes to housing, which is 1/5.Perform the calculation: (1/5) * $30,600 = $6,120.Therefore, the amount spent on housing by the family is $6,120 per year.
figure 1 is dilated to get figure 2.
What is the scale factor.
enter your answer, in simplest form, in the box
What is the answer to 1 and 2?
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What is the measure of AC ?
Enter your answer in the box.
Jordan has 11.40 to spend at the used book store.each book costs 2.85. How many books can Jordan buy
what is the perimeter of triangle UVW
given a and b are numbers,and a+b =180,which statement also must be true ? a=180-b , a-180=b , 360=2a+2b, a=90 and B=90
The statement 'a=180-b', '360=2a+2b', and 'a=90 and b=90' must be true given that a+b=180.
Explanation:To determine which statement must also be true given that a+b=180, we can substitute the value of a+b in each statement.
a=180-b: If we substitute a+b=180, we get 180-b+b=180. This simplifies to 180=180, which is always true. So, the statement a=180-b must be true.
a-180=b: If we substitute a+b=180, we get a-180+b=0+b. This simplifies to a-180=0, which is not always true. So, the statement a-180=b is not always true.
360=2a+2b: If we substitute a+b=180, we get 360=2a+2b. This simplifies to 360=360, which is always true. So, the statement 360=2a+2b must be true.
a=90 and b=90: If we substitute a+b=180, we get 90+90=180. This simplifies to 180=180, which is always true. So, the statement a=90 and b=90 must be true.
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help me please i dont know the ans
I need help with 5 & 6 please
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isaac played a video game 20 times and wont about 70% of the games. how many games did he win
A carpenter has several boards of equal length. He cuts 3/5 of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with?
A rectangle has vertices at these coordinates.
(1, 7), (1, 3), (9, 3)
What are the coordinates of the fourth vertex of the rectangle?
Enter the coordinates in the boxes.
I need help with 3 math questions. Here they are: A study of 50 high school students showed that exactly 25 of them took Biology, exactly 20 of them took Chemistry, and exactly 12 of them took both subjects. How many of the 50 students took neither Biology nor Chemistry? From a pile of coins containing nickels (N), dimes (D), and quarters (Q), Tom picked 10 coins with a total value of $1.00. The 10 coins had a different number of each of the three types and at least 1 coin of each type. How many coins of each type did he pick? An Olympiad team is made up of students from the 4th, 5th, and 6th grades only. Seven students are 5th graders, eleven students are 6th graders, and one third of the entire team are 4th graders. How many students are on the team? If you can even answer one question that would be very helpful! Thanks a lot!
List from least to greatest. 0, |−14|, 13, −12, |−16|, 17
A. |−16|, |−14|, 13, −12, 0, 17
B. −12, 0, 13,|−14|,|−16|, 17
C. −12, |−14|, |−16|, 0, 13, 17
D. 0, −12, 13, |−14|, |−16|, 17
Is my math answer correct or no?
what is negative 3 times negative one half
State a true conclusion.
1) If it is June, then it is summer.
2) It is summer.
Conclusion:
In the conditional logic given, 'If it is June, then it is summer' and 'It is summer', we can infer the conclusion 'It can be June'. However, it is important to note this is a potential conclusion and not a definite one since other months exist in the summer. This kind of conclusion is an example of the converse fallacy, or affirming the consequent.
Explanation:The question provided presents a logical statement in the form of a conditional statement. In logical reasoning and mathematics, a conditional statement is a statement of the form 'if P then Q', where P and Q are both statements. Here, the statement 'If it is June, then it is summer' is the given condition. The statement 'It is summer' is the second statement. A conclusion can be drawn using both of these statements. According to the rules of the logic, we can conclude that 'It can be June.' Remember, we cannot definitively say it 'is' June because there could be other months during the summer. This type of conclusion comes under the inference rule known as the 'converse fallacy' or 'affirming the consequent', where if the consequent (Q - the 'then' clause) is true, the antecedent (P - the 'if' clause) might also be true, but it could also possibly be false due to other factors.
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Which of the following represents the most accurate estimation of 388 - 212?
The temperature changed from 78°F to 70°F in the past hour. Write an absolute value statement to describe how much the temperature decreased.
Final answer:
The absolute value of the temperature change from 78°F to 70°F is 8 degrees Fahrenheit.
Explanation:
To describe how much the temperature decreased from 78°F to 70°F using an absolute value statement, we need to look at the magnitude of the change in temperature, without regard to the direction of change (increase or decrease). The change in temperature can be calculated as the final temperature ([tex]T_f[/tex]) minus the initial temperature ([tex]T_i[/tex]). In mathematical terms, this is expressed as [tex]\\(\Delta T = T_f - T_i)[/tex].
For this specific temperature change:
[tex]\Delta T = T_f - T_i[/tex] = 70°F - 78°F = -8°F
The absolute value of the temperature change is then:
|ΔT| = |-8°F| = 8°F
Therefore, the absolute value statement that describes how much the temperature decreased is "8 degrees Fahrenheit".
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Katenka cross country skied a trail that was 3/4 mile each way. after skiing 2/3 of the trail she turned around. What fraction of a mile did katenka ski before she turned around. And I'm sorry that is her name katenka
Yesterday it rained 5/8 inch. Today it rained 1/8 inch. What is the total amount of rain for the two days?
The total amount of rain for the two days is 2/3 inch.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Yesterday it rained 5/8 inch.
and, Today it rained 1/8 inch.
So, in two days the amount of rain fall
= 5/8+ 1/8
= 6/8
= 2/3
Hence, total amount of rain is 2/3 inch.
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The number $12345678910111213..........979899 consists of all the integers from 1 through 99 written back to back. That's a very big number! Is it a multiple of 9?
A round above-ground swimming pool has a diameter of 15 ft and a height of 4.5 ft. What is the volume of the swimming pool?
Mr. Anderson's 5th grade class is getting a class pet. 7 students voted to get a gerbil three voted for fish six voted for a mouse and 4 vote for a lizard. What is the model of the data? What does it mean for this situation?
Is the answer b? I'm not sure.
what is the slope of the line?
A. 0
B. 6
C. 9
D. undefined
Answer:
Option A 0
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(2,9)\ B(4,9)[/tex]
Substitute the values
[tex]m=\frac{9-9}{4-2}[/tex]
[tex]m=\frac{0}{2}=0[/tex]
evaluate the volume of the cone.Use ñ=3.14
The circumference of the base is 40 cm, and this equals 2*pi*r. The radius, r, is found as follows:
40 cm
r = ------------ = 6.369 cm. The area of the base, A = pi*r^2, = 3.14*40.570
2(3.14)
The volume here is V = (1/3)(area of base)*(height)
= (1/3)(127.45)(9) cm^3 = 382.36 cm^3 (answer)