The scenario describes calculating the multiple of growth in the US national debt from 1970 to 1990 using scientific notation, showing that the debt was nearly 9 times larger in 1990 than in 1970
Let's create a scenario involving the United States' national debt from two different decades using multiplication in scientific notation. Imagine the government wanted to compare the debt from 1970 to that of 1990 to analyze the growth. The debt in 1970 was approximately $370.9 billion, and in 1990, about $3,233.3 billion. To find out how many times larger the debt was in 1990 compared to 1970, we'd convert these numbers into scientific notation and divide the 1990 figure by the 1970 figure.
In scientific notation, the 1970 debt is 3.709 x 1011 dollars, and the 1990 debt is 3.2333 x 1012 dollars. To perform the division, we have (3.2333 x 1012) / (3.709 x 1011) which gives us approximately 8.71. This means the national debt in 1990 was nearly 9 times larger than it was in 1970
The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?
Answer: the answer is D
Step-by-step explanation:
What is the rate of change of the volume of a ball with respect to the radius when the radius is?
One fourth of a number q is 3 more than three times a number w. Solve for q.
To solve for q, multiply both sides of the equation 1/4q = 3 + 3w by 4. This eliminates the fraction and gives us q = 12 + 12w.
Explanation:To solve for q, we need to translate the given information into an equation. The problem states that one fourth of q is 3 more than three times a number w. Written as an equation, this is represented as:
1/4 q = 3 + 3w
To solve for q, we can multiply both sides of the equation by 4 to eliminate the fraction:
q = 12 + 12w
This gives us the solution for q in terms of w.
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For what value of the constant c is the function f continuous on (-infinity, infinity) for the equation f(x) = cx^2 + 2x if x < 2 and x^3 - cx if x> or = 2
To find the constant c that makes the given piecewise function continuous for all real numbers, the two parts of the piecewise function need to be equal at x = 2. By setting these two equal and solving for c, you will find the value that makes the function continuous.
Explanation:The question presents a piecewise function and asks for which value of the variable c does it become continuous for all real numbers. To make a function continuous at a certain point, both parts of the function must be equal at that point. In this case, the two parts meet at x = 2. We need to set the two parts equal to each other at x = 2 and then solve for c.
For the first part of the piecewise function,
[tex]f(x) = cx^2 + 2x[/tex], when we substitute x = 2, it becomes f(2) = 4c + 4.
For the second part of the piecewise function,
[tex]f(x) = x^3 - cx[/tex], substituting x = 2 again gives us f(2) = 8 - 2c.
In order for the function to be continuous, these two results must be equal. We set 4c + 4 = 8 - 2c and solve it for c. Solving this equation will provide the value of c for which the function is continuous for all x .
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Factor completely p^2 - 8p + 7
How to get "4" of 4s to equal 4 using any order of operation
at 3:00a.m,the temperature is -5°F. Between 3:00a.m. and 6:00 a.m.,the temperature drops by 12°F. Between 6:00a.m. and 9:00a.m., the temperature rises by 4°F. What is the temperature at 9:00a.m.?
The altitude of an equilateral triangle is 9 inches. Find the perimeter of the triangle in inches.
The perimeter of the triangle will be 31.18 inches.
what is perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
If we draw a perpendicular line from one of the vertices of the triangle we get 2 right angled triangles each with altitude 9 ins and vertex angle = 30 degrees. So:-
[tex]Cos 30 =\dfrac{ 9} {h}[/tex]
where h = one of the sides of the equilateral triangle
[tex]h = \dfrac{9 }{ cos 30} = 10.392 \ inches[/tex]
Therefore the perimeter of the triangle =
[tex]3 \times 10.392 = 31.1769 \ inches[/tex]
Answer is 31.18 inches to the nearest hundredth.
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What is 30 1/4% as a fraction in simplest form
The simplest form is 3/40
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given:
30 * 1/4%
= 30* 1/400
= 30/400
=3/40
=0.075
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X and y are supplementary angles y measures 97
if x is a prime number, then x+1 is not a prime number. A counterexample is x=
Answer: The required example is x = 5.
Step-by-step explanation: Given that if x is a prime nu mber, then x+1 is not a prime number.
We are to give a counterexample for this.
Let us consider that
[tex]x=5.[/tex]
Then, we know that x is a prime number.
But, we get
[tex]x+1=5+1=6,[/tex] which is not a prime number.
Thus, the required example is x = 5.
Please help ;u;
which expression shows how 5 . 37 can be rewritten using the distributive property?
1) 5 . 30 + 5 . 37
2) 15 . 30 + 5 . 37
3) 5 . 30 + 5 . 7
4) 5 . 30 + 7
Answer:
5x30 + 5x7
Step-by-step explanation:
hope this helps :)
which points lies on the line described by the equation? y+4=(x-3)
Need help asap please!
lincoln high school has 98 teachers. of them 48 teachers, 9 of them teach math. one-fifth of them teachers teach math
Write a compound inequality that represents the situation. On a road in the city of Rochester, the maximum speed is 50 miles per hour, and the minimum speed is 20 miles per hour.
A. 20 ≥ x ≥ 50
B. 20 > x > 50
C. 20 < x < 50
D. 20 ≤ x ≤ 50
In the Founder's Day Parade in Happy, USA, many organizations participate by building floats. The Float Committee has issued a decree that each float can only have 300,000 flowers on it this year. The Happy Campers have already attached 15,625 flowers to their float. If the flowers come in containers which hold 125 flowers, which equation represents how many more containers they can use on their float?
A. 125x + 15,625 = 300,000
B. 125x = 300,000 + 15,625
C. 0x = 300,000 + 125
D. 0x + 125 = 300,000
what is the name of the line that the function approaches?
a. y-axis
b. there is no such line
c. the unknown line
d. asymptote
solve this equation 3\5(x-10)=18-4x-1
Simplify using distributive property. Which number can be distributed across two terms inside parentheses?
Answer choices:
-10
3\5
x
3/5 is the number which can be distributed across two terms inside parentheses
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 3/5 (x-10) = 18-4x-1
According to the distributive property, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
To solve the above equation we have to distribute 3/5 on LHS
3/5x-30/5 = 18-4x-1
3/5x-6 = 17-4x
Hence, 3/5 is the number which can be distributed across two terms inside parentheses
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4v=64 how do I solve this and what’s the answer
A circle with a radius of inches has a central angle of 0.25 radians that intercepts an arc of inches.
Answer:
Step-by-step explanation:
Given that there is a circle of .... inches with central angle 0.25 inches
by formula we have arc = radius *central angle in radians
The radii are given three options as 10,20,4 and corresponding arcs as
25,5, 16 inches.
By matching we find that 10(0.25) not equals 25
But 20(0.25) = 5 inches
Also 4(0.25) not equals 16 inches
Hence correct answer is radius = 20 and central arc = 5 inches
Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute. At what time will Malory's steps catch up to Dori's steps?
By what transformation can the set representing the inverse of a function be found? 1) reflection in the origin 2) reflection in the line y = x 3) rotation of 90o about the origin
Answer:
2) reflection in the line y = x
Step-by-step explanation:
A function is transformed to its inverse by swapping the independent and dependent variables. Reflection in the line y = x does that.
The cube will be enlarged by a scale factor of 8.
What will be the volume of the new cube?
8 cubic units
64 cubic units
192 cubic units
4,096 cubic units
What is the simplified form of the following expression?
4/7^3
A: 343/64
B: 21,952
C:407
D: 64/343
Answer:
The correct option is D.
Step-by-step explanation:
The given expression is
[tex](\frac{4}{7})^3[/tex]
According to the property of exponent.
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]
Using this property the given expression can be written as
[tex](\frac{4}{7})^3=\frac{4^3}{7^3}[/tex]
[tex](\frac{4}{7})^3=\frac{64}{343}[/tex]
The simplified form of the given expression is [tex]\frac{64}{343}[/tex].
Therefore the correct option is D.
What is the reason for each step in the solution of the equation? 2x−1=4(x+1)2x−1=4(x+1)
Drag and drop the reasons into the boxes to correctly complete the table.
2x−1=4(x+1)2x−1=4(x+1)-
2x−1=4x+42x−1=4x+4-
2x=4x+52x=4x+5-
−2x=5−2x=5-
x=−52-
Given
Distributive property
Commutative property
Addition or suptraction property of equality
How do you tell the difference between a obtuse angle, a right angle and a acute angle?
2/11 x 5/7 = ? PLEASE ALSO EXPLAIN THAAAANKS
How to factor: 15x^2y^3 + 10xy^2z
What is the measure of angle S?
132 + 56 + 79 = 267
360 - 267 = 93
answer is 93 degrees